460 
Intro-Class and Inter-Class Correlations 
Summarizing the results from these tables as under illustration (III — Ab) 5, 
we have : 
8 [n (n - 1)] = 159484, 
S[(n- 1)2(0] =7120158, I =44-644967, 
S[(n- 1)2 {l' 2 )] = 318370242, of = 3'078842, 
8 [2 = 320370295, S [2 (l' 2 )] = 2468393, 
8 [(n -1)2 {b')] = 527756S, b = 33-091520, 
S[(n- 1)2 (6' 2 )] = 174844798, <ri = 1-266907, 
8 [2 (b')f = 176007866, 8 [2 (6' 2 )] = 1357942. 
Whence by (vi, ix) as illustrated in greater detail under (III — Ab) 4—5 above 
I get: 
r hh =-046 ± -019, r/#, = 2-41, 
r blh} = -036 ± -019, rjE r = 1-85, 
where the probable errors are calculated on the basis of the actual number of 
eggs, or N— 1240. 
Such a test as the above can never replace the R.L.D. (relative local difference) 
or the R.R.D. (relative racial difference) as the case may be, of Tocher and Pearson. 
But there are cases, as for instance the present and several unpublished series, 
where, now that a (relatively) rapid method of computation is available, it may be 
very useful. 
Illustration {III — Ab) 7. Inheritance of Milk Yield in the Male Line. 
The test of the inheritance of a character like " milk yield " through the male 
must be made either by correlating between the milk yield of a cow and her 
parental granddam, or by determining the correlation between the daughters of 
individual bulls. 
The methods here described are particularly useful for cases of this kind, for 
while the number of daughters in a family may not be large, the range of variation 
in yield is apt to be very great thus rendering the tables cumbersome in size, 
whether or not heavy in number of entries. 
As an illustration I take a series of data from a paper by James Wilson, M.A., 
B.Sc, "On inheritance of Milk Yield in Cattle*." One of his tables (pp. 103—105), 
gives the milking record of the daughters of eleven Red Danish bulls. Our prob- 
lem is to determine the correlation in milk production between the daughters of 
the same sire, in order to ascertain whether there be an inheritance of milking 
quality in the male line. 
The data are of course very rough since they are apparently for the most part 
recorded to the nearest fifty gallon point. The yields range from 650 to 1400 
gallons. Omitting all records indicated as questionable, I sum the yields and 
* Wilson, J., Scientific Proc. Roy. Dublin Society, n. s. Vol. xin, pp. 89—113, 1911. 
