300 iNDUCTiorJ. 



CHAPTER XV. 



OF PKOGRESSIVE EFFECTS; AND OF THE CONTtNUEU ACTION OF CAUSES. 



§ 1. In the la^t four chapters, we have traced the general outhnes 

 -of the theory of the generation of derivative laws fi-om ultimate 

 ones. In the present chapter our attention will be directed to a 

 particular case of the derivation of laws from other laws, but a case 

 so general, and so important, as not only to repay but to require a 

 separate examination. This is, the case of a complex phenomenon 

 resulting from one simple law, by the continual addition of an effect to 

 itself. 



There are some phenomena, some bodily sensations for example, 

 which are essentially instantaneous, and whose . existence can only be 

 prolonged by the prolongation of the existence of the cause by which 

 they are produced. But most phenomena are in their own nature 

 permanent ; having begun to exist, they would exist for ever unless 

 some cause intervened having a tendency to alter or destroy them. 

 Such, for example, are all the facts or phenomena which we call bodies. 

 Water once produced, will not of itself relapse into the state of hydro- 

 gen and oxygen ; such a change requires some agent ha\'ing the power 

 of d-ecomposing the compound. Such, again, are the positions in 

 space, and the movements, of bodies. No object at rest alters its 

 position without the intei'vention of some conditions extraneous to 

 itself; and when once in motion, no object returns to a state of rest, 

 or alters either its direction or its velocity, unless some new external 

 conditions are superinduced. It, therefore, perpetually happens that 

 a temporary cause gives rise to a permanent effect. The contact of 

 iron with moist air for a few hours, produces a rust which may endure 

 for centuries ; or a projectile force which launches a cannon ball into 

 space, produces a motion which would continue for ever unless some 

 other force counteracted it. 



Between the two examples which we have here given, there is a 

 difference worth pointing out. In the former, (in which the phenom- 

 enon produced is a substance, and not a motion of a substance,) 

 since the rust remains for ever and unaltered unless some new cause 

 sujjervenes, we may speak of the contact of air a hundred years ago 

 as even the proximate cause of the rust which has existed from that 

 time until now. But when the effect is motion, which is itself a change, 

 we must use a different language. The permanency of the effect is 

 ,now only the permanency of a series of changes. The second foot, 

 or inch, or mile of motion, is not the mere, prolonged duration of 

 the first foot, or- inch, or mile, but another fact which succeeds, and 

 which may in some respects be very unlike the former, since it 

 carries the body through a different region of space. Now, the 

 original projectile force which set the body moving is the remote 

 cause of all its motion, however long continued, but the proximate 

 cause of no motion except that which took place at the first instant. 

 The motion at any subsequent instant is proximately caused by the 

 motion which took place at the instant preceding. It is on that, 

 and not on the original moving cause, that the motion at any given 



