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    THE MICROSCOPE.

    BEING THE ARTICLE CONTRIBUTED BY

    ANDREW ROSS


    TO THE “PENNY CYCLOPÆDIA,” PUBLISHED BY THE SOCIETY
    FOR THE DIFFUSION OF USEFUL KNOWLEDGE.

    FULLY ILLUSTRATED.


    NEW YORK:
    THE INDUSTRIAL PUBLICATION COMPANY.
    1877.




THE MICROSCOPE.


Microscope, the name of an instrument for enabling the eye to see
distinctly objects which are placed at a very short distance from it,
or to see magnified images of small objects, and therefore to see
smaller objects than would otherwise be visible. The name is derived
from the two Greek words, expressing this property, MIKROS, _small_,
and SKOPEO, _to see_.

So little is known of the early history of the microscope, and so
certain is it that the magnifying power of lenses must have been
discovered as soon as lenses were made, that there is no reason for
hazarding any doubtful speculations on the question of discovery. We
shall proceed therefore at once to describe the simplest forms of
microscopes, to explain their later and more important improvements,
and finally to exhibit the instrument in its present perfect state.

In doing this we shall assume that the reader is familiar with the
information contained in the articles “Light,” “Lens,” “Achromatic,”
“Aberration,” and the other sub-divisions of the science of Optics,
which are treated of in this work.

The use of the term _magnifying_ has led many into a misconception of
the nature of the effect produced by convex lenses. It is not always
understood that the so-called magnifying power of a lens applied to
the eye, as in a microscope, is derived from its enabling the eye to
approach more nearly to its object than would otherwise be compatible
with distinct vision. The common occurrence of walking across the
street to read a bill is in fact magnifying the bill by approach; and
the observer, at every step he takes, makes a change in the optical
arrangement of his eye, to adapt it to the lessening distance between
himself and the object of his inquiry. This power of spontaneous
adjustment is so unconsciously exerted, that unless the attention be
called to it by circumstances, we are totally unaware of its exercise.

In the case just mentioned the bill would be read with eyes in a very
different state of adjustment from that in which it was discovered on
the opposite side of the street, but no conviction of this fact would
be impressed upon the mind. If, however, the supposed individual
should perceive on some part of the paper a small speck, which he
suspects to be a minute insect, and if he should attempt a very close
approach of his eye for the purpose of verifying his suspicion, he
would presently find that the power of natural adjustment has a limit;
for when his eye has arrived within about ten inches, he will discover
that a further approach produces only confusion. But if, as he
continues to approach, he were to place before his eye a series of
properly arranged convex lenses, he would see the object gradually and
distinctly increase in apparent size by the mere continuance of the
operation of approaching. Yet the glasses applied to the eye during
the approach from ten inches to one inch, would have done nothing more
than had been previously done by the eye itself during the approach
from fifty feet to one foot. In both cases the magnifying is effected
really by the approach, the lenses merely rendering the latter periods
of the approach compatible with distinct vision.

A very striking proof of this statement may be obtained by the
following simple and instructive experiment. Take any minute object, a
very small insect for instance, held on a pin or gummed to a slip of
glass; then present it to a strong light, and look at it through the
finest needle-hole in a blackened card placed about an inch before it.
The insect will appear quite distinct, and about ten times larger than
its usual size. Then suddenly withdraw the card without disturbing the
object, which will instantly become indistinct and nearly invisible.
The reason is, that the naked eye cannot see at so small a distance as
one inch. But the card with the hole having enabled the eye to
approach within an inch, and to see distinctly at that distance, is
thus proved to be as decidedly a magnifying instrument as any lens or
combination of lenses.

This description of magnifying power does not apply to such
instruments as the solar or gas microscope, by which we look not at
the object itself, but at its shadow or picture on the wall; and the
description will require some modification in treating of the compound
microscope, where, as in the telescope, an image or picture is formed
by one lens, that image or picture being viewed as an original object
by another lens.

It is nevertheless so important to obtain a clear notion of the real
nature of the effect produced by a lens applied to the eye, that we
will adduce the instance of spectacles to render the point more
familiar. If the person who has been supposed to cross the street for
the purpose of reading a bill had been aged, the limit to the power of
adjustment would have been discovered at a greater distance, and
without so severe a test as the supposed insect. The eyes of the very
aged generally lose the power of adjustment at a distance of thirty or
forty inches instead of ten, and the spectacles worn in consequence
are as much magnifying glasses to them as the lenses employed by
younger eyes to examine the most minute objects. Spectacles are
magnifying glasses to the aged because they enable such persons to see
as closely to their objects as the young, and therefore to see the
objects larger than they could themselves otherwise see them, but not
larger than they are seen by the unassisted younger eye.

In saying that an object appears larger at one time, or to one person,
than another, it is necessary to guard against misconception. By the
apparent size of an object we mean the angle it subtends at the eye,
or the angle formed by two lines drawn from the centre of the eye to
the extremities of the object. In Fig. 1, the lines A E and B E drawn
from the arrow to the eye form the angle A E B, which, when the angle
is small, is nearly twice as great as the angle C E D, formed by lines
drawn from a similar arrow at twice the distance. The arrow A B will
therefore appear nearly twice as long as C D, being seen under twice
the angle, and in the same proportion for any greater or lesser
difference in distance. The angle in question is called the angle of
vision, or the visual angle.

[Illustration: Fig. 1.]

The angle of vision must, however, not be confounded with the angle of
the pencil of light by which an object is seen, and which is explained
in Fig. 2. Here we have drawn two arrows placed in relation to the eye
as before, and from the centre of each have drawn lines exhibiting the
quantity of light which each point will send into the eye at the
respective distances.

[Illustration: Fig. 2.]

Now if E F represent the diameter of the pupil, the angle E A F shows
the size of the cone or pencil of light which enters the eye from the
point A, and in like manner the angle E B F is that of the pencil
emanating from B, and entering the eye. Then, since E A F is double E
B F, it is evident that A is seen by four times the quantity of light
which could be received from an equally illuminated point at B; so
that the nearer body would appear brighter if it did not appear
larger; but as its apparent area is increased four times as well as
its light, no difference in this respect is discovered. But if we
could find means to send into the eye a larger pencil of light, as for
instance that shown by the lines G A H, without increasing the
apparent size in the same proportion, it is evident that we should
obtain a benefit totally distinct from that of increased magnitude,
and one which is in some cases of even more importance than size in
developing the structure of what we wish to examine. This, it will be
hereafter shown, is sometimes done; for the present, we wish merely to
explain clearly the distinction between apparent magnitude, or the
angle under which the object is seen, and apparent brightness, or the
angle of the pencil of light by which each of its points is seen, and
with these explanations we shall continue to employ the common
expressions magnifying glass and magnifying power.

[Illustration: Fig. 3.]

The magnifying power of a single lens depends upon its focal length,
the object being in fact placed nearly in its principal focus, or so
that the light which diverges from each point may, after refraction by
the lens, proceed in parallel lines to the eye, or as nearly so as is
requisite for distinct vision. In Fig. 3, A B is a double convex lens,
near which is a small arrow to represent the object under examination,
and the cones drawn from its extremities are portions of the rays of
light diverging from those points and falling upon the lens. These
rays, if suffered to fall at once upon the pupil, would be too
divergent to permit their being brought to a focus upon the retina by
the optical arrangements of the eye. But being first passed through
the lens, they are bent into nearly parallel lines, or into lines
diverging from some points within the limits of distinct vision, as
from C and D. Thus altered, the eye receives them precisely as if they
emanated from a larger arrow placed at C D, which we may suppose to be
ten inches from the eye, and then the difference between the real and
the imaginary arrow is called the magnifying power of the lens in
question.

From what has been said it will be evident that two persons whose eyes
differed as to the distance at which they obtained distinct vision,
would give different results as to the magnifying power of a lens. To
one who can see distinctly with the naked eye at a distance of five
inches, the magnifying power would seem and would indeed be only half
what we have assumed. Such instances are, however, rare; the focal
length of the eye usually ranges from six to twelve or fourteen
inches, so that the distance we first assumed of ten inches is very
near the true average, and is a convenient number, inasmuch as a
cipher added to the denominator of the fraction which expresses the
focal length of a lens gives its magnifying power. Thus a lens whose
focal length is one-sixteenth of an inch is said to magnify 160 times.

