On the OPTICAL POWERS of the MICROSCOPE.
By P. G. RYLANDS, Esq.
THE period has not yet arrived when even all those who
employ the microscope methodically, as a means of scientific
investigation, possess an intelligent comprehension of the
principles on which it is constructed and the nature of its
powers as an optical instrument. There is a large region
beyond mere manipulation, into which few apparently care to
enter. The writers of our introductory treatises have been
curiously imitative in dealing with this portion of their duty.
They indulge us with nearly the same very elementary
diagrams, refer us to Boss's capital article " Microscope," in
the ' Penny Cyclopaedia/ and then, with here and there only
a trifling exception, leave the matter pretty much as they
found it. Surely the time has arrived which calls for more
than this; Avhen an optical treatise on the microscope, worthy
of the name, is not only desired by the few but required for
the many. In the meantime, until this boon be granted,
your pages will continue to do good service by dealing with
these matters, and, as heretofore, in such a manner as to
secure to your readers a large store of information.
I had hoped that some more able hand than mine would
have undertaken the subject on which I now propose to occupy
a portion of your space; but it has not been so, and I therefore offer the following remarks on the optical powers of these
instruments to your readers, without further introduction.
The first power which I shall mention requires little
remark. It is the one which has attracted the greatest share
of attention, from being that which constitutes the most
prominent characteristic of the microscope. I mean magnifying power. For our present purpose it is sufficient to
remind the reader that magnifying power has to do with size,
and size only. It expresses simply the dimensions of the
enlarged image presented to the eye of observers, as compared
with the size of the natural object when viewed at the adopted
standard distance, ten inches, from the eye. Or, in other
words, it may be said to express the magnitude of the angle
subtended by the enlarged image, at the eye, as compared
with that subtended by the object itself under the circumstances named.
The second, or penetrating power, is a subject which
cannot be dismissed so easily. The origin of the term will
be found in the 'Phil. Trans.' for 1800, in an article by Sir
William Herschel, entitled, " On the Power of Penetrating
28
ltYLANDS, OX THE MICROSCOPE.
into Space possessed by Telescopes." In that article we are
told that when, owing to the darkness, a distant churchsteeple was invisible; a certain telescope described showed the
time by the clock upon it very clearly. This, adds Sir
William, was not owing to magnifying power alone, for the
steeple could not be discerned by the naked eye.
Following out the suggestions of this incident in a truly
philosophic spirit, the author has given us, in the article
referred to, all that is required to apply the term correctly to
the microscope.
Unless I am mistaken, the first use of the word in connexion with the microscope occurs in the 'Microscopic
Cabinet.' Judging from the manner in which it is there
employed, we should perhaps define it as synonymous with
angular aperture. Most persons, I fancy, were at a loss to
see the connexion between the name and the thing signified,
for, while some few writers were content to adopt the term
with the explanation given, others, considering it an entire
misnomer, began to speak of angle of aperture, and have
since defined "penetrating power" to mean superior definition,
thickness of field, &c. This has naturally led to confusion,
and that not amongst those only who make small pretensions.
Dr. Carpenter, in his ' Manual/ tells us that the penetrating
power of an object-glass " depends upon the degree of distinctness with which parts of the object that are a little out
of focus can be discerned," or, in other words, longitudinal
focal range or thickness of field. The editors of the ' Micrographic Dictionary' mention " two distinct kinds of penetrating power," one the same as defining power, and the other
angular aperture, combined with oblique illumination. They
propose that the term should be laid aside as tending to confusion ! I think it may be shown that the confusion is not
altogether attributable to the term, and that the whole
difficulty not only admits of an easy solution, but that the
subject is sufficiently important to warrant a careful investigation.
The authors of the ' Microscopic Cabinet' had in their
minds, there is no doubt, the true origin and meaning of the
term. They erred in not giving a sufficient explanation.
They borrowed it from the telescope, and, seeing that the
telescope and the microscope are essentially the same instrument, but modified to adapt them to different purposes, the
use they made of it was perfectly justifiable; at the same
time it must plainly be used to mean the same thing in both
cases. Sir William Herschel has shown, in the article
already referred to, that the words penetrating power have a
RYLANDS, ON THE MICROSCOPE.
