ures, and the
general diffusion of education, have affected the {376} state of things; I
speak of the time during which the present system took its rise, and of the
circumstances under which many of its most effective promoters were
trained. In all this there is nothing which stands out, like the
state-nourished academy, with its few great names and brilliant single
achievements. This country has differed from all others in the wide
diffusion of the disposition to speculate, which disposition has found its
place among the ordinary habits of life, moderate in its action, healthy in
its amount."

THE OLD MATHEMATICAL SOCIETY.

Among the most remarkable proofs of the diffusion of speculation was the
Mathematical Society, which flourished from 1717 to 1845. Its habitat was
Spitalfields, and I think most of its existence was passed in Crispin
Street. It was originally a plain society, belonging to the studious
artisan. The members met for discussion once a week; and I believe I am
correct in saying that each man had his pipe, his pot, and his problem. One
of their old rules was that, "If any member shall so far forget himself and
the respect due to the Society as in the warmth of debate to threaten or
offer personal violence to any other member, he shall be liable to
immediate expulsion, or to pay such fine as the majority of the members
present shall decide." But their great rule, printed large on the back of
the title page of their last book of regulations, was "By the constitution
of the Society, it is the duty of every member, if he be asked any
mathematical or philosophical question by another member, to instruct him
in the plainest and easiest manner he is able." We shall presently see
that, in old time, the rule had a more homely form.

I have been told that De Moivre[766] was a member of this {377} Society.
This I cannot verify: circumstances render it unlikely; even though the
French refugees clustered in Spitalfields; many of them were of the
Society, which there is some reason to think was founded by them. But
Dolland,[767] Thomas Simpson,[768] Saunderson,[769] Crossley,[770] and
others of known name, were certainly members. The Society gradually
declined, and in 1845 was reduced to nineteen members. An arrangement was
made by which sixteen of these members, who where not already in the
Astronomical Society became Fellows without contribution, all the books and
other property of the old Society being transfe