74 ON THE ALGEBRAICAL SOLUTION OF 

 If in this we replace # 4 by # 4 i/ 4 we obtain 



( (x 2 c 8 - X 2 6 8 )] 4 + */[2x jx6c( (x 2 c 8 - X 2 & 8 )z] 4 (5) 



Equation (5) is an algebraical solution of the equation 



for all finite values of X, (z, and v. 



Thus, putting c=#=2, b=y=l, equation (5) becomes 



(6) 

 For example X=2, jx=l, ^=3 gives 



3 4 + 2- 33 4 + 3- 14 4 = 1 7 4 + 2- 23 4 + 3- 28 4 . 



r=r r=r 



Again, if in (4) we replace i/x 4 by 2ive r 4 Sv r 2/ r 4 , we obtain 



an equation 



*) (7) 

 which is an algebraical solution of the equation 



<J T ~~ = '^ 





for all values of r except r=0. 



Finally, if in (7) we put all the ?/'s equal to zero, we obtain 



-X 2 6 4 ((x 2 c 8 -X 2 6 8 )] 4 



j] 4 +( A [2( A 3 c 4 ^ r ^ 4 



(8) 



