MR. R. C. ROWE OR ABEL’S THEOREM. 
741 
m x m 2 
n 1 [x l roots of the form y —Cart n 2 y 2 of the form y=Cx^ + • • • > an d s0 01l > 
the number is 
= %n r m r n s p 3 -\-\'tn~mp—\'tnm—ff < n—^n-\r 1—A —B .... (G) 
s>r 
(the last two terms —A — B corresponding to a correction which is in general zero). 45 ' 
21. It may be well to render these methods and formulae plainer by applying them 
to an example. We will choose for this purpose the simple case already considered in 
the note on p. 734. 
Our last formula for the value of /x — a gives, if we assume that, as in general is 
the case, the values of A and B are zero, writing 
= 3 
/H = 2 
)ii — 1 i — I 
m 2 — — 1 
7b— 1 
n,= 1 
<r. 2 = — 1 
F -a=3(l)+i(6-l)-i(3-l)-i(2)_f+l 
= 3. 
We wdl next find the values of< 7 0 , < 24 , q. 2 , or, as we have written them, [0], [l], [2], 
We have 
Pi = 2 or 1 
/h> = 0 
Let us take p x = 2.t 
Then, by the formulae (F), 
[ 2 ]=[ 2 ] 
[1]=[2]+|-A i; so A t =n [1]=[2]+1 
[ 0 ]=[ 0 ] 
* In the most simple case, when 
y n +P 1 y n ~ l + • • • +p«-i!/+pn 
is the completely general function (y, *, l) n 
n^n, 73^=1, /(j—1 
and 
/< — a.— |re 2 — \n-\-\=\(n-~-Y)(n—%) 
= deficiency of general -re-tic curve. 
This is a case of the result shown by Professor Cayley in the Addition to be universally true, 
f We might have taken p x —1 with a similar result. This multiplicity of solution will generally occur. 
