[ 389 ] 
IV. Remarks on Mr. Harley’s paper on Quintics. 
By G. B. JeRRarp. 
[Concluded from vol. xix. p. 274.] 
4, ‘ey my former paper I contented myself with showing, from 
a comparison of certain results at which Mr. Harley had 
arrived, that there were decisive marks of the existence of an 
error in his processes, leaving to him and Mr. Cockle the task 
of tracing the error to its source. But after the lapse of man 
months they have as yet failed to perform the part thus fitly 
assigned to them. ‘This is the more remarkable, as, in answer 
to an attempt made by the latter mathematician to infer the 
failure of my researches from the failure of theirs, I said at the 
time, in a postcript to my paper, what ought, I think, to have 
suggested to their minds the true origin of their error, and 
thence have shown them the irrelevancy of the objections urged 
against my method of solving equations of the fifth degree. 
Mr. Cockle, however, not seeing the meaning of my words, still 
adheres to his objections. I must now, therefore, abandoning 
suggestions the drift of which may escape observation, have 
recourse to statements of the plainest kind. 
d. If I were asked in what respect the method first explained 
by me in the Philosophical Magazine for June 1845, and after- 
wards given at greater length in Chapter II. of my ‘ Essay on 
the Resolution of Equations*,’ differed from all other methods 
constructed for the purpose of solving equations,—on what, while 
all these were seen to have failed, I grounded my hope of success, 
—I should answer by pointing to the theorem + 
Onflab)(ea) = 
EC, trae oH Ona, + Ux.) (ab) (¢ d) a8 
if On, Kad)(ea).. =45(O), ,) (ab) (ed) “e 
or 
(v) 
On, s(ab) (ed). = 
5 (aut Bayt Mo, +a, + oe)(ab) (ed) 
if On, “ab)(ea).. =U"(O,, ) (ab) (ed) one 
From this theorem we learn that, in constructing equations 
~ 3 r) 
* Published by Taylor and Francis, Red Lion Court, Fleet Street, 
London. 
t ‘Essay,’ p. 75. 
