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from that college. It was subsequently discovered in a sale-room by the late Abbé Macpherson, rector of the same college, who purchased it and sent it to Blairs, where it has been for, now, a good many years. That it is a portrait of Beaton's time is certain; but the artist is unknown, and the picture has sustained damage. It is attributed, by a competent judge, who has himself painted two careful copies of it, to Titian, not only from its general style and handling, but from certain peculiarities of canvas, &c.; on which latter circumstances, however, he does not lay much stress, taking them only as adminicles in proof. The portrait is a halflength, about 2 ft. 6 in. by 2 ft. it is that of a fresh-coloured, intellectual man, of forty-five or upwards: hazel eyes; hair slightly reddish, or auburn, just becoming tinged with grey; a thin, small beard; costume similar to that of Holbein's Cardinal Wolsey, in the hall of Christchurch, Oxford. It bears this inscription, painted at the bottom of the portrait, and over the original finished painting, and therefore of a subsequent

date:

“David Betonius, S.R.E., Card. Archiep. S. Andreæ in Scotia, ab Hostibus Fidei Barbare Trucidatus."

Beaton was elected to the Cardinalate in Dec. 1538; did he visit Rome after that? He was at all events in Paris. The Scotch College at Rome was a natural habitat for a portrait of a Scottish churchman so famous as Cardinal Beaton, and it would be strange indeed if they had not one of him where they affected a collection of portraits of British prelates. I propose to have this portrait engraved, if its probable authenticity cannot be shaken. Did Pinkerton engrave any portrait of Beaton? There is none in my copies of his Iconographia Scotica, 1797, and his Scottish Gallery, 1799. These contain several duplicates; but it is rare to meet with copies that can be warranted perfect. If the portrait be published, it will probably be accompanied by a short memoir, correcting from authentic documents some of the statements of his biographers: any information either as to the portrait or his life will be thankfully acknowledged. One or two letters from Lord Buchan, on the subject of Scottish Portraits, appeared in the Gentleman's Magazine, vol. lxv., but not relating to this particular one. SCOTUS.

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"things;" and the same pointing is used in the recent editions of Mr. Knight, Barry Cornwall, and Mr. Collier.

It occurred to me that this pointing gave a meaning quite out of harmony with what directly follows, and also with the spirit in which Lafeu speaks. Let the comma be placed after “familiar,” and the whole passage be read thus:

Lafeu. "They say miracles are past; and we have our philosophical persons to make modern and familiar, things supernatural and causeless. Hence is it, that we make trifles of terrors; ensconcing ourselves into seeming knowledge, when we should submit ourselves to

an unknown fear."

Lafeu apparently is speaking somewhat sarcastically of those who say miracles are past, and who endeavour to explain away the wonderful into something common and well-known. Subsequently I found that Mr. Coleridge, in his Literary mentioned passage, placing the comma after "faRemains (vol. ii. p. 121.), had adduced the abovemiliar." He does not, however, make any observation on the other pointing; but remarking that Shakspeare often uses "modern" for "common," proceeds thus:

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Shakspeare, inspired, as it might seem, with all knowledge, here uses the word causeless in its strict philosophical sense; cause being truly predicable only of phenomena, that is, things natural, and not of noumena, or things supernatural."

It is, perhaps, rather curious, that although Mr. Collier, in his note on Lafeu's speech, has quoted the above from Mr. Coleridge, the improved pointing should have escaped that gentleman's notice.

Looking into Theobald's Shakspeare, I find that he also had placed the comma as Mr. Coleridge has. Mr. Theobald adds this note:

66

opposite to our poet's and his speaker's meaning. As This, as it has hitherto been printed, is directly I have stopped it, the sense quadrates with the context: and surely it is one unalterable property of philosophy to make seeming strange and preternatural phenomena familiar and reducible to cause and reason."

