Undulatory Theory of Light. 271 
cule on the opposite side of m; consequently the signs of the 
odd products of the variations will be changed, while the ab- 
solute values of the variations and of their products remain 
the same for both molecules. This supposition respecting the 
arrangement of the molecules is due to M. Cauchy, and ap- 
pears very probable; because it seems impossible to conceive 
how the equilibrium could subsist unless it were true. It is 
also probable that the sphere of the influence of each mole- 
cule comprehends a great number of other molecules; and 
accordingly we shall assume this as an hypothesis. Now, as 
we cannot suppose the molecules, in their state of equilibrium, 
to be more crowded in one part of the sphere than another, it 
follows that the terms of the other sums =. (r) Ay A 2’, 
V(r) AyAxr, =.y (7) AZAz, =. (7) Az Az’, &c., in 
which there are odd powers of the variations, will be about 
half of them positive and half negative, and will nearly destroy 
each other, and consequently these sums will nearly vanish. 
Neglecting them as well as the former, the first of the equa- 
tions (3.) becomes, by the substitution, 
ae Age ae 
Tea me{ (He) +9008). (Fae +58 Ae 4 ke) | 
The second and third of the equations (3.) are of the same 
form as the first; consequently, if we transform them in the 
same manner, and, for the sake of abridgement, put 
> =. (¢ (7) + b(r) Az*) Ax? = 3? 
m™ f " : 
aage (or) + ¥ (7) Aw’) Act = 
&e. &e. 
F=-(¢ (r) + W(r) Ay’) Aa? = s? 
(1.) 
mE. (O(r) +H (r) Ay?) Artes 5) 
2.3.4 
&e. &ce. 
m 
a = .(¢ (7) + P(r) Az’) Aa? = a 
bee 
or Z.(o(r) + ¥(r7) Ar) Aat= af" 
&ec. &e. 
we shall have 
