TEMPERATURE OP ASCENDING CURRENTS VON BEZOLD 341 



The performance of this amount of work requires the consumption 

 of a quantity of heat expressed by 



dQ = AdL = Adh 



If this quantity of heat is to be drawn from a body whose specific 

 heat is c then we have 



dQ = - cdt 

 or 



dt = - ~dt (4) 



which is exactly as found above, if we take the heat from the air and 

 if the abstraction of the heat can go on under constant pressure so 

 that c can be put equal to c p . 



But all this is not possible under the conditions that prevail in a 

 steady ascending current in the atmosphere. The specific mass of 

 air is not enclosed in an envelope that has no weight, in a vacuous 

 space, but it floats in its surrounding atmosphere. 



But even if the above-mentioned condition were fulfilled still the 

 mass would not rise and thereby cool any more than a mass of iron 

 would rise from the earth without the application of exterior forces 

 and would thereby cool 2.09 per rise of 100 meters, as results if we 

 substitute for c the value 0.1 13 as the specific heat of iron. 



On the other hand, the mass of iron will certainly rise and that 

 too without cooling when it forms one member in an endless chain 

 that glides frictionless over a roller and to which there has once been 

 given a velocity, no matter how small. 



"It is therefore a purely arbitrary arithmetical operation when 

 in the formula (4) we substitute for c the value c p as the specific 

 heat of air under constant pressure and thus bring about an apparent 

 agreement with the values deduced from the formulae (1) and (2)." 



The fact that in this treatment the introduction of the specific 

 heat under constant pressure rests on no secure basis, is evident 

 also from the fact that Schmidt himself thought that instead of this, 

 one must substitute the value c v or the specific heat for constant 

 volume instead of the specific heat for constant pressure as used by 

 Guldberg and Mohn. 



The only logical conclusion that we ought to draw from this 

 simultaneous consideration of the work of expansion and the work 

 of lifting is that of a clearer understanding of the results attained by 

 the first-named process. 



