d from isolated remarks in the periodicals of the
time, they may be held up as a pattern worthy of the imitation of the
philosophers of our own time in respect to the generosity and strict honour
which marked their intercourse with one another.

Mathematicians seldom grow up solitarily in any locality. When _one_
arises, the absence of all external and social incentives to the study can
only betoken an inherent propensity and constitutional fitness for it. Such
a man is too much in earnest to keep his knowledge to himself, or to wish
to stand alone. He makes disciples,--he aids, encourages, guides them. His
own researches are fully communicated; and this with a prodigality
proportioned to his own great resources. He feels no jealousy of
competition, and is always gratified by seeing others successful. Thus such
bodies of men are created in wonderfully short periods by the magnanimous
labours of one ardent {438} spirit. These are the men that found societies,
schools, sects; wherever one unselfish and earnest man settles down, there
we invariably find a cluster of students of his subject, that often lasts
for ages. Take, for instance, Leeds. There we see that John Ryley created,
at a later period, the Yorkshire school of geometers; comprising amongst
its members such men as Swale, Whitley, Ryley ("Sam"), Gawthorp, Settle,
and John Baines. This, too, was in a district in many respects very
analogous to Lancashire, but especially in the one to which the argument
more immediately relates:--it was a district of weavers, only substituting
wool for cotton, as cotton had in the other case been substituted for the
silk of Spitalfields.

We see nothing like this in the agricultural districts; neither do we in
those districts where the ordinary manufacturing operations themselves
require the employment of the head as well as the hands and feet. With the
exception, indeed, of the schoolmaster, and the exciseman, and the
surveyor, there are comparatively few instances of persons whose employment
was not strictly sedentary having devoted their intellectual energies to
mathematics, independent of early cultivation. To them the subject was more
or less professional, and their devotion to it was to be expected--indeed
far more than has been realised. It is professional now to a larger and
more varied class of men, and of course there is a stronger body of
non-academic mathematicians now than at any former period. At the same time
it may