86 ON DIFFERENTIAL EQUATIONS OF THE SECOND ORDER. 



[NOTE. Added 17th March, 1898. As indicated in the introductory remarks, 

 the theory given in this paper is applicable when the number of independent 

 variables is greater than two, and when the order of the differential equation is 

 higher than the first ; its application is not restricted to the case of an equation of 

 the second order in three independent variables. 



A brief sketch of the theory for an equation of order m in n independent variables 

 is prefixed to a paper* which contains the integration of some differential equations 

 of types represented by 



a_ a a \ _ 



+ *i + x * H h *"-' 



when the iteration of the differential operator is purely symbolical.] 



* " On some Differential Equations in the Theory of Symmetrical Algebra," Camb. Phil. Trans., 

 vol. xvi. (1898), pp. 291-325. 



. 



