84 Mr. J. F. W. Herschel on the action of 
The last column of this table exhibits the deviations in 
excess or defect of the values of the quantity h, so computed 
from the mean of all of them. Their smallness, in comparison 
with the quantity itself, and their alternations of sign, are 
evident proofs of the constancy of this coefficient, and we are 
therefore authorized to take sin 9 x sin 9 ' as the general value 
of \p( 9 } 9 '). The observations on Rochelle salt, presently 
to be noticed, confirm this law.* If we denote by l the mini- 
mum length of a double oscillation, or the space passed over 
during one complete period by a ray transmitted at right 
angles to both axes, we have k = y ; and consequently h = y , 
lz= ht. If we substitute for h and t their values above found, 
we obtain 
/ = 0-00076497 inch 
for the minimum length of a period performed by a mean red 
ray in mica. 
* When QnO', as in crystals with one axis, we have 4 (0, 0') zz sin 0*, a result 
long since confirmed by the accurate experiments of Brewster and Biot. The 
velocity of the extraordinary ray in such crystals is given by the formula tArzV 1 -!- 
a . sin 0’\ Following this analogy, we may conclude that in crystals with two axes 
we should have v a — V 1 -!- a . sin 0 . sin 6'. Now this is precisely the expression at 
which M. Biot has recently arrived. This very simple and elegant result was 
communicated to me by that eminent philosopher in the spring of this year, and 
subsequently in a letter of the zd May. His Memoir on the subject, which appears 
(by the Ann. de Chim.) to have been read to the Institute in April, I have not seen, 
nor do I know by what precise steps he was led to it, but presume it must have 
been by some considerations of the nature above described. In the foregoing investi- 
gation of the law of periodicity, I beg leave therefore to disclaim all intention of 
arrogating to myself any share in this beautiful discovery, but have thought it ne- 
cessary to state the steps in the text, in order to demonstrate a truth essential to the 
investigations to follow, which could not have been taken for granted, or deduced by 
any legitimate reasoning, independent of experiment, from the equation rA —V 1 -f- 
a. . sin 9 . sin S', by reason of our ignorance of the nature and mode of action of the 
polarising forces ; and, have purposely abstained from entering any farther into the 
general laws of double refraction and polarisation than I could possibly avoid. 
