f 250 ) 



value of —f or y, must then I)e smalh'i' than that calculated from 



(4). If we then find a negative value for ip^, the case of fig. 5 is 

 entirely excluded for the given values of 7\, 1\ and q^. In the 

 equation (4) we have therefore at any rate a criterion to determine 

 whether or no the case of fig. 5 can occur, wlien the value ofji' 

 lies between those to which the figures 3 and 6 ap})ly. 



3. Another important question will be, when the point of inflection 

 L with oblique tangent (fig. 7) will disappear, and whether it can 

 still be present e.g. with ^' = 0. 



dT d'T 



Let us for this pur])ose determine the values -— and 



We found before (I.e. p. 155): 





d.v (1 — .v')w^-^,v'w^ 



where 



ö'S 



ET 



dT 

 dx 



dii 



T- 



dx 



..'■i ' 



<■"-'•■' d-. 



I 

 V 



(1 — x)rv^-\-xw^ 

 RT 



d.r' x{\-x) 



u.\ = ^j -f ax- — a'x'^ 



Hence we get: 



RT 

 (x—x') — 

 dT 



— 2 «', 



dx'-' x'{l—x') 



-= — T 



x{\-x) 



{l-x')w^-j-.r'w^ 



dT 



1^' 



{x-x') 



— - T- 



RT 



a^{l-o^) 



2«' 



(1— .;;)«'i+.m'. 



, (6) 



dT dT 



from which we see i. a., that when e.g. -— has been calculated, — -, 



dx dx 



can be found by substituting ./"' for .t, — 7' for T', — a' for a' and 



— a for a and by then reversing the sign of the second member. 



d'^T dn' 



The same holds for — - , when - — is determined. From (6) follows 



dx djr 



far the point .1, whei-e T=:7\, .c=,c':=i), y\=q^: 

 RT^Y /,/A \ /dT\ RT 



~ ~ " ' d^' 



(-) = 



(7) 



71 V Wo/ V'-'Vo Qi 



The initial direction depends therefore on the limit of the value of 



. We found for this expression (I.e. p. 156) : 





T. 



(8) 



