314 
MR. J. C. Me CONNER ON AN EXPERIMENTAL INVESTIGATION 
Kettler are still further from the truth. The other five, MacCullagh, Clebsch, 
Lang, Boussinesq, and Voigt have the first form of expression, giving 
Pi= 
a + ba — b 
2 a a? A, 
15-306. 
Thus Sarrau alone succeeds in explaining the observations satisfactorily, though 
Voigt does put in a proviso that his D 0 may vary with <f>. 
In obtaining the above figures the difficulty arose that a—b was known only roughly 
from spectrometer observations. I have, therefore, had to use the value of a—b 
deduced on Sarrau’s or MacCullagh’s theories from the observations on the very 
large values of <f>, viz., a — b= ’003793^'000002.* It might perhaps be objected that 
it is not fair to test one theory with the value of constant obtained from another. 
But it should be remembered that the separation between the two sheets changes 
very slowly with </> when <f> is nearly 90°, and that I have obtained a measurement for 
*/>= 85° 37'. Thus on any theory I should have obtained much the same value of a — b 
from this measurement. 
Of the above writers Cauchy, Lommel, and Lang give the actual expressions I 
have quoted. The others only give equations to the wave-surface, from which I have 
had to deduce the expressions given above. MacCullagh, Clebsch, Lang, 
Boussinesq, and Voigt all give the same wave-surface, viz., 
(s 2 — a 2 ) (s 2 — a 2 cos 3 (f > — b 2 sin 3 <£) = q 2 
where q is a constant depending on the rotatory power. Sarrau’s wave-surface, 
neglecting certain constants, J\ and q v which he says are probably small, is 
(s 2 — a 2 )(s 2 — a 2 cos 3 <£— b 2 sin 3 <j)) = q 2 cos 4 <£. 
Thus these six theories agree with the Huyghenian construction when the rotatory 
term is neglected. This is d 'priori a great point in their favour, since we know from 
Stokes’s and Glazebrook’s observations that in Iceland Spar the Huyghenian 
construction is a very close approximation to the truth. 
The more complete form of Sarrau’s wave-surface will be examined towards the 
end of the paper. 
The references are as follows :— 
MacCullagh, Trans. Roy. Ir. Acad., vol. 17 (1837), p. 463. 
Cauchy, Ann. de Chim. et de Phys., ser. 3, tome 30 (1850), p. 68 ; a paper 
by Jamin. 
* A better value is ‘0037945+ ‘0000005, -which gives for Sarrau P i =15‘312 + ‘002. Thus, though 
Sarrau’s formula agrees with observation much better than any of the others, there is a small out¬ 
standing discrepancy in the three larger rings in Table II., which is as hard to account for by errors of 
observation, as the great drop in the first ring. This is discussed, and an explanation given near the end 
of the paper.—[May 31, 1886.] 
