THE AID OF THE ACHROMATIC FRINGES. 



41 



the operation is not easy. Leaving these details for further consideration, 

 the procedure for angular measurement may advantageously be treated here. 

 For this purpose the half -silver P and one opaque mirror, n, for instance, are 

 mounted on a rigid bar with an axis at P. The other mirror m is to remain 

 fixed. If the bar is now rotated over a small angle 

 a, figure 23, the mirror at n is displaced to n' and 

 the ray Sn prolonged (intercept %) is now reflected 

 from n' to q and thence along T into the spectro- 

 telescope, parallel to its original direction or to 

 the other ray mp. Hence the interferences remain 

 intact, but many fringes pass during the transfer. 

 The persistence of parallelism is easily seen, be- 

 cause the angle between the incident and reflected 

 ray at n is decreased by 20. when n passes to n', 

 but is again increased by 2 a owing to the rotation 

 of PP\ to PP' over the angle a. 



To control the fringes either the mirror at n (or at m} may be displaced 

 on a micrometer screw normal to itself, or the half-silvered plate at P may 

 be displaced parallel to itself. If the angle of incidence at n is i and the nor- 

 mal displacement of n is e, the path-difference introduced will be 2e cos i. 

 Similarly if the normal displacement of the plate P is e' and the angle of 

 incidence i 1 ', the path-difference will be ze' cos i'. 



As in the preceding experiment, the mirror at n may be a half -silver, so 

 that the ray d' passes through it and may then be returned in its own path 

 by a mirror at n" on a fixed standard. The displacement of this mirror over 

 a distance e, parallel to itself, introduces the path-difference ze, so that the 

 cosines are avoided. But a much more important result is the fact that the 

 rays np or n'g now are stationary. The strips of light originally at p do not 

 therefore travel over each other while one passes from p to q and the inter- 

 ferences are kept at full intensity throughout. This is a great advantage. 

 Moreover, the half -silver plate at n compensates the half -silver Pp, which 

 is a further advantage, since both paths within are glass paths with high dis- 

 persion coefficients. It is obvious that the path-excess nn" on the d' side, 

 must be separately compensated on the d side. The method of doing this 

 by an air compensator (fig. 21) will presently be considered, as a long glass 

 compensator would not in general be desirable because of the sluggish motion 

 of the small ellipses thus produced. 



22. Equations. The equations for this case are apparently very compli- 

 cated. If in figure 23, m and n are in the same phase and Pp is symmetrical, 

 there will be no path-difference at p. When Pn is rotated over an angle a. into 

 Pn', the path on the right becomes nn'+n'q+qs while (ps wave-front) the 

 path on the left remains mp as before. The path-difference is thus the differ- 

 ence of these quantities, to which, however, the increased glass path at PP' 

 would have to be deducted, and the surface PP'.must pass through the axis P, 



