HYDROGRAPHY.

One article only is contained in this Clafs, in which M. Pingré gives an account of fome nautical and aftronomical obfervations made during a voyage to and from the West Indies, in the Ifis, one of the King's frigates, exprefsly fitted out in order to make a trial of the methods propofed for the discovery of the longitude at fea; and more particularly to examine the going of two inarine clocks made by M. Berthoud +, which on trial were never found to have erred above two minutes of time in the space of fix weeks.

MECHANICS.

This Clafs likewife contains only one Memoir, in which that celebrated Mechanician, M. de Vaucanfon, describes and illuftrates, in feveral plates, the improvements which he has made in the Machine conftructed by him for the ufe of the Royal Silk Manufactory at Aubenas.

The Hiftories of the Arts published this year are, I. That of the Organ Builder, 2d and 3d parts, by Dom. Bedos de Celles, a Benedictine. II. That of the Joiner, part 2d. by the Sieur Ronbo. III. The art of making Indigo, by M. de BeauvaisRafeau. And IV. That of the Embroiderer.

Among the inventions prefented to and approved of by the Academy, we particularly obferve a propofed improvement of Reaumur's Spirit Thermometer, by the Abbé Soumille. On account of its inconvenient and unavoidable bulk, and in order 'that the degrees on its fcale may be enlarged, he has divided it into four smaller diftinct Thermometers; the first of which has its highest degree marked at the freezing point, and the scale continued 20 degrees below that point. The scale of the fecond Thermometer commences below, where the former terminates above; beginning at the freezing point, and proceeding to 20 degrees above it. The third and fourth are constructed on fimilar principles; fo that the laft carries the scale up to 60°. At the top of each tube there is a refervoir to receive the spirit, whenever it is exposed to a heat greater than that to which its fcale extends. By this ingenious contrivance, fays the Hiftorian of the Academy, the inftrument is rendered more portable, and the intervals on the fcale greatly enlarged.

Without meaning to detract from the undoubted merit of M. Reaumur, in having been one of the firft who constructed a comparable Thermometer; the account of this ingenious device, we think, exhibits a pleasant inftance of national partiality in favour of an inconvenient and defective inftrument. To correct one of its many imperfections, an apparatus is to be conftructed, confifting of a quadripartite affemblage of tubes and

+ See the enfuing Article.

balls;

balls; all the purposes of which are, and have long been, effectually answered by a fingle mercurial Thermometer, equally portable, with a fufficient range and extent of intervals, and much more fenfible and accurate.

The remaining contents of the prefent volume are-a Memoir presented by the Academy at Montpelier, on the heat of wine in the first stage of fermentation; and the Eloges of the Abbé Nollet, M. Rouelle, and the Earl of Morton. B.

ART. VIII.

Traité des Horloges marines, &c.-A Treatife of marine Clocks; containing the Theory, the Conftruction, and the Execution of thefe Machines; with the Method of trying them, in order (by means of fuch Clocks) to rectify the Charts, and determine the Longitude at Sea. With Copper Plates. By M. Ferdinand Berthoud, Clock-Maker to the King, &c. and Fellow of the Royal Society of London. 4to. 590 Pages. Paris. 1773.

M

R. B. begins his introduction to this work, with explaining the nature of that famous problem which has employed both the fcholars and the artifans of feveral ages, viz. to find the longitude at fea. He obferves, that all the methods of folving it may be reduced to two; either by aftronomical obfervations, or by machines capable of measuring time at fea. It is this laft method only that the Author confiders; being by far the most fimple, and what is within the reach of every feaman both to comprehend and practile.

