Chapter 3

Similar remarks evidently apply to Horrocks and Crabtree (1641); for although _both_ were natives of Lancashire, and the latter a resident in the vicinity of Manchester, their early death would prevent the exertion of any considerable influence; nor does it appear that they ever paid any attention to the study of the ancient geometry. Richard Towneley, Esq., of Towneley (1671), is known to have been an ardent cultivator of science, but his residence was principally in London. It may, however, be mentioned to his honour, _that he was the first to discover what is usually known as "Marriotte's Law"_ for the expansion of gases. At a later period (1728-1763), the name of "John Hampson, of Leigh, in Lancashire," appears as a correspondent 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 promoter of the study of the ancient geometry in Lancashire; 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 cursory glance at some of the mathematical periodicals of that date will readily furnish the names of Ainsworth, whose elegant productions in pure geometry adorn the pages of the _Gentleman's_ and _Burrow's Diaries_; Taylor, the distinguished tutor of Wolfenden; Fletcher, whose investigations in the _Gentleman's Diary_ and the _Mathematical Companion_ entitle him to the highest praise; Wolfenden, acknowledged by all as one of the most profound mathematicians of the last century; Hilton, afterwards the talented editor of that "work of rare merit" the _Liverpool Student_; and last, though not least, the distinguished Butterworth, whose elegant and extensive correspondence occupies so conspicuous a place in the _Student_, the _Mathematical Repository_, the _Companion_, the _Enquirer_, the _Leeds Correspondent_, and the _York Courant_. Besides these, we find the names of Mabbot, Wood, Holt (Mancuniensis), Clarke (Salfordoniiensis), as then resident at Manchester and in constant communication 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 considerable influence upon the minds of such distinguished proficients as Cunliffe, Campbell, Lowry, Whitley, and Swale.

Hence it would seem that _many_, and by no means improbable, reasons may be assigned for "the very remarkable circumstance of the geometrical analysis of the ancients having been cultivated with eminent success in the northern counties of England, and particularly in Lancashire." Mr. Harvey, at the York meeting of the British Association in 1831, eloquently announced "that when Playfair, in one of his admirable papers in the _Edinburgh Review_, expressed a fear that the increasing taste for analytical science would at length drive the {58} ancient geometry from its favoured retreat in the British Isles; the Professor seemed not to be aware that there existed a devoted band of men in the north, resolutely bound to the pure and ancient forms of geometry, who in the midst of the tumult of steam engines, cultivated it with unyielding ardour, preserving the sacred fire under circumstances which would seem from their nature most calculated to extinguish it." Mr. Harvey, however, admitted his inability clearly to trace the "true cause of this remarkable phenomenon," but at the same time suggested that "a taste for pure geometry, something like that for entomology among the weavers of Spitalfields, may have been transmitted from father to son; but who was the distinguished individual _first_ to create it, in the peculiar race of men here adverted to, seems not to be known." However, as "the two great restorers of ancient geometry, Matthew Stewart and Robert Simson, it may be observed, lived in Scotland," he asks the important questions:--"Did their proximity encourage the growth of this spirit? Or were their writings cultivated by some teacher of a village school, who communicated by a method, which genius of a transcendental order knows so well how to employ, a taste for these sublime inquiries, so that at length they gradually worked their way to the anvil and the loom?"

