NATURE OF FUNCTIONAL EQUATIONS. 129 



The preceding remarks contain, I think, the outline of a 

 natural arrangement of the science of symbols. It is not difficult 

 to overrate the importance of a mere classification ; but I hope 

 to be able to show, that the considerations now suggested are 

 not without some degree of utility. 



As the distinction between functional and common equations 

 depends on the order of operations, it follows that, when part 

 of the solution of an equation does not vary with the nature 

 of the operation subjected to the resolving process, this part 

 is applicable as much to functional equations as to any other. 

 The special application of this principle to the discussion of a 

 class of differential functional equations will be the object of a 

 subsequent paper. 



In the preceding remarks, operations of derivation, such as 

 D, A, &c. are supposed to be replaced by functional operations 

 in every case in which this can be effected. 



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