MR. POWER ON THE ABSORPTION OF THE SOLAR RAYS. ETC. 
31 
front of the wave, that it is necessary, in order to account for a succession of pulses 
on the retina, giving- for different, values of a the impression of different colours ana- 
logous to different musical notes in the phenomenon of sound. 
To this I reply, that the phases of maxima vis viva will succeed with equal rapidity 
in both cases, which is a complete answer to the objection. 
In fact, if we adopt the hypothesis of a rippled front, the vis viva due to any transverse 
section as it enters the pupil, will have for its expression an integral of the form 
On r Onr 27T 
1$! cos 2 ^-(fl/+c 1 )-)-B 2 cos 2 — (a^-f-c 2 )-l-B 3 cos 2 — (e^-|-c 3 )-f-&c., 
which, writing 
1 -f cos 2 1 
in the place of cos 2 u, and expanding each term, will give an 
expression of the form 
that is, of the form 
or 
or 
A-f-B cos (^~^j +C sin 
/ 47rflA 
T ’ 
A+ A, cos ( ~ A, 
47 zat , . .47 r . 47r at 
cos — -j- A[ sin — A 2 sin — ? 
A+A, coS'y (at-\- A 2 ), 
A— A I -[-2A 1 sin 2 -— (tf£-f-A 2 ), 
A 
whose maximum value, (A + A,) (as also its minimum value (A — A,)), recurs after 
A 2A 
intervals -» — , &c., as is easily seen ; these intervals, in fact, hold for phases of any- 
given denomination, just as in the case of any single elementary portion of the front 
of the wave. 
31. Let us now consider the effect of the divisor 1+s in the formula 
1 l 
/V 
-■(X 
L qa 
1 + s 1 + S qp, 
since 
p.. vis viva communicated to the medium 
s= — = 
p j vis viva of the refracted ray 
We see, that, according as the absorption is greater or less, the values of s may 
range between infinity and zero ; corresponding to which will range between zero 
and (X , the refractive index when there is no absorption. 
But the equation 
sin &,= — sin 
h 
sin d, 
shows that will as soon as 
l+s 
sin d= 1, 
or sind=— • ■ 
l + s 
Hence if s be considerable, 6 must be small in order that there may be a refracted 
