1888.] Prof. A. Macfarlane on ProUem in Bdationshi'p, 117 
i,e. 
mis = , 
f e., tlie father of S is his own grandson. 
Again, there are eight which are legally impossible, because a 
person may not marry his or her grandparent, namely, 
mmmf, mmfm, mfmm, fmmm^ 
fffm, ffmf, fmff, mfff. 
For example, 
S = cmcm}-cmcf ^-^ , 
c c 
S = cmcmc/is, 
m-S = mcmc/-S, 
i.e., the father of S marries his own grandmother. 
There remain the four cases 
mmff, mfmf, ffmni, fmfm\ 
each of which is legally and physiologically possible. For there is 
nothing to prevent two persons, each twenty years old say, from 
marrying each the appropriate parent of the other, each of whom 
may he forty years old, and the Smith and Jones of the problem 
may he the result of these contemporaneous marriages. For 
example, take the first of these, 
S = cw^c77^ic/q/■is 
G G 
. *. mi^TTzis^ = 77zi^/c^/is^ ; 
z.e., the father of Smith’s father marries the daughter of Smith’s 
mother. 
Thus there are four solutions — (1) Two men marry each the mother 
of the other. (2) Two women marry each the father of the other. 
(3) A man and a woman marry the mother and father of one another, 
which comprehends the two cases of Smith being the son of the 
old woman, and Smith being the son of the young woman. 
Note , — Here Smith and Jones are taken as arbitrary names, 
equivalent for example to Tom and Hugh. If the convention about 
surnames is taken into account — that a child’s surname is identical 
with that of his father — then only the first and second solutions are 
possible. 
