Of the Earth and Moon

The Earth our present Habitation, you’ll find situationed in the System between the Orbit of Mars and that Venus.

The Atmosphere or fluctuating Region of all exhal’d Vapours, in its greatest Degree of Elevation or elastic Levitym is never above 60 Miles high, or in its most compress’d or dense State less than 40. Its height at any time may be found by the Solution of a right-angled Triangle, knowing the Sun’s Depression below the sensible Horizon, at the Beginning or end of the Crepusculum. (See the Earth and her Atmosphere, Tab. III.)

The Twilight generally commences, or disappears when the Sun is advanc’d within 18^deg. of the Horizon, or depress’d as much below it.

Let E represent the Sun in the Horizon at d, and 18^deg. below the Horizon of e, at which time L will be the highest Point of the Atmosphere, reflecting Light upon the Earth, and will then be in the Horizon of e; bisect the Angle eLd, and there will be given, in both the similar rectangled Triangles, the Radius of the Earth, and the Angle at g. Hence gL may easily be found, and consequently the Excess above the Earth’s surface may be known; but this Excess never continues the same, and as this changes the Angles must also vary.

And for the same Time will remain the siderial Motion, 4^min. 20^2ds. of the Aphelion.

But Sir Isaac Newton in his Principia makes this, for the same Space of Time, but 3^min. 32^2ds. or rather seems to destroy the former and produces another of 10^2ds. 36^3ds. per Annum in its stead.

The Earth’s siderial or periodical Revolution round the Sun, is perform’d in respect of the fix’d Stars,

In 365^days. 6^hours. 9^min. 14^2ds.

But the Time it takes up in passing from any one Point of the Ecliptic, and returning to the same again, which is call’d the² natural or tropical Year,

Is 365^days. 5^hours. 48^min. 57^2ds.

While——She from West, her silent Course advance,
With inoffensive Pace, that spinning sleeps
On her soft Axle.——Milton.

This, in respect of the Sun and true equal Time, is performed in 24 Hours, but with regard to the Stars, and the same equal Measure of Time in 23^h. 56^m.

The Velocity of the Earth’s equatorial Surface, is above 1000 Miles per Hour.

Sir Isaac Newton, supposing the Earth to be made originally of a fluid Matter (tho’ now condensed to a very hard Substance), from the Laws of Motion affected by the centripetal Force, proves it to be of an oblate spheroidical Figure, and by the same Principles he proves all the rest of the Planets, less or more, to put on the same Figure.

The polar Diameter he finds to be in Proportion to the equatorial one, nearly as 229 is to 230, the Difference in Miles being 17⅙. Hence the Quantity of a Degree near the Poles, will be something less than that of one at the Equator, but not sensible enough to be taken notice of, in the common Solution of geographical Problems.

The Obliquity of the Earth’s Axis, to the Plain of the Ecliptic, has been observed of late Years to be³ 66^deg. 31^m.

The Figure of the Earth being more gibbose, near the Equator, than at the Poles, is found to have occasioned a great and notable Change in the general Position of the Stars, with respect to the Circles of the Sphere; by which the equinoctial Points, which were formerly placed at or near the first Star of the Aries, have appeared to go backwards, as moving in antecedentria, and is perpetually receding at the rate of 50^2ds. 0^3ds. 40^4ths. per Year, insomuch that the Pole-star in the use at the Creation, is now removed above the 20 Degrees from its primitive Situation.⁴ This has ever been Matter of the choicest Speculation, ever since Astronomy came to any Maturity, and has always employ’d the nicest Observers, in all Ages to determine its true Quantity. But the real Cause from whence it proceeded, was never discovered till Sir Isaac Newton having found out, and solv’d a like retrograde Motion of the Moon’s Nodes took it into Consideration.

The Moon is the most irregular of all the heavenly Bodies, by reason of her Orbit daily changing its Position to the Earth, and perpetually varying its elliptical Form or Species. The Regulation of her Motion being subject to so many Irregularities arising from the Laws of Gravity or mutual Tendency fo all material Bodies, has employ’d the greatest Skill of the ablest Philosophers and the very best Astronomers to effect; which before Sir Isaac Newton’s Time was almost despair’d of, and is not compleated even now.

The greatest Distance of the Moon from the Earth, when her Orbit is near its middle State of Excentricity,

But of such Parts as her mean distance from the Earth,
Is 10,000. The other Dimensions of her Orbit is ever varying and putting on a new Figure in Proportion to the following Excentricities.

In Proportion to that of the Earth, her true Diameter, is as 100 to 365, and Mr Whiston makes it 2170 Miles.

Her mean Perigeon Shadow, in Conjunction with the Sun, her Distance from the Earth, being then about 56 Semidiameters of the Earth, and the Earth at Aphelion,

Is nearly 234,303 Miles.

