744 



to those, which are ah-eady written down, viz. |', $ii, etc. ^dP 

 and ndP are wanting. L represents the first term of (12). For the 

 sake of simpHfication {y,) has been replaced by y. 

 If we expand (5) into a series, we find: 



i2rg, + if,tj,^-(F,-.)^P-è(^^ -^)^^^+^. + (2/.-^)^>.=0 (14) 



Herein R^ contains only terms, infinitely small with respect to 

 those preceding, L, represents the second term of (12); (i/,), has 

 been replaced by y^. 



Now, in the point H the denominator of (8) (XI) is equal to zero, 



therefore : 



(2/: - i5) v+{y- y.) V + (/? - .V) v,^o. 



We write this condition in the form : 



V-v V-v V-V 



= - = = (u (15) 



Now we have the four relations (11), (12), (13) and (14) between 

 the five variables. If we multiply (13) with y,—^ and (14) with 

 {y — (S) then follows: 



iii-^ 



/ OF dv . _ 



-t 



(y-i3) 



/OF dc , 



. (16) 



+ 



These equations may be satistied when we take § and S,^ of the 

 order dP' and ii and ii, of the order dP. From ri2), f 13) and (14) 

 then follow^s: 



OF OF, 



tii-^^dP=t,v^+^dP 

 dy dy, 



f ÖF\ 



^^ii = ft 





dP 



(17) 

 (18) 

 (19) 



These last three equations are, as is seen immediately, dependent 

 on one another. Substituting i\ from (18) and i]^ from (19) in ^16 

 we find : 



2 RT 



{y.-?)-{y-i^) 



el' 



^ = a.dP' 



(20) 



Herein §i : § is fixed by (11) ; further is 



