Produced by Walter MacDonald II




                         A PLAN

                           FOR

                  SECURING OBSERVATIONS

                         OF THE

                     VARIABLE STARS.


                           BY
                   EDWARD C. PICKERING,
        DIRECTOR OF THE HARVARD COLLEGE OBSERVATORY.





                       CAMBRIDGE:
                   JOHN WILSON AND SON.
                    University Press
                         1882.









            A PLAN FOR SECURING OBSERVATIONS

                  OF THE VARIABLE STARS.

                         ________

FOR several reasons the investigations here proposed are especially
suited to observers under very various conditions. The work is
capable of indefinite sub-division. Small as well as large telescopes
may be employed and many observations are needed which can best be
made with an opera-glass or field-glass, or even with the naked eye.
No attachment is needed to an ordinary telescope, so that no additional
expense on this account is required. Useful observations may be made
by an unskilled observer provided that he is capable of identifying
a star with certainty. The work is quantitative, and the observer has,
therefore, a continual test of the increased accuracy he has acquired
by practice. As a portion of the investigation will probably lead to
the discovery of interesting objects, the observations will possess
an interest often wanting in quantitative research. The aid of the
professional astronomer is earnestly requested for this scheme.
Suggestions by which it may be modified and improved will be gratefully
received. The professional astronomer, in consequence of his greater
skill, instrumental appliances, and command of his own time, could
fill gaps in the work, and thus greatly increase its value as a
whole. Such observations could often be made in the intervals of
other work or at times unsuitable for the observations to which he
was especially devoting himself. It should be added that especial
care will be taken not to interfere with observations of variable
stars now in progress. Observers of these objects are particularly
requested to notify the writer what work they propose to carry
out, so that a needless repetition of it may be avoided.

It is on the amateur and student of astronomy that we must depend
largely for the success of the plan here proposed. Many such persons
spend evening after evening at their telescopes without obtaining
results of any permanent value. Either no publication is made and
the results are therefore valueless, or time is spent on objects
that can be much more usefully examined with a larger instrument.
Most commonly the observer has no special plan and spends many
hours without result, while the same time might have been employed
with equal pleasure to himself and results of great value collected.
Those who have not tried it do not realize the growing interest in
a systematic research and the satisfaction in feeling that by one's
own labors the sum of human knowledge has been increased.

Much valuable assistance might be rendered by a class whose aid in
such work has usually been overlooked. Many ladies are interested in
astronomy and own telescopes, but with two or three noteworthy
exceptions their contributions to the science have been almost
nothing. Many of them have the time and inclination for such work,
and especially among the graduates of women's colleges are many who
have had abundant training to make excellent observers. As the work
may be done at home, even from an open window, provided the room
has the temperature of the outer air, there seems to be no reason
why they should not thus make an advantageous use of their skill.
It is believed that it is only necessary to point the way to secure
most valuable assistance. The criticism is often made by the opponents
of the higher education of women that, while they are capable of
following others as far as men can, they originate almost nothing,
so that human knowledge is not advanced by their work. This reproach
would be well answered could we point to a long series of such
observations as are detailed below, made by women observers.

Variable stars may be defined as those which exhibit a varying degree
of brightness at different times. The following classification of
them is believed to be a natural one. (Proc. Amer. Acad. xvi, 1, 257.)

I. Temporary stars, or those which shine out suddenly, sometimes
with great brilliancy, and gradually fade away. Examples, Tycho
Brahe's star of 1572, new star in Corona, 1866.

II. Long period variables, or those undergoing great variations
of light, the changes recurring in periods of several months.
Examples _omicron Ceti_ and _chi Ceti_.

III. Stars undergoing slight changes according to laws as yet
unknown. Examples, _alpha Orionis_ and _alpha Cassiopeiae_.

IV. Short period variables, or stars whose light is continually
varying, but the changes are repeated with great regularity in a
period not exceeding a few days. Examples, _beta Lyrae_ and _delta
Cephei_.

V. Algol stars, or stars which for the greater portion of the time
undergo no change in light, but every few days suffer a remarkable
diminution in light for a few hours. This phenomenon recurs with
such regularity that the interval between successive minima may be
determined in some cases within a fraction of a second. Examples _beta
Persei_ (Algol) and _S Cancri_.

