ON THE ENERGY OF STORMS MARGULES 593 



SK + (R) = C p | j (T t - TO dm, + !! j (T 2 - T' 2 ) dm 2 \ 



= C p ^ { T\ (p 0l - p h ) + T 2 (£ 02 - ft,) - gl l (p Q2 + p h ) ) 



This is the same value as before, and now the same considerations 

 as in §25 lead to the approximate formula (I) of that article for the 

 velocity V. We arrive at the same result as if instead of the 

 fictitious gas in chamber 2 we had used dry air of the same average 

 temperature. The reason why this happens is shown by the course 

 of the analysis. The change of P + I for the unit mass remains the 

 same no matter whether chamber 2 is filled with dry air or with the 

 gas; the amount that the mass 1 contributes to the available kinetic 

 energy remains unchanged. 



The contribution of mass 2 by simple change of location only, or 



the change of p + I for this mass, (which is C p j (T 2 — T f 2 )dm 2 ), 



is in the new case (for the fictitious gas) smaller than for dry air 

 since the gas cools less by expansion and therefore T' 2 is larger. 



But on account of the development of heat associated with the 

 expansion (which we have, introduced as equivalent to the latent 

 heat of condensation) there is (Q) to be added to the expression 

 £ K + (R) and for the fictitious gas the expression 



«3) +C p j(T 2 -T' 2 )dm 2 



is as large as the second term alone would be for dry air. 



Thus it is that the addition of heat by virtue of the expansion 

 causes no increase in the available kinetic energy, but serves only 

 to warm the expanding mass or to diminish its cooling. 



§(40) The difference between the fictitious gas and the moist air. 



In order to simplify the analysis and investigate separately 

 the influence of the latent heat of condensation we have given the 

 fictitious gas that has replaced moist air the properties of dry air 

 and have only introduced the condition that it shall expand when 

 heat is added. In order that it might more nearly resemble moist 

 air we should have also assumed its density smaller and its R to be 

 variable with its condition. 



