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  A Quantitative Study of the Nocturnal
  Migration of Birds

  BY

  GEORGE H. LOWERY, JR.

  University of Kansas Publications
  Museum of Natural History

  Volume 3, No. 2, pp. 361-472, 47 figures in text
  June 29, 1951

  University of Kansas
  LAWRENCE
  1951




  UNIVERSITY OF KANSAS PUBLICATIONS, MUSEUM OF NATURAL HISTORY

  Editors: E. Raymond Hall, Chairman; A. Byron Leonard,
  Edward H. Taylor, Robert W. Wilson

  UNIVERSITY OF KANSAS
  Lawrence, Kansas

  PRINTED BY
  FERD VOILAND, JR., STATE PRINTER
  TOPEKA, KANSAS
  1951

  [Union Label]

  23-1020




  A Quantitative Study of the Nocturnal
  Migration of Birds

  By

  GEORGE H. LOWERY, JR.




CONTENTS


                                                                   Page

  INTRODUCTION                                                      365

  ACKNOWLEDGMENTS                                                   367

  PART I. FLIGHT DENSITIES AND THEIR DETERMINATION                  370

     Lunar Observations of Birds and the Flight Density Concept     370

     Observational Procedure and the Processing of Data             390

  PART II. THE NATURE OF NOCTURNAL MIGRATION                        408

     Horizontal Distribution of Birds on Narrow Fronts              409

     Density as a Function of the Hour of the Night                 413

     Migration in Relation to Topography                            424

     Geographical Factors and the Continental Density Pattern       432

     Migration and Meteorological Conditions                        453

  CONCLUSIONS                                                       469

  LITERATURE CITED                                                  470




LIST OF FIGURES


   Figure                                                          Page

   1. The field of observation as it appears to the observer        374

   2. Determination of diameter of cone at any point                375

   3. Temporal change in size of the field of observation           376

   4. Migration at Ottumwa, Iowa                                    377

   5. Geographic variation in size of cone of observation           378

   6. The problem of sampling migrating birds                       380

   7. The sampling effect of a square                               381

   8. Rectangular samples of square areas                           382

   9. The effect of vertical components in bird flight              383

  10. The interceptory potential of slanting lines                  384

  11. Theoretical possibilities of vertical distribution            388

  12. Facsimile of form used to record data in the field            391

  13. The identification of co-ordinates                            392

  14. The apparent pathways of birds seen in one hour               393

  15. Standard form for plotting the apparent paths of flight       395

  16. Standard sectors for designating flight trends                398

  17. The meaning of symbols used in the direction formula          399

  18. Form used to compute zenith distance and azimuth of the moon  400

  19. Plotting sector boundaries on diagrammatic plots              402

  20. Form to compute sector densities                              403

  21. Determination of the angle [alpha]                            404

  22. Facsimile of form summarizing sector densities                405

  23. Determination of net trend density                            406

  24. Nightly station density curve at Progreso, Yucatán            407

  25. Positions of the cone of observation at Tampico, Tamps        411

  26. Average hourly station densities in spring of 1948            414

  27. Hourly station densities plotted as a percentage of peak      415

  28. Incidence of maximum peak at the various hours of the
        night in 1948                                               416

  29. Various types of density-time curves                          418

  30. Density-time curves on various nights at Baton Rouge          422

  31. Directional components in the flight at Tampico, Tamps        428

  32. Hourly station density curve at Tampico, Tamps                429

  33. The nightly net trend of migrations at three stations in 1948 431

  34. Stations at which telescopic observations were made in 1948   437

  35. Positions of the cone of observation at Progreso, Yucatán     443

  36. Hourly station density curve at Progreso, Yucatán             444

  37. Sector density representation on two nights at
        Rosedale, Miss.                                             451

  38. Over-all sector vectors at major stations in spring of 1948   455

  39. Over-all net trend of flight directions shown in Figure 38    456

  40. Comparison of flight trends and surface weather conditions
        on April 22-23, 1948                                        460

  41. Winds aloft at 10:00 P. M. on April 22 (CST)                  461

  42. Comparison of flight trends and surface weather conditions
        on April 23-24, 1948                                        462

 43. Winds aloft at 10:00 P. M. on April 23 (CST)                   463

  44. Comparison of flight trends and surface weather conditions
        on April 24-25, 1948                                        464

  45. Winds aloft at 10:00 P. M. on April 24 (CST)                  465

  46. Comparison of flight trends and surface weather conditions
        on May 21-22, 1948                                          466

  47. Winds aloft at 10:00 P. M. on May 21 (CST)                    467




INTRODUCTION


The nocturnal migration of birds is a phenomenon that long has
intrigued zoologists the world over. Yet, despite this universal
interest, most of the fundamental aspects of the problem remain
shrouded in uncertainty and conjecture.

Bird migration for the most part, whether it be by day or by night, is
an unseen movement. That night migrations occur at all is a conclusion
derived from evidence that is more often circumstantial than it is
direct. During one day in the field we may discover hundreds of
transients, whereas, on the succeeding day, in the same situation, we
may find few or none of the same species present. On cloudy nights we
hear the call notes of birds, presumably passing overhead in the
seasonal direction of migration. And on stormy nights birds strike
lighthouses, towers, and other tall obstructions. Facts such as these
are indisputable evidences that migration is taking place, but they
provide little basis for evaluating the flights in terms of magnitude
or direction.

Many of the resulting uncertainties surrounding the nocturnal
migration of birds have a quantitative aspect; their resolution hinges
on how many birds do one thing and how many do another. If we knew,
for instance, how many birds are usually flying between 2 and 3 A. M.
and how this number compares with other one-hour intervals in the
night, we would be in a position to judge to what extent night flight
is sustained from dusk to dawn. If we could measure the number of
birds passing selected points of observation, we could find out
whether such migration in general proceeds more or less uniformly on a
broad front or whether it follows certain favored channels or flyways.
This in turn might give us a clearer insight into the nature of the
orienting mechanism and the extent to which it depends on visual
clues. And, if we had some valid way of estimating the number of birds
on the wing under varying weather conditions, we might be able to
understand better the nature and development of migration waves so
familiar to field ornithologists. These are just random examples
suggesting some of the results that may be achieved in a broad field
of inquiry that is still virtually untouched--the quantitative study
of migratory flights.

This paper is a venture into that field. It seeks to evaluate on a
more factual basis the traditional ideas regarding these and similar
problems, that have been developed largely from circumstantial
criteria. It is primarily, therefore, a study of comparative
quantities or volumes of migration--or what may be conveniently called
flight densities, if this term be understood to mean simply the number
of birds passing through a given space in a given interval of time.

In the present study, the basic data permitting the numerical
expression of such migration rates from many localities under many
different sets of circumstances were obtained by a simple method. When
a small telescope, mounted on a tripod, is focused on the moon, the
birds that pass before the moon's disc may be seen and counted, and
their apparent pathways recorded in terms of coördinates. In bare
outline, this approach to the problem is by no means new.
Ornithologists and astronomers alike have recorded the numbers of
birds seen against the moon in stated periods of time (Scott, 1881a
and 1881b; Chapman, 1888; Libby, 1889; West, 1896; Very, 1897;
Winkenwerder, 1902a and 1902b; Stebbins, 1906; Carpenter, 1906).
Unfortunately, as interesting as these observations are, they furnish
almost no basis for important generalizations. Most of them lack
entirely the standardization of method and the continuity that would
make meaningful comparisons possible. Of all these men, Winkenwerder
appears to have been the only one to follow up an initial one or two
nights of observation with anything approaching an organized program,
capable of leading to broad conclusions. And even he was content
merely to reproduce most of his original data without correlation or
comment and without making clear whether he fully grasped the
technical difficulties that must be overcome in order to estimate the
important flight direction factor accurately.

The present study was begun in 1945, and early results obtained were
used briefly in a paper dealing with the trans-Gulf migration of birds
(Lowery, 1946). Since that time the volume of field data, as well as
the methods by which they can be analyzed, has been greatly expanded.
In the spring of 1948, through the cooperation and collaboration of a
large number of ornithologists and astronomers, the work was placed on
a continent-wide basis. At more than thirty stations (Figure 34, page
437) on the North American continent, from Yucatán to Ontario, and
from California to South Carolina, observers trained telescopes
simultaneously on the moon and counted the birds they saw passing
before its disc.

Most of the stations were in operation for several nights in the full
moon periods of March, April, and May, keeping the moon under constant
watch from twilight to dawn when conditions permitted. They have
provided counts representing more than one thousand hours of
observation, at many places in an area of more than a million square
miles. But, as impressive as the figures on the record sheets are,
they, like the published observations referred to above, have dubious
meaning as they stand. Were we to compare them directly, station for
station, or hour for hour, we would be almost certain to fall into
serious errors. The reasons for this are not simple, and the measures
that must be taken to obtain true comparisons are even less so. When I
first presented this problem to my colleague, Professor William A.
Rense, of the Department of Physics and Astronomy at Louisiana State
University, I was told that mathematical means exist for reducing the
data and for ascertaining the desired facts. Rense's scholarly insight
into the mathematics of the problem resulted in his derivation of
formulae that have enabled me to analyze on a comparable basis data
obtained from different stations on the same night, and from the same
station at different hours and on different nights. Astronomical and
technical aspects of the problem are covered by Rense in his paper
(1946), but the underlying principles are discussed at somewhat
greater length in this paper.

Part I of the present paper, dealing with the means by which the data
were obtained and processed, will explore the general nature of the
problem and show by specific example how a set of observations is
prepared for analysis. Part II will deal with the results obtained and
their interpretation.




ACKNOWLEDGMENTS


In the pursuit of this research I have received a tremendous amount of
help from my colleagues, students, and other friends. In the first
place, in order to obtain much of the data on which the study was
based, it was necessary to enlist the aid of many persons in various
parts of the country and to draw heavily on their time and patience to
get all-night telescopic counts of migrating birds. Secondly, the
processing of the primary data and its subsequent analysis demanded
that I delve into the fields of astronomy and mathematics. Here, from
the outset, I have enjoyed the constant and untiring help of Professor
W. A. Rense of the Department of Physics and Astronomy at Louisiana
State University. Without his collaboration, I would not have been
able to do this work, for he not only supplied formulae whereby I was
able to make desired computations, but time and again he maneuvered me
through my difficulties in the mathematical procedures. Moreover,
Professor Rense has manifested a great interest in the ornithological
aspect of the problem, and his trenchant advice has been of
inestimable value to me. No less am I indebted to my associate, Robert
J. Newman, with whom I have spent untold hours discussing the various
aspects of the problem. Indeed, most of the concepts that have evolved
in the course of this study have grown out of discussions over a
four-year period with both Rense and Newman. Whatever merit this work
may have may be attributable in no small part to the help these two
men have given me. In the preparation of many of the illustrations, I
am further obligated to Newman for his excellent creative ideas as
well as draftsmanship, and to Miss Helen Behrnes and A. Lowell Wood
for their assistance.

The mathematical computations required in this study have been
laborious and time-consuming. It is estimated that more than two
thousand man-hours have gone into this phase of the work alone.
Whereas I have necessarily done most of this work, I have received a
tremendous amount of help from A. Lowell Wood. Further assistance in
this regard came from Herman Fox, Donald Norwood, and Lewis Kelly.

The recording of the original field data in the spring of 1948 from
the thirty-odd stations in North America involved the participation of
more than 200 ornithologists and astronomers. This collaboration
attests to the splendid cooperative spirit that exists among
scientists. Many of these persons stayed at the telescope, either as
observer or as recorder, hours on end in order to get sets of data
extending through a whole night.

The following were responsible for much of the field data herein used:
J. R. Andrews, S. A. Arny, M. Dale Arvey, H. V. Autrey, Charles C.
Ayres, Mr. and Mrs. Roy Bailey, Irwin L. Baird, Maurice F. Baker,
Rollin H. Baker, Bedortha and Edna Baldwin, Mrs. A. Marguerite
Baumgartner, T. A. Becket, Paul Bellington, Donald Bird, Carl Black,
Jr., Lea Black, Lytle Blankenship, Mr. and Mrs. J. Stewart Boswell,
Bruce Boudreaux, Frank Bray, Mr. and Mrs. Leonard Brecher, Homer
Brewer, Mrs. Harvey Broome, Heyward Brown, Floyd Browning, Cyril
Broussard, Paul Buress, Ralph M. Burress, Robert Cain, Don Carlos,
Mrs. Reba Campbell, Mr. and Mrs. E. Burnham Chamberlain, Laura Chaney,
Van B. Chaney, Jr., Edward Clebsch, Mr. and Mrs. Ben B. Coffey,
William Cook, Dr. Jack Craven, Hugh C. and William Davis, Katherine
Davis, Richard Davis, Richard DeArment, Robert E. Delphia, J. C.
Dickinson, Mr. and Mrs. Otto Dietrich, John Dietrich, Clara Dixon,
Nina Driven, John J. Duffy, Mr. and Mrs. R. J. Dunbar, Betty Dupre,
Bernard E. Eble, Jr., Robert G. Eble, Dr. and Mrs. William H. Elder,
C. C. Emory, Davis Emory, Alice H. Farnsworth, James Fielding, William
R. Fish, Mr. and Mrs. Myron Ford, W. G. Fuller, Louis Gainey, Dr. Mary
E. Gaulden, Mr. and Mrs. John J. Giudice, Lt. L. E. Goodnight, Earl R.
Greene, Max Grilkey, W. W. H. Gunn, Noel Maxwell Hall, Jr., A. J.
Hanna, Paul Hansen, Harold W. Harry, Joseph Healy, Dorothy Helmer, Mr.
and Mrs. John H. Helmer, Philip E. Hoberecht, William D. Hogan, Dr.
and Mrs. Joseph C. Howell, E. J. Huggins, Mrs. Walter Huxford, Hugh
Iltis, W. S. Jennings, William M. Johnson, William Kasler, Luther F.
Keeton, Lawrence C. Kent, W. H. Kiel, L. P. Kindler, Mr. and Mrs.
Joseph E. King, Harriet Kirby, E. J. Koestner, Roy Komarek, Ann
Knight, Mr. and Mrs. N. B. Langworthy, Mr. and Mrs. C. F. Lard,
Prentiss D. Lewis, Ernest Liner, Dr. and Mrs. R. W. Lockwood, Dr.
Harvey B. Lovell, William J. Lueck, Don Luethy, James Major, Mr. and
Mrs. Russell L. Mannette, Mrs. John B. Mannix, Donald Mary, Dale E.
McCollum, Stewart McConnell, Mr. and Mrs. M. L. McCroe, Robert L.
McDaniel, Mr. and Mrs. Frank McGill, Thomas Merimer, Mr. and Mrs. I.
S. H. Metcalf, Ann Michener, John Michener, T. H. Milby, D. S. Miller,
Burt Monroe, Jr., Burt Monroe, Sr., Mrs. R. A. Monroe, Gordon
Montague, Duryea Morton, James Mosimonn, Don L. Moyle, Grant Murphy,
John T. Murphy, Mrs. H. F. Murphy, Mrs. Hill Myers, Mr. and Mrs.
Robert J. Newman, William Nichols, R. A. Norris, Floyd Oaks, Eugene P.
Odum, Mrs. E. E. Overton, Lennie E. Pate, Kenneth Patterson, Ralph
Paxton, Louis Peiper, Marie Peiper, Mr. and Mrs. Harold S. Peters,
Mary Peters, Mr. and Mrs. D. W. Pfitzer, Betty Plice, Max Plice,
Lestar Porter, D. R. Power, Kenneth Price, George Rabb, Marge Reese,
Wayne L. Reeve, C. L. Riecke, R. D. Ritchie, V. E. Robinson, Beverly
J. Rose, Mary Jane Runyon, Roger Rusk, Bernd Safinsley, Mr. and Mrs.
Glen C. Sanderson, Lewis L. Sandidge, John Sather, J. Benton Schaub,
Evelyn Schneider, Henry W. Setzer, Mr. and Mrs. Walter Shackleton, Mr.
and Mrs. Francis P. Shannon, Mr. and Mrs. Charles Shaw, Paul H.
Shepard, Jr., Alan C. Sheppard, Mabel Slack, Alice Smith, R. Demett
Smith, Jr., Nat Smith, Major and Mrs. Charles H. Snyder, Albert
Springs, Dr. and Mrs. Fred W. Stamm, J. S. Steiner, Mrs. Paul
Stephenson, Herbert Stern, Jr., Herbert Stoddard, Mr. and Mrs. F. W.
Stomm, Charles Strull, Harold P. Strull, Mrs. Fan B. Tabler, Dr. and
Mrs. James T. Tanner, S. M. H. Tate, David Taylor, Hall Tennin, Scott
Terry, Mr. and Mrs. S. Charles Thacher, Olive Thomas, G. A. Thompson,
Jr., Dr. and Mrs. S. R. Tipton, Robert Tucker, Tom Uzzel, Mr. and Mrs.
M. G. Vaiden, Richard Vaught, Edward Violante, Brother I. Vincent,
Marilyn L. Walker, Mr. and Mrs. Willis Weaver, Mr. and Mrs. W. L.
Webb, Margaret M. L. Wehking, W. A. Welshans, Jr., Mrs. J. F.
Wernicke, Francis M. Weston, Miss G. W. Weston, Dr. James W. White,
John A. White, A. F. Wicke, Jr., Oren Williams, J. L. Wilson III, W.
B. Wilson, Dr. and Mrs. Leonard Wing, Sherry Woo, Rodney Wuthnow,
Grace Wyatt, Mr. and Mrs. Malcom Young, Mr. and Mrs. A. J. Zimmerman.
To the scores of other people who assisted in making these
observations I extend my hearty thanks.

Drs. E. R. Hall, Edward H. Taylor, and H. B. Hungerford of the
University of Kansas have read the manuscript and have made valuable
suggestions, as have also Dr. W. H. Gates of Louisiana State
University and Dr. Donald S. Farner of the State College of
Washington. Dr. Farner has also been of great help, together with Drs.
Ernst Mayr, J. Van Tyne, and Ernst Schüz, in suggesting source
material bearing on the subject in foreign literature. Dr. N. Wyaman
Storer, of the University of Kansas, pointed out a short-cut in the
method for determining the altitude and azimuth of the moon, which
resulted in much time being saved. For supplying climatological data
and for guidance in the interpretation thereof, I am grateful to Dr.
Richard Joel Russell, Louisiana State University; Commander F. W.
Reichelderfer, Chief of the U. S. Weather Bureau, Washington, D. C.;
Mr. Merrill Bernard, Chief of the Climatological and Hydrologic
Services; and Mr. Ralph Sanders, U. S. Weather Bureau at New Orleans,
Louisiana.

Acknowledgment is made to Bausch and Lomb Optical Company for the loan
of six telescopes for use in this project. Messrs. G. V. Cutler and
George Duff of Smith and Johnson Steamship Company, operators of the
Yucatán Line, are to be thanked for granting me free passage on the
"S. S. Bertha Brøvig" to Progreso, Yucatán, where I made observations
in 1945 and 1948. I am also indebted to the Louisiana State University
Committee on Faulty Research for a grant-in-aid.




PART I. FLIGHT DENSITIES AND THEIR DETERMINATION


A. LUNAR OBSERVATIONS OF BIRDS AND THE FLIGHT DENSITY CONCEPT

The subject matter of this paper is wholly ornithological. It is
written for the zoologist interested in the activities of birds. But
its bases, the principles that make it possible, lie in other fields,
including such rather advanced branches of mathematics as analytical
geometry, spherical geometry, and differential calculus. No exhaustive
exposition of the problem is practicable, that does not take for
granted some previous knowledge of these disciplines on the part of
all readers.

There are, however, several levels of understanding. It is possible to
appreciate _what_ is being done without knowing _how_ to do it; and it
is possible to learn how to carry out the successive steps of a
procedure without entirely comprehending _why_. Some familiarity with
the concepts underlying the method is essential to a full
understanding of the results achieved, and details of procedure must
be made generally available if the full possibilities of the
telescopic approach are to be realized. Without going into proof of
underlying propositions or actual derivation of formulae, I shall
accordingly present a discussion of the general nature of the problem,
conveyed as much as possible in terms of physical visualization. The
development begins with the impressions of the student when he first
attempts to investigate the movements of birds by means of the moon.


_What the Observer Sees_

Watched through a 20-power telescope on a cloudless night, the full
moon shines like a giant plaster hemisphere caught in the full glare
of a floodlight. Inequalities of surface, the rims of its craters, the
tips of its peaks, gleam with an almost incandescent whiteness; and
even the darker areas, the so-called lunar seas, pale to a clear,
glowing gray.

Against this brilliant background, most birds passing in focus appear
as coal-black miniatures, only 1/10 to 1/30 the apparent diameter of
the moon. Small as these silhouettes are, details of form are often
beautifully defined--the proportions of the body, the shape of the
tail, the beat of the wings. Even when the images are so far away that
they are pin-pointed as mere flecks of black against the illuminated
area, the normal eye can follow their progress easily. In most cases
the birds are invisible until the moment they "enter," or pass
opposite, the rim of the moon and vanish the instant they reach the
other side. The interval between is likely to be inestimably brief.
Some birds seem fairly to flash by; others, to drift; yet seldom can
their passing be counted in seconds, or even in measureable fractions
of seconds. During these short glimpses, the flight paths tend to lie
along straight lines, though occasionally a bird may be seen to
undulate or even to veer off course.

