70 PROFESSOR J. J. SYLVESTER AND MR. J. HAMMOND 



Ar = st* 



and so on. 



Hence (7) becomes 



Order | = f 6 - 



Dividing this throughout by -| s, and then writing 



6- = <a (1 - y ) and y = | t~*u* (1 + y), 



we obtain in exactly the same manner as before, merely altering the letters in the 

 previous work, 



9 it I 1 .1 1 Q ^ Q 



. .1 ,*_ fl/W * /i/'J ^ J/3 



^^~ J) J ^^^ ^T S ft 



Order | ; ^ 



where quantities of the order \, or less, are now neglected. 

 Similarly 



| Bs* = tit* 



and so on. 



Thus (8) becomes 



