504 THE CONSERVATION OF ENERGY 



theory, merely to show that there are no evident inconsistencies 

 between this theory and observation. The mechanical explanation 

 of natural phenomena must depend to a gz'eat extent upon the 

 advances to be made in hydrodynamics and its cognate sciences. 



We shall now show that potential energy can be predicated of a 

 system of bodies only in a few instances. 



(1.) One case is that in which there are only two bodies in the 

 system, whatever be the law of attraction, provided it be a function 

 of the distance. The distance between the bodies at any instant is 

 that due to their potential energy. Thus in a falling body, its distance 

 at any instant above the earth's surface is tha.t due to its potential 

 energy. 



(2.) When there are any number of bodies in the system, provided ' 

 that the law of attraction is that of the direct distance. In this 

 case, the point to which potential energy can be referred is the com- 

 mon centre of gravity of the system. 



Besides these two general cases, there are many what may be 

 called solitary cases, in which a system may have potential energy, 

 but which cannot be classed under any general head. 



To illustrate this still further. Suppose a system of say six bodies 

 attracting according to the law of gravitation, and let them move 

 from rest at a given instant. Will they fall together 1 No ; in such 

 a system there is no point, line or surface to which potential energy 

 can be referred. If such a system has no potential energy, can the 

 principle of conservation be affirmed of its actual energy 1 No ; its 

 actual energy is constantly changing. Can it even be asserted that 

 the actual energy wiil periodically go through the same changes'? 

 No ; to assert this we should have to calculate the motions, and the 

 problem is so complex in its general form, that it is beyond the power 

 of mathematical analysis to solve it. What assertion can be made 

 then with, regard to its energy 1 We can only say that the chances 

 are almost infinite against a periodic restoration of energy. 



Again, there are no instances of case two in nature, as far aS' we 

 know, nor of case one. We know of no instances in nature of a system 

 of two bodies entirely unaffected by the presence of other bodies ; 

 that is to say, all systems of two bodies really form parts of a larger 

 system, and thus cannot have a common point to which potential 

 energy can be referred. All the instances which we have of potential 

 energy, are instances in which the word is used in an approximate 



