d6l2 Mr. G. B. Jerrard on a Met/iod of Transforming Equations, 

 Reverting to equation (ej), let us now take 



and we shall have, on eliminating Q, 



an equation which is of the same form indeed as the preceding 

 one designated by (e^, but which involves two additional inde- 

 terminate quantities fi and a. In effect 



b' = b + o-, c' = c + 2/A. 



We see, then, that equation {e^') may be reduced to the bi^Qr 

 mial form 



2Dg-|-aS2=0, {ej'^ 



by assigning such values to a- and fj, as will make b' and c' vanish. 

 Again, if we eliminate P, R, and Q from the third of the 

 equations (e), we shall arrive at an homogeneous equation of the 

 third degree relatively to D, q, and S, 



F(D,?,S)3=0, W 



where F is expressive of a rational and integral function. 



It only therefore remains to satisfy the simultaneous equations 



Now if, assuming S = l, we designate by 



?2^ + B,t2' + BJ2^+ .. +B6=0, 



the final equation in D, and by 



f + C,q'-^C^q'+ .. +C,= 0, 



that in 5^ ; we may without difficulty perceive that 



B„=C„, 



n being equal to any number in the series 1, 2, 3, 4, 5, 6. i 



For let 2 



q''^ = q, — -D = b; 

 ^ a 



then, since by equation {e^") 

 or rather 



it follows that the first members of the equations 4 



must be identical. Now in order that the corresponding coeffi- 

 cients in these equations may be equal, they must all of them be 



