INTO THE FORM OF THE WAVE-SURFACE OF QUARTZ. 
315 
Clebsch, ‘ Crelle’s Journal/ band 57 (1859), p. 356. 
Sarrau, Liouville, ser. 2, tome 13.(1868), p. 101. 
Boussinesq, Liouville, ser. 2, tome 3 (1868), p. 335. 
Lang, Pogg. Ann. Ergbd., band 8 (1878), p. 622. 
Lommel, Wied. Ann., band 15 (1882), p. 389. 
Kettler, Wied. Ann., band 16 (1882), p. 109. 
Voigt, Wied. Ann., band 19 (1883), p. 898. 
For some account of most of these theories see Glazebrook’s ‘ Report on Physical 
Optics,’ Brit. Assoc., 1885. 
Corrections for error of axis in Plate 1. 
The calculations were made as though the ODtic axis were coincident with the 
normal to the faces. To compensate for this certain small corrections have to be 
applied to the observed diameters. The error parallel to plane A was 1° 45', parallel 
to plane B 18'. First consider the measurements in plane A, and take the error 
a— 1° 45' by itself. It is clear that we may calculate what the error would be, on the 
assumption that MacCullagh’s theory were true, for any value of </> which is near 
the true value, and take this with sufficient accuracy to be the actual error on any one 
of the theories. 
Let 4>=4>i give a band on one side. The angle of refraction is then fa — a, so we 
have 
iW (<»,-.) = Pi s 3^,4 ^ +Do » 
Solving we get fa, and from the equation sin ((f)i~ a) = a sin q we obtain q, the angle 
of incidence on that side. 
Similarly, putting a for —a we obtain i 3 the angle of incidence on the other side. 
The observed diameter is then q-ffiq, and we take fa to be the value of <f> which would 
give the dark band in a piece correctly cut, where sin fa=a sin 
£i + to. 
But the true 
value is fa where 
P COS 2 (j) i 
T 2 
= P X 2 shPfa+D [} 
By calculating fa and fa we obtain the proper correction to apply to fa, and therefore 
to the observed diameter. In practice I found that the correction could be obtained 
with sufficient accuracy on the assumption that <f>i = (f> 2 =fa- 
On this score I had to subtract from the observed diameters of the successive rings 
1/ 
2 
1 ' 
2 
3/ 
4 
r p u' 2' 
2 s 2 
