uable researches in this direction still further.

It cannot be doubted that MR. WILKINSON has traced with singular acumen the
manner in which the _spirit_ of geometrical research was diffused amongst
the operative classes, and the class immediately above them--the exciseman
and the country schoolmaster. Still it is not to be inferred, that even
these classes did not contain a considerable number of able geometers
anterior to the period embraced in his discussion. The Mathematical Society
of Spitalfields existed more than half a century before the Oldham Society
was formed. The sameness of pursuit, combined with the sameness of
employment, would rather lead us to infer that geometry was _transplanted_
from Spitalfields to Manchester or Oldham. Simpson found his way from the
country to London; and some other Simpson as great as Thomas (though less
favourably looked upon by fortune in furnishing stimulus and opportunity)
might have migrated from London to Oldham. Or, again, some Lancashire
weaver might have adventured to London (a very common case with country
artisans after the expiration of apprenticeship); and, there having
acquired a taste for mathematics, as well as improvement in his mechanical
skill, have returned into the country, and diffused the knowledge and the
tastes he took home with him amongst his fellows. The very name betokens
Jeremiah Ainsworth to have been of a Lancashire family.

But was Ainsworth really the earliest mathematician of his district? Or,
was he merely the first that made any figure in print as a correspondent of
the mathematical periodicals of that day? This question is worthy of MR.
WILKINSON's further inquiry; and probably some light may be thrown upon it
by a careful examination of the _original_ Ladies' and Gentleman's Diaries
of the period. In the reprints of these works, only the names, real or
assumed, of those whose contributions were actually printed, are
inserted--not the list of all correspondents.

Now one would be led to suppose that the study of mathematics was
peculiarly suited to the daily mode of life and occupation of these men.
Their employment was monotonous; their life sedentary; and their minds were
left perfectly free from any _contemplative_ purpose they might choose.
Algebraic investigation required writing: but the weaver's hands being
engaged he could not write. A diagram, on the contrary, might lie before
him, and be carefully studied, whilst his hands and fee