astro 
their orbits remain und'fturbed, it is manifeft that the 
fyftem can never be deftroyed, all the irregularities being 
periodical, and confined to ftich Small limits as to produce 
no inconvenience. Thefe are circumftances which furnifh 
great matter for our attention ; the liability of the fyftem 
thews the power and wifdom of the framer. 
Of the Phases of the Moon. 
As the Moon revolves round the Earth in a much fmaller 
orbit than that in which the Earth revolves round the Sun, 
fometiir.es more, fometimes Id's, and fometimes no part, 
of her enlightened half will be towards us ; hence fhe is 
incefiantly varying her appearance ; fometimes fhe looks 
full upon us, and her vifage is all luftre; fometimes fhe 
fhews’only half her enlightened face, foon fhe appears as 
a radiant crefcent, in a little time all her brightnel's va- 
ni flies, and.the becomes a beanilefs orb. The full Moon, 
or oppofition, is that (fate in which her whole difk is en¬ 
lightened, and we fee it all bright, and of a circular figure. 
The new Moon is w hen fhe is in conjunction v\ ith the Sun; 
in this (late, the whole furface turned towards us is dark, 
and is therefore invifible to us. The firft quarter of the 
Moon fhe appears in the form of a femicircle, whofe cir¬ 
cumference is turned towards the weft. At the laft quar¬ 
ter flie appears again under tire form of a femicircle, but 
with the circumference turned towards the eaft. Thefe 
phafe'f may be illuflrated in a very pleafing manner, by 
expofingan ivory ball to the Sun, in a variety of pofitions, 
by which it may prefent a greater or fmaller part of its 
illuminated furface to the oblerver. If it be held nearly 
in oppolition, fo that the eye of rlie obfervet be almoft 
immediately between it and the Sun, the greateft part of 
the enlightened fide will be feen ; but if it be moved in a 
circular orbit, towards the Sun, the vifible enliglr ened 
part will gradually decreafe, and at laft difappear, w hen 
the ball is held direCtly towards the Sun. Or to apply the 
experiment more immediately to cur purpofe ; it the ball, 
at any time when the Sun and Moon are both vifible, be 
held direCtly between the eye of the oblerver and the 
Moon, that part of the bail on w hich the Sun (bines, will 
appear exactly of the fame figure as the' Moon itfelf. 
The pbafes of the Moon, like thofe of Venus, may alfo 
be illuftrated by a diagram ; thus, in Jig. 2, of the Aftro- 
nomical-Plate IV. let S reprefent the Sun, T the Earth, 
and ABCD, &c. the Moon’s orbit. Now, w hen the Moon 
is at A, in conjunction with the Sun S, her dark fide be¬ 
ing entirely towards the Earth, flie will be invisible, as at 
c, and is then called the new Moon. When (he comes to 
her firft octant at B, or has run through the eighth part of 
her orbit, a quarter of her enlightened hemifphere w ill be 
turned towards the Earth, and flie will then appear horned, 
as at b. When fhe has run through the quarter of her or¬ 
bit, and arrived at C, flie (hews us the half of her enlight¬ 
ened hemifphere; as at c, when it is faid fhe is one half full. 
At D file is in her fecond off ant, and, by (hewing us more 
of her enlightened hemifphere than at C, fhe appears gib¬ 
bous, as at d. At her oppofition at E, her whole en¬ 
lightened fide is turned towards the Earth, when fhe ap¬ 
pears round, as at e, and fhe is faid to be full ; having in¬ 
creased all the way round from A to E. On the other fide 
fhe decreafes again all the way from E-to A : thus, in her 
third oCtant at F, part of her dark fide being turned to¬ 
wards the Earth, fhe again appears gibbous, as at f. At 
G (lie appears (till farther decreafed, (hewing again juft 
one half of her illuminated fide, as at g. But when (lie 
comes to her fourth oCtant at H, fhe prefents only a quar¬ 
ter of her enlightened hemifphere, and fhe again appears 
horned, as at h. And at A, having now completed her 
courfe, fhe again difappears or becomes a new Moon again, 
as at firft. 
