18 The Rev. B. Bronwin on the Inverse Calculus 



The equation 



r(nM9)^e--=4;(«), 



found in this investigation, gives 



and 



T{n)f{&)\r v-Pdv{l-v)P-^s-^CO=J v-Pdv 



Differentiate this for a, then 

 Make 1 =.27, and 



V 



r v-P-^ dv{ 1 - v) p- ^ s-'v«y 



*y 



will be transformed into 







.—ra 



J Q rP 



and the preceding will become 



Multiply by aP, and operate with ( ;t- ) j there results 

 After changing the function (p, as before, we now have 



(ra)'"«4/>-'*(>-^)'-<l)-J 



The formulae (5.) and (4 ) are the same as those given by 

 Mr, Boole in the paper before referred to. From the last 