The least or Apogeon Shadow is 226,374 Miles. Being then distant from the arth about 65 Semidiameters, and the Earth in Perihelion.

Her mean 230,333 Miles.

And in Opposition 231,708 in both being 60½ Semidiameters of the Earth distant from us, and the Earth at a mean Distance from the Sun.

Her mean siderial Revolution is perfored in the Space of 27^days 7^hours. 43^min.

And her mean Sinodical one in 29^d. 12^h. 44^m.

The Obliquity of her Orbit, the Nodes being Syzygia, is 5^deg. 17^min. 20^2ds.

But when the Moon is in Syzygia, and the Nodes in Quadrature, it is only 4^deg. 59^min. 35^2ds.

The Moon’s Form nearly resembles that of an Egg; the longest Axis exceeding the shorter about 186 Feet. And the easiest Way (of the many made use of) to determine the Quantity of Matter in the Moon, to that in the Earth, is as follows.

Procure two Observations of the apparent Diameter of the Sun; one at the Time of the new Moon, the other at the Full, and both are near the same Place in the Heavens as possible: Then, as the apparent Diameter of the Sun nearly increases, as the distance decreases, &c. it will be,

As the Sine of the least Angle,
Is to the known middle Distance of the Earth, from the Sun in that Point;
So is the Sine of the mean Angle, i.e. of the two Observations,
To the extream Distance fo the Earth at the same Point.

And the lesser Distance taken out of the greater, leaves the true Excentricity, or Distance of the Earth’s Center, from the common Center of Gravity of the Earth and Moon.

Now,

As the Moon’s Distance from the Earth in any part of her Orbit, from her Theory is known; and the Ratio of the Earth and Moon’s Gravity towards the Sun being, nearly, as their Distance from the common Center of Gravity inversly; the Quantity of Matter in the Earth to the Quantity of Matter in the Moon may thus be determined, i.e.

Thus the matter, in the Moon, to the Matter in the Earth, will be found nearly,

Then, the accelerating Gravity at the Moon’s Surface, being to the accelerating Gravity on the Earth’s Surface, in a Ratio compounded of the simple Ratio of the Quantity of Matter in the Moon, to the Quantity of Matter in the Earth, and the duplicate Ratio of the Semidiameter of the Earth, to the Semidiameter of the Moon; the Weight of a Body in the Moon, to the Weight of the same, or an equal Body on the Earth will be,

And the Density of the Earth to the Density of the Moon, will be

As 100 to 123.5.

The Moon having no real rotation round her own Axis, but what relatively, in respect of the Sun, proceeds from her Motion round the Earth, it follows that her Nychthemeron, or natural Day, must of Consequence, be exactly equal to her sinodical Revolution, i.e. to 29 Days, &c. The mean diurnal or nocturnal Arches, being nearly 14 Days each.

But the Obliquity of the Moon’s Orbit, to the Plain of the Ecliptic, being at a Mean 5 Degrees, there is always a constant Libration of Light, near the solar Horizon; which makes not only a small Vicissitude in the Lunar Days, to different Parts of the Moon, but likewise some material Difference in the Change of Seasons, like those of our Earth; arising from the Position of the Nodes at different ties of the Year.

This Alteration upon the Moon's Disk, view’d from the Earth, is call’d the Moon’s Libration in Latitude, and always obtends an Angle at the Moon’s Center, equal to her Distance from the Ecliptic.

Besides this, the Moon’s Orbit being excentric, with regard to the Earth, there is also a Libration of the Longitude, which would not be, if the Moon mov’d in a perfect Circle. This Change of Phænomena, by which the Moon endeavours to turn away her Face, altering the Position of the Spots upon her Disk, that are towards us, is always greatest at the Moon’s middle Distance from the Earth, and least of all, or rather none at all in the Absides, i.e. the Apogeon or Perigeon Points.

To find this, there is always given the Moon’s Excentricity, Distance, and Anomaly, and it may be determined by a Solution of the 5th Case of plain oblique Triangles.

The principal Phænomena to an Observer of the Moon, are these; our Earth always appears stationary, in point of Position and Elevation, but the Stars are altogether continually approaching her on one Side, and retiring from her on the other, ever retreating and advancing by a slow Motion equal to that of the Moon’s thro’ the Zodiac.

The Poles of the World, by a liberating Motion, alternately show themselves upon the Disk of the Earth, and the apparent Revolution of the most remarkable Kingdoms, serve the lunar Inhabitants, (if any such there be) for an horary Sun-dial.

The Earth’s apparent mean Semidiameter to the Moon,

Is 57^min. 18^2ds.

