292 
, : dé od dv 
ait tjut he) =— (F442) 
_fdv du 
+i(F-2) 
fhe sa 
TJ dz dz 
+4($-): (51) 
The President having taken the Chair, 
The Rev. Charles: Graves read a paper by Mr. George 
Boole, of Lincoln, containing investigations supplementary 
to his former papers on Discontinuous Functions and Definite 
Multiple Integrals. 
The author commences his observations by pointing out 
a distinction among integrals which constitute the limits of 
more general forms, according as they are supposed to be 
obtained by the vanishing of one or of more constants. The 
2) 
integral \, dz cos (qx) «"—', n being positive, considered as 
D 
the limit of ‘ due—** cos (gz) x"—', he designates a limiting 
integral of the first class, because it involves the consideration 
of one vanishing constant. The same integral, when 7 is 
negative, he regards as the limit of the more general form. 
a dxe—"* cos gz cos (nv tan— 2) 
0 (RP + a?) 
two constants & and &’ vanishing’; and designates it a limiting 
integral of the second class. Under this assumption he 
assigns as its value 
®dxzcosqe — ~(+q)"" 
Bcd ny pe BAR) 
