122 THE RATE OF GROWTH [ch. 



producing their several variations, deviations or errors; and potent 

 in their combinations, permutations and interferences*. 



We begin to see why bodily dimensions lend, or submit, them- 

 selves to this masterful law. Stature is no single, simple thing; 

 it is compounded of bones, cartilages and other elements, variable 

 each in its own way, some lengthening as others shorten, each 

 playing its little part, hke a single pin in Galton's toy, towards a 

 ''fortuitous" resultant. "The beautiful regularity in the statures 

 of a population (says Galton) whenever they are statistically 

 marshalled in the order of their heights, is due to the number of 

 variable and quasi-independent elements of which stature is the 

 sum." In a bagful of pennies fresh from the Mint each coin is 

 made by the single stroke of an identical die, and no ordinary 

 weights and measures suffice to differentiate them; but in a bagful 

 of old-fashioned hand-made nails a slow succession of repeated 

 operations has drawn the rod and cut the lengths and hammered 

 out head, shaft and point of every single nail — and a curve of 

 error depicts the differences between them. 



The law of error was formulated by Gauss for the sake of the 

 astronomers, who aimed at the highest possible accuracy, and 

 strove so to interpret their observations as to eliminate or minimise 

 their inevitable personal and instrumental errors. It had its 

 roots also in the luck of the gaming-table, and in the discovery 

 by eighteenth-century mathematicians that "chance might be 

 defined in terms of mathematical precision, or mathematical 'law'." 

 It was Quetelet who, beginning as astronomer and meteorologist, 

 applied the "law of frequency of error" for the first time to 

 biological statistics, with which in name and origin it had nothing 

 whatsoever to do. 



The intrinsic significance of the theory of probabihties and the 

 law of error is hard to understand. It is sometimes said that to 

 forecast the future is the main purpose of statistical study, and 

 expectation, or expectancy, is a common theme. But all the theory 



* "The curve of error would seem to carry the great lesson that the ultimate 

 differences between individuals are* simple and few ; that they depend on collisions 

 and arrangements, on permutations and combinations, on groupings and inter- 

 ferences, of elementary qualities which are limited iyi variety and finite in extent'' 

 (J. M. Keynes). A connection between this law and Mendelian inheritance is 

 discussed by John Brownlee, P.R.S.E. xxxi, p. 251, 1910. 