An attentive consideration of these questions in all their bearings has produced in the mind of the writer a full conviction that we must look to other sources for the revival of the study of the ancient geometry than either the writings of Stewart or Simson. It has been well observed by the most eminent geometer of our own times, Professor Davies--whose signature of PEN-AND-INK (Vol. ii., p. 8.) affords but a flimsy disguise for his well-known _propria persona_--that "it was a great mistake for these authors to have written their principal works in the Latin language, as it has done more than anything else to prevent their study among the only geometers of the eighteenth century who were competent to understand and value them;" and it is no less singular than true, as the same writer elsewhere observes, "that whilst Dr. Stewart's writings were of a kind calculated to render them peculiarly attractive to the non-academic school of English geometers, they remain to this day less generally known than the writings of any geometer of these kingdoms." The same remarks, in a slightly qualified form, may be applied to most of the writings of Simson; for although his edition of Euclid is now the almost universally adopted text-book of geometry in England, at the time of its first appearance in 1756 it did not differ so much from existing translations as to attract particular attention by the novelty of its contents. Moreover, at this time the impulse had already been given and was silently exerting its influence upon a class of students of whose existence Dr. Simson appears to have been completely ignorant. In one of his letters to Nourse (_Phil. Mag._, Sept. 1848, p. 204.) he regrets that "the taste for the ancient geometry, or indeed any geometry, seems to be quite worn out;" but had he instituted an examination of those contemporary periodicals either wholly or partially devoted to mathematics, he would have been furnished with ample reasons for entertaining a different opinion.

We have every reason to believe that the publication of Newton's _Principia_ had a powerful effect in diffusing a semi-geometrical taste amongst the academical class of students in this country, and it is equally certain that this diffusion became much more general, when Motte, in 1729, published his translation of that admirable work. The nature of the contents of the _Principia_, however, precluded the possibility of its being adapted to form the taste of novices in the study of geometry; it served rather to exhibit the _ne plus ultra_ of the science, and produced its effect by inducing the student to master the rudimentary treatises thoroughly, in order to qualify himself for understanding its demonstrations, rather than by providing a series of models for his imitation. A powerful inducement to the study of pure geometry was therefore created by the publication of Motte's translation: ordinary students had here a desirable object to obtain by its careful cultivation, which hitherto had not existed, and hence when Professor Simpson, of Woolwich, published his _Algebra_ and the _Elements of Geometry_ in 1745 and 1747, a select reading public had been formed which hailed these excellent works as valuable accessions to the then scanty means of study. Nor must the labours of Simpson's talented associates, Rollinson and Turner, be forgotten when sketching the progress of this revival. The pages of the _Ladies' Diary_, the _Mathematician_, and the _Mathematical Exercises_, of which these gentlemen were severally editors and contributors, soon began to exhibit a goodly array of geometrical exercises, whilst their lists of correspondents evince a gradual increase in numbers and ability. The publication of Stewart's _General Theorems_ and Simson's edition of _Euclid_, in 1746 and 1756, probably to some extent assisted the movement; but the most active elements at work were undoubtedly the mathematical periodicals of the time, aided by such powerful auxiliaries as Simpson's _Select Exercises_ (1752) and his other treatises previously mentioned. It may further be observed that up to this period the mere English reader had few, if any means of obtaining access to the elegant remains of the ancient geometers. Dr. Halley had indeed given his restoration of Apollonius's _De Sectione Rationis_ and _Sectione Spatii_ in 1706. Dr. Simson had also issued his edition of the _Locis Planis_ in 1749; but unfortunately the very language in which these valuable works were written, precluded the possibility of {59} these unlettered students being able to derive any material advantages from their publication: and hence arises another weighty reason why Simpson's writings were so eagerly studied, seeing they contained the leading propositions of some of the most interesting researches of the Alexandrian School.

