416 
Proceedings of the lioyal Society 
Practical Astronomy in the University of Edin. (Edin. 1818). In 
the University Library there is a second edition of a part of the same 
work with the title Scientific Aphorisms (Edin. 1827), I bring them 
before the notice of the Society, as they contain an explanation of 
gravitation, &c., almost identical with that of Le Sage, to which 
our attention was lately recalled by our President. Professor Blair 
seems to have invented this explanation for himself — because, 
though he gives frequent references to other authors, whose results 
he quotes, he makes, so far as I have seen, no reference to Le Sage. 
On a future occasion I may enter on a discussion of the points 
of resemblance and difference of these two theories. 
5. 
Note on an Identity. By 
Professor Tait. 
Whatever be p and q it 
is obvious that 
1 1 
+ 
1 
p q 
q 
V 
Hence 
1 _ 1 
+ 
P -C + 
02 -P 
!) 
P 0i 
0i 
\02 
02 
pj 
and so on. 
Finally we 
see that 
i =1 + 
<h~P 1 , <h~P 
• 4 • 
02 ~P 
1 
— + . 
P 0i 
01 02 
0i 
02 
03 
... + ?i “ 
P %-v 
qa-l-p 
. 1 
rP 02^ 
• 
P qn -p 1 
0! 
.02 
071-1 
0» 01 02 
071 P 
absolutely without any restriction on the values of the quantities 
involved. 
It is obvious that an immense number of curious results in the 
form of sums of series, &c. can be derived with great ease from this 
expression and from various modifications of it. I give, therefore, 
only a few very simple examples. 
Take q v q 2} &c., as the first n of the natural numbers, and the 
series becomes 
1 1 p - \ p - \ p — 2 
p ~ + ~2~ ‘ 
, .n-ip-l p-2 p-n-l, p-l p-2 p~nl 
2 * 3 n K } 1 * 2 * ’ * n p’ 
