SBCT. III. VARIATION LN THE ECCENTRICITY. 17 



two periods arises from a retrograde motion in the 

 equinoctial point, which meets the advancing axis be- 

 fore it has completed its revolution with regard to the 

 stars. The major axis of Jupiter's orbit requires no 

 less than 200,610 years to perform its sidereal revolution, 

 and 22,743 years to accomplish its tropical revolution 

 from the disturbing action of Saturn alone. 



A variation in the eccentricity of the disturbed planet's 

 orbit, is an immediate consequence of the deviation from 

 elliptical curvature, caused by the action of the dis- 

 turbing force. When the path of the body, in pro- 

 ceeding from its perihelion to its aphelion, is more curved 

 than it ought to be from the effect of the disturbing forces, 

 it falls within the elliptical orbit, the eccentricity is di- 

 minished, and the orbit becomes more nearly circular ; 

 when that curvature is less than it ought to be, the path 

 of the planet falls without its elliptical orbit (N. 66), and 

 the eccentricity is increased : during these changes, the 

 length of the major axis is not altered, the orbit only 

 bulges out, or becomes more flat (N. 70). Thus the 

 variation in the eccentricity arises from the same cause 

 that occasions the motion of the apsides (N. 67). There 

 is an inseparable connection between these two ele- 

 ments ; they vary simultaneously, and have the same 

 period ; so that while the major axis revolves in an im- 

 mense period of time, the eccentricity increases and 

 decreases by very small quantities, and at length returns 

 to its original magnitude at each revolution of the ap- 

 sides. The terrestrial eccentricity is decreasing at the 

 rate of about 40 miles annually ; and, if it were to de- 

 crease equably, it would be 39,861 years before the 

 earth's orbit became a circle. The mutual action of 

 Jupiter and Saturn occasions variations in the eccentri- 

 city of both orbits, the greatest eccentricity of Jupiter's 

 orbit corresponding to the least of Saturn's. The 

 period in which these vicissitudes are accomplished is 

 70,414 years, estimating the action of these two planets 

 alone : but if the action of all the planets were estimated, 

 the cycle would extend to millions of years. 



That part of the disturbing force is now to be con- 

 sidered which acts perpendicularly to the plane of the 

 orbit, causing periodic perturbations in latitude, secular 

 2 B2 



