DERIVATIVES ASSOCIATED WITH LINEAR DIFFERENTIAL EQUATIONS. 459 

 And in the case when 



the degenerate form of A is easily proved to be 



(n- 1)1 



so that we may take 



u 







As in 87, 98, it would be proved that X x = z and that all the primin variants vanish. 

 It is not proposed to consider here what are the possible methods of forming for 

 the general equation of order n the associate equations in the different variables, 

 nor therefore to verify, as was done in 107 for the quartic, the general theorems 

 enunciated in 62. 



SECTION VII. 

 QUOTIENT-DERIVATIVES. 

 The Derivatives of Odd Order. 

 110. Writing down the series of quantities with binomial numerical coefficients 



and forming determinant squares as above, viz , the first element of the first line only; 

 the first two elements of the two lines after the first one ; the first three elements of 



3 N 2 



