VARIATION OF THE TROPICAL YEAR. 371 



progression of the equinoxes. If the movement of the equi- 

 noctial points arising from these combined causes was uniform, 

 the length of the tropical year would be manifestly invaria- 

 ble. 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 diminish- 

 ing. 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 Hip- 

 parchus. 



Limits of variation of the tropical year modified by the dis- 

 turbing action of the sun and moon upon the terrestrial sphe- 

 roid. The tropical year will not continue indefinitely to di- 

 minish in leno-th. When it has once attained a certain mini- 



O 



mum value, it will then increase until finally having attained an 

 extreme value in the opposite direction, it will again begin to 

 diminish, and thus it will perpetually oscillate between certain 

 fixed limits. Laplace found that the extent to which the tropi- 

 cal year is liable to vary from this cause, amounts to thirty-eight 

 seconds. If it were not for the effect produced upon the 

 inclination of the equator to the ecliptic by the mean disturb- 

 ing action of the sun and moon upon the terrestrial spheroid, 

 the extent of variation would amount to 162 seconds. 



Motion of the perihelion of the terrestrial orbit. The major 

 axis of the orbit of each planet is in a state of continual move- 

 ment from the disturbing action of the other planets. In some 

 cases, it makes the complete tour of the heavens ; in others, it 

 merely oscillates around a mean position. In the case of the 

 earth's orbit, the perihelion is slowly advancing in the same 

 direction as that in which all the planets are revolving around 

 the sun. The alteration of its position with respect to the stars 

 amounts to about 11" in a year, but since the equinox is 

 regressing in the opposite direction at the rate of 50" in a 

 year, the whole annual variation of the longitude of the ter- 

 restrial perihelion amounts to 61". Laplace has considered 

 two remarkable epochs in connection with this fact ; viz : the 



