cluded, that the Sun's Parallax might be duly determined by fuch Obfervations, if Mercury being nearer the Earth, had a greater Parallax, when feen from the Sun; for, this Difference of Parallaxes is fo very inconfidera

ble, as to be always lefs than the Sun's Parallax, which is fought; confequently, tho' Mercury is to be frequently feen within the Sun's Difk; he will scarcely be fit for the prefent PurVIII. Therepofe. ‡ (To be continued.)

T

S

E

‡ The Sun's Parallax having been stated at 12" the Parallax of Mercury is eafily known by the known Ratio of its Distance from the Sun and Earth, but this will be best explained by a Diagram; therefore let S be the Sun, M Mercury, and E the Earth, whofe Semi-diameter is É T, draw the Lines SE, ST, and MT, then is the Angle TSE 12" the Sun's Parallax, and E M T is the Parallax of Mercury, and the Dif Now as thefe Parallaxes, and their ference of thofe Parallaxes is the Angle MTS. Difference, are proportional to the Lines MT, ST, and S M, which are in a given Ratio to each other, they will also have a conftant Proportion among themselves, and therefore when any one of them is known, or fuppofed to be known, the others will be known according to that Hypothefis.

For Example, if the Solar Parallax TS E be 12", then it will be MT: ST(or ME :SE):: 6129: 10000 :: 12": 20" TME, the Parallax of Mercury, nearly; then the Difference is 7 for the Angle M TS, on the above Suppofition. Now this Difference of Parallaxes is lefs than the Sun's by more than 4"; and fince the Parallax of the Sun is to be found by the Difference of the Parallaxes from Obfervation; the Planet Mercury will not be fo proper for this Purpose as Venus, where the Difference of Parallaxes will be fo much more confiderable,

MATHEMATICAL QUESTIONS Answered.
Question 266, answered by Mr. Charles Green.

IRST correcting the Prefs by putting x2 x2 instead of x2 y2, then by making y to

FIRST

x

flow we get y=

and by making z to flow we have ≈ =

xx

then by fub

xx x4

ftituting their Values we have a4

- x4 X
4

X

which fluxed, and reduced pro

4

perly, gives x = 17,6 y=35,2 and x 12,201. QER.

Mr. Chapman's own Numbers are different from the above, for be makes x=352,04464, and y = 176,02232, and z = 248,933.

LE

Question 267, anfwered by the Propofer.

ET 36 Chains, then its first or leaft Side is a, then let e 3, i=7, and 10, from which the four Sides -i. A

will be thus found; a =

B

Question 268, anfwered by the Proposer Mr. Barak Longmate;

N the annexed Scheme let A be the

Sloop, B the Ship, A B 2,5, BC the Sloop's Courfe, CD the Race of the Current in Proportion: BC as 2 to 6, and

DCB

45. Now as the Current fets equally to them both, it caufes no Alteration in the Courfe which the Sloop must steer, which is plain must be A C, therefore VAB2+B CAC6 Miles the Sloop fails, to overtake the Ship in the leaft Time poffible; and to find the Course, say as A C: Radius:: BC to Sine 4 CAB

B

A

C

67° 23', its Complement 22o, 37′ —4 C, whence the Course was E. N. E. 7'E. To find the Bearing and Distance of D from B, fay as BC+DC: BC-DC::/ 4D+ 4 B 4D-4B :t .. 4B 17° 8', whence the Courfe made good by the

2

2

Sloop was Eaft by North, 5° 53' East; and as Sine ▲ B : DC; : Sine ▲ C:BD= 4,8 Miles diftance from the Ship at B, and the Chafe will last one Hour.

N. B. This Queftion was proposed as Mr. Carter's by mistake.

Mr. Charles Green also anjqvered this Queftion in Numbers, nearly agreeing with the Propofer's.

IN

Question 269, anfwered by Mr. George Redaway.

N the Triangle ABC, we have given all the Angles; and
AC, whence A B 66,3224, and BC 44,7352 make
DB FG EH, and HEC to the Current's
Courfe, then in the Triangle HEC we have all the Angles and
HE, whence HC 10,3566, and EC 27,062; alfo in the
Triangle ADF we have all the Angles and ADAB-DB D
41,3224, whence A F49,84427, and DF 27,872 ·.· F C
AC-AF30,15573, then in the Triangle G F C fimilar to
DAF, we have all the Angles and G F H E given, whence
GC = 16,86178 ; ·.· G C — HCGH FE+DF DE
34,37858 the Departure, A E53,7925 the Distance 39°
43 N. E. the Ship's Courfe made good, and E C 27,062 the A
Rate of the Current per Day. W.W, R.

G

B

GHC

New QUESTIONS to be answered.

Question 276.

By Mr. James Garden.

IVEN the folid Content of the Fruf

tum of a Cone 35,4520833 Feet, the flant Height 81,394103 Inches, and the Difference of Diameters = 30 Inches,

to find the Diameters ?

A Calculation of the Lunar Eclipse, by Mr. T. Smith, at Lamberhurst.

Apparent Time 1761,
May 18, London.

Middle of
Eclipfe.

End of
Tot.Dark.

Beginning Beginning

Eclipfe. Tot.Dark.

End of
Eclipfe.

h/

h

1

}

Duration of Total Dark,

1 34 30

3 23 24
17°34 15

An Eclipfe of the Moon, May 29, 1760, by Mr. B. Talbot.

