IIG 
Procee-dings of Royal Society of Edinburgh, [jan. 16 , 
Monday, l^th January 1888. 
Professoe CHRYSTAL, LL.D., Vice-President, 
in the Chair. 
The following Communications were read : — 
1. Obituary Notices of former Vice-Presidents of the 
Society. 
2. Problem in Relationship. By Professor 
A. Macfarlane, D.Sc. 
The following problem was sent me by Mr Kirkman, F.R.S.; its 
solution illustrates the Calculus of Relationship, Proc. Roy. Soc. 
Edinh., vol. xi. pp. 5 and 162: — 
Two hoys, Smith and Jones, of the same age, are each the 
nephew of the other ; how many legal solutions 1 
The statements are that Smith is the nephew of Jones, and Jones 
the nephew of Smith. Let c denote child, then ^ denotes parent, 
and the equations are 
S = cc- J and J = cc-S . 
c e 
Hence S = cc-cc-S . 
c e 
Let m denote male and / female : then all the varieties of 
relationship are obtained by introducing m or / before the second, 
third, fifth, and sixth symbols ; for the sex of the first and fourth 
symbols is given to be m. 
Thus there are sixteen varieties in all. 
Of these mminm, mffm, fmmf, and ffff are chronologically 
impossible, because they make a man his own grandson, or a woman 
her own granddaughter. For example, 
S = cmcf- cfcfni-Si , 
c c 
reduces to 
S = CMcfcm-^ , 
