224 
Proceedings of the Boyal Society 
3. On Some New Bases of the Lencoline Series. Part II. 
By Mr G-. Carr Robinson and Mr W. L. Goodwin. 
4. On a Calculus of Relationship. By Alexander Macfarlane, 
M.A., D.Sc., F.R.S.E. 
1. Be Morgan read a paper on the “ Logic of Relations” before 
the Cambridge Philosophical Society, and the paper is printed in 
their Transactions. He attempts to deal not only with the idea of 
relationship , but with the idea of relation in general. As he does 
not deal with exact ideas, he cannot give any exact results. 
2. Among the writings of Leslie Ellis there are printed some 
notes on Boole’s “Laws of Thought,” and there he refers to the idea 
of relation. He makes the important remark: — “It seems to me 
that the mind passes from idea to idea in accordance with various 
principles of suggestion, and that, in correspondence with the 
different classes of such principles of suggestion, we ought to 
recognise different branches of the general theory of inference.” 
But he proceeds to discuss equations expressing any kind of rela- 
tion, thus neglecting his own principle of making a special investi- 
gation tor each really different kind of idea, 
3. What I have attempted to do is to devise a complete analytical 
notation for what can be represented graphically hy means of a 
genealogical tree, to consider how data about relationships should 
be expressed, and to point out rules for manipulating these data. 
4. The distinction between the relationship and the persons 
between whom the relationship exists , can be represented by means 
of small letters in contradistinction to large letters — e.g., 
sA = B + C + D 
The sons of A are B, and C, and B. 
5. The symbol s has a definite arithmetical value, which is an 
integer. It is a multiplier, or operating symbol, which changes A 
into B and C and B. 
6. To express any relationship whatever, we require only four 
fundamental symbols expressing the four fundamental relationships 
(1) of a father to his sons, (2) of a father to his daughters, (3) of a 
