On the OPTICAL POWERS of the MICROSCOPE. By P. G. RYLANDS, Esq.

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1 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

2 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

3 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." We 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.

4 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, 025 in.; the mean of the whole being 02 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 x n 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.

5 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

6 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 w n 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) d M = 540, V, cannot exceed d M = 870, V, does not reach 320.