After the death of Simpson, the Rev. John Lawson, who appears to have inherited no small portion of the spirit of his predecessors, began to take the lead in geometrical speculations; and having himself carefully studied the principal writings of the ancient geometers, now formed the happy project of unfolding these treasures of antiquity to the general reader, by presenting him with English translations of most of these valuable remains. With this view he published a translation of Vieta's restoration of _Apollonius on Tangencies_, in 1764, and to this, in the second edition of 1771, was added the _Treatise on Spherical Tangencies_, by Fermat, which has since been reprinted in the _Appendix to the Ladies' Diary_ for 1840. In 1767 appeared Emerson's _Treatise on Conic Sections_; a work which, notwithstanding its manifest defects, contributed not a little to aid the student in his approaches to the higher geometry, but whose publication would probably have been rendered unnecessary, had Dr. Simson so far loosened himself from the trammels of the age, as to have written his own admirable treatise in the English language. The frequency, however, with which Mr. Emerson's treatise has been quoted, almost up to the present date, would appear to justify the propriety of including _it_ amongst the means by which the study of geometry was promoted during the last generation. The success which attended Mr. Lawson's first experiment induced him to proceed in his career of usefulness by the publication, in 1772, of the _Treatise on Determinate Section_; to which was appended an amended restoration of the same work by Mr. William Wales, the well-known geometer, who attended Captain Cook as astronomer, in one of his earlier voyages. In 1773 appeared the _Synopsis of Data for the Construction of Triangles_, which was followed in 1774 by his valuable _Dissertations on the Geometrical Analysis of the Ancients_; and although the author used an unjustifiable freedom with the writings of others, Dr. Stewart's more especially, it is nevertheless a work which probably did more to advance the study of the ancient geometry than any other separate treatise which could be named. As these publications became distributed amongst mathematicians, the _Magazines_, the _Diaries_, and various other periodicals, began to show the results of the activity which had thus been created; geometrical questions became much more abundant, and a numerous list of contributions appeared which afford ample proof that their able authors had entered deeply into the spirit of the ancient geometry. During the year 1777 Mr. Lawson issued the first portion of Dr. Simson's restoration of _Euclid's Porisms_, translated from the _Opera Reliqua_ of that distinguished geometer; and though the work was not continued, sufficient had already been done to furnish the generality of students with a clue to the real nature of this celebrated enigma of antiquity. The last of these worthy benefactors to the non-academic geometers of the last century was Mr. Reuben Burrow, who by publishing in 1779 his _Restitution of Apollonius Pergæus on Inclinations_ gave publicity to a valuable relic which would otherwise have remained buried in the Latin obscurity of Dr. Horsley's more elaborate production.

During the greater portion of the time just reviewed, Mr. Jeremiah Ainsworth was resident in the neighbourhood of Manchester, and so early as 1761 was in correspondence with the editors of the _Mathematical Magazine_. He subsequently associated with Mr. George Taylor, a gentleman of kindred habits, then resident in the immediate vicinity, and these worthy veterans of science, as time wore on, collected around them a goodly array of pupils and admirers, and hence may truly be said not only to have laid the foundation of the "Oldham Society," but also to have been the fathers of the Lancashire school of geometers. Such then was the state of affairs in the mathematical world at the period of which we are speaking; all the works just enumerated were attracting the attention of all classes of students by their novelty or elegance; Dr. Hutton and the Rev. Charles Wildbore had the management of the _Diaries_, each vieing with the other in offering inducements for geometrical research; whilst both, in this respect, for a time, had to contend against the successful competition of Reuben Burrow, the talented editor of Carnan's _Diary_: correspondents consequently became numerous and widely extended, each collecting around him his own select circle of ardent inquirers; and thus it was, to use the words of Mr. Harvey, and answer the questions proposed, that inquiries which had hitherto been "locked up in the deep, and to them unapproachable recesses of Plato, Pappus, Apollonius and Euclid * * porisms and loci, sections of ratio and of space, inclinations and tangencies,--subjects confined among the ancients to the very greatest minds, (became) familiar to men whose condition in life was, to say the least, most unpropitious for the successful prosecution of such elevated and profound pursuits."

The preceding sketch is respectfully submitted as an attempt to answer the queries of PEN-AND-INK, so far as Lancashire is concerned. It is not improbable that other reasons, equally cogent, or perhaps corrective of several of the preceding, may be advanced by some of your more learned correspondents, whose experience and means of reference are superior to my own. Should any such {60} be induced to offer additions or corrections to what is here attempted, and to extend the inquiry into other localities, your pages will afford a most desirable medium through which to compare _notes_ on a very imperfectly understood but most important subject of inquiry.

