A 
Remarks on Professor Wallace’s Reply io B. 301 
had been made by B. and of course it is not necessary to dis- 
cuss the subject. It may not however be inexpedient to 
state that every result given by Professor Wallace can easily 
be obtained from the binomial theorem ; and mathematicians 
ae usually developed such quantities by means of that theo- 
“Thus having the identical equation 
mAL 
Ax mAg 
{ (1-+-nz)” “ =(1-+-nz) ” 
by substituting the developments of 
(eng) bad (1-+-nz) 
given by the binomial theorem, we obtain the equation 
MAL 
ie PL —2n 8 
(4yetp 2 +o z + &e. r: =1+ 
mAx mAx <= ns 
a4 
a ep 
putting now m=1, z=1 0, it becomes like Professor 
Wallace’s formula, Vol. VII. p wage 283, 
1 A A2x? A%yr3 
Udita g+paythe). Vesta a = a rr +&c. 
By eats the series in the first member 14] ratte 
Az A 
=e, feticcotnan oe] = —— a7 - - Bin 
A 
and by nee =a, or A=/.a, we get 
= w?l.a? 
being the same as Professor Wallace has given in Vol. VI. 
page 284. In like manner, his expression of log. (1+2) 
&c. may be found, but it is unnecessary here to sapest these 
calculations. It may however, be proper to observe, that Pro- 
fessor Wallace is not correct in his assertion that the multi- 
#. 
ge ae 
