24 
MR. POWER ON THE ABSORPTION OF THE SOLAR RAYS, ETC. 
upper sign must therefore be taken, and we shall have generally without ambiguity. 
A 2 -* 2 2 7TC , //, , (A 2 -* 2 ) , 
tan ?= — sec X + V ( 1 + -uv sec 
2ttc\ 
The other value expresses the orientation of the axis minor , since the product of the 
two values is — 1 . 
20. It may be worth observing, that if one of these values had been mistaken for 
the other, it would have made a difference of 90 ° in the direction of vibration in the 
case of a plane polarized ray, for which c— 0, and we should thus be brought back 
to the hypothesis of Fresnel. I mention this merely to show how easily error may 
be introduced in proceeding from one formula to another, and I would suggest the 
possibility that the discrepancies of different theorists on this particular point may 
in some instances be removed by a closer attention to the meaning of ambiguous 
signs. 
21. From the last expression for tan y we may derive those for tan y' and tan y, ; 
for this purpose we have merely to write h 1 k', or k t in the place of h k, and after- 
wards to substitute for h! k' h l k l their values in terms of h k and 6. The results 
would probably admit of simplification in some degree, but I shall content myself 
with having pointed out the mode of obtaining them. 
22. I now proceed to the case in which a portion of the vis viva of the incident 
ray is supposed to be communicated to the refracting medium during the same shock 
which splits up the incident beam into the reflected and refracted rays. 
Denoting by p the vis viva of'the primary component of the incident ray, and by 
P PiP a expenditure of the same upon the reflected ray, the refracted ray and the 
medium respectively, and denoting the angles of incidence and refraction and the 
different amplitudes as before, we shall have 
p=p'+p,+p lP 
Pu 
or putting ‘-f=s, 
P=p'+{l+s)Pr 
But we have already found by integration, 
2t r 2 /i 2 
P~~ 3~ OVM COS 0 
Consequently 
2 t r 2 // 2 
avco cos 0 
2 7 T 2 // 2 
p^-jp-afucos 0 r 
“i 
JPa cos @ /Pa cos 0 (1+ s)h 
*#3 » 3 
We shall further have, as before, 
h! _sin (0 — 0 ; ) 
h sin (0 + 6') 
h / sin (20) 
li sin (0 + 0,)" 
