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An Artempt towards obtaining invariable Measures of Length, Capacity, and che Weight, froin the Menfuration of Time, indipendent of the mechanical Operd

tims requisite to ascertain the Centre of Oscillation, or the true Length of Pen

dulums. By John Whitehurst, F. R. Š. 4to. Bent. 1787 *. k. T HE necellity of a method by ny other circumstances were to be con

1 which the true quantities of fidered, beside those which were supmeasures may, at all times, and in all posed neceffary to determine the true places, be ascertained, will be evident, length of pendulum. The difficulty if we consider the disorder and confu- of finding the centre of oscillation

lion that arise from those accidents to seemed an unsurmountable obstacle : WC which arbitrary standards are liable to mention all the impediments which

The standards of our own country these gentlemen met with, would be an ci and to 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 derved. tant of the precise quantities of the unskilled in the theoretical part of medige o's weight and measure used in England chanics; we shall therefore proceed to

before the time of Henry VIII. Our explain the method proposed by Mr 753 in the neighbours on the continent are in the Whitehurst, and to examine whether within the same predicament; and as to the an- he has ascertained the length of a mea

The bits cients, the great uncertainty of the sure, which may, if the standard were fche non true quantities of their weights and lost or damaged, be again accurately sze cbt measures is fufficiently apparent from determined by a repetition of the same midas, was the numberless contests of the learned experiments whence it was originally bat element concerning them.'

obtained. nawigate Mouton, Wren, Huygens, and ma- In 1779, a method was proposed to WE ny other ingenious mechanics, have in the Society of Arts, &c. by Mr Hat-e of the vain employed their thoughts to in- ton, in consequence of a premium, ziber raté vent such a fixed and permanent mea- which had been four years advertised caules i Jure as would have no need of artificial by that institution, of a gold medal, ning acusé Standards to perpetuate it. Some of or 100 guineas,' for obtaining invacare bene the methods used for obtaining this riable standards for weights and meaEine font universal measure were merely chime- faresy camnitinicable at all times and to coming the

prical; many however were well found- all nations. Mr Hatton's plan, as we Varese conted, especially such as depend on the are told in the preface to this work, the best in motion of pendulums ; for it was consisted in the application of a movehe known that the yibrations of a pendu- able point of suspension to one and the without lum of a determinate length were al- fame pendulum, in order to produce

ways performed in the same time ; and the full and absolute effect of two pen-
it was concluded, that, in order to dulums, the difference of whose lengths
determine the length of any pendulum, was the intended measure.'-. Several
nothing more was necessary than to .years elapsed, and no steps were ap-
mark the number of vibrations which parently taken by Mr Hatton, toward
it performed in a given time; and as a more effectual application of the
a certain number of vibrations in a principle he suggested; it was there-
given time would always produce the fore generally supposed, that the in-
fame length of pendulum, this was ventor of this machine had totally de-
considered as the properest method for clined any farther consideration of the
obtaining a permanent meafure. When subject. These considerations, toge-
this method was applied to practice, it ther with the favourable opinion I en-
was found not to fucceed, because ma- tertained of his scheme, induced me
Vol. VI. No 36.

- 3 C
* Monthly Roview.

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to attempt some improvement in the cured by another forew passing through construction of Mr Harton's appara- a notch, so as to confine the ruler tus, in order to preserve his idea from from Thaking, but not from expanding being too hastily abandoned.' or contracting in length, by a change

