shows the application of these powers to all grades of work, from that which is ordinarily done with a pocket lens to the extreme limits of microscopical vision:

It has not been my purpose to lay down any single set of objectives as the only proper one, but to indicate the principles on which selection should be made, and the relation of aperture to amplifying power, and to show that there is at present no good theoretical reason for the use of objectives of greater amplifying power than the 1/8 in."

Dr. Blackham, it will be seen, advocates the use of eye-pieces as high as 1/4 in. which is largely in excess of Prof. Abbe's figures, which do not go beyond an amplification of 15 times.*

Mr. J. D. Cox believes † " Dr. Blackham has the verdict of experience with him when he says four or five lenses with a proper number of eye-pieces will cover the whole range of microscopical examination. In such a number of lenses you may get all the necessary combination of the three qualities of angle, power, and working distance which you may need. Different investigators may choose different series, but no one need have a greater number in the series. Economy is to be considered in deciding whether we shall choose one or another lens; but this is also consistent with the state

* See this Journal, iii. (1883) p. 808.

† Proc. Amer. Soc. Micr., 6th Ann. Meeting, 1883, pp. 229-30.

ment that all the elements, including economy, may be combined in such a small series. The lowest glass may be anything from a 11⁄2 in. to a 3 in. If of an angle of 20° to 25° it will have plenty of working distance and penetration. The next glass should be of 40° angle, or very near it, as this is the maximum normal angle for binocular vision of opaque objects. Its working distance should be enough to allow the use of dissecting-needles under it, and the easy illumination of dry opaque objects. These conditions are found in good glasses ranging from 1 in. to 1/2 in. objectives. The third glass should also be a dry glass, having working distance enough to accommodate work with the animalcule-cages and compressors, and upon rough histological material. Its angle should be from 100° upwards, to as wide an angle as is consistent with the necessary working distance. These conditions are found in glasses ranging from 4/10 in. objectives to 1/6 in. Beyond the three lenses thus generally described, a single immersion lens of widest possible angle seems to give all the advantages that can be attained in the present condition of the art of making objectives.

In the third and fourth of the series, the angle should be the widest consistent with the other conditions specially named, and this is the only demand of the practical microscopist in which, as it seems to me, the phrase 'wide angle' can have any appropriate place."

*

Dr. J. Edwards Smith says that he has practically, for the past four years, confined himself to the use of four object-glasses, namely, a 1 in. or 2/3 in. of 45° or 50°, a 1/2 in. of 38°, a 1/6 in. immersion, balsam angle ranging from, say 87° to 95°, according to the position of its collar, and a 1/10 in. immersion having a constant angle of 100°. Of the last two glasses, the 1/6 in. has a working distance of 1/50 of an inch. The 1/10 in. will work readily through covers 1/100 of an inch thick. A large amount of his work is on urinary deposits. For the examination of malignant growths and for minute pathology generally, a dry 1/4 in. of 100° is in reserve.

Mr. E. M. Nelson's † view is to give the beginner a 1 in. and a 2/3 in.; later on a 1/6 in. may be added, and as a higher power a 1/12 in. immersion of 1.43 N.A. "For all working purposes the battery would then be complete, and the microscopist equipped to repeat any results hitherto obtained. As luxuries, a 3 in., 1/3 in., and 1/25 in. might be got. It sometimes happened that the high initial magnifying power of the 1/25 in. enabled the observer to find some hitherto unknown object, or portion of an object, more easily than with the 1/12 in.; but when once found its details of structure would be better made out with the 1/12 in. So far it had not been possible to construct a 1/25 in. as perfectly as a 1/12 in., nor with so high an aperture; hence it would rarely bear any eye-piece beyond the lowest. The 1/12 in., however, with proper manipulation, would bear the 1 in. eye-piece, and then reveal structure that could not be made out with 1/25's, as hitherto constructed.

*How to see with the Microscope,' 1880, pp. 202, 203, and 206.
† Engl. Mech., xxxix. (1884) p. 48.

"Half-inch objectives had been made with apertures of 80o. Some authorities had declared that 40° was the highest aperture that could be usefully employed with that focal length. He had obtained one of the best examples of the 1/2 in. of 80°, and had made a careful series of trials with it. He had applied diaphragms above the back combination to cut down the aperture to 60° and 40° respectively, and the results might be briefly told. Taking the proboscis of the blow-fly and viewing it with the 1/2 in. diaphragmed down to 40° aperture, and arranging the illumination in the most favourable manner, he noted every detail of the picture, the sharpness and blackness of the points of the bristles, the transparency and clearness and general precision of the image; then removing the diaphragm behind the lens, he increased the aperture to 60°, and he found the image improved in every way. Increasing the aperture to the fullest extent, 80°, gave no advance upon the quality of image seen with 60° up to the 1 in. eye-piece; for this reason he concluded that 60° was the really useful aperture for a 1/2 in., and gave as much resolving power as the eye could well sustain with that combined power. No doubt the extra 20° would give the lens a higher resolving power with a stronger eye-piece, but he thought that might be better obtained with a lens of shorter focal length.'

Mr. Nelson gives the following table of apertures for objectglasses (with 1 in. eye-piece on a 10 in. tube), and says that "if ideal perfection is to be reached, the values given in the above table must be aimed at."

