( S97 ) 



The equation (14) tells us then 



- i,{F,x-{-F;,y)=zc, 

 (>!• with the aid of ihc iiomogeneous equation (13) 



thus 



and 



or 



c 



'^ = y: ■ 



d.v cFy 



F^dx 



dt, = — — , 

 ' czF, 



(25) 



(26) 



(27) 



where the factor c has been introduced in the denominator for the 

 sake of homogeneity. 



Differentiation of (26) according to t^ gives : 



^_„ ^ ^ F~F,;-F^FJ ^ ^ F:{F,^x'^F ,,,i,')~F,{F,,x'-\-F,,>j') 



F^ 



Fz 



^^ VF,{F,,F, -F,„F^^ - F,{F,,F;,-F,,F,)\ 



= J_. U'\{^\,F,-F,,,F,) - F,{F,,F,,-F,,F,)]. 



B^- application of the formulae 



{n — l)Fx — xF_,j. + yF^.;, + i^^, etc., 

 n{„—\)F = .r^F,,, + 2xyF:ni + y'F,,,i + -IxF,, -f 2///'^, -\^ F,, = 

 the form between [ J can be i-educed to 



I J^ XX^ -^ XJ/^ ^ xz 



X '\ 



Fxi/i Fffif, F,f. 

 Fx~., Fy,, F,, 



Let us put 



we then lind 



{n-Xf 



Fxx^ Fj;/, F_i-~ I 



F,,/, F,,,,, F,,, z=zH, (28) 



Fxz-, Fuzt F~z 



(n — iyFJ 



X, 



2V 