Now and again, in contrast to this typical picture, more eerie effects
may be noted. Some of them are quite startling--a minute,
inanimate-looking object drifting passively by like a corpuscle seen
in the field of a microscope; a gigantic wing brushing across half the
moon; a ghost-like suggestion of a bird so transparent it seems
scarcely more than a product of the imagination; a bird that pauses in
mid-flight to hang suspended in the sky; another that beats its way
ineffectually forward while it moves steadily to the side; and flight
paths that sweep across the vision in astonishingly geometric curves.
All of these things have an explanation. The "corpuscle" is possibly a
physical entity of some sort floating in the fluid of the observer's
eye and projected into visibility against the whiteness of the moon.
The winged transparency may be an insect unconsciously picked up by
the unemployed eye and transferred by the _camera lucida_ principle to
the field of the telescope. It may be a bird flying very close, so
drastically out of focus that the observer sees right through it, as
he would through a pencil held against his nose. The same cause,
operating less effectively, gives a characteristic gray appearance
with hazy edges to silhouettes passing just beneath the limits of
sharp focus. Focal distortions doubtless also account for the precise
curvature of some flight paths, for this peculiarity is seldom
associated with distinct images. Suspended flight and contradictory
directions of drift may sometimes be attributable to head winds or
cross winds but more often are simply illusions growing out of a
two-dimensional impression of a three-dimensional reality.

Somewhat more commonplace are the changes that accompany clouds. The
moon can be seen through a light haze and at times remains so clearly
visible that the overcast appears to be behind, instead of in front
of, it. Under these circumstances, birds can still be readily
discerned. Light reflected from the clouds may cause the silhouettes
to fade somewhat, but they retain sufficient definition to distinguish
them from out-of-focus images. On occasion, when white cloud banks
lie at a favorable level, they themselves provide a backdrop against
which birds can be followed all the way across the field of the
telescope, whether or not they directly traverse the main area of
illumination.


_Types of Data Obtained_

The nature of the observations just described imposes certain
limitations on the studies that can be made by means of the moon. The
speed of the birds, for instance, is utterly beyond computation in any
manner yet devised. Not only is the interval of visibility extremely
short, but the rapidity with which the birds go by depends less on
their real rate of motion than on their proximity to the observer. The
identification of species taking part in the migration might appear to
offer more promise, especially since some of the early students of the
problem frequently attempted it, but there are so many deceptive
elements to contend with that the results cannot be relied upon in any
significant number of cases. Shorn of their bills by the diminution of
image, foreshortened into unfamiliar shape by varying angles of
perspective, and glimpsed for an instant only, large species at
distant heights may closely resemble small species a few hundred feet
away. A sandpiper may appear as large as a duck; or a hawk, as small
as a sparrow. A goatsucker may be confused with a swallow, and a
swallow may pass as a tern. Bats, however, can be consistently
recognized, if clearly seen, by their tailless appearance and the
forward tilt of their wings, as well as by their erratic flight. And
separations of nocturnal migrants into broad categories, such as
seabirds and passerine birds, are often both useful and feasible.

It would be a wonderful convenience to be able to clock the speed of
night-flying birds accurately and to classify them specifically, but
neither of these things is indispensable to the general study of
nocturnal migration, nor as important as the three kinds of basic data
that _are_ provided by telescopes directed at the moon. These
concern:--(1) the direction in which the birds are traveling; (2)
their altitude above the earth; (3) the number per unit of space
passing the observation station.

Unfortunately none of these things can be perceived directly, except
in a very haphazard manner. Direction is seen by the observer in terms
of the slant of a bird's pathway across the face of the moon, and may
be so recorded. But the meaning of every such slant in terms of its
corresponding compass direction on the plane of the earth constantly
changes with the position of the moon. Altitude is only vaguely
revealed through a single telescope by the size and definition of
images whose identity and consequent real dimensions are subject to
serious misinterpretation, for reasons already explained. The number
of birds per unit of space, seemingly the easiest of all the features
of migration to ascertain, is actually the most difficult, requiring a
prior knowledge of both direction and altitude. To understand why this
is so, it will be necessary to consider carefully the true nature of
the field of observation.


_The Changing Field of Observation_

Most of the observations used in this study were made in the week
centering on the time of the full moon. During this period the lunar
disc progresses from nearly round to round and back again with little
change in essential aspect or apparent size. To the man behind the
telescope, the passage of birds looks like a performance in two
dimensions taking place in this area of seemingly constant
diameter--not unlike the movement of insects scooting over a circle of
paper on the ground. Actually, as an instant's reflection serves to
show, the two situations are not at all the same. The insects are all
moving in one plane. The birds only appear to do so. They may be
flying at elevations of 500, 1000, or 2000 feet; and, though they give
the illusion of crossing the same illuminated area, the actual breadth
of the visible space is much greater at the higher, than at the lower,
level. For this reason, other things being equal, birds nearby cross
the moon much more swiftly than distant ones. The field of observation
is not an area in the sky but a volume in space, bounded by the
diverging field lines of the observer's vision. Specifically, it is an
inverted cone with its base at the moon and its vertex at the
telescope.

Since the distance from the moon to the earth does not vary a great
deal, the full dimensions of the Great Cone determined by the diameter
of the moon and a point on the earth remain at all times fairly
constant. Just what they are does not concern us here, except as
regards the angle of the apex (roughly 1/2°), because obviously the
effective field of observation is limited to that portion of the Great
Cone below the maximum ceiling at which birds fly, a much smaller
cone, which I shall refer to as the Cone of Observation (Figure 1).

    [Illustration: FIG. 1. The field of observation, showing
       its two-dimensional aspect as it appears to the observer and
       its three-dimensional actuality. The breadth of the cone is
       greatly exaggerated.]

    [Illustration: FIG. 2. Method for determining the diameter
       of the cone at any point. The angular diameter of the moon
       may be expressed in radians, or, in other words, in terms of
       lengths of arc equivalent to the radius of a circle. In the
       diagram, the arc between C and E, being equivalent to the
       radius CO, represents a radian. If we allow the arc between A
       and B to be the diameter of the moon, it is by astronomical
       calculation about .009 radian, or .009 CO. This ratio will
       hold for any smaller circle inscribed about the center O;
       that is, the arc between A´B´ equals .009 C´O. Thus the width
       of the cone of observation at any point, expressed in degrees
       of arc, is .009 of the axis of the cone up to that point. The
       cone is so slender that the arc between A and B is
       essentially equal to the chord AB. Exactly the same
       consideration holds true for the smaller circle where the
       chord A´B´ represents part of the flight ceiling.]

The problem of expressing the number of passing birds in terms of a
definite quantity of space is fundamentally one of finding out the
critical dimensions of this smaller cone. The diameter at any distance
from the observer may be determined with enough accuracy for our
purposes simply by multiplying the distance by .009, a convenient
approximation of the diameter of the moon, expressed in radians (see
Figure 2). One hundred feet away, it is approximately 11 inches; 1000
feet away, nine feet; at one mile, 48 feet; at two miles, 95 feet.
Estimating the effective length of the field of observation presents
more formidable difficulties, aggravated by the fact that the lunar
base of the Great Cone does not remain stationary. The moon rises in
the general direction of east and sets somewhere in the west, the
exact points where it appears and disappears on the horizon varying
somewhat throughout the year. As it drifts across the sky it carries
the cone of observation with it like the slim beam of an immense
searchlight slowly probing space. This situation is ideal for the
purpose of obtaining a random sample of the number of birds flying out
in the darkness, yet it involves great complications; for the size of
the sample is never at two consecutive instants the same. The nearer
the ever-moving great cone of the moon moves toward a vertical
position, the nearer its intersection with the flight ceiling
approaches the observer, shortening, therefore, the cone of
observation (Figure 3). The effect on the number of birds seen is
profound. In extreme instances it may completely reverse the meaning
of counts. Under the conditions visualized in Figure 3, the field of
observation at midnight is only one-fourth as large as the field of
observation earlier in the evening. Thus the twenty-four birds seen
from 7 to 8 P. M., represent not twice as many birds actually flying
per unit of space as the twelve observed from 11:30 to 12:30 A. M.,
but only half the amount. Figure 4, based on observations at Ottumwa,
Iowa, on the night of May 22-23, shows a similar effect graphically.
Curve A represents the actual numbers of birds per hour seen; Curve B
shows the same figures expressed as flight densities, that is,
corrected to take into account the changing size of the field of
observation. It will be noted that the trends are almost exactly
opposite. While A descends, B rises, and _vice-versa_. In this case,
inferences drawn from the unprocessed data lead to a complete
misinterpretation of the real situation.

    [Illustration: FIG. 3. Temporal change in the effective
       size of the field of observation. The sample sections, A and
       B, represent the theoretical densities of flight at 8:20 and
       12:00 P. M., respectively. Though twice as many birds are
       assumed to be in the air at midnight when the moon is on its
       zenith (Z) as there were at the earlier hour, only half as
       many are visible because of the decrease in size of the cone
       of observation.]

    [Illustration: FIG. 4. Migration at Ottumwa, Iowa, on the
       night of May 22-23, 1948. Curve A is a graphic representation
       of the actual numbers of birds seen hourly through the
       telescope. Curve B represents the same figures corrected for
       the variation in the size of the cone of observation. The
       dissimilarity in the two curves illustrates the deceptive
       nature of untreated telescopic counts.]

Nor does the moon suit our convenience by behaving night after night
in the same way. On one date we may find it high in the sky between 9
and 10 P. M.; on another date, during the same interval of time, it
may be near the horizon. Consequently, the size of the cone is
different in each case, and the direct comparison of flights in the
same hour on different dates is no more dependable than the misleading
comparisons discussed in the preceding paragraph.

The changes in the size of the cone have been illustrated in Figure 3
as though the moon were traveling in a plane vertical to the earth's
surface, as though it reached a point directly over the observer's
head. In practice this least complicated condition seldom obtains in
the regions concerned in this study. In most of the northern
hemisphere, the path of the moon lies south of the observer so that
the cone is tilted away from the vertical plane erected on the
parallel of latitude where the observer is standing. In other words it
never reaches the zenith, a point directly overhead. The farther north
we go, the lower the moon drops toward the horizon and the more,
therefore, the cone of observation leans away from us. Hence, at the
same moment, stationed on the same meridian, two observers, one in the
north and one in the south, will be looking into different effective
volumes of space (Figure 5).

    [Illustration: FIG. 5. Geographical variation in the size
       of the cone of observation. The cones A and B represent the
       effective fields of observation at two stations situated over
       1,200 miles apart. The portions of the great cones included
       here appear nearly parallel, but if extended far enough would
       be found to have a common base on the moon. Because of the
       continental scale of the drawing, the flight ceiling appears
       as a curved surface, equidistant above each station. The
       lines to the zenith appear to diverge, but they are both
       perpendicular to the earth. Although the cones are shown at
       the same instant in time, and have their origin on the same
       meridian, the dimensions of B are less than one-half as great
       as those of A, thus materially decreasing the opportunity to
       see birds at the former station. This effect results from the
       different slants at which the zenith distances cause the
       cones to intersect the flight ceiling. The diagram
       illustrates the principle that northern stations, on the
       average, have a better chance to see birds passing in their
       vicinity than do southern stations.]

As a further result of its inclination, the cone of observation,
seldom affords an equal opportunity of recording birds that are flying
in two different directions. This may be most easily understood by
considering what happens on a single flight level. The plane parallel
to the earth representing any such flight level intersects the
slanting cone, not in a circle, but in an ellipse. The proportions of
this ellipse are very variable. When the moon is high, the
intersection on the plane is nearly circular; when the moon is low,
the ellipse becomes greatly elongated. Often the long axis may be more
than twice the length of the short axis. It follows that, if the long
axis happens to lie athwart the northward direction of flight and the
short axis across the eastward direction, we will get on the average
over twice as large a sample of birds flying toward the north as of
birds flying toward the east.

In summary, whether we wish to compare different stations, different
hours of the night, or different directions during the same hour of
the night, no conclusions regarding even the relative numbers of birds
migrating are warranted, unless they take into account the
ever-varying dimensions of the field of observation. Otherwise we are
attempting to measure migration with a unit that is constantly
expanding or contracting. Otherwise we may expect the same kind of
meaningless results that we might obtain by combining measurements in
millimeters with measurements in inches. Some method must be found by
which we can reduce all data to a standard basis for comparison.


_The Directional Element in Sampling_

In seeking this end, we must immediately reject the simple logic of
sampling that may be applied to density studies of animals on land. We
must not assume that, since the field of observation is a volume in
space, the number of birds therein can be directly expressed in terms
of some standard volume--a cubic mile, let us say. Four birds counted
in a cone of observation computed as 1/500 of a cubic mile are not the
equivalent of 500 × 4, or 2000, birds per cubic mile. Nor do four
birds flying over a sample 1/100 of a square mile mathematically
represent 400 birds passing over the square mile. The reason is that
we are not dealing with static bodies fixed in space but with moving
objects, and the objects that pass through a cubic mile are not the
sum of the objects moving through each of its 500 parts. If this fact
is not immediately apparent, consider the circumstances in Figures 6
and 7, illustrating the principle as it applies to areas. The relative
capacity of the sample and the whole to intercept bodies in motion is
more closely expressed by the ratio of their perimeters in the case of
areas and the ratio of their surface areas in the case of volumes. But
even these ratios lead to inaccurate results unless the objects are
moving in all directions equally (see Figure 8). Since bird migration
exhibits strong directional tendencies, I have come to the conclusion
that no sampling procedure that can be applied to it is sufficiently
reliable short of handling each directional trend separately.

    [Illustration: FIG. 6. The problem of sampling migrating
       birds. The large square in the diagram may be thought of as a
       square mile on the earth's surface, divided into four equal
       smaller squares. Birds are crossing over the area in three
       directions, equally spaced, so that each of the subdivisions
       is traversed by three of them. We might be tempted to
       conclude that 4 × 3, or 12, would pass over the large square.
       Actually there are only seven birds involved all told.
       Obviously, the interceptive potential of a small square and a
       larger square do not stand in the same ratio as their areas.]

For this reason, the success of the whole quantitative study of
migration depends upon our ability to make directional analyses of
primary data. As I have already pointed out, the flight directions of
birds may be recorded with convenience and a fair degree of
objectivity by noting the slant of their apparent pathways across the
disc of the moon. But these apparent pathways are seldom the real
pathways. Usually they involve the transfer of the flight line from a
horizontal plane of flight to a tilted plane represented by the face
of the moon, and so take on the nature of a projection. They are
clues to directions, but they are not the directions themselves. For
each compass direction of birds flying horizontally above the earth,
there is one, and only one, slant of the pathway across the moon at a
given time. It is possible, therefore, knowing the path of a bird in
relation to the lunar disc and the time of the observation, to compute
the direction of its path in relation to the earth. The formula
employed is not a complicated one, but, since the meaning of the lunar
coördinates in terms of their corresponding flight paths parallel to
the earth is constantly changing with the position of the moon, the
calculation of each bird's flight separately would require a
tremendous amount of time and effort.

    [Illustration: FIG. 7. The sampling effect of a square. In
       Diagram A eight evenly distributed birds are flying from
       south to north, and another four are proceeding from east to
       west. Three appear in each of the smaller squares. Thus, if
       we were to treat any of these smaller sections as a directly
       proportionate sample of the whole, we would be assuming that
       3 × 16, or 48, birds had traversed the square mile--four
       times the real total of 12. If we consider the paths
       separately as in Diagram B, we see quite clearly what is
       wrong. Every bird crosses four plots the size of the sample
       and is being computed into the total over and over a
       corresponding number of times. Patently, just as many
       south-north birds cross the bottom tier of squares as cross
       the four tiers comprising the whole area. Just as many
       west-east birds traverse one side of the large square as
       cross the whole square. In other words, the inclusion of
       additional sections _athwart_ the direction of flight
       involves the inclusion of additional birds proceeding in that
       direction, while the inclusion of additional sections _along_
       the direction does not. The correct ratio of the sample to
       the whole would seem to be the ratio of their perimeters, in
       this case the ratio of one to four. When this factor of four
       is applied to the problem it proves correct: 4 × 3 (the
       number of birds that have been seen in the sample square)
       equals 12 (the exact number of birds that could be seen in
       the square mile).]

    [Illustration: FIG. 8. Rectangular samples of square areas.
       In Diagram A, where as many birds are flying from west to
       east as are flying from south to north, the perimeter ratio
       (three to eight) correctly expresses the number of birds that
       have traversed the whole area relative to the number that
       have passed through the sample. But in Diagram B, where all
       thirty-two birds are flying from south to north, the correct
       ratio is the ratio of the base of the sample to the base of
       the total area (one to four), and use of the perimeter ratio
       would lead to an inaccurate result (forty-three instead of
       thirty-two birds). Perimeter ratios do not correctly express
       relative interceptory potential, unless the shape of the
       sample is the same as the shape of the whole, or unless the
       birds are flying in all directions equally.]

Whatever we do, computed individual flight directions must be frankly
recognized as approximations. Their anticipated inaccuracies are not
the result of defects in the mathematical procedure employed. This is
rigorous. The difficulty lies in the impossibility of reading the
slants of the pathways on the moon precisely and in the
three-dimensional nature of movement through space. The observed
coördinates of birds' pathways across the moon are the projected
product of two component angles--the compass direction of the flight
and its slope off the horizontal, or gradient. These two factors
cannot be dissociated by any technique yet developed. All we can do is
to compute what a bird's course would be, if it were flying horizontal
to the earth during the interval it passes before the moon. We cannot
reasonably assume, of course, that all nocturnal migration takes place
on level planes, even though the local distractions so often
associated with sloping flight during the day are minimized in the
case of migrating birds proceeding toward a distant destination in
darkness. We may more safely suppose, however, that deviations from
the horizontal are random in nature, that it is mainly a matter of
chance whether the observer happens to see an ascending segment of
flight or a descending one. Over a series of observations, we may
expect a fairly even distribution of ups and downs. It follows that,
although departures from the horizontal may distort individual
directions, they tend to average out in the computed trend of the
mean. The working of this principle applied to the undulating flight
of the Goldfinch (_Spinus_) is illustrated in Figure 9.

    [Illustration: FIG. 9. The effect of vertical components in
       bird flight. The four diagrams illustrate various effects
       that might result if a bird with an undulating flight, such
       as a Goldfinch, flew before a moon 45° above the horizon. In
       each case the original profile of the pathways, illustrated
       against the dark background, is flattened considerably as a
       result of projection. In the situation shown in Diagram A,
       where the high point of the flight line, GHJ, occurs within
       the field of the telescope, it is not only obvious that a
       deviation is involved, but the line GJ drawn between the
       entry and departure points coincides with the normal
       coördinates of a bird proceeding on a horizontal plane. In
       Diagrams B and C, one which catches an upward segment of
       flight, and the other, a downward segment, the nature of the
       deviation would not be detectable, and an incorrect direction
       would be computed from the coördinates. Over a series of
       observations, including many Goldfinches, one would expect a
       fairly even distribution of ups and downs. Since the average
       between the coördinate angles in Diagrams B and C, +19° and
       -19°, is the angle of the true coördinate, we have here a
       situation where the errors tend to compensate. In Diagram D,
       where the bird is so far away that several undulations are
       encompassed within the diameter of the field of view, the
       coördinate readings do not differ materially from those of a
       straight line.]

Since _individually_ computed directions are not very reliable in any
event, little is to be lost by treating the observed pathways in
groups. Consequently, the courses of all the birds seen in a one-hour
period may be computed according to the position of the moon at the
middle of the interval and expressed in terms of their general
positions on the compass, rather than their exact headings. For this
latter purpose, the compass has been divided into twelve fixed
sectors, 22-1/2 degrees wide. The trends of the flight paths are
identified by the mid-direction of the sector into which they fall.
The sectoring method is described in detail in the section on
procedures.

    [Illustration: Fig. 10. The interceptory potential of
       slanting lines. The diagram deals with one direction of
       flight and its incidence across lines of six different
       slants, lines of identical length oriented in six different
       ways. Obviously, the number of birds that cross a line
       depends not only on the length of the line, but also on its
       slant with respect to the flight paths.]

The problem remains of converting the number of birds involved in each
directional trend to a fixed standard of measurement. Figure 7A
contains the partial elements of a solution. All of the west-east
flight paths that cross the large square also cross one of its
mile-long sides and suggest the practicability of expressing the
amount of migration in any certain direction in terms of the assumed
quantity passing over a one-mile line in a given interval of time.
However, many lines of that length can be included within the same set
of flight paths (Figure 10); and the number of birds intercepted
depends in part upon the orientation of the line. The 90° line is the
only one that fully measures the amount of flight per linear unit of
front; and so I have chosen as a standard an imaginary mile on the
earth's surface lying at right angles to the direction in which the
birds are traveling.


_Definitions of Flight Density_

When the count of birds in the cone of observation is used as a sample
to determine the theoretical number in a sector passing over such a
mile line, the resulting quantity represents what I shall call a
Sector Density. It is one of several expressions of the more general
concept of Flight Density, which may be defined as the passage of
migration past an observation station stated in terms of the
theoretical number of birds flying over a one-mile line on the earth's
surface in a given interval of time. Note that a flight density is
primarily a theoretical number, a statistical expression, a _rate_ of
passage. It states merely that birds were moving through the effective
field of observation at the _rate_ of so many per mile per unit of
time. It may or may not closely express the amount of migration
occurring over an actual mile or series of miles. The extent to which
it does so is to be decided by other general criteria and by the
circumstances surrounding a given instance. Its basic function is to
take counts of birds made at different times and at different places,
in fields of observation of different sizes, and to put them on the
statistically equal footing that is the first requisite of any sound
comparison.

The idea of a one-mile line as a standard spacial measurement is an
integral part of the basic concept, as herein propounded. But, within
these limitations, flight density may be expressed in many different
ways, distinguished chiefly by the directions included and the
orientation of the one-mile line with respect to them. Three such
kinds of density have been found extremely useful in subsequent
analyses and are extensively employed in this paper: Sector, Net
Trend, and Station Density, or Station Magnitude.

