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

The remaining contents of the present volume are- 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.

ART. VIII. Traité des Horloges marines, &c.—A Treatise of marine Clocks ;

containing the Theory, the Construction, and the Execution of these Machines ; with the Method of trying them, in order (by, means of such Clocks) to rectify the Charts, and determine the Longitude at Sea. With Copper Plates. By M. Ferdinand Ber. thoud, Clock-Maker to the King, &c. and Fellow of the Royal Society of London. 4to. 590 Pages. Paris. 1773.

R. B. begins his introduction to this work, with explain

ing the nature of that famous problem which has employed both the scholars and the artisans of several ages, viz. to find the longitude at sea. He observes, that all the methods of solving it may be reduced to two; either by astronomical observations, or by machines capable of measuring time at sea. It is this last method only that the Author considers; being by far the most simple, and what is within the reach of every seaman both to comprehend and practise *.

Mr. B. recounts the several attempts made in France, and says, that himself is the first after Sully (in 1726) that has attempted it again t. Being employed by the Public, Mr. B. thought it his duty to publish, without reserve, all his discoveries. He has, accordingly, in this work, not only explained the construction of his marine clocks, and given drawings of them, but also set down the dimensions of every part, the experiments he made, and the reasoning 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

Mr. B. takes notice that one single astronomical 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 fhip's time. The use of that instrument in taking altitudes at sea, being necessary for finding the latitude, is now become familiar to every leaman.

† Mr. Henry Sully, an Englith watchmaker, settled at Versailles in 1718, where he eitablished a manufactory of watches, under the patronage of the regent Duc de Orleans. After two years he returned to England, but soon after went back and established another manufactory at St. Germains. In 1726 he published an account of a longi. tude 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, which may be ranged into three classes. 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, so as to make them less cumbersome in the ship. 3. Those in which he has endeavoured to reduce the buik and also the expence -So far Mr. B. in his Introduction.

The work itself is divided into four parts. 1. The theory on which these marine clocks are constructed. 2. The construction 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 defeats. The appendix contains certificates and authentic documents relative to the trial of such of them as have been sent to fea. To this is added a short fupplement; being some matiers omitted in the course of the work. Each of thele pares is divided into chapters. The beads 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 sea. 2. Preliminary rules in constructing marine clocks, serving as a theory of their construction. 3. Of fri&tion, and the effects of oil. 4. Of the regulating power of marine clocks. 5. Of the escapement , 6. Of the wheel-werk. 7. Of the first mover. 8. Of the fufpenfion of the clock. Mr. B. is very Mort upon the three first of these, but is diffufive on the next, which he subdivides into three articles. 1. Of the balance.

2. Of the isochronism of the vibrations by the spiral spring. 3. Of the machinery for compensating the effects of heat and cold.

There runs through the whole of what Mr. B. calls theory, a great want of clear and precise ideas, and an ulter ignorance of juft and logical reasoning. Loole discourses, tricked out with the parade of mathematical terms and algebraic symbols, are put off for real deironftrations. Mr. B. is continually laying down proportions between quantities not capable of mathematical comparison ; such as have not in themselves a natural measure of their own magnitude, and for which no artificial one is established: a very common case with those who having a smattering of mathematics, will pretend to reason on phyfical subjects I. It is a well-known theorem, that if a body be acted upon by a force which is as the distance of that body from a given center, its time of descent (to that center) will

Of this fort is the rule for determining the mathematical proportion of the g'odness 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 whiteness of two pie es of paper,


be the same from whatever point the body falls. From this it follows, that if a balance be made to vibrate by means of a spring whose force is as its compression or expansion, all vibrations of that balance will be performed in the same time. Let the Reader compare the proof of this physical proposition in Newton, Cutes, or MacLaurin, with article 141, and he will be convinced how far this article is from being a real demonstration.-We shall, however, take notice of the principal propofitions in this theory, without inquiring whether they be strictly. demonstrated 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 discharged from the wheel-work; and speaks of a pendulum which described an arch of 10 degrees, so 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 truest, whose pendulum is so suspended as to preserve its motion longest when left to itself. The suspension upon two points only, is more delicate than that upon an edge. How very susceptible of every the least imprellion such a pendulum is, appears by the experiments of the late Mr. Ellicott (related in the Philosophical Transactions) which were made on two pendulums so suspended ; notwithstanding which, Mr. Ellicote himself, and all experienced clock-makers, haye ever preferred the suspension on a spring.

