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theory of its motions with nearly the to call itURANUS; M. de Sivry,CYBELE; fame 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 propofe ;* and perhaps telefcope, is not greatly different from their propofitions might be made bethat ot' a fixed itar of the fifth or sixth fore they knew that Mr. Herschel had magnitude, being something less bright alligned any name to it. M. de la Lande than No. 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 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 learnmerer, and its light is more diluted ed men, to, puisue his steps, in adthan that of the fixed stars.

vancing the sciences, 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 feconds: the observations of pofe, 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 scifrom about 3" 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 fol. rent 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 liappy here, whose lafore, conclude froin the observations of bours and discoveries are of themselves Dr. Maskelyne 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- moft liberal manner, to pursue their stance near 1900,000,000 miles. studies for the advancement of science.

I cannot corclude this paper without Mr. Herschel's name will not want the remarking, and rather with concern, aids, M. de la Lande proposes, to perpe that foreign astronomers seem to fettuate 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 still 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 assured us that the Christian religion, accorsing to his cale eolations, 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 deliring the dormant thunderer would take notice he had paid him that piece of respect when his fortunes were at a very low ebb, and therefore hoped it would be "remembered to him for good” if ever his godihip came into play again. Is it not possible these in. genious gentlemen may entertain suspicions of a like kind, and therefore 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 I.
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 tal

Q. E. D.

the two squares, cutting the legs of the triangle in F and H: 1 say that BF hall be equal to BH and each of them to the fide 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

P
KL: BH; and AE: ED: :AB :
BF. Now, as the three firít terms in
each proportion are respectively equal,

A

B

H 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 fimilar, DE : FB : : AD: AF:;CD : FZ. Hence as CDDE, FZ = FB = HB; confequently HZ is equal and parallel to LF, and the figure HBFZ is equilateral. More-l K

L over the angles at B and F being right angles by construction, the opposite ones at 2 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 similar, 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 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 BCR, are similar by Euclid VI. 8. Moreover, because the angles HGF and BGC are right, and the angles GHF and GBC stand on the same arc, GF, the triangle HGF is also fimilar 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.

angles

PROPOSITION V. The fame conftruction 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

MATHEMATICAL QUESTIONS.

QUESTION I. by SLOKE. From the equation x5+

12 + sez

*3 +rx? +sx+1=1, 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 star; it is required to determine the declination of this last, so that the difference of their velocities in azimuth may be the grease eft 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, cne of the angles, and the difference of the including fides of a plane triangle, to construct it.

QUESTION V. by CAPUT MORTUUM. To surround 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 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 light 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 fent (poft 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

THI

ON THE FUNERALS OF THE ANCIENT BRITONS..

Hæc nosse, et dulce et utile. VARRO. HE ancient Britons and Gauls, we lurion which follows our mode of bu.

are well afsured, burned the bo- rial. When the bones were thus redies 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 almoit every part of considerably larger than those of the this kingdom, these urns are frequent- human body, being found in these beaps 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 foldiers, 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 fo great an indulgence. At corated.

the funeral of Patroclus, we are told The ancients fometimes 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 tilk. 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 Philofophical 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 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. 396. 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 stone, rious. Lacrymatories, lamps, and other in order to defend them against all appendages of mourning, are found in prefsure.

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 ashes, and particularly the larger ones. helmets, fwords, fields, or parts of By these neans, 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 as. tyrant 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 flowi 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 fome person of low condition, or whose vices had rendered him

“ Nor yet the pile, where dead Patroclus lies,

Smokes, nor as yet the fullen fames arile; odivus. On these accounts, the fune

But, fait beride, 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 promiled, and libations cast treatinent of the dead, indeed, might To gentle Zephyr and the Bureai itaft: be occafioned by the hurry and contu. He called th' acria! puw'rs along the skies

To breathe, and whilper to the pies to rife. fion of war, as well as by the disrespect The winged Iris heard the hers's call. which arises from vice and tyranny. And insiant haitend 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 She thone amidst them, on her painted bow's

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 fet off " Not so (the dame reply d) I hate to go

To facred Ocean and the foods below: « The last fad honours that await the dead,"

E'cn now our fulemn hecatomis atiend, are consumed, we may infer that the Ar.d heav'n is feasting on the world's green end, deceased were either of high quality, With righteous Ethiovs (uncorrupted train!)

Far on th' extremeft limits of the main." or such, as by their virtues had rendered themselves beloved and respected. The Western Spirit, and the North to rise;

But Peleus' son intreats, with sacrifice, For the funeral obsequies were per- Let on Patroclus' pile your blast be driven, formed in these cases with all possible 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
Moribus inftituas.

JUVENAL
IN the tablature of Cebes, Life is genius. The great difficulty, however,

painted under the form of a spacious is to adopt a proper method for conmansion, of which infancy forms the veying this advice. Austerity and ria entrance. Fancies and opinions, as in- gour should not be equally exerted fnite in their number, as they are va- against 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 fupprefiion tract the affections of every stranger of vice has been intended, have inwho approaches; while a good genius culcated a distaite for virtue. For of teaches them to discriminate between virtue, the inherent attracticris are in truth and failehood, and points out themselves without meretricious ornathe appearances which are fallacious, ments, or fecondary 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 Lörd. Mac. July 1533

E

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