This is a diagram painted on glass and showing the colors as we know them. It would take two or three hours if I were to explain the subject of spectrum analysis to-night. We must tear ourselves away from it. I will just read out to you the wave lengths corresponding to the different positions in the sun's spectrum of certain dark lines commonly called "Fraunhofer's lines." I will take as a unit the one-hundred-thousandth of a centimeter. A centimeter is 0.4 of an inch; it is a rather small half an inch. I take the thousandth of a centimeter and the hundred of that as a unit. At the red end of the spectrum the light in the neighborhood of that black line A has for its wave length 7.6; B has 6.87; D has 5.89; the "frequency" for A is 3.9 times 100 million million; the frequency of D light is 5.1 times 100 million million per second.
Now, what force is concerned in those vibrations as compared with sound at the rate of 400 vibrations per second? Suppose for a moment the same matter was to move to and fro through the same range but 400 million million times per second. The force required is as the square of the number expressing the frequency. Double frequency would require quadruple force for the vibration of the same body. Suppose I vibrate my hand again, as I did before. If I move it once per second, a moderate force is required; for it to vibrate ten times per second, 100 times as much force is required; for 400 vibrations per second, 160,000 times as much force.
If I move my hand once per second through a space of a quarter of an inch; a very small force is required; it would require very considerable force to move it ten times a second, even through so small a range; but think of the force required to move a tuning fork 400 times a second; compare that with the force required for a motion of 400 million million times a second. If the mass moved is the same, and the range of motion is the same, then the force would be one million million million million times as great as the force required to move the prongs of the tuning fork. It is as easy to understand that number as any number like 2, 3, or 4.
Consider gravely what that number means, and what we are to infer from it. What force is there in space between my eye and that light? What forces are there in space between our eyes and the sun and our eyes and the remotest visible star! There is matter and there is motion, but what magnitude of force may there be?