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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 clofer, 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 interefting experiments relating to the force of spiral fprings. In one of thefe, No. 206, a fpiral fpring being coiled up wide, so 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 lefs 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 springs, it should not be specified in each cafe, whether the force to be measured arofe from the compreffion or expanfion of the fpring, and that Mr. B. fhould neglect to try whether if the fame fpiral spring be equally compreffed or expanded, the elastic force will alfo be equal or not. Nor does Mr. B. always inform his reader before-hand, whether the fpring 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 cir. cumftance, the dipping. Tremper is to dip, and alfo to temper. + It would be useful also 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 fpring is faid to fet, in French fe rendre. It would be proper also to try the effect of keeping a fpiral fpring 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 strength of the fpring, that is the alteration both of the law and the degree of its force; the former of which he fuppoles to vary with the length of the fpring, as was faid before. For the particulars of this machinery, Mr. B. refers us to 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 fteel rods in the form of a grid-iron*.. We fhall only add that in inquiring what are the most proper materials of which to make the balance, Mr. B. reckons gold the best, only too expenfive, the balances of his machines being very large. He rejects fteel 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 thofe palets where the force of the clock is opposed to the motion of the pendulum in any part of the vibration; that is all those palets where the escapement wheel has a recoil, or retrograde motion t. After the wheel has given an impulse to the pendulum, he would then have the pendulum left to itself, and not checked in its motion. There are thofe 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. For the force of gravity on a pendulum vibrating in a circular arch,

* Mr. B. is difpleased with M. Le Roy for faying that Mr. B. made ufe of the gridiron of Mr. Harrifon. Mr. B. in reply fays, the gridiron was not employed in the marine watch of Mr. Harrifon, 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 Harrison'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. Harrifon did not use this frame of compenfation in his latt-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 fhown 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.

is too little towards the end of the arch, and requires an addition to give it that force which produces ifochronous vibrations. We will not affirm thefe are Mr. Harrison's fentiments in the case of pendulums, but from fome expreflions in the very concise account of his principles, we are inclined to think fo. The cafe of balances moved by a spiral spring is very dif. ferent 1.

Mr. B. recounts fome particular efcapements. He mentions first the dead escapement of Mr. Graham, (L'échappement à repos) which has the effential condition he requires of leaving the pendulum at liberty at the end of the vibration; but he dislikes it on account of fiction, and for other reafons.

The next efcapement is that of Mr. Cumming §; which Mr. B. fays, in fpight of the feeming advantages, had fufficient friction and difficulties in the execution, to deter him from making use of it.

Mr. B then mentions Mr. Harrison's efcapement, made ufe of in his three firft machines, and by which, as Mr. B. fays, the whole force of the escapement wheel is communicated to

one.

The efcapement of Mr. H.'s laft time-piece is a very unusual The crown wheel and its teeth are of the common form, only the ftraight fide of the tooth is quite upright. As foon as one tooth has efcaped, the upright face of the oppofite tooth meets the edge of the other palet. The balance at that time has paffed its point of reft, and is going on to the extremity of its vibration. The edge of the palet therefore goes up the face of the tooth till it arrives at the point of the tooth. The point of the tooth then goes round the edge of the palet, and acts against the back of the palet (which is circular or bump-backed) to the end of the vibration. While the tooth thus acts against the back of the palet (which it does near the extremity of each vibration) the force of the crown wheel affifts the balance in going forwards, and retards its return. The force of the wheel in most other escapements has either a contrary effect at the extremity of the vibrations, or none at all. In other parts of the vibration, the force of the wheel on the balance is nearly the fame as in the very common crown wheel escapement.

§ Cumming's Elements of Clock and Watch-work, page 75. Mr. B. does not tell us that Mr. Cumming had publifhed a defcription and drawing of thefe palets, nor does he tell us that the former efcapement was Mr. Graham's, nor the next Mr. Harrison's; for the laft escapement he mentions (that of free vibrations) he does indeed fay Mr. Mudge fhowed him one of that fort in 1766 that had been made a long time. An escapement of this kind was alfo in the hands of the late Mr. Ellicott about the year 1746.-It is poffible that ingenious men may hit on the fame invention. We have here four inventions, every one of which has been made by Englishmen, and published to the world long ago.

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the regulator: but he rejects this escapement as having a recoil, alfo being complicated and difficult to execute.

