I/O' 
' vom the centre, that the same conjunction 
which pives a total eclipse at one place, shall 
not occasion the Smallest obscuration of the 
Sun when beheld at the same instant from 
another part of the Earth, 
W e are now to consider an eclipse of the 
Moon. It is evident, that the difference in 
the phenomena of a solar eclipse would not 
take place it the parallax of each luminary 
were the same ; because, whatever mutation 
ot place the parallax might occasion in the 
one, the same would be produced in the 
other, and they would neither approach nor 
recede from each other on that account, 
Mow the section of the Earth’s shadow passed 
through by the Moon in a lunar eclipse, 
being at the same distance from the Earth as 
the Moon itself, must be subject to the same 
parallax at equal altitudes ; and since the in- 
dividual points of immersion, emersion, or 
other periods of the eclipse, must in the sha- 
dow have- the same altitudes as the parts of 
the Moon they, as it were, lie on and obscure, 
the effects of parallax must be the same on 
both. Rejecting, therefore, the consideration 
of parallax, the Earth’s shadow A B (fig. 16) 
may be taken to occupy a place in the hea- 
vens diametrically opposite to the Sun, and 
having an equal and similar motion to the ap- 
parent motion of that luminary : its apparent 
diameter, seen from the Earth, will be equal 
to the difference between the apparent dia- 
meters of the Earth and Sun, as seen from the 
moon ; or it will be equal to twice the hori- 
zontal parallax of the Moon, diminished by the 
subtraction ot the Sun’s apparent diameter. 
And if the inclination of the orbit of the 
Moon be found, there will be a certain dis- 
tance of the node N from the centre of the 
shadow C, that will require the Moon near the 
opposition to pass through the Earth’s shadow, 
and be consequently eclipsed. From the 
greater or less distance of the node N, or M, 
it will be determined whether the eclipse will 
be partial or total ; and from the respective 
places, the quantity and direction of the rela- 
tive velocity, together with the apparent 
magnitudes of the shadow and the Moon, all 
the particulars of the eclipse may be known 
without difficulty. 
It may with great reason be demanded, 
how it happens that the Moon, which is af- 
firmed to emit no light of itself, but only by 
reflection of the Sun, is nevertheless sufficient- 
ly luminous, even in the very middle of a total 
eclipse, to be distinctly seen of a dusky red- 
dish colour. The Earth’s atmosphere, or 
body of air that surrounds it, is the cause of 
this phenomenon. In fact, the shadow of the 
Earth itself never extends so far as the 
Moon’s orbit ; though the shadow occasioned 
by the dispersion or reflection of the light that 
falls on tlie atmosphere may, with a very 
small allowance, be taken for the shadow 
which the Earth would have had if the light 
had passed close by it without interruption. 
We cannot with regularity explain the refrac- 
tion of light in this place. It will therefore 
be sufficient to observe, that in the event now 
under consideration the Sun’s light falling 
obliquely on the atmosphere, is bent or turn- 
ed out of its course, so as to converge sooner 
to a point than it would otherwise have done ; 
the spherical atmosphere performing, in some 
measure, the office of a large convex lens, or 
burning-glass. The more obliquely the rays 
fall, the greater is their deviation from their 
astronomy. 
original course ; and those rays that pass close 
to the Earth are found, by observations on the 
setting Sun and other heavenly bodies, to suf- 
fer a refraction of about 33 minutes of mea- 
sure. 1 he laws' 1 of optics, hereafter to be ex- 
plained, require that they should undergo an 
equal refraction in passing out through the 
opposite part of the atmosphere. Each ex- 
terior ray of the real shadow, will therefore 
pass 66 minutes within the rays that would 
have formed the cone CKD, fig. 13. and con- 
sequently, the angle at the vertex of the cone 
will be 132 minutes, or 2° 12', greater than it 
would have been ; that is, it will be equal to 
the diameter of the Sun 32, added to 2° 12', 
which gives 2°. 44b Hence the axis of the 
cone, or length of the shadow, is found to be 
no more than 42 semidiameters of the Earth ; 
whereas the radius of the Moon’s orbit, or 
mean distance of the Moon, is about 60 se- 
midiameters of the Earth. In the space be- 
tween the penumbra and the Earth’s real 
shadow, it is much darker than the penumbra, 
though that space is illuminated by the rays of 
the Sun ; which are variously refracted, ac- 
cording to the density of the air they pass 
through. Many rays are reflected back, and 
the rays that go forward are such whose na- 
ture does riot admit of their being easily re- 
flected. Hence it is that the Moon in an 
eclipse appears red ; and a spectator on the 
Moon would, after losing sight of the Sun, 
behold the Earth environed with a narrow 
luminous edge of bright red light, shaded off 
with yellow on the outside. 
