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WINTER. AN ODE. By the late Dr. SAMUEL JOHNSON. more the morn, with tepid rays,
N° Unfolds the flow'r of various hue;
Noon fpreads no more the genial blaze,
With fighs we view the hoary hill,
The fnow-topp'd cot, the frozen rill.
Congeal'd, impetuous fhowers defcend;
With light and heat my little fphere:
Nor love, nor wine, the spring restore.
EPITAPH on Dr. JOHNSON.
YE vain, licentious wits, your distance keep?
And, if you never wept, now learn to weep. Learning hath loft her prop in Johnson's end, Virtue her boast, and Piety her friend. Prefume not to this fhrine too near to draw, `Or, if you dare approach, approach with awe. The fcythe of time fhall canker o'er with ruft, Lofe its keen edge, and fplinter into duft; Himfelf, too, ficken, and in anguish pine, Ere he fhall gain a harvest fo divine. But tho' thy form be fnatch'd from mortal eye, Johnfon! thy fpotlefs fame fhall never die. Clos'd as thou art in Death's eternal cave, Thy work fhall live, and bloffom from the grave. W. WOTY.
Dec. 20, 1784.
On the Death of Dr. SAMUEL JOHNSON. ATE aim'd ý blow-"the cruel arrow fped;"
FAnd Johnion now lies number d with y dead.
Shall I not drop one melancholy tear
Improv'd, O great philologer, by thee
Teddington, Jan. 13, 1785.
Written by GEORGE COLMAN, Efq. life is a bubble, and breaks with a glafs, mult your wine, if you'd it
For the bubble may well be deftroyed with a puff,
'Tis a very good thing understood the right way;
This life is no more than a journey 'tis faid,
EPITAPH on a favourite HORSE.
Your kind affiftance, gentle Muses, lend,
ANSWERS TO MATHEMATICAL QUESTIONS. 80. QUESTION (I. Dec.) not answered. QUESTION (II. Dec.) anfwered by the propofer.
LET S represent the fun, & the earth, and M the planet in its orbit AMMB. Draw SM and EM, and produce the latter to e; then I fay that the part of the enlightened disk of an inferior planet which can be feen from the earth will always be as the verfed fine of the angle SMe; that is, as the verfed fine of the fupplement of the angle contained between lines drawn from the planet to the earth and fun. For ac being drawn perpendicular to SM, bd to EM, and ar to bd; it is manifeft that abc will be the enlightened difk of the planet, ab that portion of it which is visible to à fpectator on the earth at E; and br, which is the verfed fine of the arc ba, will be the apparent breadth of it. But br is the verfed fine of the arch ba, which is equal to ne, the measure of the exterior angle SMe, of the triangle SME, because aMS, and ¿Me are both right angles. Now it is demonftrated by the writers on menfuration, that the areas of fuch lunula as form the visible parts of the enlightened disks of the planets are as the rectangles contained by the greateft breadths of them and the diameters of the fpheres on which they are formed: but, in this cafe, the diameter of the planet being a conftant quantity, the areas will be as their greatest apparent breadth; that is, as the versed fines br of the angle SMe, which, according to ME+MS+SEXME+MS-SE
trigonometrical writers is equal to
fore, a SE, b-SM, and x=EM,
2MSX ME x+b+axx+b-a 2bx
will be as the illuminated
part of the planet feen from the earth. But the intensity of the light of any lumi nous object is directly as the illuminated furface, and inverfely as the fquare of its x+b+axx+b-a I 2bx x2
X is conftantly
distance from the fpectator; confequently, as the intensity of the light of mercury, which will be greatest when —2bx4x8b2x3x+6a2bx2x—6b3a2x, its fluxion, is equal o; that is, when x+4bx=3a2 -362, and then x √3a2+b2 —2b.,
Let a be expounded by 1; then, according to Dr. Halley's Tables, b will be ,3871; and x, or EM, 1,00058. Hence, the angle ESM, or the difference be tween the heliocentric longitude of the planet and that of the earth will be 78° 55' 41'; whereas the fame angle, at the time of the planet's greateft elongation from the fun is only 67° 13'; Mercury is therefore brightest between the time of its greatest elongation and that of its fuperior conjunction; and its elongation at that time, or the angle SEM, is 22° 18′47′′.
