52 Mr. E. C. Snow. Correlations between Collaterals [June 3, 
Table VIII.—Somatic Correlation between Cousins. 
(Factor 64st? (»+¢q)* omitted.) 
| 
First cousin. 
Second | 
cousin. | Totals. 
(A). (Not A). 
(A) 4 (16s—1) p*+16 (16s—1) p*¢ 4A (24s—1) pq? +3 (20s—1) p2q?| 4(16s—1) (p+¢)*p (p +29) 
+ (260s—17) p2q?7+4(8s—1) pq? 
(Not A) 4 (24s—1) pg? +38 (20s—1) pq? 4(16s— igs oe 1) pq? 4(16s—1) q° (p+q) 
+ (4s—1) p? 
_ Totals 4(16s—1) (p+q)*p (p+2q) | 4(16s—1)q?(pt+q) | 4(16s—1) (p+q)* 
(17) Gametic Correlation—From Table VII we find, after simplification— 
ee (16s—1) p—8sq igh 8sp—(16s—1) 9 
(iG sie) eae (16s—1) (p+q) 
ye ee Fie Jase 
2(16s—1)(p+q) pt 
From these, #i—Y2 = Sy = Y2—Y3 = 7. Hence the regression again 
is linear, and the correlation ee : - 
16s—1 When s is indefinitely large this 
becomes 4 
(18) Somatic Correlation.—In this case, after reduction, we find— 
ne P(p+29) LGsS)) pare ise 
oro 4(16s—1)(p+2q) 
Hence in the case of cousins also the somatic correlation depends upon the 
ratio of p tog. The range of r for different values of p and g extends from 
4s—1 5 8s—1 36s—5 
4(16s—1) 2(16s—1) 12 are 
finitely large, the range is from -4, to 4, with the value ;3; when p = q. 
(19) In Table EX; all the orrelanone which havé been worked out from 
the Mendelian hypothesis of “unit characters” are collected together. The 
values of the parental and grandparental correlations are from Prof. 
Pearson’s paper.* The rest have been obtained in the present paper. 
and = %—Y2= 
If p = g its value is When s is inde- 
* “On the Ancestral Correlations of a Mendelian Population,” ‘Roy. Soc. Proc.,’ B, 
1909, vol. 81. 