Mr. B. recounts the feveral attempts made in France, and fays, that himself is the first after Sully (in 1726) that has attempted it again †. Being employed by the Public, Mr. B. thought it his duty to publifh, without referve, all his difcoveries. He has, accordingly, in this work, not only explained the construction of his marine clocks, and given drawings of them, but also fet down the dimenfions of every part, the experiments he made, and the reafoning that led him to every determination in a work of twenty years labour and application. Eleven different clocks for measuring time at sea are here describ

The

Mr. B. takes notice that one fingle aftronomical observation is necessary in every method, namely the finding the altitude of the fun, or a ftar, by Hadley's octant, in order to get the ship's time ufe of that inftrument in taking altitudes at fea, being neceffary for finding the latitude, is now become familiar to every feaman.

Mr. Henry Sully, an English watchmaker, fettled at Versailles in 1718, where he established a manufactory of watches, under the patronage of the regent Duc de Orleans. After two years he returned to England, but foon after went back and established another manufactory at St. Germains. In 1726 he published an account of a longitude clock he had invented, and from which he expected great things; but foon found himself disappointed. He died in 1728.

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ed,

ed, which may be ranged into three claffes. 1. Those in which no attention was paid either to their bulk or expence. 2. Those in which Mr. B. endeavoured to reduce the bulk, fo as to make them lefs cumbersome in the ship 3. Those in which he has endeavoured to reduce the bulk and also the expence So far Mr. B. in his Introduction.

The work itself is divided into four parts. 1. The theory ohich thefe marine clocks are conftructed. 2. The conftruction of each particular clock. 3. The execution of these machines, with an account of the more confiderable and uncommon tools. 4. The method of examining these marine clocks, and correcting their defects. The appendix contains certificates and authentic documents relative to the trial of fuch of them as have been fent to fea. To this is added a short fupplement; being fome matters omitted in the courfe of the work. Each of these parts is divided into chapters. The heads of those in the first part (on the Theory) are, 1. The degree of accuracy required in a marine clock, and the difficulties to be overcome to make clocks useful at fea. 2. Preliminary rules in conftructing marine clocks, ferving as a theory of their conftruction. 3. Of friction, and the effects of oil. 4. Of the regulating power of marine clocks. 5. Of the escapement. 6. Of the wheel-work. 7. Of the first mover. 8. Of the fufpenfion of the clock. Mr. B. is very fhort upon the three firft of thefe, but is diffufive on the next, which he subdivides into three articles. 1. Of the balance. 2. Of the ifochronism of the vibrations by the fpiral fpring. 3. Of the machinery for compenfating the effects of heat and cold.

There runs through the whole of what Mr. B. calls theory, a great want of clear and precife ideas, and an utter ignorance of juft and logical reafoning. Loofe difcourfes, tricked out with the parade of mathematical terms and algebraic fymbols, are put off for real demonftrations. Mr. B. is continually laying down proportions between quantities not capable of mathematical comparison; fuch as have not in themselves a natural measure of their own magnitude, and for which no artificial one is established a very common cafe with those who having a fmattering of mathematics, will pretend to reafon on phyfical fubjects. It is a well-known theorem, that if a body be acted upon by a force which is as the diftance of that body from a given center, its time of defcent (to that center) will

Of this fort is the rule for determining the mathematical proportion of the goodness or advantage of one regulator to another. We may as well go about to determine the mathematical proportion of the goodness or virtue of one man to another; or the ratio of the whitenefs of two pieces of paper.

be

be the fame from whatever point the body falls. From this it follows, that if a balance be made to vibrate by means of a fpring whofe force is as its compreffion or expanfion, all vibrations of that balance will be performed in the fame time. Let the Reader compare the proof of this phyfical propofition in Newton, Cates, or MacLaurin, with article 141, and he will be convinced how far this article is from being a real demonftration. We fhall, however, take notice of the principal propofitions in this theory, without inquiring whether they be strictly demonftrated à priori or not.

