An Attempt towards obtaining invariable Meafures of Length, Capacity, and Weight, from the Menfuration of Time, independent of the mechanical Operations requifite to afcertain the Centre of Ofcillation, or the true Length of Pendulums. By John Whitehurit, F. R. Š. 4to. Bent. 1787 *.

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HE neceffity of a method by ny other circumftances were to be conwhich the true quantities of fidered, befide those which were fupmeasures may, at all times, and in all pofed neceffary to determine the true places, be afcertained, will be evident, length of pendulums. The difficulty if we confider the disorder and confu- of finding the centre of ofcillation fion that arife from thofe accidents to feemed an unfurmountable obstacle which arbitrary standards are liable. to mention all the impediments which The ftandards of our own country these gentlemen met with, would be an have, from time to time, undergone affront to the judgment of our learned various changes. We are even igno readers, and tedious to those who are ant of the precife quantities of the unskilled in the theoretical part of me weight and measure ufed in England chanics: we fhall therefore proceed to before the time of Henry VIII. Our explain the method proposed by Mr neighbours on the continent are in the Whitehurst, and to examine whether fame predicament; and as to the an- he has afcertained the length of a meacients, the great uncertainty of the fure, which may, if the standard were true quantities of their weights and left or damaged, be again accurately meafures is fufficiently apparent from determined by a repetition of the fame the numberless contests of the learned experiments whence it was originally concerning them. obtained.

Mouton, Wren, Huygens, and many other ingenious mechanics, have in vain employed their thoughts to invent fuch a fixed and permanent meafure as would have no need of artificial Standards to perpetuate it. Some of the methods ufed for obtaining this univerfal measure were merely chimerical; many however were well founded, especially fuch as depend on the motion of pendulums; for it was known that the vibrations of a pendulum of a determinate length were always performed in the fame time; and it was concluded, that, in order to determine the length of any pendulum, nothing more was neceffary than to mark the number of vibrations which it performed in a given time; and as a certain number of vibrations in a given time would always produce the fame length of pendulum, this was confidered as the propereft method for obtaining a permanent meafure. When this method was applied to practice, it was found not to fucceed, because maVOL. VI. No 36.

In 1779, a method was propofed to the Society of Arts, &c. by Mr Hatton, in confequence of a premium, which had been four years advertised by that inftitution, of a gold medal, or 100 guineas, for obtaining invariable Standards for weights and meafures, communicable at all times and to all nations.' Mr Hatton's plan, as we are told in the preface to this work,

confifted in the application of a moveable point of fufpenfion to one and the fame pendulum, in order to produce the full and abfolute effect of two pendulums, the difference of whofe lengths was the intended measure.' Several years elapfed, and no fteps were apparently taken by Mr Hatton, toward a more effectual application of the principle he fuggefted; it was therefore generally fuppofed, that the inventor of this machine had totally declined any farther confideration of the fubject. Thefe confiderations, toge ther with the favourable opinion I entertained of his fcheme, induced me 3 C Monthly Review.

to attempt fome improvement in the cured by another fcrew paffing through conftruction of Mr Hatton's appara- a notch, fo as to confine the ruler

tus, in order to preferve his idea from being too hastily abandoned.'

from fhaking, but not from expanding or contracting in length, by a change in the temperature of the atmosphere. Against the edge of this ruler flide two pillars, that carry a brafs plate with the moveable point of fufpenfion. The upper edge of this plate is per fectly horizontal, and confequently tranfverfe to the ruler, against which it flides up and down; this edge will then ferve as a ruler for ruling straight lines tranfverfely on the brafs ruler

Mr Whitehurst's plan is, to obtain a measure of the greateft length that conveniency will permit, from two pendulums whofe vibrations are in the ratio of 2: 1, and whofe lengths coincide with the English ftandard in whole numbers. The numbers which he hath chofen fhew great ingenuity. On the fuppofition that the length of a fecond's pendulum, in the latitude of London, is 39.2 inches, the length that is inlaid into the plank. The of one vibrating 42 times in a minute must be 80 inches; and of another vibrating 84 times in a minute, muft be zo inches; and their difference, 60 inches, or 5 feet, is his ftandard measure. By the experiments, how ever, the difference of the lengths of the two pendulums was found to be 59.892 inches, instead of 60, owing to the error in the affumed length of the feconds pendulum, 39.2 inches being greater than the truth.

