92 DISPLACEMENT INTERFEROMETRY BY 



superposed, : -^- =0.031 of a fringe would pass for the given radius of 



OO /\ I O 



cylinder (^ = 5.3 cm.) at 100 turns. A cylinder 30 cm. in diameter (about a 

 foot) would therefore show 0.28 fringe, and since this may be doubled by 

 reversing the rotation of the cylinder (by which the strains due to centrifugal 

 force are also eliminated) , something short of two-thirds of a fringe should be 

 observed. 



With an ocular micrometer divided in o.i mm., there should be no difficulty 

 in making the fringes 3 mm. apart, so that a displacement of 20 scale-parts 

 may be expected, 10 for each of the directions of rotation. 



In the present experiment the reflection within the cylinder can not be total, 

 for it is obvious that if a ray gets into the cylinder it will under like conditions 

 come out again. Some advantage would be obtained from a thin coat of silver. 

 If x is the fraction of light reflected, that entering the telescope should be 

 proportional to x(i x) 2 , which is a maximum when x = ^3. The experiments, 

 however, show no serious difficulty from deficient light, 



67. Equations. Two reflections. The equations for this case are somewhat 

 more involved than the preceding; but it suffices to accept for the angle of 

 incidence i at the cylinder G, figure 89, the value given by the old-fashioned 

 theory of the rainbow, viz, 



(12) 8 cos 2 i=ju 2 i 



The chord C from c to d, etc., and its distance h from the axis a will be, as 

 before, C = 2R cos r, h = Rsm r, where r is the angle of refraction and R the 

 radius of the cylinder. Finally, equation (8) for the average speed v along a 

 chord also applies. Hence with the inclusion of equation (4), the path- 

 difference on rotation may be written, c being the velocity of light. 



(13) P.r>.= 3 X2CW<;)(i-i//i) 



since there are three chords, C, on sequence. This equation may be reduced 

 by the equations for C, h, v, to 



(14) P.D. 



and by equation (12) to 



cos r(i + a sinV) 



sin r 



H) 



c 

 a form convenient for computation 



a orm convenent for computation. 



Data similar to the above may now be inserted, viz, for a small cylinder 

 of water (to be used in the experiments below), R = $ cm.; M=i-33,' w = 6.28; 

 = 1 ' 1 



= 3Xio 1 ' 1 , whence 



P - V - = 9 3 X2.7oxVo.o82/ 4 .o9 = 1.82 X ic- 6 cm. 



X 10 



