217 



and Eternal Source. Strengthened by this high thought, — our feel- 

 ings raised and spirituahzed by this habit, — there is no danger that 

 we sliall give place to the weak apprehension (which is but a subtle 

 form of unbelief itself), that any portion of Truth can ever prove 

 inconsistent with any other. And the same principle, while it saves us 

 from slavish fear, will also guard us from presumption. Standing in 

 thepresence of confessed and established truth, we shall feel that we 

 are treading upon holy ground ; and we shall demean ourselves, not 

 with the elation and pride of conquest, but with the devotion of wor- 

 ship and of love." 



It was Resolved, — That the President be requested to 

 permit his Address to be printed in the Proceedings of the 

 Academy. 



The Rev. Charles Graves read a paper by Mr. George 

 Boole, of Lincoln, on a Certain Definite Multiple Integral. 



It has for some time been known that the evolution of 

 definite multiple integrals can, in many cases, be etFected by 

 the employment of discontinuous functions. In illustration 

 of this fact, the author notices the researches of M. Lejeune 

 Dirichlet, founded on the properties of the discontinuous in- 

 tegral \ — -, and those of Mr. Ellis based on 



Jo i> 



Fourier's theorem. In his own investigations he employs the 

 formula of triple integration, 



by the aid of which he deduces the value of the multiple defi- 

 nite integral, 



/X^ X^ Xn'-\ 



v = SS . . ofxi d%. . ■ dxnfi^ji + a;^ + • + v^ 



\ (a, — ic,)"- + {fli - x^Y . . -f. (a„ _ Xnf\'^ 



the limits of the integrations being given by the condition 



