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,

21

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 scen 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. the film is in the right condition so that it can be stretched to a sufficient degree of tenuity, this light

If

OPTICAL EFFECTS OF SOAP-BUBBLES.

tint will be succeeded by a gray tint,

..

23

and there

it appears in irregular patches at the upper border. But in an instant all has vanished, for the film has broken, as it always breaks, soon after the gray tint appears.

Having now seen the phenomena, you will be better prepared to appreciate the strength of the argument to which I now have to ask your careful attention. You know that the red and dark bands seen in the last experiment, when we used the red glass, are caused by the interference of the rays of light, which are reflected from the opposite surfaces of the film. It is evident that the path of the rays reflected from the back surface must be longer than that of those reflected from the front surface by just twice the thickness of this film of water; and, as Prof. Tyndall has so beautifully shown you in the course of lectures just finished, whenever this difference of path brings the crests of the waves of one set of rays over the troughs of the second set, we obtain this wonderful result that the union of the two beams of light produces darkness. It would, at first sight, seem that

such a result must be produced in the case of our film whenever its thickness is equal to 1, 4, 4, 7, or any odd number of fourths of the length of a wave of red light, and this would be the case were it not for the circumstance that, in consequence of certain mechanical conditions, the rays of light reflected from the back of the film lose one-half of a wave-length in the very act of reflection. But, without entering into details, which have been so recently and so beautifully illustrated in this place, let me call your attention to this diagram, which tells the whole story:

You thus see that the theory of light enables us to measure the thickness of the film, and we know that where that gray tint appeared in our experiment the thickness of the film was less than of the length of a wave of red light, or less than 156,000 of an inch, and no wonder that the film broke when it reached such a degree of tenuity as that.

But, having followed me thus far, and being assured, as I hope you are, that we are on safe ground, and talking about what we do know, your curiosity will lead you to inquire whether we can stretch the film any farther.

The facts are that, after the appearance of the gray tint, although the film evidently stretches to a limited