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tionibus, as restored by Vieta, under the name of Apollonius Gallus, and his deficiencies supplied by Marinus Ghetaldus. We have taken the pains to compare this treatise with the original, and also with the abstract and translation of it in the Cursus Mathematicus of Peter Herigone, vol. I. page 915, edit. Paris; and have the pleasure to find, that Mr. Lawson has 1newn himself both a faithful Tranfator, and an able Geometrician. But we could wish he had added, in his Supplement, fome of the constructions of the moderns, as many of the most important problems concerning Tangencies, are performed by them in a far more concise and elegant manner, than any to be met with in the works of the antients.
Perhaps it will not be disagreeable to our mathematical Readers, if we add a fimple method by which many of thele problems n:ay be constructed with the utmost facility.
Having two points given, B and D, and likewise a circle, whole center is A, to describe another circle which mall pafs through the given points, and touch the given circle.
CONSTRUCTION. Let D B be joined, and through those points describe a circle, cutting the given one in the two points E F; join these points with the right line E F. Produce E F and D B till they interfeet, as in H. From H draw a tangent, as HK, to the given circle. Then through the points D, B, K, describe the circle DKBL, which will touch the proposed circle in K.
DEMONSTRATION. EHXFH=DHX BH, and EHXFH = HK,
by by the nature of the circle; therefore D H XBHS HK; and consequently H K is a common tangent to the circles K E F, and DKBL, which pafies through the points I, K, B.
Philosophical Transactions, &c. Vol. LIII. Continued from
Papers in EXPERIMENTAL PHILOSOPHY.
communicated in a letter to Dr. Franklin. Some of them are well imagined, and others puerile* enough. Those which Mr. Kinnersley effected by means of his newly-contrived electrical air-thermometer, are curious and interesting. The inArument itself also, is an ingenious contrivance for estimating the force of electrical explosions; but, as we cannot give the Rcader a descriprion of it without the plate, we shall content ourselves with the following specimens of this Writer's experiments and reasoning.
Dr. Franklin, it seems, before his last voyage to England, had suggested to Mr. Kinnersley, that it would be worth trying, whether, by hanging a weight to the end of a piece of brals wire, and sending a great charge of electrical fire through it, the cohesion of the constituent particles of the wire might not so far relax, as that the weight would cause a separation. This experiment being tried, not only turned out as Dr. Franklin suggested, but the wire absolutely became red-hot; and on a second charge was fairly melted; a circumstance, of which, Mr. Kinneisley says, neither he nor the Doctor had entertained the least suspicion.
That he might not be mistaken also, in the wire's being acłually hot as well as red, he repeated the fame experiment on anotker piece of the same wire encompassed with a goose-quill filled with loose grains of gun-powder ; which took fire as readily as
As for exampl:, • I formed a cross of two pieces of wood of equal lengths, intersecting each other at night angles in the middle; hung it, horizontally, on a central pin, and set a light hoise, with his rider, upon each extremity; wher: upon, the whole being nicely balanced, and each courfer urged on by an electrised point, instead of a pair of spurs, I was entertained with an electrical horse-race.'- A mighiy pretty entertainment for a Philosopher truly!
if it had been touched with a red-hot poker. Tinder, tied to another piece of wire, also kindled by it: tho' from a wire twice as big, no such effects could be produced.
Llence this Writer concludes, that lightning does not melt metal by a cold fusion, as was formerly suppored*; but that when it pafis through the blade of a sword, if the quantity be not very great, it may heat the point so as to melt it, while the broadeit and thickelt part may not be sensibly warmer than before. To this observation Mr. Kinnersley adds several pertinent reflections on the effects of thunder-storms; with the means of preferyation against such awful and destructive phenomena. The recent instances we have had of these effects, and particularly on St. Bride's church in Fleet-street, may render the following relation acceptable to such persons as are defirous of taking thofe means of prevention, which have now for some years been found, from experience, highly efficacious on the continent of North-America.
As ihe fact related serves to corroborate the above experiment of Mr. Kinnersley's, we shall give the whole in his own words, extracted from his letter to Dr. Franklin.