Does not Mr. Theobald, in his closing remark, turn what in Lafeu is really an ironical outburst on would-be philosophers, into something like a serious common-place? A. ROFFE.

Query, In a work entitled Philosophy of Shakspeare, by W. H. Roukin, Lafeu's speech is quoted, and one word changed; "and we have our philosophical persons," &c., becomes "yet we have," &c. Is there any authority for such a change?

FOLK LORE.

A. R.

The bigger the Ring, the nearer the Wet.-On Sunday evening, the 20th Oct., the moon had a

very fine ring round it, which apparently was based near the horizon, and spread over a considerable area of the heavens. This was noticed by myself and others as we returned home from church; and upon my mentioning it to my man-servant, who is a countryman, he said he had been noticing it, and that it reminded him of the old saying, "the bigger the ring, the nearer the wet." On the next day, however, it was fine and windy, and my faith began to be shaken as to the truth of the saying; but the almost incessant rain of the four or five subsequent days fully proved its correctness. J. A.

Power of prophesying before Death.-To the passages on this subject lately supplied by your correspondents (Vol. ii., pp. 116. 196.) may be added the following from Tertullian, De Anima, c. 53. (vol. ii. col. 741., ed. Migne, Paris, 1844): "Evenit sæpe animam in ipso divortio potentius agitari, sollicitiore obtutu, extraordinariâ loquacitate, dum ex majori suggestu, jam in libero constituta, per superfluum quod adhuc cunctatur in corpore enuntiat quæ videt, quæ audit, quæ incipit nosse."

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J. C. R. Change in the Appearance of the Dead. -A woman near Maidstone, who had had much experience as a sick-nurse, told me some years ago that she had always noticed in corpses a change to a more placid expression on the third day after death; and she supposed this to be connected with our Lord's resurrection. I omitted to ask her

whether the belief were wholly the result of her own observation, or whether it had been taught her by others, and were common among her neighbours.

roots, and so every layer one upon another, and put in fine gold and some pearl, and cover the pot as close as may bee with coarse dow, and so let it distill a good while, and so reserve it for your use till such time as you have need thereof.”

I could select some exceedingly ludicrous prescriptions (for the book contains 400 pages), but the most curious unfortunately happen to be the most indelicate. Besides this, I am afraid the subject is scarcely worthy of much space in such an important and useful work as "NOTES AND QUERIES." ALEXANDER ANDREWS.

Abridge, Essex.

Mice as a Medicine (Vol. i., p. 397.).—An old woman lately recommended an occasional roast mouse as a certain cure for a little boy who wetted his bed at night. Her own son, she said, had got over this weakness by eating three roast mice. I am told that the Faculty employ this remedy, and that it has been prescribed in the Oxford Infirmary. J. W. H.

Omens from Birds.-It is said that for a bird to fly into a room, and out again, by an open window, surely indicates the decease of some inmate. Is this belief local ? J. W. H.

MODE OF COMPUTING INTEREST.

year

--

The mode of computing interest among the respects the same as that now prevailing in India, ancient Greeks appears to have been in many which has probably undergone no change from a very remote period. Precisely the same term, too, J. C. R. is used to denote the rate of interest, namely, Strange Remedies.-I find some curious pre- TÓKOS in Greek, and taka or tuka in the languages of scriptions in an old book entitled The Pathway to Western India. Tóкoe idéкaтoi, in Greek, and Health, &c. (I will not trouble you with the full dus také, in Hindostanee, respectively denote ten title), "by Peter Levens, Master of Arts in Ox-per cent. At Athens, the rate of interest might be ford, and Student in Physick and Chirurgery." calculated either by the month or by the "Printed for J. W., and are to be sold by Charles each being expressed by different terms (Böckh. Tym, at the Three Bibles on London Bridge, Pub. Econ. of Athens, i. 165.). Precisely the same MDCLXIV." The first is a charm system prevails here. Pono taka, that is, three quarters of a taka, denotes per cent. per month. Nau také, that is, nine také, denotes nine per cent. per annum. For the Greek mode of reckoning interest by the month, see Smith's Dictionary of Greek and Roman Antiquities, p. 524. At Athens, the year in calculating interest, was reckoned at 360 days (Böckh, i. 183.). Here also, in all native accounts-current, the year is reckoned at 360 days.