Another rule Mr. B. lays down is, that the greater number of vibracions a balance makes in a given time, the less it is sufceptible of any disturbance. The disturbance Mr. B. has particularly in view, is what arises 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 opposing 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 Jatter but little. The effect of this disturbing 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 cach vibration, and if the absolute 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,

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

Another maxim laid down is, that when a long and render spiral spring is applied to a balance, its greater vibrations take up more time than the lesser ones; the contrary when a short spring is used. Mr. B. concludes, that there is a particular length of spring that will render all vibrations isochronous. This is an important point, but the attempt to demonftrate it in the paragraph numbered 142 is absurd enough. It is indeed no other than the fuppofition of a particular case from which a general conclusion is to be drawn. And it is a supposition only; for the case can never really exist, if the force of the spring be accurately as its compression or expansion. If there be any such difference between a long spring and a short one, it must be owing to the elastic force not following the law before mentioned ; but its ariation from that law must be determined by experiment, not by argument


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

ll To make all the vibrations of the balance isochronous Mr. Hare rison used, in his last time piece, an invention very ingenious and perfectly original. Between the stud (le piton) to which the outer end of the balance spring was fastened, and the notch through which the spring passed (le pince spiral) was about an inch. Every time the balance in vibrating winds up the spiral spring; the spring will press against the inner face of the notch. The notch being fixed (as a fülcrum) the part of the spring between the notch and the stod 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 retted some little time, when it retired inwards in the alternate vibrations. While the spring continues to press upon the pin, it has its force increased. Accord ing to Mr. H. the spring leaving the pin for a longer time in the Jarger vibrations than the smaller ones, has its force less increased, and of course the return of the balance is less accelerated in the former case than in the latter. The pin could be set farther from or closer to the spring, 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 is chronous.

It should be observed here, that Mr. H.'s method of compensation or thermometer, and his cycloid, do not permit the pince-spiral to lay hold of a different part of the spring, sufficiently diitant, to alter the rate of the going of the watch. Such a change would require both thermometer and cycloid to be re-adjufled. Mr. H.'s timekeeper cannot be adjusted to keep mean time. This was once intended, but laid aside (see plate X. fig. 15, of Mr. H.'s Principles, &c.) Nor is this material : if the inftrument keeps its rate of going according to any fixed and known rule, it is sufficient for the purpole Mr. B. directs the balance spring to be made of the finest cast steel, and to be left of a much higher tcmper than the main spring; as high as may be, so that it can but be coiled up. The balance spring not being so violently compressed as the main spring, may be left much higher without danger of breaking in doing its office. Our Author then lays down the grounds on which he builds his method of coiling up these springs; which is by coiling them by degrees first wider and then closer, and warming the springs at each operation. This process is described very circumstantially in the third book.

Mr. B. afterwards gives a variety of curious and interesting experiments relating to the force of spiral springs. In one of these, No. 206, a spiral spring being coiled up wide, so as to make 3 turns, and 15 lines in diameter, had its force when compresied, greater than in the ratio of its compression. The same spring coiled up closer, so as to make 5 turns and 8 lines in diameter, had a force very nearly as its compression in all moderate degrees of compreslion, but in one extreme degree its force was less than in the ratio of the compression. We say when compressed, but we gather this only from the drawing of the machine by which the force of this spring was tried. It is a great defect that in giving an account of such a number of experiments on spiral springs, it should not be specified in each case, whether the force to be measured arose from the compression or expansion of the spring, and that Mr. B. should neglect to try whether if the same spiral spring be equally compressed or expanded, the elastic force will also be equal or not. Nor does Mr. B. always inform his reader before-hand, whether the spring on which an experiment is to be tried, be tempered or not. We are left to collect from what he afterwards says, No. 224, that the springs were not always tempered by being heated and then quenched *, but had force only as far as drawing or hammering could give them elasticity t.

of finding the longitude, whatever that rate be; nay it is not neces. sary the rate should be uniform. The rate of going may be in any manner accelerated or retarded, provided that manner be known.

* The French express this whole process of tempering by one circumstance, the dipping. Tremper is to dip, and also to temper.

+ It would be useful also to make experiments not only to find the force of springs when compressed or expanded; but also to find out the effect of moderate degrees of heat and cold, not only in altering their force proportionably, but in occasioning them to lose a part of their elasticity, so as when bent not to return perfectly to their first form but continue bent. lo this case the spring is said to Set, in French se rendre. It would be proper also to try the effect of keeping a spiral spring a long time, in a state of moderate compression or expansion,


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