66o 



NATURE 



[October 31, 1901 



whole of the following table starts into life, evolved from that of 

 the "probability integral." It expresses the distribittion of 



Table I. — Normal Distribution {to the nearest per ten-thousand 

 and to the nearest per hundred). 



35 I 180 672;i6r3 2500 2500 1613, 672 iSo 35 10,000 

 2 f 7! 16] 25 ^j j6] 7 2 100 , 



any normal quality, or any group of normal qualities, amonj^ 

 10,000 persons in terms of the normal-talent. The M in the 

 upper line occupies the position of Mediocrity, or that of the 

 average of what all have received : the + 1°, + 2°, etc., and 

 ihe -1°, -2°, etc., refer to normal talents. These numerals 

 stand as graduations at the heads of the vertical lines by which 

 the table is divided. The entries between the divisions are the 

 numbers per lO.OCO of those who receive sums between the 

 ainounls specified by those divisions. Thus, by the hypothesis, 

 2500 receive more thati M but less than M + 1°, 161 3 receive 

 more than M ,+, 1° but less than M + 2^ and so on. The 

 terminals have only. an inner limit, thus 35 receive niore' than 4°, 

 some , to, perhaps, a very large but indefinite anipunt. The 

 divisions niight have been carried much farther, but tlie numbers 

 iiithe^ classes between them would become less and less trust- 

 worthy." The left half, of the series exactly reflects, the right 

 half. . As it will be useful henceforth, to distinguish these classes, 

 I have used the capital ox large letters R, S, T, U, V, for those 

 above mediocrity and corresponding italic or small letters, r, s, 

 t. 11, v, for those below mediocrity, r being the counterpart of 

 R, s of S, and so on. 



In the lowest line the same values are given, but more 

 roughly, to the nearest whole percentage. 



It will assist in comprehending the values of different grades 

 of civic worth to compare them with the corresponding grades 

 of adult male stature in our nation. I will take the figures 

 from my *' Natural Inheritance," premising that the distribution 

 of stature in various peoples has been well investigated and 

 shown to be closely normal. The average height of the adult 

 males, to whom my figures refer, was nearly 5 feet S inches, 

 and the value of their '' normal-talent " (which is a measure of 



the spread of distribution) was very nearly if inches. From 

 these data it is easily reckoned that Class U would contain men 

 whose heights exceed 6 feet ij inches. Even they are tall enough 

 to overlook a hatless mob, while the higher classes, such as 

 V, W and X, tower above it in an increasingly marked degree. 

 So the civic worth (however that term may be defined) of 

 U-class men, and still more of V-cIass, are notably superior 

 to the crowd, though they are far below the heroic order. The 

 rarity of a V-class man in each specified quality or group of 

 qualities is as 35 in 10,000, or say, for the convenience of 

 using round numbers, as i to 300. A man of the W class 

 is ten times rarer, and of the X class rarer still : but I shall 

 avoid giving any more exact definition of X than as a value 

 considerably rarer than V. This gives a general but just 

 idea of the distribution throughout a population of each and 

 every quality taken separately so far as it is normally dis- 

 tributed. As already mentioned, it does the same for any 

 group of normal qualities ; thus, if marks for classics and for 

 mathematics were severally normal in their distribution, the 

 combined marks gained by each candidate in both those sub- 

 jects would be distributed normally also, this being one of the 

 many interesting properties of the law of frequency. 



Comparison of the Normal Classes with those of Mr. Booth. — 

 Let us now compare the normal classes with those into which 

 Mr. Charles Booth has divided the population of all London, in 

 a way that corresponds not unfairly with the ordinary conception 

 of grades of civic worth. He reckons them from the lowest 

 upwards, and gives the numbers in each class for East London. 

 Afterwards he treats all London in a similar manner, except 

 that sometimes he combines two classes into one and gives the 

 joint result. For my present purpose, I had to couple them 

 somewhat "differently; first disentangling them as I best could. 

 There seemed no better way of doing this than by assigning to 

 the members of 'each couplet the same proportions that they had 

 in East London. Though this was certainly not accurate, it is 

 probably not far wrong. Mr. Booth has taken unheard-of pains 

 in this great work of his to arrive at accurate results, but he 

 emphatically says that his classes cannot be separated sharply 

 from one another. On the contrary, their frontiers blend, and 

 this, justifi.es me in taking slight liberties with his figures. His 

 class A consists of criminals, semi-criminals, loafers and some 

 others, who are in number at the rate of i per cent, in all 

 London — ^^that is 100 per 10,000, or nearly three times as many 

 as the V class : they therefore include the whole of r' and spread 

 upwards into the u. , His cl.ass B consists of very poor persons 

 who subsist on casual earnings, many of whom are inevitably 

 poor from shiftlessness, idleness or drink. The numbers in this 

 and the A class combined closely correspond with those in / and 

 all below /. 



T.ABLE \\. — Comparison of Mr. Booth's Classification of All London with the Normal Classes. 



The two columns headed " Nos." gi\ 



NO. 1670, VOL. 64] 



1000 1000 1000 



■espectively the numbers p-r thousand in Mr. Boo-h's and in the normal da 