"For all manner of falling evils.—Take the blood of his little finger that is sick, and write these three verses following, and hang it about his neck : "Jasper fert Mirrham, Thus Melchior Balthazar Aurum, Hæc quicum secum portat tria nomina regum, Solvitur à morbo, Domini pietate, caduca.' and it shall help the party so grieved."

“For a man or woman that is in a consumption.— Take a brasse pot, and fill it with water, and set it on the fire, and put a great earthen pot within that pot, and then put in these parcels following:-Take a cock and pull him alive, then flea off his skin, then beat him in pieces; take dates a pound, and slit out the stones, and lay a layer of them in the bottom of the pot, and then lay a piece of the cock, and upon that some more of the dates, and take succory, endive, and parsley

The word Tókos, as applied to interest, was unfrom TíKTW, "to produce," i. e. money begetting derstood by the Greeks themselves to be derived money; the offspring or produce of money lent out. Whether its identity may not be established with the word in current use for thousands of years in this country to express precisely the same meaning, is a question I should like to see dis_

cussed by some of your correspondents. The word taka signifies anything pressed or stamped, anything on which an impression is made, hence a coin; and is derived from the Sanscrit root, tak, to press, to stamp, to coin: whence,

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 coun try schoolmaster. Still it is not to be inferred,

that even these classes did not contain a consider

tank, a small coin; and tank-sala, a mint; and (query) 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 able number of able geometers anterior to the a half-penny, penny, &c., stamped with the name period embraced in his discussion. The Matheof the issuer, and denominated "tokens," to be matical Society of Spitalfields existed more than issued in large quantities by shopkeepers as a sub-half a century before the Oldham Society was sidiary currency, and received at their shop in formed. The sameness of pursuit, combined with payment of goods, &c. May not ticket, defined by the sameness of employment, would rather lead us Johnson," a token of any right or debt upon the to infer that geometry was transplanted from delivery of which admission is granted, or a claim Spitalfields to Manchester or Oldham. Simpson acknowledged," and tick, score or trust, (to go found his way from the country to London; and on tick), proceed from the same root? J. S. some other Simpson as great as Thomas (though Bombay. 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 the expiration of apprenticeship); and, there having (a very common case with country artisans after 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.

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 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.

*

*Although at one period of our life we took great pains to make a collection of the periodicals which, during the last century, were devoted wholly or partially to mathematics, yet we could never even approximate towards completeness. It was not, certainly, from niggardly expenditure. Indeed, it is doubtful whether a complete set exists, or could even be formed

now.

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 contribulist of all correspondents. tions were actually printed, are inserted—not the

of mathematics was peculiarly suited to the daily Now one would be led to suppose that the study employment was monotonous; their life sedentary ; mode of life and occupation of these men. Their and their minds were left perfectly free for 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 feet may be performing their functions with an accuracy almost instinctive. Nay more: an exceedingly complicated diagram which has grown up gradually as the result of investigations succes

sively made, may be carried in the memory and become the subject of successful peripatetic contemplation. On this point a decided experimental opinion is here expressed: but were further instances asked for, they may be found in Stewart, Monge, and Chasles, all of whom possessed this power in an eminent degree. Indeed, without it all attempts to study the geometry of space (even the very elements of descriptive geometry, to say nothing of the more recondite investigations of the science) would be entirely unproductive. It is, moreover, a power capable of being acquired by men of average intellect without extreme difficulty; and that even to the extent of "mentally seeing" the constituent parts of figures which have never been exhibited to the eye either by drawings or models.