Stars belonging to the first of these classes are seen so rarely
that the apparent discovery of one is to be received with the utmost
caution. On the other hand, the importance of early observations of
such an object is so great that no pains should be spared to secure
an early announcement if one is really found. On the best star charts
many stars are omitted of the brightness of the faintest objects
given. But any star much brighter than these should be measured by
the method given below, and a watch kept to see if any change takes
place. If it proves to be a temporary star an immediate announcement
should be made. If a telegram is sent to this Observatory the object
will be at once examined, and, if verified, notification will be made
in this country and in Europe with the name of the discoverer or
sender of the telegram. A similar notification may be sent of any
suspected objects, which will be examined in the same way, and
announced at once if they prove to be of interest. It is essential
that the position of the object should be given with all the precision
practicable, and that a letter should be sent by the next mail
giving the observations in detail. This often proves of the greatest
value in case the object is not readily found. It also serves to
establish the claims of the first discoverer.

Nearly three quarters of the known variables belong to the second
class. Most of them undergo very large changes of light, and may
therefore be observed with comparative ease. Our knowledge of their
variations is however very defective. Hitherto the attention of
observers has been directed principally to determining the times
at which they attain their maximum light, while their light at
intermediate times has been neglected. It is now proposed to secure
observations of these objects once or twice in every month, so that
their light curves or variations throughout their entire periods may
be determined. Again, many observers are accustomed to state their
brightness in magnitudes without giving any clue to the scale which
they employ. In most cases such observations have little value owing
to the uncertainty of the scale of the fainter magnitudes.

According to Dr. Gould and some other observers most of the visible
stars undergo slight changes of light and should therefore be assigned
to the third class of variables. It is probable that our Sun also
belongs to this class, as it is not likely that its light is the same
during the maximum and minimum of the sun spot period. At present we
are unable to tell in which case the light would be greatest. It by
no means follows that when the spots are most abundant the Sun's
total light is least, for the remaining portions of the Sun may
then have an increased brightness more than compensating for their
diminished area. As long as the suspected variations in light of the
stars are small, not exceeding half a magnitude for instance, they
seem in the present state of science to have comparatively little
interest. They are so liable to be affected, or even caused, by
errors of observation, that the observation of such objects does
not seem now to be advisable. Doubtless many such so-called variables
are really due to errors caused by moonlight, the proximity of
brighter stars, varying position of the images on the retina of the
observer, and other similar causes. They will not therefore be
considered further in this paper.

The stars of the fourth class as compared with the second are
relatively few in number, and the changes in light small. While
many of them need observation, especially to determine their light
curves more precisely, it is advised that this work be left to
those who have acquired a high degree of skill in these observations.
That the work may be of value it is essential that the errors should
be extremely small. As, however, nearly all are visible in an
opera-glass, a skilful observer unprovided with a telescope may
secure valuable results by their observation. This remark applies
with especial force to many of those discovered in the southern
heavens by Dr. Gould.

The phenomena of the Algol stars are in many respects the most
striking of any. The rapidity of the changes, their surprising
regularity, and the comparative rarity of these objects, combine
to render the discovery of each new one a matter of unusual interest.
As in the case of stars of the fourth class, however, the study of
their light curves should be left to those who have acquired especial
skill in this work. This is particularly desirable, when, as in this
case, the unaided eye enters into competition with photometric
apparatus, by which, as some think, it should properly be altogether
replaced.

