96 G. P. YOUNG ON ABEL’S FORMS, ETC. 
By means of (16) and (17), (13) becomes 
k D 
A=ptavl+te+vfrdtetavate); 
7 

which, by writing q for ae is Abel’s form for 4, in (6). 
IV.—NUMERICAL VERIFICATION. 
§ 5. The above results may be readily verified by taking any equation such as (1), with 
numerical co-efficients related as in (2). The writer has calculated the values of A,, A2, &c., 
6,, Ao, ete., &, dy ete, Q,, Q,, etc. in the case of the equation 
a + » + 3750 = 0; 
and has found that the separate numbers of the expression for x in (5), when arranged in 
the order, 
4 
? hs a,’ Chee À, a @ ‘ 
1 We) 
have respectively the values of the separate members of the expression in (9), taken in 
the order in which they are written in (9). 