The heavenly Bodies move very slow, near the lunar Horizon, and amazingly fast near the Meridian.

The mean Velocity in her Orbit is about 2400 Miles per Hour.

The mean menstrual Parallax of her Orbit, is about 10^min. and her Globe would fall to the Earth by its natural Gravity, in about 4^d. 20^h.

The Point of Suspension, or of equal Attraction betwixt the Moon and the Earth, I make 8.27 Semidiameters of the Earth from the Moon’s Center.

1. Eratosthenes was the first who attempted the Measure of the Earth, which he ingeniously effected thus, he first made choice of two remarkable Cities, both under the same Meridian, namely Alexandria and Siene. Secondly, at the Moment he knew the Sun to be vertical to the one, he carefully observed his Zenith’s Distance at the other, which he found to be 7 Deg. 12 Min. then from their known Distance assunder, viz. 5000 Furlongs, he found the Circumference of the Earth, i.e. as 7 Deg. 12 Min. was to 5000 so was 360 Deg. to the Thing require’d (See Euclid, B. I. Prop. 27.)

   The Measure of the Earth has since been determined by many, in particular the Quantity of one Degree, which gives by Analogy the Whole;

   Dr Barnard found the Quantity of a Degree,

   • To be 73.14 English Miles.
   • To be 67.4 Catholick Miles.
   • And 66,½ Arabick Miles.

   Mr Norwood concluded, a Degree must contain

   • 69.5 Miles English, and

   Mr Picard made a Degree equal to 69\(\frac{9}{55}\) Miles, or
   To = 365,184 Feet.

2. This has ever been Matter of much Observation amongst the Astronomers, and has been variously determin’d as follows, viz.

   	D.	H.	M.	S.
   Philolaus concluded it to be	365	0	0	0
   Harpalus made it	365	12	0	0
   Democritus	365	6	9	0
   OEnopides,	365	9	0	0
   Meton,	365	6	19	0
   Calippus, Archimedes and Aristarchus	365	6	0	0
   Hipparchus and Ptolomy	365	5	55	12
   Galen	365	5	45	36
   Albategnius	365	5	57	36
   Azaphius and Avarius	365	5	49	30
   Alphonsus	365	5	48	15
   and Copernicus	365	5	47	29

   The Indians and Jews made it 365 d. 5 h. 48 m. and the Persians the same as Copernicus, from whence Massohalah his Tables of the Sun’s mean Motion. The Correctors of the old Egyptian Calendar have it 365 d. 5 h. 49 m. 11 s.

3. The Quantity of thsi Obliquity seems to have continually increased from the following Observations, made of the Sun’s greatest Declination, but how far they may be depended upon, we leave to be farther consider’d.

   	Deg.	Min.	Sec.
   Aristarchus and Aratus found it	24	0	0
   Hipparchus and Eratosthenes	23	51	30
   Ptolemy	23	51	30	Anno Dom. 140.
   Almamon King of Arabia, Machometes Aratenses, and Albategnius	23	35	0	from 740 to 900.
   Arzahel the Spaniard	23	34	0	1070.
   Almehon, Son of Albumasar	23	33	30	1140.
   Prophatius the Jew	23	32	0	1300.
   Purbachius and Regiomontanus	23	29	30	1480.

   But of later Years by Copernicus 23 deg. 28 min. 30 sec. by Tycho, 23 deg. 31 min. 30 sec. by Johannes Warneres, and P. Nonias, 23 deg. 28 min. 30 sec. by Hevelius 23 deg. 30 min. 20 sec. by Mouton and Ricciolus 23 deg. 30 sec. and by Mr De la Hire 23 deg. 29 min.

4. In the Time of Thales, 634 Years before Christ, the first Star of Aries was in 28 deg. of Pisces, and about the Year of the World 3517, it was seen by Meton, at the Beginning of Aries. Since Timocharis 300 Years before Christ, observed it in Aries, 2 deg. 24 min. and Hipparchus in which Ptolemy afterwards found to be but 3 deg. Albumasar found the first Star of Aries in 17 deg. 50 min. of Aries; Alberenus the same in 18 deg. 10 min. Arzachel in 19 deg. 37 min. Anno Dom. 1090; Alphonsus in 23 deg. 48 min. And Copernicus in 27 deg. 21 min. and from these the Procession of the Equinoxes have been determined as follows.

   • By Albategnius 1 deg. in 66 Years.
   • By VlughBeigh 1 deg. in 70 Years.

   By {

   	D.	M.	S.	T.
   Tycho	1	25	00	00
   Copernicus	1	23	40	12
   Ricciolus and Flamstead	1	23	30	00
   Street	1	20	00	00
   Bullialdus	1	24	54	00
   Hevelius	1	24	56	50

   } By 100 Years.