70 
this reduction was first effected by our own countryman, 
Mr. Jerrard, whose “Mathematical Researches,” published 
about thirty years ago, gave a new impulse and direction to 
the efforts of those analysts who were labouring to conquer 
the difficulties connected with the higher equations. Mr. 
Jerrard has certainly taken a large and comprehensive view 
of the subject, and by his original researches has laid all 
cultivators of algebra under great obligations to him. But in 
his reduction of the general quintic equation to the trinomial 
form, by taking away its second, third, and fourth terms at 
once, he was anticipated, it seems, by Bring. 
In a Paper entitled “A Contribution to the History of the 
Problem of the Reduction of the General Equation of the 
Fifth Degree to a Trinomial Form,” about to appear in No. £1 
of the Quarterly Journal of Pure and Applied Mathematics, 
I have briefly indicated what has been done in this problem 
by different investigators, and I have particularly noticed the 
labours of Mr. Jerrard, Sir W. R. Hamilton, Mr. Cockle, 
Professor Sylvester, M. Serret, and Mr. Cayley, as well as of 
E. S. Bring, whose reduction, written in Latin, I have given 
in extenso. 
My object in this communication is simply to draw atten- 
tion to Bring’s investigation ; and I shall now content myself 
with giving a brief sketch of the process which he employs. 
Starting with the quadrinomial form, 
z* pz 2 qz r — 0 . . . (A) 
to which, as is well known, Tschirnhausen’s quadratic trans- 
formation enables us to reduce the general equation of the 
fifth degree, and assuming 
2 * -p dz' 1 -p cz -p bz -p ci -p y — 0 . . . (B), 
Bring, by the elimination of z between (A) and (B), arrives 
at an equation in y of the form 
y* + oy 4 + by # -pcy* + &c. = 0. . . (C) 
where a, b, c, &c. are rational functions of the given 