T. T. WILKINSON.

Burnley, Lancashire, June 5. 1850.

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QUERIES ANSWERED, NO. 8.

Passing over various queries of early date, on which it has been my intention to offer some suggestions, I have _endeuoyred me_, as Master Caxton expresses it, to illustrate three subjects recently mooted.

_Trianon_ (No. 27.).--The origin of this name is thus stated by M. Dolort, in his excellent work entitled _Mes voyages aux environs de Paris_, ii. 88.

"_Le grand Trianon._--Appelé au 13^e siècle _Triarmun_, nom d'une ancienne paroisse, qui était divisée en trois villages dépendant du diocèse de Chartres. Cette terre, qui appartenait aux moines de Sainte-Geneviève, fut achetée par Louis XIV. pour agrandir le parc de Versailles, et plus tard il y fit coustruire le château."

_Wood paper_ (No. 32.).--At the close of the last century a patent was granted to Matthias Koops for the manufacture of paper from _straw_, _wood_, &c. In September 1800, he dedicated to the king a _Historical account of the substances which have been used to describe events_, in small folio. The volume is chiefly printed on paper _made from straw_; the appendix is on _paper made from wood alone_. Both descriptions of paper have borne the test of time extremely well. Murray, in his _Practical remarks on modern paper_, speaks of Koops and his inventions with much ignorance and unfairness.

_Tobacco in the East_ (No. 33.).--Relying on the testimony of Juan Fragoso, physician to Felipe II. of Spain, I venture to assert that tobacco is not indigenous to the East. To the same effect writes Monardes. Nevertheless, it was cultivated in Java as early as the year 1603. Edmund Scott, factor for the East India Company at Bantam, thus describes the luxuries of the Javans:--

"They are very great eaters--and they haue a certaine hearbe called _bettaile_ which they vsually have carryed with them wheresoeuer they goe, in boxes, or wrapped vp in cloath like a suger loafe: and also a nutt called _pinange_, which are both in operation very hott, and they eate them continually to warme them within, and keepe them from the fluxe. They doe likewise take much _tabacco_, and also _opium_."--_An exact discovrse_ etc. _of the East Indians_, London, 1606. 4^o. Sig. N. 2.

BOLTON CORNEY.

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MEANING OF "BAWN."

_Bawn_ (Vol. i, p. 440.) has been explained as "the outer fortification, inclosing the court-yard of an Irish castle or mansion, and was generally composed of a wall with palisadoes, and sometimes flankers."

The word _bawn_ or _bane_ (the _a_ pronounced as in the English word _hat_) is still applied in the south of Ireland to the spot of ground used as a place for milking the cows of a farm, which, for obvious reasons, is generally close to the farm-house. Before the practice of housing cattle became general, every country gentleman's house had its _bawn_ or _bane_. The necessity for having such a place well fenced, and indeed fortified, in a country and period when cattle formed the chief wealth of all parties, and when the country was infested by Creaghadores and Rapparees, is obvious; and hence the care taken in compelling the "undertakers in Ulster" to have at least "a good bawn after the Irish fashion." In Munster the word _bane_ or _bawn_ is used to express land that has been long in grass; _tholluff bawn_ being used to signify grass land about to be brought into cultivation; and _tholluff breagh_, or _red land_, land which has been recently turned. To _redden land_ is still used to express either to plough land, or, more generally, to turn land with the spade.

Now the _milking field_ was, and is always kept in grass, and necessarily receiving a good deal of manure, would usually be _white_ from the growth of daisies and white clover. Hence such a field would be called the _white_ field: and from this to the general application of the phrase to grass land the transition is easy and natural. It may be proper to add, that in Kerry, particularly, the word is pronounced _bawn_, in speaking _Irish_; but the same person will call it _bane_, if mentioning such land in English. The _a_ in the latter word is, as I said before, pronounced like the _a_ in hat.

