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POPULAR SCIENCE MONTHLY. 



normally to a fair degree of approximation, and consequently we may 

 infer that our results are trustworthy indications of real facts. 



A talent is a sum whose exact value few of us care to know, although 

 we all appreciate the inner sense of the beautiful parable. I will, there- 

 fore, venture to adapt the phraseology of the allegory to my present 

 purpose by substituting for 'talent' the words 'normal-talent.' The 

 value of this normal-talent in respect to each and any specified quality 

 or faculty is such that one-quarter of the people receive for their 

 respective shares more than one normal-talent over and above the aver- 

 age of all the shares. Our normal-talent is therefore identical with 

 what is technically known as the 'probable error.' Therefrom the 

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

 'probability integral/ It expresses the distribution of any normal 



Table I. — Normal Distribution (to the nearest per ten thousand and to 



the nearest per hundred). 



quality, or any group of normal qualities, among 10,000 persons in 

 terms of the normal-talent. The M in the upper line occupies the posi- 

 tion of Mediocrity, or that of the average of what all have received: 

 the +1°, +3°, etc., and the — 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 divisons are 

 the numbers per 10,000 of those who receive sums between the amounts 

 specified by those divisions. Thus, by the hypothesis, 2,500 receive 

 more than M but less than M + l°, 1,613 receive more than M-]-l° 

 but less than M-|-2°, and so on. The terminals have only an inner 

 limit, thus 35 receive more than 4°, some to perhaps a very large but 

 indefinite amount. The divisions might have been carried much 

 farther, but the numbers in the classes between them would become less 

 and less trustworthy. The left half of the series exactly reflects the 

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

 T have used the capital or large letters, E, S, T, U, V, for those above 

 mediocrity and corresponding italic or small letters, r, s, t, u, 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 



