408 Mr Murphy on the Inverse Method of Definite Integrals. 



writing y for .A in this equation, and making h indefinitely small, when 

 -j is usually represented by -j- , and — j — = fa. 1. (/) we get 

 F (£)■<!>(*) = if (f)-F(h.lt)-f (3), 



where the appendage is, as before, to be annexed. 



To reduce functions containing positive power of x, and zero to the 

 form fif(f) . t' belongs to the next part ; but we may here indicate, that 

 the series given for discontinuous functions, may be used in this case, 

 to reduce the proposed functions to forms to which the principles of this 

 part may be applied. 



It was necessary to make the preceding remarks on Operative Func- 

 tions, to explain more fully the allusions in reference to this subject in 

 the Introduction. 



Caius College, R. MURPHY. 



May 26, 1832. 