Sector Density has already been referred to. It may be defined as the
flight density within a 22-1/2° directional spread, or sector,
measured across a one-mile line lying at right angles to the
mid-direction of the sector. It is the basic type of density from the
point of view of the computer, the others being derived from it. In
analysis it provides a means of comparing directional trends at the
same station and of studying variation in directional fanning.

Net Trend Density represents the maximum net flow of migration over a
one-mile line. It is found by plotting the sector densities
directionally as lines of thrust, proportioned according to the
density in each sector, and using vector analysis to obtain a vector
resultant, representing the density and direction of the net trend.
The mile line defining the spacial limits lies at right angles to this
vector resultant, but the density figure includes all of the birds
crossing the line, not just those that do so at a specified angle.
Much of the directional spread exhibited by sector densities
undoubtedly has no basis in reality but results from inaccuracies in
coördinate readings and from practical difficulties inherent in the
method of computation. By reducing all directions to one major trend,
net trend density has the advantage of balancing errors one against
the other and may often give the truer index to the way in which the
birds are actually going. On the other hand, if the basic directions
are too widely spread or if the major sector vectors are widely
separated with little or no representation between, the net trend
density may become an abstraction, expressing the idea of a mean
direction but pointing down an avenue along which no migrants are
traveling. In such instances, little of importance can be learned from
it. In others, it gives an idea of general trends indispensable in
comparing station with station to test the existence of flyways and in
mapping the continental distribution of flight on a given night to
study the influence of weather factors.

Station Density, or Station Magnitude, represents all of the migration
activity in an hour in the vicinity of the observation point,
regardless of direction. It expresses the sum of all sector densities.
It includes, therefore, the birds flying at right angles over several
one-mile lines. One way of picturing its physical meaning is to
imagine a circle one-mile in diameter lying on the earth with the
observation point in the center. Then all of the birds that fly over
this circle in an hour's time constitute the hourly station density.
While its visualization thus suggests the idea of an area, it is
derived from linear expressions of density; and, while it involves no
limitation with respect to direction, it could not be computed without
taking every component direction into consideration. Station density
is adapted to studies involving the total migration activity at
various stations. So far it has been the most profitable of all the
density concepts, throwing important light on nocturnal rhythm,
seasonal increases in migration, and the vexing problem of the
distribution of migrating birds in the region of the Gulf of Mexico.

Details of procedure in arriving at these three types of flight
density will be explained in Section B of this discussion. For the
moment, it will suffice to review and amplify somewhat the general
idea involved.


_Altitude as a Factor in Flight Density_

A flight density, as we have seen, may be defined as the number of
birds passing over a line one mile long; and it may be calculated from
the number of birds crossing the segment of that line included in an
elliptical cross-section of the cone of observation. It may be thought
of with equal correctness, without in any way contradicting the
accuracy of the original definition, as the number of birds passing
through a vertical plane one mile long whose upper limits are its
intersection with the flight ceiling and whose base coincides with the
one mile line of the previous visualization. From the second point of
view, the sample becomes an area bounded by the triangular projection
of the cone of observation on the density plane. The dimensions of two
triangles thus determined from any two cones of observation stand in
the same ratio as the dimensions of their elliptical sections on any
one plane; so both approaches lead ultimately to the same result. The
advantage of this alternative way of looking at things is that it
enables us to consider the vertical aspects of migration--to
comprehend the relation of altitude to bird density.

If the field of observation were cylindrical in shape, if it had
parallel sides, if its projection were a rectangle or a parallelogram,
the height at which birds are flying would not be a factor in finding
out their number. Then the sample would be of equal breadth
throughout, with an equally wide representation of the flight at all
levels. Since the field of observation is actually an inverted cone,
triangular in section, with diverging sides, the opportunity to detect
birds increases with their distance from the observer. The chances of
seeing the birds passing below an elevation midway to the flight
ceiling are only one-third as great as of seeing those passing above
that elevation, simply because the area of that part of the triangle
below the mid-elevation is only one-third as great as the area of that
part above the mid-elevation. If we assume that the ratio of the
visible number of birds to the number passing through the density
plane is the same as the ratio of the triangular section of the cone
to the total area of the plane, we are in effect assuming that the
density plane is made up of a series of triangles the size of the
sample, each intercepting approximately the same number of birds. We
are assuming that the same number of birds pass through the inverted
triangular sample as through the erect and uninvestigable triangle
beside it (as in Figure 11, Diagram II). In reality, the assumption is
sound only if the altitudinal distribution of migrants is uniform.

    [Illustration: FIG. 11. Theoretical possibilities of
       vertical distribution. Diagram I shows the effect of a
       uniform vertical distribution of birds. The figures indicate
       the number of birds in the respective areas. Here the sample
       triangle, ABD, contains the same number of birds as the
       upright triangle, ACD, adjacent to it; the density plane may
       be conceived of as a series of such alternating triangles,
       equal in their content of birds. Diagram II portrays, on an
       exaggerated scale, the situation when many more birds are
       flying below the median altitude than above it. In contrast
       to the 152 birds occurring in the triangle A´C´D´, only
       seventy-two are seen in the triangle A´B´D´. Obviously, the
       latter triangle does not provide a representative sample of
       the total number of birds intersecting the density plane.
       Diagram III illustrates one method by which this difficulty
       may be overcome. By lowering the line F´G´ to the median
       altitude of bird density, F´´G´´ (the elevation above which
       there are just as many birds as below), we are able to
       determine a rectangular panel, HIJK, whose content of birds
       provides a representative sample of the vertical
       distribution.]

The definite data on this subject are meagre. Nearly half a century
ago, Stebbins worked out a way of measuring the altitude of migrating
birds by the principle of parallax. In this method, the distance of a
bird from the observers is calculated from its apparent displacement
on the moon as seen through two telescopes. Stebbins and his
colleague, Carpenter, published the results of two nights of
observation at Urbana, Illinois (Stebbins, 1906; Carpenter, 1906); and
then the idea was dropped until 1945, when Rense and I briefly applied
an adaptation of it to migration studies at Baton Rouge. Results have
been inconclusive. This is partly because sufficient work has not been
done, partly because of limitations in the method itself. If the two
telescopes are widely spaced, few birds are seen by both observers,
and hence few parallaxes are obtained. If the instruments are brought
close together, the displacement of the images is so reduced that
extremely fine readings of their positions are required, and the
margin of error is greatly increased. Neither alternative can provide
an accurate representative sample of the altitudinal distribution of
migrants at a station on a single night. New approaches currently
under consideration have not yet been perfected.

Meanwhile the idea of uniform vertical distribution of migrants must
be dismissed from serious consideration on logical grounds. We know
that bird flight cannot extend endlessly upward into the sky, and the
notion that there might be a point to which bird density extends in
considerable magnitude and then abruptly drops off to nothing is
absurd. It is far more likely that the migrants gradually dwindle in
number through the upper limits at which they fly, and the parallax
observations we have seem to support this view.

Under these conditions, there would be a lighter incidence of birds in
the sample triangle than in the upright triangle beside it (Figure 11,
Diagram III). Compensation can be made by deliberately scaling down
the computed size of the sample area below its actual size. A
procedure for doing this is explained in Figure 11. If it were applied
to present altitudinal data, it would place the computational flight
ceiling somewhere below 4000 feet. In arriving at the flight densities
used in this paper, however, I have used an assumed ceiling of one
mile. When the altitude factor is thus assigned a value of 1, it
disappears from the formula, simplifying computations. Until the true
situation with respect to the vertical distribution of flight is
better understood, it seems hardly worthwhile to sacrifice the
convenience of this approximation to a rigorous interpretation of
scanty data. This particular uncertainty, however, does not
necessarily impair the analytical value of the computations. Provided
that the vertical pattern of migration is more or less constant,
flight densities still afford a sound basis for comparisons, wherever
we assume the upper flight limits to be. Raising or lowering the
flight ceiling merely increases or reduces all sample cones or
triangles proportionately.

A more serious possibility is that the altitudinal pattern may vary
according to time or place. This might upset comparisons. If the
divergencies were severe enough and frequent enough, they could throw
the study of flight densities into utter confusion.

This consideration of possible variation in the altitudinal pattern
combines with accidents of sampling and the concessions to perfect
accuracy, explained on pages 379-385, to give to small quantities of
data an equivocal quality. As large-scale as the present survey is
from one point of view, it is only a beginning. Years of intensive
work and development leading to a vast accumulation of data must
elapse before the preliminary indications yet discernible assume the
status of proved principles. As a result, much of the discussion in
Part II of this paper is speculative in intent, and most of the
conclusions suggested are of a provisional nature. Yet, compared with
similar procedures in its field, flight density study is a highly
objective method, and a relatively reliable one. In no other type of
bird census has there ever been so near a certainty of recording _all_
of the individuals in a specified space, so nearly independently of
the subjective interpretations of the observer. The best assurance of
the essential soundness of the flight density computations lies in the
coherent results and the orderly patterns that already emerge from the
analyses presented in Part II.


B. OBSERVATIONAL PROCEDURE AND THE PROCESSING OF DATA

At least two people are required to operate an observation
station--one to observe, the other to record the results. They should
exchange duties every hour to avoid undue eye fatigue. Additional
personnel are desirable so that the night can be divided into shifts.

Essential materials and equipment include: (1) a small telescope;
(2) a tripod with pan-tilt or turret head and a mounting cradle;
(3) data sheets similar to the one illustrated in Figure 12. Bausch
and Lomb or Argus spotting scopes (19.5 ×) and astronomical telescopes
up to 30- or 40-power are ideal. Instruments of higher magnification
are subject to vibration, unless very firmly mounted, and lead to
difficulties in following the progress of the moon, unless powered by
clockwork. Cradles usually have to be devised. An adjustable lawn chair
is an important factor in comfort in latitudes where the moon reaches
a point high overhead.

    [Illustration: FIG. 12. Facsimile of form used to record
       data in the field. One sheet of the actual observations
       obtained at Progreso, Yucatán, on April 24-25, 1948, is
       reproduced here. The remainder of this set of data, which is
       to be used throughout the demonstration of procedures, is
       shown in Table 1.]

  [Transcription of Figure 12's Data]

  ORIGINAL DATA SHEET

  DATE  24-25 April 1948     LOCALITY  Progreso, Yucatán

  OBSERVERS  Harold Harry; George H. Lowery

  WEATHER  Moderate to strong "trade" winds along coast, slightly
           N of E. Moon emerged above low cloud bank at 8:26.

  INSTRUMENT  B. & L. 19.5 Spotting Scope; image erect

  REMARKS  Observation station located 1 mile from land, over Gulf of
           Mexico, at end of new Progreso wharf

  -----------+------+-------+----------------------------------------
     TIME    |  IN  |  OUT  |                   REMARKS
  -----------+------+-------+----------------------------------------
    C.S.T    |      |       |
    8:26     |  --  |  --   | observations begin; H.H. observing
      50     | 4:30 |  9    | slow; small
      56     | 3    | 10    | medium size
    9:00     | 2    | 10:30 | very small
      11     | 5    |  9:30 | moderately fast
      25     | 5    | 10    | very small; rather slow
      26     | 3    | 11    |     "            "
      36     | 5    | 10    | medium size
      40     | 3    | 10    |   "     "
      43     | 5:30 |  9    |   "     "
      46     | 3:30 | 10    | small
      56     | 4:30 | 10    | medium size
  9:58-10:00 |  --  |  --   | time out to change observers; G.L. at
   10:05     | 4:30 | 11:30 | scope small
      06     | 3    | 11    |
      12     | 5    |  8    | very small
      25     | 5    | 12    | very fast; small
      30     | 4    | 10    | small
      32     | 4    | 11    |   "
      32     | 2    | 11    |   "
      33     | 5    | 11    |   "
      33     | 4    |  1    |   "
      33     | 5:30 | 11    |   "
      35     | 4:30 | 10    | swallow-like
      36     | 5    |  1:30 |


As much detail as possible should be entered in the space provided at
the top of the data sheet. Information on the weather should include
temperature, description of cloud cover, if any, and the direction
and apparent speed of surface winds. Care should be taken to specify
whether the telescope used has an erect or inverted image. The entry
under "Remarks" in the heading should describe the location of the
observation station with respect to watercourses, habitations, and
prominent terrain features.

The starting time is noted at the top of the "Time" column, and the
observer begins the watch for birds. He must keep the disc of the moon
under unrelenting scrutiny all the while he is at the telescope. When
interruptions do occur as a result of changing positions with the
recorder, re-adjustments of the telescope, or the disappearance of the
moon behind clouds, the exact duration of the "time out" must be set
down.

    [Illustration: FIG. 13. The identification of coördinates.
       These diagrams illustrate how the moon may be envisioned as a
       clockface, constantly oriented with six o'clock nearest the
       horizon and completely independent of the rotation of the
       moon's topographic features.]

    [Illustration: FIG. 14. The apparent pathways of the birds
       seen in one hour. The observations are those recorded in the
       11:00-12:00 P. M. interval on April 24-25, 1948, at
       Progreso, Yucatán (see Table 1).]

Whenever a bird is seen, the exact time must be noted, together with
its apparent pathway on the moon. These apparent pathways can be
designated in a simple manner. The observer envisions the disc of the
moon as the face of a clock, with twelve equally spaced points on the
circumference marking the hours (Figure 13). He calls the bottommost
point 6 o'clock and the topmost, 12. The intervals in between are
numbered accordingly. As this lunar clockface moves across the sky, it
remains oriented in such a way that 6 o'clock continues to be the
point nearest the horizon, unless the moon reaches a position directly
overhead. Then, all points along the circumference are equidistant
from the horizon, and the previous definition of clock values ceases
to have meaning. This situation is rarely encountered in the northern
hemisphere during the seasons of migration, except in extreme
southern latitudes. It is one that has never actually been dealt with
in the course of this study. But, should the problem arise, it would
probably be feasible to orient the clock during this interval with
respect to the points of the compass, calling the south point
6 o'clock.

When a bird appears in front of the moon, the observer identifies its
entry and departure points along the rim of the moon with respect to
the nearest half hour on the imaginary clock and informs the recorder.
In the case of the bird shown in Figure 13, he would simply call out,
"5 to 10:30." The recorder would enter "5" in the "In" column on the
data sheet (see Figure 12) and 10:30 in the "Out" column. Other
comment, offered by the observer and added in the remarks column, may
concern the size of the image, its speed, distinctness, and possible
identity. Any deviation of the pathway from a straight line should be
described. This information has no bearing on subsequent mathematical
procedure, except as it helps to eliminate objects other than birds
from computation.

The first step in processing a set of data so obtained is to
blue-pencil all entries that, judged by the accompanying remarks,
relate to extraneous objects such as insects or bats. Next, horizontal
lines are drawn across the data sheets marking the beginning and the
end of each even hour of observation, as 8 P. M.-9 P. M., 9 P. M.-10
P. M., etc. The coördinates of the birds in each one-hour interval may
now be plotted on separate diagrammatic clockfaces, just as they
appeared on the moon. Tick marks are added to each line to indicate
the number of birds occurring along the same coördinate. The slant of
the tick marks distinguishes the points of departure from the points
of entry. Figure 14 shows the plot for the 11 P. M.-12 P. M.
observations reproduced in Table 1. The standard form, illustrated in
Figure 15, includes four such diagrams.

Applying the self-evident principle that all pathways with the same
slant represent the same direction, we may further consolidate the
plots by shifting all coördinates to the corresponding lines passing
through the center of the circle, as in Figure 15. To illustrate, the
6 to 8, 5 to 9, 3 to 11, and 2 to 12 pathways all combine on the 4 to
10 line. Experienced computers eliminate a step by directly plotting
the pathways through center, using a transparent plastic straightedge
ruled off in parallel lines.

    [Illustration: FIG. 15. Standard form for plotting the
       apparent paths of flight. On these diagrams the original
       coördinates, exemplified by Figure 14, have been moved to
       center. In practice the sector boundaries are drawn over the
       circles in red pencil, as shown by the white lines in Figure
       19, making it possible to count the number of birds falling
       within each zone. These numbers are then tallied in the
       columns at the lower right of each hourly diagram.]


    TABLE 1.--Continuation of Data in Figure 12, Showing Time
                and Readings of Observations on 24-25 April 1948,
                Progreso, Yucatán

  ==============================+==============================
  Time          In       Out    |  Time          In       Out
  ------------------------------+------------------------------
  10:37-10:41  Time out         | 11:15        8          9:30
  10:45        5:30      10     | 11:16        4         11
               6          9     |              5          9
               5:30      10     | 11:17        5         11:30
  10:46        6          8     | 11:18        5         12
               3:30      11     |              6         11:30
               5         12     | 11:19        5:30      11:30
  10:47        3:15       1     | 11:20        6         10
               6          8:30  |              3         12
               5:45      11:45  |              5         12
               5         10     | 11:21        5:45      11
  10:48        6          9:45  |              5         11
  10:50        5:30      11     | 11:23        5         12
  10:51        4         11     | 11:25        5         10:30
  10:52        4          2     |              6         11
               5:30      11     |              6         12
  10:53        5:30      11:30  | 11:27        6         10
               5         11     | 11:28        6         11:30
  10:55        5         12     |              5:30      12:30
               5         11     | 11:29        6         11:30
  10:56        6         10     |              4         12
  10:58        4:30      11:30  |              6:30      10:30
               5:45      11:45  |              6         11
  10:59        6:30      10:30  | 11:30        3         10
  11:00        3:30      12     |       (2 birds at once)
               6:30      11     | 11:31        5         10:30
        (2 birds at once)       |              5:30      10:30
  11:03        6         11     | 11:32        6         11:30
  11:04        3         12     | 11:33        7:30       9:30
               5         12     |              4         10:30
  11:05        6         10     |              6         11:30
               5         11     |              8          9:30
  11:06        6         10:30  | 11:35        7         10
  11:07        3         10     |              4:30       1
  11:08        6         11     | 11:38        6:30      11
  11:10        7          9:30  | 11:40        5:30      12
  11:11        5          9:15  | 11:42        4          2
  11:13        5         12     |              5         12
  11:14        6:30      10     |              6         10
               5:30       1     |              4          2
               4         12     |              5         12
  ------------------------------+------------------------------

               Table 1.--_Concluded_
  ==============================+==============================
  Time          In       Out    |  Time          In       Out
  ------------------------------+------------------------------
  11:44        8          9:30  |               8         10:15
               7         11     |  12:16        3:30       1:30
               6         10     |               8         11
  11:45        5         12     |  12:23        7          1:30
               6         10:30  |               6         12:30
               5:45      11     |  12:36        8         11
               4         12     |  12:37        7:30       1
  11:46        7         11     |  12:38        7         12:30
               6         12     |  12:40        8          1
  11:47        8         10     |  12:45        7:30       1
  11:48        6         10     |  12:47        5:30       1
  11:49        6:30      10:30  |  12:48        7          1
  11:51        8         10     |  12:52        5:30       1:30
               8         10     |  12:54-12:55  Time out
               8         10     |  12:56        8         10:45
               8         10     |  12:58        5:30       1:30
               6         10     |               7          1:30
               8         10     |               7          2
               6         11     |  12:59        5          3
               7         12     |   1:00-1:30   Time out
  11:52        5          1     |   1:37        8         12
  11:54        7         11     |   1:38        8         12
               6         12:30  |   1:48        7          1
  11:55        5         12     |               7          1
  11:56        7         10     |   1:51        5:30      11
               5         12     |   1:57        8          1
  11:58        8         11     |   2:07        7          2
  11:59        5:30      12     |   2:09        9         12
  12:00-12:03  Time out         |   2:10        8          1
  12:03        5:30      11:30  |   2:17        9         12
  12:04        8         11     |   2:21        6          2
  12:07        6         12:30  |   2:30        5:30       3:15
               7:30       1     |   2:32        8          2
  12:08        5         10:30  |   2:46        7          1
  12:09        5:30       1     |   3:36        9          2
               7:30       2     |   3:39        8:30       2
  12:10        6:30      12:45  |   3:45        6          4
  12:13        8         11     |   3:55        9          2
  12:14        7          1     |   4:00        8          3
  12:15        7         12:30  |   4:03        9          2
               7:15       1:30  |   4:30        Closed station
  ------------------------------+------------------------------

We now have a concise picture of the apparent pathways of all the
birds recorded in each hour of observation. But the coördinates do not
have the same meaning as readings of a horizontal clock on the earth's
surface, placed in relation to the points of the compass. They are
merely projections of the birds' courses. An equation is available for
reversing the effect of projection and discovering the true directions
of flight. This formula, requiring thirty-five separate computations
for the pathways reproduced in Figure 12 alone, is far too-consuming
for the handling of large quantities of data. A simpler procedure is
to divide the compass into sectors and, with the aid of a reverse
equation, to draw in the projected boundaries of these divisions on
the circular diagrams of the moon. A standardized set of sectors, each
22-1/2° wide and bounded by points of the compass, has been evolved
for this purpose. They are identified as shown in Figure 16. The zones
north of the east-west line are known as the North, or N, Sectors, as
N_{1}, N_{2}, N_{3}, etc. Each zone south of the east-west line bears
the same number as the sector opposite, but is distinguished by the
designation S.

    [Illustration: FIG. 16. Standard sectors for designating
       flight trends. Each zone covers a span of 22-1/2°. The N_{6}
       and N_{8}, the N_{5} and N_{7}, and their south complements,
       where usually few birds are represented, can be combined and
       identified as N_{6-8} and N_{5-7}, etc.]

Several methods may be used to find the projection of the sector
boundaries on the plot diagrams of Figure 15. Time may be saved by
reference to graphic tables, too lengthy for reproduction here,
showing the projected reading in degrees for every boundary, at every
position of the moon; and a mechanical device, designed by C. M.
Arney, duplicating the conditions of the original projection, speeds
up the work even further. Both methods are based on the principle of
the following formula:

    tan [theta] = tan ([eta] - [psi]) / cos Z_{0}    (1)

    [Illustration: FIG. 17. The meaning of symbols used in the
       direction formula.]

