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
Light Waves and Their Uses
the number of waves in its length with an equal degree of accuracy.
I will give the description of this process somewhat more in detail. In Fig. 72 mm' represents the first or the shorter
standard viewed from above. This standard rests on a carriage which can be moved with a screw. The second standard nn' is twice as long as the first, and is placed as close as possible to the first and rigidly connected with some part of the frame. The mirror d is the
FIG. 72 £ i ,
The two front mirrors of the two standards are adjusted to give fringes in white light with the reference plane. The central fringe in the white-light system is black; the others are colored. Hence we can always distinguish the central fringe. When the central fringes occur in the same relative position upon the two front mirrors m and n, then these two surfaces are exactly in the same plane. Now, if we move the reference plane backward through the length of the shorter standard, its surface will coincide with the mirror m\ and at this instant fringes in white light will appear. Thus we have the means of knowing when the reference plane has been moved the length of the first standard to an order of accuracy of one-tenth or one-twentieth of a fringe.
1 Better, tho image of d in a and />, which in the figure would coincido with the front surfaces of m and n.