• We had four houses in this city, and a vessel at one of the wharís, struck, and damaged, by lightning last summer. One of the houses was ftruck iwice in the same storm. But I have the pleasure to inforın you, that your method of preventing such terrible ditafers, has, by a fact, which had like to have escaped our knowlege, given a very convincing proof of its great utility, and is now in higher repute with us than ever,
• Wearing a few days ago, that Mr. William West, Merchant in this city, suspected that the lightning, in one of the thunder storms last summer, had passed through the iron conductor, which he had provided for the security of his house, I waited on him, to enguire what ground he might have for such fufpicion. Mr. Weit informed me, that his family and neighbouis were ail stunned with a very terrible explosion, and that the Main and crack were seen and heard at the same instant: whence he concluded, that the lightning must have been very near; and as no house in the neighbourhood had suffered by it, that it must have pailed through his conductor, Mr. White, his Clerk, told me, that he was sitting at the time by a window, about two feet from the conductor, leaning again't the brick wall with which it was in contact; and that he felt a smart sensation, like an electrical shock, in that part of his body which touched the wall. Mr. Weft farther informed me, that a person of undoubted veracity assured him, that, being in the door of an opposite house on the other side of Water-street, (which you know is but narrow) he saw the lightning diffused over the pavement, which was then very wet with rain, to the distance of two or three yards from the foot of the conductor. And that another person, of very good credit, told him, that he, being a few doors off, on the other side of the street, saw the lightning above, darting in such dire&ion, that it appeared to him to be dire&ly over that pointed rod.
* Mr. Kinnersley, however, is not the first who hath drawn this con. clufion of the çrfećts of lightning. Dr. Knight haib made the fane petection, in 2 paper inserted in the Philosophical Transactions, vol. Ll. put b.See Monthly Review, vol. XXIII. page 192.
• Upon receiving this information, and being desirous of farther fatisfaction, there being no traces of the lightning to be discovered in the conductor, as far as we could examine it below, I proposed to Mr. West, our going to the top of the house, to examine the pointed rod; assuring him, that if the lightning had passed through it, the point mult have been melted; and, to our great satisfaction, we found it so. This iron rod extended in height about nine feet and a half above a stack of chimnies to which it was fixed; (but I suppose, three or four feet would have been sufficient). It was fomewhat more than half an inch diameter in the thickest part, and tapering to the upper end. The conductor, from the lower end of it to the earth, consisted of square iron nail-rods, not much above a quarter of an inch thick, connected together by interlinking joints. It extended down the cedar roof to the eaves, and froin thence down the wall of the house, four story and a half, to the pavement in Water-street; being fastned to the wall, in several places, by small iron hooks. The lower end was fixed to a ring in the top of an iron stake, that was driven about four or five feet into the ground. The above-mentioned iron rod had a hole in the top of it, about two inches deep, wherein was inserted a brass wire, about two lines thick, and when first put there, about ten inches long, terminating in a very acute point; but now its whole length was no more than seven inches and a half, and the top very blunt. Some of the metal appears to be milling; the Nenderest part of the wire being, as I suspect, consumed into smoke. But some of it, where the wire was a little thicker, being only melted by the lightning, funk down while in a fluid fate, and formed a rough irregular cap, lower on one side than the other, round the upper end of what remained, and became intimately united therewith.
- This was all the damage that Mr. ,West sustained by a tersible stroke of lightning: A most convincing proof of the great utility of this method of preventing its dreadful effects. Surely
it will now be thought as expedient to provide conductors for the lightning as for the rain !' Art. 35. A Letter from Mr. George Edwards to Dr. Birch, con
cerning an Observation made by him in Optics. This letter being short, and the observation contained in it somewhat fingular, we shall give it the Reader verbatim.
• I having lately accidentally discovered, that the shadows of things floating in water, a little below iis furface, are reflected from the air above the water, more strongly (to my apprehenfion) than objects above the surface of the water are reflected from the water; and, consequently, that filhes playing beneath the surface of a ftill water, may see their images diftinctly playing in the air, with this advantage over men, who view their faces in the water; for things in air, that are reflected from the water, must have, when placed over the water, their dark or thadowed fides reflected from it, which renders the images obscure. On the contrary, the inhabitants of the waters have alinost a hemisphere of light falling on their upper fides, which are the sides that are reflected from the air, which consequently renders such images lighter, and more striking to the eye, than reflections of obscured things in air, when reflected from the water. As I have never heard of, or read, any account of this discovery, I imagine it may be new : but you, Sir, in far more extensive reading, may be acquainted with such a discovery. If so, I acknowlege my ignorance of it; and ask pardon for giving you this trouble, and desire it may be laid afide; but, if it be thought worthy communicating to the Royal Society, I will be ready, in a very fimple and easy manner, to demonstrate the truth of the above discovery. I do not see any use of this discovery at present, more than an amusing speculation ; tho', perhaps, when it is reconsidered by persons superior to me in penetrating into the secrets of Optics, some real use may be made of it.' Art. 51. Ratio conficiendi Nitrum in Podolia. Auctore
. Wolf, M. D. This paper contains an account of the method of making Salt petre in Poland; the process of which is particularly described.
Art. 54. A Letter from Mr. B. Wilson to Mr, Æpinus of
Petersburg We have been sometimes unjustly censured for speaking Nightly of the abilities and labours of our modern Philofophers, as if we intended, in checking the presumption of some forward and ignorant Experimentalists, to depreciate the merit or utility