89 They are not, how cause. à Paris fur la meilleure conftruction des Bouffoles de declination. Recueil des pieces courounées, tom. v. Euleri opufcula, tom. iii. continens Theoriam Mag. netis, Berlin, 1751. Epini Oratio Academica, 1758. pini item Comment. Petrop. nov tom. x. Anton. Brugmanni tentam. Phil. de materia Magnetica, Francqueræ, 1765. There is a German tranflation of this work by Ei. fenbach, with many very valuable additions. Scarella de Magnete, 2 tom fol. Van Swinden Tentamina Magnetica, 4to. Van Swinden fur l'Analogie entre les phenomenes Electriques et Magnetiques, 3 tom. 8vo. Differtation fur les Aimans artificielles par An. theaume. pofitive and negative electric. Some have inferred a fameness of origin of these two species of powers from thofe various circumftances of refemblance; but the original caufes feem to be distinct on many accounts. Electricity is common to all bodies. The cause of magnetifm can operate only on iron. Although lightning or an electrical fhock gives polarity to a needle, we need not infer the identity of the cause, because the polarity which it gives is always the fame with that gi ven by great heat; and there is always intense heat in this operation. The phenomenon which looks the most like an indication of identity of the origin of electricity and magnetism is the direction of the rays of the aurora borealis-they converge to the fame point of the hea. vens to which the elevated pole of the dipping needle directs itfelf. But this is by no means a fufficient foundation for establishing a famenefs. Electricity and magnetifm may, however, be related by means of fome powers hitherto unknown. But we are decidedly of opinion, that the electric and magnetic fluid are totally different, although their mechanical actions are fo like that there is hardly a phenomenon in the one which has not an exact counterpart in the other. But we fee them both operating, with all their marks of diftinction, in the fame body; for iron and loadftones may be electrified, like any other body, and their magnetifm fuffers no change or modification. We can fet these two forces in oppofition or compofition, juft as we can oppofe or compound gravity with either. While the iron filings are arranging themfelves round a magnet, the mechanical action of electricity may be employed either to promote or hinder the arrangement. They are therefore diftinct powers, inherent in different fubjects. But there are abundance of other phenomena which fhew this diversity. There is nothing in magnetifm like ever, effects a body overcharged or undercharged in toto. There is of the fame nothing which indicates the prefence of the fluid to the other fenfes-nothing like the spark, the fnap, the vifible diffipation; becaufe the magnetic fluid enters into no union with air, or any thing but iron. There is nothing refembling that inconceivably rapid motion which we fee in electricity; the quickeft motion of magnetifm feems inferior (even beyond comparifon) with the floweft motion along any electric conductor. Therefore there is no poffibility of difcharging a magnet as we difcharge a coated plate. Indeed, the refemblance between a magnet and a coated plate of glafs is exceed ingly flight. The only refemblance is between the magnet and an inconceivably thin ftratum of the glafs, which ftratum is pofitive in one fide and negative in the other. The only perfect refemblance is between the induced magnetilm of common iron, and the induced electricity of a conductor. The following feem the moft inftructive differtations on magnetism, either as valuable collections of obfervations, or as judicious reafonings from them, or as the fpeculations of eminent or ingenious men concerning the nature of magnetism. Gilbertus de Magnete, Lond. 1600, fol. Pieces qui ont emporté le prix de l'Acad. des Sciences Experiences fur les Aimans artificielles par Nicholas, Fuls, 1782. Effai fur l'Origine des Forces Magnetiques par-Mr Prevoft. Sur les Aimans artificielles par Rivoir, Paris 1752. Differtatio de Magnetifmo par Sam. Klingentier et Jo. Brander, Holm. 1752. Defcription des Courants Magnètiques, Strafbourg, 1753. Traité de l'Aiman par Dalancé, Amft. 1687. Befides these original works, we have feveral differta. tions on magnetical vortices by Des Cartes, Bernoulli, Euler, Du Tour, &c. published in the collections of the works of thofe authors, and many differtations in the memoirs of different academies; and there are many popular treatifes by the traders in experimental philofophy in London and Paris. Dr Gown Knight, the perfon in Europe who was moft eminently skilled in the knowledge of the phenomena, alfo published a differtation intitled, An attempt to explain the Phenomena of Nature by two principles, Attraction and Repulfion, Lond. 1748, 4to, in which he has included a theory of magnetifm. It is a very curious work, and thould be ftudied by all those who have recourfe without fcruple to the agency of invifible fluids, when they are tired of patient thinking. They would there fee what thought and combination are neceffary before an invifible fluid can be really fitted for performing any office we choose to affign it. And they will get real inftruction as to what fervices we may expect of fuch agents, and from what tasks they muft be excluded. The Doctor's theory of magnetifm is very unlike the reft of the performance; for he does not avail himself of the vaft apparatus of propofitions which he had eftablished, and adopts without any nice adjustment the most common notions of an impulfive vortex. Both the production and mainte nance of this vortex, and its mode of