It will be seen that there is a wide divergence between Mr. Nelson's and Prof. Abbe's figures. For instance, for N.A. 0.65 Prof. Abbe suggests an objective of 1/8 in. and Mr. Nelson a 4/10 in.

Lastly, we may give Dr. W. B. Carpenter's views as expressed in his latest publication on the subject.†

"The 1/8 in. is (according to the writer's experience, which is confirmed by the theoretical deductions of Prof. Abbe) the lowest objective in which resolving power should be made the primary qualification, the 1/6, 1/5, 1/4, and 4/10 in. being specially suited to kinds of biological work in which this is far less important than focal depth and dioptric precision. This view is strengthened by the very important consideration that the resolving power given by

* Engl. Mech., xxxviii. (1883) pp. 367-8.

+ Encyclopædia Britannica,' 9th ed., xvi. (1883) pp. 269-70.

wide aperture cannot be utilized, except by a method of illumination that causes light to pass through the object at an obliquity corresponding to that at which the most divergent rays enter the objective. Now, although in the case of objects whose markings are only superficial such may not be productive of false appearances (though even this is scarcely conceivable), it must have that effect when the object is thick enough to have an internal structure; and the experience of all biological observers who have carried out the most delicate and difficult investigations is in accord, not only as to the advantage of direct illumination, but as to the deceptiveness of the appearances given by oblique, and the consequent danger of error in any inferences drawn from the latter. Thus, for example, the admirable researches of Strasburger, Fleming, Klein, and others upon the changes which take place in cell-nuclei during their subdivision can only be followed and verified (as the writer can personally testify) by examination of these objects under axial illumination, with objectives of an angle so moderate as to possess focal depth enough to follow the wonderful differentiation of component parts brought out by staining processes through their whole thickness.

The most perfect objectives for the ordinary purposes of scientific research, therefore, will be obviously those which combine exact definition and flatness of field with the widest aperture that can be given without an inconvenient reduction of working distance and loss of the degree of focal depth suitable to the work on which they are respectively to be employed. These last attributes are especially needed in the study of living and moving objects; and in the case of these, dry objectives are decidedly preferable to immersion, since the shifting of the slide which is requisite to enable the movement of the object to be followed is very apt to produce disarrangement of the interposed drop. And, owing to the solvent power which the essential oils employed for homogeneous immersion have for the ordinary cements and varnishes, such care is necessary in the use of objectives constructed to work with them, as can only be given when the observer desires to make a very minute and critical examination of a securely mounted object."

A table is then given which in addition to the magnifying-powers of objectives with the A and B eye-pieces also "specifies the angle of aperture which, in the writer's judgment, is most suitable for each. He has the satisfaction of finding that his opinions on this latter point, which are based on long experience in the microscopic study of a wider range of animal and vegetable objects than has fallen within the purview of most of his contemporaries, are in accordance with the conclusions drawn by Professor Abbe from his profound investigations into the theory of microscopic vision, which have been carried into practical accomplishment in the excellent productions of Mr. Zeiss." An extract from the table will be found on the next page.

"For ordinary biological work, the 1/8, 1/10, and 1/12 objectives, with angles of from 100° to 200°, will be found to answer extremely well if constructed on the water-immersion system."

Ser. 2.-VOL. IV.

2 H

"It must be understood that there is no intention in these remarks to undervalue the efforts which have been perseveringly made by the ablest constructors of microscopic objectives in the direction of enlargement of aperture. For these efforts, besides increasing the resolving-power of the instrument, have done the great service of producing a vast improvement in the quality of those objectives of moderate aperture which are most valuable to the scientific biologist; and the microscopist who wishes his armamentum to be complete will provide himself with objectives of those different qualities as well as different powers which shall best suit his particular requirements."

66

'High-angled" Objectives.t-Dr. J. Edwards Smith "prefers to regard as 'high-angled,' any, and all glasses, without reference to their focal lengths, which are endowed with the widest apertures obtainable. If this be accepted, then it will occur that a 1 in. of 50° should be classed as a high-angled objective, and similarly a 2 in. of 25°. And, again, it would also then occur that a 1/6 in. of 130°, which fifteen years ago ranked as a wide, would now be classed as a glass of medium power.'

Zeiss's A* Variable Objective and "Optical Tube-Length."The demonstration of the important influence of "optical tube-length" on the magnifying power of the Microscope explains what has hitherto seemed a curious anomaly in the action of this objective.

It will be remembered that it has a considerable range of power according as its two lenses are "closed" (when they are 44 mm. apart) or "open" (when they are at a distance of 52 mm.), the closing and opening being effected by rotating the collar on the objective.

In the closed position the equivalent focal length of the objective is 54.1 mm., and in the open 39.7 mm., or a ratio of approximately 43. The power of the Microscope is however increased not in the ratio of 3: 4 only, but of 3: 5.28.

The explanation of this difference is found in the fact that A, or the optical tube-length, varies considerably according to the position of the lenses of the objective. When they are closed the posterior focal plane is 153.6 mm. from the back lens of the objective, but when open 125.7 mm. only. A is therefore (with a tube-length of 10 in. or 250 mm. from the back lens of the objective to the anterior focal plane of the ocular) 250 153.6 96.4 mm., or 250 125.7 124.3 mm.

=

=

'How to see with the Microscope,' 1880, p. 104. Cf. also p. 146.