PROGRESSIVE EFFECTS. 361 



CHAPTER XV. 



OP PROGKESSIVE EFFECTS ; AND OF THE CONTINUED ACTION OF CAUSES. 



§ 1. In the last four chapters we have traced the general outlines of the 

 theory of the generation of derivative laws from 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 con- 

 tinual 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 pro- 

 duced. But most phenomena are in their own nature permanent ; having 

 begun to exist, they would exist forever unless some cause intervened hav- 

 ing a tendency to alter or destroy them. Such, for example, are all the 

 facts of phenomena which we call bodies. Water, once produced, will not 

 of itself relapse into a state of hydrogen and oxygen ; such a change re- 

 quires some agent having the power of decomposing the compound. Such, 

 again, are the positions in space and the movements of bodies. No object 

 at rest alters its position without the intervention of some conditions ex- 

 traneous 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 exter- 

 nal 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 cen- 

 turies; or a projectile force which launches a cannon-ball into space, pro- 

 duces a motion which would continue forever unless some other force 

 counteracted it. 



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

 ence worth pointing out. In the former (in which the phenomenon pro- 

 duced is a substance, and not a motion of a substance), since the rust re- 

 mains forever and unaltered unless some new cause supervenes, 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 lan- 

 guage. 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 mo- 

 tion 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 moment depends. For, suppose that 

 the body passes through some resisting medium, which partially counter- 