The apparatus, by which the difference of the pendulums was determined, is of curious conftruction, and demands attention; we fhall describe it as perfectly as we can without the explanatory plates.

The frame is a strong deal plank about fix feet long, placed with great exactness in a perpendicular direction. Down the middle of this plank is a longitudinal flit, about an inch wide. By the fide of this flit a brass ruler, 62 inches long and a quarter of an inch thick (and, we believe, an inch broad) is inlaid into the plank, having its furface flush with that of the deal. At the lower end it is firmly fixed with a fcrew; and at the upper end, it is fe

pillars juft mentioned pafs quite thro' the flit in the frame, and are furnished behind with binding fcrews, fo that the plate may be fixed at any height. On the anterior furface of the plate a time-piece is fixed; which may be connected with, or released from, the pendulum when required. The clockwork is not effentially different from that of a common eight-day clock. The train and numbers are as usual, except the first pinion, which has 12 leaves (in order to render the impetus on the pendulum more equable,) and the pendulum wheel, which has 21 teeth, to fuit the vibrations 42 and 84 in a minute it has the dead fcapement, and a counterpoife to the pallets.

The pendulum confifts of a spherical leaden ball, 2 inches diameter, weighing 25 oz. 10 dit. 11gr. Troy, fufpended by a flat, tempered, steel wire, 80 inches of which weigh only three grains *. This pendulum hange on a nut, moveable by means of a very fine, equally-cut ferew, placed at the top of the wooden frame, by which the pendulum-rod could be eafily adjufted to the 1000th part of an inch.

To

* The extreme fineness of this wire almoft paffes credibility. Its length and breadth are not given: but by calculation, 80 inches in length weighing 3 grains, and the specific gravity of tempered fteel being 7.704, its tranfverfe section mult have been lefs than the 52,000th part of a fquare inch: and had it been a fquare rod, it must have been only the 228th part of an inch thick. It nevertheless. fupported above 2 lb. of lead. What an inftance of the attraction of cohesion!

Whitehurst sn Invariable Measures, So.

To the inner frame of the clock, at its loweft extremity, a graduated arc of a circle is fixed, by which the lengths of the vibrations of the pendulum are measured.

With this apparatus Mr Whitehurst proceeds to make his experiments. Having flid the clock, with the moveable point of fufpenfion, to the top of the frame, it was there fixed and attached to the pendulum, which was then about 80 inches long. A maintaining power was applied to the clock, and the pendulum was adjufted from time to time until it vibrated 42 times in a minute, defcribing an arc of 30 20'. In this pofition a tranfverfe line was drawn on the brafs ruler along the edge of the plate that carries the moveable point of fufpenfion. During the whole of these and the fubfequent operations, the machine was kept in the temperature of 60 of Fahrenheit's thermometer.

The clock was now detached from the pendulum, and brought down fo low as to make the distance between the moveable point of fufpenfion and the centre of the ball, about 20 inches. Here the clock was again fet agoing, and was, from time to time, by means of an adjusting screw, moved upward or downward, until the pendulum was found to vibrate 84 times in a minute; and in order to make it vibrate in the fame arc, the clock was leffened from 33 to 8 ounces*.

