358 Mr. A. Cayley’s Remarks on the Rev. B. Bronwin’s 
where the principle developed in the first of these Theo- 
rems is frequently applied with much simplicity, elegance and 
advantage. Iam not without a hope that the publication of 
that volume will materially contribute to the improvement of 
the taste of the young geometer, not only from the great 
number of original and well-chosen discussions which are in- 
troduced into it, but also from the many beautiful investiga- 
tions with which it is enriched. 
I have also to add that my attention was called to the prin- 
ciple of combining the equations of straight lines as here 
employed by my colleague Mr. Fenwick, and that some fur- 
ther inquiries of this kind will appear in a tract which I am, 
in conjunction with that gentleman, about to publish, and 
which may possibly be succeeded by others of a similar nature. 
LX. Remarks on the Rev.B.Bronwin’s paper on M. Jacobi’s 
Theory of Elliptic Functions. By A. Caytry, Esq., B.A., 
F.C.P.S., Fellow of Trinity College, Cambridge. 
To the Editors of the Philosophical Magazine and Journal. 
GENTLEMEN, 
ALLow me to insert in your Magazine a few remarks on 
a paper “On M. Jacobi’s Theory of Elliptic Functions,” 
which appeared in your last Number, in which the author, 
Mr. Bronwin, attempts to show that some of M. Jacobi’s for- 
mulze are erroneous. As far as I can understand his argu- 
ment, he wishes to deduce from the equation 
u 
say 
(numbered (3.) in the paper referred to) the conclusion that 
C is necessarily, in all cases in which the formula exists at all, 
given by the equation 
=Csausa(u+2o)..sa(u+ 2(n—1)o) 
1 
“cha + SAMSAS WeeeeeeeSa(2N —~ 1)o. 
Omitting for the present his remarks upon the form 
o= Sita for the three remaining forms of a, 
Q@r+1K 427K! VV —1 
n , 
QrK 4+ 2741K'V—1 
a= 2 
oe SEHK + 2 + 1K'V—1 
n 
viz. ® = 
> 
> 
