( 627 ) 

 of intersection with the curve [ — ) = 0, and where maximum Dres- 



\dvJxT 



sure is found. In fig. 1 some more isobars have now been drawn 

 besides this one. We obtain the course of the isobars for lower value 

 of p by drawing a curve starting from the left at higher value of 

 v, bearing in mind that two ^-lines of different value of /> can 

 never intersect, because the p is univalent for given value of x 



/dp\ 



and v. Such an isobar cuts the curve — =0 on the left of the 



\dvJ xT 



isobar with the double point in two points, where ( — j = oo, then 



passes through the curve ( — ) = in a point where ( - ) = 0, 



\dxJ vT \dxJvT 



and has then also on the right of the said isobar again two points 



fdp\ 



of intersection with the curve I — = 0, in which points of intersection 



\dvJxT 



■ f dü } 

 again — = oo. 



b \dxJrT 



An isobar of somewhat higher value of p has split up into two 



isolated branches. One of them starts on the right at somewhat smaller 



value of V; further this branch follows the course of the isobar with 



the loop, but must not cut it. Arrived in the neighbourhood of the 



double point it is always obliged to remain at small volumes; there 



fdp\ fdv\ 



it meets the curve —1 = 0, and it has — =0. From this point 

 \dxj„ \dxjp 



it proceeds to smaller volumes, till a new meeting-point with the same 



curve causes this branch again to turn to larger volumes. But the 



second branch of this isobar of higher value of p is entirely inclosed 



within the loop of the loop-isobar. Such a branch forms a closed 



curve surrounding the point which we have called the second point 



fdp\ f dp\ 



of intersection of the curves — = and — = 0. Such a 



\dvj x \dsBj v 



fdp\ 

 closed branch passes twice through I — I = 0, and also twice through 



\dtvy „ 



dp\ . fdv\ 



— = 0, and has again in the first eases — 1 = 0, in the second 



dvj x \dxj p 



fdv\ 

 points of intersection — = oo . 



\dmj p 



With ascending value of p the detached portion of the />-line 



contracts more and more, till it has contracted to a single point. So 



at still higher value of p only one single branch of the j?-line remains. 



