Undulatory Theory of Light. 505 
tation, an extremely small quantity, we may reject its powers 
above the first; therefore « = BS . The quantities x, k, a 
approach, as x increases, towards the values which they have 
in the case of plane waves, which values are independent of a. 
And since the small portion of a wave contained within the 
sphere of influence of any molecule cannot, at any sensible 
distance from the centre of agitation, differ sensibly from the 
same portion of a plane wave, we may regard 7, k, a as con- 
stant for all parts of the cone. If then we retain @ to denote 
B 
Bg, the constant part of —*, we have 
oi “ sin (nt — kw + a): 
and, in general, for any cone taken as we have supposed, we 
have, from the equations (2.), 
es (sinnt+hk a+b), 
f=. = sin (nt—ka+a)+ =. 
a . C 
i sh ra sin (n,t—hk,x+a,)+ = . Pi sin (n,t+k,x+b,), (4.) 
s sin (2, f+h,c+0,). 
When the waves all move from the centre of agitation, the 
second sums in the equations (4.) will vanish: and limiting 
our view to a single term of one of the first sums, we have an 
expression for the displacement virtually the same as that 
which Professor Airy, in his valuable tract on the Undulatory 
Theory of Optics, has partly assumed and partly borrowed 
from the theory of sound*. 
It may be observed, by the way, that the method adopted 
in this paper of expressing the displacement of the molecules, 
is analogous to that employed so successfully in physical astro- 
nomy to express the differences between the mean and true 
places of the planets. 
When the molecules are so arranged that the sums s’, s/’, 
s,2, &c. are different for different directions of the coordinates, 
waves going and returning to and from a centre of agitation 
will not be spherical. The most simple case of such waves 
will probably furnish a subject for another paper. 
I am, Gentlemen, yours, &c. 
Evesham, April 15, 1836. Joun Tovey. 
P.S. I perceive that throughout my last paper I inadver- 
tently called the differences Aw, Ay, Az variations. 
* Mathemat. Tracts, p. 271. 
Third Series. Vol. 8. No. 49. June 1836. 3F 
pee irks 
= ea sin (2,t—k,«+,) + - 
