2 Prof. Buff on the Relation between the 



and likewise v 



- = 10* 273+t (2) 



By combining equations (1) and (2), it follows that 



, 273 + ^ + t 

 log 



and 



MZ + t ,OV 



, /P 273 + < V * " ' w 



^VTars+f+J 



p 7 ^»«. . . . (4) 



If the difference V— V indicate an expansion of the original 

 volume, t becomes negative ; and the fraction u, the cooling con- 



V 



sequent to the expansion of the volume by ^r — *- , is nega- 

 tive likewise; in other respects the same expressions as before 

 hold good. 



It is known that the value of « is constant for air, that is, it 

 is independent of temperature and degree of density ; it is also 

 assumed to be true for all permanent gases. We can determine 

 the extent to which liquefiable gases obey this law when we 

 measure the changes that such gases undergo in temperature 

 and tension by different degrees of compression, the latter never 

 being sufficiently great to cause the gases to become liquid. 



We know with great accuracy the temperatures corresponding 

 to the maximum tensions of vapours, those of water especially, 

 for widely varying densities. The question therefore whether 

 a, for aqueous vapour for instance, is a constant or a changeable 

 magnitude may be decided by help of equation (8). We must 

 of course make the supposition, which though probably not 

 strictly exact is still very nearly correct, that the coefficient of 

 expansion of vapour agrees with that of air. 



Assuming this, the following question might be asked : If 

 saturated aqueous vapour at t° and under p millims. pressure 

 obtain at (*° + t°) and under P millims. pressure a maximum 

 density again, what is the mean value of a between these limit- 

 ing temperatures ? Or, to put the question in another form : 

 How great is the quantity of heat, expressed in fractional parts 

 of a therm ometric degree, which becomes latent or is set free by 



an expansion or contraction amounting to of a change- 



able volume V, which volume at t° and under the pressure p 

 occupies the space V ? 



