J.S.

Bombay.

* * * * *

ON THE CULTIVATION OF GEOMETRY IN LANCASHIRE.

If our Queries on this subject be productive of no other result than that of eliciting the able and judicious analysis subsequently given by MR. WILKINSON (Vol. ii., p. 57.), they will have been of no ordinary utility.  The silent early progress of any strong, moral, social, or intellectual phenomenon amongst a large mass of people, is always difficult to trace:  for it is not thought worthy of record at the time, and before it becomes so distinctly marked as to attract attention, even tradition has for the most part died away.  It then becomes a work of great difficulty, from the few scattered indications in print (the books themselves being often so rare[1] that “money will not purchase them"), with perhaps here and there a stray letter, or a metamorphosed tradition, to offer even a probable account of the circumstances.  It requires not only an intimate knowledge of the subject-matter which forms the groundwork of the inquiry, both in its antecedent and cotemporary states, and likewise in its most improved state at the present time; it also requires an analytical mind of no ordinary powers, to separate the necessary from the probable; and these again from the irrelevant and merely collateral.

MR. WILKINSON has shown himself to possess so many of the qualities essential to the historian of mathematical science, that we trust he will continue his valuable 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.