The symbols have these meanings:

[theta] is the position angle of the sector boundary on the lunar
clock, with positive values measured counterclockwise from 12 o'clock,
negative angles clockwise (Figure 17A).

[eta] is the compass direction of the sector boundary expressed in
degrees reckoned west from the south point (Figure 17B).

Z_{0} is the zenith distance of the moon's center midway through the
hour of observation, that is, at the half hour. It represents the
number of degrees of arc between the center of the moon and a
point directly over the observer's head (Figure 17C).

[psi] is the azimuth of the moon midway through the hour of
observation, measured from the south point, positive values to the
west, negative values to the east (Figure 17D).

    [Illustration: FIG. 18. Form used in the computation of the
       zenith distance and azimuth of the moon.]

The angle [eta] for any sector boundary can be found immediately by
measuring its position in the diagram (Figure 16). The form (Figure 18)
for the "Computation of Zenith Distance and Azimuth of the Moon"
illustrates the steps in calculating the values of Z_{0} and [psi]_{0}.
From the American Air Almanac (Anonymous, 1945-1948), issued annually
by the U. S. Naval Observatory in three volumes, each covering four
months of the year, the Greenwich Hour Angle (GHA) and the declination
of the moon may be obtained for any ten-minute interval of the date in
question. The Local Hour Angle (LHA) of the observation station is
determined by subtracting the longitude of the station from the GHA.
Reference is then made to the "Tables of Computed Altitude and Azimuth,"
published by the U. S. Navy Department, Hydrographic Office (Anonymous,
1936-1941), and better known as the "H.O. 214," to locate the altitude
and azimuth of the moon at the particular station for the middle of the
hour during which the observations were made. The tables employ three
variables--the latitude of the locality measured to the nearest degree,
the LHA as determined above, and the declination of the moon measured
to the nearest 30 minutes of arc. Interpolations can be made, but this
exactness is not required. When the latitude of the observation
station is in the northern hemisphere, the H.O. 214 tables entitled
"Declinations Contrary Name to Latitude" are used with south
declinations of the moon, and the tables "Declinations Same Name as
Latitude," with north declinations. In the sample shown in Figure 15,
the declination of the moon at 11:30 P. M., midway through the 11 to
12 o'clock interval, was S 20° 22´. Since the latitude of Progreso,
Yucatán is N 21° 17´, the "Contrary Name" tables apply to this hour.

Because the H.O. 214 expresses the vertical position of the moon in
terms of its altitude, instead of its zenith distance, a conversion is
required. The former is the number of arc degrees from the horizon to
the moon's center; therefore Z_{0} is readily obtained by subtracting
the altitude from 90°. Moreover, the azimuth given in the H.O. 214 is
measured on a 360° scale from the north point, whereas the azimuth
used here ([psi]_{0}) is measured 180° in either direction from the south
point, negative values to the east, positive values to the west. I
have designated the azimuth of the tables as Az_{n} and obtained the
desired azimuth ([psi]_{0}) by subtracting 180° from Az_{n}. The sign
of [psi]_{0} may be either positive or negative, depending on whether
or not the moon has reached its zenith and hence the meridian of the
observer. When the GHA is greater than the local longitude (that is,
the longitude of the observation station), the azimuth is positive.
When the GHA is less than the local longitude, the azimuth is
negative.

Locating the position of a particular sector boundary now becomes a
mere matter of substituting the values in the equation (1) and
reducing. The computation of the north point for 11 to 12 P. M. in
the sample set of data will serve as an example. Since the north point
reckoned west from the south point is 180°, its [eta] has a value of
180°.

    [Illustration: FIG. 19. Method of plotting sector
       boundaries on the diagrammatic plots. The example employed is
       the 11:00 to 12:00 P. M. diagram of Figure 15.]


    tan [theta]_{Npt.} = tan (180° - [psi]_{0}) / cos Z_{0}

Substituting values of [psi]_{0} found on the form (Figure 18):

    tan [theta]_{Npt.} = tan [180° - (-35°)] / cos 50°
                       = tan 215° / cos 50° = .700 / .643 = 1.09

    [theta]_{Npt.} = 47°28´


    [Illustration: FIG. 20. Form for computing sector
       densities.]

Four angles, one in each quadrant, have the same tangent value.
Since, in processing spring data, we are dealing mainly with north
sectors, it is convenient to choose the acute angle, in this instance
47° 28´. In doubtful cases, the value of the numerator of the equation
(here 215°) applied as an angular measure from 6 o'clock will tell in
which quadrant the projected boundary must fall. The fact that
projection always draws the boundary closer to the 3-9 line serves as
a further check on the computation.

    [Illustration: FIG. 21. Determinationn of the angle [alpha]]

In the same manner, the projected position angles of all the pertinent
sector boundaries for a given hour may be calculated and plotted in
red pencil with a protractor on the circular diagrams of Figure 15. To
avoid confusion in lines, the zones are not portrayed in the black and
white reproduction of the sample plot form. They are shown, however,
in the shaded enlargement (Figure 19) of the 11 to 12 P. M. diagram.
The number of birds recorded for each sector may be ascertained by
counting the number of tally marks between each pair of boundary lines
and the information may be entered in the columns provided in the plot
form (Figure 15). We are now prepared to turn to the form for
"Computations of Sector Densities" (Figure 20), which systematizes the
solution of the following equation:

         (220) 60/T (No. of Birds) (cos^2 Z_{0})
    D =  ---------------------------------------                   (2)
         (1 - sin^2 Z_{0} cos^2 [alpha])^0.5


    [Illustration: FIG. 22. Facsimile of form summarizing
       sector densities. The totals at the bottom of each column
       give the station densities.]


    [Illustration: FIG. 23. Determination of Net Trend Density.]


Some of the symbols and factors, appearing here for the first time,
require brief explanation. D stands for Sector Density. The constant,
220, is the reciprocal of the quotient of the angular diameter of the
moon divided by 2. T is Time In, arrived at by subtracting the total
number of minutes of time out, as noted for each hour on the original
data sheets, from 60. "No. of Birds" is the number for the sector and
hour in question as just determined on the plot form. The symbol
[alpha] represents the angle between the mid-line of the sector and
the azimuth line of the moon. The quantity is found by the equation:

    [alpha] = 180° - [eta] + [psi]_{0}                             (3)

The symbol [eta] here represents the position of the mid-line of the
sector expressed in terms of its 360° compass reading. This equation
is illustrated in Figure 21. The values of [eta] for various zones are
given in the upper right-hand corner of the form (Figure 20). The
subsequent reductions of the equations, as they appear in the figure
for four zones, are self-explanatory. The end result, representing the
sector density, is entered in the rectangular box provided.

After all the sector densities have been computed, they are tabulated
on a form for the "Summary of Sector Densities" (Figure 22). By
totaling each vertical column, sums are obtained, expressing the
Station Density or Station Magnitude for each hour.

An informative way of depicting the densities in each zone is to plot
them as lines of thrust, as in Figure 23. Each sector is represented
by the directional slant of its mid-line drawn to a length expressing
the flight density per zone on some chosen scale, such as 100 birds
per millimeter. Standard methods of vector analysis are then applied
to find the vector resultant. This is done by considering the first
two thrust lines as two sides of an imaginary parallelogram and using
a drawing compass to draw intersecting arcs locating the position of
the missing corner. In the same way, the third vector is combined
with the invisible resultant whose distal end is represented by the
intersection of the first two arcs. The process is repeated
successively with each vector until all have been taken into
consideration. The final intersection of arcs defines the length and
slant of the Vector Resultant, whose magnitude expresses the Net Trend
Density in terms of the original scale.

The final step in the processing of a set of observations is to plot
on graph paper the nightly station density curve as illustrated by
Figure 24.

    [Illustration: FIG. 24. Nightly station density curve at
       Progreso, Yucatán, on April 24-25, 1948.]




PART II. THE NATURE OF NOCTURNAL MIGRATION


Present day concepts of the whole broad problem of bird migration are
made up of a few facts and many guesses. The evolutionary origin of
migration, the modern necessities that preserve its biologic utility,
the physiological processes associated with it, the sensory mechanisms
that make it possible, the speed at which it is achieved, and the
routes followed, all have been the subject of some investigation and
much conjecture. All, to a greater or less extent, remain matters of
current controversy. All must be considered unknowns in every logical
equation into which they enter. Since all aspects of the subject are
intimately interrelated, since all have a bearing on the probabilities
relating to any one, and since new conjectures must be judged largely
in the light of old conjectures rather than against a background of
ample facts, the whole field is one in which many alternative
explanations of the established phenomena remain equally tenable.
Projected into this uncertain atmosphere, any statistical approach
such as determinations of flight density will require the accumulation
of great masses of data before it is capable of yielding truly
definitive answers to those questions that it is suited to solve. Yet,
even in their initial applications, density analyses can do much to
bring old hypotheses regarding nocturnal migration into sharper
definition and to suggest new ones.

The number of birds recorded through the telescope at a particular
station at a particular time is the product of many potential
variables. Some of these--like the changing size of the field of
observation and the elevation of flight--pertain solely to the
capacity of the observer to see what is taking place. It is the
function of the density and direction formulae to eliminate the
influences of these two variables insofar as is possible, so that the
realities of the situation take shape in a nearly statistically true
form. There remain to be considered those influences potentially
responsible for variations in the real volume of migration at
different times and places--things like the advance of season,
geographic location, disposition of terrain features, hourly activity
rhythm, wind currents, and other climatological causes. The situation
represented by any set of observations probably is the end result of
the interaction of several such factors. It is the task of the
discussions that follow to analyze flight densities in the light of
the circumstances surrounding them and by statistical insight to
isolate the effects of single factors. When this has been done, we
shall be brought closer to an understanding of these influences
themselves as they apply to the seasonal movements of birds. Out of
data that is essentially quantitative, conclusions of a qualitative
nature will begin to take form. It should be constantly borne in mind,
however, that such conclusions relate to the movement of birds _en
masse+ and that caution must be used in applying these conclusions to
any one species.

Since the dispersal of migrants in the night sky has a fundamental
bearing on the sampling procedure itself, and therefore on the
reliability of figures on flight density, consideration can well be
given first to the horizontal distribution of birds on narrow fronts.


A. HORIZONTAL DISTRIBUTION OF BIRDS ON NARROW FRONTS

Bird migration, as we know it in daytime, is characterized by spurts
and uneven spatial patterns. Widely separated V's of geese go honking
by. Blackbirds pass in dense recurrent clouds, now on one side of the
observer, now on the other. Hawks ride along in narrow file down the
thermal currents of the ridges. Herons, in companies of five to fifty,
beat their way slowly along the line of the surf. And an unending
stream of swallows courses low along the levees. Everywhere the
impression is one of birds in bunches, with vast spaces of empty sky
between.

Such a situation is ill-suited to the sort of sampling procedure on
which flight density computations are based. If birds always traveled
in widely separated flocks, many such flocks might pass near the cone
of observation and still, by simple chance, fail to enter the sliver
of space where they could be seen. Chance would be the dominating
factor in the number of birds recorded, obscuring the effects of other
influences. Birds would seldom be seen, but, when they did appear, a
great many would be observed simultaneously or in rapid succession.

When these telescopic studies were first undertaken at Baton Rouge in
1945, some assurance already existed, however, that night migrants might
be so generally dispersed horizontally in the darkness above that the
number passing through the small segment of sky where they could be
counted would furnish a nearly proportionate sample of the total number
passing in the neighborhood of the observation station. This assurance
was provided by the very interesting account of Stone (1906: 249-252),
who enjoyed the unique experience of viewing a nocturnal flight as a
whole. On the night of March 27, 1906, a great conflagration occurred in
Philadelphia, illuminating the sky for a great distance and causing the
birds overhead to stand out clearly as their bodies reflected the light.
Early in the night few birds were seen in the sky, but thereafter they
began to come in numbers, passing steadily from the southwest to the
northeast. At ten o'clock the flight was at its height. The observer
stated that two hundred birds were in sight at any given moment as he
faced the direction from which they came. This unparalleled observation
is of such great importance that I quote it in part, as follows: "They
[the birds] flew in a great scattered, wide-spread host, never in
clusters, each bird advancing in a somewhat zigzag manner.... Far off in
front of me I could see them coming as mere specks...gradually growing
larger as they approached.... Over the illuminated area, and doubtless
for great distances beyond, they seemed about evenly distributed.... I
am inclined to think that the migrants were not influenced by the fire,
so far as their flight was concerned, as those far to the right were not
coming toward the blaze but keeping steadily on their way.... Up to
eleven o'clock, when my observations ceased, it [the flight] continued
apparently without abatement, and I am informed that it was still in
progress at midnight."

Similarly, in rather rare instances in the course of the present
study, the combination of special cloud formations and certain
atmospheric conditions has made it possible to see birds across the
entire field of the telescope, whether they actually passed before the
moon or not. In such cases the area of the sky under observation is
greatly increased, and a large segment of the migratory movement can
be studied. In my own experience of this sort, I have been forcibly
impressed by the apparent uniformity and evenness of the procession of
migrants passing in review and the infrequence with which birds
appeared in close proximity.

As striking as these broader optical views of nocturnal migration are,
they have been too few to provide an incontestable basis for
generalizations. A better test of the prevailing horizontal
distribution of night migrants lies in the analysis of the telescopic
data themselves.

    [Illustration: FIG. 25. Positions of the cone of observation
       at Tampico, Tamps., on April 21-22, 1948. Essential features
       of this diagrammatic map are drawn to scale, the triangular
       white lines representing the projections of the cone of
       observation on the actual terrain at the mid-point of each
       hour of observation. If the distal ends of the position lines
       were connected, the portion of the map encompassed would
       represent the area over which all the birds seen between
       8:30 P. M. and 3:30 A. M. must have flown.]

The distribution in time of birds seen by a single observer may be
studied profitably in this connection. Since the cone of observation
is in constant motion, swinging across the front of birds migrating
from south to north, each interval of time actually represents a
different position in space. This is evident from the map of the
progress of the field of observation across the terrain at Tampico,
Tamaulipas, on April 21-22, 1948 (Figure 25). At this station on this
night, a total of 259 birds were counted between 7:45 P. M. and
3:45 A. M. The number seen in a single hour ranged from three to
seventy-three, as the density overhead mounted to a peak and then
declined. The number of birds seen per minute was not kept with stop
watch accuracy; consequently, analysis of the number of birds that
passed before the moon in short intervals of time is not justified. It
appears significant, however, that in the ninety minutes of heaviest
flight, birds were counted at a remarkably uniform rate per fifteen
minute interval, notwithstanding the fact that early in the period the
flight rate overhead had reached a peak and had begun to decline. The
number of birds seen in successive fifteen-minute periods was
twenty-six, twenty-five, nineteen, eighteen, fifteen, and fifteen.

Also, despite the heavy volume of migration at this station on this
particular night, the flight was sufficiently dispersed horizontally
so that only twice in the course of eight hours of continuous
observation did more than one bird simultaneously appear before the
moon. These were "a flock of six birds in formation" seen at 12:09 A. M.
and "a flock of seven, medium-sized and distant," seen at 2:07 A. M.
In the latter instance, as generally is the case when more than one
bird is seen at a time, the moon had reached a rather low altitude,
and consequently the cone of observation was approaching its maximum
dimensions.

The comparative frequency with which two or more birds simultaneously
cross before the moon would appear to indicate whether or not there is
a tendency for migrants to fly in flocks. It is significant, therefore,
that in the spring of 1948, when no less than 7,432 observations were
made of birds passing before the moon, in only seventy-nine instances,
or 1.1 percent of the cases, was more than one seen at a time. In
sixty percent of these instances, only two birds were involved. In one
instance, however, again when the moon was low and the cone of
observation near its maximum size, a flock estimated at twenty-five
was recorded.

The soundest approach of all to the study of horizontal distribution at
night, and one which may be employed any month, anywhere, permitting the
accumulation of statistically significant quantities of data, is to set
up two telescopes in close proximity. Provided the flight overhead is
evenly dispersed, each observer should count approximately the same
number of birds in a given interval of time. Some data of this type are
already available. On May 19-20, at Urbana, Illinois, while stationed
twenty feet apart making parallax studies with two telescopes to
determine the height above the earth of the migratory birds, Carpenter
and Stebbins (_loci cit._) saw seventy-eight birds in two and one-half
hours. Eleven were seen by both observers, thirty-three by Stebbins
only, and thirty-four by Carpenter only. On October 10, 1905, at the
same place, in two hours, fifty-seven birds were counted, eleven being
visible through both telescopes. Of the remainder, Stebbins saw
seventeen and Carpenter, twenty-nine. On September 12, 1945, at Baton
Rouge, Louisiana, in an interval of one hour and forty minutes, two
independent observers each counted six birds. Again, on October 17,
1945, two observers each saw eleven birds in twenty-two minutes. On
April 10, 1946, in one hour and five minutes, twenty-four birds were
seen through one scope and twenty-six through the other. Likewise on May
12, 1946, in a single hour, seventy-three birds were counted by each of
two observers. The Baton Rouge observations were made with telescopes
six to twelve feet apart. These results show a remarkable conformity,
though the exceptional October observation of Carpenter and Stebbins
indicates the desirability of continuing these studies, particularly in
the fall.

On the whole, the available evidence points to the conclusion that night
migration differs materially from the kind of daytime migration with
which we are generally familiar. Birds are apparently evenly spread
throughout the sky, with little tendency to fly in flocks. It must be
remembered, however, that only in the case of night migration have
objective and truly quantitative studies been made of horizontal
distribution. There is a possibility that our impressions of diurnal
migration are unduly influenced by the fact that the species accustomed
to flying in flocks are the ones that attract the most attention.

These conclusions relate to the uniformity of migration in terms of
short distances only, in the immediate vicinity of an observation
station. The extent to which they may be applied to broader fronts is a
question that may be more appropriately considered later, in connection
with continental aspects of the problem.


B. DENSITY AS FUNCTION OF THE HOUR OF THE NIGHT

There are few aspects of nocturnal migration about which there is less
understanding than the matter of when the night flight begins, at what
rate it progresses, and for what duration it continues. One would think,
however, that this aspect of the problem, above most others, would have
been thoroughly explored by some means of objective study. Yet, this is
not the case. Indeed, I find not a single paper in the American
literature wherein the subject is discussed, although some attention has
been given the matter by European ornithologists. Siivonen (1936)
recorded in Finland the frequency of call notes of night migrating
species of _Turdus_ and from these data plotted a time curve showing a
peak near midnight. Bergman (1941) and Putkonen (1942), also in Finland,
studied the night flights of certain ducks (_Clangula hyemalis_ and
_Oidemia fusca_ and _O. nigra_) and a goose (_Branta bernicla_) and
likewise demonstrated a peak near midnight. However, these studies were
made at northern latitudes and in seasons characterized by evenings of
long twilight, with complete darkness limited to a period of short
duration around midnight. Van Oordt (1943: 34) states that in many cases
migration lasts all night; yet, according to him, most European
investigators are of the opinion that, in general, only a part of the
night is used, that is, the evening and early morning hours. The
consensus of American ornithologists seems to be that migratory birds
begin their flights in twilight or soon thereafter and that they remain
on the wing until dawn. Where this idea has been challenged at all, the
implication seems to have been that the flights are sustained even
longer, often being a continuation far into the night of movements begun
in the daytime. The telescopic method fails to support either of these
latter concepts.

    [Illustration: FIG. 26. Average hourly station densities in
       spring of 1948. This curve represents the arithmetic mean
       obtained by adding all the station densities for each hour,
       regardless of date, and dividing the sum by the number of
       sets of observations at that hour (CST).]


_The Time Pattern_

When the nightly curves of density at the various stations are plotted
as a function of time, a salient fact emerges--that the flow of birds is
in no instance sustained throughout the night. The majority of the
curves rise smoothly from near zero at the time of twilight to a single
peak and then decline more or less symmetrically to near the base line
before dawn. The high point is reached in or around the eleven to twelve
o'clock interval more often than at any other time.

    [Illustration: FIG. 27. Hourly station densities plotted as
       a percentage of peak. The curve is based only on those sets
       of data where observations were continued long enough to
       include the nightly peak. In each set of data the station
       density for each hour has been expressed as a percentage of
       the peak for the night at the station in question. All
       percentages for the same hour on all dates have been averaged
       to obtain the percentile value of the combined station
       density at each hour (CST).]

Figure 26, representing the average hourly densities for all stations on
all nights of observation, demonstrates the over-all effect of these
tendencies. Here the highest density is reached in the hour before
midnight with indications of flights of great magnitude also in the hour
preceding and the hour following the peak interval. The curve ascends
somewhat more rapidly than it declines, which fact may or may not be
significant. Since there is a great disproportion in the total volume of
migration at different localities, the thought might be entertained that
a few high magnitude stations, such as Tampico and Progreso, have
imposed their own characteristics on the final graph. Fortunately, this
idea may be tested by subjecting the data to a second treatment. If
hourly densities are expressed as a percentage of the nightly peak, each
set of observations, regardless of the number of birds involved, carries
an equal weight in determining the character of the over-all curve.
Figure 27 shows that percentage analysis produces a curve almost
identical with the preceding one. To be sure, all of the individual
curves do not conform with the composite, either in shape or incidence
of peak. The extent of this departure in the latter respect is evident
from Figure 28, showing the number of individual nightly station curves
reaching a maximum peak in each hour interval. Even this graph
demonstrates that maximum densities near midnight represent the typical
condition.

    [Illustration: FIG. 28. Incidence of maximum peak at the
       various hours of the night in 1948. "Number of stations"
       represents the total for all nights of the numbers of station
       peaks falling within a given hour.]

