217 
and Eternal Source. Strengthened by this high thought,—our feel- 
ings raised and spiritualized by this habit,—there is no danger that 
we shall 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.’ 
Iv was Resotvepv,—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 effected 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- 
* do sin cos 7p 
tegral \ $ 
_____ Fourier’s theorem. In his own investigations he employs the 
formula of triple integration, 
Fi Ae) 
, and those of Mr. Ellis based on 
= =. rn) {. \ : ( dadv dw cos (ca —x)v— to-+ns) w"—1 f(a), 
by the aid of which he deduces the value of the multiple defi- 
nite integral, 
We... andr. den f Fs tate FS) 
ta ay Fa — %). ee Ce) se 
the limits of the integrations being given by the condition 
