theory of its motions with nearly the to call itURA NUS; M. de Sivry,Cybele; fame exactness that the motions of the and M. Profperin, of Upfal, NEPTUNE. other planets are settled. M. de la Lande acknowledges that the The appearance of this planet, when three latter gentlemen have no reason viewed with the naked eye, or a small for what they propose ;* and perhaps telescope, is not greatly different from their propofitions might be made bethat ot' a fixed ftar of the fitth or fixth fore they knew that Mr. Herschel had magnitude, being something less bright alituned any name to it. M. de la Lande than No. 132 of Taurus in Flamited's has not that excufe; but he alledges catalogue: but when examined with a that gratitude to the author of fuch a good telescope which magnifies 200 rare discovery, and the arduur which times or upwards, it is far otherwise; immortalizing his name, by calling the as it then appears under a sensible dia- planet after it, will give to other learnmeter, and its light is more diluted ed men, to pu.fue liis fteps, in adthan that of the fixed ftars. rancing the Iciences, are his motives With respect to its diameter, we are for it. I must confefs I have no idea told that Dr. Maskelyne estimates it at of that gratitude which leads us to op3 or 4 seconds: the observations of pose, in the most direct manner, the Mr. Herschel, printed in the Philo- wishes of the person that we pretend sophical Transactions for 1781, vary to express it for: and I conceive scifiom about 31 to st". M. de la ence will be most essentially encouraged Lande has calculated that if its appa- if we can excite other monarchs to folrent diameter be 3'', its real diameter low the example of our most gracious will be about 28,000 miles, or 3į forereign, in rendering the lives of times that of the earth: we may, there those easy and happy here, whose lafore, conclude froin the observations of bours and discoveries are of themselves Dr. Makelyne and Mr. Lierschel, that fufficient to perpetuate their names its real diameter is not less than 4 hereafter, and in enabling them, in the times that of the earth, and its real di- moft liberal manner, to pursue their stance near 1800,000,000 miles. studies for the advancement of science. I cannot conclude this paper without Mr. Herschel's name will not want the remarking, and rather with concern, aids, M. de la Lande proposes, to perpethat foreign astronomers seem to set tuate it. The names of Galileo and their faces against the name which the Callini would have been in no more ingenious discoverer of this planet has danger of perishing than they now are thought proper to give it; though, at if the Satellites of Jupiter and Saturn the fame time, they are not agreed had still retained the names of Medicean amongit themselves in this matter. M. and Lodovicean itars, as they wished de la Lande will call it the PLANET OF them to do. HERSCHEL;M.Bode,of Berlin, proposes * Perhaps M. de la Lande may be mistaken. A very facetious, if not a very pious divine, of our own country, has repeatedly assured us that the Christian religion, accorting to his calá eulations, founded on the rate at which it has decayed in the course of the last 50 years, cannot poffibly last above 50 years longer. In consequence, I suppose, when he was at Rome, he made a very reverend bow to the statue of Jupiter, which still remains in the Pantheon ; at the same time defring the dormant thunderer would take notice he had paid him that piece of respe&t when his fortunes were at a very low ebb, and therefore hoped it would be “ remem. bered to him for good” if ever his godhip came into play again. Is it not possible there in. genious gentlemen may entertain suspicions or a like kind, and thereto e are paying their court to these gentry, that they may be " received into their kingdom” at their restoration ? DEMONSTRATIONS OF SOME PROPERTIES RELATING TO RIGHT-ANGLED PLANE TRIANGLES. BY MR. JOSEPH KEECH. PROPOSITION 1. L ET ABC be a plane triangle, right angled at B; and let the squares ABLK, BCDE be described on the two legs AB, BC; also let the straight lines AD, CK be drawn from the two acute angles to the opposite angles D and K of the the two squares, cutting the legs of the triangle in F and H: 1 say that BF shall be equal to BH and each of them to the side of a square HBFZ, inscribed in the triangle ABC. DEMONSTRATION. Since AB=BL, and BC=BE; AE =CL. And because the triangles R AED, ABF are similar, as well as the Z triangles CLK, CBH, CL : CB :: F H I the last must be equal also; that is BH =BF. Draw FZ parallel to AB, and, consequently, to CD, also join HZ. Then because the triangles AZF and ACD are similar, DE : FB :: AD: AF:;CD : FZ. Hence as CDDE, FZ = FB = HB; consequently HZ is equal and parallel to F, and the figure HBFZ is equilateral. More-l K L over the angles at B and F being right angles by construction, the oppofite ones at Z and H are right angles also, and the figure HBFZ is a square. Q. E. D. PROPOSITION II. The same things remaining as in the last propofition: I say that BF (=BH) is a mean proportional between the other segments AH and FC of the legs of the triangle ABC. DEMONSTRATION. The triangles KAH, CBH are similar, as well as the triangles ABF, DCF; therefore AK (AB) : BC :: AH : BH :: BF : FC; and therefore, BH being equal to BF by proposition I. AH : BH :: BH (or BF): FC. Q. E. D. PROPOSITION III. If the fame construction remain, and if the square HBFZ be circumscribed by the circle HBF2, meeting the side AC of the triangle again in G; and if GB, GH, and GF be drawn: I say that the angles