228 
Proceedings of the Royal Society 
Then 
1 A 1 1 , 
— S 9 8* A = — -y M , 
^2 2 4 S 1 d l 
and 
Also 
and 
7 *2 = 1 ( Art - 24 )» 
6 2 
1 1 
A = ^ q M - 
(i) 
a 
r_i l r xT 
ii 
<1 
GO** 
r-H 
CO 
(2) 
d x «]_ A = M ; 
(3) 
111 
A = -T- M 
Sa s, d. 
(4) 
Hence the rule for changing a relationship function from one side of 
an equation to the other is, 
Invert each symbol of the function which is to be transposed , 
reverse the order of the symbols , and prefix before the function ivliicli 
is on the other side. 
1 8. As an example of the value of the notation of this calculus, 
considered merely as a shorthand, I may express the relationship 
between Queen Victoria and Mary Queen of Scots — 
V = d s 4 s 1 s 1 s 1 oq cr M . 
Here there is no need in two cases to put a suffix, because d = 1 
and cr = 1 . 
This relationship can he expressed in nine other forms, each equi- 
valent to the above form, by taking over d , ds^, ds 4: s 1 , &c., to the 
other side, after having transformed the expression in accordance 
with the Rule of Art. 17. 
In two cases I have used a and b because I am uncertain of 
the actual numbers. 
19. The signs > and < . 
B + C + D = s A 
asserts that B, C, and D, and no others, were sons of A. 
B + C<sA 
asserts that B and G, at least, were sons of A. 
Thus the sign < means are included in, as in the analysis of 
quality. 
