228 
Proceedings of the Royal Society 
and 
Then 
(i) 
(Art. 24), 
Also 
d 1 s 4 A = M ; (3) 
and 
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 which 
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 — 
Here there is no need in two cases to put a suffix, because d — 1 
and <t = 1 . 
This relationship can be expressed in nine other forms, each equi- 
valent to the above form, by taking over d , ds±, ds^s^ &c., to the 
othel* side, after having transformed the expression in accordance 
with the Rule of Art. 1 7. 
In two cases I have used a and b because I am uncertain of 
the actual numbers. 
19. The signs > and < . 
asserts that B and C, at least, were sons of A. 
Thus the sign < means are included in , as in the analysis of 
quality. 
V = d s. S-, S-, s 1 a--, S a d b cr M . 
>4 8 1 S 1 S 1 oq o tt a b 
B + C + D = sA 
asserts that B, C, and D, and no others, were sons of A. 
B + C < «? A 
