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ftrument that Mr. Le Cerf has invented will answer this purpose or not, rests folely on the bare affertion of the inventor. He does not pretend that even the proportion, on which its construction depends, is the result of a mathematical inveftigation, but that it is only derived from experiments; by means of which he has found, that if the diameter of any wheel be made in such proportion to that of the pinion it is to work with, as the number of tecth in the wheel is to the number of leaves in the pinion, that wheel will be too large; and its diameter must afterwards be reduced : and the quantity of that reduction he finds by a rule which is in lubítance as follows. Subtract unity from the number of revolutions which the pi. nion makes in one revolution of the wheel, and multiply the remainder by the quotient arising from dividing the diameter of the pinion by the number of leaves which are in it: the product will express the quantity by which the diameter of the wheel is to be leffened, expressed in such measures as the diameter of the pinion was taken in. Or this rule may be expressed by the following analogy: As the number of leaves in the pinion is to the excess of the number of revolutions which the pinion makes, above that which is made by the wheel, so is the diameter of the pinion to the reduction of the diameter of the wheel. Thus if the diameter of the pinion be to, its leaves 12, and the teeth of the wheel g6; then the diameter of the wheel, according to Mr. Derham, will be t'o X 96 12=; and, according to Mr. Le Cerf, 12 is to-(=7) as 15 : 7 Xit + 12 = tici consequently 0 -116= will be the true diameter of a wheel of 96 teeth, which is proper to work with a pinion of 12 leaves, and one-tenth of an inch diameter.

That this mode of reduction may be sufficiently near the truth for mechanical purposes, may possibly be a fact : but that it is ftrictly true, notwithstanding Mr. Le Cerf’s assertions, may admit of a doubt. For aught that appears to the contrary, several other laws of reduction may be afligned that will answer equally well,-perhaps better. On the whole, it seems that the rule having occurred to Mr. Le Cerf, its fimplicity and uniformity pleased him, and the work, formed by it, happening to work freely, convinced him that it was true : but this is no abfolute proof that it is so. Mr. Le Cerf's measures may have been taken rather inaccurately; or, poflibly, some of his pinions might have worked still better, on a farther, or a less reduction. We do not mean, by what we have said, to depreciate Mr. Le Cerf's invention : his pursuits are truly laudable and useful, the thought ingenious, and may be true ;-we only wish to convince him that he is pofitive without proof.

The form and construction of Mr. Le Cerf's compafles cannot be gathered with certainty from the paper before us, as his

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description of them is very concise, although his paper, in other respects, is diffufive; and, which is a much greater defect, there is no drawing of them annexed to it: therefore, although his matter might appear very clear to the learned Society to whom it is addressed, when the instrument was before them, yet we apprehend that few workmen will be able to gather much information, even from the original French. As to the English tranflation-we give it up entirely—those may read it who can. But is it not a most extraordinary circumstance that so learned a body of men as the Council of the Royal Society may be supposed to consist of (for the Society at Jarge we well know have no concern in it) should suffer such translations as this, and some other late ones, to appear in their publication !

Mr. Le Cerf, in the course of his paper, takes occafion to mention the form which the teeth ought to have, so that one wheel, moving uniformly, may drive another with an uniform velocity likewise. Nothing can be more obvious than thas when the sides of the teeth are planes, or nearly so, if the driving wheel has an uniform motion round its center, the motion of the wheel which is driven by it will be very unequal; moving with great velocity when any tooth first begins to act on it, and scarcely at all when the planes of the two teeb make a great angle with each other. The figures which the faces of the teeth of the driven wheel ought to have, in order that both wheels may move uniformly, is not difficult to investigate ; and, perhaps, not very difficult to work, sufficiently near the truth, were it an object of importance enough to merit it. This, however, Mr. Le Cerf has not attempted to do, but advises a method that has long been practised by the best English watchmakers, namely, putting the highest numbers in the wheels and pinions that the caliber of the watch will admit of. For it is evident, that by this means, any single tooth acts on its fellow for a less time; that is, while the wheels move through a less angular space, and of course does not act under such a varicty of angles as they must unavoidably do when the numbers in the wheels and pinions are lower. We may add, that the unequal action of the teeth, or even that of the main-spring, which is undoubtedly sometimes much greater, has but little effect on the going of a watch, the balance of which has sufficient momentum,-such as all the watches that are made by the best English artists now have : the figure of the teeth is therefore but of little consequence. In watches of Mr. Harrison's construction these inequalities cannot poflibly have any effect, because that part of the watch which measures time is moved by a small spring that acts on the contrate wheel; aad, consequently, whatever irregularities there may be in the

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forces which act on the other wheels, they can noway affect the going of the watch.

The Author adds an account of another instrument which he bas invented, and sent along with the Proportional Compasses to the Royal Society ; but the vague manner in which he speaks of it, joined to the want of a drawing, renders it impossible for us to form a just idea either of its construction or merits. He concludes his paper with tables of the dimensions of the several pinions generally used in clock and watch work, ac. cording to the principles which he has before laid down. CHE MIS TRY.

