Most persons are probably aware that for various purposes of science and art extensive mathematical tables are requisite, such as tables of the squares and cubes-the square roots and cube roots-of numbers; the logarithms of numbers; the sines, tangents, and other trigonometrical measurements of angles; and numerous others. Such tables have been computed from time to time, principally at the expense of the various governments of Europe, but sometimes at the cost of private individuals. The names of Vega, Callet, Hutton, Gardner, Taylor, Vlacq, Briggs, Barlow, Babbage, &c. are familiar to mathematicians as the authors

of such tables.

to select those which were most readily adapted to
simple numerical calculation by many individuals em-
ployed at the same time. This section had little or
nothing to do with the actual numerical work; for it
had merely the preparation of certain formulæ or forms
of proceeding, which, when completed, were handed
up to the second section. The first section may be
considered as the architects of the undertaking.
The second section consisted of seven or eight per-
sons having considerable acquaintance with mathema-
tics, but not necessarily so profound as the members
of the first section. Their duty was to bring the
labours of the first section to a greater degree of sim-
plicity, so as to be clearly understood by the humbler
labourers of the lowest or third section. The forms of
proceeding, or patterns, as prepared by the second
section from the labours of the first, were by them
delivered to the members of the third section. The
latter gave the finished calculations to the second sec-
tion, the members of which had certain means of veri-
or even of examining the whole of the work done by
the third section. The second section may perhaps be
likened to master-builders, who put the architects'
plans into a form fit to be understood and worked out
by the workmen.

During the fevered state of excitement which followed the commencement of the French Revolution, vast changes were made not only in the constitution and government of the country, but also in matters relating to science. Among the most celebrated of these was the preparation of a decimal system of weights, measures, and calculations in general; and the French government was desirous of producing a series of ma-fying the calculations without the necessity of repeating thematical tables which should facilitate the adoption and the extension of this system. The most distinguished mathematicians and philosophers were invited to construct such tables on the most extensive scale; and in the year 1792, M. Prony, a man of science, who died only two or three years ago, was placed at the head of the commission to whom this office was entrusted.

The mode in which the division of labour' came to be specially employed in this undertaking is exceedingly curious. The professed object was to produce a set of logarithmic and trigonometrical tables, which should not only be adapted to the decimal system of weights and measures, but should also " form a monument of calculation the most vast and the most imposing that had ever been executed, or even conceived." The logarithms of numbers from 1 to 200,000 formed a necessary portion of this labour; and Prony saw very well that even if he were associated with three or four able men, the greatest presumable length of life would not suffice for him to see the conclusion of the great work. While occupied with anxious thoughts as to the mode in which he might execute his gigantic task, he chanced to see in a bookseller's shop at Paris a copy of Smith's Wealth of Nations,' published about sixteen years before. He opened the book at the part where Smith illustrates the advantages of division of labour by reference to the pin-manufacture; and instantly conceived the idea of applying the same principle to calculations. He was about that time lecturing at l'Ecole Polytechnique, on a part of mathematics to which such a division might be easily applied, and his mind was thus prepared for the reception of the hint. He then passed some days in the country, where he formed, in conjunction with Legendre, a plan of operations. To use his own language: "I gave myself up to the task with all the ardour of which I was capable, and occupied myself at first with the general plan of operation. All the conditions which I had to fulfil rendered necessary the employment of a great number of calculators; and it occurred to me to apply to the preparation of these tables the division of labour,' from which the manufacturing arts derive such great advantages, by uniting to the perfection of manufacture the economy of time and expense."

The plan adopted by Prony was to collect three different sets of assistants, possessing three different kinds of talent, the most numerous body being composed of persons having a very limited range of ability. The first section or body was composed of five or six of the most eminent mathematicians in France. The duty of this section was, by entering into a profound investigation of various mathematical doctrines and processes,

The third section consisted of nearly a hundred individuals, who were divided into two parts, meeting in two workshops (if we may use the term), and making separately the same calculations, which were thus reciprocally verified. These persons received certain numbers from the second section, and, using nothing more than simple addition and subtraction, produced the whole of the tables required. It is worthy of remark that nine-tenths of this section had no knowledge of arithmetic beyond its two first rules, which they were thus called upon to exercise, and that these persons were usually found more correct in their calculations than those who possessed a more extensive knowledge of the subject.