When the focal length of a lens is very small, it is difficult to
measure accurately the distance between its centre and its object. In
such cases the best way to obtain the focal length for parallel or
nearly parallel rays is to view the image of some distant object
formed by the lens in question through another lens of one inch solar
focal length, keeping both eyes open and comparing the image presented
through the two lenses with that of the naked eye. The proportion
between the two images so seen will be the focal length required. Thus
if the image seen by the naked eye is ten times as large as that shown
by the lenses, the focal length of the lens in question is one-tenth
of an inch. The panes of glass in a window, or courses of bricks in a
wall, are convenient objects for this purpose.

In whichever way the focal length of the lens is ascertained, the
rules given for deducing its magnifying power are not rigorously
correct, though they are sufficiently so for all practical purposes,
particularly as the whole rests on an assumption in regard to the
focal length of the eye, and as it does not in any way affect the
actual measurement of the object. To calculate with great precision
the magnifying power of a lens with a given focal length of eye, it is
necessary that the thickness of the lens be taken into the account,
and also the focal length of the eye itself.

We have hitherto considered a magnifying lens only in reference to its
enlargement of the object, or the increase of the angle under which
the object is seen. A further and equally important consideration is
that of the number of rays or quantity of light by which every point
of the object is rendered visible. The naked eye, as shown in Fig. 2,
admits from each point of every visible object a cone of light having
the diameter of the pupil for its base, and most persons are familiar
with that beautiful provision by which in cases of excessive
brilliancy the pupil spontaneously contracts to reduce the cone of
admitted light within bearable limits. This effect is still further
produced in the experiment already described, of looking at an object
through a needle-hole in a card, which is equivalent to reducing the
pupil to the size of a needle-hole. Seen in this way the object
becomes comparatively dark or obscure; because each point is seen by
means of a very small cone of light, and a little consideration will
suffice to explain the different effects produced by the needle-hole
and the lens. Both change the angular value of the cone of light
presented to the eye, but the lens changes the angle by bending the
extreme rays within the limits suited to distinct vision, while the
needle-hole effects the same purpose by cutting off the rays which
exceed those limits.

It has been shown that removing a brilliant object to a greater
distance will reduce the quantity of light which each point sends into
the eye, as effectually as viewing it through a needle-hole; and
magnifying an object by a lens has been shown to be the same thing in
some respects as removing it to a greater distance. We have to see the
magnified picture by the light emanating from the small object, and it
becomes a matter of difficulty to obtain from each point a sufficient
quantity of light to bear the diffusion of a great magnifying power.
We want to perform an operation just the reverse of applying the card
with the needle-hole to the eye--we want in some cases to bring into
the eye the largest possible pencil of light from each point of the
object.

Referring to Fig. 3, it will be observed that if the eye could see the
small arrow at the distance there shown without the intervention of
the lens, only a very small portion of the cones of light drawn from
its extremities would enter the pupil; whereas we have supposed that
after being bent by the lens the whole of this light enters the eye as
part of the cones of smaller angle whose summits are at C and D. These
cones will further explain the difference between large and small
pencils of light; those from the small arrow are large pencils; the
dotted cones from the large arrow are small pencils.

In assuming that the whole of this light could have been suffered to
enter the eye through the lens A B, we did so for the sake of not
perplexing the reader with too many considerations at once. He must
now learn that so large a pencil of light passing through a single
lens would be so distorted by the spherical figure of the lens, and by
the chromatic dispersion of the glass, as to produce a very confused
and imperfect image. This confusion may be greatly diminished by
reducing the pencil; for instance, by applying a stop, as it is
called, to the lens, which is neither more nor less than the
needle-hole applied to the eye. A small pencil of light may be thus
transmitted through a single lens without suffering from spherical
aberration or chromatic dispersion any amount of distortion which will
materially affect the figure of the object; but this quantity of light
is insufficient to bear diffusion over the magnified picture, which is
therefore too obscure to exhibit what we most desire to see--those
beautiful and delicate markings by which one kind of organic matter is
distinguished from another. With a small aperture these markings are
not seen at all: with a large aperture and a single lens they exhibit
a faint nebulous appearance enveloped in a chromatic mist, a state
which is of course utterly valueless to the naturalist, and not even
amusing to the amateur.

It becomes therefore a most important problem to reconcile a large
aperture with distinctness, or, as it is called, _definition_; and
this has been done in a considerable degree by effecting the required
amount of refraction through two or more lenses instead of one, thus
reducing the angles of incidence and refraction, and producing other
effects which will be shortly noticed. This was first accomplished in
a satisfactory manner by--

    DR. WOLLASTON’S DOUBLET,

invented by the celebrated philosopher whose name it bears; it
consists of two plano-convex lenses (Fig. 4) having their focal
lengths in the proportion of 1 to 3, or nearly so, and placed at a
distance which can be ascertained best by actual experiment. Their
plane sides are placed towards the object, and the lens of shortest
focal length next the object.

[Illustration: Fig. 4.]

It appears that Dr. Wollaston was led to this invention by considering
that the Achromatic Huyghenean Eye-piece, which will be hereafter
described, would, if reversed, possess similar good properties as a
simple microscope. But it will be evident when the eye-piece is
understood, that the circumstances which render it achromatic are very
imperfectly applicable to the simple microscope, and that the doublet,
without a nice adjustment of the stop, would be valueless. Dr.
Wollaston makes no allusion to a stop, nor is it certain that he
contemplated its introduction, although his illness, which terminated
fatally soon after the presentation of his paper, may account for the
omission.

The nature of the corrections which take place in the doublet is
explained in the annexed diagram (Fig. 5), where L O L´ is the object,
P a portion of the pupil, and D D the stop, or limiting aperture.

Now, it will be observed that each of the pencils of light from the
extremities L L´ of the object is rendered eccentrical by the stop,
and of consequence each passes through the two lenses on opposite
sides of their common axis O P; thus each becomes affected by opposite
errors, which to some extent balance and correct each other. To take
the pencil L, for instance, which enters the eye at R B, R B; it is
bent to the right at the first lens, and to the left at the second;
and as each bending alters the direction of the blue rays more than
the red, and, moreover, as the blue rays fall nearer the margin of the
second lens, where the refraction, being more powerful than near the
centre, compensates in some degree for the greater focal length of the
second lens, the blue and red rays will emerge very nearly parallel,
and of consequence colorless to the eye. At the same time the
spherical aberration has been diminished by the circumstance that the
side of the pencil which passes one lens nearest the axis passes the
other nearest the margin.

This explanation applies only to the pencils near the extremities of
the object. The central pencil, it is obvious, would pass both lenses
symmetrically; the same portions of light occupying nearly the same
relative places on both lenses. The blue light would enter the second
lens nearer to its axis than the red, and being thus less refracted
than the red by the second lens, a small amount of compensation would
take place, quite different in principle and inferior in degree to
that which is produced in the eccentrical pencils. In the intermediate
spaces the corrections are still more imperfect and uncertain; and
this explains the cause of the aberrations which must of necessity
exist even in the best-made doublet. It is, however, infinitely
superior to a single lens, and will transmit a pencil of an angle of
from 35° to 50° without any very sensible errors. It exhibits,
therefore, many of the usual test-objects in a very beautiful manner.

[Illustration: Fig. 5.]

[Illustration: Fig. 6.]

The next step in the improvement of the simple microscope bears more
analogy to the eye-piece. This improvement was made by Mr. Holland,
and it consists (as shown in Fig. 6) in substituting two lenses for
the first in the doublet, and retaining the stop between them and the
third. The first bending, being thus effected by two lenses instead of
one, is accompanied by smaller aberrations, which are therefore more
completely balanced or corrected at the second bending, in the
opposite direction, by the third lens. This combination, though called
a triplet is essentially a doublet, in which the anterior lens is
divided into two. For it must be recollected that the first pair of
lenses merely accomplishes what might have been done, though with less
precision, by one; but the two lenses of the doublet are opposed to
each other; the second diminishing the magnifying power of the first.
The first pair of lenses in the triplet concur in producing a certain
amount of magnifying power, which is diminished in quantity and
corrected as to aberration at the third lens by the change in relation
to the position of the axis which takes place in the pencil between
what is virtually the first and second lens. In this combination the
errors are still further reduced by the close approximation to the
object which causes the refractions to take place near the axis. Thus
the transmission of a still larger angular pencil, namely 65°, is
rendered compatible with distinctness, and a more intense image is
presented to the eye.

