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; but 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-\-dVy 

 andjemoving a quantity of heat equal to the thermal equivalent 



oi 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 5 denote the volume 



of a pound of vapour at saturation at any temperature t, and 



s-\-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 



* " On the Changes of Temperature produced by the Earefaction and Con- 

 densation of Air," commumcated to the Eoyal Society June 20, 1844, and 

 published in the " Philosophical Magazine," 1845, first half year. 



