40 DISPLACEMENT INTERFEROMETRY BY 



pensator c of the same thickness and g]ass may be placed in the beam mP 

 on the left. If c and n are parallel, both originally at an angle /3/2 to the 

 beams traversing them, it is obvious that the compensation will not be de- 

 stroyed by the rotation of the rail, provided c is fixed while n rotates. If c 

 is effectively thicker than , the part of the coefficient due to the compensator 

 may become negative. This is apparently the case in the following experi- 

 ments, in which a compensator was installed as in figure 15 at c: 



AATXio 3 = o.o .4 1.4 2.8 4.0 5.2 cm. 

 AaXio 3 = o.o 2.6 5.9 9.3 12.2 16.0 



The rate here is AN/Aa = 0.31, so that the zero value is exceeded. How- 

 ever, the path-difference in the compensator of thickness e at an angle of 

 incidence i and refraction r, viz, e (cos i sin i tan r) a, where 2 = 90 

 jS/2, here becomes 0.77 (0.816 0.578X0. 6i8)a = o. 3530:, so that the whole 

 difficulty is not explained away. 



Finally, a few experiments were made to compare the effect of displacing 

 (A7V) the micrometer at n" (fig. 15) as compared with the effect of a microm- 

 eter (AN') which displaces P in the direction of its plane of symmetry. 

 The latter (AN 1 ) is zero when a = o. Generally if e is the normal displacement 

 of the prismatic faces, the path-difference is 



ze (cos (45 a) cos (45 -fa)) = 2AN sin a. 

 since e = AN sin 45. Hence, as AA f is a normal displacement 



AN /AN' sin a 

 The results obtained were 



io 3 AiV' = o.o 50 100 150 200 225 cm. 

 io 3 &N =0.0 1.5 3.4 5.4 7.2 9.2 cm. 



Thus the mean rate is a = AN /AN' = 0.036 or a is a little over 2. To obtain 

 these data the achromatic fringes were used as above. When the slit-images 

 seen in the telescope are not quite parallel, they may be made so by slightly 

 rotating the slit on a horizontal axis normal to its plane. The images 

 rotate in opposite directions. A slight angle between the images is, however, 

 of no consequence. 



21. Second method. In view of certain difficulties encountered in the use 

 of reflecting prisms, in particular the loss of rays at the edge, the limitation 

 to half -ellipses, etc., the method of figure 22 enlarged in figure 23 was devised. 

 In this the prism is replaced by a half -silvered plate PP'. Hence the rays 

 issuing at 5 and reflected by the opaque mirrors at m and n are thereafter 

 respectively transmitted and reflected by the half -silvered plate at p, and then 

 reach the spectro-telescope at T together. When the path-differences are 

 sufficiently equal, elliptic interference fringes will be seen in the spectrum. 

 When first found they are usually very fine straight lines; but they may be 

 rectified by plate compensators in the beams d and d' or mp and np, though 