That such men, if once imbued with a love for geometry, and having once got over the drudgery of elementary acquisition, should be favourably situated for its cultivation, follows as a matter of course. The great difficulty lay in finding sufficient stimulus for their ambition, good models for their imitation, and adequate facilities for publishing the results at which they had arrived. The admirable history of the contents of their scanty libraries, given by MR. WILKINSON, leaves nothing more to be said on that head; except, perhaps, that he attributes rather more to the influences of Emerson's writings than I am able to do.* As regards their facilities for publication, these were few, the periods of publication being rarely shorter than annual; and amongst so many competitors, the space which could be allotted to each (even to "the best men") was extremely limited. Yet, contracted as the means of publication were, the spirit of emulation did something; from the belief that insertion was an admitted test of superiority, it was as much an object of ambition amongst these men to solve the " prize question" as it was by philosophers of higher social standing to gain the "prize" conferred by the Académie des Sciences, or any other continental society under the wing of Royalty, at the same period. The prize (half a dozen or a dozen copies of the work itself) was not less an object of triumph, than a Copley or a Royal medal is in our own time amongst the philosophers of the Royal Society.

These men, from similarity of employment, and inevitable contiguity of position, were brought into intercourse almost of necessity, and the formation of a little society (such as the "Oldham") the natural result-the older and more experienced men taking the lead in it. At the same time, there can be little doubt that the Spitalfields Society was the pattern after which it was formed; and there can be as little doubt that one or more of its founders had resided in London, and

* See Philosophical Magazine, Sept. 1850.

"wrought" in the metropolitan workshops. Could the records of the "Mathematical Society of London" (now in the archives of the Royal Astronomical Society) be carefully examined, some light might be thrown upon this question. A list of members attending every weekly meeting, as well as of visitors, was always kept; and these lists (I have been informed) have been carefully preserved. No doubt any one interested in the question would, upon application to the secretary (Professor De Morgan), obtain ready access to these documents.

The preceding remarks will, in some degree, furnish the elements of an answer to the inquiry, "Why did geometrical speculation take so much deeper root amongst the Lancashire weavers, than amongst any other classes of artisans ?" The subject was better adapted to the weaver's mechanical life than any other that could be named; for even the other favourite subjects, botany and entomology, required the suspension of their proper employment at the loom. The formation of the Oldham Society was calculated to keep alive the aspiration for distinction, as well as to introduce novices into the arcanum of geometry. There was generous co-operation, and there was keen competition, -the sure stimulants to eminent success. The unadulterated love of any intellectual pursuit, apart from the love of fame or the hope of emolument, is a rare quality in all stages of society. Few men, however, seem to have realised Basil Montagu's idea of being governed by "a love of excellence rather than the pride of excelling," so closely as the Lancashire geometers of that period - uncultivated as was the age in which they lived, rude as was the society in which their lives were passed, and selfish as the brutal treatment received in those days by mechanics from their employers, was calculated to render them. They were surrounded, enveloped, by the worst social and moral influences; yet, so far as can now be gathered from isolated remarks in the periodicals of the time, they may be held up as a pattern worthy of the imitation of the philosophers of our own time, in respect to the generosity and strict honour which marked their intercourse with one another.

Mathematicians seldom grow up solitarily in any locality. When one arises, the absence of all external and social incentives to the study can only betoken an inherent propensity and constitutional fitness for it. Such a man is too much in earnest to keep his knowledge to himself, or to wish to stand alone. He makes disciples, -he aids, His own researches encourages, guides them. are fully communicated; and this with a prodigality proportioned to his own great resources. He feels no jealousy of competition, and is always gratified by seeing others successful. Thus such bodies of men are created in wonderfully short periods by the magnanimous labours of one ardent

spirit. These are the men that found societies, schools, sects; wherever one unselfish and earnest man settles down, there we invariably find a cluster of students of his subject, that often lasts for ages. Take, for instance, Leeds. There we see that John Ryley created, at a later period, the Yorkshire school of geometers; comprising amongst its members such men as Swale, Whitley, Ryley ("Sam"), Gawthorp, Settle, and Jolin Baines. This, too, was in a district in many respects very analogous to Lancashire, but especially in the one to which the argument more immediately relates:- it was a district of weavers, only substituting wool for cotton, as cotton had in the other case been substituted for the silk of Spitalfields.

