ftrument that Mr. Le Cerf has invented will answer this purpofe or not, refts folely on the bare affertion of the inventor. He does not pretend that even the proportion, on which its conftruction depends, is the refult 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 fuch proportion to that of the pinion it is to work with, as the number of teeth 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 fubftance as follows. Subtract unity from the number of revolutions which the pinion makes in one revolution of the wheel, and multiply the remainder by the quotient arifing from dividing the diameter of the pinion by the number of leaves which are in it: the product will exprefs the quantity by which the diameter of the wheel is to be leffened, expreffed in fuch measures as the diameter of the pinion was taken in. Or this rule may be expreffed 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, fo is the diameter of the pinion to the reduction of the diameter of the wheel. Thus if the diameter of the pinion be, its leaves 12, and the teeth of the wheel 96; then the diameter of the wheel, according to Mr. Derham, will be To X 96÷121%; and, according to Mr. Le Cerf, 12 is to 991 (7) as: 7X10÷12=1: confequently 1%-746-12% 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. 8 T That this mode of reduction may be fufficiently near the truth for mechanical purposes, may poffibly be a fact but that it is ftrictly true, notwithstanding Mr. Le Cerf's affertions, may admit of a doubt. For aught that appears to the contrary, feveral other laws of reduction may be affigned 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 pleafed 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 fo. Mr. Le Cerf's measures may have been taken rather inaccurately; or, poffibly, fome of his pinions might have worked ftill better, on a farther, or a less reduction. We do not mean, by what we have faid, to depreciate Mr. Le Cerf's invention: his purfuits are truly laudable and ufeful, the thought ingenious, and may be true;-we only wish to convince him that he is pofitive without proof. The form and conftruction of Mr. Le Cerf's compaffes cannot be gathered with certainty from the paper before us, as his description 2 defcription of them is very concife, although his paper, in other relpects, 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 addrefled, when the inftrument 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-thofe may read it who can. But is it not a most extraordinary circumftance that fo learned a body of men as the Council of the Royal Society may be fuppofed to confift of (for the Society at large we well know have no concern in it) should fuffer fuch tranflations as this, and fome other late ones, to appear in their publication? Mr. Le Cerf, in the courfe 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 likewife. Nothing can be more obvious than that when the fides of the teeth are planes, or nearly fo, 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 fcarcely at all when the planes of the two teeth 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 inveftigate; and, perhaps, not very difficult to work, fufficiently near the truth, were it an object of importance enough to merit it. This, however, Mr. Le Cerf has not attempted to do, but advifes a method that has long been practifed by the beft 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 fingle tooth acts on its fellow for a lefs time; that is, while the wheels move through a lefs angular fpace, and of courfe does not act under fuch a variety of angles as they muft unavoidably dó 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 maia-fpring, which is undoubtedly fometimes much greater, has but little effect on the going of a watch, the balance of which has fufficient momentum,-fuch as all the watches that are made by the best English artists now have: the figure of the teeth is therefore but of little confequence. In watches of Mr. Harrifon's conftruction thefe inequalities cannot poflibly have any effect, because that part of the watch which measures time is moved by a fall fpring that acts on the contrate wheel; and, confequently, whatever irregularities there may be in the forces . forces which act on the other wheels, they can noway affect the going of the watch. The Author adds an account of another inftrument which he has invented, and fent 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 impoffible for us to form a juft idea either of its construction or merits. He concludes his paper with tables of the dimensions of the feveral pinions generally used in clock and watch work, according to the principles which he has before laid down. CHEMISTRY. W. Article 39. Chemical Experiments and Obfervations 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 fpecific gravities of various lead ores, and even of different parts of the fame lump of ore. Notwithstanding this circumftance, we are told that the purchafing 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 mineralifed in the ore (particularly in the feelgrained and teffelated galenas) could be feparated from it in clofe veffels, or by diftillation, as is the cafe with respect to fome kinds of the pyrites; he diftilled 16 ounces of fome teffelated Derbyshire lead ore in an earthen retort. Though he gave the retort a white heat, no fulphur was fublimed: but the ore loft a 32d part of its weight. The matters feparated from the ore were a small quantity of a black fubftance, that rofe up into the neck of the receiver; and which appeared to be pure lead ore, fublimed without being decompounded :—a small portion of a liquid, that had a pungent fmell, refembling that of the volatile vitriolic acid, and which had an acid tafte i though it did not effervefce with alcalis, nor produce any change in the colour of blue paper:-and