Hamilton presented a report to the Sixth Meeting of the British Association for the Advancement of Science, held at Bristol in August 1836, entitled
Inquiry into the Validity of a Method recently proposed by George B. Jerrard, Esq. for Transforming and Resolving Equations of Elevated Degrees.
This report is available in the following formats:
George. B. Jerrard had developed methods for transforming polynomial equations, which he published in a monograph entitled Mathematical Researches. In particular, he claimed that his methods enabled one to solve quintic equations without in the process needing to solve any polynomial equation of degree greater than four. At the meeting of the British Association for the Advancement of Science at Dublin in 1835 Hamilton presented an announcement by Jerrard of his work on polynomial equations, and commented briefly on it. Hamilton subsequently presented a more detailed report on Jerrard's Method at the next meeting of the British Association, at Bristol in 1836. Hamilton found that Jerrard had indeed constructed a general method for transforming polynomial equations to simpler forms by means of suitable Tschirnhaus transformations, but that the transformations only yielded a non-trivial result if the degree of the original polynomial equation was sufficiently large. Jerrard's methods proved to be of no assistance in solving the general quintic equation. (Indeed Abel had shown that it was not possible to solve the general quintic equation by radicals, and Hamilton was later to publish a detailed exposition of Abel's proof in the Transactions of the Royal Irish Academy.
Hamilton also published two short papers in the Philosophical Magazine in 1836, containing two theorems that he had proved in the course of his investigation into Jerrrard's work.
These papers available in the following formats: