to the inch. These bands are numbered from the 1st to the 19th, and are used for microscopic tests. I am indebted to our friend Mr. Stodder for the opportunity of exhibiting to you a beautiful photograph of the 19th band, containing over 112,000 lines to the inch (Fig. 3). The photograph was made with one of Tolles's

microscopes, and any microscopist will tell you that to resolve this band is a great triumph of art, and that you could have no better evidence of the skill of our eminent optician than this photograph affords. In projecting the image on the screen, some of the sharpness is lost, but I think the separate lines of the band must be distinctly visible to all who are not too far off.

Now, the distance between the lines on the original plate is not very different from one-half of the mean length of a wave of violet light, or one-third of a wavelength of red light; and, what is still more to the purpose, these very bands give us the means of measuring the dimensions of the waves of light themselves. Evidently, then, the dimensions with which we are dealing are not only conceivable, but wholly within the range

THE INTERSPACES IN GLASS.

27

of our perceptions, aided as they have been by the appliances of modern science.

But, to return to my argument: these values, if they are not wave-lengths, are real magnitudes, which differ from each other in size just as the above measurements show. Moreover, we have reason to believe that the various color-giving rays differ in nothing else, and it is certain from astronomical evidence that they all pass through the celestial spaces with the same velocity. Now, when a beam of light enters a mass of glass, not only does its velocity diminish, but, what is more remarkable, the different rays assume at once different velocities, and, according to the well-known principles of wave-motion, the unequal bending that results is the necessary effect of the unequal change in velocity which the rays experience. But, if the material of the glass were perfectly homogeneous throughout, it is impossible to conceive, either on the wave theory or any other theory of light we have been able to form, how a mere difference in size in what we now call the luminous waves should determine this unequal velocity with the accompanying difference of refrangibility, and the fact that such a difference is produced is thought by many to be strong evidence that there is not an absolute continuity in the material; in fine, that there are interstices in the glass, although they are so small that it requires the tenuity of a ray of light to detect them.

Still we cannot make our conceptions the measure of the resources of Nature, and I, therefore, do not attach much value to this additional evidence of the molecular structure of matter. But the importance of these optical phenomena lies in this, that, assuming the other evidence sufficient, they give us a rough measure of the size of the molecules. For, as is evident

from our illustration with the wire meshes, the size of the molecular spaces cannot be very different from that of the waves of light. Our diagram shows that the red waves are only half as long again as the violet, and if the molecular spaces were, say, either ten thousand times larger or ten thousand times smaller than the mean length, the glass could produce no appreciable difference of effect on the different colored rays. We are thus led to the result that, if the glass is an aggregate of molecules, the magnitude of these molecules' is not very different from the mean length of a wave of light. Accepting the undulatory theory of light, we can submit the question, as Sir William Thompson has done, to mathematical calculation; and the result is that, though the effects of dispersion could not be produced unless the size of the molecules were far less than that of the wave-lengths, yet it is not probable that the size is less than say 500.000.000 of an inch.

Before closing the lecture, allow me to dwell, for a few moments, on the second of the two classes of facts for which I have already bespoken your attention, since they confirm the results we have just reached, in a most remarkable manner. Every one has blown soap-bubbles, and is familiar with the gorgeous hues which they display. Many of you have doubtless heard that blowing soap-bubbles may be made more than a pleasant pastime, and I will endeavor to show how it can be made a philosophical experiment, capable of teaching some very wonderful truths. It is almost impossible to show the phenomena to which I refer to a large audience, and I cannot, therefore, feel any confidence in the success of the experiment which I am about to try; but I will show how you can all make the experi

1 The mean distance between the centres of contiguous molecules.

HOW TO MAKE SOAP-BUBBLES.

29

ment for yourselves. And, first, I must tell you how to prepare the soap-suds.

Procure a quart-bottle of clear glass and some of the best white castile-soap (or, still better, pure palm-oil soap). Cut the soap (about four ounces) into thin shavings, and, having put them into the bottle, fill this up with distilled or rain-water, and shake it well together. Repeat the shaking until you get a saturated solution of soap. If, on standing, the solution settles perfectly clear, you are prepared for the next step; if not, pour off the liquid and add more water to the same shavings, shaking as before. The second trial will hardly fail to give you a clear solution. Then add to two volumes of soap-solution one volume of pure, concentrated glycerine.

Those who are near can see what grand soap-bubbles we can blow with this preparation. The magnificent colors which are seen playing on this thin film of water are caused by what we call the interference of light. The color at any one point depends on the thickness of the film, and by varying the conditions we can show that this is the case, and make these effects of color more regular. For this purpose I will pour a little of the soap-solution into a shallow dish, and dip into it the open mouth of a common tumbler. By gently raising the tumbler it is easy to bring away a thin film of the liquid covering the mouth of the glass. You can all easily make the experiment, and study at your leisure the beautiful phenomena which this film presents. To exhibit them to a large audience is more difficult, but I hope to succeed by placing the tumbler before the lantern in such a position that the beam of light will be reflected by the film upon the screen, and then, on interposing a lens, we have at once a distinct image

of the film. Success now depends on our keeping perfectly still, as the slightest jar would be sufficient to break this wonderfully delicate liquid membrane. See! the same brilliant hues which give to the soapbubble its beauty are beginning to appear on our film, but notice that they appear in regular bands, crossing the film horizontally. As I have already stated, the color at any point depends on the thickness of the film, and, as it is here held in a vertical position, it is evident that the effect of gravity must be to stretch the liquid membrane, constantly thinning it out, beginning from the upper end-which, however, it must be remembered, appears on the screen at the lower end, since the lens inverts the image-and notice that, as the film becomes thinner and thinner, these bands of color which correspond to a definite thickness move downward, and are succeeded by others corresponding to a thinner condition of the film, which give place to still others in their turn. These colors are not pure colors, but the effect is produced by the overlapping of very many colored bands, and, in order to reduce the conditions to the simplest possible, we must use pure colored light-monochromatic light, as we call it. Such a light can be produced by placing a plate of red glass (colored by copper) in front of the lantern. At once all the particolors vanish and we have merely alternate red and dark bands. Watch, now, the bands as they chase each other, as it were, over the film, and notice that already new bands cease to appear, and that a uniform light tint has spread over the upper half (lower in the image) of the surface. Now comes the critical point of our experiment. If the film is in the right condition so that it can be stretched to a sufficient degree of tenuity, this light