158 
COLLECTIONS AND RECOLLECTIONS. 
will appear to be, not an exact ellipse, but an undulated curve, like 
that represented in the figure to article 272, only that the number of 
undulations in a whole revolution is but thirteen, and the actual 
deviation from the general ellipse, which serves them as a central 
line, is comparatively very much smaller, so much so indeed, that 
every part of the curve described by either the earth or moon is con¬ 
cave towards the sun. The excursions of the earth on either side 
of the ellipse, indeed are so very small as to be hardly^appreciable. 
In fact, the centre of gravity of the earth and moon lies always with¬ 
in the surface of the earth, so that the monthly orbit described by 
the earth’s centre about the common centre of gravity is compre¬ 
hended within a space less than the size of the earth itself. The 
effect is nevertheless, sensible in producing an apparent monthly 
displacement of the sun in longitude, of a parallactic kind which is 
called the menstrual equation; whose greatest amount is, however, 
less than the sun, horizontal parallax, or than 8. 6". 
The moon, as we have seen, is about 60 radii of the earth distant 
from the centre of the latter. Its proximity, therefore, to its centre 
of attraction, thus estimated, is much greater than that of the planets 
to the sun; of which Mercury, the nearest is 84, and Ulranus 2026 
solar radii from its centre. It is owing to this proximity that the 
moon remains attached to the earth as a satellite. Were it much 
farther, the feebleness of its gravity towards the earth, would be in¬ 
adequate to produce that alternate acceleration and retardation in its 
motion about the sun, which divests it of the character of an inde¬ 
pendent planet, and keeps its movements subordinate to those of the 
earth. The one would outrun, or be left behind the other, in their 
revolutions round the sun, (by reason of Kepler’s third law,) accor¬ 
ding to the relative dimensions of their heliscentric orbits, after 
which the whole influence of the earth would be confined to produ¬ 
cing some considerable periodical disturbance in the moon’s motion, 
as it passed or was passed by it in each synodical revolution. 
At the distance at which the moon really is from us, its gravity 
towards the earth is actually less than towards the sun. That this is 
the case, appears sufficiently from what we have already stated, that 
the moon’s real path, even when between the earth and sun, is con¬ 
cave towards the latter. But it will appear still more clearly if, from 
the known periodic times in which the earth completes its annual 
and the moon its monthly orbit, and from the dimensions of those 
orbits, we calculate the amount of deflection, in either, from their 
tangents, in equal very minute portions of time, as one second. 
