fquares of the distances, while others affirm it to be in the inverfe ratio of the cubes, or a mean proportional between both, &c. With regard to the nature and pofition of the innumerable curves formed by the currents of magnetical matter, which are fuppofed to circulate between the poles of the earth; the perfect knowledge of which would be fo ufeful in geography and navigation; it is evident that thefe cannot be determined a priori, without a perfect acquaintance with the laws of magnetifm, and a knowledge of the magnitude, figure, pofition, and powers of the central magnet or magnets, which are fuppofed to produce these curves, and give the needle its particular direction. By actual obfervations indeed the direction of the magnetical curves has been ascertained in various parts of the earth: but these obfervations have not been fufficiently numerous or accurate, nor made at the fame point of time. It feems however at first fight eafy to imitate Nature on a fmaller fcale, by fubftituting an artificial magnet, of a determinate fize, figure, and power, in the room of the central or terreftrial magnet or magnets [for greater clearnefs we will fuppofe but one, ; and by prefenting to it fucceffively, in different fituations, a magnetical needle, and noticing its different pofitions in the tangents of the various curves defcribed by the magnetical currents, in their circulation round this artificial fubftitute, in the fame manner as they are supposed to move round the terrestrial mag net. One feemingly infuperable difficulty occurs, however, in the execution of this project. It appears neceffary, during this propofed course of experiments, to annihilate the action of the terrestrial magnet, which, when the needle is drawn out of its meridian direction, muft neceffarily interfere with, and greatly difturb, the refults. The Author gets over this difficulty, feemingly with great ease, not certainly by annihilating the central magnet, which is impoffible, but by conducting the experiments in fuch a manner, as to deftroy its difturbing power. We shall endeavour to give fuch an idea of his method, as can be conveyed in a few words, and without the affiftance of figures. A fmall magnetical needle is fixed in the centre of a large graduated circle, while the centre (or middle of the axis) of an artificial magnetical bar, placed on a long ruler which turns on the fame point, is fucceffively moved through different degrees of its circumference, in fuch a manner that, at every ftation, the needle is ftill made to continue in the magnetical meridian, in confequence of the bar's being occafionally turned upon its' own centre, fo as to prefent its attracting and repelling poles to it in different fituations. To explain this, it may be proper to ob ferve, that, as it is evident that the needle will continue in its natural pofition, if the bar, for inftance, be placed in the magnetical meridian of the needle, or in the fame right line with it; and that the fame effect will follow, if the centre of the bar be placed at 90 degrees, or due eaft or weft, from that of the needle, prcvided its axis be in a line parallel to the meridian, and its two poles be of equal power: fo in every other intermediate pofition between these two fituations, the needle will maintain its natural direction, if the magnetical bar be inclined to the meridian with certain degrees of obliquity. For as each of the two poles of the bar and needle attract or repel each other, with a force modified by the diftances and different angles of incidence; it is evident that the bar may be turned on its centre in fuch a manner, that thefe four forces fhall exactly counterbalance each other, and the needle continue in the meridian equally undif turbed as if no magnet had been prefented to it. Now, altho' the needle is, in all thefe cafes, undoubtedly acted upon by the terreftrial as well as the artificial magnet; yet, as it is always kept in the meridian, the influence of the former does not interfere with or difturb the attracting and repelling powers of the latter while the precife measure of thefe powers is obtained by obferving the angle which the axis of the bar makes with the needle, or magnetical meridian; the quantity of which angle is known by means of a fmall graduated femicircle, on the centre of which the bar revolves. By means of experiments made with the artificial magnet, thus fucceffively placed at every tenth degree of the large circle, at different diftances from the needle, and turned upon its own centre, fo as to preferve the needle in its natural direction, the Author obtains data, from whence, as well as by fubfequent proceffes and calculations, he endeavours to difcover the nature, and to trace the true figures of the magnetical curves, and deduce from thence the laws and properties of the magnetical matter. From the whole of his experiments, calculations, and deductions, we collect, that the effect of the action of a magnet upon a needle is in the direct fimple ratio of the fine of incidence, that is, the fine of the particular angle at which each particle of the magnet acts upon it, and not in the ratio of the fquare of that fine, as is the cafe, he obferves, in the percuffion of fluids. M. Lambert accordingly is inclined to confider the action of the magnetical matter rather as a fimple preffure, than the percuffion of a fluid. With regard to the force of magneti cal attraction or repulfion at different diftances, he determines that the power of each particle of the magnet on each particle of the needle, is proportional to the abfolute force of these particles, and is in the inverfe ratio of the fquares of the distances. As to the discovery of the absolute force however of each particle of a magnetic magnetic bar, and of the proportion in which it increases or fame. MEMOIR VI. On the fame Subject: containing Problems on the We give only the titles of thefe and of fome of the following Memoirs, which are of fuch a nature as to preclude all attempts to abridge them. We fhould obferve too, that we have not yet noticed the first article of this clafs, which contains only the botanical characters of a plant, named Zietenia, by Mr. Gleditfch. MATHEMATICS. MEMOIR I. On the Conflruction of compound Object Glaffes, which produce no Confufion, either in Confquence of their Figure, or of the different Refrangibility of the Rays of Light: with the most advantageous Method of conftructing Telescopes with them. By M. L. Euler. Although M. Euler has already frequently and largely difcuffed this curious and interefting fubject, he here again returns to it with redoubled