Cubes of the Semi-tranfverfe Axes. Let us take the Moon, whole mean Distance from the Centre of the Earth d b is 60 Semi-Diameters, and its Period = 27: 7:43 Or 39343 Minutes, and compare it with one that revolves at the Earth's Superficies.

By the above Rules: As,

60×60×60 : IXIXI :: 39343 × 39343: 7166.07. whofe Square Root is 84.68 equal to the Number of Minutes the Body would perform its Period in, in the Orbit

"

pq=1:24:40 5040. But the Periphery of its Orbit is equal to the Circumference of the Earth = 24928 Miles, Ergo its Velocity is fuch, as makes it go 4.92 &c. Miles each Second: But the Body in P goes only 1.5 Miles in the fame time, confequently the Velocity in, is to the Velocity in P as 4.92 c. to 1.5. Therefore the duplicate Ratio of the Velocity in p to the Velocity in P will be the Ratio of 242064 to 22500. And this Ratio compounded with the dupli-. cate Ratio of the Perpendiculars let fall upon PR and pr, viz. with the Ratio of 1 to 75 makes the Ratio of the Number 242064 to 1687500. I fay then as 242064: 1687500: 2 (equal to the Latus Rectum of the Orbit pa): 13.943; the Latus Rectum of the Orbit PQ. Therefore L=13.943 and confequently the Figure defcribed is an Ellipfis, and 2 SP2PK-L 16.05 Then to find PH: Ifay, As (2SP+2 PK—L) 16.057 (L) 13.943 (SP) 10: PH 8.683 Hence SP+ PH namely the Greater Axis of the defcribed Ellipfis is 18.683; All this is abundantly manifeft from Cor. 1. Prop. 16. and from Prop. 17. of Lib. I. of Newton's Principia.

:

=

The Conjugate Axis of the Section M w is =VSP+PHXL = 16. 140; And from the Square of the Semi-Tranfverfe, fubtracting the Square of the Semi-Conjugate Axis, there remains CH or the Eccentri city of the Figure 4.705; Hence the greatest Diftance of the Body when in the Apogeum will be 14.046; And the leaft in the Perigeum = 4.637 ; And thus much for the Form.

=

D

As

As to what refpects the Pofition, fince SH is known, and KH = PH-PK 3.863 and the Angle SKH right, or 90 Degrees: the Angle KSH will be found

d

23:3 But the Angle KSP is 30 Degrees, fince SPK is = 60 Degrees: Hence the whole Angle PSH

d

will be 533 therefore the Pofition of the Tranfverfe Axis, and confequently of the whole Figure, is known. Laftly, that the Periodic Time may be known, it's to be confidered, that the Periodic Time in the Orbit pq b · above found is 1: 24: 26 or 5066, which Number fquared produces 25664756; I fay then, As the Cube of the Semi-Tranfverfe Axis of the Orbit pq (1) is to the Cube of the Semi-Tranfverfe Axis of the Orbit PQ in round Numbers (875.) So is the Square of the Periodic Time in the Orbit pq (25664756) To the Square of the Periodic Time in the Orbit PQ= 20916450140. The Square

Root of which gives 144631. for the Periodic Time in d b the Orbit PQ, which reduced is = 1:16:10: 31.

2. E. J.

New

I

New ÉNIGMAS to be answered.

(1.) ENIGMA the 17th, by Live beneath the tow'ring Height Of Etna's flaming Head, the Circle of the Globe, Earth's Centre is my Bed:

I

ran ge

I give the sweetness to the Grape,
I paint the Violet blue,

1 caufe the Diamond to fhine,
And I diftill the Dew:

I thaw the frozen Alps, and throw
The flowing Rivers down,

I make the mighty Mountains quake,
And hurl them on the Town:
The Thund'ring Cannons I discharge,
I burft the Sable Cloud,

I make the dreadful Lightnings flash,
And Thunder roar aloud :

I make the Springs afcend the Hills,
I cloath the Vales below,

I give to ev'ry Beast its Food,
I make the Rivers flow.

Towns, Fields and Forefts I deftroy
By my avenging Power,

For when my Fury I exert,
proves a fatal Hour,

It

I tear up Mountains by the Roots,
I raise the Vallies high,

I penetrate beneath the Sea,

I drink the Rivers dry :

In the laft Scene I'll act my Part,

With Nature I begun,

I'll bear an univerfal Sway

E'er yet my Race be run.