If, inftead of Mercury, we would inquire into the fituation of the planet Venus, when its fplendour is greatest, the very fame equation will refolve the problem: for retaining a, the mean distance of the earth from the fun, 1, that of Venus, by Halley's Table, will be .72333, for the value of b; from whence we fhall have EM (x) in this cafe, .43036, and the angle ESM 22° 20′ 57′′; whereas that angle, at the time of the planet's greatest elongation is 43° 40'. Confequently, Venus is brightest between the time of her greatest elongation, and her inferior conjunction;
M m 2
junction, contrary to what happens to the planet Mercury; agreeable to the obfervation of your ingenious correfpondent B Algol, drawn, as it should feem, wholly from his obfervations.
It is by no means difficult to account for this phenomenon: for the variation of the light in each planet being as the apparent breadth of the disk of the planet di. rectly, and as the fquare of its diftance from the earth inverfely; and the variation arifing from the former caufe being nearly alike in both planets, while that arising from the latter is much greater in Venus than it is in Mercury, on account of Venus altering her diftance much more, and approaching much nearer to the earth than Mercury does; it follows, that when the planets are moving from their superior conjunctions toward their inferior ones, the increase of light, on account of the latter caufe, remains greater than the decrease of light, arifing from the former, for a longer time in Venus than it does in Mercury; that is, until the planet gets farther from the place of its fuperiour conjunction. And, on the contrary, when they are proceeding from their inferior conjunction towards the fuperior one, the decrement of light arifing from the increased distance becomes fooner equal to the increment of it which arifes from an increase of the enlightened disk in Venus than it does in Mercury.
82. QUESTION (III. Dec.) answered by Mr. WILLIAM KAYE, of Wakefield. Let AFH and CDG be the given circles, AC and DF the two lines which touch both, the former in A and H, and the latter in C and D ; and let CD and AF be the two lines joining the points of contact, and meeting each other in E; alfo let ED meet AC in B. Becaufe BD=BC, the angle BCD (ACE) the angle BDC, = the angle EDF, by Euc. I. 15. Alfo, because ABFB, the angle BFE the angle BAE. Confequently, the triangles ACE, FDE, having two angles in the one refpectively equal to two angles in the other, each to each, these triangles are fimilar, and have the fides about the equal angles proportional; that is, CE : AE::DE: FE; and alternately, CE: DE;;AE: FE. Q. E. D.
83. QUESTION (I. Jan.) anfwered by the propofer, SENEX.
Mr. Emerson (to whofe characters I refer) makes the gravity at P the fame as at A; which, though the difference is very fmall, occafions a very confiderable error in the conclufion. His value of the perturbating force of S, on a particle at D, is also erroneous
and the gravity at A will
be to the gravity at Pas b to 1+
we have the abole fiuents of -fy the whole fluents of
Therefore, instead of his equation
= 1+3B × ag; and confequently B being by that equation =
will be =
ftead of being: Which agrees with Mr. Maclaurin's computation, and with my correction of Mr. Simpfon's in the Lond. Mag. for January last: a being=AC; b=CP; R=CS; p= the periodical time of the earth round the fun in feconds; g=32.2 feet; 3.1416; f:
;x= CE; y=CD; and
Given the fum of the fides of a plane triangle, the difference of the fegments of the base made by the perpendicular, and the line bifecting the vertical angle and terminating in the bafe to determine the triangle?
96. QUESTION II. by the fame Gentleman.
Given the diameter of a circle circumfcribing a plane triangle, the difference of the angles at the base of the triangle, and the fum of the base and perpendicular to determine the triangle?
