novices into the arcanium of geometry. There was generous co-operation, and
there was keen competition,--the sure stimulants to eminent success. The
unadulterated love of any intellectual pursuit, apart from the love of fame
or the hope of emolument, is a rare quality in all stages of society. Few
men, however, seem to have realised Basil Montagu's idea of being governed
by "a love of _excellence_ rather than the pride of _excelling_," so
closely as the Lancashire geometers of that period--uncultivated as was the
age in which they lived, rude as was the society in which their lives were
passed, and selfish as the brutal treatment received in those days by
mechanics from their employers, was calculated to render them. They were
surrounded, enveloped, by the worst social and moral influences; yet, so
far as can now be gathered 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