The Irish for a _cow_ being _bo_, the phrase may have had its origin therefrom. On this matter, as on all relating to Irish antiquities, the readers of "NOTES AND QUERIES" may be glad to have a sure person to refer to; and they cannot refer to a more accomplished Irish scholar and antiquarian than "Eugene Curry". His address is, "Royal Irish Academy, Grafton Street, Dublin."

KERRIENSIS.

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Replies To Minor Queries.

_Births, Marriages, &c., Taxes on_ (Vol. ii., p. 10.).--The first instance, that I am aware of, of a tax on marriages in this country, occurs in the 5 of Wm. and Mary, c. 21. The war in which William engaged soon rendered it necessary to tax other incidents of humanity; and accordingly the 6 & 7 Wm. III. c. 6. was passed, granting to his Majesty certain {61} rates and duties upon marriages, births, deaths, and burials, and upon bachelors and widowers (a widely-spread net), for the term of five years, "for carrying on the war against France with vigour." The taxes on births, marriages, and burials were continued indefinitely by the 7 & 8 Wm. III. c. 35. I know not when this act was repealed; but by the 23 George III. c. 67., taxes were again imposed on burials, births, marriages, and christenings; and by 25 George III. c. 75. these taxes were extended to Dissenters. By the 34 George III. c. 11., the taxes were repealed, and they ceased on October 1st, 1794. The entries in the parish register noticed by ARUN, refer to these taxes. Query, Were our ancestors justified in boasting that they were "free-born" Englishmen as long as one of these taxes existed?

C. ROSS.

_M._ or _N._ (Vol. i., p. 415.).--These must, I think, be the initials of some words, and not originating in a corruption of nom, as suggested. We have in the marriage service:--

"'I publish the banns of marriage between M. of ---- and N. of ----.' "The curate shall say unto the man, "M. 'Wilt thou have this woman,' &c. "The priest shall say unto the woman, "N. 'Wilt thou have this man,' &c. "The man says: 'I, M. take thee N. to my wedded wife,' &c. "The woman says: 'I, N. take thee M. to my wedded husband,'" &c. Again, "Forasmuch as M. and N. have consented together," &c.

All these passages would go to show that the letters are initials either of some word by which the sex was denoted, or of some very common Christian names of each sex, which were formerly in use.

I grant that, in the baptismal service, N. may possibly stand for nomen.

THOS. COX.

Preston.

_Arabic Numerals._--I am not entitled to question either the learning or the "acumen" of the Bishop of Rochester; but I am entitled to question the _interpretation_ which E. S. T. tells us (Vol. ii., p.27.) he puts upon the Castleacre inscription. My title to do so is this:--that in the year of grace 1084 the Arabic numerals were not only of necessity unknown to the "plaisterers" of those walls, but even (as far as evidence has been yet adduced) to the most learned of England's learned men.

As to the regular order in crossing himself, that will entirely depend upon whether the plaister was considered to be a knight's shield, and the figures the blazonry, or not. Is it not, indeed, stated in one of your former numbers, that this very inscription was to be read 1408, and not 1048? I have already hinted at the necessity of _caution_ in such cases; and Mr. Wilkinson of Burnley has given, in a recent number of your work, two exemplifications. The Bishop of Rochester certainly adds another; though, of course, undesignedly.

T. S. D.

Shooter's Hill, June 7.

_Comment. in Apocalypsin_ (Vol. i., p. 452.).--There was a copy of this volume in the library of the Duke of Brunswick; and in the hope that Sir F. Madden may succeed in obtaining extracts, or a sight of it, I intimate just as much, though not in this kingdom. (See Von der Hardt's _Autographa Lutheri et Coætaneorum_, tom. iii. 171.) You do not seem to have any copy whatever brought to your notice. This collection was, it appears from the _Centifolium Lutheranum_ of Fabricius (p. 484.), bequeathed by the Duke to the library at Helmstad.

NOVUS.