As the Moon, by reflected light from the Sun, illumi¬ 
nates the Earth, fo the Earth does more than repay her 
kindnefs, in enlightning the furface of the Moon, by the 
Sun’s reflex light, which fhe diffufes more abundantly upon 
the Moon, than the Moon does upon us j for the Surface 
N O M Y. 37f 
of the Earth is confiderably greater than that of the Moon, 
and consequently, if botli bodies reflect light in proportion 
to their fize, the Earth will refleCt much more light upon 
the Moon, than it receives from it. In the new Moon, 
the illuminated fide of the Earth is fully turned towards 
the Moon, and the Lunarians wall have a full Earth, as 
we, in a ftmilar pofition, have a full Moon. And from 
thence arifes that dirn light which is obferved in the old 
and new Moons, whereby, befldes the bright and (hilling 
horns, we can perceive the reft of her body behind them, 
though but dark and obfeure. Now, when the Moon 
conies to be in oppofition to the Sun, the Earth, feen from 
the Moon, will apper in conjunction with him, and its 
dark fide will be turned towards the Moon, in which po¬ 
fition the Earth will be invifible to the Lunarians; after 
t'nis, the Earth will appear to them as a crefcent. In a 
word, the Earth exhibits the fame appearance to the in¬ 
habitants of the Moon, as the Moon does tons. 
To determine the periodical and fynodical months, or 
the period of the Moon’s revolution about the Earth, and 
the period between one oppofition or conjunction and ano¬ 
ther, obferveas follows : in the middle of a lunar eclipfe, 
the Moon is in oppofition to the Sun : compute therefore 
the time between two fuch eclipfes, at Some considerable 
diftance of time from each other ; and divide this by the 
number of lunations that have palled in the mean time j 
fo Shall the quotient be the quantity of the fynodical month. 
Compute alfo the Sun’s mean motion during the time.of 
this fynodical month, which add to 360°. Then, as the 
fum is to 360°, fo is the fynodical to the periodical month. 
For example, Copernicus obferved two eclipfes of the 
Moon, the one at Rome on November 6, 1500, at twelve 
at night, and the other at Cracow on Auguft 1, 1523, at 
4I1 25'. the difference of meridians being oh. 29' hence the 
quantity of the fynodical month is thus determined : 
2d Observation i 5 My 237b. 4-h. 25m, 
ift Obfervation 1500 310 o 29 
Difference 22 292 3 5.6 
Add intercalary days 5 
Exa6t interval 
22 297 3 56 
which divided by 282, the number of lunar.ons in that 
time, gives the fynodical month 29b. 12I1. 4ifn. 
f rom two other obfervations of ecliples, the one at Cra¬ 
cow', the other at Babylon, the fame author determines 
more accurately the quantity of the fynodical month to be 
29d. 1 ah. 43m. &c. and from other obfervations, probably 
more accurate (till, the fame is fixed at 29d. 12I1. 44m., 
The Sun’s mean motion in that time 29°6' 24" 18''', add¬ 
ed to 360°, gives the Moon’s motion 339° 6' 24" 18"'; there¬ 
fore the periodical month is 2;d. 7b. 43'. 5". 
According to the obfervations of Kepler, the mean fy¬ 
nodical month is 29b. 12h.-4.4T 3''. 2'", and the mean pe¬ 
riodical month 27d. 7I1. 43’. 8". 
Hence, 1, the quantity of the periodical month being 1 
given, by the Rule of Three are found the Moon’s diurnal 
or horary motion, &c. and thus may tables of the mean 
motion of the Moon he conftruCted. 2. If the mean di¬ 
urnal motion of the Sun be Subtracted from that of the 
Moon, the remainder will give the Moon’s diurnal motion 
from tiie Sun : and thus may a table of this motion be 
conftructed. 3. Since the Moon is in the node at the 
time of a total eclipfe, if the Sun’s place be found for 
that time, and fix Signs be added to the fame, the Sum 
will give the place of that node. 4. By comparing the- 
ancient obfervations with the modern, it appears, that the 
nodes have a motion, and that they proceed in antece¬ 
dents, or backwards from Taurus to Aries, from Aries 
to Pifces, &c. Therefore if the diurnal motion of the 
nodes be added to the Moon’s diurnal motion, the fum will 
be the motion of the Moon from the node ; and thence 
by the Rule of Three, may be found in what time the 
Moon goes 360° from the Dragon’s Head, or afeending 
node, or in what time fhe goes from, and returns to it ; 
that is, the quantity of the Dracontie month. 5. If the 
? motion. 