Mr. Babbage (Economy of Machinery and Manufactures') observes: "When it is stated that the tables thus computed occupy seventeen large folio volumes, some idea may perhaps be formed of the labour. From that part executed by the third class, which may almost be termed mechanical, requiring the least knowledge and by far the greatest labour, the first class were entirely exempt. Such labour can always be purchased at an easy rate. The duties of the second class, although requiring considerable skill in arithmetical operations, were yet in some measure relieved by the higher interest naturally felt in those more difficult operations. The exertions of the first class are not likely to require, upon another occasion, so much skill and labour as they did upon the first attempt to introduce such a method."

These vast tables, which were completed in the space of two years, consisted of-an introduction, containing the analytical formulæ and the mode of using the tables; an extensive table of sines of angles, to 25 places of decimals; logarithms of sines, to 14 places of decimals; logarithms of numbers from 1 to 200,000, to 14 places of decimals, and in half of them to 19 places; together with other tables comprehended only by mathematicians.

It was intended to print this valuable collection of tables, but from various causes the measure stopped short of completion, and the MS. remained at Paris. In 1820 the English government proposed to the Board of Longitude at Paris to print an abridgement of these tables at the joint expense of the two countries. Five thousand pounds was named as the sum which our government was willing to advance for this purpose; but the proposal was declined; and the great

4

THE PENNY MAGAZINE.

[JANUARY 1,

tables are still confined, in manuscript, to the library | arms in the royal cause, but is suddenly overpowered, of the Paris Observatory. A writer in the Edinburgh sent to the Tower, and is executed not long after Review' for 1834, while speaking of these tables, says: Charles himself, with but little sympathy from any "The printing of them was commenced by Didot, quarter. During one of the periods of his adhesion to and a small portion was actually stereotyped, but the parliamentary cause, Holland House became the never published. Soon after the commencement of scene of an important meeting. When the Presby the undertaking, the sudden fall of the assignats rendered it impossible for Didot to fulfil his contract with head, were vainly endeavouring to stop the progress of terian party, in 1647, with Hollis and others at their the government. The work was accordingly aban- the army towards London, a body of the Independents, doned, and has never since been resumed. before us a copy of one hundred pages folio of the dred commoners, advanced to meet their general We have including no less than fifteen lords and above a hunportion which was printed at the time the work was Fairfax, and Holland House became the scene of the stopped, given to a friend on a late occasion by Didot conference that ensued. It was there that they signed himself." thence that they all returned in solemn and imposingthe declaration issued by the army; and it was from looking procession with Fairfax to London, and resumed their places in parliament. Soon after this, we find Fairfax residing here, and during this period, no doubt, took place the famous interview on the lawn, between Ireton and Cromwell, on matters of the highest importance, most probably in connection with that remarkable paper called the Proposals' of the officers, wherein "they provided for the general reform and re-settlement of the kingdom upon principles of the largest liberty, both civil and religious, and of a glorious toleration, which Europe had not yet even seen in theory."* author, but to have had the assistance of his great Ireton is understood to have been the father-in-law.

The great work here alluded to illustrates in an instructive manner the doctrine which Adam Smith promulgated. Not only were the time and talents of the distinguished mathematicians spared from a drudgery of calculation altogether beneath them, but the calculations were actually made with more correctness and rapidity by persons of humbler talent. A statement appeared in the Quarterly Review' a short time back, illustrating a somewhat similar instance of division of mental labours. In the great Trigonometrical Survey of Ireland, which has been carried on for several years, and is still in progress, the country is parcelled out into a number of very large triangles, which are subsequently divided into smaller ones. The measurement of the larger triangles requires all the resources of refined science; but the smaller ones, after being obtained by instrumental observation, are worked out by simple addition and subtraction. The officers of the survey have found numbers of peasant boys in Ireland who have made these calculations at a halfpenny a triangle.

