( 626 ) 



(ho same value. But for the second point of intersection the two 



sections are concave seen from below - and there are no real lines 



of intersection. This second point is a real point of maximum pressure. 



With all these properties, and also with those mentioned before or 



d'a 1 ... 



still to be mentioned, — is assumed to be positive. l ) 



dx 2 



Now the curve p = constant passing through the first point of 



(dp\ fdp\ 



intersection which the curves - =0 and [ — = have in 



\dvJxT \dxJ üT 



common, is the isobar whose shape we can give, which shape 



at the same time is decisive for all those following, either for 



larger or smaller value of p. In the adjoined figure 1 its course is 



represented. Coming from the left it retains its direction to the 



fdp\ 

 right also in the point of intersection with the curve 1—1=0, 



\llX J 



the convex side all the time turned to the .u-axis till it is directed 

 straight downward in the point where it meets the vapour 



branch of the curve ( — J = 0. There it has a tangent // v-axis, and 

 \dvJ x T 



from there it has turned its concave side to the -r-axis. When it 



meets the curve f — ] = 0, ( — ) is equal to for (his as for all 

 \dxJ vT \dxj p 



fdp\ fdv\ 

 isobars. Passing again through the curve I — 1 , I — J is again infi- 

 nitely large, and pursuing its course, it passes for the second time 

 through the double point, and further moves to the right, always 

 passing to smaller values of v, till it has again a tangent // to the 



axis of ,r, when it meets the curve ( — - J = once more, after which 



it proceeds to larger value of v. It is clear that in the path it describes 

 from the double point till it passes through this point for the second 

 time, it has passed round the point we have called the second point 



fdp\ 



l ) That the characters of the two points of intersection of the curve — = 



\dxJ vT 



with the curve ( — ) = are different appears among others from this that when 



\dvJxT 

 these points of intersection coincide as is the case when these curves touch each 



d*p d*p ( d*p Y a , . 



other, the quantity *— = 0. The character of the points of mter- 



dv' 2 dx* \dx dvj 



section depends on this quantity being positive or negative. 