Mr Whitehurst's plan is, to obtain in the temperature of the atmosphere. a measure of the greateit length that Against the edge of this ruler side conveniency will permit, from two two pillars, that carry a brass plate pendulums whose vibrations are in the with the moveable point of suspension. ratio of 2:1, and whose lengths coin- The upper edge of this plate is percide with the English standard in fectly horizontal, and consequently whole numbers. The numbers which transverse to the ruler, against which he hath chosen Thew great ingenuity. it fides up and down; this edge will On the supposition that the length of then serve as a ruler for ruling Itraight a second's pendulum, in the latitude lines transversely on the brass ruler of London, is 39.2 inches, the length that is inlaid into the plank. The of one vibrating 42 times in a minute pillars just mentioned país quite thro' must be 80 inches; and of another the lit in the frame, and are furnished vibrating 84 times in a minute, must behind with binding screws, so that be 20 inches; and their difference, the plate may be fixed at any height. 60 inches, or 5 feet, is his standard On the anterior surface of the plate a measure. By the experiments, how- time-piece is fixed; which may be conever, the difference of the lengths of nected with, or released from, the penthe two pendulums was found to be dulum when required. The clock59.892 inches, instead of 60, owing work is not essentially different from to the error in the assumed length of that of a common eight-day clock. the seconds pendulum, 39.2 inches The train and numbers are as usual, being greater than the truth.

except the first pinion, which has 12 The apparatus, by which the dif- leaves (in order to render the impeference of the pendulums was deter- tus on the pendulum more equable, mined, is of curious construction, and and the pendulum wheel, which has demands attention ; we shall describe 21 teeth, to suit the vibrations 42 and it as perfectly as we can without the 84 in a minute :—it has the dead explanatory plates.

scapement, and a counterpoise to the The frame is a strong deal plank a- pallets. bout fix feet long, placed with great. The pendolum confists of a spheriexactness in a perpendicular direction. cal leaden ball, 2 inches diameter, Down the middle of this plank is a weighing 250z. 10 dwt. II gr. Troy, longitudinal sit, about an inch wide. suspended by a flat, tempered, steel By the side of this flit a brass ruler, wire, 80 inches of which weigh only 62 inches long and a quarter of an inch three grains *. This pendulum hange thick (and, we believe, an inch broad) on a nut, moveable by means of a veis inlaid into the plank, having its sur- ry fine, equally-cut screw, placed at face flush with that of the deal. At the top of the wooden frame, by which the lower end it is firmly fixed with a the pendulum-rod could be easily adscrew; and at the upper end, it is fe- justed to the 10ooth part of an inch.

To * The extreme fireness of this wire almof pafíes credibility. Its length and breadth are not given : but by calculation, 80 inches in length weighing 3 grains, . and the specific gravity of tempered steel being 7.704, its transverse section must have been less than the 52,00oth part of a square inch: and had it been a square rod, it must have been only the 228th part of an inch thick. It neverthelets. Tupported above 2 lb. of lead. What an instance of the attraction of cohefion !


Whitehurst sn Invariable Measures, &c.

395 To the inner frame of the clock, at difference of the lengths of two pena its lowest extremity, a graduated arc dulums vibrating 84 and 42 times in of a circle is fixed, by which the a minute ; so that the centre of of. lengths of the vibrations of the pen- cillation is no where concerned in the dulum are measured.

measure. With this apparatus Mr Whitehurst These experiments seem to have proceeds to make his experiments. been made with the utmost care and Having slid the clock, with the move- accuracy. In a word, while the meable point of suspension, to the top of .chanic admires the author's ingenuity the frame, it was there fixed and at- in contriving the apparatus, the philotached to the pendulum, which was sopher will approve his judgement in then about 80 inches long. A main- successfully applying it. Mr Whitea taining power was applied to the clock, hurft has fully accomplished bis deand the pendulum was adjusted from sign, and shewn how, an invariable time to time until it vibrated 42 times standard may, at all times, be found. in a minute, describing an arc of -30 He hath also ascertained a fact, as ac20'. In this position a transverse line curately as human powers seem cawas drawn on the brass ruler along pable of ascertaining it, of great conthe edge of the plate that carries the sequence in natural philosophy. The moveable point of suspension. During difference of the lengths of the rods the whole of these and the subsequent of two pendulums whose vibrations are operations, the machine was kept in known, is a datum whence the true the temperature of 60 of Fahrenheit's lengths of pendulums, the spaces thro? thermometer.