HOLLAND HOUSE, KENSINGTON. THIS picturesque-looking mansion, the name of which has been made so familiar to us, in connection with the memories of Addison and Fox, and of its late lamented possessor, derives that name from a remarkable man, who may almost be looked upon as its founder. Henry Rich, earl of Holland, the favourite of Henrietta Maria, and the alternate supporter and opponent of her royal husband during the civil war, became the owner of the manor-house of Abbotts Kensington, which had been built by his father-in-law, Sir Walter Cope, on the death of the latter, and then not only altered its name to Holland House, but added to the place most of the peculiar magnificence which subsequently characterized it. piers that we see, one at each extremity of the court The two detached stone before the house, as we stand on the foot-path that divides the latter from the lawn in front, are evidences of the taste both of the artists, Inigo Jones and Mr. Stone, and of their noble employer, in making the improvements and additions referred to. earl's turbulent discontented disposition and his utter But the want of a steady principle left him little leisure for enjoying the comforts and splendour of such a home, and on more than one occasion the leisure that he did obtain he would willingly have dispensed with:-twice he was made prisoner here. We have not space, nor is it worth while, to follow the career of such a man; but it may be noticed, as a curious evidence of his fickle, untrustworthy character, as well as of the confidence that was for a time reposed in him, that whilst at one period he is found sitting at Charles's councilboard, at another he comes from the parliament to Newcastle as the bearer of their famous declaration, which he reads to the king, not without interruptions of a disagreeable nature; later still he again takes

The parliament seems to have dealt gently with the Holland House was restored to her, when it became earl's widow, for no very long period elapsed before famous for a new kind of attraction. During the civil war, the actors generally fought under the royal banners, and distinguished themselves by their zeal and courage. If there had been no other reason therefore, it would not have been surprising to find them treated with little favour after the king's failure and death; in the eyes of the Puritans, who generally disliked but their loyalty was after all the least of their crimes their art; so that when a few of those whom the war had spared met again in London, and began to give secret representations at their old place of meeting, the Cock-pit, they were soon stopped, and for a time imprisoned. The Protectorate seems to have been less severe upon the "poor players." They began to play at various places a little without the town, and generally in the hall of some nobleman's or gentleman's mansion: among these Holland House became conspicuous.

Holland House by becoming a resident, on his marriage It was in 1716 that Addison gave a new interest to The interest unfortunately is more of a painful than with the Dowager Countess of Warwick and Holland. pleasant nature. Some one observed at the period, "Holland House is a large mansion, but it cannot contain Mr. Addison, the Countess of Warwick, and one guest, Peace!" The tradition of Addison's visits, in company neighbouring tavern, is but a natural consequence: with his friends Steele, Phillips, Davenant, &c., to a the place is supposed to be the inn known as the White Horse. It was said that Addison's acquaintance with the countess arose from his having been appointed tutor to her son, the earl of Warwick, but that has been denied. Addison at all events took so great an interest in the young man's welfare as to remember him in his dying moments. Few can have forgotten that scene. looking room at the western termination of the central division of the house that the youthful earl, who is said It was in a large but somewhat gloomy to have led a very irregular life, found the great moralist, who had summoned him thither. After a pause, the youth said, "Dear sir, you sent for me, I believe, * Pictorial England,' vol. iii., p. 370.

1

Soon after the discovery of America had opened a new market for woven fabrics, a commercial company at Appenzell established dyeing and bleaching establishments, and the cotton manufacture became added to that of linen. A feeling of jealousy between the manufacturers of the contiguous cantons of St. Gall and Appenzell led the merchants of the latter to find a market for their goods without the aid of the former as heretofore; and officers, called Experts, were sworn in to measure and mark the quality and value of the pieces of cloth exhibited for sale. For some years the average sale was more than three hundred thousand pieces annually. During the early half of the last century the manufacturers of Appenzell added several new kinds of manufacture to those previously carried on there; such as embroidered linens; gauze linens, sought after by the Americans as a protection from the mosquitoes at night; and bazins or cambric muslins. When the war broke out between England and France in 1756, the supply of cottons to the East Indies was greatly disturbed; and the manufacturers of Appenzell took advantage of the circumstance to establish new bleaching-factories, dye-houses, dressing machines, and calico-printing machines. One of the manufacturers invented a way of weaving a shirt without a seam; and another introduced the embroidery trade by starting a fashion of embroidering the wristbands of shirts.

