1885.] Form of the Wave Surface of Quartz. 411 



Thus Sarrau alone succeeds in explaining the observations satisfac- 

 torily. 



For the larger values of 0, I calculated on Sarrau's theory what 

 value of a — b was required to give the retardation observed in each 

 ring, and obtained as follows : — 



<p 15° 14' 18° 21' 23° 16J' 28° 7|' 32° 7' 35° 34' 38° 36' 



a-b ... -0037916 '0037922 -0037927 '0037931 -0037939 0037932 , '0037936 



The observations on the plate cut parallel to the axis gave — 



<p 53° 58' 57° ll 7 64° 45' 72° 13' 79° 53' 83° 40' 85° 37' 



a-b ... -0037949 -0037947 -0037945 '0037944 -0037943 -0037946 -0037944 



In this last set the retardation amounted to about 300 wave-lengths, 

 so that the bands corresponding* to the two D lines were consider- 

 ably separated, and the bands seen were consequently ill defined. 

 Fortunately, however, a large angular error only produced a small 

 change in a — b, so that these results are far more accurate than those 

 of the other two sets. For 0>5O° the rotatory term is negligible, and 

 Sarrau's theory is reduced to the simple Huyghenian construction. 

 So our observations show that for 0>5O° the Huyghenian construc- 

 tion represents the wave surface in quartz with great accuracy. 



From 0=15° to 0=50° there is a slight but persistent increase of 

 a — b with 0. It is shown in the paper that this may be satisfactorily 

 accounted for by using the more general form of Sarrau's wave 

 surface, viz., (s 2 — a 2 ) (s 2 — a 2 cos 2 0— b 2 sin 2 0). 



- (92 cos2 +fi sin2 0) (02 cos3 0— 9\ s^ 2 0) • 



Here s is the wave velocity and a, b, g 2 , / 1? g 1 are constants, g% 

 depending on the rotatory power. Up to this point we have been 

 supposing /j and g Y are negligible. If now we make ^ 2 u 2 g !2 (g 1 —f 1 ) 

 = "00033(a 2 — 6 2 ) 2 X 2 , we find that Sarrau's theory agrees with observa- 

 tion throughout within the limits of experimental error, even in the 

 case of the first ring. 



The observations were taken in the Cavendish Laboratory, Gam- 

 bridge, during the months of March and June, 1885. 



For full- details as to the apparatus, the plates of quartz used, the 

 mode of observation, the precautions necessary, the temperature 

 effects, and the calculations, reference must be made to the paper. 



2 e 2 



