have been measured with as much accuracy as the dimensions of astronomy, although they are at the opposite extreme of the scale of magnitude. We represent these dimensions to our imagination as wave-lengths, that is, as the distances from crest to crest of our assumed ether-waves, and we shall find it difficult to think clearly upon the subject without the aid of this wave-theory, and every student of physics will bear me out in the statement that, though our theory may be a phantom of our scientific dreaming, these magnitudes must be the dimensions of something. Here they are:

You know that the sensation we call white light is a very complex phenomenon, and is produced by rays of all colors acting simultaneously on the eye. A very pretty experiment will illustrate this point. I have projected on the screen the image of a circular disk made of sectors of gelatine-paper, variously colored. By means of a very simple apparatus, I can revolve the disk, and thus cause the several colors to succeed each other at the same point with great rapidity, and you notice that the confused effect of the different colors produces the impression you call white, or, at least, nearly that.

The sunbeam produces the same impression, be

MAGNITUDES OF ETHER-WAVES.

25

cause it contains all these colored rays; and, if we pass it through a prism, the several rays, being bent unequally by the glass, diverge on emerging, so that, if we receive the beam thus divided on a screen placed at a sufficient distance, we obtain that magnificent band of blending hues we call the solar spectrum.

To each of the colored rays which fall along the line of the spectrum corresponds a definite wavelength. In the diagram, we have given the wavelengths, corresponding to only a few selected points, one in each color, and marked in the solar spectrum itself by certain remarkable dark lines by which it is crossed. These values always create a smile with a popular audience, which makes it evident that, by those unfamiliar with the subject, they are looked upon as unreal if not absurd. But this is a prejudice. In our universe the very small is as real as the very great; and if science in astronomy can measure distances so great that this same swift messenger, light, traveling 192,000 miles a second, requires years to cross them, we need not be surprised that, at the other end of the scale, it can measure magnitudes like these.

Let not, then, these numbers impair your confidence in our results; but remember that the microscope reveals a universe with dimensions of the same order of magnitude. Moreover, the magnitudes with which we are here dealing are not beyond the limits of mechanical skill. It is possible to rule lines on a plate of glass so close together that the bands of fine lines thus obtained cannot be resolved even by the most powerful microscopes; and I am informed that the German optician, Nobert, has ruled bands containing about 224,000 lines to the inch. He regularly makes plates with bands consisting of from about 11,000 to 112,000 lines

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 300.000.000 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

The mean distance between the centres of contiguous molecules.