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-