The last efcapement he mentions, and which he prefers to all others, is that in which the pendulum receives a push, or rather a blow in the middle of its vibration, and is then left to itfelf for the remaining part of that vibration, and alfo for the fubfequent returning vibration, so that this impulse is given only every other vibration. Between one impulfe and the next, the escapement wheel is locked up by a detent, and is unlocked by the pendulum juft before the next impulfe. The pendulum being thus at liberty to fwing out at the end of each vibration, he calls in the efcapement of free vibrations. Notwithftanding a long encomium upon this, Mr. B. fays he is so little fatisfied with the trial of all these inventions, that he is now employed in improving the common dead escapement by means of ruby palets, and a wheel of steel made perfectly hard; but laments greatly the indispensable neceffity of ufing oil in fuch a conftruction t.

There is nothing in the chapter on the wheel-work but what is common; our author recommends high numbers, and direas stopping the pivot holes with pot brafs.

The 7th chapter is on the first mover of the clock. Mr. B. makes a comparison between the advantages of using a weight or a spring; and is against using a spring even for marine time

This will or will not be, according as the feveral centers of mo tion are placed. Upon the placing of thefe centers it likewife depends, whether the force of the efcapement wheel on the regulator fhall be uniform, increafing or decreafing during the time of the action of the wheel on the palets.

• The manner of doing this is circumftantially described part ii. chapter xii.

Mr. H. in his three firft machines, endeavoured to avoid the neceffity of ufing oil, by leffening as much as poffible the relative motion of thofe parts which touched each other. In the action of the balance wheel on the palets the relative motion of the tooth and palet was wholly taken away, and the palet was made of wood. In his laft time-keeper (fent to the West Indies) the ufe of oil was abfolutely neceffary, but no peculiar provifion made against its effects. Indeed all the contrivances to procure ifochronous vibrations, even though the force fhould vary, may be confidered as one remedy; and the making the balance-wheel of steel and hard, and the palets of diamond as another. It was remarkable that though this timepiece had been in conftant going for a long while, and the nature of the efcapement fuch as occafioned a great relative motion of the tooth and palet, yet there was not in 1765 the least trace or mark of the palet having worn the tooth,-it was not to be expected the tooth fhould make any impreffion on the palet.

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pieces. His objections are, that a spring is liable to break, that it changes its force by heat and cold, that it is apt to fet, and that the coils fhould always be kept oiled.-Experience fhows we need not fear the first of these objections. The others are all obviated by applying a very tender fpring to the escapement wheel, to give to that wheel its force. When this fpring has unrolled itself a little way, it is then to be wound up by the force of the main-fpring. This little fpring in Mr. Harrison's time piece is wound up eight times in a minute ‡.`

Our Author, has at the end of this chapter, a fhort article on the proportion the moving force of the clock ought to have to that of the regulator. We did expect he would have confidered this at the beginning of his theory. What he fays in this place is loofe and confufed; he here, and in many other places, ufes the words force and motion as fynonimous terms, and standing for precifely the fame idea.

The laft chapter in this part, is on the fufpenfion of marine clocks, that is, the manner of fupporting or carrying them at fea. He lays down two principles, one that the clock fhould be fo fufpended, as to keep its pofition always horizontal, without partaking of the motion of the ship, the other that the suf penfion fhould have (with this freedom in yielding to the motion of the fhip) great firmness and folidity.-Such a folidity that the balance may not fet in motion the cafe by which the time-keeper is defended from the external air. Our Author recommends Cardan's method of fufpenfion §; he would have the clock kept in a fort of closet to defend it from the sea-air, and placed as near as conveniently may be to the center of gravity of the fhip. He alfo ufes fpiral fprings to break the force of fudden fhocks.

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The machinery for doing this is called a Remontoir; sometimes the machinery for keeping a clock in going while it is wound up, is also called (but improperly) a remontoir.

§ Cardan's method of fufpenfion is that of the fea-compafs, called by feamen Gimbols; it is the fame with the mechanism of the rolling lamp in Defagulier's Lectures, page 57.-This contrivance feems to be the parent of the univerfal joint; one of the moft ufeful inventions in mechanics. The univerfal joint is largely treated of by Hocke in one of his lectures at Gresham College, who reprefents it as his own invention, but, nevertheless, mistakes a little in giving an account of its very fingular properties. Hooke's lecture is printed in 1678, but the first account of it is in Schottus's Technica Curiofa, p. 664, printed in 1664. Schottus feems to have picked it up in Germany; which, abounding in metals, has ever been the nursery of the mechanic arts, especially while the Hans towns retained their independency.

Mr. Harriton in his three great machines used spiral springs to break the fhocks, but applied in a manner very different from that

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