694 Lord Kelvin : The Problem of 
"Whence, by (6), we find 
dt _ k — 1 g 
dz~ T~S .... 
and, I (2) repeated) 
(13); 
HtF* ^ 
§ 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, suffi- 
ciently 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)/(&S) for the different gases or gaseous 
mixtures. 
§ 15. For the terrestrial atmosphere we have by (4) 
t—t= 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 Centi- 
grade, per 27*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 conden- 
sation 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 he with no disturbance from radiation in 
air saturated with moisture, at 4° C. 
