1894.] 



Covariants of Twisted Curves, &c. 



275 



where R contains squares and products of i/o>, u>^ u-'z^/f^i w^ 

 &c., where w and have a significance similar to that of y n and z n . 

 In the earlier part of the paper I have shown that, if f = x + q^y and 

 ID = l+px -f qy, where the coefficients are small, 



A,, = a n qi {(n 3) yia n 



+p {2 O 3) xa n +(n2) _!} 

 + q{x [(n 3) 2/,a n + Sma M y B _ m+1 ] +(w 3) 2/a + (w 2) T/JCTM-I 



+ S (m l)a OT 2 



and therefore we can determine the functions and ^ and get 



A. = t- 



U} n _ 3 I 



2 --3- 



and similarly 



T-, f tai n>& wo?! 



I ~^~ 2 u*-wl\ n 



i2) (n l)- 



If we now choose the new axes to be the canonical axes, we shall 

 have, at the origin 



Q6,Q 8 3 \ 



r 2 