In thefe Computations I have added as many Seconds, as the Moon's Parallax contained Minutes; alfo it may be obferved, as the Earth is not an exa& Sphere, its Shadow cannot be fo, but Elliptical, and may caufe a Variation in the Duration of Eclifpes. Therefore the Middle (if it can be observed or obtained from fome other Obfervations made during an Eclipfe) is most proper to compare with Computations, in order to prove the Tables in Longitude. It's therefore hoped, the Middle of the foregoing Computa tions will agree very nearly with correct Observations. I am your's &c.

Newport, Shropshire,

March 10, 1760.

Benj. Talbot, Teacher of Mathematics.

BAROMETRICAL and THERMOMETRICAL OB SERVATIONS made at Hull, by B. Waddington, in Mard

N. B. In answer to a Query of an ingenious Correfpondent, whether a Man who walks quite round the Globe of the Earth (Jupposed to be a perfe Sphere) walks moft up Hill or down? We anfwer, That fuch a Perfon can neither walk up Hill nor down, for no one goes up Hill, unless he goes farther from the Center of the Earth, nor down Hill, unless he approaches nearer to the faid Center; but the Perfon in Queftion, is always at an equal Distance from the Earth's Center, therefore, &c.

A fmile, the thought, would drefs her looks too gay,

A frown, might feem too fad, and blast the day.

But while nor this, nor that, her will could bow,

She walk'd and look'd-and charm'd and knew not how.

Our hands at length th unchanging fiat

bound,

And our glad fouls fprung out to greet the found.
Joy meeting joys, unite and ftronger fhine,
For paffions purity'd grow half divine.
Aurelia, thou art mine, Icry'd, -and fhe
Sigh'd foft- -now, Damon, thou art lord of me.
But wilt thou, whisper'd the, the knot now
ty'd,

Which only death's keen weapon can divide,
Wilt thou, ftill mindful of thy raptures paft,
Permit the fummer of love's hope to laft;
Shall not cold wint'ry frofts come on too foon;
Ah, fay what mean the world, by honey-

moon?

If we fo fhort a space our blifs enjoy,
What toils does love for one poor month em-
ploy !

Women, thus us'd, like bubbles blown with

air,

Owe to their outward charms a fun-gilt glare:
Like them we gl.tter to the distant eye,
But grafp'd, like them, we do but weep and
die.

Leaft more, faid I, thou should't profane
the blifs,

I'll feal thy dang 'rous lips with this clofe kifs;
Nor thus the heav'n of marriage hopes blaf-
pheme,

But learn from me to speak on this lov'd theme.
There have been wedlock joys of swift decay,
Like light'ning feen, at once, and shot away:
But theirs were hopes, which all unfit to pair,
Like fire and powder, kifs'd and flash'd to air.
Thy foul and mine, by mutual courtship won,
Meet like two mingling flames, and make but

one.

Union of hearts, not hands, does marriage make,

*Tis fympathy of mind keeps love awake: Our growing days increase of joys fhall know, And thick-fown comforts leave no room for

woe.

Thou the foft fwelling vine, shall fruitful laft,
I the ftrong elm, will prop thy beauties fast:
Thou shalt ftrew fweets, to foften life's
rough way;
[fway,
And when hot paffions my proud withes
Thou, hike fome cooling breeze, fhalt in

my bofom play.

Thou for protection, fhait on me depend,
And I, on thee, for a foft, faithful friend.
I, in Aurelia, fhall for ever view,
At once my care, my fear, my comfort.too.

Thou shalt first partner in my pleasures be,
But all my pains shall last be known to thee.
Aurelia heard, and view'd me with a smile,
Which feen'd at once to cherish and revile.
Oh, god of love! the cry'd, what joys were
thine,

If all life's race were wedding-days like mine!
To the fubfcribing LADIES of the
Circulating Library, in War-
rington, Dec. 14, 1759.

Ell me, bright nymphs! why with fuch
coft and care,

Thofe fleeting charms you labour to repair?
Why do thofe ears, with brilliant rubies glow?
And why, uncover'd, fhine thofe mounts of
(now ?

While all undreft, unpolish'd, unrefin'd,
Uncultivated, lies th' immortal mind?
That gem, which once improv'd, no clouds
can hide;

Which dart more light than earth can boaft
befide.

Think then, moft fair! if 'tis not low and
bafe,

To fee angelic beauteous fingers chafe
The ftubborn needle, with unrivall'd skill,
Yet never move with grace the noble quill?
That quill which paints all beauties of the
mind;

And to whofe motion empires ftand confin'd:
That quill which makes all real worth survive,
And ev'ry grace and virtue keeps alive:
That quill, which when with years your
charms fhall fly,

The mortal stamps, with immortality:
That quill, which wafts your thoughts where
feas can roll,

Convey'd without a blush from pole to pole.

As ever, therefore, you defire in fate,
A man of fenfe and prudence for your mate;
To tread th' remainder of life's narrow round;
Let beauties of the mind your wishes bound
Mindlefs, befides, of what the fun goes round.
Only from faithlefs men at diftance keep,
And 'midft ten thousand dangers, fafe you'll
fleep.

What's wealth and riches, but a gilded toy,
Which the afflicted never once enjoy;
Which, more we gather, ftill we covet more;
And pine the most amid ft the greatest store.

What's fame and honour, but an empty blaft,
To footh conceit, and feldom found to last:
A fleeting tranfitory bubble, blown;
Elate, this moment, but the next is gone.

What's love and beauty, but a fleeting joy,
Which very foon will taftelefs grow, or cloy:
A momentary blifs, unknown to stay ;
But, like all earthly pleafures, will away:
Remember this, bright nymph! and dread
delay.