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 

 51' 30". 



Limits of the obliquity of the ecliptic modified by the. action 

 of the sun and moon upon the terrestrial spheroid. The eclip- 

 tic 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 53' 

 33" 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' 45". 



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 



