in this direction. Meanwhile he made shift with such tools as came to hand—"a commin Knife and a Clout," as he says "instead of the many more helps which such a Work requires[1]." When he could not ascertain directly the number, weight or measure of some phenomenon in which he was interested, he reckoned out what he desired to know upon the basis of what he already knew. In other words he pursued the method of political arithmetic as distinguished from statistics. Statistics demands enumeration. The validity of its inferences depends upon the theory of probabilities as expressed in the Law of Large Numbers. Therefore it adds, it does not multiply. Political arithmetic, as exemplified by Petty, multiplies freely; and the value of its results varies according to the nature of the terms multiplied. For example, in the absence of a census Petty had to calculate the population of London, of England, and of Ireland. His calculations for London[2] are based upon the number of burials and upon the number of houses, facts which at least bear some relation to the number of people. The burials he multiplies by thirty, an arbitrary figure for which he pleads Graunt's authority[3]; the houses he multiplies, now by six[4], and now by eight[5] as suits his purpose. The sources of probable error are obvious. The population of England, he further estimates at eleven times that of London because London pays one eleventh of the assessment. The chance of error is thus raised to the second degree. Nevertheless the calculation is not altogether unreasonable, and Petty asserts that the results "do pretty well agree" with the accounts of the hearth money, the poll money, and the bishops' numbering of the communicants[6]—figures which he neglects to give. To see from what refractory materials he can extract a result when hard pushed, we must turn to his discussion of the Irish rebellion of 1641. He finds that above one-third more "superfluous oxen and sheep, butter and beef" was exported from that kingdom in 1664 than before the rebellion, "which shows there were ⅓ more people in 1641 than in 1664[7]." Unfortunately the use of rash calculations grew upon
- ↑ P. 130.
- ↑ Pp. 459—460, 528.
- ↑ Cf. pp. 332, 393. Graunt's solution of the same problem for London is on pp. 383—386.
- ↑ Pp. 527, 534.
- ↑ P. 459.
- ↑ Cf. p. 461, note, where it appears that the agreement between Petty's estimate and the bishops' survey is not strikingly close.
- ↑ P. 149. Cf. the more elaborate calculation of the same problem on pp. 608, 609. Other striking examples may be found on pp. 175, 311, 462—469, 566—567.
