101 
of Edinburgh, Sessio7i 1875-70. 
the primeval pig, and the mew of the pre-Adamitie kitten, those 
who with me look on Darwinism as a mere pleasant conceit of men 
besotted in the one-sided study of physical science, can, so far as 
philological conclusions are concerned, leave the conceit to shift for 
itself, being firmly convinced that whenever reason does show itself 
whether on the original appearance of man or at some after-stage 
of his development, it appears as a force altogether different from, 
and in some of its functions, as Professor Ferrier wisely maintained, 
essentially contradictory of, and antagonistic to, every kind and 
degree of mere sensation ; and in this character brings forth lan- 
guage as the natural manifestation and organised body of itself. 
Monday , 1th February 1876. 
Sir WILLIAM THOMSON, President, in the Chair. 
The following Communications were read : — 
1. Note on Certain Formulae in the Calculus of Operations. 
By Professor Stokes, Hon. F.R.S.E. (In a letter to Pro- 
fessor Tait.) 
“ January lith, 1876. 
“Formulae like those you sent me* are readily suggested by 
supposing the function operated on to be of the form %Ax a , or say, 
for shortness, *«, with the understanding that no transformations 
are to be made which are not equally valid for 2Ar«. 
Thus 
fdL%dL\x a = a 2 (a— l) 2 . . . (a — n -f Y)‘ 1 x a ~ n 
\dx ax) 
= a (a — 1) . . . (a — n + 1)^-^^ x u 
-(s) v (a) v ‘ 
and 
(x x^ x a = (a+ l)(a + 2) . . . (a + n)x a + n 
= (a + ii)(a -j- n — 1) . . . (a+l)<r ft ‘*‘” 
nf d \ n n a 
= X ( -~ ) X X . 
\dxj 
See ante , p. 95. 