which heavy bodies fall in a given The clock was now detached from time, and many other particulars relathe pendulum, and brought down so tive to the doctrine of gravitation, the low as to make the distance between figure of the earth, &c. &c. may be the moveable point of suspension and obtained. Mr Whitehurst has insert. the centre of the ball, about 20 inch, ed an investigation, communicated to es. Here the clock was again set a- him by a friend, of the length of th: going, and was, from time to time, by seconds pendulum, and the space of a means of an adjusting screw, moved heavy body's descent in the first seupward or downward, until the pen- cond of its fall. The method of sodulum was found to vibrate 84 times lution is concise and ingenious, but it in a minute ; and in order to make it is defective. The ratio of the weight vibrate in the same arč, the clock of the pendulum-rod to the weight of was lessened from 33 to 8 ounces*, the ball is neglected : the length of

The place of the clock where the the long pendulum rod was about 80 pendulum vibrated 84 times in a mi- inches and its weight 3 grains, and nute being ascertained, another trans- the weight of the ball 2502. 10 dwt. verse line was drawn on the brass ru- ligr. i. e. 12251 grains, to which 3 ler, along the edge of the plate carry- grains bear only a small proportion, ing the point of suspension, as before. and of a grain, the weight of the

The distance between the lines thus shorter pendulum-rod, bears a much drawn' on the brass ruler, viz. 59.892 less'; yet this small quantity causes, by inches, is the measure proposed. It being neglected,an error of 9-10,00oths is in fact the difference of the lengths of an inch in the length of the seconds of two pendulum-rods, and not the pendulum, which is stated to be 39.1196

3 C 2

inches ; * This is a curious fact;the short pendulum was one fourth the length of the ong one, and vibrated in the same arc with one fourth the force that was necessary for the other. Hence, when pendulum's of different lengths vibrate in the same or e qual 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 dasideration produces a much greater er- tum whence all these conclufoos mult ror ; it is said, that · heavy bodies be made: and it is from this number descend through 16.087 fect in onc that we have deduced, 14, 39.1187 second.' This result is deduced from the length of a seconds pendulum via the length 39.1196, which is the brating in a circular arc of 30 20'; Jength of a seconds pendulum vibra- 2d, 39.1362 the length of a seconds ting in an arc of 30 20%; but the fpa- pendulum vibrating in a cycloid and ces fallen thro' by heavy bodies must in vacuo ; 3d, 16.0941 the space fala be deduced from pendulums vibrating len through in the first second of a either in cycloids, or in infinitely small heavy body's dcfcent. arcs of circles. The length of a fe. The remainder of the work before conds pendulum vibrating in a cycloid ụs contains several directions, fhewing is 39.1362, as may be deduced from how the measure of length may be ap39.1187, the accurate length of a se. plied to determine the meafures of caconds pendulum vibrating in a circu. pacity and weight, which do not ad. lar arc of 30 20', and hence heavy mit of abridgment; and the author bodies will fall, in the first second of has added some tables of the compas their descent, through 16.0941 feet. rative weights and measures of differa

Let not what we have here advan- ent nations, the uses of which, in phia ced, be interpreted as intended to de- losophical and mercantile affairs, are preciate Mr Whitehạrst's determina- felf-evidenta

Recherches Historiques sur les Maures, 3 tom. 8vo. Paris. T H IS work is just published, ca ; it is probable that the barren des

1 and, as we mcan occasionally farts they inhabit will for ever keep to furnith our readers with some ex. them strangers to us, especially when tracts from it, we have thought it ne- we consider that we have hardly a cessary to translate the following ac- tolerable idea of the Moors, even on count of the author's plan.

