Compiitation of the Functions Ctq^i), and 39 



If, secondly, n be even, the equation gives 



whence X»+i = — (X;i + Y^O - 



271 



Yft+i = — (Y». - Xj7,) — Yji_i 



(18). 



The most important special cases are when n = \ and n = 2. In the 

 first, remembering that Xq = X, Y^ = - Y (Article G), equations (17) 

 give 



Xo = 5LtZi_X 



Yo = Il--_^i+Y 



(19). 



In the second case (18) gives 



X3 = i(X, + Yo)-Xn 



(20). 



Y3 = ^(Y,-X,)-Y,, 



In these derivations no labour is involved, except that of addition of 

 known quantities, and division by a;. 



