466 MR WILLIAM SWAN ON THE 
On the other hand, rays proceeding to the eye from the edge of the sun in the 
direction B®, will pass obliquely through the stratum, which, from its small thick- 
ness, may be regarded as a lamina, bounded by parallel planes perpendicular to 
Bb.. The thickness 60’ of the medium traversed by the rays, will therefore be 
tsec BOC = ¢ cosec a, 
where a is the angle BC/; and the number of rays that escape absorption will be 
1 cosec a SEC a 
(a- 5) e _— wre 
Then, putting /,,/,, for the apparent brightnesses of the sun’s disc at A and 
B, as seen from the earth, the ratio of /, to /, will be that of the numbers of rays 
transmitted at the points 0’ d’ ; or, 
h, ME core —_Mw (cosec « — 1) 
hh, Me 
Now, the nearer a ¢ is to the surface of the sun, the smaller is a, and for a 
small angle, cosec a will be very large; hence, for a stratum near the surface, 
since M is less than unity, the ratio of /, to h, will be very great.’ On the other 
hand, as the distance of the stratum from the surface increases, cosec a approaches 
to unity, and h, becomes nearly equal to h,. 
It thus appears that the effect of the oblique transmission of the lateral rays 
through the sun’s atmosphere in increasing the absorption of those rays, and hence 
diminishing the apparent brightness of the sun’s limb, as compared with his centre, 
is very great in the case of those strata of the atmosphere which are near his sur- 
face; but that it rapidly diminishes, as the strata are more and more removed from 
the surface of the sun. Hence, even if we suppose the solar atmosphere equally 
dense and equally absorptive throughout its whole extent, the diminished bright- 
ness of the sun’s limb contrasted with that of his centre, would be due chiefly to 
the action of those portions of the atmosphere which are near his surface. But, 
besides this, from the necessarily rapid diminution of their density, the absorp- 
tive action of the successive strata of the solar atmosphere on light must quickly 
diminish, as their height above the surface increases ; and this will conspire, with 
the continually lessening obliquity with which the sun’s lateral rays traverse the 
higher strata of his atmosphere, so as to render their action in causing the di- 
minished brightness of the sun’s limb probably insensible. 
Since, then, the observed darkness of the sun’s limb, is due chiefly to a com- 
paratively thin layer of atmosphere near his surface, the very notable amount 
of that darkness renders it necessary for us to regard those portions of the atmo- 
’ sphere as very highly absorptive. The thin envelope of cloud which has been 
supposed to surround the sun, near his surface, is precisely such an agent as 
would produce the phenomenon now under consideration; and we may thus, 
perhaps, regard the diminished brightness of the sun’s limb as a corroborative 
proof of the existence of such an envelope. 
ale i ee 
Aelia: 

