128 WM. THOMSON ON THE CONVECTIVE EQUILIBRIUM 



equal to what would be produced by keeping it at constant 

 volume^ V + dv, and removing a quantity of beat equal to 



tbe thermal equivalent oipdv. This is expressed by -^pdv, 



if we adopt the usual notation_, J, for the dynamical equi- 

 valent of the thermal unit. Now, if t and t + dt denote 

 the primitive and the cooled temperatures, so that —dt 

 expresses the cooling eflPect (which is positive, dt being 

 negative), the bulk of the vapour, if at saturation in each 



s -\~ ds 

 case, would tend to be v if s denote the volume of a 



' s 



pound of vapour at saturation at any temperature t, and 

 s-\-ds its volume at temperature t + dt. Hence if, as it 



ds 

 will be seen is the case, ?;— is greater than dv, a portion 



ds 

 equal in bulk to v dv of the water primitively in 



vapour, must become condensed. Hence the abstraction 



of the heat y pdv produces two effects ; it cools the mass 



of air at constant volume from temperature t to tempera- 

 ture t + dtj and it condenses a bulk 



ds , 



V dv 



s 



of vapour. Hence, if L denote the latent heat of a cubic 

 foot of vapour of water at temperature t, and N the specific 

 heat of one pound of air in constant volume, we have 



I / ds \^ 



^pdv='N X { — dt)-i-'Llv dvj) 



if we suppose the mass of air considered to weigh 1 lb. 



* If L=o, this equation becomes 



Ipdv^-Nxi-dt), 



