of Edinburgh, Session 1883-84. 
613 
3 + 7 
4 + 6 
5 + 5 
10 
The order of these parts is thus simple ; their coefficients also are 
readily found ; thus for the part 
or cl . 
^10 
> 
we observe that the number of its parts is 6, so that it must have 
come from A®, as belonging to which power, its multiplier must be 
1 . 2 . 3 . 4 . 5 . 6 
1 . 2 . 3 . 1 . 2 . 1 
- 60 , 
wherefore as coming from it is 
6 
^10 
In this way it is a matter of mere labour to write out the parts of 
the term, and to sum them. 
In the case of the logarithmic cosine this part becomes 
60/ y/ cd y/ y 
6 \1 . 2 A 1 . 2 . 3 . 4/ VI • 2 . 3 . 4 . 5 . 6/ , 
and for log the corresponding part is 
60/ cd y/ y/ cd \ 
■'‘TVl . 2 . 3^ 6 • 2 . 3.4..V \1 • 2 • 3 . 4 . 5 . 6 . 7A 
For facilitating the multiplication of these denominators it is con- 
venient to make a list of the continued products of the natural 
numbers, thus — 
(2) = 2 
(3) = 2 *3 
(4) = 2^ -3 
(5) = 23 • -5 
(6) = 24 -32 -5 
(7) = 24 •32*5 -7 
(8) = 27 -32 -5 *7 
(9) = 27 -34 -5 -7 
(10) = 28 -34 -52 -7 
(11) = 28 • 34 -52 • 7 -11 
(12) = 2i« • 35 •52-7 • 11 
