PROGRESSIVE EFFECTS. 35 



by the amount and direction of the motion, and the amount 

 and direction of the sun's action, at the previous instant : and 

 if we speak of the entire revolution of the planet as one pheno- 

 menon (which, as it is periodical and similar to itself, we often 

 find it convenient to do,) that phenomenon is the progressive 

 effect of two permanent and progressive causes, the central 

 force and the acquired motion. Those causes happening to 

 be progressive in the particular way which is called periodical, 

 the effect necessarily is so too ; because the quantities to be 

 added together returning in a regular order, the same sums 

 must also regularly return. 



This example is worthy of consideration also in another 

 respect. Though the causes themselves are permanent, and 

 independent of all conditions known to us, the changes which 

 take place in the quantities and relations of the causes are 

 actually caused by the periodical changes in the effects. The 

 causes, as they exist at any moment, having produced a certain 

 motion, that motion, becoming itself a cause, reacts upon the 

 causes, and produces a change in them. By altering the dis- 

 tance and direction of the central body relatively to the planet, 

 and the direction and quantity of the force in the direction of 

 the tangent, 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 re- 

 action upon the causes, renders the next motion again 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 beep 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 con- 

 tinue to recur again and again in the same periodical order, 



32 



