818 
Proceedings of the Boyal Society 
Ray. 
Scale Reading. 
Mean. 
Angle. 
Corresp. 
Total 
Rotation 
D 
21®, 23°, 22y, 21°, 2iy, 21°, 21", 22®, 22°, 22® 
22® 
78’ 
1518° 
E 
128®, 128|°, 128®, 129®, 128®, 128®, 128§ 
128® 
128° 
1928® 
b 
72°, 73°, 73°, 72®, 72° 
72^° 
271° 
20071® 
F 
129®, 129®, 131®, 129®, 129°, 129°, 130®, 130°, 129®, 129° 
129° 
151° 
2311® 
To find the multiple of 7 r to be added to the measured rotation 
for the ray D, let y— the ratio of the length of the long quartz to 
the length of the short, cq = the rotation for D in the short quartz, 
oq' = the rotation for D in the long quartz above the nearest dark 
band in the less refrangible part of the spectrum, then, 
a^y = mr + cq'. 
Similarly for the ray E, a 2 y = mr + a 2 ', where a 2 ' is equal to 
27r+ 128°. Combining the equations for the different rays, 
y%o? = mr%a + %aa. 
This equation gives n = 8. Hence 
P (D) = 91080 = A + g + C , 
P (E) = 115680 = A + | + C, 
p(F) = 138660 = A + B + C 
The values obtained for the constants are A = 5289(1 0) 5 , 
B= - 4896(10) 8 , C = 1509(10) 12 . 
Using these values, p(b) = 120200'. The observed rotation is, 
120450'. Beducing the constants to their value per mm., we get, 
for the short quartz, 
A = 7485(10) 3 , B= - 4756(10) 6 , C = 1326(10) 10 ; 
and for the long quartz, 
A = 7557(10) 3 , B= - 6995(10) 6 , C = 2156(10) 10 . 
