Aug. 15,1925 
Coefficients of Inbreeding and Relationship 
379 
It is necessary that the sample lines be chosen wholly at random. 
For obvious reasons, common ancestors are more likely to be males, 
in livestock breeding, than females. Thus straight male or straight 
female lines can not give a fair basis for calculating the number of 
ties between two pedigrees. 
A system of alternating male and female lines has been tried out 
by the writers; and, whale it gives fairly satisfactory results, the 
theory of sampling can not be applied in a simple way to calculate a 
probable error. If it could be calculated, the probable error would 
undoubtedly be somewhat larger than where truly random lines are 
used. With this or any other regular sequence of sires and dams 
the same lines tend to recur in different pedigrees and contribute 
more or less than would a random line, depending on whether im¬ 
portant foundation animals happen to be represented in them or not. 
A truly random line of ancestry can be obtained by letting the 
sequence of sires and dams which is to be traced back in the herdbook 
be that of the heads and tails, respectively, in a coin-tossing experi¬ 
ment. The same sequence should not, of course, be used frequently 
in the same study. The writers use a record of 1,000 coin tossings 
as material for obtaining random sequences. The sequence for each 
new line is begun where the last leaves off. A given sequence has little 
chance of repetition, since the number of generations in the lines 
varies. % 
The simplest possible sample which can show a connection between 
sire and dam is obtained by tracing back two ancestral lines, one On 
the sire's side and one on the dam's side. The scheme is illustrated in 
Tables I and II. 
Table 1 .—A two-line pedigree sample of the Shorthorn hull Millionaire (79488) 
[An example of a case in which an ancestral connection is shown] 
Millionaire (79438) 
White Bear (75896) 
D Amethyst 
D Artless 
D Amy 
S Grand Duke 36th (43306) 
S Grand Duke 30th (38373) 
D Grand Duchess 24th 
S 3d Duke of Clarence (23727) 
D Duchess 80th 
D Duchess 72d 
D Duchess 67th 
D Duchess 59th 
S 2d Duke of Oxford (9046) 
D Oxford 2d 
S Short Tail (2621) 
S Belvedere (1706) 
D Angelina 2d 
S Young Wynyard (2859) 
S Wellington (680) 
S Comet (155) 
S Favourite (252) 
S Bolingbroke (86) 
D Young Strawberry 
D Favourite Cow 
D Unknown 
S Smith’s Bull (608) 
Granny's Wealth 
S Sign of Riches (66324) 
S Lord Mayor (61193) 
D Lady Mysie 5th 
S Field Marshal (47870) 
S Roan Gauntlet (35284) 
D Princess Royal 
S Champion of England (17526) 
D Virtue 
S Plantagenet (11906) 
S Duke of Lancaster (10929) 
S Duke (9032) 
D Hartforth Cherry 
S Major Bown (2243) 
S Charles II (879) 
S Percy (1321) 
S Charles (127) 
D Cora 
D Maria 
D Gaudy 
S Favourite (252) 
D Phoenix 
D Favourite Cow 
S Alcock's Bull (19) 
S Unknown 
