38 INDUCTION. 



causes, as they exist at any moment, having produced 

 a certain motion, that motion, becoming itself a 

 cause, reacts on the causes, and produces a change 

 in them. By altering the distance and direction of 

 the central body relatively to the planet, and the 

 direction and quantity of the tangential force, it alters 

 the elements which determine the motion at the next 

 succeeding instant. This change renders the next 

 motion somewhat different ; and this difference, by a 

 fresh reaction upon the causes, renders the next 

 motion still more different, and so on. The original 

 state of the causes might have been such, that this 

 series of actions modified by reactions would not 

 have been periodical. The sun's action, and the 

 original impelling force, might have been in such a 

 ratio to one another, that the reaction of the effect 

 would have been such as to alter the causes more and 

 more, without ever bringing them back to what they 

 were at any former time. The planet would then 

 have moved in a parabola, or an hyperbola, curves 

 not returning into themselves. The quantities of the 

 two forces were, however, originally such, that the 

 successive reactions of the effect bring back the causes, 

 after a certain time, to what they were before ; and 

 from that time all the variations continue to recur 

 again and again in the same periodical order, and 

 must so continue while the causes subsist and are 

 not counteracted. 



$ 3. In all cases of progressive effects, whether 

 arising from the accumulation of an unchanging or of 

 changing elements, there is an uniformity of succes- 

 sion not merely between the cause and the effect, but 

 between the first stages of the effect and its subsequent 

 stages. That a body in vacua falls sixteen feet in the 



