results; that these qualities are of a class that are found, whenever they have been tested, to vary 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, therefore, 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 average 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_.” TABLE I.—_Normal distribution (to the nearest_ per _ten-thousand and to the nearest_ per _hundred.)_ ─────┬───┬───┬────┬────┬─┬────┬────┬───┬───┬──────┬────── │–4°│–3°│ –2°│ –1°│M│ +1°│ +2°│+3°│+4°│ │ ─────┼───┼───┼────┼────┼─┼────┼────┼───┼───┼──────┼────── _v_ │ │ │ │ │ │ │ │ │ │V and │ and │_u_│_t_│_s_ │_r_ │ │ R │ S │ T │ U │above.│Total below│ │ │ │ │ │ │ │ │ │ │ ─────┼───┼───┼────┼────┼─┼────┼────┼───┼───┼──────┼────── 35│180│672│1613│2500│ │2500│1613│672│180│ 35 │10,000 ─────┴───┼───┼────┼────┼─┼────┼────┼───┼───┴──────┼────── 2 │ 7│ 16│ 25│ │ 25│ 16│ 7│ 2 │ 100 ─────────┴───┴────┴────┴─┴────┴────┴───┴──────────┴──────