An elaborate bibliographical work on the variable stars has been
undertaken at this Observatory by Mr. Chandler. It will include the
collection of all available published observations of known or
suspected variables. A catalogue of suspected variables has thus
been prepared, doubtless containing many stars which are really
important variables. But it is also likely that many objects have
been introduced in the list by errors in the original observations.
Such stars often appear in one catalogue after another of suspected
variables, and it is difficult to prevent the continued circulation
of such an error. Of course if an experienced observer at any time
estimates a star as above or below its normal brightness, it is
impossible to prove that the observation was not correct, and the
star really variable. No amount of subsequent observing could prove
that it had not then, and then only, an abnormal brightness. We can,
however, prove that in all probability it does not belong to one or
more of the above classes, and thus make it more and more probable
that the observation is due to an error. If the star varies in light
by one magnitude, what will be the chances that we shall get a series
of observations having a range of variation of one fifth of a
magnitude? Evidently on the average, there will be only one chance
out of five that any observation shall fall in the same fifth of a
magnitude as another. The chances for three such observations
will be only 1/25 and for four 1/125, etc. These ratios expressed
decimally are .2, .04, .008, 0016, .0003, etc. Since the separate
determinations of the light of a constant star by the method given
below should not differ more than two or three tenths of a magnitude,
it is obvious that if the variations of the star are large, a few
observations would generally establish this fact. If the star belongs
to class four, observations on half a dozen evenings would hardly fail
to show the variation. Conversely, if no such variation is detected we
may be almost certain that the star is not a variable of that class, or
at least that the variation, if any, is not large. If the star belongs
to class two, it will change so slowly when near its maximum or
minimum that a variation might not be noted if the observations are
near together. An interval of several months should therefore be
allowed to take place, or perhaps it would be better to wait until
the star is again visible the following year. The total variation
in light is usually so great in these stars that the change will
often be visible at the first glance.

To prove that a star does not belong to the fifth class is a matter
of much greater difficulty. In fact it is almost impossible to prove
that it may not be an Algol star with a long period between the
minima. Since these stars may have their full brightness for nine
tenths of the time, it is obvious that they may be examined again
and again without happening to be seen at the time of a minimum.

On the other hand, during a considerable portion of the time when
it is varying, the light will be so much less than usual that a
careful measurement is not needed to detect the change. Moreover, it
will be useless to look for an increase of light, and the observation
may be so planned as to detect a diminution only.

If we assume that only during one tenth of the time the change in
light will be sufficient to be perceptible, the chance on any given
evening will be 9 out of 10 or 9/10 that the star will have its full
brightness. For two evenings the chance will be (9/10)^2 for three
(9/10)^3, etc. These quantities expressed decimally are .9, .81,
.73, .66, .59, .53, .48, etc. Even after seven nights' observations,
on which no change is noted, it will only be about an even chance
that the star may not still be of the Algol type. A different method
of observing is therefore recommended when the star is supposed to
belong to this class. Select for comparison a star slightly fainter,
so that a moment's glance will satisfy the observer that the suspected
variable is the brighter. It is only necessary to repeat this
observation night after night. If the star is bright enough to be
visible with a field glass, a few seconds will be sufficient for this
observation after the observer has become familiar with the vicinity.
The fact that the light is normal, and the time to the nearest minute,
should be recorded after each observation. When convenient, it is
well to repeat the inspection two or more times during the night,
as in determining the period all the observations will have a value,
provided that they are separated by intervals of more than two or
three hours. If the star is ever found below its normal brightness,
comparisons should be made with the adjacent stars, and continued
as long as possible, or until it has regained its usual brightness.
The most complete proof that a star was not of the Algol type would
be for observers in the polar regions to examine it at intervals
of a few hours for several days, or for observers in different
longitudes to make the same observations. If it could thus be watched
for a week or fortnight by enough observers to avoid interference by
clouds, it would be nearly certain that it is not an Algol star
unless its period is greater than that of any such object as yet
discovered.

The problems to be undertaken may be defined as follows:--

1. To observe all the long period variables once or twice every
month throughout their variations according to such a system that
all the observations may be reduced to the same absolute scale
of magnitudes.

2. To observe the stars whose variability is suspected and prove
either that they are really variable, or that in all probability
they do not belong to the first, second, or fourth class. If any
are thought to belong to the fifth class, to watch them until such
a variation is proved, or is shown to be improbable.