The place of the clock where the pendulum vibrated 84 times in a minute being ascertained, another tranf verfe line was drawn on the brafs ruler, along the edge of the plate carrying the point of fufpenfion, as before. The distance between the lines thus drawn on the brafs ruler, viz. 59.892 inches, is the measure propofed. It is in fact the difference of the lengths of two pendulum-rods, and not the

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difference of the lengths of two pendulums vibrating 84 and 42 times in a minute; fo that the centre of ofcillation is no where concerned in the measure.

Thefe experiments feem to have been made with the utmost care and accuracy. In a word,-while the mechanic admires the author's ingenuity in contriving the apparatus, the philo fopher will approve his judgement in fuccefsfully applying it. Mr Whitehurft has fully accomplished his defign, and fhewn how an invariable ftandard may, at all times, be found. He hath alfo afcertained a fact, as accurately as human powers feem capable of afcertaining it, of great confequence in natural philofophy. The difference of the lengths of the rods of two pendulums whofe vibrations are known, is a datum whence the true lengths of pendulums, the spaces thro which heavy bodies fall in a given time, and many other particulars relative to the doctrine of gravitation, the figure of the earth, &c. &c. may be obtained. Mr Whitehurst has inferted an investigation, communicated to him by a friend, of the length of the feconds pendulum, and the space of a heavy body's defcent in the first fecond of its fall. The method of folution is concise and ingenious, but it is defective. The ratio of the weight of the pendulum-rod to the weight of the ball is neglected: the length of the long pendulum rod was about 80 inches and its weight 3 grains, and the weight of the ball 250z. 10dwt. 11gr. i. e. 12251 grains, to which 3 grains bear only a fmall proportion, and of a grain, the weight of the fhorter pendulum-rod, bears a much lefs; yet this fmall quantity caufes, by being neglected,an error of 9-10,000ths of an inch in the length of the seconds pendulum, which is ftated to be 39.1196 inches;

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*This is a curious fact; the fhort pendulum was one fourth the length of the long one, and vibrated in the same arc with one fourth the force that was neceflary for the other. Hence, when pendulums of different lengths vibrate in the fame or equal arcs, the forces impelling them are in the direct ratio of their lengths.

inches; but the neglect of another con- tion. The number 59.892 is the da

fideration produces a much greater error;—it is faid, that heavy bodies defcend through 16.087 feet in one fecond.' This refult is deduced from the length 39.1196, which is the length of a feconds pendulum vibrating in an arc of 30 20'; but the fpaces fallen thro' by heavy bodies muft be deduced from pendulums vibrating either in cycloids, or in infinitely fmall arcs of circles. The length of a feconds pendulum vibrating in a cycloid is 39.1362, as may be deduced from 39.1187, the accurate length of a feconds pendulum vibrating in a circular arc of 30 20', and hence heavy bodies will fall, in the firft fecond of their defcent, through 16.0941 feet.

Let not what we have here advanced, be interpreted as intended to depreciate Mr Whitehurst's determina

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tum whence all thefe conclufions must be made: and it is from this number that we have deduced, 14, 39.1187 the length of a feconds pendulum vibrating in a circular arc of 3° 20′; 2d, 39.1362 the length of a feconds pendulum vibrating in a cycloid and in vacuo; 3d, 16.0941 the space fallen through in the firft fecond of a heavy body's descent.

Recherches Hiftoriques fur les Maures, 3 tom. 8vo. Paris. HIS work is just published, and, as we mean occafionally to furnish our readers with fome extracts from it, we have thought it neceffary to tranflate the following account of the author's plan.

ALTHOUGH by the industry and fuccefs of modern travellers we are acquainted with the relative productions and native riches of most climates, as well as with the manners and political intereft of almost every people, yet there are still fome nations of the earth with regard to whom our ideas are but very vague and imperfect, If thefe have not excited the attention and curiofity of travellers, it is because of the small concern they have had in great events; of the little inftruction that is to be gained by inveftigating the principles of their legislation, their religion, and customs; or of the difficulty in overcoming the obftacles occafioned by the climate they live in, or the ferocity of their manners. Such are the people in the centre of Afri

ca; it is probable that the barren de farts they inhabit will for ever keep them ftrangers to us, especially when we confider that we have hardly a tolerable idea of the Moors, even on the northern borders of that country. The empire of Morocco, which is only feparated from Europe by a strait of five leagues, is perhaps lefs known to us than the most diftant regions.

