44 Mr. E. C. Snow. Correlations between Collaterals: [June 3, 
(B.) Correlation between Uncle and Nephew. 
(11) In this case we require not only the various types of families given 
in Table J, but also the offspring of these families when mated at random. 
But it will not be sufficient to mate the nine types of families given by 
Table I with the general population in which the proportions possessing 
the protogenic, hybrid, and allogenic constituents are p*(AA), 2pq(Aa), and 
q’ (aa), for any particular mating will be of a member of one type of family 
with a member of the same or another type. An avuncular relationship 
will arise with the members of both families from which the mating couples 
are selected. Thus we must discover the offspring which arise from the 
mating of each type of family in Table I with itself and with each other. 
This is given in Table LV, in which 4¢ is taken to be the number of matings 
of each pair. This allows for a possible change of fertility in consecutive 
generations. 
(12) To explain Table IV, consider, for example, the mating of the family 
of type 4s(AA)+8s(Aa)+4s(aa) [Type «] with the ee of type 
8s(AA)+8s(Aa) [Type B]. Of the 8s(AA) of Type 8 :— 
2s will mate with 2s of the 4s(AA) from Type a, giving 4¢{2s(AA) } 
offspring. 
4s will mate with 4s of the 8s(Aq@) from Type a, giving 2¢{4s(AA) }+ 
2t {4s(Aq) } offspring. 
2s will mate with 2s of the 4s(aa) from Type «, giving 4¢ {2s (Aa) } 
offspring. 
Of the 8s(Aa) of Type 8 :— 
2s will mate with 2s of the 4s(AA) from Type «, giving 2¢ {2s(AA) }+ 
2¢ {2s(Aa) } offspring. 
4s will mate with 4s of the 8s(Aqa) from Type 2, giving ¢t {4s(AA)} + 
2t {4s(Aa) } +2 {4s (aa) } offspring. 
2s will mate with 2s of the 4s(aa) from Type «, giving 2¢ {2s (Aa) }+ 
2¢ {2s(aa) } offspring. 
The complete result will consist of the aggregation of the six combinations 
written out. Since the frequency of the Type « family is 4p79?, and of the 
Type 8 is 4p°q, there will be altogether 16p°g* such aggregations as the 
above. The result is represented in the table, in which the faimilies derived 
through any particular individual exhibiting the constituent (AA), (Aq), or 
(aa) are written in the same horizontal or vertical line as the constituent 
itself. The remaining aggregations can be read off in like manner. : 
(13) From Table IV we can pick out uncle and nephew in pairs according 
