ACOUSTICS AND GRAVITATION. 69 



It would furthermore be necessary, to insure synchronism, or a definite ratio 

 of frequencies in the two revolving disks tt and DD, by gearing or otherwise. 

 Moreover, the telescope must always be in the position of observation when the 

 revolving mirror flashes. This is a difficult thing to do with two disks. It 

 might seem (erroneously, however) as if a single disk ti, figure 94, could be used 

 for both purposes, P being the telescopic objective and P' a counterpoise. In 

 such a case T is to be replaced by the auxiliary mirror n, figure 94, which 

 reflects light to a similar mirror under the objective P, the reading being made 

 in an eyepiece above P. The eyepiece is so placed that the telescope is com- 

 pleted when the revolving mirror flashes. The possibilities of this plan will 

 be considered presently. Obviously, the fringes must move in a direction 

 differing from that of the objective. Hence they must be easily controllable 

 as to inclination and size. Compensators C and C 1 may be set symmetrically 

 (vertical and horizontal axes) by hand for this purpose. The same result is 

 secured by putting M and N on vertical axes (with tangent screws) and M t 

 and N' on horizontal axes (plane-dot-slot device) . 



62. Control fringes. As the revolving mirror R starts from rest to attain 

 its maximum speed, the line EE' in figure 97 will be more and more deflected 

 from the original position bb to some position as indicated (EE'). Simul- 

 taneously, the retardation due to the time consumed by light in passing twice 

 over the distance S will move EE' in the direction dd'. As it is this displace- 

 ment which must be measured, the accomplishment would be difficult. One 

 may, however, establish a set of control fringes independent of the distance 

 5. To do this the half-silver plate hh', figure 95, is inserted between the 

 mirrors m and R and adjusted until the two slit-images from the distant m' 

 and the near hh' coincide. Thus the fringes from hh' will not depend for 

 position on the line dd' on the speed of R and may be used to define the zero 

 of displacement. 



Obviously hh' must be good optic plate. If this is not the case, not only 

 will the pairs of slit-images fail to coincide at the same time, but the fringes 

 will differ in size and inclination and appear for different positions of the 

 revolving mirror R, or of the micrometer s, at M 1 ' 



63. Sensitiveness. At this stage of progress a large number of experiments 

 were made, using the equipment, figures 94, 95, 96. Providing the revolving 

 mirror R (kept stationary) with a divided arc-and-tangent screw, a number 

 of direct tests bearing on the sensitiveness were carried out, all referring 

 to the velocity of light to fix the ideas. Thus the distance passed in t seconds 

 is d = ct, while in the revolving mirror of frequency n, if 6 is the corresponding 

 angle, t = 6/2irn, whence d = c9/2irn. But if 5 is the corresponding number of 

 ocular scale-parts passed over by the fringes and k is the constant, d*=ks; 

 and finally, if / is the number of fringes (/) to the scale-part (5), f=ls. 



Hence 6 = kf/l, and if =io, d = 