(2.) ENIGMA the 18th, by I, H, M.

EST mihi parva Domus felidis circumdata Muris,
Tale fed rs Caftrum condere dota nequit ;
Turus in hac latitans, plaeidis indulgeo Somnis,
Nec minuunt Vires Tempora Longa meas;

D 2

Solares

Solares Eftus, concretaque Frigora sperno,
Imbre licet Niveo fæva Procella ruat.
Hic torpens requiefco, Oculis non Vifus acutis,
Ferrea dum fubitam dant mihi Tela fugam
Protinus, in Lucem productus, pabula pofco,
Quers fi non potiar, langueo Morte cità.
Donec adhuc Mundus primevo flore juvente
Gaudebat, Genti cuique benignus eram,
Vera tamen fateor, quod pofterioribus annis,
Belli fanguineis Artibus arma dedi,

Si mihi quid nomen, que fit quoque manfio certa,
Tu bene conjicias, OEdipus alter eris.

(3.) The above ENIGMA tranflated.
Ithin a clofe compacted Citadel,

WIthin

Surpaffing all that Art can boaft, I dwell:
And whilft of fuch a ftrong Defence poffeft,
Secure from all furrounding Dangers reft.
The keen Affaults of Heat and Froft defy,
Nor fear the Rage of a tempeftuous Sky:
Here, I in Silence fleep my Time away,
Nor will my Native Properties decay,
Though I fhould reach the Years of old Methuselah.
In this unactive State I muft remain,
Till force of Arms my Liberty obtain ;
Then I like One by fudden Fright awake,
With nimble Speed my drowfy Bed forfake.
The very Moment I am brought to Light,
I have a moft impatient Appetite :

And if the Food, my Nature does require
Should be deny'd, I inftantly expire;
By Providence I feem'd at first defign'd,
A publick Benefit to Human kind;
But of late Years, have had a guilty Share
In the destructive Miseries of War.

Pray tell my Name, and Place of my Abode,
And I your Wit, (fair Ladies) will applaud."
(4.) ENIGMA the 20th, by OEdipus Eboracenfis.
W Her
Here Politenefs prevail'd, I feldom e'er fail'd
A juft Veneration to claim ;
Yet, who was my Father, 'tis doubtful to gather
From all the beft Records of Fame.

Upon

Upon a Review, 'tis probably true,

That to the old World I was known

"

But in Procefs of Time, Men of Genius fublime,
Entail'd on my Merit a Crown.

Scarce a beautiful Part, of Nature or Art,
But of my fweet Bounty hath tafted;
And to my Difgrace) on Things vile and base,
My Treafure has often been wafted.

Drefs'd in modifh Fashion, a great Reputation
With Perfons of Honour 1 gain;

And of this can glory, that both Whig and Tory,
My Interest help to maintain :

But although I find Entertainment fo kind
Amongst both the Learned and Great,

I free trom all Pride) condefcend to refide
With fome of interior State.

By Night or by Day, when my Temper is gay,
To Pleafure and Mirth I excite;

But fpiteful do prove, if mine Anger you move,
And often moft cruelly bite.

A virtuous Saint, I fo lovely can paint,
That I feem of Extraction divine;

But at certain Times, the lewdeft of Crimes,
To propagate bafely incline:

To Myft'ries prophetick, in Language pathetick,
I formerly made a Pretence;

But in thefe wifer Days, fuch Kind of Effays,
Are ridicul'd by Men of Senfe.

N°

(5.) ENIGMA the 21ft, by J. H. M.

Wonder that, in Countries, where the Prince.
With uncontrouled Power his Scepter fways,
Th' unhappy Subjects (tripp'd of all Defence)
In painful Hardfhips linger out their Days.
But I, a Native of the British Inle,

Where Liberty and Property abound,
Though guilty of no Injury or Guile,
Have yet the most inhuman Ufage found.
My Publick Service, and Majeftick Form,
For Favour and Compaffion loudly call;
Yet, like an ufelefs defpicable Worm,

To barb'rous Mirth a Sacrifice I fall :

The