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370 LAPLACE, 
ecliptic for the year 1100 before the Christian era, to be 
23° 54 2.5. According to the principles of the theory of 
gravitation, the obliquity for the same epoch would be 23° 
51r 300. . , 
Limits of the obliquity of the ecliptic modified by the action 
of the sun and moon upon the terrestrial spheroid.—The eclip- 
tie will not continue indefinitely to approach the equator. 
After attaining a certain limit it will then vary in the oppo- 
site direction, and the obliquity will continually increase in 
like manner as it previously diminished. Finally, the incli- 
nation of the equator and the ecliptic will attain a certain 
maximum value, and then the obliquity will again diminish. 
Thus the angle contained between the two planes will per- 
petually oscillate within certain limits. ‘The extent of varia- 
tion 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 obli- 
quity of the ecliptic. Now, as the plane of the ecliptic ap- 
proaches 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° 537 
83 on each side of a mean value, but that when the move- 
ments of both planes are taken into account, the extent of 
oscillation is reduced to 1° 33 45r. 
Variation of the length of the tropical year.—The disturbing 
action of the sun and moon upon the terrestrial spheroid occa- 
sions 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 varia- 
tion of the plane of the ecliptic, which tends to produce a 