Every increase in the number of lenses is attended with one drawback,
from the circumstance that a certain portion of light is lost by
reflection and absorption each time that the ray enters a new medium.
This loss bears no sensible proportion to the gain arising from the
increased aperture, which, being as the square of the diameter,
multiplies rapidly; or, if we estimate by the angle of the admitted
pencil, which is more easily ascertained, the intensity will be as the
square of twice the tangent of half the angle. To explain this, let D
B (Fig. 7) represent the diameter of the lens, or of that part of it
which is really employed; C A the perpendicular drawn from its
centre, and A B, A D, the extreme rays of the incident pencil of light
DAB. Then the diameter being 2 C B, the area to which the intensity of
vision is proportional will be (2 C B)², and C B is evidently the
tangent of the angle C A B, which is half the angle of the admitted
pencil D A B. Or, if _a_ be used to denote the angular aperture, the
expression for the intensity is (2 tan. ½_a_)² which increases so
rapidly with the increase of _a_ as to make the loss of light by
reflection and absorption of little consequence.

[Illustration: Fig. 7.]

The combination of three lenses approaches, as has been stated, very
close to the object; so close, indeed, as to prevent the use of more
than three; and this constitutes a limit to the improvement of the
simple microscope, for it is called a simple microscope, although
consisting of three lenses, and although a compound microscope may be
made of only three or even two lenses; but the different arrangement
which gives rise to the term compound will be better understood when
that instrument is explained.

Before we proceed to describe the simple microscope and its
appendages, it will be well to explain such other points in reference
to the form and materials of lenses as are most likely to be
interesting.

A very useful form of lens was proposed by Dr. Wollaston, and called
by him the Periscopic lens. It consisted of two hemispherical lenses,
cemented together by their plane faces, having a stop between them to
limit the aperture. A similar proposal was made Mr. Coddington, who,
however, executed the project in a better manner, by cutting a groove
in a whole sphere, and filling the groove with opaque matter. His
lens, which is the well-known Coddington lens, is shown in Fig. 8. It
gives a large field of view, which is equally good in all directions,
as it is evident that the pencils A A and B B pass through under
precisely the same circumstances. Its spherical form has the further
advantage of rendering the position in which it is held of
comparatively little consequence. It is therefore very convenient as
a hand-lens, but its definition is of course not so good as that of a
well-made doublet or achromatic lens.

[Illustration: Fig. 8.]

Another very useful form of doublet was proposed by Sir John Herschel,
chiefly like the Coddington lens, for the sake of a wide field, and
chiefly to be used in the hand. It is shown in Fig. 9; it consists of
a double convex or crossed lens, having the radii of curvature as 1 to
6, and of a plane concave lens whose focal length is to that of the
convex lens as 13 to 5.

Various, indeed innumerable, other forms and combinations of lenses
have been projected, some displaying much ingenuity, but few of any
practical use. In the Catadioptric lenses the light emerges at right
angles from its entering direction, being reflected from a surface cut
at an angle of 45 degrees to the axes of the curved surfaces.

[Illustration: Fig. 9.]

It was at one time hoped, as the precious stones are more refractive
than glass, and as the increased refractive power is unaccompanied by
a correspondent increase in chromatic dispersion, that they would
furnish valuable materials for lenses, inasmuch as the refractions
would be accomplished by shallower curves, and consequently with
diminished spherical aberration. But these hopes were disappointed;
everything that ingenuity and perseverance could accomplish was tried
by Mr. Varley and Mr. Pritchard, under the patronage of Dr. Goring. It
appeared, however, that the great reflective power, the
doubly-refracting property, the color, and the heterogeneous structure
of the jewels which were tried, much more than counterbalanced the
benefits arising from their greater refractive power, and left no
doubt of the superiority of skillfully made glass doublets and
triplets. The idea is now, in fact, abandoned; and the same remark is
applicable to the attempts at constructing fluid lenses, and to the
projects for giving to glass other than spherical surfaces--none of
which have come into extensive use.

By the term _simple_ microscope is meant one in which the object is
viewed directly through a lens or combination of lenses, just as we
have supposed an arrow or an insect to be viewed through a glass held
in the hand. When, however, the magnifying power of the glass is
considerable, in other words, when its focal length is very short, and
its proper distance from its object of consequence equally short, it
requires to be placed at that proper distance with great precision: it
cannot, therefore, be held with sufficient accuracy and steadiness by
the unassisted hand, but must be mounted in a frame having a rack or
screw to move it towards or from another frame or stage which holds
the object. It is then called a microscope, and it is furnished,
according to circumstances, with lenses and mirrors to collect and
reflect the light upon the object, and with other conveniences which
will now be described.

One of the best forms of a stand for a simple microscope is shown in
Fig. 10, where A is a brass pillar screwed to a tripod base; B is a
broad stage for the objects, secured to the stem by screws, whose
milled heads are at C. By means of the large milled head D, a
triangular bar, having a rack, is elevated out of the stem A, carrying
the lens-holder E, which has a horizontal movement in one direction,
by means of a rack worked by the milled head F, and in the other
direction by turning on a circular pin. A concave mirror G reflects
the light upwards through the hole in the stage, and a lens may be
attached to the stage for the purpose of throwing light on an opaque
object, in the same way that the forceps H for holding such objects is
attached. This microscope is peculiarly adapted, by its broad stage
and its general steadiness, for dissecting; and it is rendered more
convenient for this purpose by placing it between two inclined planes
of mahogany, which support the arms and elevate the wrists to the
level of the stage. This apparatus is called the dissecting rest. When
dissecting is not a primary object, a joint may be made at the lower
end of the stem A, to allow the whole to take an inclined position;
and then the spring clips shown upon the stage are useful to retain
the object in its place. Numerous convenient appendages may be made to
accompany such microscopes, which it will be impossible to mention in
detail; the most useful are Mr. Varley’s capillary cages for
containing animalculæ in water, and parts of aquatic plants; also his
tubes for obtaining and separating such objects, and his phial and
phial-holder for preserving and exhibiting small living specimens of
the Chara, Nitella, and other similar plants, and observing their
circulation. The phial-microscope affords facilities for observing the
operations of minute vegetable and animal life, which will probably
lead to the most interesting discoveries. The recent volumes of the
Transactions of the Society of Arts contain an immense mass of
information of this sort, and to these we refer the reader.

[Illustration: Fig. 10.]

The mode of illuminating objects is one on which we must give some
further information, for the manner in which an object is lighted is
second in importance only to the excellence of the glass through which
it is seen. In investigating any new or unknown specimen, it should be
viewed in turns by every description of light, direct and oblique, as
a transparent object and as an opaque object, with strong and with
faint light, with large angular pencils and with small angular pencils
thrown in all possible directions. Every change will probably develop
some new fact in reference to the structure of the object, which
should itself be varied in the mode of mounting in every possible way.
It should be seen both wet and dry, and immersed in fluids of various
qualities and densities, such as water, alcohol, oil, and Canada
balsam, for instance, which last has a refractive power nearly equal
to that of glass. If the object be delicate vegetable tissue, it will
be in some respects rendered more visible by gentle heating or
scorching by a clear fire placed between two plates of glass. In this
way the spiral vessels of asparagus and other similar vegetables may
be beautifully displayed. Dyeing the objects in tincture of iodine
will in some cases answer this purpose better.

But the principal question in regard to illumination is the magnitude
of the illuminating pencil, particularly in reference to transparent
objects. Generally speaking the illuminating pencil should be as large
as can be received by the lens, and no larger. Any light beyond this
produces indistinctness and glare. The superfluous light from the
mirror may be cut off by a screen having various-sized apertures
placed below the stage; but the best mode of illumination is that
proposed by Dr. Wollaston, and called the Wollaston condenser. A tube
is placed below the stage of the instrument containing a lens A B
(Fig. 11), which can be elevated or depressed within certain limits at
pleasure; and at the lower end is a stop with a limited aperture C D.
A plane mirror E F receives the rays of light L L from the sky or a
white cloud, which last is the best source of light, and reflects them
upwards through the aperture in C D, so that they are refracted, and
form an image of the aperture at G, which is supposed to be nearly
the place of the object. The object is sometimes best seen when the
image of the aperture is also best seen; and sometimes it is best to
elevate the summit G of the cone A B G above the object, and at others
to depress it below: all which is done at pleasure by the power of
moving the lens A B. If artifical light (as a lamp or candle) be
employed, the flame must be placed in the principal focus of a large
detached lens on a stand, so that the rays L L may fall in parallel
lines on the mirror, or as they would fall from the cloud. This will
be found an advantage, not only when the Wollaston condenser is
employed, but also when the mirror and diaphragm are used. A good mode
of imitating artificially the light of a white cloud opposite the sun
has been proposed by Mr. Varley; he covers the surface of the mirror
under the stage with carbonate of soda or any similar material, and
then concentrates the sun’s light upon its surface by a large
condensing lens. The intense white light diffused from the surface of
the soda forms an excellent substitute for the white cloud, which,
when opposite the sun, and of considerable size, is the best daylight,
as the pure sky opposite to the sun is the worst.

