ed, which may be ranged into three claffes.

1. Thofe in which no attention was paid either to their bulk or expence. 2. Thofe in which Mr. B. endeavoured to reduce the bulk, fo as to make them lefs cumbersome in the fhip. 3. Thofe in which he has endeavoured to reduce the buik and alfo the expence-So far Mr. B. in his Introduction.

The work itself is divided into four parts. I. The theory on which these 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 thofe 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 fubdivides into three articles. 1. Of the balance. 2. Of the ifochronifm 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 comparifon; fuch as have not in themfelves 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 distance 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 whiteness of two pie es 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, Cotes, 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 fmall; but we are not to expect, that clock will always go the trueft, whofe 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 least impression such 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 suspension on a spring.

Another rule Mr. B. lays down is, that the greater number of vibrations a balance makes in a given time, the lefs it is fufceptible of any disturbance.-The disturbance Mr. B. has 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 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 fmall, 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,

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 short fpring is used. Mr. B. concludes, that there is a particular length of fpring that will render all vibrations ifochronous. This is an important point, but the attempt to demonftrate it in the paragraph numbered 142 is abfurd enough. It is indeed no other than the fuppofition of a particular cafe from which a general conclufion is to be drawn. And it is a fuppofition only; for the cafe can never really exist, 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 short 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. Harrison's time-keeper, page 21.

Mr.

To make all the vibrations of the balance ifochronous Mr. Harrifon ufed, in his laft 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 fpring retted 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. Accord ing to Mr. H. the fpring leaving the pin for a longer time in the Jarger 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 spring, to augment its effect more or less. This is what Mr. H. calls his artificial cycloid, from the fhare it has in making the vibrations ifochronous.

It should be obferved here, that Mr. H.'s method of compenfation or thermometer, and his cycloid, do not permit the pince-fpiral 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-adjufled. Mr. H.'s timekeeper cannot be adjufted 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 inftrument keeps its rate of going according to any fixed and known rule, it is fufficient for the purpole

of

Mr. B. directs the balance fpring to be made of the fineft caft fteel, and to be left of a much higher temper than the main fpring; as high as may be, fo that it can but be coiled up. The balance fpring not being fo violently compreffed as the main fpring, 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 thefe fprings; which is by coiling them by degrees first wider and then closer, and warming the fprings at each operation. This process is defcribed very circumftantially in the third book.

Mr. B. afterwards gives a variety of curious and interesting experiments relating to the force of fpiral fprings. In one of thefe, No. 206, a fpiral fpring being coiled up wide, fo as to make 3 turns, and 15 lines in diameter, had its force when compreffed, greater than in the ratio of its compreffion. The fame fpring coiled up clofer, fo as to make 5 turns and 8 lines in diameter, had a force very nearly as its compreffion in all moderate degrees of compreffion, but in one extreme degree its force was less than in the ratio of the compreffion. We fay when compreffed, but we gather this only from the drawing of the machine by which the force of this fpring was tried. It is a great defect that in giving an account of fuch a number of experiments on fpiral fprings, it should not be specified in each cafe, whether the force to be measured arofe from the compreffion or expansion of the spring, and that Mr. B. should neglect to try whether if the fame fpiral fpring be equally compreffed or expanded, the elaftic force will alfo 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 fays, No. 224, that the fprings were not always tempered by being heated and then quenched, but had force only as far as drawing or hammering could give them elasticity +.

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

The French exprefs this whole procefs of tempering by one circumftance, the dipping. Tremper is to dip, and also to temper. + It would be ufeful alfo to make experiments not only to find the force of springs when compreffed 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 occafioning them to lose a part of their elafticity, fo as when bent not to return perfectly to their first form but continue bent. In this cafe the spring is faid to fet, in French fe rendre. It would be proper alfo to try the effect of keeping a fpiral spring a long time, in a ftate of moderate compreffion or expansion.

Under

Under the article of making compenfation for the effects of heat and cold, Mr. B. confiders two effects; the alteration in the fize of the balance, and the alteration both of the length and the ftrength of the fpring, that is the alteration both of the law and the degree of its force; the former of which he fuppofes to vary with the length of the fpring, as was faid before. For the particulars of this machinery, Mr. B. refers us the defcription of his marine clocks in the next part. The whole of it confifts in applying, in various ways, the well known combination of brafs and steel rods in the form of a grid-iron*. We shall only add that in inquiring what are the most proper materials of which to make the balance, Mr. B. reckons gold the beft, only too expenfive, the balances of his machines being very large. He rejects steel as being fubject to ruft, and to become magnetical, even by the procefs of forming it into a balance; and fixes upon brass.

In the chapter of efcapements, Mr. B. utterly rejects all those palets where the force of the clock is opposed to the motion of the pendulum in any part of the vibration; that is all thofe palets where the efcapement wheel has a recoil, or retrograde motion +. After the wheel has given an impulfe to the pendulum, he would then have the pendulum left to itself, and not checked in its motion. There are those who think it an advantage to have the motion of the pendulum checked and controuled by the palets. They think it gages the arch of vibration, and keeps the pendulum from flying out; that a force oppofing the pendulum near the end of its afcent, and aiding it in the beginning of its defcent, co-operates with the force of gravity, and tends to make the vibrations ifochronous. the force of gravity on a pendulum vibrating in a circular arch,

For

*Mr. B. is difpleafed with M. Le Roy for faying that Mr. B. made ufe of the gridiron of Mr. Harrison. Mr. B. in reply fays, the gridiron was not employed in the marine watch of Mr. Harrison, and that he invented his method of compenfation 20 years ago, before he knew the name of Harrison, and that his frame of compenfation differed from Harrifon's. See Reponse au Precis de M. Le Roy, p. 38. We shall obferve on this controverfy, that the only difference between Mr. Harrifon's gridiron and Mr. B.'s frame of compenfation is, that in the former the bars or rods were round, in the latter. fquare: and though Mr. Harrison did not ufe this frame of compenfation in his last-made time-keeper, yet he employed it in every one of his first great machines. Mr. Harrifon's gridiron (as it was called) was publicly shown by him in 1736, and, fome time after, imitated by an itinerant teacher of experimental philofophy, who exhibited it in his public course of lectures.

+ The balance wheel is that which immediately acts upon the balance. The wing wheel is that which acts upon the pendulum. We want a word for the general idea including both. The French term is La roue de rencontre, or La roue d'échappement.