Of the Tides. 
The first person who clearly pointed out 
the cause of the tides, and shewed its 
agreement with the effects, was sir Isaac 
Newton. The Moon he presently saw was 
the principal agent which produces these 
motions of the waters ; and, by applying his 
new principles of geometry and attraction, 
he soon shewed the manner in which they are 
effected. To follow him through all his cal- 
culations and enquiries, would carry us beyond 
our limits. 
The ocean, it is well known, covers more 
than one half the globe ; and this large body 
of water is found to be in continual motion, 
ebbing and flowing alternately, without the 
least intermission. For instance, if tin* tide is 
now at high water mark, in any port or har- 
bour which lies open to the ocean, it will pre- 
sently subside, and flow regularly back for 
about six hours, when it will be found at low 
water mark. After this, it will again gradu- 
ally advance for six hours ; and then return 
back, in the same time, to its former situation, 
rising and falling alternately twice a day, or in 
the space of about twenty-four hours. The 
interval between its flux and reflux is, how- 
ever, not precisely six hours, but there is a 
little difference in each tide ; so that the time 
of high water does not always happen at the 
same hour, but is about three quarters of an 
hour later every day, for about thirty days, 
when it again recurs as before. For example, 
if it is high water to-day at noon, it will be 
low water at eleven minutes after six in the 
evening ; and, consequently, after two changes 
more, the time of high water the next day 
will be at about three quarters of an hour 
after noon ; the day following it will be at 
about half an hour after one, the day after 
that at a quarter past two, and so on for 
thirty days ; when if will again be found to 
be high water at noon, as on the day the ob- 
servation was first made. And this exactly 
answers to the motion of the moon : she rises 
every day about three quarters of an hour 
later than upon the preceding one; and, by 
moving in this manner round the earth, com- 
pletes her revolution in about thirty days, and 
theft begins to rise again at the same time as 
before. 
To make the matter still plainer ; suppose, 
at a certain place, it is high water at three 
o’clock in the afternoon, upon the day of the 
new moon ; the following day it will be high 
water at three quarters of an hour after three ; 
the day after that at half an hour past four ; 
and so on till the next new moon, when it 
will again be high water exactly at three 
o’clock, as before. And by observing the 
tides continually at the same place, they will 
always be found to follow the same rule ; 
the time of high water, upon the day of every 
new moon, being exactly at the same hour ; 
and three quarters of an hour later every suc- 
ceeding day. 
The nature of the tides is in such exact con- 
formity with the motion of the Moon, that, 
independant of all mathematical considera- 
tions, a considerate person would certainly be 
induced to look to her as their cause. 
Neglecting therefore, for the present, all 
such exceptions as affect not the truth of the 
theory, we shall now proceed to shew, from 
the Newtonian principles, that these pheno- 
mena are occasioned principally by the 
Moon’s attraction. 
The waters at Z on the side of the earth, 
ABCDEFGtl, next the Moon M, (fig. 17) 
are more attracted than the central parts of 
the earth O by the Moon, and the central 
parts are more attracted by her than the 
waters on the opposite side of the earth at n ; 
and therefore the distance between the earth’s 
centre and the waters on its surface under 
and opposite to the Moon will be increased. 
For, let there be three bodies at H, O, and D ; 
if they are all equally attracted by the body 
M, they will all move equally fast towards it, 
their mutual distances from each other con- 
tinuing the same. If the attraction of M is 
unequal, then that body which is most strong- 
ly attracted will move fastest, and this will 
increase its distance from the other body. M 
will attract H more strongly than it does O, 
by which the distance between Ii and O will 
be increased, and a spectator on O will per- 
ceive H rising higher toward Z. In like 
manner, O being more strongly attracted than 
D, it will move farther towards M than D 
does ; consequently the distance between O 
and D will be increased ; and a spectator on 
O, not perceiving his own motion, will see D 
receding farther from him towards n ; all ef- 
fects and appearances being the same, whether 
D recedes from O, or O from D. 
Suppose now there is a number of bodies, 
as A, B, C, D, E, F, G, IT, placed round O, 
so as to form a flexible or fluid ring : then, as 
the whole is attracted towards M, the parts 
at H and D will have their distance from O 
increased ; whilst the parts at B and F being 
nearly at the same distance from M as O is, 
these parts will not recede from one another ; 
but rather by the oblique attraction of M, 
they Will approach near to O. Hence, the 
fluid ring will form itself into an ellipse 
Z n L N, whose longer axis n Q Z produced 
