( 733 ) 



The (/-line which passes through the first point where the above 

 condition is negative, has, therefore, a real double point, and runs round 

 the other point, of intersection before passing through this double point 



for the second time. In Fig. 6 the dotted closed curve - - = has 



dx* 



been traced, and also the dotted curve [ -~ j = — ( ( -LjL ) — 0. The 



\dxj \dvdxj 



point of intersection lying on the left, is the double point. According 

 to what was stated before, — - is negative in this point, and the 



d\p 



quantity is positive, which is also to be deduced from what was 



dxdv 



d*p d\p 



mentioned previously about the sign of = . So the cri- 



dxdv dxdv 1 



terion by which the reality of the two directions of ( — ) is tested is 



\dxj q 



satisfied in that point of intersection. In the second point of inter- 

 chip dhp 



section — — is positive, and is also positive. It is true that it 



dx z dxdv 9 l 



, • , dh P d *ty ^ f &ty\ % 

 does nat tollow from this that > | - — but 1 it 



dx* dxdv 9 ^ \dvdx % ) 



appears in the drawing of the loop-g-line that there is no other 

 possibility but that it runs round the second point of intersection, 

 and 2 it appears, that just as we have mentioned in the analogous 

 case for the shape of the p-lines (Footnote p. 626), only when the 



two points of intersection coincide, so when the two curves = 



dx* 



, (?^ n . d'w d*w ( d*tv V 



and — — = touch, the quantity — — — — — — — - is equal to 



dxdv dx* dxdv 2 \dvdx*J 



0. In the case that -j-^ = has greater dimensions, so at lower 



dx~* 



temperature, the loop-(/-line will, of course, extend still much more 



to the right, and the higher (/-lines must be strongly compressed at 



f<lp\ 

 the point where the curve 1 — 1=0 cuts the second axis (the line 



x = 1). 



This loop-ry-line determines the course of all the other (/-lines. 



Thus in fig. (> a somewhat higher (/-line passes through = 0, 



in vertical direction just above the double point, rises then till it 



50* 