W. Article 39. Chemical Experiments and Observations on Lead Ore.

By Richard Watson, D. D. F. R. S. &c. In this paper, Dr. Watson first takes notice of the difference in the specific gravities of various lead ores, and even of different parts of the same lump of ore. Notwithstanding this circumstance, we are told that the purchasing of lead ore by the measure, is the general, though not the universal custom in Derbyshire. To find whether the fulphur with which lead is generally mineralised in the ore (particularly in the steelgrained and tesselated galenas) could be separated from it in close veffels, or by distillation, as is the case with respect to some kinds of the pyrites; he distilled 16 ounces of some teffelated Derbyshire lead ore in an earthen retort. Though he gave the retort a white heat, no sulphur was sublimed: but the ore loft a 32d part of its weight. The matters separated from the ore were—a small quantity of a black substance, that rofe up into the neck of the receiver ; and which appeared to be pure lead ore, sublimed without being decompounded :-a small portion of a liquid, that had a pungent smell, resembling that of the volatile vitriolic acid, and which had an acid taste; though it did not effervesce with alcalis, nor produce any change in the colour of blue paper :-and lastly, a quantity of air or elastic Auid ; which, at the beginning of the process, had the smell of inflammable air. In the following experiment, however, he not only separated the fulphur from the ore, but was enabled to ascertain its quantity.

Five ounces of the strongest fuming spirit of nitre, diluted with an equal quantity of water, were poured on ten ounces of lead ore.

A violent effervescence ensued; and when the folution was completed, there remained floating upon the surface of the menftruum, a cake of fine yellow sulphur, perfe&tly refembling common sulphur. This substance, edulcorated and dried, generally amounted to one-third of the weight of the ore.

This matter however is not pure sulphur, but is a mixture of that substance and a calx of lead: for on putting some of it on a red hot iron, a greyith calx remains, after the fulphur is

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consumed; which on being put on a piece of ignited charcoal, is reduced, at least in part; to a metallic state. The Author confidering the great quantity of fulphur contained in the Der. byshire lead ores, where about 10,000 tuns are smelted annually, proposes to the confideration of the lead smelters the practicability of collecting it; both as a lucrative business to themselves, and a great saving to this country, where, it seems, we at present import the fulphur we use. For this purpose, he suggests the poffibility of collecting it, in long, large, and winding horizontal chimneys, connected with the furnaces in which the ore is roasted : in the same manner as is practised in Saxony, where arsenic is procured by a similar contrivance; the ar fenical vapour being condensed, and attaching itself, like foot, to the sides of the chimney; from which the arsenic is, from time to time, swept out.

At the end of this paper, the Author relates some experiments from which it appears that, though the surface of pure melted lead becomes covered with a pellicle of various colours ; yet these appearances do not occur if a finall portion of tin be mixed with the lead, even when the weight of the tin scarce exceeds the fo'szth part of the weight of the lead. Zinc poffefses the same property, in this particular respect, as tin. After the tin has been reduced to a calx, by the continuance of the heat, the lead again acquires its property of forming colours ; which successively appear in the following order : yellow, purple, blue, yellow, purple, green, pink, green, pink, green. 'The rationale of these appearances may be deduced from the well-known experiments and theory of Sir Isaac Newton, lately illustrated and confirmed by Mr. Delaval, in his ingenious Experimental Enquiry respecting the changes of colours in bodies

MISCELLANEOUS ARTICLES. Article 26. An Account of the Island of St. Miguel, By Mr.

Francis Masson, This island is one of the principal of the Azores. The only particulars relating to it, that can entitle this account of it to a place in the Philosophical Transactions, are contained in a general description of some fountains, from which the water boils up fo hot, that a person cannot dip his finger into it without being scalded. A steam likewise rises, to a considerable height, from several apertures, which is so hot, that no one can approach it with the hand. In other places, says the Author, a person would think that a hundred smiths bellows were blowing altogether, and fulphureous steams issuing out [iffue out) in thousands of places, so that native sulphur is found in

* See an account of that work in the 57th volume of our Review, P. 221. Rey. Jan. 1778.

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cvery chink, and the ground covered with it like hoar frolt even the bushes that happen to lie near these places are covered with pure brimstone, condenling from the steam that issues out of the ground, which in many places is covered over with a substance like burnt alum.' Though the Author appears to have been in poffeffion of a thermometer; no account is given of the Ritual temperature of these waters.

Near these boiling fountains, there are several cold mineral {prings; two of which are said to fend forth waters' which have a very ftrong mineral quality, of an acid taste, and bitter to the tongue.' - Seven specimens of these and other waters have been sent home, and are enumerated at the end of this Article. The firft of these was taken from one of these cold fountains ; which is described giving a frong acid water.'-As this Arong acid water appears to us a very great curiosity, we couid have wilhed that its analysis had been subjoined to this Article ; as well as, indeed, that of the hot waters above mentioned, which are said to possess considerable virtues in the cure of the dead pally, eruptions, and more particularly the gout. While the Author resided near these waters,“ several old gentlemen, who were quite worn out with the said disorder, were ufing the waters, and had received incredible benefit from them.' He accordingly bints, that` should any person venture so far for his health, a small stock of the superfluities of life only need to be Jaid in, as the island yields every necessary,' and the climate is very temperate. Article 27. An Account of a remarkable Imperfection of Sight. In

a Lecter from Mr. J. Scott, &c. The person who here communicates several extraordinary particulars of an hereditary infirmity in the visual organs, with respect to colours, can see objects at a distance, and diftinguish their form and bulk as well as most men : but such is bis an. gular idiosincrasy with respect to their colour, that he declares,

though his business was behind a counter many years, where he had to do with a variety of colours' be does not know any green in the world; a pink colour, and a pale blue are alike. He has often thought a full red and a full green the fame, or a good match : though he can discern the difference between yellow and a full blue. He relates an anecdote of his having been offended at an intended son-in-law's having entered bis house, on the day preceding his marriage, in a new fuit of cloaths, which appeared as much a black to his eyes, as any black that ever was dyed ; while the gentleman bad actually decorated bimself with a fine rich claret-coloured drefs.'

We have called this imperfection hereditary; but, like fexdigitisin, it appears to have affected only fome individuals of his fainily. He derived it from his father, but his mother had

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