III. Size of Matter Molecules.-I am not willing to conclude this chapter without some explanation of the manner in which the dimensions of these light-waves throw light upon the dimensions of the molecules of matter itself. We are forced to conceive of matter as consisting of detached molecules, or separate very small portions, on account of the enormous power of expansion when heated which matter possesses. Moreover, while water and alcohol expand as one to three in the liquid form for the same increase of temperature, in vapour they expand in the same ratio,1 which we can only account for on the supposition that the molecules are now at enormously greater distances, so that their special action on one another has ceased, and they only obey the general laws of gases exposed to heat. We are therefore confronted with these detached molecules of matter; and some of the main questions physicists are now investigating, are, What are the probable sizes and other properties and relations of these molecules ?

Now on the first of these questions the measurements we have just obtained throw very considerable light. First, the molecules must be considerably less than those waves in dimensions, or they would be at least partially visible with the powerful microscopes we now possess. Nobert's testlines of 112,000 to the inch-half the dimensions of a blue wave-were resolved in America by Dr. Woodward. Moreover, in many transparent bodies at least, as the waves pass through amongst the molecules without being very sensibly destroyed or affected, this is another proof that such waves are large in proportion; as they plainly are not split up amongst them, but as it were surge grandly over them with little resistance. And yet, secondly, the molecules cannot be infinitely less relatively-or, shall we say, tremendously less; because if they were, it is easy to see that a difference in 1 About for each rise of 1° Fahrenheit.

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the waves of one half, (we may take red light as 36,000 and violet as of an inch,) could not so profoundly affect the phenomena as it does. To use an illustration I have seen somewhere, sawdust would show no perceptible difference in its effects upon water waves 30 feet and 50 feet apart; but logs of wood probably would. All this is indefinite, and yet it does give us a notion of what physicists call the class, or order, of magnitudes involved; and from some other considerations of this kind which cannot be given here,1 it has been argued with very great probability that the average distance from molecule to molecule can hardly be more than a thousandth part, and hardly less than one ten-thousandth part, of the average length of a wave.

It is a little singular that very analogous deductions may be drawn from the phenomena of a soap film. With a good solution, if a film is stretched upon a ring as in Fig. 96, and carefully observed, after a while coloured bands cease to form, and a large white patch appears, answering to the first bright ring.. This we know (§ 110) to be a thickness of onefourth of a wave-length. But after this comes a patch of very dark grey, often called black.2 Now the peculiarity about this is, that the boundary edge is perfectly sharp, as if cut with scissors! It is not so with Newton's lenses, where the diminution of thickness is gradual; and the only conclusion is, that there is here some sudden change in the thickness and therefore physical constitution of the film. It cannot be nearly one-fourth of a wave-length, or a considerable portion of light would be reflected. It must be as compared with the wave-length practically nil, for either (1)

1 Most of them are discussed towards the end of Tait's Recent Advances in Physical Science (Macmillan and Co.).

2 It is often stated that this grey only comes in patches, and that the film almost immediately bursts. With solutions made as described on page 161, I have had half the film remain of the dark grey for hours.

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the two reflecting surfaces are so close that the retardation is practically nothing, and discordance is produced solely by the half-wave difference of phase due to the denser medium ; or (2) the film is so thin that the air on both sides is in optical contact and there is no reflection at all. Obviously the first supposition is the true one; and it is very easy to see that if the film exceeded in thickness one-fortieth of a wave-length, we must have some traces of colour. We have here, then, apparently an abrupt transition from 100.000 of an inch to something almost certainly not much greater than 2,000,000 of an inch ; and it is difficult not to believe that this must be due to some peculiar change in the physical plan, or constitution of the film; which again must almost certainly be in fairly numerical relation with the size of the molecules. And as we know that the mechanical equivalent of the heat required to vaporise a grain of water would not be sufficient (according to the law of capillary attraction) to reduce it to a thickness of 500.000.000 of an inch, and therefore at that thickness the molecules could no longer hold together, but would separate in vapour, we seem to have here two outside limits between which the size of the molecules, or rather the distances between their centres, must lie.1

Finally, however, we can hardly suppose that a film only one molecule thick would hold together at all. We must therefore multiply the lesser limit by some figure, at least 2; and we shall be quite within the mark in estimating the molecules in the film's thickness at from 2 to 5. And even this low figure brings the limits of measurement for the molecules of this form of matter as something like 2.000.000 of an inch for the greatest possible distance between the

1 Sir William Thomson believes that the molecules of gas cannot exceed of an inch; and Mr. Sorby estimates various molecules as probably from 0 to booʊ of an inch.

centres, and 250.000.000 to 100.000.000 (according to the multiplier we assume) for the least distance.

It is remarkable that several other lines of investigation lead to similar conclusions; but they need not be mentioned here. Only the merest outlines of the optical argument have been given; but these will suffice to show how Light is still, in another sense, a Revealer of those minute elements which can never be seen by mortal eyes.

APPENDIX TO CHAPTER IX.

Diffraction in the Microscope.

The phenomena of diffraction described in this chapter have a very important bearing upon microscopical investigation, and especially upon the advantage of increased angular "aperture" in microscope objectives. That the increased angles obtainable by immersing object and objective in a fluid, instead of observing the object in air, gave marvellously increased powers of definition, had long been known; but so long as this was supposed to be due merely to greater illumination, or the collecting of a larger pencil of light from the object, it could not be satisfactorily accounted for. At length Professor Abbe pointed out the true nature of the advantage gained, and the matter was soon demonstrated by ingenious experiments devised by himself, Mr. Stephenson, and Mr. Frank Crisp, so well known as principal editor of the admirable Fournal of the Royal Microscopical Society. The following brief explanation is condensed from Mr. Crisp's lucid summary of the subject in that journal for April, 1881, to which I am also indebted for the diagrams by which it is illustrated.

It will at once be understood, from the phenomena of "gratings" already investigated, that if between the reflecting mirror and the stage of the microscope we interpose a

very small opening in the diaphragm, and on the stage lay a "grating" of ruled lines, on removing the eye-piece and looking down the tube we observe a series of images of the aperture like Fig. 112, all circular in homogeneous light, but the outer ones consisting of spectra in white light. The small pencil admitted through the diaphragm is "diffracted," just as we

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FIG. 112.

have already found. We next lay upon the stage a slide such as Fig. 113, consisting of, let us say, a circle containing both wide and narrow lines ruled on glass. Removing the eye-piece as before, we have of course, on looking down the

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FIG. 113.

FIG. 114.

tube, the appearance presented in Fig. 114, the coarse lines giving diffraction spectra twice as close and numerous as those caused by the fine lines. The reason for this we have already seen (§ 110): the present point is, what influence these diffracted rays have upon the image, and it is here that the experiments just referred to are so important and interesting,