the light proceeds be infinitely small, the image still consists of a spot of finite size surrounded by dark and bright rings. That this must be so may be shown by general considerations without any calculations. If a lens is absolutely free from aberration, the secondary waves issuing from the different parts of its hinder surface agree perfectly in phase at the focal point. Let us consider the illumination at a neighbouring point in the focal plane. If the distance between the two points is so small that the difference of the distances between the point under consideration and the nearest and furthest parts of the object-glass is but a small fraction of the wave-length (A), the group of secondary waves are still sensibly in agreement, and therefore give a resultant illumination the same as before. At a certain distance from the focal point the secondary waves divide themselves into two mutually destructive groups, corresponding to the nearer and further parts of the object-glass. There is therefore here a dark ring. Further out there is again light, then another dark ring, and so on, the intensity of the bright rings, however, rapidly diminishing.

The radius of the first dark ring subtends at the centre of the lens an angle given by

sin 0='61*,

where R is the radius of the lens. If f be the focal length, we have

Let us now suppose that the problem is to cover a square inch with 3000 lines. On account of the curvature of the field it would be impossible to obtain extreme definition over the surface of a square inch with a less focal distance than (say) four inches. If we take f=4 and λ=

1 40,000'

we find

1 3000'

which gives R='2 for r= That is to say, if the focal length were 4 inches and aperture 4 inch, the first dark ring corresponding to one of the lines would fall on the focal point of the neighbouring one-a state of things apparently inconsistent with good definition. It is true that the aperture might well be greater than half an inch, so that it may seem possible to satisfy the requirements of the case. But the result of the

* Verdet, Leçons d'Optique Physique, vol. i. p. 305.

above calculation, being founded on the supposition of entire freedom from aberration, both spherical and chromatic, is subject in practice to a large modification. In astronomical telescopes, where every thing is sacrificed to the requirement of extreme definition at the centre of the field, the theoretical limit is sometimes closely approached; but the case is very different with a photographic lens. In fact the very first thing it occurs to a photographer to do, when he wishes to improve the definition, is to contract the aperture of his lens by means of a stop-a course which would be attended with the opposite result in the case of a perfect object-glass, or even a good astronomical telescope. While, therefore, it might be too much to say that the reproduction of 3000 lines in an inch by lens and camera is impossible, the attempt to do so without very special appliances appears in a high degree unpromising. It would certainly require a lens more than usually free from spherical aberration, and unlike either a telescopic or a photographic object-glass*, achromatic (if the expression may be allowed) for the chemical rays, unless indeed the latter requirement could be evaded by using approximately homogeneous light. It must be understood that nothing is here said against the practicability of covering a small space with lines at the rate of 3000 to the inch, a feat probably well within the powers of a good microscopic object-glass.

The method of contact-printing, on the other hand, is free from optical difficulties. The photographic film prepared on a flat piece of glass (or other support) may be brought by moderate pressure in a printing-frame within a very short distance of the lines of the original grating; and if the source of light be moderately small and the rays fall perpendicularly, the copy rarely fails in definition, unless through some photographic defect. When direct processes not depending on development are employed, the unclouded light of the sun is necessary. To avoid too much diffused light, I usually place the printing-frame on the floor of a room into which the sun shines, and adjust its position until the light reflected from the plate-glass front is sent back approximately in the direction of the sun. Too much time should not be lost in this operation, which requires no particular precision. Usually I cut off part of the extraneous light by partially closing the shutters; but I cannot say whether this makes any difference in the result. Those who are accustomed to this kind of experimenting will know that it is often less trouble to take a precaution than to find out whether it is really

*Photographic lenses are corrected on the principle of making the "visual and chemical foci" coincident, which leads to a different construction from what would be adopted were the chemical rays alone attended to.

necessary. In an early stage of an investigation, when the causes of failure are numerous and unknown, it is best to exclude every thing that can possibly be supposed to be prejudicial. When the principal difficulties have been overcome, it will be time enough to determine what precautions are necessary, if the question has not been already settled by accidental experience.

In the case of developed plates there is more choice of lights in consequence of the higher sensitiveness. I have used successfully cloud or skylight reflected horizontally from the zenith by a mirror through a hole of two or three inches diameter in the shutter of a darkened room, the frame being set up in a vertical plane at a few feet distance. The principal objection to this plan is the difficulty of estimating the exposure with proper precision a difficulty which is more felt than in ordinary photography, as it is convenient to develop a good many copies at once. On a really fine day the image of the sun formed by a condensing-lens of short focus placed in the shutter (as used in diffraction experiments) constitutes a very convenient source of light. As the exposure is only a few seconds, there is no difficulty in dodging isolated clouds, whose progress may be watched from within by examining their image with a coloured glass. When there is any haze, this method is not more satisfactory than the other.

With the more sensitive processes artificial light may be employed. I have done a good many copies by the aid of a moderator-lamp (without the globe) at two feet distance from the frame. An Argand gas-flame would probably be still better.