29
definite meaning, and that the amount of this power possessed
by a telescope can be obtained by calculation. This must be
true of a microscope also. This power must not be confused
Avith angular aperture, which has reference to the objective
alone; neither has it any connexion with either definition or
thickness of field. In one word, as magnifying power
expresses the angle subtended by an object or image at the
eye of the observer, so penetrating power is the measure of
the angle subtended by the eye at the object, or the equivalent
of that angle in the case of telescopic or microscopic vision.
The one is the measure of size, the other of brightness. This
latter, however, must not be confused with "illumination."
The one power is neither less important nor less essential to
distinct vision than the other. There required little magnifying power, and there was no illumination, in the case of the
church-steeple, still the hour could be read on the dial. It is
the power by which this was accomplished that we have to
consider.*
Referring those who wish to investigate this matter fully
to the paper in the 'Phil. Trans./ I shall content myself with
making use of such portions of Sir W. HerschePs formula as
is sufficient for our present purpose. This may be given as
follows:
Putting P for the penetrating power of a refracting telescope,
w for the proportion of light which remains for
purposes of vision after passing through a
single lens,
n for the number of lenses in the instrument,
A for the available diameter of the object-glass,
and a for the diameter of the pupil of the eye; we
have—
P=
V
fj*:.
a
By applying this to the microscope, we shall obtain that
which alone can be correctly called " penetrating power."
W e shall see clearly in what the value of increased angular
aperture really consists, and I think we shall come to the
conclusion that the term under consideration represents something sufficiently important to prevent its being laid aside on
account of any foregone carelessness or confusion.
The great distinction between the telescope and the micro* We are not told what magnifying power was employed in viewing the
church-steeple, but I gathered from something in the paper that the penetrating power of the telescope was about forty times that of natural vision.
30
RYLANDS, ON THE MICROSCOPE.
scope exists in the fact that while the former, practically
speaking, is suited to receive parallel rays from a distant
object, the latter has to deal with rays which are sensibly
divergent from a closely approximate point. On this account
the formula will require some modification.
In natural vision the rays emergent from any point of an
object, which are employed for the purposes of vision, form a
cone having the area of the pupil of the eye for its base.
When the microscope is applied, the available aperture of its
anterior lens takes the place of the pupil, and a cone of very
different proportions is substituted. It is on the relative
magnitude of the angles at the vertices of these cones—
allowance being made in the latter case for the light lost in
its passage through the instrument—that penetrating power
depends. Thus the connexion with angular aperture is seen
to be sufficiently close to form some excuse, perhaps, for one
definition which has been given.
It is only necessary to premise further that the formula
may be stated in a rather more convenient form, thus :
If A be now made to stand for half the angle of aperture
of an objective, and a half the angle subtended by the pupil
of the eye at ten inches, instead of the diameters of these
apertures as before, the formula applicable to microscopes
will be—
tan A ,—
P=
VaT
tan a
Further, if we are content to adopt 0-2 inch as the mean
or standard diameter of the pupil, which is sufficiently exact
for general purposes, the equation becomes—
P = 100 tan A \/~^- *
* Erom two series of measurements of the diameter of the pupil I obtained the following results:
Iu full daylight, near the window of a well-lighted room, 0'15 in.; at the
most convenient distance for distinct vision from a Highley's argand gas
lamp, 0 2 5 in.; the mean of the whole being 0 2 iu.
As simplicity is a great matter in such calculations as the one now under
notice, it may be worth while to remark, that if the value of xn for the instruments of our best English makers should be found to be sufficiently constant, which is quite probable, the expression, so far as they are concerned,
may be reduced to a single operation, and the value of P taken almost at
sight from a table of tangents.
The angle of aperture of an objective should be obtained by Mr. Lister's
method (' Phil. Trans.,' vol. exxi; see also Quekett, p. 464), separately with
each eye-piece and length of draw-tube.
