SECT. III. VARIATION IN EXCENTRICITY. 17 



which is direct in all the orbits except that of the planet Venus, 

 is irregular, and so slow that it requires more than 109,830 

 years for the major axis of the earth's orbit to accomplish a 

 sidereal revolution (N. 68), that is, to return to the same stars ; 

 and 20,984 years to complete its tropical revolution (N. 69), or 

 to return to the same equinox. The difference between these 

 two periods arises from a retrograde motion in the equinoctial 

 point, which meets the advancing axis before 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 22,748 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 excen- 

 tricity arises from the same cause that occasions the motion of 

 the apsides (N. 67). There is an inseparable connection between 

 these two elements : they vary simultaneously, and have the 

 same period ; so that, whilst the major axis revolves in an im- 

 mense 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 excen- 

 tricity is decreasing at the rate of about 40 miles annually ; 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 esti- 

 mated, the cycle would extend to millions of years. 



