INTO THE FORM OF THE WAVE-SURFACE OF QUARTZ. 
323 
3 rings <j>= 8° to 6° a—b lies between '0037860 and '0037954 
[1 ring (f>= 4° 24' „ „ '0037620 „ '0037808 
Taking into consideration the probable accuracy of tbe observations the discrepancy is 
about equally strongly marked in tbe case of the first ring and tbe three rings 13° to 
8°, and to a minor degree in the case of some of tbe others. The observations on 
Plate 1 are not here included, as we do not know tbe ratio of the thickness of Plate 1 
to that of Plate 3 with sufficient accuracy.'"'] 
Up to this point we have been treating certain constants, f x and g x , which appear 
in Sarrau’s expressions as negligibly small. We will now examine whether by the 
aid of these constants we can obtain a more satisfactory agreement with observation. 
Sarrau’s wave-surface is given by 
47 T“Cl 
(s 3 —a 3 )!*’ 3 — a~ cos 3 (f> — b 3 sin 3 </>) = ■ - (g 2 cos 3 <f>-\-f x sin 3 4>)(g% cos 3 < f>—g x sin 3 (f>) 
Putting <f)= 90°, we obtain for the equatorial radii a and /3. 
(.9 3 -n 3 )(s 3 -6 3 ) 
47T 2 « 
We might treat this equation to the wave-surface exactly as we have treated the 
simpler one, and obtain values of a — /3 from the observations on the different values 
of <f). But it may be shown without difficulty that if we equate the values of a—b 
previously found to 
(a—/3)(1 d -k cot 3 <f>) 
where 
St rV —g x ) 
A 3 (a 2 —6 2 ) 2 
we shall attain the same result. In this it is, of course, assumed that f x and g x are 
small. 
I have found that a suitable value of k is —'000033. Using this value we obtain 
the following figures :— 
• 90° 
to 
53° 
a —/3 lies between '0037941 
and 
'0037949 
39° 
to 
26° 
„ „ '0037931 
•0037943 
25° 
to 
14° 
„ „ '0037919 
5? 
•0037943 
13° 
to 
8° 
„ „ '0037914 
5 ? 
•0037956 
8° 
to 
6° 
„ „ -0037943 
5 ? 
•0038037 
4° 
24' 
„ „ '0037830 
;? 
•0038018 
* Added May 31, 1886. 
2 t 2 
