2S6 MR. HARGREAVE ON THE RESOLUTION OF LINEAR EQUATIONS, ETC. 
cases of linear equations resolves itself into the inquiry, in what cases can a series 
whose scale is of the wth order be resolved into a number of series whose scale is of 
the lirst order. 
•20. I have not thought it necessary here to extend these solutions in series to 
linear partial differential equations. The process by which the extension can be 
made is well known, and has no peculiar relation to the methods here developed. 