[Illustration: Fig. 11.]

_The Compound Microscope_ may, as before stated, consist of only two
lenses, while a simple microscope has been shown to contain sometimes
three. In the triplet for the simple microscope, however, it was
explained that the effect of the two first lenses was to do what might
have been accomplished, though not so well, by one; and the third
merely effected certain modifications in the light before it entered
the eye. But in the compound microscope the two lenses have totally
different functions; the first receives the rays from the object, and,
bringing them to new foci, forms an image, which the second lens
treats as an original object, and magnifies it just as the single
microscope magnified the object itself.

[Illustration: Fig. 12.]

The annexed figure (12) shows the course of the rays through a
compound microscope of two lenses. The rays proceeding from the object
A B are so acted upon by the lens C D, near it, and thence called the
object glass, that they are converged to foci in A´ B´, where they
form an enlarged image of the object, as would be evident if a piece
of oiled paper or ground glass were placed there to receive them. They
are not so intercepted, and therefore the image is not rendered
visible at that place; but their further progress is similar to what
it would have been had they really proceeded from an object at A´ B´.
They are at length received by the eye-lens L M, which acts upon them
as the simple microscope has been described to act on the light
proceeding from its objects. They are bent so that they may enter the
eye at E in parallel lines, or as nearly so as is requisite for
distinct vision. When we say that the rays enter the eye in nearly
parallel lines, we mean only those which proceed from one point of the
original object. Thus the two parallel rays M E have proceeded from
and are part of the cone of rays C A D, emanating from the point A of
the arrow; but they do not form two pictures in the eye, because any
number of parallel rays which the pupil can receive will be converged
to a point by the eye, and will convey the impression of one point to
the mind. In like manner the rays L E are part of the cone of rays
emanating from B, and the angle L E M is that under which the eye will
see the magnified image of the arrow, which is evidently many times
greater than the arrow could be made to occupy in the naked eye at any
distance within the limits of distinct vision. The magnifying power
depends on two circumstances: first, on the ratio between the anterior
distance A C or B D and the posterior focal length C B´ or D A´; and
secondly, on the power of the eye-lens L M. The first ratio is the
same as that between the object A B and the image A´ B´; this and the
focal length or power of the eye lens are both easily obtained, and
their product is the power of the compound instrument.

Since the power depends on the ratio between the anterior and
posterior foci of the object-glass, it is evident that by increasing
that ratio any power may be obtained, the same eye-glass being used;
or having determined the first, any further power may be obtained by
increasing that of the eye-glass; and thus, by a pre-arrangement of
the relative proportions in which the magnifying power shall be
divided between the object-glass and the eye-glass, almost any given
distance (within certain limits) between the first and its object may
be secured. This is one valuable peculiarity of the compound
instrument; and another is the large field, or large angle of view,
which may be obtained, every part of which will be nearly equally
good; whereas with the best simple microscopes the field is small, and
is good only in the centre. The field of the compound instrument is
further increased by using two glasses at the eye-end; the first being
called, from its purpose, the field-glass, and the two constituting
what is called the eye-piece. This will be more particularly explained
in the figure of the achromatic compound microscope presently given.

For upwards of a century the compound microscope, notwithstanding the
advantages above mentioned, was a comparatively feeble and inefficient
instrument, owing to the distance which the light had to traverse, and
the consequent increase of the chromatic and spherical aberrations. To
explain this we have drawn in Fig. 12 a second image near A´ B´, the
fact being that the object-glass would not form one image, as has been
supposed, but an infinite number of variously-colored and
various-sized images, occupying the space between the two dotted
arrows. Those nearest the object-glass would be red, and those nearest
the eye-glass would be blue. The effect of this is to produce so much
confusion, that the instrument was reduced to a mere toy, although
these errors were diminished to the utmost possible extent by limiting
the aperture of the object-glass, and thus restricting the angle of
the pencil of light from each point of the object. But this involved
the defects, already explained, of making the picture obscure, so that
on the whole the best compound instruments were inferior to the simple
microscopes of a single lens, with which, indeed, all the important
observations of the last century were made.

Even after the improvement of the simple microscope by the use of
doublets and triplets, the long course of the rays, and the large
angular pencil required in the compound instrument, deterred the most
sanguine from anticipating the period when they should be conducted
through such a path free both from spherical and chromatic errors.
Within twenty years of the present period, philosophers of no less
eminence than M. Blot and Dr. Wollaston predicted that the compound
would never rival the simple microscope, and that the idea of
achromatizing its object-glass was hopeless. Nor can these opinions be
wondered at when we consider how many years the achromatic telescope
had existed without an attempt to apply its principles to the compound
microscope. When we consider the smallness of the pencil required by
the telescope, and the enormous increase of difficulty attending every
enlargement of the pencil--when we consider further that these
difficulties had to be contended with and removed by operations on
portions of glass so small that they are themselves almost microscopic
objects, we shall not be surprised that even a cautious philosopher
and most able manipulator like Dr. Wollaston should prescribe limits
to improvement.

Fortunately for science, and especially for the departments of animal
and vegetable physiology, these predictions have been shown to be
unfounded. The last fifteen years have sufficed to elevate the
compound microscope from the condition we have described to that of
being the most important instrument ever bestowed by art upon the
investigator of nature. It now holds a very high rank among
philosophical implements, while the transcendant beauties of form,
color and organization, which it reveals to us in the minute works of
nature, render it subservient to the most delightful and instructive
pursuits. To these claims on our attention, it appears likely to add a
third of still higher importance. The microscopic examination of the
blood and other human organic matter will in all probability afford
more satisfactory and conclusive evidence regarding the nature and
seat of disease than any hitherto appealed to, and will of consequence
lead to similar certainty in the choice and application of remedies.

We have thought it necessary to state thus at large the claims of the
modern achromatic microscope upon the attention of the reader, as a
justification of the length at which we shall give its recent history
and explain its construction; and we are further induced to this
course by the consideration that the subject is entirely new ground,
and that there are at this time not more than two or three makers of
achromatic microscopes in England.

Soon after the year 1820 a series of experiments was begun in France
by M. Selligues, which were followed up by Frauenhofer at Munich, by
Amici at Modena, by M. Chevalier at Paris, and by the late Mr. Tulley
in London. In 1824 the last-named excellent artist, without knowing
what had been done on the Continent, made the attempt to construct an
achromatic object-glass for a compound microscope, and produced one of
nine-tenths of an inch focal length, composed of three lenses, and
transmitting a pencil of eighteen degrees. This was the first that had
been made in England; and it is due to Mr. Tulley to say, that as
regards accurate correction throughout the field, that glass has not
been excelled by any subsequent combination of three lenses. Such an
angular pencil, and such a focal length, would bear an eye-piece
adapted to produce a gross magnifying power of one hundred and twenty.
Mr. Tulley afterwards made a combination to be placed in front of the
first mentioned, which increased the angle of the transmitted pencil
to thirty-eight degrees, and bore a power of three hundred.

While these practical investigations were in progress, the subject of
achromatism engaged the attention of some of the most profound
mathematicians in England. Sir John Herschel, Professor Airy,
Professor Barlow, Mr. Coddington, and others, contributed largely to
the theoretical examination of the subject; and though the results of
their labors were not immediately applicable to the microscope, they
essentially promoted its improvement.

For some time prior to 1829 the subject had occupied the mind of a
gentleman, who, not entirely practical, like the first, nor purely
mathematical, like the last-mentioned class of inquirers, was led to
the discovery of certain properties in achromatic combinations which
had been before unobserved. These were afterwards experimentally
verified; and in the year 1829 a paper on the subject, by the
discoverer, Mr. Joseph Jackson Lister, was read and published by the
Royal Society. The principles and results thus obtained enabled Mr.
Lister to form a combination of lenses which transmitted a pencil of
fifty degrees, with a large field correct in every part; as this paper
was the foundation of the recent improvements in achromatic
microscopes, and as its results are indispensable to all who would
make or understand the instrument, we shall give the more important
parts of it in detail, and in Mr. Lister’s own words.

