436 



NOTES AND QUERIES. 



[No. 57. 



cussed by some of your correspondents. The word 

 taka signifies any thing pressed or stamped, any- 

 thing on which an inij^ression is made, hence a 



coin ; and is derived from the Sanscrit root "^ ^i", 



♦ 



tak, to press, to stamp, to coin : whence, "P^ ^, 



tank, a small coin; and tunk-sala, a mint; and 

 ((juery) the English word token, a piece of stamped 

 metal given to communicants. Many of your 

 readers will remember that it used to be a common 

 practice in England for copper coins, representing 

 a half-penny, penny, &c., stamped with the name 

 of the issuer, and denominated "tokens, "to be 

 issued in large quantities by shopkeepei'S as a sub- 

 sidiary currency, and received at their shop in 

 payment of goods, &c. May not ticket, defined by 

 Johnson, " a token of any right or debt upon the 

 delivery of which admission is granted, or a claim 

 acknowledged," and tick, score or trust, (to go 

 on tick), proceed from the same root ? 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 AIr. 

 Wilkinson (Vol. ii., p. 57.), they will have been 

 of no ordinary utility. The silent early progress 

 of any strong, moral, social, or intellectual pheno- 

 menon 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 dis- 

 tinctly marked as to attract attention, even tradi- 

 tion has for the most part died away. It then 

 becomes a work of great difficulty, from the lew 

 scattered indications in print (the bf)oks them- 

 selves being often so rare* that "money will not 

 purchase them"), with pe.-haps here and there a 

 stray letter, or a metamorphosed tradition, to offer 

 even a ])robable account of the circumstances. It 

 requires not only an intimate knowledge of the 

 subject-matter which forms the groundwork of 

 the incjuiry, both in its antecedent and cotempo- 

 rary states, and likewise in its most improved stnte 

 at the present time ; it also requires an analytical 

 mind of no ordinary powers, to separate the neces- 

 sary trom the probable ; and these again from the 

 irrelevant and merely collateral. 



* Although at one period of our life we took great 

 pains to make a collection of the perioilicals which, 

 during the last century, were devoted wholly or par- 

 tially to mathematics, yet we could never even ap- 

 proximate towards completeness. It was not, certainly, 

 from niggardly expenditure. Indeed, it is doubtful 

 whether a complete set exists, or could even be formed 

 now. 



Mr. Wilkinson has shown himself to possess so 

 many of the qualities essential to the historian of 

 mathematical science, that we trust he will con- 

 tinue 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 imme- 

 diately above them — the exciseman and the coun- 

 try schoolmaster. Still it is not to be inferred, 

 that even these classes did not contain a consider- 

 able number of able geometers anterior to the 

 period embraced in his discussion. The Mathe- 

 matical Society of Spitalfields existed more than 

 half a century before the Ohlham Society was 

 formed. The sameness of pursuit, combined with 

 the sameness of employment, would rather lead us 

 to infer that geometry was transplanted from 

 Spitullields to Manchester or Oldham. Simpson 

 found his way from the country to London ; and 

 some other Simpson as great as Thouuis (though 

 less favourably looked upon by fortune in furnish- 

 ing stimulus and opportunity) might have migrated 

 from Loudon to Oldham. Or, again, some Lan- 

 cashire weaver might have adventured to London 

 (a very conunon case with country artisans after 

 the expiration of apprenticeship) ; and, there having 

 ac(juired a taste for mathematics, as well as im- 

 provement in his mechanical skill, have returned 

 into the country, and diffused the knowledge and 

 the tastes he took home with him amongst his fel- 

 lows. The very name betokens Jeremiah Ains- 

 worth to have been of a Lancashire family. 



But was Ainsworth really the earliest mathe- 

 matician of his district ? Or, was he merely the 

 first that made any figure in print as a cori-espon- 

 dent of the nuithematical periodicals of that day ? 

 This (piestion is worthy of AIr. Wilkinson's fur- 

 ther 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 wdiose contribu- 

 tions 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 pur[)0se they might choose. Alge- 

 braic investigation required writing : but the 

 weaver's hands being ensraiied he coidd not write. 

 A diagram, on the contrary, might lie before him, 

 and be carefully studied, whilst his hands and fiset 

 may be performing their functions with an accu- 

 racy almost instinctive. Nay more: an exceed- 

 ingly complicated diagram which has grown up 

 gradually as the result of investigations succes- 



