332 Dr. J. Kerr on Rotation of the Plane of Polarization 

 tions X' and Y' inclined at 45° to X ; and let 



o/ = mcos (0-/3), 



y = mcos(0— 7). 



Identifying the second members of these equations with the 

 proper sums of resolved parts of x and y, we find easily 



m 2 =i(b 2 + b' 2 ), 



tan/ij= — -j-, tan 7= 7- 

 t> 



And therefore, if 8 be determined by the equation 



ta 

 we see that, finally, 



tanS= i=£=A tana ' • • • • (*> 



x' = mco$ (0 + 8), \ .-. 



?/ = mcos(0-8)J " * ^ 



By any adequate action upon the reflected ray at any point 

 between the iron mirror and the analyzer, let the component 

 x' be retarded relatively to y', so as to undergo a relative 

 change of phase equal to 28. As the components x' and y' 

 have already equal amplitudes, and are equally inclined to X, 

 it is evident that by this change of phase of x' the elliptic vi- 

 bration (5) is transformed into a rectilinear in the primitive 

 direction X. And thus the compensation of effect of the 

 operation R is fully effected, without displacement of the 

 second Nicol. 



k 

 If we assign to j the value J, which is probably near the 



truth, as its value in the case of steel, measured both by Jamin 

 and by Senarmont, lies between *5 and *6, and if we give 

 effect to the condition that a is a very small angle, we find 

 from equation (4), approximately, 



k k 



28=2 tan -1 . T tan« = 2 7 « = a. 

 h 11 



However, it is sufficient for our present purpose to observe that 

 the compensating change of phase 28 is a small quantity de- 

 termined by a, and of the same order as «, and also of the 

 same sign. 



16. The Compensator. — This is a slip of plate glass held in 

 the hands, and strained either by flexure round its thickness, 

 or by simple tension or compression from the two ends. In 

 the present experiments the slips used were of the best plate, 



