, Science and Arts
Division.]

[Footnote 234: This is the estimate furnished me by two mathematical
masters in one of our great public schools of the proportion of boys who
have any special taste or capacity for mathematical studies. Many more,
of course, can be drilled into a fair knowledge of elementary
mathematics, but only this small proportion possess the natural faculty
which renders it possible for them ever to rank high as mathematicians,
to take any pleasure in it, or to do any original mathematical work.]

[Footnote 235: I am informed, however, by a music master in a large
school that only about one per cent have real or decided musical talent,
corresponding curiously with the estimate of the mathematicians.]

[Footnote 236: In the latter part of his essay on Heredity (pp. 91-93 of
the volume of _Essays_), Dr. Weismann refers to this question of the
origin of "talents" in man, and, like myself, comes to the conclusion
that they could not be developed under the law of natural selection. He
says: "It may be objected that, in man, in addition to the instincts
inherent in every individual, special individual predispositions are
also found, of such a nature that it is impossible they can have arisen
by individual variations of the germ-plasm. On the other hand, these
predispositions--which we call talents--cannot have arisen through
natural selection, because life is in no way dependent on their
presence, and there seems to be no way of explaining their origin except
by an assumption of the summation of the skill attained by exercise in
the course of each single life. In this case, therefore, we seem at
first sight to be compelled to accept the transmission of acquired
characters." Weismann then goes on to show that the facts do not support
this view; that the mathematical, musical, or artistic faculties often
appear suddenly in a family whose other members and ancestors were in no
way distinguished; and that even when hereditary in families, the talent
often appears at its maximum at the commencement or in the middle of the
series, not increasing to the end, as it should do if it depended in any
way on the transmission of acquired skill. Gauss was not the son of a
mathematician, nor Handel of a musician, nor Titian of a painter, and
there is no proof of any special talent in the ancestors of these men of
genius, who at once developed the most marvellous pre-eminence in their
respective talents. And after showing