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.