40 
MR. POWER ON THE ABSORPTION OF THE SOLAR RAYS, ETC’. 
When is >1, as in the case of dense refracting substances, glass, water, &c., t he 
better form for the polarizing angle is 
tan 6=^ 
41. If there be no absorption, g—g—f, 
and tan 0=g. 
If the primary and secondary rays are equally absorbed, 
and tanQ=g r 
42. In the theory of the primary wave, whose vibrations are performed in the plane 
of incidence, although I have supposed that these vibrations are perpendicular to the 
directions of the incident, reflected and refracted rays, yet the same demonstration 
will hold whatever be the inclination of the vibrations to the rays, provided it be the 
same for all the three rays. If we denote by s this constant angle of vibration, 
the only change necessary to be made in the wording of No. 14. is, for “transverse” 
to read oblique , and instead of the words “each turned from right to left through a 
right angle,” to read each turned from right to left through an angle (s). Hence, 
whatever be the value of s, the intensity of the reflected ray will be properly repre- 
sented by sin J — ^1- If £ = 0, the vibrations are longitudinal, as in the case of sound. 
If g= 0, we have exactly the case which has been treated by Mr. Green*; as is 
manifest from his symbols-, though his language is indefinite as regards the direction 
of vibration. 
It is therefore extremely interesting to compare Mr. Green’s expression for the 
intensity of the reflected ray, or rather the square of his expression (for he seems to use 
the word intensity in a different sense, namely, that of comparative velocity), with the 
expression observing beforehand, that, from the way in which he has sim- 
plified the calculus, we ought to expect nothing more than an approximate coinci- 
/g; cotJ/V 
dence. The square of Mr. Green’s expression is — jTTT a PPty’ n g bis for- 
(f+Su') 
inula to the case of two gases of different densities, whose constitution admits of 
their remaining in juxtaposition under the same pressure, he in the first place deduces 
the equation 
§> sin 2 0, 
from the known experimental relations between the pressure and the expansion of such 
gases, combined with other parts of his theory; and this substitution being made, the 
square of his formula becomes ^n 2 (0 + 0 ' y which, singularly enough, coincides with 
* Cambridge Transactions, vol. vi. p. 403. 