On this empire, and on the Moors in general, I propofe to make fome obfervations. I have collected fome fragments, scattered up and down in books, like these tribes in their deferts, that I might join in fome fort of connection what I have myself seen, with what has already been faid of thefe people, who, after a fucceffion of ages, ftill exhibit the picture of men in the first stage of fociety. After having fhared for a moment in the brilliant revolutions of Europe, the Moors withdrew again into obfcurity; like thofe torrents that a fudden tempeft has formed, which, after having defo

lated

Hiftory of the Moors.

lated a few vallies, precipitate themfelves into the abyfs of the ocean, and hardly leave the memory of the ravages they occafioned.

My defign at firft was only to write the Hiftory of Morocco, with the constitution of which I had become acquainted by being engaged in a variety of affairs that neceffarily required a long refidence in the country. I afterwards enlarged my plan, without, perhaps, fufficiently attending to the difficulties that would obftruct the fuccefsful performance of it. Wishing to investigate the origin of the Moors, I found myself obliged to trace them through all the revolutions to which they have ever been subject. They were engaged either by political convention, by vicinity of fituation, by uniformity of intereft, or by natural inconfiftency of difpofition, in the wars that fubfifted between Rome and Carthage. After the destruction of this laft empire, when the Moors were expofed to the refentment and the ambition of the Romans, I follow them in their gradual depreffion to a ftate of flavery. It is impoffible, indeed, to speak of nations in the first ages of the Christian æra, without finding the Romans, who were then the mafters of the world, acting a principal part in every event. After the decline of the Roman empire, the Moors, changing masters, were for a while under the dominion of the Vandals, who took poffeffion of the northern coafts of Africa; but they foon fell again into the power of the Romans of the lower empire, that is, of the Greeks. Laftly, by an invafion more powerful than lafting, the Arabs in their turn fubjected the Moors, and established the foundations of their religion and their power, from the banks of the Euphrates to the western extremities of the earth. This nation, confounded with the people they had fubdued, made an irruption into Spain, which, at that time, groaned under the tyranny of the Goths; from whence,

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flufhed with momentary victory, they carried their arms into the fouthern' provinces of France, and were advancing to the centre, when Charles-Martel checked their progrefs, and punished their temerity. This chain of events, which becomes more interefting in proportion as it approaches our own country, encouraged me to trace the Moors through these different revolutions, and to arrange my work according to the plan which I followed in my refearches.

The particular History of modern Mauritania, though fufficiently varied by a series of ufurpations, of perfidies, and tragic events, exhibits a picture fomewhat difmal and monotonous; nor does it affect us with the fame lively interest which we feel in the history of enlightened nations who have made the moral virtues fubfervient to their ambitious defigns: we find, indeed, among the Moors the fame paffions and the fame crimes that are to be met with in every other people; but we do not find the fame principles, the fame fentiments, the fame genius; in a word, it is a barren and ungrateful foil, which produces nothing but thiftles, and which I thought it neceffary to embellish with fome foreign flowers. The fterility of the fubject has often difcouraged me, and would even have altogether withheld me from profecuting my plan, if I had not confidered it as my duty to throw, upon the em pire of Morocco, fo little known, and fo much disfigured by ignorant writers, all the light that my experience and opportunities allowed me to ac quire.

In order to treat methodically of the fubject of this inquiry, I divide my work into four books.

In the firft, I inveftigate the state of Mauritania, in thofe early ages of hiftory which, by reason of the obfcurity of the times, and the propenfity of rude nations to allegorical tradition, have received the appellation of Fabulous. The concern which the

Moors