“I would premise that the plano-concave form for the correcting flint
lens has in that quality a strong recommendation, particularly as it
obviates the danger of error which otherwise exists in centering the
two curves, and thereby admits of correct workmanship for a shorter
focus. To cement together also the two surfaces of the glass
diminishes by very nearly half the loss of light from reflection,
which is considerable at the numerous surfaces of a combination. I
have thought the clearness of the field and brightness of the picture
evidently increased by doing this; it prevents any dewiness or
vegetation from forming on the inner surfaces; and I see no
disadvantage to be anticipated from it if they are of identical
curves, and pressed closely together, and the cementing medium
permanently homogeneous.

“These two conditions then, that the flint lens shall be
plano-concave, and that it shall be joined by some cement to the
convex, seem desirable to be taken as a basis for the microscopic
object-glass, provided they can be reconciled with the destruction of
the spherical and chromatic aberrations of a large pencil.

“Now in every such glass that has been tried by me which has had its
correcting lens of either Swiss or English glass, with a double convex
of plate, and has been made achromatic by the form given to the outer
curve of the convex, the proportion has been such between the
refractive and dispersive powers of its lenses, that its figure has
been correct for rays issuing from some point in its axis not far from
its principal focus on its plane side, and either tending to a
conjugate focus within the tube of a microscope, or emerging nearly
parallel.

“Let A B (Fig. 13) be supposed such an object-glass, and let it be
roughly considered as a plano-convex lens, with a curve A C B running
through it, at which the spherical and chromatic errors are corrected
which are generated at the two outer surfaces; and let the glass be
thus free from aberration for rays F D E G issuing from the radiant
point F, H E being a perpendicular to the convex surface, and I D to
the plane one. Under these circumstances, the angle of emergence G E H
much exceeds that of incidence F D I, being probably nearly three
times as great.

“If the radiant is now made to approach the glass, so that the course
of the ray F D E G shall be more divergent from the axis, as the
angles of incidence and emergence become more nearly equal to each
other, the spherical aberration produced by the two will be found to
bear a less proportion to the opposing error of the single correcting
curve A C B; for such a focus therefore the rays will be
over-corrected.

[Illustration: Fig. 13.]

“But if F still approaches the glass, the angle of incidence
continues to increase with the increasing divergence of the ray, till
it will exceed that of emergence, which has in the meanwhile been
diminishing, and at length the spherical error produced by them will
recover its original proportion to the opposite error of the curve of
correction. When F has reached this point F´´ (at which the angle of
incidence does not exceed that of emergence so much as it had at first
come short of it), the rays again pass the glass free from spherical
aberration.

“If F be carried from hence towards the glass, or outwards from its
original place, the angle of incidence in the former case, or of
emergence in the latter, becomes disproportionately effective, and
either way the aberration exceeds the correction.

“These facts have been established by careful experiment: they accord
with every appearance in such combinations of the plano-convex glasses
as have come under my notice, and may, I believe, be extended to this
rule, that in general an achromatic object-glass, of which the inner
surfaces are in contact, or nearly so, will have on one side of it two
foci in its axis, for the rays proceeding from which it will be truly
corrected at a moderate aperture; that for the space between these two
points its spherical aberration will be over-corrected, and beyond
them either way under-corrected.

“The longer aplanatic focus may be found, when one of the plano-convex
object-glasses is placed in a microscope, by shortening the tube, if
the glass shows over-correction; if under-correction, by lengthening
it, or by bringing the rays together, should they be parallel or
divergent, by a very small good telescope. The shorter focus is got at
by sliding the glass before another of sufficient length and large
aperture that is finely corrected, and bringing it forwards till it
gives the reflection of a bright point from a globule of quicksilver,
sharp and free from mist, when the distance can be taken between the
glass and the object.

“The longer focus is the place at which to ascertain the utmost
aperture that may be given to the glass, and where, in the absence of
spherical error, its exact state of correction as to color is seen
most distinctly.

“The correction of the chromatic aberration, like that of the
spherical, tends to excess in the marginal rays; so that if a glass
which is achromatic, with a moderate aperture, has its cell opened
wider, the circle of rays thus added to the pencil will be rather
over-corrected as to color.

“The same tendency to over-correction is produced, if, without varying
the aperture, the divergence of the incident rays is much augmented,
as in an object-glass placed in front of another; but generally in
this position a part only of its aperture comes into use; so that the
two properties mentioned neutralize each other, and its chromatic
state remains unaltered. If, for example, the outstanding colors were
observed at the longer focus to be green and claret, which show that
the nearest practicable approach is made to the union of the spectrum,
they usually continue nearly the same for the whole space between the
foci, and for some distance beyond them either way.

“The places of these two foci and their proportions to each other
depend on a variety of circumstances. In several object-glasses that I
have had made for trial, plano-convex, with their inner surfaces
cemented, their diameters the radius of the flint lens, and their
color pretty well corrected, those composed of dense flint and light
plate have had the rays from the longer focus emerging nearly
parallel; and this focus has been not quite three times the distance
of the shorter from the glass: with English flint the rays have had
more convergence, and the shorter focus has borne a rather less
proportion to the longer.

“If the surfaces are not cemented, a striking effect is produced by
minute differences in their curves. It may give some idea of this,
that in a glass of which nearly the whole disk was covered with color
from contact of the lenses, the addition of a film of varnish, so thin
that this color was not destroyed by it, caused a sensible change in
the spherical correction.

“I have found that whatever extended the longer aplanatic focus, and
increased the convergence of its rays, diminished the relative length
of the shorter. Thus by turning to the concave lens the flatter
instead of the deeper side of a convex lens, whose radii were to each
other as 31 to 35, the pencil of the longer aplanatic focus, from
being greatly divergent, was brought to converge at a very small
distance behind the glass; and the length of the shorter focus, which
had been one-half that of the longer, became but one-sixth of it.

“The direction of the aplanatic pencils appears to be scarcely
affected by the differences in the thickness of glasses, if their
state as to color is the same.

“One other property of the double object-glass remains to be
mentioned, which is, that when the longer aplanatic focus is used, the
marginal rays of a pencil not coincident with the axis of the glass
are distorted, so that a coma is thrown outwards; while the contrary
effect of a coma directed towards the centre of the field is produced
by the rays from the shorter focus. These peculiarities of the coma
seem inseparable attendants on the two foci, and are as conspicuous in
the achromatic meniscus as in the plano-convex object-glass.

[Illustration: Fig. 14.]

“Of several purposes to which the particulars just given seem
applicable, I must at present confine myself to the most obvious one.
They furnish the means of destroying with the utmost ease both
aberrations in a large focal pencil, and of thus surmounting what has
hitherto been the chief obstacle to the perfection of the microscope.
And when it is considered that the curves of its diminutive
object-glasses have required to be at least as exactly proportioned as
those of a large telescope to give the image of a bright point equally
sharp and colorless, and that any change made to correct one
aberration was liable to disturb the other, some idea may be formed of
what the amount of that obstacle must have been. It will, however, be
evident that if any object-glass is but made achromatic, with its
lenses truly worked and cemented, so that their axes coincide, it may
with certainty be connected with another possessing the same
requisites and of suitable focus, so that the combination shall be
free from spherical error also in the centre of its field. For this
the rays have only to be received by the front glass B (Fig. 14) from
its shorter aplanatic focus F´´, and transmitted in the direction of
the longer correct pencil F A of the other glass A. It is desirable
that the latter pencil should neither converge to a very short focus
nor be more than very slightly if at all divergent; and a little
attention at first to the kind of glass used will keep it within this
range, the denser flint being suited to the glasses of shorter focus
and larger angle of aperture.

“The adjustment of the microscope is then perfected, if necessary, by
slightly varying the distance between the object-glasses; and after
that is done, the length of the tube which carries the eye-pieces may
be altered greatly without disturbing the correction, opposite errors
which balance each other being produced by the change.

“If the two glasses which in the diagram are drawn at some distance
apart are brought nearer together (if the place of A, for instance, is
carried to the dotted figure), the rays transmitted by B in the
direction of the longer aplanatic pencil of A will plainly be derived
from some point Z more distant than F´´, and lying between the
aplanatic foci of B; therefore (according to what has been stated)
this glass, and consequently the combination, will then be spherically
over-corrected. If, on the other hand, the distance between A and B is
increased, the opposite effects are of course produced.

