203 
y G +3ey 2 —6y+g=0, 
transform it into 
y*+3&y z —6y+gx=0, 
and proceed as before. Or we might start at once with 
y 6 -\-3ey 2 — 6y-\-5x— 0 , 
and regard x as the independent variable, and e as constant. 
The simplicity and beauty of the results obtained by Mr. 
Harley in the case of trinomial biquadratics and quintics 
suggested to me the following investigation, which I think I 
communicated to him some months ago. Let 
d n y „ . d'y 
dx n ~ r dx r ’ 
r being taken from 0 to n, and A being constants. Then n 
particular integrals are obtained from the formula 
yz=z'2u z x m +" z 
by giving to m the values 0, 1, 2,. . n , successively; z being 
taken from 0 to oo , and u being defined by 
u 
'M-i _ 
u . 
JP_ 
Q 
where 
P=S A r 7T r (m+zn), 
Q=7r n |?ra+(z+l)nj. 
The symbol w here introduced is such that 
zr r l-l (l— 1 ) (1—2) . . (l—r+ 1 ) 
is its defining relation. 
Mr. Robert Rawson, Honorary Member, read the First 
Part of a Memoir of the late Professor Eaton Ilodgkinson, 
F.R.S. Thanks having been given to Mr. Rawson, on the 
motion of Mr. Binney, seconded by Dr. Smith, 
The Rev. Mr. Kirkman said, “ It is no ordinary renown 
that the late Professor Hodgkinson secured to himself, and 
for ever will reflect on Manchester. It is a great thing to 
outstrip one’s cotemporaries in commercial competition, and 
to accumulate fairly-gathered wealth ; it is a great thing to 
