June 22. 1850.] 



NOTES AND QUERIES. 



57 



the fourteenth century ? Several documents of 

 Edw. II. are dated from Shene (Richmond) ; in 

 1318, one from IMortehik ; in 1322, one from Istel- 

 worth ; and several are dated Pountfrcyt, or Pontein 

 fractam super Thamis. (See Rymer's Fcederu.) It 

 is very clear that this Pountfrcyt on the Thames 

 must have been at no great distance from Shene, 

 Mortlake, and Isleworth, also upon the Thames ; 

 and this is further corroborated by the dates fol- 

 lowing, from tlie places alluded to, so closely. 



1^ N. 

 June 14. 1850. 



ON THE OKIGIN AND PROGRESS OF THE STUDY OF 

 GEOMETRY IN LANCASHIRE. 



The extensive study of geometry in Lancashire 

 and the northern counties generally is a fact wliich 

 has forced itself upon the attention of several ob- 

 servers; but none of these have attempted to assign 

 any reasons for so singular an occurrence. Indeed, 

 the origin and progress of the study of any par- 

 ticular branch of science, notwithstanding their 

 attractive features, have but rarely engaged the 

 attention of those best qualified for the undertak- 

 ing. Fully satisfied with pursuing their ordinary 

 courses of investigation, they have scarcely ever 

 stopped to inquire who first started the subject 

 of tlieir contemplations ; nor have they evinced 

 much more assiduity to ascertain the hoiv, the 

 when, or in what favoured locality he had his exist- 

 ence : and hence the innumerable misapprojjriations 

 of particular discoveries, the unconscious travers- 

 ing of already exhausted fields of research, and 

 many of the bickerings which have taken place 

 amongst the rival claimants for the honour of 

 priority. 



Mr. Halliwell's Letters on the Progress of 

 Science sufficiently show that the study of geo- 

 metry was almost a nonentity in England pre- 

 viously to the commencement of the eighteenth 

 century. Before this period Dr. Dee, the cele- 

 brated author of the preliminary discourse to Bil- 

 lingsley's Euclid, had indeed resided at Manches- 

 ter (151)5), but his residence here could effect little 

 in favour of geometry, seeing, as is observed by a 

 writer in the Penny Cyclopadia — 



" The character o( the lectures on Euclid was in 

 those days extremely diH'uretit from that of our own 

 time .... the propositions of Kuclld being then taken 

 as so many pegs to liang a speech upon." 



Similar remarks evidently apjily to Ilorrocks 

 and Crabtree (1(541); f()r although WAwerenatives 

 of Lancashire, and the latter a resident in the vici- 

 nity of Manchester, their early death woulil pre- 

 vent the exertion of any considerable influence; 

 nor docs it appear that they ever paid any atten- 



tion to the study of the ancient geometry. Richard 

 Towneley, Esq., of Towneley (1671), is known to 

 have been an ardent cidtivator of science, but his 

 residence was principally in London. It may, 

 however, be mentioned to his honour, that he ivas 

 the first to discover what is usually known as " Mar- 

 riotte's Laiv " for the expansion of gases. At a later 

 period (1728-1763), the name of "John Hamp- 

 son, of Leigh, in Lancashire," appears as a corre- 

 spondent to the Lady s Diary ; but since he mostly 

 confined his speculations to subjects relating to 

 the Diophantine Analysis, he cannot be considered 

 as the originator of the revival in that branch of 

 study now under consideration. Such being the 

 case, we are led to conclude that the " Oldham 

 Mathematical Society" was really the great pro- 

 moter of the study of the ancient geometry in Lan- 

 cashire ; for during the latter half of the last 

 century, and almost up to the present date, it has 

 numbered amongst its members several of the most 

 distinguished geometers of modern times. A cur- 

 sory glance at some of the mathematical periodi- 

 cals of that date will readily furnish the names of 

 Ainsworth, whose elegant productions in pure 

 geometry adorn the pages of the Gentlemari s and 

 Barrow s Diaries; Taylor, the distinguished tutor 

 ofWolfenden; Fletcher, whose investigations in 

 the Gentleman s Diary and the Mathematical Com- 

 panion entitle him to the highest praise ; Wolfenden, 

 acknowledged by all as one of the most profound 

 mathematicians of the last century ; Hilton, after- 

 wards the talented editor of that " work of rare 

 merit " the Liverpool Student ; and last, though 

 not least, the distinguished Bu*terworth, whose 

 elegant and extensive correspondence occupies so 

 conspicuous a place in the Student, the Mathema- 

 tical Repository, the Companion, the Enquirer, the 

 Leeds Correspondent, and the York Courant. Be- 

 sides these, we find the names of Mabbot, Wood, 

 Holt (Mancuniensis), Clarke (Salfordoniiensis), as 

 then resident at Manchester and in constant com- 

 munication with, if not actually members of the 

 society ; nor can it be doubted from the evidence 

 of existing documents that the predilection for the 

 study of the ancient geometry evinced by various 

 members of this Lancashire School, exercised con- 

 siderable influence upon the minds of such distin- 

 guished proficients as Cunliffe, Campbell, Lowry, 

 \Vhitlcy, and Swale. 



Hence it woidd seem that manr/, and by no means 

 improbable, reasons may be assigned for " the very 

 remarkable circumstance of the geometrical ana- 

 lysis of the ancients having been cultivated with 

 eminent success in the northern counties of Eng- 

 land, and particularly in Lancashire." Mr. Harvey, 

 at the York meeting of the British Association in 

 1831, ekxjuently announced "that when I'luyfair, 

 in one of his admirable i)apcrs in the Edinburgh 

 lieview, expressed a fear that the inci'easing taste 

 for analytical science would at length drive the 