“In combining several glasses together it is often convenient to
transmit an under-corrected pencil from the front glass, and to
counteract its error by over-correction in the middle one.

“Slight errors in color may in the same manner be destroyed by
opposite ones; and on the principles described we not only acquire
fine correction for the central ray, but by the opposite effects at
the two foci on the transverse pencil, all coma can be destroyed, and
the whole field rendered beautifully flat and distinct.”

Mr. Lister’s paper enters into further particulars, which are not
essential to the comprehension of the subject. It is sufficient to say
that his investigations and results proved to be of the highest value
to the practical optician, and the progress of improvement was in
consequence extremely rapid. The new principles were applied and
exhibited by Mr. Hugh Powell and Mr. Andrew Ross with a degree of
success which had never been anticipated; so perfect indeed were the
corrections given to the achromatic object-glass--so completely were
the errors of sphericity and dispersion balanced or destroyed--that
the circumstance of covering the object with a plate of the thinnest
glass or talc disturbed the corrections, if they had been adapted to
an uncovered object, and rendered an object-glass which was perfect
under one condition sensibly defective under the other.

This defect, if that should be called a defect which arose out of
improvement, was first discovered by Mr. Ross, who immediately
suggested the means of correcting it, and presented to the Society of
Arts, in 1837, a paper on the subject, which was published in the 51st
volume of their Transactions, and which, as it is, like Mr. Lister’s
essential to a full understanding of the ultimate refinements of the
instrument, we shall extract nearly in full:

“In the course of a practical investigation (says Mr. Ross) with the
view of constructing a combination of lenses for the object-glass of a
compound microscope, which should be free from the effects of
aberration, both for central and oblique pencils of great angle, I
combined the condition of the greatest possible distance between the
object and object-glass; for in object-glasses of short focal length
their closeness to the object has been an obstacle in many cases to
the use of high magnifying powers, and is a constant source of
inconvenience.

“In the improved combination, the diameter is only sufficient to admit
the proper pencil; the convex lenses are wrought to an edge, and the
concave have only sufficient thickness to support their figure;
consequently the combination is the thinnest possible, and it follows
that there will be the greatest distance between the object and the
object-glass. The focal length is one-eighth of an inch, having an
angular aperture of 60°, with a distance of 1-25th of an inch, and a
magnifying power of 970 times linear, with perfect definition on the
most difficult Podura scales. I have made object-glasses 1-16th of an
inch focal length; but as the angular aperture cannot be
advantageously increased, if the greatest distance between the object
and object-glass is preserved, their use will be very limited.

“The quality of the definition produced by an achromatic compound
microscope will depend upon the accuracy with which the aberrations,
both chromatic and spherical, are balanced, together with the general
perfection of the workmanship. Now, in Wollaston’s doublets, and
Holland’s triplets, there are no means of producing a balance of the
aberrations, as they are composed of convex lenses only; therefore the
best that can be done is to make the aberrations a minimum; the
remaining positive aberration in these forms produces its peculiar
effect upon objects (particularly the detail of the thin transparent
class), which may lead to misapprehension of their true structure; but
with the achromatic object-glass, where the aberrations are correctly
balanced, the most minute parts of an object are accurately displayed,
so that a satisfactory judgment of their character may be formed.

[Illustration: Fig. 15.]

[Illustration: Fig. 16.]

“It will be seen by Fig. 15, that when a certain angular pencil A O A´
proceeds from the object O, and is incident on the plane side of the
first lens, if the combination is removed from the object, as in Fig.
16, the extreme rays of the pencil impinge on the more marginal parts
of the glass, and as the refractions are greater here, the aberrations
will be greater also. Now, if two compound object-glasses have their
aberrations balanced, one being situated as in Fig. 15, and the other
as in Fig. 16, and the same disturbing power applied to both, that in
which the angles of incidence and the aberrations are small will not
be so much disturbed as where the angles are great, and where
consequently the aberrations increase rapidly.

“When an object-glass has its aberrations balanced for viewing an
opaque object, and it is required to examine that object by
transmitted light, the correction will remain; but if it is necessary
to immerse the object in a fluid, or to cover it with glass or talc,
an aberration will arise from these circumstances, which will disturb
the previous correction, and consequently deteriorate the definition;
and this effect will be more obvious with the increase of the distance
between the object and the object-glass.

[Illustration: Fig. 17.]

“The aberration produced with diverging rays by a piece of flat and
parallel glass, such as would be used for covering an object, is
represented at Fig. 17, where G G G G is the refracting medium, or
piece of glass covering the object O; O P, the axis of the pencil,
perpendicular to the flat surfaces; O T, a ray near the axis; and O
T´, the extreme ray of the pencil incident on the under surface of the
glass; then T R, T´ R´, will be the directions of the rays in the
medium, and R E, R´ E´, those of the emergent rays. Now if the course
of these rays is continued, as by the dotted lines, they will be found
to intersect the axis at different distances, X and Y, from the
surface of the glass; and the distance X Y is the aberration produced
by the medium which, as before stated, interferes with the previously
balanced aberrations of the several lenses composing the
object-glass. There are many cases of this, but the one here selected
serves best to illustrate the principle. I need not encumber the
description with the theoretical determination of this quantity, as it
varies with exceedingly minute circumstances which we cannot
accurately control; such as the distance of the object from the under
side of the glass, and the slightest difference in the thickness of
the glass itself; and if these data could be readily obtained, the
knowledge would be of no utility in making the correction, that being
wholly of a practical nature.

“If an object-glass is constructed as represented in Fig. 16, where
the posterior combination P and the middle M have together an excess
of negative aberration, and if this be corrected by the anterior
combination A, having an excess of positive aberration, then this
latter combination can be made to act more or less powerfully upon P
and M, by making it approach to or recede from them; for when the
three are in close contact, the distance of the object from the
object-glass is greatest; and consequently the rays from the object
are diverging from a point at a greater distance than when the
combinations are separated; and as a lens bends the rays more, or acts
with greater effect, the more distant the object is from which the
rays diverge, the effect of the anterior combination A upon the other
two, P and M, will vary with its distance from thence. When therefore
the correction of the whole is effected for an opaque object with a
certain distance between the anterior and middle combination, if they
are then put in contact, the distance between the object and
object-glass will be increased; consequently the anterior combination
will act more powerfully, and the whole will have an excess of
positive aberration. Now the effect of the aberration produced by a
piece of flat and parallel glass being of the negative character, it
is obvious that the above considerations suggest the means of
correction by moving the lenses nearer together, till the positive
aberration thereby produced balances the negative aberration caused by
the medium.

“The preceding refers only to the spherical aberration, but the effect
of the chromatic is also seen when an object is covered with a piece
of glass; for, in the course of my experiments, I observed that it
produced a chromatic thickening of the outline of the Podura and
other delicate scales; and if diverging rays near the axis and at the
margin are projected through a piece of flat parallel glass, with the
various indices of refraction for the different colors, it will be
seen that each ray will emerge separated into a beam consisting of the
component colors of the ray, and that each beam is widely different in
form. This difference, being magnified by the power of the microscope,
readily accounts for the chromatic thickening of the outline just
mentioned. Therefore to obtain the finest definition of extremely
delicate and minute objects, they should be viewed without a covering;
if it be desirable to immerse them in a fluid, they should be covered
with the thinnest possible film of talc, as, from the character of the
chromatic aberration, it will be seen that varying the distances of
the combinations will not sensibly affect the correction; though
object-lenses may be made to include a given fluid or solid medium in
their correction for color.

[Illustration: Fig. 18.]

“The mechanism for applying these principles to the correction of an
object-glass under the various circumstances, is represented in Fig.
18, where the anterior lens is set in the end of a tube A A, which
slides on the cylinder B containing the remainder of the combination;
the tube A A, holding the lens nearest the object, may then be moved
upon the cylinder B, for the purpose of varying the distance according
to the thickness of the glass covering the object, by turning the
screwed ring C C, or more simply by sliding the one on the other, and
clamping them together when adjusted. An aperture is made in the tube
A, within which is seen a mark engraved on the cylinder, and on the
edge of which are two marks, a longer and a shorter, engraved upon the
tube. When the mark on the cylinder coincides with the longer mark on
the tube, the adjustment is perfect for an uncovered object; and when
the coincidence is with the short mark, the proper distance is
obtained to balance the aberrations produced by glass one-hundredth of
an inch thick, and such glass can be readily supplied.

