94 Light Waves and Theib Uses
for parallelism by tiling until the requisite degree of accuracy is obtained. The parallelism cannot be made altogether perfect, and, as a matter of fact, in some cases the error may amount to as much as one-tenth of a micron or more.
Fig. 71 represents a perspective view of the same thing.
In this figure the intermediate standard rests on a carriage by means of which it may be moved as necessary for the purpose of comparing it with the whole meter. In making this comparison the surfaces must be parallel to the mirror which serves as a reference plane in the interferometer. The parallelism in this case must be of the same order of accuracy as that between the surfaces themselves. The adjustment is made by the screws at the rear, one of which turns the whole standard about a vertical axis and the other about a horizontal one.
In determining the number of waves in the meter, the first operation is to find the number of whole waves in this intermediate standard. It can readily be conceived that the counting of something like 300,000 waves would be no small matter; in fact, a little calculation would show that, if we counted two per second, it would take over forty hours to make the count. Probably a number of methods will suggest themselves of making such a process of counting automatic. Indeed, several experiments have been made, and with some promise of success; but the possibility
Light Waves as Standards of Length 95
of skipping over one fringe, through some accident, is serious. It was therefore thought desirable to use another process, very much longer and more tedious, but very much surer. This process consists in dividing the distances to be measured into a very much smaller number of parts, so that the distances to be measured in waves would be very much smaller. Thus a distance of ten centimeters contains 300.-
000 waves; half of this distance would contain 150,000. If we go on dividing in this way, until we get to the last one of nine such steps, we reach an intermediate standard whose length is something of the order of one-half millimeter. The total number of waves in this standard is about 1,200, and this number it is a comparatively simple matter to count.
The method of proceeding in counting these fringes is the same as that described above. The reference plane, as w^e will call the movable mirror in the interferometer, is moved gradually from coincidence with the first surface to coincidence with the second, and the fringes which pass are counted. Such a count was made for the three standard radiations, namely, the red, green, and blue of cadmium vapor. The result was 1,212.37 for red, 1,534.79 for green, and 1,626.18 for blue. Now, an important point is that we can measure these fractions with an extraordinary degree of accuracy; so the second decimal place is probably correct to within two or three units. The whole number we know to be correct by repeating the count and, getting the same result. Having thus obtained this number, including also the fractions of waves on the shorter standard to a very close approximation, we compare it with the second, which is, approximately, twice as long. This comparison gives us, without further counting, the whole number of waves in the second standard by multiplying the numbor in the first by two. We have the same possibility of measuring fractions on the second standard, and so can determine