FGC, FGB, BGH, and HGA are each of them equal to half a right angle. DEMONSTRATION. The angles AGB, and BGC are each of them right angles by Euc. III. 31. Now the angles, HFB and BHF are each of them half a right angle, because the angle HBF is a right angle, and BH=BF. Hence the angles HGB and BGF, which stand on the same arcs with them, are each of them half a right an. gle: and if these be taken from the two right angles AGB, BGC, there will remain the two balf right angles AGH and FGC. Q. E. D. PROPOSITION IV. The same construction remaining; if BG and DC be produced out until they meet in R: I say that FC and FB, BH and HA, FG and GH, CG and GB, also RC and CD are all in the ratio of the given legs of the triangle BC, AB. DEMONSTRATION. Because of the parallel lines AB, ZF; BC, HZ, the triangles ABC, AHZ, and ZFC are fimilar; and the triangles ABC, BGC, and BČR, are similar by Euclid VI. 8. Moreover, because the angles HGF and BGC are right, and the angles : : angles CHF and GBC stand on the fame arc, GF, the triangle HGF is also fie milar to the triangle BGC, &c. Hence BC : BA :: FC : FB (=FZ) :: BH (=HZ): HA :: FG:GH :: CG:GB :: RC: CB, or CD. Q. E. D. PROPOSITION V. The same construction still remaining; I say that the lines AD, CK interfect each other in the perpendicular, BG, let fall from the right angle, B, upon the fide, AC. DEMONSTRATION. The alternate angles PAB, and PDR being equal and also the vertical ones APB and DPR, the triangles APB, DPR are limilar; and, by Prop. IV. RC: CD :: BH : HA; consequently CH passes through the point P. Q. E. D. ** A line from H to F is omitted in the figure. rt a MATHEMATICAL QUESTIONS. QUESTION I. by SLOKE. From the equation x5+ 12 + srl 2x3 +rx? +sx+1=0, in which r, s, and are supposed given, it is required to find the value of x? QUESTION II. by ASTRONOMICUS. Supposing the right ascension and declination of a star to be given, as also the right ascension of another itar; it is required to determine the declination of this last, so that the difference of their velocities in azimuth may be the grease cft pollible when they are upon the same vertical circle, in a given latitude. QUESTION III. by Mr. WILLIAM KAY. To determine a point in a given hyperbola which is nearest to any given point in the oppofite hyperbola. QUESTION IV. by RUSTICUS. Given the area, cne of the angles, and the difference of the including lides of a plane triangle, to construct it. QUESTION V. by CAPUT MORTUUM. To furround a fish-pond of a given area, and in the form of a given trapeziuin, with a walk of a given area, and of the fame breadth every where, by a geometrical construction. N. B. This is Prob. IX. Newton's Universal Arithmetic, edit. 1720. Question VI. by Mr. J. Walson. Two numbers (47 and 59) prime to each other, being given; to find the least multiple of each of them, exceeding by unity a multiple of the other. QUESTION VII. by Mr. JAMES WEBB. What is the declination of that star which has the greatest altitude possible 34 37' after it has passed the meridian in latitude 51° 31' N. Question VIII. by N. T. Sailing N. N. W. I came in fight of two islands, the one bearing N. and the other W. After running 8 miles, I found myself equally distant from them, and when I had run 3 miles farther I was in a right line with them: it is required to find my distance from these two islands at each time of setting them, The answers to these questions are requested to be sent (post paid) to Mr. Baldwin in Paternoster-row, London, before the ift of October, 1783; as none can be inserted that come to hand after that time. AN ON THE FUNERALS OF THE ANCIENT BRITONS.. Hæc nosse, et dulce et utile. VARRO. HE ancient Britons and Gauls, we lution which follows our mode of bu. dies of their dead, and after this cere- duced, the urn was filled with them, mony, interred the remains in urns, a and whatever could not be crouded into cuftom, which, in all probability, they it, was placed round, and covered by the borrowed from the Romans. barrow. In many of the barrows, which are There are many instances of bones to be found in almost every part of considerably larger than those of the this kingdom, these urns are frequent- human body, being found in these heaps ly discovered. Those of our ancestors of stones. Let not these be supposed to are easily to be distinguished from those be the remains of giants, but rather of of the Romans, as the former are of a horses, as those animals, as well as the rude make, and formed of coarse ma- arms of soldiers, were laid on the futerials, while the latter are remarkable neral pile: an honourable distinction, for the elegance of their shape, the which could only be claimed by the neatness with which they are made, and Equites, as the foot-soldiers were not the ornaments with which they are de- permitted b great an indulgence. At corated. the funeral of Patroclus, we are told The ancients sometimes composed that these urns of very costly materials, as “ Four sprightly courfers, with a deadly groan, Homer informs us that Patroclus's was “ Pour forth their lives, and on the pyre are made of gold. Those of silver, brass, thrown.” marble, glass, and pottery ware, how Pope's Homer. Iliad xxiii. 