operation, are irreconcileable with the acknowledged laws of impulsion. Si quid novifti reius iftis, candidus imperti-fi nonbis utere mecum. Two magnetical poles being given in pofition, the 'force of each of which is fuppofed to be as the mth power of the diftance from it reciprocally, it is required to find a curve, in any point of which a needle (indefinitely fhort) being placed, its direction, when at reft, may be a tangent to the curve? I I 1. Let A and B (fig. 35.) be the poles of a magnet, Cany point in the curve required; then we may fuppofe the one of these poles to act on the needle only by repulfion, and the other only by attraction, and the direction of the needle, when at reft, will be the diagonal of a parallelogram, the fides of which reprefent thefe forces. Therefore, having joined AC and BC, let AD be drawn parallel to BC, and make AC BC::AC :AD; join CD, then CDF will touch the curve in C. 2. Hence an expreffion for AF may be obtained. AC"+ For, by the construction, AD = BC and fince BC :AD:: BF: FA, and BC - AD: AD::AB: AF, ABX AC+1 we have AF= BC+ACTM+** : 3. A fluxionary expreffion for AF may alfo be found in terms of the angles CAB, ABC. In CF take the indefinitely small part CH, draw AH, BH, and from C draw CL perpendicular to AH and CK to BH. Draw alfo BC and AM at right angles to FH. Let the angles CAB, and CBA; then CAH =, and CBH = - i; also CL = AC X ;, and CK -- BC X. Now HC: CL:: AC: AM = AC2 X; BC2 X HC HC ; and for the fame reafon BC = The firft of the above equations belongs to a fegment of a circle defcribed upon AB, which therefore would be the curve required if the magnetical force were inverfely as the distances. P If the magnetical force be inverfely as the fquare of the distance, that is, if m2, cof. ÷ + cof. ↓ is equal to a contant quantity. Hence if, befide the points A and B, any other point be given in the curve, the whole may be defcribed. For inftance, let the point E (fig. 36.) be given in the curve, and in the line DE which bifects AB at right angles. Defcribe from the centre A a circle through E, viz. QER; then AD being the cofine of DAE to the radius AE, the fum of the cofines of X will be everywhere (to the fame radius) = 2 AD = AB. Therefore to find E', the point in which any other line AN, making a given angle with AB, meets the curve, draw from N, the point in which it meets the circumference of the circle QER, NO, perpendicular to AB, so that AO may be the cofine of NAO, and from O toward A take OP = AB, then AP will be the cofine of the angle ABE'; fo to find BE', draw PQ perpendicular to AP, meeting AQ, meeting AE' in E', the point E' is in the curve. the circle in Q; join AQ, and draw BE' parallel to In this way the other points of the curve may be found. The curve will pafs through B, and will cut AB at an angle of which the cofine RB. If then E be fuch, that AE = AB, the curve will cut AB at right angles. If E" be more remote from A, the curve will make with AB an obtufe angle toward D; in other cafes it will make with it an acute angle. A conftruction fomewhat more expeditious may be Therefore fince AF: FB:: AM: BC, AF: FB :: had by defcribing the femicircle AFB, cutting AE in AC2x; BC' xi HC 2; wherefore if AB = a, AF = HC : fin. 2 fin. — a fin. 42 ¿ fin. «2 + ¿ fin. 2° 4. If this value of AF be put equal to that already found, a fluxionary equation will be obtained, by the integration of which the curve may be conftructABX AC+ Bem+ ed. Because AF= A e m+ a fin. have by fubftitution AF = a fin. 2 fin. fin. (+ a fin fin. pmt Hence, fin. ¿ fin. «2 + ø fin. 4a° fin+m+3 = and therefore i fin. & ”—1 S ¿ fin. 4 m−1 +ƒ¢ fin. + m¬1 = C. P and fince - fin.mi we fin. +m++ +; fin. ++3, ; and alfo, = F, and AE' in N, and defcribing a circle round A, with the distance AL 2AF, eutting AE' in b. If AG be applied in the femicircle AFB Nb, AG muft cut AN in a point E of the curve, because AN + BG 2 AF, and AN and GB are cofines of the angles at A and B. As the lines AN and BG may be applied either a bove or below AB, there is another fituation of their interfection E'. Thus An being applied above, and Bg below, the interfection is in e'. The curve has a branch extending below A; and if De be made = DE, and Be be drawn, it will be an affymptote to this branch.. There is a fimilar branch below B. But thefe portions of the curve evidently fuppofe an oppofite direction of one of the two magnetic forces, and therefore have no connection with the pofition of the needle. 155 WE omitted the inferting in its proper place, n° 65. Addition to a hypothefis of the celebrated aftronomer Tobias Mayerno 65. of Gottingen, by which the direction of the mariner's 5. Thefe fluents are easily found when m is any needle in all parts of the earth may be determined. He whole pofitive number. fuppofes that the earth contains a very powerful mag- 1 ! Addition to n° 64. From thefe data, it will be found that the axis of this magnet cuts the furface of the earth about the middle of the eastern fhore of Baffin's Bay, and in another point about 800 miles S. S. W. of the fouthern point of New Zealand. Profeffor Lichtenberg of Gottingen, who gives this extract from the manufcript, fays, that the hypothefis is accompanied by a confiderable lift of variations and dips calculated by it, and compared with obfervations, and that the agreement is very remark able. He gives indeed a dozen inftances in very different regions of the earth. But we fufpect that there is fome error or defect in the data given by him, because the annual changes, which he alfo gives, are fuch as are inconfiftent with the data, and even with each other. He