20 VARIATION IN THE EXCENTEICITY. [SECT. HI. 



years to perform its sidereal revolution, and 22,748 years to 

 accomplish its tropical revolution from the disturbing action 

 of Saturn alone. 



A variation in the excentricity of the disturbed planet's 

 orbit is an immediate consequence of the deviation from 

 elliptical curvature, caused by the action of the disturbing 

 force. "When the path of the body, in proceeding 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 excentricity is diminished, 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 excentricity 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 excentricity 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, whilst the major axis revolves in an immense period 

 of time, the excentricity increases and decreases by very 

 small quantities, and at length returns to its original magni- 

 tude at each revolution of the apsides. The terrestrial ex- 

 centricity is decreasing at the rate of about 40 miles an- 

 nually ; and, if it were to decrease 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 excentricity of both orbits, the greatest excentricity 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 considered 

 which acts perpendicularly to the plane of the orbit, causing 

 periodic perturbations in latitude, secular variations in the in- 



