92 NEWTON S PRINCIPIA. 



the proportion above shown to belong to a progression 

 of the apsides, equal to 3 in a revolution. In like 

 manner the orbit &quot;of the earth is not immoveable, owing 

 to the disturbing forces of the larger planets, Jupiter, 

 Saturn, Mars, and Venus. But the disturbance here is, 

 of course, incomparably more minute. The apsides of 

 the earth s orbit only move 11&quot; 53 &quot; in the year, instead 

 of 39 ; and the expression for the centripetal force is there 

 fore, as we have seen above, the inverse not of d^ 9 but 

 of d 2 6oso&amp;lt;j. The axis of the earth s orbit thus revolves in a 

 period of about 109,060 years. 



It is, however, to be observed that, although this motion 

 of the axis of the earth s orbit is the result of the theory 

 of gravitation, and indeed affords a new proof of it, Sir 

 Isaac Newton did not himself consider it as worthy of 

 attention. He regarded it as indicating so very minute 

 a deviation from the law of the inverse square of the 

 distance, as not to alter sensibly the form and position 

 of the orbits resulting from thence. He therefore did 

 not give any calculation respecting it. To say that he 

 was ignorant of it, or that he affirmed the absolute 

 quiescence of the planetary apsides, as some have done *, 

 is wholly erroneous. The statements and methods in 

 the Forty-fifth proposition and its corollaries are quite 

 general, applying to all bodies acted on by disturbing 

 forces ; so is the Sixty-seventh, with the Sixth, Seventh, 

 and Eighth corollaries, of general application ; and even 

 in the proposition (the Fourteenth of the Third book) in 

 which he affirms that the aphelia and nodes of the orbits 

 are at rest, he refers to inequalities arising from dis 

 turbing forces, while in the scholium that immediately 

 follows he expressly states the motion of the aphelion of 



* Bailly, Hist. Ast. torn. ii. 