The printing-frame I employ has a thick plate-glass front, against which the original grating and the prepared plate are pressed by screws. These are more under control than the springs generally used in the common printing-frames. When every thing is ready, the original is placed on the glass front of the frame with the engraved face upwards, care being taken to exclude all grit by means of a camel's-hair brush. The prepared plate is then placed face downwards on the grating, then a pad to equalize the pressure (I have used one of india-rubber), and on the pad the rigid back of the frame, on which the screws are made to press with a moderate force. When the film is delicate, care should be taken to place it in the proper position at once without sliding.

The two surfaces of the plate-glass front of the printing-frame and the back of the original grating may be cleaned in the ordinary way with a soft cloth or wash-leather; but the engraved face of the grating requires more delicate treatment. If touched at all with a solid (wash-leather), the greatest care should be used. I prefer to wash it, when soiled, with a stream of water

from a tap, afterwards flooding it with pure alcohol and setting it up to drain and dry spontaneously. Sometimes I have found nitric acid useful; but I always try to avoid the rubbing contact of a solid. These precautions have been so successful that, after several hundred copies have been taken, the originals have scarcely, if at all, deteriorated.

For the support of the photographic film it is no doubt most satisfactory to use optically worked "parallel" glass. Ordinary glass would fail, for two reasons. In the first place it would generally be impossible to secure a sufficiently close contact in the printing. But even if this difficulty could be surmounted, the spectrum given by the copy would not bear the magnifyingpower which it is generally desirable to apply. It is indeed evident that the glass support of the grating requires the same precision of workmanship as the object-glass of the telescope used in conjunction with it.

Although ordinary glass taken at random is inadmissible, I have done a great number of excellent gratings on selected pieces of patent plate. In order to choose the best, I lay the plates on a table in such a position that the bars of a window or skylight are seen reflected in them. Each bar appears in general double, one image corresponding to each surface. By sliding the plate about, while the head is kept still, irregularities are easily detected by the shifting or curvature of the images. From a package of two dozen 5 x 4 plates as issued by photographic dealers, three or four, often lying together, may usually be selected as flat enough for the purpose, or at any rate decidedly superior to the remainder. It is worth notice that the object aimed at is flatness of the two faces, exact parallelism being of much less consequence; for it is evident that the interposition of a truly worked prism of very acute angle would produce no evil result. A glass is therefore not to be rejected merely because the two images of the bar seen reflected in it are decidedly separated. The question is rather whether this separation remains constant as the plate is moved about without rotation. I have never seen a piece of patent plate that could not be at once distinguished from worked glass in the way described; so that the test is abundantly sufficient for the purpose. The more delicate methods by which worked glass is examined would be less practically useful.

Whatever kind of glass be used, if the photographic process be at all complicated, there is considerable economy of labour in preparing comparatively large pieces, to be afterwards cut with the diamond to the required size. A 5 × 4, or even a 4×31 plate will do very well for four gratings. In the case of worked glass economy is an object; but when patent plate is used I

should recommend 5 x 4 glasses, as a margin is convenient. Even when, as in the collodio-chloride process to be presently described, the plate for each grating is prepared separately, it is convenient to perform the preliminary operations of cleaning and albumenizing on larger pieces. The cutting of prepared plates requires a little care. I place them face downwards on a sheet of clean paper, make the diamond cuts on the back, and then, before breaking, remove as much as possible of the glass powder. As it is important to prevent any grit from getting between the film and the engraved face of the original, I usually brush the surface with a large camel's-hair brush kept scrupulously clean.

In the preparation of the plates I have used a considerable variety of methods. The process with gelatine and bichromate of potash described in my previous papers has decided advantages; but all my efforts to obtain a mastery of it have been unavailing. Plates prepared to all appearance in precisely the same manner, and even at the same time, turned out differently, while modifications purposely introduced seemed to be for the most part without effect. It required a strong scientific prejudice to hold the uniformity of nature in the face of so much adverse evidence. The uncertainty of this method is provoking, as some of the results are exceedingly good; but I gave up my attempts sooner than I might otherwise have done in consequence of the discovery of another method by which most of the advantages of the gelatine process, namely simplicity of manipulation and brilliancy of results, might be attained with much less risk of failure.

It is very possible that a photographer skilled in the employment of gelatine might succeed where I failed. In case any such should wish to make the attempt, I will mention a few points that seemed important. The solution of gelatine should be carefully filtered. For thick liquids containing gelatine, albumen, &c., the best filtering material that I know of is tow. The tow should be cleaned from grease by boiling with soda and subsequent washing, and a small plugget of it pushed with moderate force into the neck of the funnel. Some arrangement must be adopted for keeping the gelatine hot, or the operation will hardly succeed. It is important that the coat of gelatine should be even, for which object the glass must be free from grease, and the plate on which the prepared glasses are put away to set perfectly level. Even then a good deal depends on the manipulation; but this is soon learned. The uniformity of the coat may be tested by the colour when the plate is placed on a sheet of white paper and examined in a weak white light. By candlelight the colour of weak bichromate of potash is scarcely visible.