265 
1907-8.] The Problem of a Spherical Gaseous Nebula. 
Now, if the equilibrium is convective, we have by (3) 
dp = 
_ E 
1 t' 
dt 
( 11 ). 
Using this, and (2), in (10), and dividing both members by , we 
( 12 ). 
find 
Whence, by (6), we find 
and, ( (2) repeated 
dt k - 1 gp't' 
dz~~ k p 
dt k-1 g 
dz~ k S 
p 
■ (13); 
• (14). 
§ 14. These are exceedingly important and interesting results. By (13) 
we see that in any part of a wholly gaseous spherical nebula, or in a gaseous 
atmosphere around a solid or liquid nucleus, in convective equilibrium, 
sufficiently stirred to have the same chemical constitution throughout, 
the temperature-gradient of increase inwards is in simple proportion to the 
force of gravity at different distances from the centre. We also see that 
in gaseous spherical nebulas of different chemical constitutions, or in 
gaseous atmospheres of different chemical constitutions, around solid or 
liquid nucleuses, the temperature-gradients at places of the same gravity 
are simply proportional to the values of (k — 1)/ (kS) for the different gases 
•or gaseous mixtures. 
k 
15. For the terrestrial atmosphere we have by (4) 
k-1 
3*44, and by 
the table in § 12, S = 7 ’988 kilometres. The temperature -gradient according 
to (13) is therefore, at the rate of our unit of temperature, or 273 degrees 
Centigrade, per 2 7 '5 kilometres ; or 1° C. in 100*6 metres. This is much 
greater than the temperature-gradient found by Welsh, in balloon ascents 
of about fifty years ago, which was only 1° C. in 161 metres.* Joule, 
with whom I had been in discussion on the subject in 1862, suggested to me 
that the discrepance might be accounted for by the condensation of vapour 
in upward currents of air. In endeavouring to test this suggestion, I made 
some calculations of which results are shown in the following table, 
extracted from a table given in my paper of 1862, referred to in § 2 above. 
* Mr Shaw informs me that much investigation in later times gives a general average 
mean gradient of 1° C. per 164 metres. This is very nearly the same as it would be with 
no disturbance from radiation in air saturated with moisture, at 4° C. 
