11 
A Paper was read f£ On a certain class of Linear Differ- 
ential Equations,” by the Rev. Robert Harley, F.R.A.S. 
In the Philosophical Magazine for May of last year, Mr. 
Cockle showed, in a Paper entitled, “ On Transcendental 
and Algebraic Solution,” that from any algebraic equation 
of tlie degree n, whereof the coefficients are functions of a 
variable, there may be derived a linear differential equation 
of the order n — 1, which will be satisfied by any one of the 
roots of the given algebraic equation. The connexion of 
this theorem with a certain general process for the solution 
of algebraic equations led me to consider its application to 
the form 
y n — ny-\-(ii — l):r“0 ... (I) 
to which it is known that any equation of the wth degree, 
when n is not greater than 5, can, by the aid of equations of 
inferior degrees, be reduced. 
In the course of my investigations I was conducted to the 
conclusion that for all integral values of n between the limits 
n — 2, n = 5, 
both inclusive, the linear differential equation, or, as it is 
proposed to call it, the “ differential resolvent,” is of the form 
and I completely determined the constants a 0 , «i, . . . a n ^ for 
all the cases up to and including n — b. 
I found, moreover, that this result, in itself sufficiently 
remarkable, might be put under a still more simple and 
striking form by following a process of transformation pro- 
posed by Professor Boole in his Memoir on a General Method 
