( 396 ) 



We shall now find <h and / as functions of x. 

 Out of (9) follows 



dx z=zc -— . — {ic(( X — '/ ) dx — dx . / , 



3 c V 'C'ix—'i 



01', if we put 



-^^ = if^O^-) (--20) 



•■»</x — H 

 we find 



./t = l/V' - ././• ........ (21) 



According to (10) holds 



'--J*^-.i(,r-;)=^..;:(,,-)-. 



or on account of (18) and (19), 



c dx\ > y .ff/^, — r/ x(fx—fl dx \ \ 



t|.2 



1 1 



r/.rV y ouf,-(id.v x,f—(f, 



3 J 



hence 



^^VV:-2^^ , (22) 



or according to (20), 



_ (A-</'a:— </ ) <y arax — 3.ry , 3:" ^ 



If now w^e take the equation i^(a',,y) = ü or F{,c,y,z)=^0 as 

 basis of our considerations, we tind first of all 



F,x' + F,,y^ = ^. 

 If we understand by o a function for the present not closer 

 defined of t^ we can put 



.^•' = ^F., , y' = - 9F. (24 