“It is hardly necessary to observe, that the necessity for this
correction is wholly independent of any particular construction of the
object-glass; as in all cases where the object-glass is corrected for
an object uncovered, any covering of glass will create a different
value of aberration to the first lens, which previously balanced the
aberration resulting from the rest of the lenses; and as this
disturbance is effected at the first refraction, it is independent of
the other part of the combination. The visibility of the effect
depends on the distance of the object from the object-glass, the angle
of the pencil transmitted, the focal length of the combination, the
thickness of the glass covering the object, and the general perfection
of the corrections for chromatism and the oblique pencils.

“With this adjusting object-glass, therefore, we can have the
requisites of the greatest possible distance between the object and
object-glass, an intense and sharply defined image throughout the
field from the large pencil transmitted, and the accurate correction
of the aberrations; also, by the adjustment, the means of preserving
that correction under all the varied circumstances in which it may be
necessary to place an object for the purpose of observation.”

In the annexed engraving, Fig. 19, we have shown the triple achromatic
object-glass in connection with the eye-piece consisting of the
field-glass F F, and the eye-glass E E, forming together the modern
achromatic microscope. The course of the light is shown by drawing
three rays from the centre and three from each end of the object O.
These rays would, if left to themselves, form an image of the object
at A A, but being bent and converged by the field-glass F F, they form
the image at B B, where a stop is placed to intercept all light except
what is required for the formation of the image. From B B therefore
the rays proceed to the eye-glass exactly as has been described in
reference to the simple microscope and to the compound of two glasses.

[Illustration: Fig. 19.]

If we stopped here we should convey a very imperfect idea of the
beautiful series of corrections effected by the eye-piece, and which
were first pointed out in detail in a paper on the subject published
by Mr. Varley in the 51st volume of the Transactions of the Society of
Arts. The eye-piece in question was invented by Huyghens for
telescopes, with no other view than that of diminishing the spherical
aberration by producing the refractions at two glasses instead of one,
and of increasing the field of view. It was reserved for Boscovich to
point out that Huyghens had by this arrangement accidentally corrected
a great part of the chromatic aberration, and this subject is further
investigated with much skill in two papers by Professor Airy in the
_Cambridge Philosophical Transactions_, to which we refer the
mathematical reader. These investigations apply chiefly to the
telescope, where the small pencils of light and great distance of the
object exclude considerations which become important in the
microscope, and which are well pointed out in Mr. Varley’s paper
before mentioned.

[Illustration: Fig. 20.]

Let Fig. 20 represent the Huyghenean eye-piece of a microscope; F F
and E E being the field-glass and eye-glass, and L M N the two extreme
rays of each of the three pencils, emanating from the centre and ends
of the object, of which, but for the field-glass, a series of colored
images would be formed from R R to B B; those near R R being red,
those near B B blue, and the intermediate ones green, yellow, and so
on, corresponding with the colors of the prismatic spectrum. This
order of colors, it will be observed, is the reverse of that
described in treating of the common compound microscope (Fig. 12), in
which the single object-glass projected the red image beyond the blue.
The effect just described, of projecting the blue image beyond the
red, is purposely produced for reasons presently to be given, and is
called over-correcting the object-glass as to color. It is to be
observed also that the images B B and R R are curved in the wrong
direction to be distinctly seen by a convex eye-lens, and this is a
further defect of the compound microscope of two lenses. But the
field-glass, at the same time that it bends the rays and converges
them to foci at B´ B´ and R´ R´, also reverses the curvature of the
images as there shown, and gives them the form best adapted for
distinct vision by the eye-glass E E. The field-glass has at the same
time brought the blue and red images closer together, so that they are
adapted to pass uncolored through the eye-glass. To render this
important point more intelligible, let it be supposed that the
object-glass had not been over-corrected, that it had been perfectly
achromatic; the rays would then have become colored as soon as they
had passed the field-glass; the blue rays, to take the central pencil,
for example, would converge at _b_ and the red rays at _r_, which is
just the reverse of what the eye-lens requires; for as its blue focus
is also shorter than its red, it would demand rather that the blue
image should be at _r_ and the red at _b_. This effect we have shown
to be produced by the over-correction of the object-glass, which
protrudes the blue foci B B as much beyond the red foci R R as the sum
of the distances between the red and blue foci of the field-lens and
eye-lens; so that the separation B R is exactly taken up in passing
through those two lenses, and the whole of the colors coincide as to
focal distance as soon as the rays have passed the eye-lens. But while
they coincide as to distance, they differ in another respect; the blue
images are rendered smaller than the red by the superior refractive
power of the field-glass upon the blue rays. In tracing the pencil L,
for instance, it will be noticed that after passing the field-glass,
two sets of lines are drawn, one whole, and one dotted, the former
representing the red, and the latter the blue rays. This is the
accidental effect in the Huyghenean eye-piece pointed out by
Boscovich. This separation into colors at the field-glass is like the
over-correction of the object-glass; it leads to a subsequent complete
correction. For if the differently colored rays were kept together
till they reached the eye-glass, they would then become colored, and
present colored images to the eye; but fortunately, and most
beautifully, the separation effected by the field-glass causes the
blue rays to fall so much nearer the centre of the eye-glass, where,
owing to the spherical figure, the refractive power is less than at
the margin, that the spherical error of the eye-lens constitutes a
nearly perfect balance to the chromatic dispersion of the field-lens,
and the red and blue rays L´ and L´´ emerge sensibly parallel,
presenting, in consequence, the perfect definition of a single point
to the eye. The same reasoning is true of the intermediate colors and
of the other pencils.

From what has been stated it is obvious that we mean by an achromatic
object-glass one in which the usual order of dispersion is so far
reversed that the light, after undergoing the singularly beautiful
series of changes effected by the eye-piece, shall come uncolored to
the eye. We can give no specific rules for producing these results.
Close study of the formulæ for achromatism given by the celebrated
mathematicians we have quoted will do much, but the principles must be
brought to the test of repeated experiment. Nor will the experiments
be worth anything, unless the curves be most accurately measured and
worked, and the lenses centered and adjusted with a degree of
precision which, to those who are familiar only with telescopes, will
be quite unprecedented.

The Huyghenean eye-piece which we have described is the best for
merely optical purposes, but when it is required to measure the
magnified image, we use the eye-piece invented by Mr. Ramsden, and
called, from its purpose, the micrometer eye-piece. When it is stated
that we sometimes require to measure portions of animal or vegetable
matter a hundred times smaller than any divisions that can be
artificially made on any measuring instrument, the advantage of
applying the scale to the magnified image will be obvious, as compared
with the application of engraved or mechanical micrometers to the
stage of the instrument.

The arrangement is shown in Fig. 21, where E E and F F are the eye and
field glass, the latter having now its plane face towards the object.
The rays from the object are here made to converge at A A, immediately
in front of the field-glass, and here also is placed a plane glass on
which are engraved divisions of a hundredth of an inch or less. The
markings of these divisions come into focus therefore at the same time
as the image of the object, and both are distinctly seen together.
Thus the measure of the magnified image is given by mere inspection,
and the value of such measures in reference to the real object may be
obtained thus, which, when once obtained, is constant for the same
object-glass. Place on the stage of the instrument a divided scale the
value of which is known, and viewing this scale as the microscopic
object, observe how many of the divisions on the scale attached to the
eye-piece correspond with one of those in the magnified image. If, for
instance, ten of those in the eye-piece correspond with one of those in
the image, and if the divisions are known to be equal, then the image
is ten times larger than the object, and the dimensions of the object
are ten times less than indicated by the micrometer. If the divisions
on the micrometer and on the magnified scale were not equal, it
becomes a mere rule-of-three sum, but in general this trouble is taken
by the maker of the instrument, who furnishes a table showing the
value of each division of the micrometer for every object-glass with
which it may be used.

[Illustration: Fig. 21.]

While on the subject of measuring it may be well to explain the mode
of ascertaining the magnifying power of the compound microscope, which
is generally taken on the assumption before mentioned, that the naked
eye sees most distinctly at the distance of ten inches.

Place on the stage of the instrument, as before, a known divided
scale, and when it is distinctly seen, hold a rule at ten inches
distance from the disengaged eye, so that it may be seen by that eye,
overlapping or lying by side of the magnified picture of the other
scale. Then move the rule till one or more of its known divisions
correspond with a number of those in the magnified scale, and a
comparison of the two gives the magnifying power.

