PROGRESSIVE EFFECTS. 



337 



(which, as it is periodical and similar 

 to itself, we often find it convenient 

 to do,) that phenomenon is the pro- 

 gressive 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 regu- 

 larly return. 



This example is worthy of con- 

 sideration 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 actu- 

 ally caused by the periodical changes 

 in the effects. The causes, as they 

 exist at any moment, having produced 

 a certain motion, that motion, be- 

 coming itself a cause, reacts upon 

 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 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 reaction 

 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 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 suc- 



cessive 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 con- 

 tinue while the causes subsist and are 

 not counteracted. 



§ 3. In all cases of progressive 

 effects, whether arising from the 

 accumulation of unchanging or of 

 changing elements, there is an uni- 

 formity of succession not merely be- 

 tween the cause and the effect, but 

 between the first stages of the effect 

 and its subsequent stages. That a 

 body in vacuo falls sixteen feet in the 

 first second, forty -eight in the second, 

 and so on in the ratio of the odd 

 numbers, is as much an uniform se- 

 quence as that when the supports are 

 removed the body falls. The sequence 

 of spring and summer is as regular 

 and invariable as that of the approach 

 of the sun and spring, but we do not 

 consider spring to be the cause of 

 summer ; it is evident that both are 

 successive effects of the heat received 

 from the sun, and that, considered 

 merely in itself, spring might con- 

 tinue for ever, without having the 

 slightest tendency to produce summer. 

 As we have so often remarked, not 

 the conditional but the unconditional 

 invariable antecedent is termed the 

 cause. That which would not be 

 followed by the effect unless some- 

 thing else had preceded, and which 

 if that something else had preceded 

 would not have been required, is 

 not the cause, however invariable the 

 sequence may in fact be. 



It is in this way that most of those 

 uniformities of succession are gene- 

 rated which are not cases of causa- 

 tion. When a phenomenon goes on 

 increasing, or periodically increases 

 and diminishes, or goes through any 

 continued and unceasing process of 

 variation reducible to an uniform 

 rule or law of succession, we do not 

 on this account presume that any 

 two successive terms of the series are 



