14 
of Algebraic Equations,” just published in the Quarterly 
Journal of Pure and Applied Mathematics, No. 20. In the 
second aspect every differential resolvent of an order higher 
than the second gives us, at least when the dexter of its 
defining equation vanishes, a new primary form, that is to 
say, a form not recognised as primary in Professor Boole’s 
theory. And in certain cases in which the dexter does not 
vanish, a comparatively easy transformation will rid the 
equation of the dexter term, and the resulting differential 
equation will be of a new primary form. 
A Paper was read, entitled, “ Note on Differential Resol- 
vents,” by William Spottiswoode, Esq., M.A., F.R.S., &c. 
Communicated by the Rev. Robert Harley, F.R.A.S. 
The object of this note is, first, to show how the differential 
resolvent of an equation of any degree may be found by 
elimination from systems of linear equations. The method 
is exemplified in the cases of the complete quadratic and the 
complete cubic ; and in the latter case the results of some 
investigations by Mr. Harley are introduced, whereby the 
resolvent is freed from an extraneous factor, and reduced to 
its proper degree (the 10th) in the coefficients of the original 
cubic. 