97. QUESTION III. by .w
Suppofe a plane to touch the fpheroidal figure of the earth, in a given latitude; it is required to find the angle contained between this plane and a tangent drawn to any given point of the earth?
*** If we have mistaken this gentleman's meaning in the alteration we have made in his mode of expreffing his queftion, we apprehend all our correfpondents would have been liable to have done the fame, if we had not altered it: they cannot mistake it now.
The anfwers to these queftions may be directed (poft-paid) to Mr. Baldwin, in Paternofter-row, London.
TO THE EDITOR OF THE LONDON MAGAZINE.
You have had of late fo much on
the subject of air in your Magazine, that for a new writer to start on the fame grounds, would appear impertinent indeed, and I fhould be very cautious to avoid the ugly imputation, if I did not think that much ftill remains to be faid on the fubject.
Inflammable air, we find, has power, not only to carry us beyond the clouds, but to bring our thousands and ten thousands to the plains; to endanger beauty, money, and watches;
ftood, inafmuch as they occur of not to the Caro mio ben of Pacchie
There is a mufical air. The powers But I find it is the fashion to expire of this are far greater than those of in- at an opera, and therefore the ladies flammable air. Inflammable air raifes must comply, although heaven knows, us to the clouds; but mufical air raifes Sir, that this expiration at an opera, is us to Heaven itfelf- -inflammable air not justified by any of the rules of inraifes us above our fellow creatures, Spiration. but mufical air raifes us above ourfelves-tames the roughneffes of our natures, plants foftnefs and gentleness in our breafts, and animates us with a fpark of that heavenly fire which forms the incense of the eternal Hallelujah.
For my own part, indeed Mr. Editor, I am a poor weak woman, and dare not truft myfelf with mufic beyond God fave the King, Corn Riggs, or the 100th pfalm tune; particularly in the month of May, when mufical air produces effects greatly more wonderful, though not quite fo vifible, as the motions of an air-balloon.
One very fingular effect of this air was in Orpheus recovering his wife from hell; a very unfafhionable experiment, and which in our days, does not bid fair to become general. Rather than fo, our modern Orpheus's would convert their harpfichords into coffins, .to carry their wives there.
The effects of the mufical air are fometimes very pernicious. It is very apt to take away the breath, and we hear ladies at the Opera, who go up in this air, telling us they expire: to be fure, Sir, they die martyrs in good caufe, don't they? In former days, people were martyrs for religion's fake, not the fake of a fiddle; and died in obedience to their confcience, and
Next, Sir, there is an haughty air. This is an air which fills the heads of the ignorant, the upstart, rich, and the powerful. A balloon filled with this air is the most dangerous of any; more people have been known to fall from them, than from any other fpecies of balloon; and this frequently, because they happened to lose the materials of which the air was compofed.
The affable air is compofed of ingredients quite the reverfe of the former; a balloon made of this, lafts one's life-time, and always preferves its original beauty, unimpaired by time. This air has the fingular effect of giving beauty to the moft ordinary countenance, and cafting the most beautiful colouring over the failings of our nature. There is a perfume in it fo delicate, that all the world are charmed with it. Savage rudeness, however, cannot live in it; but the wife, the good, and indeed the bulk of mankind, find that it has the most beneficial effects.
There are many other fpecies of air, which I could give you an account of, but, as I have taken up a good deal of your time, and may perhaps be thought to be giving myfelf too many airs, I conclude, and am, Sir, your's,
A WEARER OF PETTICOATS. Air-fireet, Mar. 19, 1785.
FOR THE LONDON MAGAZIN E.
"A fatal paffion for cards and dice feems to have overturned, not only the "ambition of excellence, but the defire of pleafure."
THE employment of time is, of all others, a matter of the greateft importance. On this depends our happinefs. This raifes us to the wifeft and the beft, or finks us down to the lowest and most contemptible of our ecies. Yet fuch is the folly and per