RYLANDS, ON THE MICROSCOPE.
31
I shall not stay here to point out the advantages of obtaining the amount of penetrating power in the manner described ; this, and all that need be said further on the subject, will, I trust, be sufficiently clear from what follows.
The third power—the visual power of microscopes—is one
which has been so rarely recognised as distinct, that probably
even the name will be new to most of your readers.
It is well known that the extent to which vision is aided
by a telescope (for we must be indebted once more to that
instrument) is very rarely expressed by its magnifying power;
that two instruments, equal in both magnifying and defining
power, may differ widely in their visual power; and as in the
telescope, so in the microscope, for they are essentially the
same in principle.
Perhaps an example will most easily explain what is meant
by visual power, and its connexion with the two already
described.
Some years ago, when my attention was first directed to
this subject, I made the following experiment with a common
marine " day and night glass;" Having extemporised a
" pancratic tube," by which the power of the instrument was
increased to 43, I directed it to a sign-board at the distance
of 489 yards. This object had the double advantage of being
readily approachable in a direct line, and of having upon it
letters of various sizes, so that it exhibited several degrees of
legibility. Its distance, too, was ascertainable with sufficient
exactness. Having impressed upon my mind the appearance
of the board as presented by the telescope, I approached it
until it was as legible and looked the same to the naked eye.
From the peculiarity of the object, this point was ascertained
at once within the limit of three or four feet. According to
the popular idea, I ought to have been at one forty-third the
original distance, the power of the glass being 43. Instead
of this, however, I had passed over only fifteen sixteenths of
the space; that is, the visual power was only 16, although
the magnifying power was 43. This was not quite what I
expected, but the examination was not long delayed.
In order that an object shall be seen through a telescope
(or a microscope) as when viewed at one forty-third the
distance, it is necessary, not only that the angle subtended
by it at the eye—the magnifying power—but also the angle
subtended by the eye at the object—the penetrating power—
shall be increased forty-three-fold. When this is the case,
the visual power will be forty-three also. If we approach an
object bodily, these angles naturally increase in the same
proportion, but it is not so where optical instruments are
32
RTLANOS, ON THE MICROSCOPE.
used. Still, visual power must be a compound of the other
two, and calling the three powers M, P, and V respectively,
from their initials, we ought to have, in all cases—
V = -/MP
To test the experiment just related by this, the value of
P having been carefully determined at the time, we find
M = 43, P = 6, and
V = 1/43 x 6 = 1606
The value of V, as obtained by measurement, was 16"3,
which is as near as could be expected under the circumstances, although every precaution was taken to ensure correctness. Visual power is, therefore, essentially the power
of a telescope.
I need not extend this already lengthy article to show
how entirely all this is applicable to the microscope also.
I do not say that the variation will be as great in that
instrument as in the telescope, for the construction is not
only more uniform,* but the peculiarities of microscopic
vision confine the matter in one direction, at least within
narrower limits; but 1 do say that the time is long gone by
for the distinctions I have pointed out to be neglected, or for
us to have important and valuable terms drifting to and fro
in our literature without any fixed meaning, threatened with
expulsion by those in high quarters, and defined by each
succeeding writer according as it seems good in his own eyes.
Neither should yre suffer ourselves to be deceived by large
numbers, expressing amplification, it may be, but failing to
afford us their promised aid in our search after natural truth.
Fortunately the discoveries of the past quarter of a century
have led us in the right direction; what we seem now to
require is simply a correct determination of the value of wn in
the foregoing formulae; we shall then be able, with very little
trouble, to estimate the visual powers of our instruments,
and shall have our efforts systematically directed to the increase and perfection of that upon which their value mainly
depends.
* This is more especially true of tbe instruments by our best English
makers. The relative vaJue of others will probably appear in a strong light
when they are submitted to the test of visual power. The following approximate estimates, obtained from a French instrument, will not be without interest:
1st combination, M = 400, V (highest estimate) 145.
2d
„
M = 540, V, cannot exceed
205.
3d
„
M = 870, V, does not reach
320.