Having now explained the optical principles of the achromatic compound
microscope, it remains only to describe the mechanical arrangements
for giving those principles their full effect. The mechanism of a
microscope is of much more importance than might be imagined by those
who have not studied the subject. In the first place, steadiness, or
freedom from vibration, and most particularly freedom from any
vibrations which are not equally communicated to the object under
examination, and to the lenses by which it is viewed, is a point of
the utmost consequence. When, for instance, the body containing the
lenses is screwed by its lower extremity to a horizontal arm, we have
one of the most vibratory forms conceivable; it is precisely the form
of the inverted pendulum, which is expressly contrived to indicate
otherwise insensible vibrations. The tremor necessarily attendant on
such an arrangement is magnified by the whole power of the instrument;
and as the object on the stage partakes of this tremor in a
comparatively insensible degree, the image is seen to oscillate so
rapidly, as in some cases to be wholly undistinguishable. Such
microscopes cannot possibly be used with high powers in ordinary
houses abutting on any paved streets through which carriages are
passing, nor indeed are they adapted to be used in houses in which the
ordinary internal sources of shaking exist.

One of the best modes of mounting a compound microscope is shown in
the annexed view (Fig. 22), which, though too minute to exhibit all
the details, will serve to explain the chief features of the
arrangement.

A massy pillar A is screwed into a solid tripod B, and is surmounted
by a strong joint at C, on which the whole instrument turns, so as to
enable it to take a perfectly horizontal or vertical position, or any
intermediate angle, such, for instance, as that shown in the
engraving.

This movable portion of the instrument consists of one solid casting D
E F G; from F to G being a thick pierced plate carrying the stage and
its appendages. The compound body H is attached to the bar D E, and
moves up and down upon it by a rack and pinion worked by either of the
milled heads K. The piece D E F G is attached to the pillar by the
joint C, which being the source of the required movement in the
instrument, is obviously its weakest part, and about which no doubt
considerable vibration takes place. But inasmuch as the piece D E F G
of necessity transmits such vibrations equally to the body of the
microscope and to the objects on the stage, they hold always the same
relative position, and no _visible_ vibration is caused, how much
soever may really exist. To the under side of the stage is attached a
circular stem L, on which slides the mirror M, plane on one side and
concave on the other, to reflect the light through the aperture in the
stage. Beneath the stage is a circular revolving plate containing
three apertures of various sizes, to limit the angle of the pencil of
light which shall be allowed to fall on the object under examination.
Besides these conveniences the stage has a double movement produced by
two racks at right angles to each other, and worked by milled heads
beneath. It has also the usual appendages of forceps to hold minute
objects, and a lens to condense the light upon them, all of which are
well understood, and if not, will be rendered more intelligible by a
few minutes’ examination of a microscope than by the most lengthened
description. One other point remains to be noticed. The movement
produced by the milled head K is not sufficiently delicate to adjust
the focus of very powerful lenses, nor indeed is any rack movement.
Only the finest screws are adapted to this purpose; and even these are
improved by means for reducing the rapidity of the screw’s movement.
For this purpose the lower end of the compound body H, which carries
the object-glass, consists of a piece of smaller tube sliding in
parallel guides in the main body, and kept constantly pressed upwards
by a spiral spring but it can be drawn downward by a lever crossing
the body, and acted on by an extremely fine screw whose milled head
is seen at N, and the fineness of which is tripled by means of the
lever through which it acts on the object-glass. The instrument is of
course roughly adjusted by the rack movement, and finished by the
screw, or by such other means as are chosen for the purpose. One very
ingenious contrivance, but applied to the stage, instead of the body
of the microscope, invented by Mr. Powell, will be found described in
the 50th volume of the Transactions of the Society of Arts.

[Illustration: Fig. 22.]

The greater part of the directions for viewing and illuminating
objects given in reference to the simple microscope are applicable to
the compound. An argand lamp placed in the focus of a large detached
lens so as to throw parallel rays upon the mirror, is the best
artificial light; and for opaque objects the light so thrown up may be
reflected by metallic specula (called, from their inventor,
Lieberkhuns) attached to the object-glasses.

It has been recently proposed by Sir David Brewster and by M. Dujardin
to render the Wollaston condenser achromatic, and they have
accordingly been made with three pairs of achromatic lenses instead of
the single lens before described, with very excellent effect. The
last-mentioned gentleman has also projected an ingenious apparatus,
called the Hyptioscope, attached to the eye-piece for the purpose of
erecting the magnified picture.

The erector commonly applied to the compound microscope consists of a
pair of lenses acting like the erecting eye-piece of the telescope.
But this, though it is convenient for the purpose of dissection, very
much impairs the optical performance of the instrument.

[Illustration: Fig. 23.]

For drawing the images presented by the microscope the best apparatus
consists of a mirror M (Fig. 23), composed of a thin piece of rather
dark-colored glass cemented on to a piece of plate-glass inclined at
an angle of 45° in front of the eye-glass E. The light escaping from
the eye-glass is assisted in its reflection upwards to the eye by the
dark glass, which effects the further useful purpose of rendering the
paper less brilliant, and thus enabling the eye better to see the
reflected image. The lens L below the reflector is to cause the light
from the paper and pencil to diverge from the same distance as that
received from the eye-glass; in other words, to cause it to reach the
eye in parallel lines.

[Illustration: Fig. 24.]

Dr. Wollaston’s camera lucida, as shown in Fig. 24, is sometimes
attached to the eye-piece of the microscope for the same purpose. In
this instrument the rays suffer two internal reflections within the
glass prism, as will be seen explained in the article “Camera Lucida.”
In this minute figure we have omitted to trace the reflected rays,
merely to avoid confusion.

[Illustration: Fig. 25.]

[Illustration: Fig. 26.]

[Illustration: Fig. 27.]

Annexed are four engravings of microscopic objects, the true character
of which it is, however, impossible to give in wood, and is difficult
indeed to accomplish by any description of engraving.

[Illustration: Fig. 28.]

Fig. 25 shows a scale of the small insect called Podura Plumbea, the
common Skiptail, magnified about five hundred times. To define the
markings on this scale clearly is the highest test of a deep
achromatic object-glass; and this drawing is given rather to explain
what the observer should look for, than as a very correct
representation. Fig. 26 is a scale or feather of the Menelaus
Butterfly; Fig. 27 is the hair of a singular insect, the Dermestes;
and Fig. 28 is a longitudinal cutting of fir, showing the circular
glands on the vessels which distinguish coniferous woods. These latter
objects may be seen by half-inch or quarter-inch achromatic glasses.
Opaque objects are generally better exhibited by inch and two-inch
glasses, when a general view of them is required, and by higher powers
when we wish to examine their minute structure. In the latter case the
light must be obtained by condensing lenses instead of the metallic
specula.

Although the reflecting microscope is now very little used, it may be
expected that we should mention it. In this instrument, at Fig. 29,
the object O is reflected by the inclined face of the mirror M, and
the rays are again reflected and converged by the ellipsoidal
reflector R R, which effects the same purpose as the object-glass of
the compound microscope. It forms an image which is not susceptible of
the over-correction as to color before described, and which therefore
becomes colored in passing through the eye-piece. This fact, and the
loss of light by reflection, will probably always render the
reflecting microscope inferior to the achromatic refracting.

[Illustration: Fig. 29.]

The solar microscope has been so nearly superseded by the
oxy-hydrogen, that a brief description of the latter must suffice,
particularly as their optical principles are similar.

The primary object in both is to throw an intense light upon the
object, which is sometimes done by mirrors, and sometimes by lenses.
In Fig. 30, L represents the cylinder of burning lime, R R the
reflector, which concentrates the light upon the object O O; the rays
from which, passing through the two plano-convex lenses, are brought
to foci upon a screen placed at a great distance, and upon which is
formed the magnified image.

[Illustration: Fig. 30.]

Fig. 31 shows a combination of lenses to condense the light upon the
object. In either case the optical arrangements by which the image is
formed admit of the same perfection as those which have been described
for the compound microscopes. A few achromatic glasses for
oxy-hydrogen microscopes have been made, and they will ultimately
become valuable instruments for illustrating lectures on natural
history and physiology. One made by Mr. Ross was exhibited a few
months since at the Society of Arts to illustrate a lecture on the
physiology of woods. It should be observed, however, that the
oxy-hydrogen or solar microscope requires either a spherical screen,
or that the objects should be mounted between spherical glasses, in
order to bring the whole into focus at one time. This latter plan was
adopted on the occasion just mentioned with perfect success.

[Illustration: Fig. 31.]