42 Mr. E. C. Snow. Correlations between Collaterals [June 3, 
Table I1.—Gametic Correlation between Brothers. 
(Factor 16s omitted throughout.) 
First Brother. 
| 
Second 
brother. Ty i) ane Fe ea Totals. | 
(AA.) (Aa.) (aa.) | 
(AA) | (16s—1) pt+ (6s 2) 75 q 16sp%q + 8 sp7q? 4 sp*q? (16s—1) p? (p+ q)? | 
+ (4s—1) pq? 
(Aa) 16 sp°q + 8 sp*q? (16s—2) p3q +4 (12s—1) pq? 8 sp*q? + 16 spq? 2 (16s—1) pq (p+q)? 
+ (16 s—2) pq? 
(aa) Asp*¢° 8 sp°q? + 16 «pqs (4s—1) p® r p (16 s= 2)pq*| (16s—1) 9g? (p+)? 
+ (16 s—1)q! 
Totals (16 s—1) p? (p+q)? 2 (16s—1) pq (p+@)? | (16 s—1) 9? (p+q)? (16s—1) (p+q)* 
Table IIlI.—Somatic Correlation between Brothers. 
(Factor 16s omitted throughout.) 
| 
First brother. 
Second | ——_ ; Wists 
brother. | Totals. 
(A.) (Not A.) 
ye il 
(A) (16s—1) p4 ae 1) p? q + (68s— 5) pq? 12 sp2q? + 16 spq* (16s—1)p(9+9@)?(p+2Q) 
+ (16s—2) pq*. 
(Not A) 12 sp*q* + 16 spq* (4s— i) q? + (16s—2) pq? (16s—1) g? (p+ 9)" 
+ (16s—1) q* 
Totals (16s—1) p (p+q)* (p+2q) (16s—1) q?7(p+q)* (16s—1) (p+q)* 
Since the standard deviations of the totals in these tables are the same in 
both directions, the correlations can at once be found from a knowledge of 
the means of the columns. | 
(8) Gametic Correlation.—If, in Table II, 1, Yo, Y3, and y are the means of 
the first, second, and third columus, and of the whole table respectively, each 
being measured from the centre of the middle row, we find 
a (libs) ipsa: (Ose) 0 ee (16s—1)p— 
(16s—1)(p+q)? =D (Ep 
SSR) ssa) 
(16s—1)(p+q)? (i6s—1)(p+Q) 
Ug = (bs>2) pos l)g Sie elos A ag 
fe =~" (6s— Dp +9? Gor a 
ge OSs Pea) a ee ee 
16s(16s—1)(p+4q)t pt+4q 
yn 
Y2= 
