380 
Journal of Agricultural Research 
Vol. XXXI,-No. 4 
Table IT. — A two-line pedigree sample of the Shorthorn hull Scottish Victor {79925) 
[A case in which no ancestral connection is shown] 
Scottish Victor (79925) 
Cairo (72151) 
S Prince of Fashion (64597) 
D Primrose 3d 
S Norseman (56233) 
D Nonpareil 20th 
S Cumberland (46144) 
S Pride of the Isles (35072) 
D Golden Days 
S Lord Raglan (13244) 
D Brenda 
S Maunby (7223) 
S Clementi (3399) 
D Cassandra 
D Garland 
S Matchem (2281) 
D By Farmer (251) 
S Farmer (251) 
S Bumper (101) 
S Windsor (698) 
S Favourite (252) 
D Phoenix 
S Foljambe (263) 
D Haughton 
D By Colling’s Bull 
Stella 2d 
S Matchmaker (69105) 
S Pride of the Morning (64546) 
S Star of the Morning (58189) 
D Baronness 6th 
S Field Mashal (47870) 
D Azalea 
S Caesar Augustus (25704) 
S Champion of England (17526) 
D Virtue 
S Plantagenet (11906) 
D Madaline 
D Landlady 
D By Pilot (496) 
S Pilot (496) 
D Red Rose 
S By Punch (531) 
D By Broken Horn (95) 
S Broken Horn (95) 
D By Hubback (319) 
D By Bank's Bull 
S Bank’s Bull 
In the case of the Shorthorn bull Millionaire (79438) (Table I), the 
sire (White j3ear 75896) and dam (Granny’s Wealth) are both 
recorded. Random sequences of S’s and D’s are then written in 
columns below each parent, extending sufficiently to include the 
foundation stock. The line of ancestry is then traced back in the 
herdbook, the sire being looked up where S occurs in the column and 
the dam for each D. In the case of White Bear (75896), the sequence 
happened to run DDDSSD . . . , etc. Thus White Bear’s 
dam, Amethyst, is recorded, but not his sire. Then follow her dam, 
Artless, her dam, Amy, her sire, Grand Duke 36th (43306),,and so on 
until the herdbook fails. A single random line of ancestry of Mil¬ 
lionaire’s dam is tabulated in the same way, the sequence in this 
happening to run SSDSSDS ... Of course a second sample of 
the ancestry of the same animal would probably not show the same 
sequence ot sires and dams, and it may be well to make clear that a 
single sample of this sort is of practically no value as an indication 
of the inbreeding of an individual. But the average obtained from 
a large number of such samples should not differ appreciably from 
the true value. 
Two-column samples of this kind fall at once into two alternative 
categories; those which show an ancestral connection, as Millionaire 
(79438), and those which do not, as Scottish Victor (79925), Table 
II. In the latter case the coefficient is zero as far as the sample 
indicates. In the former case a contribution of (}4) n+nl+1 (l + r a ) 
is indicated if the common ancestor A is n generations back of the 
sire and n 1 back of the dam. The sire has 2 n ancestors in the nth 
generation and the dam 2 nl in the r^th generation. The sample pair 
of lines is thus only one among 2 71+711 possible pairs going back as 
far as the common ancestor. If the single pair of lines is a fair 
sample of the total, its contribution must be multiplied by 2 n+nl 
to obtain an estimate of the inbreeding of the whole pedigree. On 
carrying out this multiplication, n and n 1 disappear, and the coeffi¬ 
cient takes the simple form K(l + i^). Thus, in calculating the 