The remarkable smoothness and consistency of the curves shown in Figures
26 and 27 seem to lead directly to the conclusion that the volume of
night migration varies as a function of time. Admittedly other factors
are potentially capable of influencing the number of birds passing a
given station in a given hour. Among these are weather conditions,
ecological patterns, and specific topographical features that might
conceivably serve as preferred avenues of flight. However, if any of
these considerations were alone responsible for changes in the numbers
of birds seen in successive intervals, the distribution of the peak in
time could be expected to be haphazard. For example, there is no reason
to suppose that the cone of observation would come to lie over favored
terrain at precisely the hour between eleven and twelve o'clock at so
many widely separated stations. Neither could the topographical
hypothesis explain the consistently ascending and descending pattern of
the ordinates in Figure 28. This is not to say that other factors are
without effect; they no doubt explain the divergencies in the time
pattern exhibited by Figure 28. Nevertheless, the underlying
circumstances are such that when many sets of data are merged these
other influences are subordinated to the rise and fall of an evident
time pattern.

Stated in concrete terms, the time frequencies shown in the graphs
suggest the following conclusions: first, nocturnal migrations are not a
continuation of daytime flights; second, nearly all night migrants come
to earth well before dawn; and, third, in each hour of the night up
until eleven or twelve o'clock there is typically a progressive increase
in the number of birds that have taken wing and in each of the hours
thereafter there is a gradual decrease. Taken at its face value, the
evidence seems to indicate that birds do not begin their night
migrations _en masse_ and remain on the wing until dawn and that in all
probability most of them utilize less than half of the night.

Interestingly enough, the fact that the plot points in Figure 26 lie
nearly in line tempts one to a further conclusion. The curve behaves as
an arithmetic progression, indicating that approximately the same number
of birds are leaving the ground in each hour interval up to a point and
that afterwards approximately the same number are descending within
each hour. However, some of the components making up this curve, as
later shown, are so aberrant in this regard that serious doubt is cast
on the validity of this generalization.

Because the results of these time studies are unexpected and
startling, I have sought to explore other alternative explanations and
none appears to be tenable. For example, the notion that the varying
flight speeds of birds might operate in some way to produce a
cumulative effect as the night progresses must be rejected on close
analysis. If birds of varying flight speeds are continuously and
evenly distributed in space, a continuous and even flow would result
all along their line of flight. If they are haphazardly distributed in
space, a correspondingly haphazard density pattern would be expected.

Another explanation might be sought in the purely mathematical effects
of the method itself. The computational procedure assumes that the
effective area of the sample is extremely large when the moon is low,
a condition that usually obtains in the early hours of the evening in
the days surrounding the full moon. Actually no tests have yet been
conducted to ascertain how far away a silhouette of a small bird can
be seen as it passes before the moon. Consequently, it is possible
that some birds are missed under these conditions and that the
effective field of visibility is considerably smaller than the
computed field of visibility. The tendency, therefore, may be to
minimize the densities in such situations more than is justified.
However, in many, if not most, cases, the plotting of the actual
number of birds seen, devoid of any mathematical procedures, results
in an ascending and descending curve.

    [Illustration: FIG. 29. Various types of density-time curves.
       (A) Near typical, Ottumwa, April 22-23; (B) random fluctuation,
       Stillwater, April 23-24; (C) bimodal, Knoxville, April 22-23;
       (D) sustained peak, Ottumwa, April 21-22; (E) early peak, Oak
       Grove, May 21-22; (F) late peak, Memphis, April 23-24.]

A third hypothesis proposes that all birds take wing at nearly the
same time, gradually increase altitude until they reach the mid-point
of their night's journey, and then begin a similarly slow descent.
Since the field of observation of the telescope is conical, it is
assumed that the higher the birds arise into the sky the more they
increase their chances of being seen. According to this view, the
changes in the density curve represent changes in the opportunity to
see birds rather than an increase or decrease in the actual number of
migrants in the air. Although measurements of flight altitude at
various hours of the night have not been made in sufficient number to
subject this idea to direct test, it is hardly worthy of serious
consideration. The fallacy in the hypothesis is that the cone of
observation itself would be rising with the rising birds so that
actually the greatest proportion of birds flying would still be seen
when the field of observation is in the supine position of early
evening.

It cannot be too strongly emphasized that the over-all time curves
just discussed have been derived from a series of individual curves,
some of which differ radically from the composite pattern. In Figure
29, six dissimilar types are shown. This variation is not surprising
in view of the fact that many other causative factors aside from time
operate on the flow of birds from hour to hour. Figure 29A illustrates
how closely some individual patterns conform with the average. Figure
29B is an example of a random type of fluctuation with no pronounced
time character. It is an effect rarely observed, occurring only in the
cases where the number of birds observed is so small that pure chance
has a pronounced effect on the computed densities; its vacillations
are explicable on that account alone. Errors of sampling may similarly
account for some, though not all, of the curves of the bimodal type
shown in Figure 29C. Some variation in the curves might be ascribed to
the variations in kinds of species comprising the individual flights
at different times at different places, provided that it could be
demonstrated that different species of birds show dissimilar temporal
patterns. The other atypical patterns are not so easily dismissed and
will be the subject of inquiry in the discussions that follow. It is
significant that in spite of the variety of the curves depicted, which
represent every condition encountered, in not a single instance is the
density sustained at a high level throughout the night. Moreover,
these dissident patterns merge into a remarkably harmonious, almost
normal, average curve.

When, at some future date, suitable data are available, it would be
highly desirable to study the average monthly time patterns to
ascertain to what extent they may deviate from the over-all average.
At present this is not justifiable because there are not yet enough
sets of data in any two months representing the same selection of
stations.

_Correlations with Other Data_

It is especially interesting to note that the data pertaining to this
problem derived from other methods of inquiry fit the conclusions
adduced by the telescopic method. Overing (1938), who for several
years kept records of birds striking the Washington Monument, stated
that the record number of 576 individuals killed on the night of
September 12, 1937, all came down between 10:30 P. M. and midnight.
His report of the mortality on other nights fails to mention the time
factor, but I am recently informed by Frederick C. Lincoln (_in
litt._) that it is typical for birds to strike the monument in
greatest numbers between ten and twelve o'clock at night. At the
latter time the lights illuminating the shaft are extinguished, thus
resulting in few or no casualties after midnight. The recent report by
Spofford (1949) of over 300 birds killed or incapacitated at the
Nashville airport on the night of September 9-10, 1948, after flying
into the light beam from a ceilometer, is of interest in this
connection even though the cause of the fatality is shrouded in
mystery. It may be noted, however, that "most of the birds fell in the
first hour," which, according to the account, was between 12:30 A. M.
and 1:30 A. M. Furthermore, birds killed at the Empire State
Building in New York on the night of September 10-11, 1948, began to
strike the tower "shortly after midnight" (Pough, 1948). Also it will
be recalled that the observations of Stone (_loc. cit._), already
referred to in this paper (page 410), show a situation where the
flight in the early part of the night was negligible but mounted to a
peak between ten and eleven o'clock, with continuing activity at least
until midnight.

All of these observations are of significance in connection with the
conclusions herein advanced, but by far the most striking correlation
between these present results and other evidences is found in the
highly important work of various European investigators studying the
activity of caged migratory birds. This work was recently reviewed and
extended by Palmgren (1944) in the most comprehensive treatise on the
subject yet published. Palmgren recorded, by an electrically operated
apparatus, the seasonal, daily, and hourly activity patterns in caged
examples of two typical European migrants, _Turdus ericetorum
philomelas_ Brehm and _Erithacus rubecula_ (Linnaeus). Four rather
distinct seasonal phases in activity of the birds were discerned:
_winter non-migratory_, _spring migratory_, _summer non-migratory_,
and _autumn migratory_. The first of these is distinguished by morning
and evening maxima of activity, the latter being better developed but
the former being more prolonged. Toward the beginning of migration,
these two periods of activity decline somewhat. The second, or spring
migratory phase, which is of special interest in connection with the
present problem, is characterized by what Palmgren describes as
nightly migratory restlessness (_Zugunruhe_). The morning maximum,
when present, is weaker and the evening maximum often disappears
altogether. Although variations are described, the migratory
restlessness begins ordinarily after a period of sleep ("sleeping
pause") in the evening and reaches a maximum and declines before
midnight.

This pattern agrees closely with the rhythm of activity indicated by
the time curves emerging from the present research. Combining the two
studies, we may postulate that most migrants go to sleep for a period
following twilight, thereby accounting for the low densities in the
early part of the night. On awakening later, they begin to exhibit
migratory restlessness. The first hour finds a certain number of birds
sufficiently stimulated so that they rise forthwith into the air. In
the next hour still others respond to this urge and they too mount
into the air. This continues until the "restlessness" begins to abate,
after which fewer and fewer birds take wing. By this time, the birds
that began to fly early are commencing to descend, and since their
place is not being filled by others leaving the ground, the density
curve starts its decline. Farner (1947) has called attention to the
basic importance of the work by Palmgren and the many experimental
problems it suggests. Of particular interest would be studies
comparing the activity of caged American migrant species and the
nightly variations in the flight rates.

_The Baton Rouge Drop-off_

As already stated, the present study was initiated at Baton Rouge,
Louisiana, in 1945, and from the outset a very peculiar density time
pattern was manifest. I soon found that birds virtually disappeared
from the sky after midnight. Within an hour after the termination of
twilight, the density would start to ascend toward a peak which was
usually reached before ten o'clock, and then would begin, surprisingly
enough, a rapid decline, reaching a point where the migratory flow was
negligible. In Figure 30 the density curves are shown for five nights
that demonstrate this characteristically early decline in the volume
of migration at this station. Since, in the early stages of the work,
coördinates of apparent pathways of all the birds seen were not
recorded, I am unable now to ascertain the direction of flight and
thereby arrive at a density figure based on the dimension of the cone
and the length of the front presented to birds flying in certain
directions. It is feasible, nevertheless, to compute what I have
termed a "plus or minus" flight density figure stating the rate of
passage of birds in terms of the maximum and minimum corrections which
all possible directions of flight would impose. In other words,
density is here computed, first, as if all the birds were flying
perpendicular to the long axis of the ellipse, and, secondly, as if
all the birds were flying across the short axis of the ellipse. Since
the actual directions of flight were somewhere between these two
extremes, the "plus or minus" density figure is highly useful.

    [Illustration: FIG. 30. Density-time curves on various nights
       at Baton Rouge. (A) April 25, 1945; (B) April 15, 1946;
       (C) May 10, 1946; (D) May 15, 1946; (E) April 22-23, 1948.
       These curves are plotted on a "plus or minus" basis as
       described in the text, with the bottom of the curve
       representing the minimum density and the top of the curve
       the maximum.]

The well-marked decline before midnight in the migration rates at
Baton Rouge may be regarded as one of the outstanding results emerging
from this study. Many years of ornithological investigation in this
general region failed to suggest even remotely that a situation of
this sort obtained. Now, in the light of this new fact, it is possible
for the first time to rationalize certain previously incongruous data.
Ornithologists in this area long have noted that local storms and
cold-front phenomena at night in spring sometimes precipitate great
numbers of birds, whereupon the woods are filled the following day
with migrants. On other occasions, sudden storms at night have
produced no visible results in terms of bird densities the following
day. For every situation such as described by Gates (1933) in which
hordes of birds were forced down at night by inclement weather, there
are just as many instances, even at the height of spring migration,
when similar weather conditions yielded no birds on the ground.
However, the explanation of these facts is simple; for we discover
that storms that produced birds occurred before midnight and those
that failed to produce birds occurred after that time (the storm
described by Gates occurred between 8:30 and 9:00 P. M.).

The early hour decline in density at Baton Rouge at first did not seem
surprising in view of the small amount of land area between this
station and the Gulf of Mexico. Since the majority of the birds
destined to pass Baton Rouge on a certain night come in general from
the area to the south of that place, and since the distances to
various points on the coast are slight, we inferred that a three-hour
flight from even the more remote points would probably take the bulk
of the birds northward past Baton Rouge. In short, the coastal plain
would be emptied well before midnight of its migrant bird life, or at
least that part of the population destined to migrate on any
particular night in question. Although data in quantity are not
available from stations on the coastal plain other than Baton Rouge,
it may be pointed out that such observations as we do have, from
Lafayette and New Orleans, Louisiana, and from Thomasville, Georgia,
are in agreement with this hypothesis.

A hundred and seventy miles northward in the Mississippi Valley, at
Oak Grove, Louisiana, a somewhat more normal density pattern is
manifested. There, in four nights of careful observation, a pronounced
early peak resulted on the night of May 21-22 (Figure 29E), but on the
other three nights significant densities held up until near twelve
o'clock, thereby demonstrating the probable effect of the increased
amount of land to the south of the station.

Subsequent studies, revealing the evident existence of an underlying
density time pattern, cast serious doubt on the explanations just
advanced of the early decline in the volume of migration at Baton
Rouge. It has as yet been impossible to reconcile the early drop-off
at this station with the idea that birds are still mounting into the
air at eleven o'clock, as is implied by the ideal time curves.


C. MIGRATION IN RELATION TO TOPOGRAPHY

To this point we have considered the horizontal distribution of birds
in the sky only on a very narrow scale and mainly in terms of the
chance element in observations. Various considerations have supported
the premise that the spread of nocturnal migration is rather even, at
least within restricted spacial limits and short intervals of time.
This means that in general the flow of birds from hour to hour at a
single station exhibits a smooth continuity. It does not mean that it
is a uniform flow in the sense that approximately the same numbers of
birds are passing at all hours, or at all localities, or even on all
one-mile fronts in the same locality. On the contrary, there is
evidence of a pronounced but orderly change through the night in the
intensity of the flight, corresponding to a basic and definitely timed
cycle of activity. Other influences may interfere with the direct
expression of this temporal rhythm as it is exhibited by observations
at a particular geographical location. Among these, as we have just
seen, is the disposition of the areas that offer suitable resting
places for transient birds and hence contribute directly and
immediately to the flight overhead. A second possible geographical
effect is linked with the question of the tendency of night migrants
to follow topographical features.

_General Aspects of the Topographical Problem_

That many diurnal migrants tend to fly along shorelines, rivers, and
mountain ridges is well known, but this fact provides no assurance
that night migrants do the same thing. Many of the obvious advantages
of specialized routes in daylight, such as feeding opportunities, the
lift provided by thermal updrafts, and the possible aid of certain
landmarks in navigation, assume less importance after night falls.
Therefore, it would not be safe to conclude that _all_ nocturnal
migrants operate as do _some_ diurnal migrants. For instance, the
passage of great numbers of certain species of birds along the Texas
coast in daylight hours cannot be regarded as certain proof that the
larger part of the nocturnal flight uses the same route. Neither can
we assume that birds follow the Mississippi River at night simply
because we frequently find migrants concentrated along its course in
the day. Fortunately we shall not need to speculate indefinitely on
this problem; for the telescopic method offers a means of study based
on what night migrants are doing _at night_. Two lines of attack may
be pursued. First we may compare flight densities obtained when the
field of the telescope lies over some outstanding topographical
feature, such as a river, with the recorded volume of flight when the
cone of observation is directed away from that feature. Secondly, we
may inquire how the major flight directions at a certain station are
oriented with respect to the terrain. If the flight is concentrated
along a river, for instance, the flight density curve should climb
upward as the cone of observation swings over the river, _regardless
of the hour at which it does so_. The effect should be most pronounced
if the observer were situated on the river bank, so that the cone
would eventually come to a position directly along the watercourse.
Though in that event birds coming up the river route would be flying
across the short axis of an elliptical section of the cone, the fact
that the whole field of observation would be in their path should
insure their being seen in maximum proportions. If, on the other hand,
the telescope were set up some distance away from the river so that
the cone merely moved _across_ its course, only a section of the
observation field would be interposed on the main flight lane.

The interaction of these possibilities with the activity rhythm should
have a variety of effects on the flight density curves. If the cone
comes to lie over the favored topographical feature in the hour of
greatest migrational activity, the results would be a simple sharp
peak of doubtful meaning. However, since the moon rises at a different
time each evening, the cone likewise would reach the immediate
vicinity of the terrain feature at a different time each night. As a
result, the terrain peak would move away from its position of
coincidence with the time peak on successive dates, producing first,
perhaps, a sustention of peak and later a definitely bimodal curve.
Since other hypotheses explain double peaks equally well, their mere
existence does not necessarily imply that migrants actually do travel
along narrow topographical lanes. Real proof requires that we
demonstrate a moving peak, based on properly corrected density
computations, corresponding always with the position of the cone over
the most favored terrain, and that the flight vectors be consistent
with the picture thus engendered.

_The Work of Winkenwerder_

To date, none of the evidence in favor of the topographical hypothesis
completely fills these requirements. Winkenwerder (_loc. cit._), in
analyzing the results of telescopic counts of birds at Madison and
Beloit, Wisconsin, Detroit and Ann Arbor, Michigan, and at Lake
Forest, Illinois, between 1898 and 1900, plotted the number of birds
seen at fifteen-minute intervals as a function of the time of the
night. He believed that the high points in the resulting frequency
histograms represented intervals when the field of the telescope was
moving over certain topographically determined flight lanes, though he
did not specify in all cases just what he assumed the critical
physiographic features to be. Especially convincing to him were
results obtained at Beloit, where the telescope was situated on the
east bank of the Rock River, on the south side of the city.
Immediately below Beloit the river turns southwestward and continues
in this direction about five miles before turning again to flow in a
southeastward course for approximately another five miles. In this
setting, on two consecutive nights of observation in May, the number
of birds observed increased tremendously in the 2 to 3 A. M. interval,
when, according to Winkenwerder's interpretation of the data (he did
not make the original observations at Beloit himself), the telescope
was pointing directly down the course of the river. This conclusion is
weakened, however, by notable inconsistencies. Since the moon rises
later each evening, it could not have reached the same position over
the Rock River at the same time on both May 12-13 and May 13-14, and
therefore, if the peaks in the graph were really due to a greater
volume of migration along the watercourse, they should not have so
nearly coincided. As a matter of fact the incidence of the peak on
May 12-13 should have preceded that of the peak on May 13-14; whereas
his figure shows the reverse to have been true. Singularly enough,
Winkenwerder recognized this difficulty in his treatment of the data
from Madison, Wisconsin. Unable to correlate the peak period with the
Madison terrain by the approach used for Beloit, he plotted the
observations in terms of hours after moonrise instead of standard
time. This procedure was entirely correct; the moon does reach
approximately the same position at each hour after its rise on
successive nights. The surprising thing is that Winkenwerder did not
seem to realize the incompatibility of his two approaches or to
realize that he was simply choosing the method to suit the desired
results.

Furthermore, as shown in Part I of this paper, the number of birds
seen through the telescope often has only an indirect connection with
the actual number of birds passing over. My computations reveal that
the highest counts of birds at Beloit on May 12-13 were recorded when
the moon was at an altitude of only 8° to 15° and, that when
appropriate allowance is made for the immense size of the field of
observation at this time, the partially corrected flight density for
the period is not materially greater than at some other intervals in
the night when the telescope was not directed over the course of the
Rock River. These allowances do not take the direction factor into
consideration. Had the birds been flying at right angles to the short
axis of an elliptical section of the cone throughout the night, the
flight density in the period Winkenwerder considered the peak would
have been about twice as high as in any previous interval. On the
other hand, if they had been flying across the long axis at all times,
the supposed peak would be decidedly inferior to the flight density at
10 to 11:00 P. M., before the cone came near the river.

Admittedly, these considerations contain a tremendous element of
uncertainty. They are of value only because they expose the equal
uncertainty in Winkenwerder's basic evidence. Since the coördinates of
the birds' apparent pathways at Beloit were given, I at first
entertained the hope of computing the flight densities rigorously, by
the method herein employed. Unfortunately, Winkenwerder was apparently
dealing with telescopes that gave inverted images, and he used a
system for recording coördinates so ambiguously described that I am
not certain I have deciphered its true meaning. When, however, his
birds are plotted according to the instructions as he stated them, the
prevailing direction of flight indicated by the projection formula
falls close to west-northwest, not along the course of the Rock River,
but _at direct right angles to it_.

    [Illustration: FIG. 31. Directional components in the flight
       at Tampico on three nights in 1948. The lengths of the
       sector vectors are determined by their respective densities
       expressed as a percentage of the station density for that
       night; the vector resultants are plotted from them by
       standard procedure. Thus, the nightly diagrams are not on the
       same scale with respect to the actual number of birds involved.]


    [Illustration: FIG. 32. Hourly station density curve at
       Tampico, Tamaulipas, on the night of April 21-22, 1948 (CST).]

_Interpretation of Recent Data_

I am in a position to establish more exact correlations between flight
density and terrain features in the case of current sets of
observations. Some of these data seem at first glance to fit the idea
of narrow topographically-oriented flight lanes rather nicely. At
Tampico, where six excellent sets of observations were made in March
and April, 1948, the telescope was set up on the beach within a few
yards of the Gulf of Mexico. As can be seen from Figure 25 (_ante_),
the slant of the coastline at this point is definitely west of north,
as is also the general trend of the entire coast from southern
Veracruz to southern Tamaulipas (see Figure 34, beyond). The over-all
vector resultant of all bird flights at this station was N 11° W, and,
as will be seen from Figure 31, none of the nightly vector resultants
in April deviates more than one degree from this average. Thus the
prevailing direction of flight, as computed, agrees with the trend of
the coast at the precise point of the observations, at least to the
extent that both are west of north. To be sure, the individual sector
vectors indicate that not all birds were following this course;
indeed, some appear to have been flying east of north, heading for a
landfall in the region of Brownsville, Texas, and a very few to have
been traveling northeastward toward the central Gulf coast. But it
must be remembered that a certain amount of computational deviation
and of localized zigzagging in flight must be anticipated. Perhaps
none of these eastward vectors represents an actual extended flight
path. The nightly vector resultants, on the other hand, are so
consistent that they have the appearance of remarkable accuracy and
tempt one to draw close correlations with the terrain. When this is
done, it is found that, while the prevailing flight direction is 11°
west of north, the exact slant of the coastline at the location of the
station is about 30° west of north, a difference of around 19°. It
appears, therefore, that the birds were not following the shoreline
precisely but cutting a chord about ten miles long across an
indentation of the coast. If it be argued that the method of
calculation is not accurate enough to make a 19° difference
significant, and that most of the birds might have been traveling
along the beach after all, it can be pointed out with equal
justification that, if this be so, the 11° divergence from north does
not mean anything either and that perhaps the majority of the birds
were going due north. We are obliged to conclude either that the main
avenue of flight paralleled the disposition of the major topographical
features only in a general way or that the angle between the line of
the coast and true north is not great enough to warrant any inference
at all.

