gain diminish. Thus
the angle contained between the two planes will perpetually oscillate
within certain limits. The extent of variation is inconsiderable.
Laplace found that, in consequence of the spheroidal figure of the
earth, it is even less than it would otherwise have been. This will be
readily understood, when we state that the disturbing action of the sun
and moon upon the terrestrial spheroid produces an oscillation of the
earth's axis which occasions a periodic variation of the obliquity of
the ecliptic. Now, as the plane of the ecliptic approaches the equator,
the mean disturbing action of the sun and moon upon the redundant matter
accumulated around the latter will undergo a corresponding variation,
and hence will arise an inconceivably slow movement of the plane of the
equator, which will necessarily affect the obliquity of the ecliptic.
Laplace found that if it were not for this cause, the obliquity of the
ecliptic would oscillate to the extent of 4 deg. 53' 33" on each side of a
mean value, but that when the movements of both planes are taken into
account, the extent of oscillation is reduced to 1 deg. 33' 45".

_Variation of the length of the tropical year._--The disturbing action
of the sun and moon upon the terrestrial spheroid occasions a continual
_regression_ of the equinoctial points, and hence arises the distinction
between the sidereal and tropical year. The effect is modified in a
small degree by the variation of the plane of the ecliptic, which tends
to produce a _progression_ of the equinoxes. If the movement of the
equinoctial points arising from these combined causes was uniform, the
length of the tropical year would be manifestly invariable. Theory,
however, indicates that for ages past the rate of regression has been
slowly increasing, and, consequently, the length of the tropical year
has been gradually diminishing. The rate of diminution is exceedingly
small. Laplace found that it amounts to somewhat less than half a second
in a century. Consequently, the length of the tropical year is now about
ten seconds less than it was in the time of Hipparchus.

_Limits of variation of the tropical year modified by the disturbing
action of the sun and moon upon the terrestrial spheroid._--The tropical
year will not continue indefinitely to diminish in length. When it has
once attained a certain minimum value, it will then increase until
finally having attained an extreme value in the opposite direc