183 
Undulatory Theory of Light — Absorption, 
Put a, nt + kx + h = co, then >j = a sin w, ^ = /3 a 
sin {oo 4- y) =s ^ a (cos y sin w 4- sin y cos ca) ; which last ex- 
pression for ? gives 
(? — /3 ot cos y sin co)^ -==^ a sin y cos wf 
= (/3 a sin yY (1 — sin^ w). 
But, since a sin w = >j, this equation gives 
(^—l3 cos y. >)Y = sin yY — (/3 sin y. >j)^; 
hence we find 
/3^a‘^sin"y 
2 cosy. >3 ? , 
jSa^sin^y ’ 
( 4 ? 4 ?.) 
an equation to an ellipse of which ij and ? are the coordi- 
nates. 
Consequently, when the system is in the state of motion 
expressed by the equations (4*3.) every molecule describes an 
ellipse round its place of rest ; and the equations (35.) show 
that the general motion of the system is equivalent to a num- 
ber of coexisting motions of the same kind. 
The period of the revolutions of the molecules, in the 
• 2 TT 
movement represented by (43.), is equal to — ; where 2 tt is 
n 
the circumference of a circle whose radius is unity. And 
this movement is transmitted through the medium in a series 
of continuous waves ; the length, or rather thickness, of each 
wave being — , The direction in which the waves travel 
depends on the sign of k, supposing that of n to continue 
the same. But, by the equations (22.), it appears that the 
sign of n is arbitrary : therefore n as well as the arbitrary 
quantities a and 5, may be written either positively or nega- 
tively. Now if we change the signs of n, 5, in (43.), it is 
virtually the same thing as changing the signs of k and y, 
while those of n, 5, remain the same. Consequently, when 
we take for the positive direction of .r, that in which the 
waves travel, we may write the equations (43.) thus : 
— kx h)^ 
^ ^ a sin {nt — k X + b ^ y) , 
and suppose n and k to be positive. 
The intensity of the light is considered to be measured by 
the vis viva of the molecules, which, when other things are 
equal, is proportional to the square of the amplitude of vibra- 
tion. Thus, when the movement is represented by (45.), the 
