450 The Atmospheres of the Planets. [October, 
in fact that the depth of the atmosphere was as much as one- 
tenth the apparent diameter of the planet, the mean density 
of this would be nearly doubled. It has been often urged, 
therefore, that the real average density of these planets may 
be much greater than that usually supposed, from their real 
dimensions being far less than their apparent; the aug- 
mentation arising from the presence of cloud-bearing 
atmospheres, that on Jupiter, it is assumed, may be as much 
as eight to ten thousand miles in depth. But no attempt 
appears to have been made to ascertain how far these 
supposed great depths of cloud-bearing atmosphere are 
consistent with those known dynamical laws which 
inflexibly sway the condition of gaseous envelopes on 
the other planets beside the earth; or whether, to render 
such immense atmospheres possible on these giant planets, 
conditions must not be assumed that are inadmissible. 
The laws on which the physical condition of the atmo- 
spheric envelope of any of the planets may be regarded as 
depending have been long known, and have been applied 
with tolerable success in obtaining an approximate 
acquaintance with principal variations in the atmosphere of 
the earth, and for the higher regions of the gaseous envelope 
of any planet the theoretical constitution may be considered 
to have been determined, in so far as its solution is reduced 
to the ascertaining of the value of a single constant. Butno 
attempt seems to have been made to apply these results to 
other planets than the earth, nor have they been piaced in a 
distinét and convenient form for this purpose. A sufficiently 
approximate form of these equations can be derived very 
simply, and, as will be shown, made to afford results of con- 
siderable importance in considering the true nature of the 
planetary atmospheres. 
Let 
a = Radius of the planet. 
£0 5. fo tt = Force of gravity, density, pressure, 
and temperature of the atmosphere at the 
surface of the planet, and 
g & p ¢ = the same ata distance x above the 
surface. 
Then— 
dp=—gbdax . ea as) 
and replacing g by it value g. and change the vari- 
ee. 
(a+x)’ 
able to s where— 
x 
Ss = aK ot eo hom Mens (2) 