-

We see nothing like this in the agricultural districts; neither do we in those districts where the ordinary manufacturing operations themselves require the employment of the head as well as the hands and feet. With the exception, indeed, of the schoolmaster, and the exciseman, and the surveyor, there are comparatively few instances of persons whose employment was not strictly sedentary, having devoted their intellectual energies to mathematics, independent of early cultivation. To them the subject was more or less professional, and their devotion to it was to be expected indeed far more than has been realised. It is professional now to a larger and more varied class of men, and of course there is a stronger body of non-academic mathematicians now than at any former period. At the same time it may be doubted whether there be even as many really able men devoted to science purely and for its own sake in this country as there were a century ago, when science wore a more humble guise.

Combining what is here said with the masterly analysis which MR. WILKINSON has given of the books which were accessible to these men, it appears that we shall be able to form a correct view on the subject of the Lancashire geometers. Of course documentary evidence would be desirable -it would certainly be interesting too.

To such of your readers as have not seen the mathematical periodicals of that period, the materials for which were furnished by these men, it may be sufficient to state that the "NOTES AND QUERIES" is conceived in the exact spirit of those works. The chief difference, besides the usual subject-matter, consists in the greater formality and "stiffness" of those than of this; arising, however, of necessity out of the specific and rigid character of mathematical research in itself, and the more limited range of subjects that were open to discussion.

The one great defect of the researches of those men was, that they were conducted in a manner so desultory, and that the subjects themselves were often so isolated, that there can seldom be

made out more than a few dislocated fragments of any one subject of inquiry whatever. Special inquiries are prosecuted with great vigour and acumen; but we look in vain for system, classification, or general principles. This, however, is not to be charged to them as a scientific vice, peculiarly:-for, in truth, it must be confessed to be a vice, not only too common, but almost universal amongst English geometers; and even in the geometry of the Greeks themselves, the great object appears to have been "problem-solving" rather than the deduction and arrangement of scientific truths. The modern French geometers have, however, broken this spell; and it is not too much to hope that we shall not be long ere we join them in the development of the systems they have already opened; and, moreover, add to the list some independent topics of our own. The chief dangers to which we are in this case exposed are, classification with incomplete data, and drawing inferences upon trust. It cannot be denied, at all events, that some of our French cotemporaries have fallen into both these errors; but the abuse of a principle is no argument for our not using it, though its existence (or even possible existence) should be a strong incentive to caution.

These remarks have taken a more general form than it is usual to give in your pages. As, however, it is probable that many of your readers may feel an interest in a general statement of a very curious intellectual phenomenon, I am not without a hope that, though so far removed from the usual topics discussed in the work, they will not be altogether unacceptable or useless.

Minor Notes.

PEN-AND-INK.

Sermon's Pills.-In Guizot's Life of Monk, Duke of Albemarle, translated and edited by the present Lord Wharncliffe, it is stated (p. 313.) that when the Duke was suffering from the diseases which afterwards proved fatal to him,

"One of his neighbours, at New Hall, formerly an officer in his army, mentioned to him certain pills said to be sovereign against the dropsy, which were sold at Bristol by one Sermon, who had also served under his orders in Scotland as a private soldier. This advice and remedy from ancient comrades, inspired the old general with more confidence than the skill of the physicians. He sent for Sermon's pills, and found himself so much recovered by them for a time that he returned to London at the close of the summer."

Having "found," in the newspapers of the day, the following paragraphs illustrative of this pas sage in the great General's history, I think them sufficiently interesting "to make a Note of."

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