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Correlation and Application of Statistics to Problems of Heredity 99

record making at least to the foals. In this way Galton obtained 716 sires and 494 dams who had produced offspring satisfying the above conditions, and he classified them by the number of times they had produced such marked foals. Reduced to percentages of sires and dams the following table resulted:

Percentage numbers of Standard Performers produced by a single Sire or Dam.

 1 2 3 4 5 6-10 11-20 21-30 31-40 41-50 51 and over Sire 46 17 10 3 9 4 1 1 Dam 50 35 10 1 1 - - - - -

Galton explains the difference between sire and dam by remarking that while the sire produces some 30 foals annually, the dam produces only one, and therefore the chance of a large number of standard performers is much less for her. He even allows that some of the exceptionally noteworthy performances of the sires (Blue Bull, 60 ; Strathmore, 71 ; George Wilkes, 83 ; Happy Medium, 92; and Electioneer, 154 standard performers) may be due in part to the best mares being sent to famous sires. But he concludes that the extraordinary "tail" of high-class offspring of the sires must be due to some prepotency in some of the sires which enables them to impress their character on their offspring, and he remarks

" My conclusion is that high prepotency does not arise through normal variation, but must rank as a highly heritable sport, or aberrant variation ; in other words its causes must partly be of a different order, or else of a highly different intensity, to those concerned in producing the

normal variations of the race. In a sport the position of maximum stability seems to be slightly changed. I have frequently insisted that these sports or "aberrances`(if I may coin the word*) are probably notable factors "in the evolution of races. Certainly the successive improvements of breeds of domestic animals generally, as in those of horses in particular, usually make fresh starts from decided sports or aberrances, and are by no means always developed slowly through

the accumulation of minute and favourable variations during a long succession of generations."

Here, I think, Galton has forgotten two things

(i) The average difference between the first and second individuals in a group of 100 tabled to any character is no less than •36 of the variability of the group, and in a random sample may be still higher, but this is no adequate reason for treating the first individual (or the last) as a sport because he is not, like mediocre individuals, practically continuous with his neighbours.

(ii) That the number of distinguished offspring any individual gives rise to must be considered in relation to his total output. Galton merely says that a sire produces " some 30 foals annually." I do not think this is adequate.

Many years ago I saw a good deal of the working of a large thoroughbred stud ; the stud contained a number of stallions, some famous for their racing

* The word is quite good English, if Joseph Glanvill and Sir Thomas Browne are authorities. 13-2