All of this work will depend on the possibility of readily determining
the brightness of a star according to such a method that all the
observations can ultimately be reduced to the same system. Herschel
and Argelander have independently invented what appears to be the
true method to be followed. If a star is seen to be very nearly equal
to several others, from their light we can at any time define its
brightness. It is essential that at least one of the stars selected
should be a little brighter, another a little fainter, than the star
to be observed. The range within which its light is known is thus
also defined. Such observations will far exceed in value any direct
estimate of magnitude. When stars are to be compared many times,
it is convenient to designate them by letters for brevity. Let _v_
represent a star which is suspected to be variable, and _a_ an adjacent
star of nearly equal brightness. Owing to fluctuations in the
atmosphere, each star will appear to be constantly varying in
brightness. If the stars appear equal after a careful examination,
or if one appears brighter as often as it appears fainter than
the other, we may denote this equality by _av_ or _va_, these terms
having precisely the same meaning. If one of the stars is suspected
to be brighter, that is, if it appears sometimes brighter and
sometimes fainter, but more frequently brighter, the interval
may be designated as one grade. The observation may be written
_a_ 1 _v_ or _v_ 1 _a_, the brightest star being named first. If one
star is certainly brighter than the other, the difference, however,
being very small, so that they sometimes appear equal, the difference
will be two grades, and may be written _a_ 2 _v_ or _v_ 2 _a_. Greater
intervals may be estimated as three or four grades, but such
observations have much less value. It is found in practice that
a grade thus estimated will slightly exceed a tenth of a magnitude.
A useful exercise for an observer is to select two stars of known
magnitude and several others of intermediate brightness. Arrange
them in a series in the order of brightness, and estimate the
intervals in grades. The difference in magnitude of the first
stars divided by the total number of grades gives the value of
one grade. By using different intermediate stars, the same standard
stars may be employed repeatedly. The following well-known polar
stars will be convenient, since they are always visible:-- _a alpha
Ursae Minoris_, 2.2 magn.; gamma _Ursae Minoris_, 3.0 magn.; delta
_Ursae Minoris_, 4.4 magn.; 51 _Cephi_, 5.4 magn.; lambda _Ursae
Minoris_, 6.5 magn. The above method is essentially that of Argelander.
Sir William Herschel had already employed a method which differed
mainly in his notation, a . , and -- being equivalent to one, two, or
three grades.

In all work of this kind the observer must look directly at the
star he is observing at the moment, and never try to compare two
stars by a simultaneous inspection of both. After examining one
star until he has a distinct impression of its average brightness,
freed from the momentary changes due to atmospheric disturbance, he
should observe the other in the same manner. Alternate observations
of the two stars, each observation lasting for a few seconds, will
give a truer impression than can be derived from a simultaneous
observation in which the two images must be differently placed on
the retina.

The principal objection to this method is the difficulty of determining
the value of a grade, as it is liable to vary with the observer, the
time, the condition of the air, and the brightness of the stars.
These difficulties are avoided by the following method. Select two
stars for comparison; one, _a_, slightly brighter than the star to be
measured, _v_, the other, _b_, slightly fainter. The interval between
_a_ and _b_ should never exceed one magnitude. Estimate the brightness
of _v_ in tenths of the interval from _a_ to _b_. Thus, if _v_ is midway
between _a_ and _b_ the interval will be five tenths, and we may write
_a_ 5 _b_. If _v_ is nearly as bright as _a_, we may have _a_ 1 _b_ or
_a_ 2 _b_; if _v_ is not much brighter than _b_, we may have _a_ 8 _b_
or _a_ 9 _b_. An advantage of this method is that larger intervals in
brightness may be used between the comparison stars, and accordingly
less distant stars employed. An increase in distance of the stars always
renders the comparison more difficult. We can also obtain many
independent comparisons by using several comparison stars. If we
have _m_ stars brighter and _n_ fainter, we shall only have _m_ + _n_
independent measures by the method of grades, while we may have
_m n_ comparisons by estimating tenths, since estimates may be made
in terms of the intervals between each brighter and each fainter
star. On the other hand, especially when observing stars not very
near together, it is a decided advantage to have to compare two
stars rather than three. Each method has its advantages, and that
to be used should doubtless depend on the temperament of the observer.