the northern borders of that country, ALTHOUGH by the industry and The empire of Morocco, which is success of modern travellers we are ac- only separated from Europe by a strait quainted with the relative productions of five leagues, is perhaps less know? and native riches of most climates, as to us than the most distant regions. well as with the manners and political On this empire, and on the Moors interest of almost every people, yet in general, I propose to make some there are still some nations of the earth observations. I have collected fome with regard to whom our ideas are fragments, scattered up and down in but very vague and imperfect, If these books, like these tribes in their de have not excited the attention and cu- ferts, that I might join in fome sort of riosity of travellers, it is because of connection what I have myself seen, the small concern they have had in with what has already been said of great cvents; of the little instruction these people, who, after a succeffion that is to be gained by investigating of ages, still exhibit the picture of men the principles of their legislation, their in the first Itage of society. After ha. religion, and customs; or of the diffi- ving shared for a moment in the brilculty in overcoming the obstacles oc- liant revolutions of Europe, the Moors casioned by the climate they live in, withdrew again into obscurity ; like or the ferocity of their manners. Such those torrents that a sudden tempert are the people in the centre of Afri- has formed, which, after having delo:

History of the Moors.

391 lated a few vallies, precipitate them- flushed with momentary victory, they selves into the abyss of the ocean, and carried their arms into the southern hardly leave the memory of the ra- provinces of France, and were advanvages they occasioned.

cing to the centre, when Charles-MarMy design at first was only to write tel checked their progress, and punishthe History of Morocco, with the con- ed their temerity. This chain of estitution of which I had become ac- vents, which becomes more interesting quainted by being engaged in a varie, in proportion as it approaches our own ty of affairs that necessarily requi- country, encouraged me to trace the red a long residence in the country. Moors through these different revoluI afterwards enlarged my plan, with- tions, and to arrange my work ac-' out, perhaps, sufficiently attending to cording to the plan which I followed the difficulties that would obstruct the in my researches. successful performance of it. Wishing The particular History of modern to investigate the origin of the Moors, Mauritania, though sufficiently varied I found myself obliged to trace them by a series of usurpations, of perfidies, through all the revolutions to which and tragic events, exhibits a picture they have ever been subject. They somewhat dismal and monotonous; nor were engaged either by political con- does it affect us with the same lively vention, by vicinity of situation, by interest which we feel in the history of uniformity of interest, or by natural enlightened nations who have made the inconsistency of disposition, in the wars morai virtues subservient to their ambithat subsisted between Rome and Car- tious designs : we find, indeed, among thage. After the destruction of this the Moors the same passions and the fame last empire, when the Moors were crimes that are to be met with in eve. exposed to the resentment and the ry other people ; but we do not find ambition of the Romans, I follow the same principles, the famg senti. them in their gradual depression to ments, the fame genius ; in a word, a state of slavery. It is impossible, it is a barren and ungrateful foil, which indeed, to speak of nations in the produces nothing but thistles, and first ages of the Christian æra, with, which I thought it necessary to emout finding the Romans, who were bellish with some foreign flowers. The then the masters of the world, acting sterility of the subject has often difa principal part in every event. After couraged me, and would even have the decline of the Roman empire, the altogether withheld me from profecuMoors, changing masters, were for a ting my plan, if I had not considered while under the dominion of the Van- it as my duty to throw, upon the em. dals, who took possession of the north- pire of Morocco, so little known, and ern coasts of Africa ; but they soon so much disfigured by ignorant wri. fell again into the power of the Ro- ters, all the light that my experience mans of the lower empire, that is, of and opportunities allowed me to acthe Greeks. Lastly, by an invasion quire. more powerful than lasting, the Arabs In order to treat methodically of in their turn subjected the Moors, and the subject of this inquiry, I divide established the foundations of their re- my work into four books. ligion and their power, from the banks In the fir!t, I investigate the state of the Euphrates to the western ex- of Mauritania, in those early ages of tremities of the earth. This nation, history which, by reason of the obconfounded with the people they had scurity of the times, and the propensifubdued, made an irruption into Spain, ty of rude nations to allegorical trawhich, at that time, groaned under the dition, have received the appellation tyranny of the Goths ; from whence, of Fabulous. The concern which the


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