209. ever, were the more common. They The bones were closely confined in were tricked out with ribbands, flows the urns, by earth placed over them, ers, and filk. Lycurgus, however, con- and sometimes they were cemented with fined those of Sparta, to the fober dress mortar, to prevent the admission of the of olives and myrtles. air, or any impure mixture. Achilles, These urns are generally found in in Homer, orders the bones of his the middle of the barrow, and even friend Patroclus to be covered with a near the edge, as Dr. Williams has in- double coat of fat: formed us, in the Philosophical Tran Then as the rites direct, factions, for the year 1740. This cir- The hero's bones with careful view releat: cumstance is supposed to have been occafioned by a fecond interment; when These, wrapt in double cawls of fat, prepare; the skirt of the barrow alone was open And in the golden vase dispose with care." ed, that the remains, first intombed, Pope's Il. xxiii. 296. might not be disturbed. Sometimes, By imbibing the oil from this fat, however, it should seem, that a whole which the bones would do when they family was buried in the same barrow, were hot, the successions of drought as several urns have been found placed and moisture would lose great part of near one another. their effect. These urns are most commonly in- The contents of these urns are vaclosed in little ceils, formed of fione, rious. Lacrymatories, lamps, and other in order to defend them against all appendages of mourning, are found in pressure. them; and sometimes pieces of weaThe bones, however, before they pons, or at least little bits of metal. were depofited, were burned, almost to This circumstance seems a proof, that alhes, and particularly the larger ones. helmets, swords, shields, or parts of By these nieans, they were, in some armour were thrown into the fire, that measure, freed from the filth and pol- consumed the body of an hero. Sometimes Sometimes the bones are found not smaller bones were entirely consumed, above half consumed, which may, per- and the larger were not put into the haps, enable us to distinguish the bar- urn, until blanched quite white. But rows of the rich and virtuous, from this could be produced only by a long those of the poor and profligate. For and fierce flame, which crery method we are informed by Suetonius, in his was taken to raise and preserve. On life of Tiberius, that the body of that this account, Achilles intreats the astyrant was ordered to be half burned fiftance of the deities, when he finds in the amphitheatre. In all probability the funeral pile of Patroclus burn flow then, where the bones are found in any ly, as Homer tells us in the following quantity, unconsumed, the barrow was beautiful allegory: erected over foine person of low condition, or whose vices had rendered him Smokes, nor as yet the fullen Hames arile; “ Nor yet the pile, where dead Patroclus lies, odivus. On these accounts, the fune. But, fait befide, Achilles food in pray'r, ral was carelessly attended, and the re- Invok'u the gods whole spirit moves the air. mains gathered hastily together. This And victims prornited, and libations cast treatinent of the dead, indeed, might To gentle Zephyr and the Boreai ilait: He called th' aerial pow'rs along the skies be occasioned by the hurry and contu To breathe, and whilper to the pres to rise. fion of war, as well as by the disrespect The winged Iris heard the hers's call. which arises from vice and tyranny. And infiant huitend to their airy hall, : On the contrary, however, where Where, in old Zephyr's open courts on high, there are evidences, that the fire was Sat all the bluit ring biethren of the sky. strong, and of long continuance, fo The rocky pavement glittered with the show. She thone amidst them, on her painted bows that not only the bones, but even the All from the banquet rise, and each invites armour and all the various trappings The various goddess to partake the rites. which decorated the pile, and fet off “ Not so (the dame reply'd) I hatte to go To facred Ocean and the foods below: « The laft sad honours that await the dead," E'cn now our folemn hecatomos attend, are consumed, we may infer that the Ard heav'n is feasting on the world's green end, deceased were either of high quality, Far on in extremeft limits of the main.” With righteous Ethiops (uncorrupted train!) or such, as by their virtues had ren But Peleus' fon intreats, with facrifice, dered themselves beloved and respected. The Western spirit, and the North to rise; For the funeral obsequies were per- Let on Patroclus'pile your blaft be driven, formed in these cases with all posible And bear the blaging honours high to heav'n.' care, and the fires watched, till all the Pope. Il. xxiii. 236. ON EDUCATION. Quibus artibus, et quibus hunc tu JUVENALI painted under the form of a spacious is to adopt a proper method for conmansion, of which infancy forms the veying this advice. Aufterity and ria entrance. Fancies and opinions, as in- gour should not be equally exerted fnite in their number, as they are va- againft the good and the bad, or the rious in their pursuits, are described generous and the froward. As a want attending the gate of this dwelling, of method and measure in punishment. in order to engage the notice, and at- rery frequently when the fupprefiion tract the affections of every stranger of vice has been intended, have inwho approaches; while a good genius culcated a distalte for virtue. For of teaches them to discriminate between virtue, the inherent attractions are in truth and failehood, and points out themselves without meretricious ornathe appearances which are fallacious, ments, or fecondary motives, sufficient and those on which they may depend. to lead the hearts of youth to noble ac In our infant state, it is the duty of tions, and to incite them to pursue our parents to perform the part of this with ardour the paths of learning Lord. MAG. July 1983. E |