and the paintings; the carving, the grotesque gilding, | number of commercial officers were appointed at the and the enigmatical mottoes. With peculiar fondness same town, who were bound upon oath to inspect and they will recall that venerable chamber in which all examine every piece of linen which came to market, the antique gravity of a college library was so sin- and to affix thereon a mark expressive of its quality gularly blended with all that female grace and wit and current value. By about the year 1500 there apcould devise to embellish a drawing-room. They will pear to have been two classes of master manufacturers recollect, not unmoved, those shelves loaded with the in St. Gall and Appenzell; one of which consisted of varied learning of many lands and many ages; those master weavers settled at St. Gall, and members of a portraits in which were preserved the features of the guild of that town, who employed spinners and weavers best and wisest Englishmen of two generations. They of the canton of Appenzell; the other consisted of will recollect how many men who have guided the master weavers in Appenzell, who had no connection politics of Europe-who have moved great assemblies with the guild at St. Gall, but sold their linen cloths to by reason and eloquence-who have put life into the merchants of that town. bronze and canvas, or who have left to posterity things so written as it shall not willingly let them die-were there mixed with all that was loveliest and gayest in the society of the most splendid of capitals. They will remember the singular character which belonged to that circle, in which every talent and accomplishment, every art and science had its place. They will remember how the last debate was discussed in one corner, and the last comedy of Scribe in another; while Wilkie gazed with modest admiration on Reynolds's Baretti;' while Mackintosh turned over Thomas Aquinas to verify a quotation; while Talleyrand related his conversations with Barras at the Luxembourg, or his ride with Lannes over the field of Austerlitz. They will remember, above all, the grace-and the kindness, far more admirable than grace-with which the princely hospitality of that ancient mansion was dispensed. They will remember the venerable and benignant countenance, and the cordial voice of him who bade them welcome. They will remember that temper which years of pain, of sickness, of lameness, of confinement, seemed only to make sweeter and sweeter; and that frank politeness which at once relieved all the embarrassment of the youngest and most timid writer or artist, who found himself for the first time among ambassadors and earls. They will remember that constant flow of conversation, so natural, so animated, so various, so rich with observation and anecdote; that wit which never gave a wound; that exquisite mimicry which ennobled instead of degrading; that goodness of heart which appeared in every look and accent, and gave additional value to every talent and acquirement. They will remember too, that he whose name they hold in reverence was not less distinguished by the inflexible uprightness of his political conduct than by his loving disposition and winning manners. They will remember that in the last lines which he traced, he expressed his joy that he had done nothing unworthy the friend of Fox and Grey; and they will have reason to feel similar joy, if on looking back on their troubled years they cannot accuse themselves of having done anything unworthy of men who were distinguished by the friendship of Lord Holland."

For many years after this period, while other countries were playing at the expensive game of war, the Swiss manufactures were in a flourishing state; but when peace succeeded, trade flowed into its old channels, and Swiss products were somewhat lessened. The first spinning-machine introduced into Appenzell (1783) was for twisting the threads for embroidery. A few years after this a gradual change took place in the mode of conducting the cotton-manufacture in the canton. Up to that time the weavers had employed yarn spun by hand in their own dwellings; but the astonishing improvements made in the mode of spinning cotton in England enabled the manufacturers to export yarn from England at a price which rendered it cheaper for the Appenzell weaver to purchase machine-spun yarn than to spin it at home or to buy it home-spun. For some years the new manufacture was objected to, many persons thinking that it was not so strong and durable as the cottons made from handspun yarn; but a different opinion gradually prevailed, and the intervening time enabled the hand spinners to turn their attention to the arts of weaving and of embroidery, as a resource when their labours as handspinners would be no longer valuable.

In proportion as England invented new machines, so did the manufacturers of Appenzell find it necessary to introduce new improvements of some kind or other, in order to keep pace with their powerful rivals. Accelerated modes of weaving, of bleaching, and of dressing cloth were from time to time introduced, producing those results which always follow such improvements, viz. a reverse of fortune to those manufacturers who either cannot or will not bend to the new