# Michelson A. A. Light waves and their uses (1903)  Light Waves as Standards of Length 97

The next process is to move the first standard backward through the same distance. Then the white-light fringes will again appear on the front mirror m. Finally we move the reference plane again through the same distance and, if the second standard is twice as long as the first, we get interference fringes on the two rear mirrors of the two intermediate standards. If there is any difference, then the central fringe of the white-light system will not be in the same position on both mirrors, and we shall know that one is twice as long as the other less, say, two fringes, which would mean less one-half micron. In this way we can tell whether one is exactly twice as long as the other or not; and if not, we can determine the difference to within a very small fraction of a wave.

When we multiply the number of waves in the first standard by two, any error in the fractional excess is, of course, also multiplied by two. So the fraction of a wave which must be added to the second number is uncertain. If we observe the fringes produced by one radiation, for example the red, we get a system of circular fringes upon both mirrors of the standard; and if these two systems have the same appearance on the upper mirror as on the lower, then we know this fraction is zero; and the number of waves in the second standard is then the nearest whole number to the number determined. If this is not the case, we can by a simple process tell what the fraction is, and can obtain this fractional excess to any required degree of accuracy. As an example, we may multiply the numbers obtained for the first standard by two, and we find 2,424.74 for the number of red waves in standard No. 2. The correct value of this fraction for red light was found to be .93 instead of .74. Thus the same degree of accuracy which was obtained in measuring the first standard can be obtained in all the standards up to the last. We have thus the means of find

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Light Waves and Their Uses

ing accurately the whole number of waves in the last standard. The whole number obtained by this process of “stepping off” for the red radiation of cadmium was found to be 310,078. The fraction was then determined by the circular fringes, as described above, and found to be .48. In the same way the number for the green radiation was determined as 393,307.93; and for the blue radiation as 416,735.8(5. To give an idea of the order of accuracy,

I would state that there were three separate determinations made at different times and by different individuals, as follows:

 Determination Red Green Blue I...................... 310,678.48 310,678.65 310,678.68 393,307.92 393,308.10 393,308.09 416,735.86 416,736.07 416,736.02 II...................... Ill.....................

The fact that these determinations were made at entirely different times, separated by an interval of whole months, and by different individuals, and that we still were able to get, not only the same whole number of waves, but also so nearly the same fractions, gives us a confidence, which we could not otherwise feel, in the possibilities of the process.

In comparing the standards with one another the temperature made no difference, if only it were uniform throughout the instrument, because two intermediate standards side by side, made of the same substance, would expand in exactly the same way, provided we could be sure that both had the same temperature. But in the determination of the number of waves in standard No. 9 it is extremely important to know the temperature with the very highest degree of accuracy. For this pur[>ose some of the best thermome