Consideration of the Tampico density curves leads to similarly
ambiguous results. On the night of April 21-22, as is evident from a
comparison of Figures 25 and 32, the highest flight density occurred
when the projection of the cone on the terrain was wholly included
within the beach. This is very nearly the case on the night of April
23-24 also, the positions of the cone during the peak period of
density being only about 16° apart. (On the intervening date, clouds
prevented continuous observation during the critical part of the
night.) These correlations would seem to be good evidence that most of
these night migrants were following the coastline of the Gulf of
Mexico. However, the problem is much more complicated. The estimated
point of maximum flight density fell at 10:45 P. M. on April 21-22
and 11:00 P. M. on April 23-24, both less than an hour from the peak
in the ideal time curve (Figure 26, _ante_). We cannot be sure,
therefore, that the increase in density coinciding with the position
of the moon over the beach is not an increase which would have
occurred anyway. Observations conducted several nights before or after
the second quarter, when the moon is not on or near its zenith at the
time of the predictable peak in the density curve, would be of
considerable value in the study of this particular problem.

The situation at Tampico has been dealt with at length because, among
all the locations for which data are available, it is the one that
most strongly supports the topographical hypothesis. In none of the
other cases have I been able to find a definite relation between the
direction of migration and the features of the terrain. Studies of
data from some of these stations disclose directional patterns that
vary from night to night only slightly more than does the flight at
Tampico. In three nights of observation at Lawrence, Kansas, marked by
very high densities, the directional trend was north by
north-northeast with a variation of less than 8°, yet Lawrence is so
situated that there seems to be no feature of the landscape locally or
in the whole of eastern Kansas or of western Missouri that coincides
with this heading. At Mansfield, Louisiana, in twelve nights of
observation, the strong east by northeast trend varied less than 15°,
but again there appears to be no correlation over a wide area between
this direction and any landmarks. And, at Progreso, Yucatán, where the
vector resultants were 21° and 27° on successive nights, most of the
birds seen had left the land and were beginning their flight northward
over the trackless waters of the Gulf of Mexico. Furthermore, as I
have elsewhere pointed out (1946: 205), the whole northern part of the
Yucatán Peninsula itself is a flat terrain, unmarked by rivers,
mountains, or any other strong physiographic features that conceivably
might be followed by birds.

    [Illustration: FIG. 33. The nightly net trend of migrations
       at three stations in 1948. Each arrow is the vector resultant
       for a particular night, its length expressing the nightly
       density as a percentage of the total station density for the
       nights represented. Thus, the various station diagrams are
       not to the same scale.]

In Figure 33 I have shown the directional patterns at certain stations
where, unlike the cases noted above, there is considerable change on
successive nights. Each vector shown is the vector resultant for one
particular night. The lengths of the vectors have been determined by
their respective percentages of the total computed density, or total
station magnitude, for all the nights in question. In other words, the
lengths of the individual vectors denote the percentile rôle that each
night played in the total density. From the directional spread at
these stations it becomes apparent that if most of the birds were
traveling along a certain topographic feature on one night, they
could not have been traveling along the same feature on other nights.

The possibility should be borne in mind, however, that there may be
more than one potential topographic feature for birds to follow at
some stations. Moreover, it is conceivable that certain species might
follow one feature that would lead them in the direction of their
ultimate goal, whereas other species, wishing to go in an entirely
different direction, might follow another feature that would lead them
toward their respective destination. It would seem unlikely, however,
that the species composition of the nocturnal flights would change
materially from night to night, although there is a strong likelihood
that it might do so from week to week and certainly from month to
month.

By amassing such data as records of flight direction along the same
coast from points where the local slant of the shoreline is materially
different, and comparisons of the volume of migration at night along
specialized routes favored during the day with the flight densities at
progressive distances from the critical terrain feature involved, we
shall eventually be able to decide definitely the rôle topography
plays in bird migration. We cannot say on the basis of the present
ambiguous evidence that it is not a factor in determining which way
birds fly, but, if I had to hazard a guess one way or the other, I
would be inclined to discount the likelihood of its proving a major
factor.


D. GEOGRAPHICAL FACTORS AND THE CONTINENTAL DENSITY PATTERN

A study of the total nightly or seasonal densities at the various
stations brings forth some extremely interesting factors, many of
which, however, cannot be fully interpreted at this time. A complete
picture of the magnitude of migration at a given station cannot be
obtained from the number of birds that pass the station on only a few
nights in one spring. Many years of study may be required before hard
and fast principles are justifiable. Nevertheless, certain salient
features stand out in the continental density pattern in the spring of
1948. (The general results are summarized in Tables 2-5; the location
of the stations is shown in Figure 34.) These features will be
discussed now on a geographical basis.

    TABLE 2.--Extent of Observations and Seasonal Station
                Densities at Major Stations in 1948

  ==========================================================================
                       |Nights of observation| Hours of observation|
  OBSERVATION STATION  |---------------------+---------------------|Season
                       |March|April|May|Total|March|April|May|Total|density
  ---------------------+-----+-----+---+-----+-----+-----+---+-----+--------
  CANADA               |     |     |   |     |     |     |   |     |
    Pt. Pelee          |     |     | 1 |  1  |     |     | 6 |   6 |   2,500
                       |     |     |   |     |     |     |   |     |
  MEXICO               |     |     |   |     |     |     |   |     |
    S. L. P.: Ebano    |  1  |     |   |  1  |  3  |     |   |   3 |   1,300
    Tamps.: Tampico    |  3  |  3  |   |  6  | 20  | 20  |   |  40 | 140,300
    Yuc.: Progreso     |     |  3  |   |  3  |     | 18  |   |  18 |  60,500
                       |     |     |   |     |     |     |   |     |
  UNITED STATES        |     |     |   |     |     |     |   |     |
    Fla.: Pensacola    |     |  2  | 2 |  4  |     |  8  | 7 |  15 |   1,500
      Winter Park      |     |  5  | 6 | 11  |     | 39  |38 |  77 |  21,700
    Ga.: Athens        |     |  2  |   |  2  |     | 10  |   |  10 |   4,000
      Thomasville      |     |  1  | 1 |  2  |     |  8  | 8 |  16 |   4,700
    Iowa: Ottumwa      |     |  5  | 5 | 10  |     | 16  |28 |  44 | 134,400
    Kans.: Lawrence    |  2  |  1  |   |  3  | 16  |  4  |   |  20 |  68,700
    Ky.: Louisville    |     |  3  | 2 |  5  |     | 20  |14 |  34 |  49,300
      Murray           |     |  2  |   |  2  |     | 13  |   |  13 |  26,200
    La.: Baton Rouge   |     |  3  |   |  3  |     | 15  |   |  15 |  11,000
      Lafayette        |     |  1  |   |  1  |     |  5  |   |   5 |   2,800
      Mansfield        |  1  |  5  | 4 | 10  |  2  | 16  |22 |  40 |  22,400
      New Orleans      |  1  |  1  |   |  2  |  5  |  2  |   |   7 |   1,900
      Oak Grove        |     |  2  | 2 |  4  |     | 16  |15 |  31 |  33,900
    Mich.: Albion      |     |  1  |   |  1  |     |  3  |   |   3 |   1,100
    Minn.: Hopkins     |     |     | 1 |  1  |     |     | 4 |   4 |   2,000
    Miss.: Rosedale    |     |  1  | 1 |  2  |     |  6  | 8 |  14 |  12,600
    Mo.: Columbia      |     |  2  | 1 |  3  |     |  8  | 6 |  14 |  13,100
    Liberty            |     |  1  | 1 |  2  |     |  7  | 7 |  14 |   4,800
    Okla.: Stillwater  |  1  |  2  | 1 |  4  |  5  | 11  | 3 |  19 |   8,400
    S. Car.: Charleston|  1  |  1  | 1 |  3  |  5  |  8  | 9 |  22 |   3,000
    Tenn.: Knoxville   |     |  2  | 2 |  4  |     | 18  |14 |  32 |  35,400
      Memphis          |  2  |  3  | 2 |  7  | 13  | 20  |12 |  45 |  29,700
    Tex.: College      |     |  3  | 1 |  4  |     | 19  | 8 |  27 |  32,200
      Station Rockport |     |  1  |   |  1  |     |  4  |   |   4 |   6,200
  --------------------------------------------------------------------------

    TABLE 3.--Average Hourly Station Densities in 1948

  ========================================================
  OBSERVATION STATION     | March | April |  May  | Season
  ------------------------+-------+-------+-------+-------
  CANADA                  |       |       |       |
    Pt. Pelee             |       |       |   400 |   400
                          |       |       |       |
  MEXICO                  |       |       |       |
    S. L. P.: Ebano       |   400 |       |       |   400
    Tamps.: Tampico       |   700 | 6,300 |       | 3,500
    Yuc.: Progreso        |       | 2,800 |       | 2,800
                          |       |       |       |
  UNITED STATES           |       |       |       |
    Fla.: Pensacola       |       |     0+|   200 |   100
      Winter Park         |       |   300 |   200 |   300
    Ga.: Athens           |       |   400 |       |   400
      Thomasville         |       |   500 |   100 |   300
    Iowa: Ottumwa         |       | 1,700 | 3,800 | 3,100
    Kans.: Lawrence       | 4,000 | 1,400 |       | 3,400
    Ky.: Louisville       |       | 2,000 |   700 | 1,500
      Murray              |       | 2,000 |       | 2,000
    La.: Baton Rouge      |       |   700 |       |   700
      Lafayette           |       |   600 |       |   600
      Mansfield           |     0 |   700 |   800 |   600
      New Orleans         |    60 |   800 |       |   300
      Oak Grove           |       | 1,400 |   800 | 1,100
    Mich.: Albion         |       |   400 |       |   400
    Minn.: Hopkins        |       |       |   500 |   500
    Miss.: Rosedale       |       | 1,100 |   700 |   900
    Mo.: Columbia         |       |   400 | 1,700 |   900
      Liberty             |       |   500 |   200 |   300
    Okla.: Stillwater     |   500 |   200 | 1,000 |   400
    S. Car.: Charleston   |   200 |   200 |     0+|   100
    Tenn.: Knoxville      |       | 1,300 |   800 | 1,100
      Memphis             |   300 |   800 |   900 |   700
    Tex.: College Station |       | 1,100 | 1,500 | 1,200
      Rockport            |       | 1,600 |       | 1,600
  --------------------------------------------------------

    TABLE 4.--Maximum Hourly Station Densities in 1948

  ======================================================
  OBSERVATION STATION     |  March  |  April  |   May
  ------------------------+---------+---------+---------
  CANADA                  |         |         |
    Pt. Pelee             |         |         |  1,400
                          |         |         |
  MEXICO                  |         |         |
    S. L. P.: Ebano       |    600  |         |
    Tamps.: Tampico       |  3,100  | 21,200  |
    Yuc.: Progreso        |         | 11,900  |
                          |         |         |
  UNITED STATES           |         |         |
    Fla.: Pensacola       |         |    100  |    700
      Winter Park         |         |  2,300  |  1,000
    Ga.: Athens           |         |    900  |
      Thomasville         |         |  1,500  |    200
    Iowa: Ottumwa         |         |  3,800  | 12,500
    Kans.: Lawrence       | 14,500  |  2,200  |
    Ky.: Louisville       |         |  5,000  |  1,400
      Murray              |         |  3,700  |
    La.: Baton Rouge      |         |  3,400  |
      Lafayette           |         |  1,800  |
      Mansfield           |         |  2,100  |  1,600
      New Orleans         |    200  |  1,100  |
      Oak Grove           |         |  2,700  |  2,500
    Mich.: Albion         |         |    700  |
    Minn.: Hopkins        |         |         |  1,100
    Miss.: Rosedale       |         |  2,200  |  1,400
    Mo.: Columbia         |         |    800  |  3,400
      Liberty             |         |    800  |    800
    Okla.: Stillwater     |    900  |    700  |  1,400
    S. Car.: Charleston   |    400  |    600  |    200
    Tenn.: Knoxville      |         |  5,800  |  1,900
      Memphis             |  1,200  |  3,400  |  2,100
    Tex.: College Station |         |  3,400  |  3,100
      Rockport            |         |  2,400  |
  ------------------------------------------------------

    TABLE 5.--Maximum Nightly Densities at Stations with More
                Than One Night of Observation

  ======================================================
  OBSERVATION STATION     |  March  |  April  |   May
  ------------------------+---------+---------+---------
                          |         |         |
  MEXICO                  |         |         |
    Tamps.: Tampico       |  5,500  | 63,600  |
    Yuc.: Progreso        |         | 31,600  |
                          |         |         |
  UNITED STATES           |         |         |
    Fla.: Winter Park     |         |  6,200  |
    Ga.: Athens           |         |  2,600  |
      Thomasville         |         |  3,900  |
    Iowa: Ottumwa         |         | 15,300  | 54,600
    Kans.: Lawrence       | 51,600  |  5,400  |
    Ky.: Louisville       |         | 17,000  |  8,400
      Murray              |         | 16,400  |
    La.: Baton Rouge      |         |  6,200  |
      Mansfield           |         |  4,900  |  5,200
      Oak Grove           |         | 13,600  |  5,800
    Miss.: Rosedale       |         |  6,800  |  5,800
    Mo.: Columbia         |         |  1,400  | 10,300
    Okla.: Stillwater     |  2,700  |  1,900  |  3,000
    Tenn.: Knoxville      |         | 15,200  |  9,000
      Memphis             |  3,600  |  7,900  |  7,000
    Tex.: College Station |         |  6,200  | 13,200
  ------------------------------------------------------

    [Illustration: FIG. 34. Stations at which telescopic
       observations were made in 1948.]

_Gulf Migration: A Review of the Problem_

In view of the controversy in recent years pertaining to migration
routes in the region of the Gulf of Mexico (Williams, 1945 and 1947;
Lowery, 1945 and 1946), the bearing of the new data on the problem is
of especial interest. While recent investigations have lent further
support to many of the ideas expressed in my previous papers on the
subject, they have suggested alternative explanations in the case of
others. In the three years that have elapsed since my last paper
dealing with Gulf migration, some confusion seems to have arisen
regarding the concepts therein set forth. Therefore, I shall briefly
re-state them.

It was my opinion that evidence then available proved conclusively
that birds traverse the Gulf frequently and intentionally; that the
same evidence suggested trans-Gulf flights of sufficient magnitude to
come within the meaning of migration; that great numbers of birds move
overland around the eastern and western edges of the Gulf; that it was
too early to say whether the coastal or trans-Gulf route was the more
important, but that enough birds cross the water from Yucatán to
account for transient migration in the extreme lower Mississippi
Valley; and, that, in fair weather, most trans-Gulf migrants continue
on inland for some distance before coming to land, creating an area of
"hiatus" that is usually devoid of transient species. I tried to make
it emphatically clear that I realized that many birds come into Texas
from Mexico overland, that I did not think the hordes of migrants
normally seen on the Texas coast in spring were by any means all
trans-Gulf migrants. I stated (1946: 206): "Proving that birds migrate
in numbers across the Gulf does not prove that others do not make the
journey by the coastal routes. But that is exactly the point. No one
has ever pretended that it does." Although some ornithologists seem to
have gained the impression that I endorse only the trans-Gulf route,
this is far from the truth. I have long held that the migrations
overland through eastern Mexico and southern Texas on one hand, and
the over-water flights on the other, are each part of the broad
movement of transients northward into the United States. There are
three avenues of approach by which birds making up the tremendous
concentrations on the Texas coast may have reached there: by a
continental pathway from a wintering ground in eastern and southern
Mexico; by the over-water route from Yucatán and points to the
southward; and, finally, by an overland route from Central America via
the western edge of the Gulf. As a result of Louisiana State
University's four-year study of the avifauna in eastern Mexico, I
know that migrants reach Texas from the first source. As a consequence
of my studies in Yucatán of nocturnal flight densities and their
directional trends, I strongly believe that migrants reach Texas from
this second source. As for the third source, I have never expressed an
opinion. I am not prepared to do so now, for the reason that today, as
three years ago, there is no dependable evidence on which to base a
judgment one way or another.

    TABLE 6.--Computed Hourly Densities at Tampico, Tamps.,
                in Spring of 1948

  =========================================================================
             |                    Average hour of observation
    DATE     |-----+------+-------+-------+------+------+------+------+----
             | 8:30| 9:30 | 10:30 | 11:30 |12:30 | 1:30 | 2:30 | 3:30 |4:30
  -----------|-----+------+-------+-------+------+------+------+------+----
  22-23 March|  600|  700 | 1,000 |   800 |  100 |  100 |    0 |  100 | ..
  23-24 March|    0|  400 | 1,200 | 3,100 |  800 |  ..  |  ..  |  ..  | ..
  24-25 March|  300|  700 |   800 | 1,600 |1,100 |  ..  |  ..  |  ..  | ..
  21-22 April|1,100|7,000 |14,900 |12,900 |8,100 |3,800 |3,500 |  200 | ..
  22-23 April|  700|2,900 | 7,500 |   ..  |  ..  |  ..  |  ..  |  ..  | ..
  23-24 April|  600|4,700 |19,100 |21,200 |5,500 |5,900 |4,000 |2,000 |200
  -------------------------------------------------------------------------


_Western Gulf Area_

Among the present flight density data bearing on the above issues, are
the six sets of observations from the vicinity of Tampico, Tamaulipas,
already referred to. These were secured in the spring of 1948 by a
telescope set up on the Gulf beach just north of the Miramar pavilion
and only a hundred feet from the surf (see Figure 25, _ante_). The
beach here is approximately 400 feet wide and is backed by
scrub-covered dunes, which rapidly give way toward the west to a
rather dense growth of low shrubs and trees. One might have expected
that station densities at Tampico in March would be rather high.
Actually, though they are the second highest recorded for the month,
they are not impressive and afford a striking contrast with the record
flights there in April (Table 6). Unfortunately, only a few stations
were operating in March and thus adequate comparisons are impossible;
but the indications are that, in March, migration activity on the
western edges of the Gulf is slight. It fails even to approach the
volume that may be observed elsewhere at the same time, as for
example, in eastern Kansas where, however, the migration is not
necessarily correlated with the migration in the lower Gulf area.
Strangely enough, on the night of March 22-23, at Tampico,
approximately 85 per cent of the birds were flying from north of an
east-west line to south of it, opposite to the normal trend of spring
migration. This phenomenon, inexplicable in the present instance, will
be discussed below. On the other two nights in March, the directional
trend at Tampico was northward with few or no aberrant components.
Observations made approximately thirty-five miles inland from the
Gulf, at Ebano, San Luis Potosí, on the night of March 25-26, show
lower station densities than the poorest night at Tampico, but since
they cover only a three-hour watch, they reveal little or nothing
concerning the breadth of the so-called coastal flyway.

April flight densities at Tampico are the highest recorded in the
course of this study. The maximum hourly density of 21,200 birds is 46
per cent higher than the maximum hourly density anywhere else. The
average hourly density of 6,300 in April is more than twice as great
as the next highest average for that month. These figures would seem
to satisfy certain hypotheses regarding a coastwise flight of birds
around the western edge of the Gulf. Other aspects of the observations
made at that time do not satisfy these hypotheses. Texas
ornithologists have found that in periods of heavy spring migration,
great numbers of birds are invariably precipitated by rainy weather.
On April 23, in the midst of the record-breaking telescopic studies at
Tampico, Mr. Robert J. Newman made a daytime census immediately
following four hours of rain. He made an intensive search of a small
area of brush and low growth back of the beach for traces of North
American migrants. In his best hour, only thirteen individual birds
out of seventy-five seen were of species that do not breed there. The
transient species were the Ruby-throated Hummingbird (1),
Scissor-tailed Flycatcher (1), Western Wood Pewee (1), Black-throated
Green Warbler (2) Orchard Oriole (7), and Baltimore Oriole (1), all of
which winter extensively in southern Mexico. Perhaps, however, the
apparent scarcity of transients on this occasion is not surprising in
the light of the analysis of flight density in terms of bird density
on the ground which I shall develop beyond. My only point here is to
demonstrate that rain along the coast does not always produce birds.

As large as the nocturnal flights at Tampico have so far proved to be,
they are not commensurate with the idea that nearly all birds follow a
narrow coastwise route around the Gulf. To establish the latter idea,
one must be prepared to show that the migrant species returning to the
United States pass along two flyways a few miles wide in the immense
volume necessary to account for their later abundance on a 1500-mile
front extending across eastern North America. One might expect at
least ten to twenty fold the number observable at any point in the
interior of the United States. In actuality, the highest nightly
density of 63,600 birds at Tampico is barely sufficient to account for
the highest nightly density of 54,600 at Ottumwa, Iowa, alone.

Of course, there is no way of knowing how closely a ratio of anywhere
from ten to one through twenty to one, employed in this comparison,
expresses the true situation. It may be too high. It could be too low,
particularly considering that preliminary studies of flight density in
Florida indicate that the western shores of the Gulf of Mexico must
carry the major part of the traffic if migratory flights back to the
United States in spring take place only along coastwise routes.
Consideration of the data obtained in Florida in 1948 will serve to
emphasize the point.

