173 
There are difficulties connected with the radiation of air 
and earth out into space, and of heat from the sun to air and 
earth ; hut I think a full consideration of all the circum- 
stances must explain the smallness of the decrease of tem- 
perature which observation shows. 
Dr. Joule having suggested that condensation of vapour 
in upward currents of air might account, to a considerable 
extent if not perfectly, for the smallness of the lowering of 
temperature actually found in going up, the Author has added 
the following investigation, in which 'the effect of condensa- 
tion is taken into account. 
If a quantity of air, dry or moist, is allowed to expand 
from bulk v to bulk v+dv, it will do an amount of work 
equal to pdv on the surrounding matter. Now, by the 
principle established approximately by Dr. Joule, in his 
experiments on air in 1844,* the change of temperature which 
the mass will experience will be almost Exactly equal to what 
would be produced by keeping it at constant volume, v-\- dv, 
and’removing a quantity of heat equal to the thermal equivalent 
of pdv. This is expressed by \-pdv, if we adopt the usual 
notation, J, for the dynamical equivalent of the thermal unit. 
Now, if t and t-\-dt denote the primitive and the cooled tem- 
peratures, so that — dt expresses the cooling effect (which is 
positive, dt being negative), the bulk of the vapour, if at 
• . ds 
saturation in each case, would be v — if s denote the volume 
of a pound of vapour at saturation at any temperature t, and 
s-f ds its volume at temperature t-\-dt. Hence if, as it will 
ds 
be seen is the case, v — is greater than dv, a portion equal 
ds 
in bulk to v — - — dv of the water primitively in vapour, must 
s 
# “ On the Changes of Temperature produced by the Rarefaction and Con- 
densation of Air,” communicated to the Royal Society J line 20, 1844, and 
published in the “ Philosophical Magazine,” 1845, first half year. 
