( «36 ) 



be found such that, proceeding along that same #-line 





So from this follows immediately 1. that the points of the said locus 



fdp\ 

 restrict themselves to those values of x in which the curve -—1=0 



\dx,J v 



occurs, 2. that the points must be found with smaller volumes than 



those of ( — ] = 0. For such points with smaller volume is viz. 

 \dxj v 



( ) positive, and for points with greater volume negative — 

 \dasj v 



however when the volume may be considered as a gas volume this 



negative value has an exceedingly small amount. And even without 



GO 



drawing up the equation If — ) dv = 0, we conclude that the said locus 



has the same ^-asymptote as ( — ) = itself, and is further to be 



\dwj v 



found at smaller volumes. Hence it will also have a point where 

 its tangent runs // t r-axis. There is even a whole series of loci to be 

 given of more or less importance for our theory, which have a 



course analogous to that of ( — ) = and |( — Wu = 0. 



\dxj v J yd.vju 



V 



The latter is obtained from f— ) by integration with respect to v ; 



\dxj c 



all the differential quotients with respect to v of the same function 



fdp\ d 2 p 



I — put equal to have an analogous course — thus = 



\dxj v dxdv 



which is a locus of great importance for our theory. That it has the same 



x asymptote as I — J =0 itself, and that all its other points are to 



\dxj ü 



be found at higher value of v, follows immediately from the follow- 



fdp\ 

 ing consideration. For a point of the line — =0 the value of 



\dxJ oT 



fdp\ 



I — = 0. tor points of the same x and smaller v this value is 



\dxj 



positive — but for points with larger v negative. For v = oo this negative 



value has, however, again returned to 0. So there must have been 



a maximum negative value for a certain volume larger than that 