laftly, a quantity of air or elaftic fluid; which, at the beginning of the process, had the smell of inflammable air. In the following experiment, however, he not only feparated the fulphur from the ore, but was enabled to afcertain its quantity. Five ounces of the strongest fuming fpirit of nitre, diluted with an equal quantity of water, were poured on ten ounces of lead ore. A violent effervefcence enfued; and when the folution was completed, there remained floating upon the surface of the menftruum, a cake of fine yellow fulphur, perfectly refembling common fulphur. This fubftance, edulcorated and dried, generally amounted to one-third of the weight of the ore. This matter however is not pure fulphur, but is a mixture of that fubftance and a calx of lead: for on putting fome of it on a red hot iron, a greyish calx remains, after the fulphur is confumed; confumed; which on being put on a piece of ignited charcoal, is reduced, at leaft in part, to a metallic ftate. The Author confidering the great quantity of fulphur contained in the Derbyfhire lead ores, where about 10,000 tuns are smelted annually, proposes to the confideration of the lead fmelters the practicability of collecting it; both as a lucrative business to themselves, and a great saving to this country, where, it feems, we at prefent import the fulphur we ufe. 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 roafted in the fame manner as is practifed in Saxony, where arfenic is procured by a fimilar contrivance; the arfenical vapour being condensed, and attaching itself, like foot, to the fides of the chimney; from which the arfenic is, from time to time, fwept out. At the end of this paper, the Author relates fome experiments from which it appears that, though the furface of pure melted lead becomes covered with a pellicle of various colours; yet these appearances do not occur if a fmall portion of tin be mixed with the lead, even when the weight of the tin fcarce exceeds theth part of the weight of the lead. Zinc poffeffes the fame property, in this particular refpect, 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 fucceffively appear in the following order: yellow, purple, blue, yellow, purple, green, pink, green, pink, green. The ra tionale of these appearances may be deduced from the well-known experiments and theory of Sir Ifaac Newton, lately illuftrated and confirmed by Mr. Delaval, in his ingenious Experimental Enquiry refpecting the changes of colours in bodies MISCELLANEOUS ARTICLES. Article 26. An Account of the Island of St. Miguel. Francis Maffon, By Mr, 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 Philofophical Tranfactions, are contained in a general defcription of fome fountains, from which the water boils up fo hot, that a perfon cannot dip his finger into it without being fcalded.' A fteam likewife rifes, to a confiderable height, from several apertures, which is fo hot, that no one can approach it with the hand. In other places, fays the Author, a person would think that a hundred fmiths bellows were blowing altogether, and fulphureous fteams iffuing out [iffue out] in thousands of places, fo that native fulphur is found in * See an account of that work in the 57th volume of our Review, P. 221. REV. Jan. 1778. E every every chink, and the ground covered with it like hoar froft even the bushes that happen to lie near these places are covered with pure brimftone, condenling from the fteam that iffues out of the ground, which in many places is covered over with a fubftance like burnt alum.' Though the Author appears to have been in poffeffion of a thermometer; no account is given of the actual temperature of these waters. Near thefe boiling fountains, there are feveral cold mineral fprings; two of which are faid to fend forth waters which have a very strong mineral quality, of an acid tafte, and bitter to the tongue.'-Seven fpecimens of thefe and other waters have been fent home, and are enumerated at the end of this Article. The firft of these was taken from one of thefe cold fountains; which is described as giving a frong acid water.'-As this Arong acid water appears to us a very great curiofity, we could have wifhed that its analyfis had been fubjoined to this Article; as well as, indeed, that of the hot waters above mentioned, which are faid to poflefs confiderable virtues in the cure of the dead pally, eruptions, and more particularly the gout. While the Author refided near thefe waters, feveral old gentlemen, who were quite worn out with the said disorder, were using the waters, and had received incredible benefit from them.' He accordingly hints, that fhould any perfon venture fo far for his health, a fmall stock of the fuperfluities of life only need to be laid in, as the ifland yields every necessary,' and the climate is very temperate. Article 27. An Account of a remarkable Imperfection of Sight. In a Letter from Mr. J. Scott, &c. The perfon who here communicates feveral extraordinary particulars of an hereditary infirmity in the vifual organs, with refpect to colours, can fee objects at a distance, and diftinguifh their form and bulk as well as most men: but fuch is his fingular idiosincrafy with refpect to their colour, that he declares, though his bufinefs was behind a counter many years, where he had to do with a variety of colours'- he 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 difcern the difference between yellow and a full blue. He relates an anecdote of his having been offended at an intended fon-in-law's having entered his 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 had actually decorated himself with a fine rich claret-coloured drefs.' We have called this imperfection hereditary; but, like fexdigitifin, it appears to have affected only fome individuals of his family. He derived it from his father; but his mother had |