ASTRONOMY. 
titn. The difference of the sun’s attraction, 
therefore, on the sides of the earth under 
and opposite to him, will be much less than 
the difference of the moon’s attraction on 
the sides of the earth under and opposite to 
her; and for this reason, the moon must 
raise the tides much higher than they can 
be raised by the sun. Newton calculated 
the effect of the sun’s influence in this case, 
and found that it is about three times less 
than that of the moon. The action of the 
sun alone would therefore be sufficient to 
produce a flux and reflux of the sea ; blit 
the elevations and depressions occasioned 
by this means would be about three times 
less than those produced by the moon. The 
tides, then, are not the sole production of 
the moon, but of the joint forces of the sun 
and moon together : or, properly speaking, 
there are two tides, a solar one, and a lunar 
one ; which have a joint or opposite effect, 
according to the situation of the bodies 
which produce them. When the actions of 
the sun and moon conspire together, as at 
the time of new and full moon, the flux and 
reflux become more considerable; and in 
this case they are called the spring tides. 
But when one tends to elevate the waters, 
whilst the other depresses them, as at the 
moon's first and third quarters, the effect will 
be exactly the contrary ; the flux and re- 
flux, instead of being augmented as before, 
will now be diminished ; and they are then 
called the neap tides. But as this is a matter 
of some importance, it may be worth while to 
enter into a more minute explanation of it. 
For this purpose, let S (fig. 5) represent 
the sun, ZHNR the earth, and FC the 
moon at her full and change. Then, be- 
cause the sun S, and the moon C, are nearly 
in the same right line with the centre of the 
earth O, their actions will conspire toge- 
ther, and raise the water about the zenith Z, 
or the point immediately under them, to a 
greater height than if only one of these 
forces acted alone. But it has been shewn, 
that when the ocean is elevated at the ze- 
nith Z, it is also elevated at the opposite 
point, or nadir, N, at the same time ; and, 
therefore, in this situation of the sun and 
moon, the tides will be augmented. Again, 
whilst the full moon F raises the waters at 
N and Z, directly under and opposite to 
her, the sun, S, acting in the same right line, 
will also raise the waters at the same points, 
Z and N, directly under and opposite to 
him; and therefore, in this situation also, 
the tides will be augmented; their joint ef- 
fect being nearly the same at the change as 
at the full ; and in both cases they occasion 
What are called the spring tides. Pursuing 
the illustration in the same way, let now F 
and T (fig. 6) be the moon in her first and 
third quarters, and the rest as before. 
Then, since the sun and moon act in the 
right lines S H and F T, which are nearly 
perpendicular to each other, their forces 
will tend to produce contrary effects ; be- 
cause the one raises the waters in that part 
where the other depresses them. The sun’s 
attraction at R and H, will diminish the ef- 
fect of the moon’s attraction at Z and N ; 
so that the waters will rise a little at the 
points under and opposite to the sun, and 
fall as much at the points under and oppo- 
site to the moon ; and of course the lunar 
tides will be diminished in those parts. This 
respects the moon only in her first quarter, 
at F ; but the same reasoning will evidently 
hold, when applied to the moon in her third 
quarter at T ; for as the sun and moon still 
act in lines which are perpendicular to each 
other, they must produce the same diminu- 
tion as before ; and in both these cases they 
occasion what are called the neap tides. But it 
must be observed, that neither the spring nor 
neap tides happen when the sun and moon 
have the precise situations here mentioned ; 
because, in this case, as in others of a simi- 
lar kind, the actions do not produce the 
greatest effect when they are the strongest, 
but some time afterwards. The effects of 
the disturbing forces of the sun and moon, 
depend likewise upon their respective dis- 
tances from tire earth, as well as upon their 
particular situations. For the less the dis- 
tances are, the greater will be their effects ; 
and, consequently, in winter, when the sun 
is nearer to the earth, the spring tides will 
be greater than in summer, when he is far- 
ther off; and the neap tides, on that ac- 
count, will be less. For a like reason, as 
the moon moves in an elliptical orbit round 
the earth, and is nearer to us at some times 
than at others, the tides will at those times 
be greater, and at the opposite points of 
her orbit, less. Some variations like- 
wise take plaee in consequence of the dif- 
ferent declinations of the sun and moon at 
different times. For if either of these lumi- 
naries were at the pole, it w'ould occasion a 
constant elevation both there and at the op- 
posite one, and a constant depression at the 
equator ; so that as the sun and moon gra- 
dually decline from the equator, they lose 
their effect, and the tides become less ; and 
when they are both in the equator, the tides 
of course become greater. 
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