124 NEWTON S PRINCIPIA. 



_ e . m 



- e f * . m&quot; . Va&quot; - &c. 



m . 



So that the eccentricities never can exceed a very small 

 quantity. 



Thus the changes which are constantly taking place in 

 the planetary orbits are confined within narrow limits; 

 and the other changes which are the consequences of this 

 alteration of the orbits, as, for instance, the acceleration 

 of the moon which we before showed arose from the varia 

 tion of the eccentricity of the earth s orbit, are equally con 

 fined within narrow limits. Those changes in the heavenly 

 paths and motions oscillate, as it were, round a given 

 middle point, from which they never depart on either 

 hand, beyond a certain small distance ; so that at the end 

 of thousands of years the whole system in each separate 

 case (each body having its own secular periods) returns to 

 the exact position in which it was when these vast succes 

 sions of ages began to roll. For similar theorems are 

 deduced with respect to other revolutions of the system, 

 whose general destiny is slow and constant change, but 

 according to fixed rules, regulated in its rate, confined 

 in its quantity, limited within bounds, and maintaining 

 during countless ages the stability of the whole universe 

 by appointed and immutable laws. 



Laplace examined in the last place the possible effects 

 upon the celestial motions of the resistance of a subtle 

 ethereal medium, and of the transmission of gravity or 

 attraction not being instantaneous, but accomplished in 

 a small period of time. The result of his analysis led 

 him to disbelieve in both these disturbing causes. He 

 found that in order to produce its known effects, the trans 

 mission of gravity, if effected in time, must be seven 



