theory of its motions with nearly the to callitURANUS; M. de Sivry,Cybele; {za me exactness that the motions of the and M. Profperin, of Upsal, 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 prope fe;* and perhaps teldeope, is not greatly different from their propofitions might be made bethat of a fixed itar of the fifth or fixth fore they knew that Mr. Herschel had magnitude, being something less bright aligned any name to it. M. de la Lande than N. 132 of Taurus in Flamited's has not that excuse; 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 ardour 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 pursue his steps, in ado than that of the fixed stars. vancing the sciences, are his motives With respect to its diameter, we are for it. I must confess I have no idea told that Dr. Maskelyne estimates it at of that gratitride which leads us to op3 or 4 seconds: the observations of pofe, in the most direcè 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 feifrom 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 3] forereign, in rendering the lives of times that of the earth : we may, there those easy and happy here, whose lafore, conelude from the observations of bours and discoveries are of themselves Dr. Maikelyne and Mr. Herschel, that sufficient 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- most 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 ihe 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 same time, they are not agreed had itill retained the names of Medicean amongit themselves in this matter. M. and Lodovicean stars, 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 allured us that the Christian religion, according to his calá ellations, founded on the rate at which it has decayed in the course of the last go years, cannot poffibly lait 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 defiring the dormant thunderer would take notice he had paid him that piece of refpe&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 godship came into play again. Is it not possible there in. genious gentlemen may entertain suspicions of a like kind, and therelole are paying their court to these gentry, that they may be a received into their kingdom” at their restoration ? DEMONSTRATIONS OF SOME PROPERTIES RELATING TO RIGHT-ANGLED PLANE TRIANGI.ES. BY MR. JOSEPH KEECH. PROPOSITION I. 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 Q. E. D. the two squares, cutting the legs of the triangle in F and H: I 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 :: KL: BH; and AE: ED: : AB : BF. Now, as the three first terms in each proportion are respectively equal, A B the last must be equal also; that is BH H =BF. Draw FZ parallel to AB, and, consequently, to CD, also join HZ. Then because the triar.gles AZF and ACD are fimilar, DE: FB :: AD: AF:;CD : FZ. Hence a6 CDDE, FZ = FB = HB; confequently HZ is equal and parallel to F, and the figure HBFZ is equilateral. More- K L over the angles at B and F being right angles by construction, the opposite ones at Z and H are right angles also, and the figure HBFZ is a square. PROPOSITION II. The same things remaining as in the last proposition: 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 fimilar, as well as the triangles ABF, DCF; therefore AK (AB) : BC :: AH : BH :: BF: FC; and therefore, BH being equal to BF by propofition I. AH: BH :: BH (or BF): FC. Q. E. D. PROPOSITION III. If the same construction remain, and if the square HBFZ be circunscribed by the circle HBFZ, meeting the fide 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 PGC 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 ftand on the same arcs with them, are each of them half a right angle: and if these be taken from the two right angles AGB, BGC, there will remain the two balf right angles AGH and FGC. 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, allo 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 BCR, are similar by Euclid VI. 8. Moreover, because the angles HGF and BGC, are right, and the angles Q. E. D. angles GHF and GBC stand on the same arc, GF, the triangle HGF is also fie milar to the triangle BGC, &c. Hence BC : BA :: FC : FB (=FZ) :: BH (=HZ): HA :: FG:GÁ:: CG:GB :: RC: CB, or CD. Q. E. D. PROPOSITION V. The fame construction still remaining; I say that the lines AD, CK intersect each other in the perpendicular, BG, Ict 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. MATHEMATICAL QUESTIONS. QUESTION I. by SLOKB. +2 +382 From the equation x5+ x3 + rx? +sx+1=1, in which r, s, and i are fupposed 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 star; it is required to determine the declination of this last, so that the difference of their velocities in azimuth may be the greafcft 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 opposite hyperbola. QUESTION IV. by RUSTICUS. Given the area, one of the angles, and the difference of the including sides 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 trapeziu in, 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 3h 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 (poft paid) to Mr. Baldwin in Pate nofter-row, London, before the ift of October, 1783; às none can be inserted that come to hand after that time. AV 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 custom, 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, thefe urns ate 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 diftinguished 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 so great an indulgence. At corated. the funeral of Patroclus, we are told The ancients sometimes compofed that these urns of very costly materials, as “ Four sprightly coursers, 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 filver, 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 silk. Lycurgus, however, con and sometimes they were ceinented with fined those of Sparta, to the sober 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 select: cumstance is supposed to have been occafioned by a second 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, Pepe'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 hoi, the fuccessions 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 stone, rious. Lacrymatories, lamps, and other in order to detend them againft ali 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, fwords, fields, or parts of By these means, 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 every 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 as. tyrant was ordered to be half burned sistance of the deities, when he finds in the amphitheatre. In all probability the funeral pile of Patroclus burn slow: then, where the bones are found in any ly, as Homer tells us in the foilowing quantity, unconsumed, the barrow was beautiful allegory: erected over fome person of low condi “ Nor yet the pile, where dead Patroclus lies, tion, or whose rices had rendered him Smokes, nor as yet the fullen Hames arife; odivus. On these accounts, the fune. But, fait beside, Achilles dood 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 promited, and libations cart treatinent of the dead, indeed, might To gentle Zepliyr and the Bureat llast: He called th' aërial pow'rs along the skies be occafioned by the hurry and contu To breathe, and whilper to the fires 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 infant haitend to their airy ball, 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. She thone amidst them, on her painted bows strong, and of long continuance, fo The rocky pavement glittered with the show. 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 set off " Not so (the dame reply'd) I hate to go To facred Ocean and the floods below: “ The last fad honours that await the dead," E'on now our fulemn hecatomis attend, are confumed, we may infer that the Ard heav'n is feasting on the world's end, deceased were either of high quality, with righteous Ethiops (un corrupted train!) Far th' extremeit limits of the main." or such, as by their virtues had ren But Peleus' son intreats, with sacrifice, dered themselves beloved and respected. The Westeru spirit, and the North to rise ; For the funeral obsequies were per- Let on Patroclus' pile your blast be driven, formed in these cases with all polible And bear the blazing honours high to heav'n. care, and the fires watched, till all the Pope. Il. xxiii. 236. green on IN ON EDUCATION. Quibus artibus, et quibus hunc tu JUVENAL. painted under the form of a spacious is to adopt a proper method for conmanfion, of which infancy forms the veying this advice. Aufterity and rientrance. 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 very frequently when the fuppretion tract the affectivns of every stranger of vice has been intended, hare inwho approaches; while a good genius culcated a distatte for virtue. For of teaches them to discriminate between virtue, the inherent attractions are in truth and faitehood, and points out themselves without meretricious ornathe appearances which are fallacious, ments, or secondary motives, sufficient and thote 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. Loxd. Mac. Juiy 1533. But |