_Eastern Gulf Area_

At Winter Park, Florida, seventy-seven hours were spent at the
telescope in April and May. This was 71 per cent more hours of actual
observation than at the next highest station. Nevertheless, the total
seasonal density amounted to only 21,700 birds. The average hourly
density was only 300 birds, with the maximum for any one hour being
2,300 birds. In contrast, forty-five hours of observation at Tampico,
Tamaulipas, in March and April, yielded a total station density of
140,300 birds. At the latter place, on the night of April 23-24,
almost as many birds passed _in a single hour_ as passed Winter Park
in all of its seventy-seven hours of observation.

Should future telescopic studies at Florida stations fail to produce
densities appreciably higher than did Winter Park in 1948, the
currently-held ideas that the Florida Peninsula is a major flyway will
be seriously shaken. But one consideration must be kept in mind
regarding the present picture. No observations were made at Winter
Park in March, when it is conceivable that densities may have been
materially higher. We know, for instance, that many of the early
migrants to the southern United States are species whose winter homes
are in the West Indies. Numbers of Vireonidae and Parulidae (notably
the genera _Vireo_, _Parula_, _Protonotaria_, _Mniotilta_, _Seiurus_,
_Geothlypis_, _Setophaga_, and certain _Dendroica_ and _Vermivora_)
winter extensively in this region and are among the first birds to
return to the southern states in the spring. Many of them often reach
Louisiana and other states on the Gulf coastal plain by mid-March. In
the same connection, it may be mentioned that many of the outstanding
instances of birds striking lighthouses in southern Florida occurred
in March and early April (Howell, 1932).

_Yucatán Area_

I have long felt that the answers to many of the questions which beset
us in our study of Gulf migration are to be found on the open waters
of the Gulf of Mexico itself or on the northern tip of the Yucatán
Peninsula. Accordingly, in the spring of 1945 I crossed the Gulf by
slow freighter for the purpose of determining how many and what kinds
of birds might be seen between the mouth of the Mississippi River and
the Yucatán Peninsula in fair weather, when it could not be argued
that the birds had been blown there by inclement weather. To my own
observations I was able to add those of other ornithologists who
likewise had been aboard ship in the Gulf.

The summary of results proved that birds of many species cross the
Gulf and do so frequently. It failed to demonstrate beyond all doubt
that they do so in large numbers. Nor had I expected it to do so. The
consensus of Gulf coast ornithologists seemed to be that transient
migration in their respective regions is often performed at too high
an elevation to be detected unless the birds are forced to earth by
bad weather. I saw no reason to anticipate that the results would be
otherwise over the waters of the Gulf of Mexico.

The application of the telescopic method held promise of supplying
definite data on the numbers of trans-Gulf migrants, however high
their flight levels. The roll and vibration of the ship had prevented
me in 1945 from making telescopic observations at sea. Since no
immediate solution to the technical difficulties involved presented
itself, I undertook to reach one of the small cays in Alacrán Reef,
lying seventy-five miles north of Yucatán and in line with the coast
of southern Louisiana. Because of transportation difficulties, my
plans to place a telescopic station in this strategic location failed.
Consequently, I returned in 1948 by freighter to Progreso, Yucatán,
where telescopic counts were made for three nights, one of which was
rendered almost valueless by the cloud cover.

    [Illustration: FIG. 35. Positions of the cone of
       observation at Progreso, Yucatán, on the night of April
       23-24, 1948, from 8:53 P. M. to 3:53 A. M. Essential
       features of this map are drawn to scale. The telescope was
       set up on the end of a one-mile long wharf that extends
       northward from the shore over the waters of the Gulf of
       Mexico. The triangular (white) lines represent the
       projections of the cone of visibility on the earth at the
       mid-point of each hour of observation. Only briefly, in the
       first two hours, did the cone lie even in part over the
       adjacent mainland. Hence, nearly all of the birds seen in the
       course of the night had actually left the land behind.]

The observation station at Progreso was situated on the northern
end of the new wharf which projects northward from the beach to
a point one mile over the Gulf. As will be seen from Figure 35, the
entire cone of observation lay at nearly all times over the intervening
water between the telescope on the end of the wharf and the
beach. Therefore, nearly all of the birds seen were actually observed
leaving the coast and passing out over the open waters of the
Gulf. The hourly station densities are shown in Table 7 and Figures
24 and 36. In the seventeen hours of observation on the nights of
April 23-24 and April 24-25, a total computed density of 59,200 birds
passed within one-half mile of each side of Progreso. This is the
third highest density recorded in the course of this study. The
maximum for one hour was a computed density of 11,900 birds. This
is the fourth highest hourly density recorded in 1948.

    [Illustration: FIG. 36. Hourly station density curve for
       night of April 23-24, 1948, at Progreso, Yucatán.]

    TABLE 7.--Computed Hourly Densities at Progreso, Yuc.,
                in Spring of 1948

  ===========+============================================================
             |               Average hour of observation
     DATE    +-----+------+------+-------+------+------+------+-----+-----
             |8:30 | 9:30 |10:30 | 11:30 |12:30 | 1:30 | 2:30 |3:30 |4:30
  -----------+-----+------+------+-------+------+------+------+-----+-----
  23-24 April| 400 |3,000 |5,100 |10,000 |9,000 |2,800 |  900 | 400 |....
  24-25 April|   0 |  500 |3,700 |11,900 |7,900 |1,900 |1,100 | 400 | 200
  -----------+-----+------+------+-------+------+------+------+-----+-----


It is not my contention that this many birds leave the northern coast
of Yucatán every night in spring. Indeed, further studies may show
negligible flight densities on some nights and even greater densities
on others. As a matter of fact several hours of observation on the
night of April 25-26, at Mérida, Yucatán, approximately twenty-five
miles inland from Progreso, indicated that on this night the density
overhead was notably low, a condition possibly accounted for by a
north wind of 10 mph blowing at 2,000 feet. I merely submit that on
the nights of April 23-24 and 24-25, birds were leaving the coast of
Yucatán _at Progreso_ at the rate indicated. But, as I have emphasized
in this paper and elsewhere (1946: 205-206), the northern part of the
Yucatán Peninsula is notably unmarked by streams or any other
physiographic features which birds might follow. The uniformity of the
topography for many miles on either side of Progreso, if not indeed
for the entire breadth of the Peninsula, makes it probable that
Progreso is not a particularly favored spot for observing migration,
and that it is not the only point along the northern coast of Yucatán
where high flight densities can be recorded. This probability must be
considered when comparisons are made between Progreso densities and
those at Tampico. The argument could be advanced that the present
densities from Tampico do not sufficiently exceed those at Progreso to
establish the coastal route as the main avenue of traffic in spring,
since there is every reason to suspect topography of exerting some
influence to produce a channeling effect in eastern Mexico. Here the
coast parallels the directional trend of the migratory movement for
more than 600 miles. Likewise the Sierra Madre Oriental of eastern
Mexico, situated approximately 100 miles inland (sometimes less), lies
roughly parallel to the coast. Because of the slant of the Mexican
land mass, many winter residents in southern Mexico, by short
northward movements, would sooner or later filter into the coastal
plain. Once birds are shunted into this lowland area, it would seem
unlikely that they would again ascend to the top of the Sierra Madre
to the west. In this way the great north-south cordillera of mountains
may act as a western barrier to the horizontal dispersion of
transients bound for eastern North America. Similarly, the Gulf itself
may serve as an eastern barrier; for, as long as migrants may progress
northward in the seasonal direction of migration and still remain over
land, I believe they would do so.

To put the matter in a slightly different way, the idea of a very
narrow flight lane is inherent in the idea of coastwise migration.
For, as soon as we begin to visualize flights of great volume over
fronts extending back more than fifty miles from the shore line, we
are approaching, if indeed we have not already passed, the point where
the phenomenon is no longer coastwise in essence, but merely overland
(as indeed my own unprocessed, telescopic data for 1949 indicate may
be the case). In actuality, those who have reported on the migration
along the western edge of the Gulf of Mexico have never estimated the
width of the main flight at more than fifty miles and have intimated
that under some circumstances it may be as narrow as two miles. No
evidence of such restrictions can be discerned in the case of the
trans-Gulf flights. If it cannot be said that they may be assumed to
be as wide as the Gulf itself, they at least have the potential
breadth of the whole 260-mile northern coast of the Yucatán Peninsula.
On these premises, to be merely equal in total magnitude, the
coastwise flights must exhibit, depending on the particular situation,
from five to 130 times the concentrations observable among trans-Gulf
migrants. This point seems almost too elementary to mention, but I
have yet to find anyone who, in comparing the two situations, takes it
into consideration.

Judged in this light, the average hourly density of 2,800 birds at
Progreso in April would appear to be indicative of many more migrants
on the entire potential front than the 6,300 birds representing the
average hourly density for the same month at Tampico.

That the Progreso birds were actually beginning a trans-Gulf flight
seems inevitable. The Yucatán Peninsula projects 200 miles or more
northward into the vast open expanses of the Gulf of Mexico and the
Caribbean Sea, with wide stretches of water on either side. The great
majority of the birds were observed _after_ they had proceeded beyond
the northern edge of this land mass. Had they later veered either to
the east or the west, they would have been obliged to travel several
hundred miles before again reaching land, almost as far as the
distance straight across the Gulf. Had they turned southward, some
individuals should have been detected flying in that direction. As can
be seen from Figures 23, 42, and 44, not one bird observed was heading
south of east or south of west on either night. No other single piece
of evidence so conclusively demonstrates that birds cross the Gulf of
Mexico in spring in considerable numbers as do flight density data
recorded from Progreso in 1948.

_Northern Gulf Area_

Unfortunately only a few data on flight density are available from
critical localities on the northern shores of the Gulf in spring. As
the density curves in Figure 30 demonstrate, several sets of
observation, including some phenomenal flights, have been recorded at
Baton Rouge. This locality, however, lies sixty-four miles from the
closest point on the Gulf coast, and the point due southward on the
coast is eighty-four miles distant. Since all of the birds seen at
Baton Rouge on any one night may have come from the heavily forested
area between Baton Rouge and the coast of the Gulf, we cannot use data
from Baton Rouge as certainly representative of incoming trans-Gulf
flights. Data from repeated observations at stations on the coast
itself are needed to judge the degree of trans-Gulf migration
northward. On the few nights of observation at such localities
(Cameron and Grand Isle, Louisiana, and Pensacola, Florida), flight
densities have been zero or negligible. To be sure, negative results
have been obtained at stations in the interior of the United States,
and flights of low density have been recorded on occasion at stations
where the flight densities are otherwise high. Nevertheless, in view
of the volume of migration departing from Progreso, Yucatán, it would
appear, upon first consideration, that we should at times record on
the coast of Louisiana enough birds arriving in a night of continuous
observation to yield a high density figure.

Upon further consideration, however, there are factors mitigating
against heavy densities of birds in northern flight on the northern
coast of the Gulf. In the first place, presuming the main trans-Gulf
flight to originate from northern Yucatán, and that there is a
directional fanning to the northward, the birds leave on a 260-mile
front, and arrive on a front 400 miles or more wide. Consequently,
other factors remaining the same, there would be only approximately
half the number of birds on the coast of arrival, at a given time and
place, as there was on the coast of departure. Secondly, we may now
presume on the basis of the telescopic studies at Progreso, that most
migrants leaving northern Yucatán do so in the few hours centering
about midnight. The varying speeds of the birds making the 580-mile
flight across the Gulf distribute them still more sparsely on the
north coast of the Gulf both in time and in space. Also we can see
only that segment of the flight, which arrives in that part of a
twenty-four hour period when the moon is up. This circumstance further
reduces the interceptive potential because the hours after dark, to
which the present telescopic studies have been restricted, comprise
the period in which the fewest migrants arrive from over the water. To
illustrate: it is a mathematical certainty that _none_ of the birds
leaving Yucatán in the hours of heaviest flight, before 12 P. M.,
and flying on a straight course at a speed of approximately 33 mph
will reach the northern Gulf coast after nightfall; they arrive in the
daytime. It will be useful to devise a technique for employing the sun
as a background for telescopic observation of birds, thereby making
observations possible on a twenty-four hour basis, so as to test these
inferences by objective data.

When a whole night's observation (1949 data not yet processed) at Port
Aransas, on the southern coast of Texas, on the great overland route
from eastern Mexico, yields in one night in April only seven birds,
the recording of no birds at a station near the mouth of the
Mississippi River becomes less significant.

As I have previously remarked in this paper, the new data obtained
since 1946, when I last wrote on the subject of migration in the
region of Gulf of Mexico, requires that I alter materially some of my
previously held views. As more and more facts come to light, I may be
compelled to alter them still further. For one thing, I have come to
doubt seriously the rigidity of the coastal hiatus as I envisioned it
in 1945. I believe instead that the scarcity of records of transient
migrants on the Gulf coastal plain in fair weather is to a very large
extent the result of a wide dispersion of birds in the dense cover
that characterizes this general region. I now question if appreciable
bird densities on the ground ever materialize anywhere except when the
sparseness of suitable habitat for resting or feeding tends to
concentrate birds in one place, or when certain meteorological
conditions erect a barrier in the path of an oncoming migratory
flight, precipitating many birds in one place.

This retrenchment of ideas is a direct consequence of the present
study, for time and again, as discussed in the case of Tampico
densities, maximal nightly flights have failed to produce a visible
abundance of transients on land the following day. A simple example
may serve to illustrate why. The highest one-hour density recorded in
the course of this study is 21,200 birds. That means that this many
birds crossed a line one mile long on the earth's surface and at right
angles to the direction of flight. Let us further assume that the
average flight speed of all birds comprising this flight was 30 mph.
Had the entire flight descended simultaneously, it would have been
dispersed over an area one mile wide and thirty miles long, and the
precipitated density on the ground would have been only 1.1 birds per
acre. Moreover, if as many as ten species had been involved in the
flight, this would have meant an average per species of less than one
bird per nine acres. This would have failed, of course, to show
appreciable concentrations to the observer in the field the following
day. If, however, on the other hand, the same flight of 21,200 birds
had encountered at one point a weather barrier, such as a cold-front
storm, all 21,200 birds might have been precipitated in one place and
the field observer would have recorded an "inundation of migrants."
This would be especially true if the locality were one with a high
percentage of open fields or prairies and if the flight were mainly of
woodland dwelling species, or conversely, if the locality were densely
forested with few open situations and the flight consisted mainly of
open-country birds. As explained on page 389, the density formula may
be too conservative in its expression of actual bird densities. Even
if the densities computed for birds in the air are only half as high
as the actual densities in the air, the corresponding ground density
of 2.2 birds per acre that results if all the birds descended
simultaneously would hardly be any more impressive than the 1.1 bird
per acre.

This consideration is doubtless highly modified by local
circumstances, but, in general, it seems to suggest a working
hypothesis that provides an explanation for many of the facts that we
now have. For example, on the coast of Texas there are great expanses
of terrain unattractive to such birds as warblers, vireos, tanagers,
and thrushes. The precipitation there by bad weather of even a
mediocre nightly flight composed of birds of the kinds mentioned would
surely produce an overwhelming concentration of birds in the scattered
woods and shrubs.

In spite of all that has been written about the great concentrations
of transient migrants on the coast of Texas in spring, I am not convinced
that they are of a different order of magnitude than those concentrations
that sometimes occur along the cheniers and coastal islands
of Louisiana and Mississippi. I have read over and over the
highly informative accounts of Professor Williams (_loci cit._) and the
seasonal summaries by Davis (1936-1940) and Williams (1941-1945).
I have conversed at length with Mrs. Jack Hagar, whom I
regard as one of the leading authorities on the bird life of the
Texas coast, and she has even permitted me access to her voluminous
records covering a period of fifteen years residence at Rockport.
Finally, I have spent a limited amount of time myself on the Texas
coast studying first-hand the situation that obtains there in order
that I might be in a position to compare it with what I have learned
from observations elsewhere in the region of the Gulf of Mexico,
Louisiana, Florida, Yucatán, and eastern Mexico.

Although the concentrations of birds on some days near the mouth of
the Mississippi River are almost incalculable, the fact remains that
in Texas the densities of transient species on the ground are more
consistently high from day to day. The reason for this may be simple.
As birds move up daily from Mexico overland, a certain percentage
would be destined to come down at all points along the route but so
dispersed in the inland forest that they might pass unnoticed.
However, that part of the same flight settling down in coastal areas,
where trees are scarce, would produce visible concentrations of
woodland species. With the advent of a cold-front storm, two
diametrically opposite effects of the same meteorological phenomenon
would tend to pile up great concentrations of migrants of two
classes--the overland and the trans-Gulf flights. During the
prepolar-front weather the strong southerly (from the south) and
southeasterly winds would tend to displace much of the trans-Gulf
segment to the western part of the Gulf. With the shift of the winds
to the north and northwest, which always occurs as the front passes,
the overland flight still in the air would tend to be banked up
against the coast, and the incoming trans-Gulf flight would be
confronted with a barrier, resulting in the precipitation of birds on
the first available land.

These postulated conditions are duplicated in part in autumn along the
Atlantic coast of the eastern United States. There, as a result of the
excellent work of Allen and Peterson (1936) and Stone (1937), a
similar effect has been demonstrated when northwest winds shove the
south-bound flights up against the coast of New Jersey and concentrate
large aggregations of migrants there.

_Interior of the United States_

Attention has been drawn already to the nature of the nightly flights
at stations immediately inland from the Gulf coast, where densities
decline abruptly well before midnight. I have suggested that this
early drop-off is mainly a result of the small amount of terrain south
of these stations from which birds may be contributed to a night's
flight. At Oak Grove, Louisiana, the flight exhibited a strong
directional trend with no significant aberrant components. Therefore,
one may infer that a considerable part of the flight was derived from
regions to the south of the station.

At Mansfield, Louisiana, thirty-eight hours of observation in April
and May resulted in flight densities that are surprisingly low--much
lower, in fact, than at Oak Grove. In eleven of the hours of
observation no birds at all were seen. A possible explanation for
these low densities lies in the fact that eastern Texas and western
Louisiana, where, probably, the Mansfield flights originated, is not
an especially attractive region to migrants because of the great
amount of deforested and second growth pine land. Oak Grove, in
contrast, is in the great Tensas-Mississippi River flood plain,
characterized by an almost solid stand of deciduous forest extending
over thousands of square miles in the lower Mississippi valley.

    [Illustration: FIG. 37. Sector density representation on
       two nights at Rosedale, Mississippi, in 1948. The white lines
       are the vector resultants.]

In further contrast to the considerable flight densities and
pronounced directional trend at Oak Grove, we have the results from
Rosedale, Mississippi, only seventy miles to the north and slightly to
the east. At Rosedale the densities were mediocre and the flight
directions were extremely divergent. Many of the nights of observation
at this locality were seriously interrupted by clouds, but such counts
as were made on those dates indicated little migration taking place.
On two nights, however, April 21-22 and May 20-21, visibility was
almost continuous and densities were moderately high. In Figure 37 I
have shown the flight directions for these two nights. The lengths of
the individual sector vectors are plotted as a percentage of the total
station density for each of the two nights (5,800 and 6,800 birds,
respectively). Although the vector resultants show a net movement of
birds to the northeast, there are important divergent components of
the flights. This "round-the-compass" pattern is characteristic of
stations on the edge of meteorological disturbances, as was Rosedale
on April 21-22, but not on the night of May 20-21. If bats are
presumed to have played a rôle in these latter observations, their
random flights would tend to cancel out and the vector resultant
would emerge as a graphic representation of the actual net trend
density of the birds and its prevailing direction of flow. Although I
do not believe that bats are the real reason for the diverse
directional patterns at Rosedale, I can offer no alternative
explanation consistent with data from other stations.

Moving northward in the valley of the Mississippi and its tributaries,
we find a number of stations that yielded significantly high densities
on most nights when weather conditions were favorable for migration.
Louisville and Murray, Kentucky, and Knoxville, Tennessee, each show
several nights with many birds flying, but only Lawrence, Kansas, and
Ottumwa, Iowa, had migrations that approach in magnitude the record
station densities at Tampico. Indeed, these were the only two stations
in the United States that produced flights exceeding the densities at
Progreso, Yucatán. The densities at Lawrence are unique in one
respect, in that they were extremely high in the month of March. Since
there were very few stations in operation then, these high densities
would be of little significance were it not for the fact that at no
time in the course of this study from 1945 to the present have
comparable densities been obtained this early in the migration period.
Examination of the "Remarks" section of the original data sheets from
Lawrence show frequent mention of "duck-like" birds passing before the
moon. We may infer from these notations that a considerable part of
the overhead flight was composed of ducks and other aquatic birds that
normally leave the southern United States before the main body of
transient species reach there. The heavy flight densities at Lawrence
may likewise have contained certain Fringillidae, Motacillidae,
Sylviidae, and other passerine birds that winter mainly in the
southern United States and which are known to begin their return
northward in March or even earlier. Observations in 1948 at Lawrence
in April were hindered by clouds, and in May no studies were
attempted. However, we do have at hand two excellent sets of data
recorded at Lawrence on the nights of May 3-4 and May 5-6, 1947, when
the density was also extremely high.

At Ottumwa, Iowa, where a splendid cooperative effort on the part of
the local ornithologists resulted in forty-four hours of observation
in April and May, densities were near the maximum for all stations.
Considering this fact along with results at Lawrence and other
mid-western stations where cloud cover did not interfere at the
critical periods of observation, we have here evidence supporting the
generally held thesis that eastern Kansas, Missouri, and Iowa lie on a
principal migratory flyway. Stations in Minnesota, Illinois,
Michigan, Massachusetts, and Ontario were either operated for only
parts of one or two nights, or else clouds seriously interfered with
observations, resulting in discontinuous counts. It may be hoped that
future studies will include an adequate representation of stations in
these states and that observations will be extensive enough to permit
conclusions regarding the density and direction of migration.