fays, that the diftance from the centre increases about four miles annually, and that thence arifes an an nual diminution of 8 minutes in the latitude and 14 in the longitude of that point where the straight line join ing the centres meets the furface. It can have no fuch confequence. He fays alfo, that the above mentioned inclination of the planes increases 8 minutes annually. The compound force of the magnet is faid to be as the fquare root of the distance inverfely. We are at a lofs to understand the meaning of this circumftance; because Mayer's hypothefis concerning the law of magnetic action is exceedingly different, as related by Mr Lichtenberg from the fame manufcript. But it was our duty to communicate this notice, though imperfect, of the fpeculations of this celebrated mathematician. See Exliben's Elem. of Nat. Phil. published by Lichtens berg 1784, p. 645. Addition to no 64. Let HZOF (fig. 37) be the plane of a magnetic meridian, Ha'O the plane of the horizon, and NS the pofition of the magnetic needle in any place, when it is at liberty to fettle in the true magnetic direction. The angle HON is the inclination or dip of the needle. Let Zn F be a vertical circle, in which a well conftructed dipping needle can freely play up and down. This needle cannot place itfelf in the magnetic direction, becaufe it can only move in a vertical plane. Its north point is impelled in the direction o, and its fouth point in the direction sp, both of which are parallel to NS. By the laws of mechanical equilibrium, it cannot reft, except in fuch a pofition that the forces no and sp. are in a plane perpendicular to the plane Zn F. Ís any other pofition, there would be a force impelling the needle toward that fide on which no makes an acute angle with the tangent rnt of the vertical circle. Therefore the fpherical triangle Nn F is right angled in n, and Co NFn: R= Tan. n F : Tan. NF, = Tan. HN: Tan. nn. Therefore Tan. HN Tan. 'n =Tan. HNX Sec. Hn. Cof. Ha Therefore, in any place, the real inclination of the mag. netical direction to the horizon is different from what is pointed out by a dipping needle when it is in a plane which declines from the magnetic meridian; and the tangent of the obferved dip of the needle exceeds that of the inclination of the magnetic direction in the proportion of radius to the cofine of the deviation HĈn',. or the proportion of the fecant of this angle to the ra dius. If therefore the dipping needle play in a magnetic eaft and welt circle, it will ftand perpendicular tothe horizon, Malefherbes. MAL MALESHERBES (Chriftian William de Lamoignon) was born December the 6th 1721. At the age of 24 he became a counsellor of Parliament, and fix years afterwards chief prefident of the cour des aides. He remained in that important fituation during a period of 25 years, and difplayed on many occafions proofs of firmnefs, eloquence, and wisdom. When the prince of Condé was fent by the king in 1768 to filence the magiftrates who oppofed the taxes, Malefherbes replied to him, "Truth, Sir, muft indeed be formidable, fince fo many efforts are made to prevent its approach to the throne." About the fame time that he became prefident of the cour des aides, he was appointed by his father, then chancellor of France, fu. Ferintendant of the prefs; an office of the greateft, importance, of which the principles, which Malefherbes had imbibed from D'Alembert rendered him very ill quali fied to discharge the duties. He was what the French called a philofopher; a term with them of the fame import with a naturalift, who openly denies revealed religion, and has no adequate notions of the moral attributes of God. The confequence was, that when the authors of impious and immoral books were brought before him in his official capacity to undergo examination, he appeared to them as adviling, affifting, and protecting them, against that very power which was vefted in himfelf; and they were commonly difmiffed with this fenfelefs obfervation, that all books of whatever tendency fhould be confidered merely as objects of com MAL merce. Had it not been for the protecting influence of Male Malefherbes, the Encyclopedie, of which the publication fherbes. was frequently fufpended (fee DIDEROT in this Supplement), would probably have been altogether suppressed; and the works of Rouffeau and Raynal, which fo powerfully contributed to that revolution in which he was overwhelmed, would certainly not have spread fo rapid ly over the kingdom of France. It was he, faid D’Alembert, who broke the backles of literature. In vain will it be replied, that he left the fame liberty to the religious as to the impious writers; for that was not always Arietly true. The Abbé Barruel has brought the teftimony of D'Alembert himself to prove, that. it was much againft his will that Malefherbes luffered worka refuting the fophifters to appear; and, as he very properly obferves, what a minifter allows with reluctance, he finds abundant means of preventing. In 1775 he refigned the office of chief president of the cour des aides, and was appointed minifter and fecretary of ftate in the place of La Vrillière. Thus placed in the centre of a frivolous yet brilliant court, Malefherbes did not in the leaft deviate from his former fimplicity of life and manners; but, in lieu of complying with the eftablished etiquette which required magirates, when they became minifters of flate, to exchange their fable habit and head drefs for a coloured fuit, bag-wig, and fword, he retained his black coat and magifterial peruke! This is recorded by a panegyrift to his honour; but we perceive not the honour |