zeal; incited, and even impelled, he acknowledges, to the further investigation of it, by the surprising discoveries which have been lately made, relative to the very fingular properties of different kinds of glafs, manifefted by their peculiar action on the rays of light. He does not blufh to own ingenuously, that, when he was first informed of thefe novelties, he received them with great diffidence and fufpicion, as judging them contrary to the beft eftablished principles of optics; for, that there fhould be two fpecies of glafs, in both of which the refraction of the mean rays fhould be nearly the fame, while that of the extreme rays fhould be enormously different, appeared to him a propofition grossly repugnant, as he exprefies himself, to the principles of common fenie. That full conviction, however, of this truth, which the account that he received of Mr. Dollond's experiments could not perfectly produce in the mind of our Author, has been completely effected by thofe lately made by M. Zeiher of Peterburgh, who has difcovered a compofi-' tion, the effects of which in the difperfion of the rays, as it is Nn 3 now now commonly called, are fo remarkable, that they have produced M. Euler's compleat converfion, and have induced him to adopt, without referve, this new and important principle, that the refractive power of two transparent fubftances may be nearly equal with regard to the mean, and yet be extremely different with refpect to the extreme rays. The calculations into which he here enters, with a view of applying this difcovery to practice, are not fufceptible of abridgment; but, as we have already, more than once, had occafion to mention the fubftance difcovered by M. Zeiher, without being then able to give any information concerning its particular nature or compofition, we here willingly embrace the opportunity, with which we are furnished by this Memoir, of gratifying that curiofity which we thereby may poffibly have excited in fome of our philofophical Readers concerning it, by collecting a few particulars relative to this curious fubject. It appears then that lead, or rather the calces of that metal, added to glafs, impart to it this fingular property of difperfing the extreme rays; at the fame time that they increase in some, though a much smaller, degree, the refraction of the mean rays. From a table here given of the refracting powers of fix different kinds of glafs made of flints and miniun, or red lead, in various proportions, we collect, that in a compofition confifting of equal parts of these two fubftances, the mean refraction of a ray paffing from air through this medium, is as 1787 to 1000; whereas the ratio of its power of difperfing the rays is to that of common crown glafs as 3259 to loco: but in a glass made of three parts of minium to one of flints, the effects of this metallic addition are ftill more ftriking; the mean refraction being as 2028 to 1000, while its refractive power with regard to the extreme rays, compared with that of crown glafs, is as 4800 to 1000, that is nearly as 5 to 1, an effect which must appear very confiderable, when we reflect that no transparent body was before known, whofe refractive power exceeded the ratio of 2 to I. From the refults contained in this table, a certain proportion is evidently obfervable between the mean refractive and the difperfive powers of thefe different compounds; the confideration of which, in the Author's opinion, may poffibly conduce to explain thefe fingular effects, and to reconcile them to known principles. But we must not omit to mention another difcovery of M. Zeiher's, on this fubject, not lefs fingular than the former, and which renders the explanation of thefe phenomena ftill more difficult. The fix pieces of metallic glafs abovementioned were See Monthly Review, Vol. xl. June 1769, p. 498, and the Appendix to Vol. xlii. P. 505. compounded compounded only of flints and minium. M. Zeiher having afterwards added fome fixed alcali to this compofition, merely with a view to give his glafs a degree of confiftence that might make it more proper for dioptrical ufes, found to his great furprize that, although this addition fcarce produced any change with regard to the difperfion, it caufed a very confiderable die minution of the mean refraction. After various trials he at laft hit on a particular compofition much fuperior, for the conftruction of telescopes, to the flint glafs of Mr. Dollond, as it produces a difperfion three times greater than that of crown glafs, wh le the mean refraction is only as 1.61 to 1. The great advantages to be drawn from thefe properties, in the conftruction of telescopes, induce M. Euler to apply to them various calculations founded on different hypothefes of conftruction. Among the different combinations here offered, we obferve one in which an achromatic telescope of 5 feet in length is propofed, which ought to exceed in magnifying power a common refractor of 120 feet, and be confiderably fuperior in every refpect to a reflecting telescope, of a greater length than its own; particularly in the quantity of light and distinctness, and above all in the largenefs of the field, the diameter of which will be fix times greater than that of the reflector. Some conftructions are likewife given, in which a magnifying power of 100 times is propofed to be produced in a telescope of this kind, onlv 131⁄2 inches in length. MEMOIR II. On compound Object-Glaffes conftructed fo as to deftroy all poffible Confufion in Telefcopes. By the fame. In this Memoir M. Euler's principal intention is to fhew in what manner a compound object-glass may be constructed, so as not only to produce no aberration itself, but likewife fo as perfectly to destroy all confufion caufed by the other glaffes combined with it. To convey, in a few words, a popular idea of his defign, in the latter of the two cafes; the object-glass is fo formed as really to caufe a certain degree of confufion; but which at the fame time fhall be equal and contrary to, and confequently deftructive of, that known to be produced by the other glaffes. MEMOIR III. Reflections on the best Manner of examining and afcertaining the refractive Power of different Kinds of Glass, by Means of Prifms. By the fame. We have formerly infifted, after M. D'Alembert †, on the abfolute neceffity of avoiding even the smallest errors in the measure of the refractive powers of the different fpecies of glass; as the fuccefs of the artift, in realifing all the great expectations raised by the calculations of the fpeculative optician, de See the Appendix to our 42d volume, page 505. Nn4 pends |