OF THE COMPOSITIONS OF NUMBERS. 
851 
Performing the summation in regard to r, 
... F) - (/X - . . . 2F , 
+ . . . 2M-) + . . . 
iP%Pz • • •, 0 ) + 
+ l 1 
1 P 2 P 3 ..., 1) + ... 
+ ^,,sf{PlP2P3 . . ., s) + . . ., 
where 
= 
1 / Vs - 1 
+ 
fL + 2\ f fJy 
s - 2 
+ 
+ 
/X + s 
that is to say 
(1 + a ;). (1 = 
r < /X, 
/(21^ 2) - 2/(2^, 2) +/(32, 2) = 0, 
verified by 
22 — 2 X 16 + 10 = 0. (See Tables, pp, 898-900.) 
r = /x, 
f{21^ .3) - 2/(2*l, 3) +/(32, 3) =/(2, 0) + 3/(2, 1) + 3/(2, 2) 
verified by 
93 - 2 X 57 + 27 = 0 + 3 X 1 + 3 X 1. 
For the summation formula 
F(l), 
= F (F) - F (2), 
= F (F) - 2F (21) -f F (3), 
= F (F) - 3F (2F) + F (22) + 2F (31) - F (4), 
= 1 , 
veiified by 
1 , 
= 3-2, 
= 1.3 - 2 X 8 + 4, 
* = 75 - 3 X 44 + 26 + 2 X 20 - 8, 
= 1; 
5 Q 2 