Mr. B. lays it down as a rule, and mentions it often, that a time-piece will be the more perfect the longer its regulator (whether pendulum or balance) will continue to vibrate when difcharged from the wheel-work; and fpeaks of a pendulum which defcribed an arch of 10 degrees, fo nicely hung upon an edge like a knife, that it kept its motion two days.-No doubt the long continuance of this motion, is a mark that the friction was very small; but we are not to expect, that clock will always go the trueft, whose pendulum is fo fufpended as to preferve its motion longeft when left to itself. The fufpenfion upon two points only, is more delicate than that upon an edge. How very fufceptible of every the leaft impreffion fuch a pendulum is, appears by the experiments of the late Mr. Ellicott (related in the Philofophical Tranfactions) which were made on two pendulums fo fufpended; notwithstanding which, Mr. Ellicott himself, and all experienced clock-makers, have ever preferred the fufpenfion on a spring.

Another rule Mr. B. lays down is, that the greater number of vibrations a balance makes in a given time, the less it is fufceptible of any disturbance.-The disturbance Mr. B. bas particularly in view, is what arifes from giving the whole machine a circular motion round the axis of the balance. Now the effect of this circular motion of the whole machine, whether concurring with, or oppofing that of the balance, manifefty depends on the relative proportion of the circular velocity of the whole machine to the circular velocity of the balance. If the former be very small, its addition to or diminution from the latter, will make the variation of the whole quantity of the latter but little. The effect of this difturbing force, will therefore depend on the velocity of the balance. Now the velocity of the balance does by no means depend wholly on the number of vibrations made in a given time, but on the arch described in each vibration, and (if the abfolute velocity be meant) on the diameter of the balance. Mr. Harrison estimates this matter rightly, when he accounts it a great advantage his timekeeper had over common watches, that, in a common watch,

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the

the balance goes through but about fix inches in a second, but in his time-keeper it goes through 24 inches §.

Another maxim laid down is, that when a long and tender fpiral fpring is applied to a balance, its greater vibrations take up more time than the leffer ones; the contrary when a fhort fpring is used. Mr. B. concludes, that there is a particular length of spring that will render all vibrations ifochronous. This is an important point, but the attempt to demonstrate it in the paragraph numbered 142 is abfurd enough. It is indeed no other than the fuppofition of a particular case from which a general conclufion is to be drawn. And it is a fuppofition only; for the cafe can never really exift, if the force of the fpring be accurately as its compreffion or expanfion. If there be any fuch difference between a long fpring and a fhort one, it must be owing to the elaftic force not following the law before mentioned; but its variation from that law must be determined by experiment, not by argument .

§ Principles of Mr. Harrifon's time-keeper, page 21.

Mr.

To make all the vibrations of the balance ifochronous Mr. Harrifon ufed, in his last time piece, an invention very ingenious and perfectly original. Between the ftud (le piton) to which the outer end of the balance fpring was faftened, and the notch through which the fpring paffed (le pince spiral) was about an inch. Every time the balance in vibrating winds up the fpiral fpring, the fpring will prefs against the inner face of the notch. The notch being fixed (as a fulcrum) the part of the fpring between the notch and the ftud will bow outwards, and will retire again inwards when the spring unwinds. Over against the middle of the bow on the concave fide was placed a pin, on which the spring refted fome little time, when it retired inwards in the alternate vibrations. While the fpring continues to prefs upon the pin, it has its force increased. According to Mr. H. the fpring leaving the pin for a longer time in the larger vibrations than the fmaller ones, has its force lefs increased, and of courfe the return of the balance is lefs accelerated in the former cafe than in the latter. The pin could be fet farther from or clofer to the fpring, to augment its effect more or less. This is what Mr. H. calls his artificial cycloid, from the share it has in making the vibrations ifochronous.

It should be obferved here, that Mr. H.'s method of compensation or thermometer, and his cycloid, do not permit the pince-jpiral to lay hold of a different part of the fpring, fufficiently diftant, to alter the rate of the going of the watch. Such a change would require both thermometer and cycloid to be re-adjufted. Mr. H.'s timekeeper cannot be adjusted to keep mean time. This was once intended, but laid afide (fee plate X. fig. 15, of Mr. H.'s Principles, &c.) Nor is this material: if the inflrument keeps its rate of going according to any fixed and known rule, it is fufficient for the purpote

of