Charleston, South Carolina, which does not conveniently fall in any of
the geographic regions so far discussed, had, to me, a surprisingly
low flight density; twenty-two hours of observation there in March,
April, and May yielded a total flight density of only 3,000 birds.
This is less, for example, than the number of birds computed to have
passed Lawrence, Kansas, in one hour, or to have passed Progreso,
Yucatán, in one twenty-minute interval! Possibly observations at
Charleston merely chanced to fall on nights of inexplicably low
densities; further observations will be required to clear up this
uncertainty.


E. MIGRATION AND METEOROLOGICAL CONDITIONS

The belief that winds affect the migration of birds is an old one. The
extent to which winds do so, and the precise manner in which they
operate, have not until rather recently been the subject of real
investigation. With modern advances in aerodynamics and the
development of the pressure-pattern system of flying in aviation,
attention of ornithologists has been directed anew to the part that
air currents may play in the normal migrations of birds. In America, a
brief article by Bagg (1948), correlating the observed abundance of
migrants in New England with the pressure pattern obtaining at the
time, has been supplemented by the unpublished work of Winnifred
Smith. Also Landsberg (1948) has pointed out the close correspondence
between the routes of certain long-distance migrants and prevailing
wind trajectories. All of this is basis for the hypothesis that most
birds travel along definite air currents, riding with the wind. Since
the flow of the air moves clockwise around a high pressure area and
counterclockwise around a low pressure area, the birds are directed
away from the "high" and toward the center of the "low." The arrival
of birds in a particular area can be predicted from a study of the
surrounding meteorological conditions, and the evidence in support of
the hypothesis rests mainly upon the success of these predictions in
terms of observations in the field.

From some points of view, this hypothesis is an attractive one. It
explains how long distances involved in many migrations may be
accomplished with a minimum of effort. But the ways in which winds
affect migration need analysis on a broader scale than can be made
from purely local vantage points. Studies of the problem must be
implemented by data accumulated from a study of the process in action,
not merely from evidence inferred from the visible results that follow
it. Although several hundred stations operating simultaneously would
surely yield more definite results, the telescopic observations in
1948 offer a splendid opportunity to test the theory on a continental
scale.

The approach employed has been to plot on maps sector vectors and
vector resultants that express the directional trends of migration in
the eastern United States and the Gulf region, and to compare the data
on these maps with data supplied by the U. S. Weather Bureau regarding
the directions and velocities of the winds, the location of high and
low pressure areas, the movement of cold and warm fronts, and the
disposition of isobars or lines of equal pressure. It should be borne
in mind when interpreting these vectors that they are intended to
represent the directions of flight only at the proximal ends, or
junction points, of the arrows. The tendency of the eye to follow a
vector to its distal extremity should not be allowed to create the
misapprehension that the actual flight is supposed to have continued
on in a straight line to the map location occupied by the arrowhead.

A fundamental difficulty in the pressure-pattern theory of migration
has no doubt already suggested itself to the reader. The difficulty to
which I refer is made clear by asking two questions. How can the birds
ever get where they are going if they are dependent upon the whim of
the winds? How can pressure-pattern flying be reconciled with the
precision birds are supposed to show in returning year after year to
the same nesting area? The answer is, in part, that, if the wind is a
major controlling influence on the routes birds follow, there must be
a rather stable pattern of air currents prevailing from year to year.
Such a situation does in fact exist. There are maps showing wind roses
at 750 and 1,500 meters above mean sea level during April and May
(Stevens, 1933, figs. 13-14, 17-18). Similarly, the "Airway
Meteorological Atlas for the United States" (Anonymous, 1941) gives
surface wind roses for April (Chart 6) and upper wind roses at 500 and
1,000 meters above mean sea level for the combined months of March,
April, and May (Charts 81 and 82). The same publication shows wind
resultants at 500 and 1,000 meters above mean sea level (Charts 108
and 109). Further information permitting a description in general
terms of conditions prevailing in April and May is found in the
"Monthly Weather Review" covering these months (_cf._ Anonymous,
1948 _a_, Charts 6 and 8; 1948 _b_, Charts 6 and 8).

    [Illustration: FIG. 38. Over-all sector vectors at major
       stations in the spring 1948. See text for explanation of
       system used in determining the length of vectors. For
       identification of stations, see Figure 34.]

    [Illustration: FIG. 39. Over-all net trend of flight
       directions at stations shown in Figure 38. The arrows
       indicate direction only and their slants were obtained by
       vector analysis of the over-all sector densities.]

First, however, it is helpful as a starting point to consider the
over-all picture created by the flight trends computed from this
study. In Figure 38, the individual sector vectors are mapped for the
season for all stations with sufficient data. The length of each
sector vector is determined as follows: the over-all seasonal density
for the station is regarded as 100 percent, and the total for the
season of the densities in each individual sector is then expressed as
a percentage. The results show the directional spread at each station.
In Figure 39, the direction of the over-all vector resultant, obtained
from the sector vectors on the preceding map, is plotted to show the
net trend at each station.

As is evident from the latter figure, the direction of the net trend
at Progreso, Yucatán, is decidedly west of north (N 26° W). At Tampico
this trend is west of north (N 11° W), but not nearly so much so as at
Progreso. In Texas, Louisiana, Georgia, Tennessee, and Kentucky, it is
decidedly east of north. In the upper Mississippi Valley and in the
eastern part of the Great Plains, the flow appears to be northward or
slightly west of north. At Winter Park, Florida, migration follows in
general the slant of the Florida Peninsula, but, the meager data from
Thomasville, Georgia, do not indicate a continuation of this trend.

It might appear, on the basis of the foregoing data, that birds
migrate along or parallel to the southeast-northwest extension of the
land masses of Central America and southern Mexico. This would carry
many of them west of the meridian of their ultimate goal, obliging
them to turn back eastward along the lines of net trend in the Gulf
states and beyond. This curved trajectory is undoubtedly one of the
factors--but certainly not the only factor--contributing to the effect
known as the "coastal hiatus." The question arises as to whether this
northwestward trend in the southern part of the hemisphere is a
consequence of birds following the land masses or whether instead it
is the result of some other natural cause such as a response to
prevailing winds. I am inclined to the opinion that both factors are
important. Facts pertinent to this opinion are given below.

In April and May a high pressure area prevails over the region of the
Gulf of Mexico. As the season progresses, fewer and fewer cold-front
storms reach the Gulf area, and as a result the high pressure area
over the Gulf is more stable. Since the winds move clockwise around a
"high," this gives a general northwesterly trajectory to the air
currents in the vicinity of the Yucatán Peninsula. In the western area
of the Gulf, the movement of the air mass is in general only slightly
west of north, but in the central Gulf states and lower Mississippi
Valley the trend is on the average northeasterly. In the eastern part
of the Great Plains, however, the average circulation veers again
slightly west of north. The over-all vector resultants of bird
migration at stations in 1948, as mapped in Figure 39, correspond
closely to this general pattern.

Meteorological data are available for drawing a visual comparison
between the weather pattern and the fight pattern on individual
nights. I have plotted the directional results of four nights of
observation on the Daily Weather Maps for those dates, showing surface
conditions (Figures 40, 42, 44 and 46). Each sector vector is drawn in
proportion to its percentage of the corresponding nightly station
density; hence the vectors at each station are on an independent
scale. The vector resultants, distinguished by the large arrowheads,
are all assigned the same length, but the nightly and average hourly
station densities are tabulated in the legends under each figure. For
each map showing the directions of flight, there is on the facing page
another map showing the directions of winds aloft at 2,000 and 4,000
feet above mean sea level on the same date (see Figures 41-47). The
maps of the wind direction show also the velocities.

Unfortunately, since there is no way of analyzing the sector trends in
terms of the elevations of the birds involved, we have no certain way
of deciding whether to compare a given trend with the winds at 2,000,
1,000, or 0 feet. Nor do we know exactly what wind corresponds to the
average or median flight level, which would otherwise be a good
altitude at which to study the net trend or vector resultant.
Furthermore, the Daily Weather Map illustrates conditions that
obtained at 12:30 A. M. (CST); the winds aloft are based on
observations made at 10:00 P. M. (CST); and the data on birds covers
in most cases the better part of the whole night. Add to all this the
fact that the flight vectors, their resultants, and the wind
representations themselves are all approximations, and it becomes
apparent that only the roughest sort of correlations are to be
expected.

However, as will be seen from a study of the accompanying maps
(Figures 40-47), the shifts in wind direction from the surface up to
4,000 feet above sea level are not pronounced in most of the
instances at issue, and such variations as do occur are usually in a
clockwise direction. All in all, except for regions where frontal
activity is occurring, the weather maps give a workable approximation
to the average meteorological conditions on a given night.

The maps (Figures 40-47) permit, first, study of the number of
instances in which the main trend of flight, as shown by the vector
resultant, parallels the direction of wind at a reasonable potential
mean flight elevation, and, second, comparison of the larger
individual sector vectors and the wind currents at any elevation below
the tenable flight ceiling--one mile.

On the whole, inspection of the trend of bird-flight and wind
direction on specific nights supports the principle that the flow of
migration is in general coincident with the flow of air. It might be
argued that when the flow of air is toward the north, and when birds
in spring are proceeding normally in that direction, no significance
can be attached to the agreement of the two trends. However, the same
coincidence of wind directions and bird flights seems to be maintained
when the wind currents deviate markedly from a northward trajectory.
Figures 46 and 47, particularly in regard to the unusual slants of the
flight vectors at Ottumwa, Knoxville, and Memphis, illustrate that
this coincidence holds even when the wind is proceeding obliquely
eastward or westward. On the night of May 22-23, when a high pressure
area prevailed from southern Iowa to the Atlantic coast, and the
trajectory of the winds was northward, migration activity at Knoxville
and Ottumwa was greatly increased and the flow of birds was again
northward in the normal seasonal direction of migration.

Further study of the data shows fairly conclusively that maximum
migration activity occurs in the regions of high barometric pressure
and that the volume of migration is either low or negligible in
regions of low pressure. The passage of a cold-front storm may almost
halt migration in spring. This was demonstrated first to me by the
telescopic method at Baton Rouge, on April 12, 1946, following a
strong cold front that pushed southeastward across the Gulf coastal
plain and over the eastern Gulf of Mexico. The winds, as usual,
shifted and became strong northerly. On this night, following the
shift of the wind, only three birds were seen in seven hours of
continuous observation. Three nights later, however, on April 15, when
the warm air of the Gulf was again flowing from the south, I saw 104
birds through the telescope in two hours. Apropos of this
consideration in the 1948 data are the nights of May 21-22 and 22-23.

    [Illustration: FIG. 40. Comparison of flight trends and
       surface weather conditions on April 22-23, 1948. The
       meteorological data were taken from the U. S. Weather Bureau
       Daily Weather Map for 12:30 A. M. (CST) on April 23. The
       nightly station densities and the average hourly station
       density (shown in parentheses) are as follows:

          5. Louisville: 9,100 (1,100)
          6. Murray: 16,300 (2,700)
          8. Stillwater: 1,900 (500)
          9. Knoxville: 15,200 (1,700)
         13. Oak Grove: 13,600 (1,700)
         16. College Station: 13,300 (1,900)
         17. Baton Rouge: 6,200 (1,000)
         19. Lafayette: 2,800 (600)
         21. Winter Park: 6,200 (700)
         23. Tampico: 11,100 (3,700)]

    [Illustration: FIG. 41. Winds aloft at 10:00 P. M. on
       April 22 (CST). Winds at 2,000 feet above mean sea level are
       shown in black; those at 4,000 feet, in white. Velocities are
       indicated by standard Beaufort Scale of Wind Force. The
       numbers in circles refer to the stations shown in Figure 40.]

    Correction: Figures 41 and 45 were inadvertently transposed.

    [Illustration: FIG. 42. Comparison of flight trends and
       surface weather conditions on April 23-24, 1948. The
       meteorological data were taken from the U. S. Weather Bureau
       Daily Weather Map for 12:30 A. M. (CST) on April 24. The
       nightly station densities and the average hourly station
       density (shown in parentheses) are as follows:

          1. Albion: 1,100 (300)
          2. Ottumwa: 5,500 (900)
          4. Lawrence: 5,400 (1,400)
          5. Louisville: 13,300 (2,700)
          6. Murray: 9,800 (1,400)
          8. Stillwater: 800 (100)
          9. Knoxville: 8,000 (900)
         10. Memphis: 7,900 (1,000)
         14. Mansfield: 4,900 (1,200)
         16. College Station: 700 (100)
         17. Baton Rouge: 1,700 (400)
         18. Pensacola: migration negligible
         20. New Orleans: 1,600 (800)
         21. Winter Park: 2,700 (300)
         23. Tampico: 63,600 (6,300)
         24. Progreso: 31,300 (3,900)]

    [Illustration: FIG. 43. Winds aloft at 10:00 P. M. on
       April 23 (CST). Winds at 2,000 feet above mean sea level are
       shown in black; those at 4,000 feet, in white. Velocities are
       indicated by standard Beaufort Scale of Wind Force. The
       numbers in circles refer to the stations shown in Figure 42.]

    [Illustration: FIG. 44. Comparison of flight trends and
       surface weather conditions on April 24-25, 1948. The
       meteorological data were taken from the U. S. Weather Bureau
       Daily Weather Map for 12:30 A. M. (CST) on April 25. The
       nightly station densities and the average hourly station
       density (shown in parentheses) are as follows:

          1. Albion: migration negligible
          2. Ottumwa: 4,600 (1,500)
          3. Columbia: 1,400 (400)
          5. Louisville: 1,700 (200)
         10. Memphis: 6,600 (900)
         12. Rosedale: 1,100 (100)
         14. Mansfield: 1,700 (400)
         18. Pensacola: migration negligible
         21. Winter Park: 600 (100)
         24. Progreso: 27,300 (3,000)]

    [Illustration: FIG. 45. Winds aloft at 10:00 P. M. on
       April 24 (CST). Winds at 2,000 feet above mean sea level are
       shown in black; those at 4,000 feet, in white. Velocities are
       indicated by standard Beaufort Scale of Wind Force. The
       numbers in circles refer to the stations shown in Figure 44.]

    Correction: Figures 41 and 45 were inadvertently transposed.

    [Illustration: FIG. 46. Comparison of flight trends and
       surface weather conditions on May 21-22, 1948. The
       meteorological data were taken from the U. S. Weather Bureau
       Daily Weather Map for 12:30 A. M. (CST) on May 22. The
       nightly station densities and the average hourly station
       density (shown in parentheses) are as follows:

          2. Ottumwa: 6,900 (1,400)
          5. Louisville: 1,500 (200)
          9. Knoxville: 3,200 (500)
         10. Memphis: 7,000 (1,200)
         13. Oak Grove: 5,800 (800)
         14. Mansfield: 2,500 (800)
         18. Pensacola: migration negligible
         21. Winter Park: 1,200 (200)]

    [Illustration: FIG. 47. Winds aloft at 10:00 P. M. on May
       21 (CST). Winds at 2,000 feet above mean sea level are shown.
       Velocities are indicated by standard Beaufort Scale of Wind
       Force. The numbers in circles refer to the stations shown in
       Figure 46.]

On the first night, following the passage of a cold front, migration
at Ottumwa was comparatively low (6,900 birds in five hours). On the
following night, when the trajectory of the winds was toward the
north, the volume of migration was roughly twice as high (22,300 birds
in eight hours). At Louisville, on May 21-22, the nightly station
density was only 1,500 birds in seven hours, whereas on the following
night, it was 8,400 birds in the same length of time, or about six
times greater.

The evidence adduced from the present study gives support to the
hypothesis that the continental pattern of spring migration in eastern
North America is regulated by the movement of air masses. The
clockwise circulation of warm air around an area of high pressure
provides, on its western edge, tail winds which are apparently
favorable to northward migration. High pressure areas exhibit a
centrifugal force outward from the center, which may tend to disperse
the migratory flight originating at any given point. In contrast, the
circulation of air in the vicinity of a low pressure area is
counterclockwise with the force tending to be directed inward toward
the center. Since the general movement of the air is from the high
pressure area toward a low pressure area, birds starting their
migrations with favorable tail winds, are often ultimately carried to
a region where conditions are decidedly less favorable. In the
vicinity of an area of low pressure the greater turbulence and high
wind velocities, combined with the possibly slightly less buoyant
property of the air, cause birds to descend. Since low pressure areas
in spring generally precede cold fronts, with an attending shift of
the wind to the north, an additional barrier to the northward
migration of birds is imposed. The extreme manifestation of low
pressure conditions and the manner in which they operate against bird
flight, are associated with tropical hurricanes. There, the
centripetal force of the wind is so great that it appears to draw
birds into the "eye" of the hurricane. A classic example of this
effect is seen in the case of the birds that came aboard the "West
Quechee" when this vessel passed through the "eye" of a hurricane in
the Gulf of Mexico in August, 1927. I have already discussed the
details of this incident in a previous paper (1946:192). There is also
the interesting observation of Mayhew (1949), in which a similar
observation was made of large numbers of birds aboard a ship passing
through one of these intense low-pressure areas.

Although the forces associated with an ordinary low-pressure area are
by no means as intense as those associated with a tropical hurricane,
the forces operating are much the same. Consequently birds conceivably
might tend to be drawn toward a focal point near the center of the
low, where the other factors already mentioned would tend to
precipitate the entire overhead flight. Visible evidence of migration
would then manifest itself to the field ornithologists.




CONCLUSIONS


  1. Telescopic counts of birds passing before the moon may be used
     to determine reliable statistical expressions of the volume of
     migration in terms of direction and of definite units of time
     and space.

  2. Night migrants fly singly more often than in flocks, creating a
     remarkably uniform dispersion on a local scale throughout the
     sky, quite unlike the scattered distributions observable in the
     daytime.

  3. The nocturnal migration of birds is apparently preceded by a
     resting or feeding pause during which there are few migrants in
     the air. It is not to an important degree a non-stop continuation
     of flights begun in the daylight.

  4. Nightly migrational activity in North America varies from hour to
     hour according to a definite temporal pattern, corresponding to
     the _Zugunruhe_ of caged European birds, and expressed by
     increasingly heavy flights up until the hour before midnight,
     followed by a pronounced decline.

  5. The visible effects of the time pattern are subject to
     modification at a particular station by its location with respect
     to the resting areas from which the night's flight originates.

  6. Quantitative and directional studies have so far failed to prove
     that nocturnal migrants favor narrow, topographically-determined
     flight lanes to an important degree.

  7. Flight densities on the east coast of Mexico, though of first
     magnitude, have not yet been demonstrated in the volume demanded
     by the premise that almost all migrants returning to the
     United States from regions to the south do so by coastal routes.

  8. Heavy flights have been recorded from the northern coast of
     Yucatán under circumstances leading inevitably to the conclusion
     that birds migrate across the Gulf of Mexico in considerable
     numbers.

  9. There is reason to believe that the importance of the Florida
     Peninsula as an April and May flyway has been over-estimated,
     as regards the numbers of birds using it in comparison with the
     numbers of birds using the Mexican and Gulf routes.

 10. The amount of migration is apparently seldom sufficient to produce
     heavy densities of transient species on the ground without
     the operation of concentrative factors such as ecological patterns
     and meteorological forces.

 11. The absence or scarcity of transients in some areas in fine
     weather may be explained by this consideration.

 12. A striking correlation exists between air currents and the
     directional flight trends of birds, suggesting that most night
     migrants travel by a system of pressure-pattern flying.



LITERATURE CITED


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  ANONYMOUS
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  BERGMAN, G.

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  DAVIS, L. I.

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  F. [ARNER], D. [ONALD] S.

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  GATES, W. H.

    1933.    Hailstone damage to birds. Science, 78:263-264.


  HOWELL, A. H.

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  LOWERY, G. H., JR.

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    1946.    Evidence of trans-Gulf migration. Auk, 63:175-211.


  MAYHEW, D. F.

    1949.    Atmospheric pressure and bird flight. Science, 109:403.


  OVERING, R.

    1938.    High mortality at the Washington Monument. Auk, 55:679.


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  THOMSON, A. L.

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  VERY, F. W.

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  WEST, R. H.

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  WILLIAMS, G. G.

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    1945.    Do birds cross the Gulf of Mexico in spring? Auk,
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  Transmitted June 1, 1949.



    []
  23-1020




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  Transcriber's Notes

  With the exception of the typographical corrections detailed below
  and some minor corrections for missing periods or extra punctuation
  (item 28 in List of Figures), the text presented here is that
  contained in the original printed version. A transcription of the
  Data presented in Figure 12 was added to illustrate the information
  contained on that sheet. Some text was moved to rejoin paragraphs.
  The list of UK publications was moved to the end of the document.

  In writing variables for formulae, superscripted characters are
  shown using a caret (^). So, X squared would be X^2. Subscripts are
  shown using an underscore. Carbon dioxide is CO_2. Where several
  superscript or subscript character(s) are required or to aid in
  clarity, they are placed in braces (ex., H_{2}O for water and
  [theta]_{Npt.} for theta degrees from the North point).

  Emphasis Notation

      _Text_  = Italics

  Typographical Corrections

  Page   Correction

  385   flght => flight
  394   diargrams => diagrams
  404   Determinaton => Determination
  411   obsever => observer
  419   Morover => Moreover
  425   Mississippii => Mississippi
  425   a => as
  430   at => and
  431   inserted "a"
         ("...traveling along a certain topographic feature...")
  442   concensus => consensus
  472   Stephens, Loyd A. => Stevens, Lloyd A.