Several precautions are needed to secure the best results. No
observations should be made near the horizon; and, when the objects
examined are at any considerable zenith distance, stars differing
several degrees in altitude should be avoided. If the stars are
bright and there is no choice, a correction may be made for the
error due to the varying absorption at these different altitudes
if the time of observation has been noted. When using a telescope
or opera-glass, the stars should be brought in turn to the centre
of the field, as when near the edge they will not appear of their
true brightness. This is found to be better than placing them at
equal distances from the centre. In selecting comparison stars,
the proximity of a brighter star is very objectionable, causing a
large error, which varies with the magnifying power used. Double
stars should be avoided if the power used is sufficient to show the
companion. Comparing stars of different colors is also objectionable.

Any persons who desire to take part in these observations are
requested to communicate with the writer, and send answers to the
questions given below.

1. What is the location of your point of observation? In the city
or in the country, on the ground, from a roof, or from a window?
Is any part of your horizon obstructed, or can you observe in all
parts of the sky?

2. What is the aperture, focal length, and name of maker of your
telescope? also the lowest magnifying power and largest field of
view you can obtain with it? Have you a field-glass or opera-glass?

3. Can you identify bright and faint stars from their designations
or right ascensions and declinations? Have you Heis' Atlas Coelestis
Novus, the Uranometria Argentina, the Durchmusterung, or other maps
and catalogues of the stars?

4. Would you prefer to observe the known or the suspected variables,
or to divide your time between them?

For convenience in making the reductions and for future reference,
it is essential that all the observations should be made according
to the same system. Observers are accordingly requested to adopt the
following form. Use half-sheets of letter paper (eight inches by
ten), writing only on one side and leaving a margin of half an inch
for binding. Begin with a new sheet every evening, and write the
date and location (township and state) on the first line. Each
sheet when completed should be signed, and all should be numbered
consecutively. When several sheets are used on the same night, the
date should be entered on each. The record should be made in pencil,
and all subsequent remarks or corrections added or interlined with
ink, taking especial care not to obliterate or render illegible the
original record.

A general statement should be made each evening of the condition
of the sky, as "clear," "hazy," "passing clouds," etc. The time
of beginning and ending work should also be noted. One
line should be assigned to each comparison. The hour and minute
should be written to the left, and the comparison next to it. The
right-hand half of the line will be left blank for reducing the
observation.

Certain evenings or portions of evenings must also be devoted to
the selection of the comparison stars of suspected variables. If
they are contained in maps which are available, the letters assigned
to each star may be marked on the maps and lines drawn to show with
what suspected variable star they are associated. If preferred, a
sketch may be made of the neighboring stars and the letters entered
on them. This sketch with a proper description should be entered on
the observing sheets described above, and a copy should be retained
for reference. Every month the observations will be interrupted by
moonlight, and accordingly, three or four days before the full moon,
all the sheets that have accumulated should be mailed, addressed
Harvard College Observatory, Cambridge, Mass. An acknowledgment will
be sent at once, so that if this is not received a second notification
should be sent.

To attain success it is particularly important that the plan should
not be local or national. Observers in the southern hemisphere are
much needed, and for some purposes those in various longitudes. It
is hoped that among the many amateurs of Europe, and especially of
England, may be found some ready to participate in this work. No
restriction regarding the observations or publication is intended;
but it is hoped that a large addition to our present knowledge of
the variable stars may be secured, without interfering with what
would otherwise be obtained. Copies of this pamphlet and further
information will be furnished on application. Any persons desiring
to participate are requested to address the writer, sending answers
to the questions given above. The details will differ with each
observer, and will be arranged by correspondence. Apart from the
value of the results attained, it is believed that many amateurs
will find it a benefit to accustom themselves to work in a systematic
manner, and that they will thus receive a training in their work not
otherwise easily obtained outside of a large observatory. The lesson
should be taught that time spent at a telescope is nearly wasted,
unless results are secured worthy of publication and having a
permanent value. Those who have once accomplished such work are
likely in the future to appreciate its value, and will often continue
to do useful work in some other department of practical astronomy,
if not in that of variable stars. The education of a class of
skilled observers would be a work of no less value than the results
anticipated from the observation of the variable stars.

EDWARD C. PICKERING.

HARVARD COLLEGE OBSERVATORY,
Cambridge, Mass.