173 
which is identical in substance with the selected portion. 
The calculation of the differential resolvents of 
y 5 - 5 if + 2 x - 0 
y 5 — 5y 2 + 3x = 0 
which seem requisite for completing the discussion of trino- 
mial forms, would in all probability throw further light upon 
the question. 
Brisbane , Queensland, Australia, 
Wednesday, Aug. 12, 1863. 
Mr. Harley added the following remarks “ On Recent 
Researches on the Theory of Equations.” 
In seeking to express a root of the general quintic equation 
in terms of a single value of the resolvent product, we are 
met with considerable practical difficulties. Starting from the 
Eulerian equations, which connect the coefficients of the 
quintic with the constituents of its roots, the question 
becomes one of elimination, and, looked at in a theoretical 
point of view, it is simple enough. But the eliminations to 
be effected are so formidable that I have not hitherto had the 
courage to attempt to carry further the calculations of my 
distinguished friend Considering, however, the enormous 
calculations which have of late years been effected in this 
department of algebra, and considering also the facilities of 
verification which recent investigations afford, I should be 
unwilling to affirm that the work is altogether impracticable. 
If any mathematician who has the necessary leisure is 
disposed to undertake the work, I shall be happy to supply him 
with a copy of the manuscript referred to in the first paragraph 
of the foregoing Paper, and to offer him such suggestions and 
assistance as I may be able. 
Tn my last communication to the Society, published at 
pp. 69-71 of the current volume of the “ Proceedings,” I have 
given a brief sketch of Bring’s reduction of the general quintic 
