1885.] K', E', J', G' in ascending powers of the modulus. 247 



Table I. 



The gaps in the last two columns of this table correspond 

 to results which involve JcK, k'K, kK' or k'K' as well as E, E', 

 I, F, &c, as appears from the following two tables, which give the 

 complete transformations of E, I, &c. and of E', T , &c. 



