in the Theory of Gravitation. 455 



actual energy is not the fact that they are separated, but the fact 

 that they tend toward each other. Distance is a necessary con- 

 dition to the action of this tendency, and, of course, the greater 

 the distance the greater is the opportunity for acting; but when 

 kinetic energy is produced in the form of vis viva or heat, &c, 

 by the approach of bodies, the equivalent in the shape of poten- 

 tial energy lost is tendency, or gravity, not distance. The foot- 

 pounds of kinetic energy produced existed previously in the sta- 

 tical condition of a tendency to approach, not in a mere relation 

 of coexistence in space. 



Let us take the case of the steam-engine. We have here also 

 two elements, the potential and the kinetic. We have (1) the 

 potential element consisting in the dead pressure of the steam in 

 the interior of the cylinder, (2) the vis viva and mechanical work 

 produced as the piston rises under the pressure. This is simply 

 a transference of force from the one condition to the other. What 

 we gain in vis viva and mechanical work we lose in pressure. 

 But space is a condition as necessary to the transference of pres- 

 sure into vis viva as of gravity into vis viva. No matter what 

 the pressure may be, if the piston is at the end of its stroke, and 

 has no further space through which to move, no transference 

 can possibly take place. The equivalent gained in vis viva and 

 mechanical work is wholly derived from the pressure of the steam, 

 not from the space. Space is simply a condition in the trans- 

 ference. The matter is precisely the same in the case of vis viva 

 generated and work performed by gravity. The actual energy 

 of the falling stone must be entirely at the expense of the dead 

 pull of gravity, the space being simply a condition in the trans- 

 ference. The same reasoning is equally applicable to the con- 

 version of statical electricity into dynamical, or of magnetic force 

 into mechanical work. Unless a path is opened up between the 

 ends of the battery through which the forces may travel, no 

 transference of statical into dynamical electricity can possibly 

 take place. Unless the magnetic engine is allowed to move, the 

 magnet does not lose any of its potential energy. In fact space 

 is a necessary condition in the transformation of force under all 

 circumstances. It seems to be metaphysically absurd to sup- 

 pose that either space or time can be in the operations of nature 

 anything more or less than simple conditions. 



The work performed by a water-wheel, for example, is as 

 really and truly derived from the pull of gravity as the work 

 performed by the rising piston is from the pressure of the 

 steam. And it is just as absurd to assert that the pull of 

 gravity is not diminished by the motion of the wheel, as to 

 assert that the pressure of the steam is not diminished by the 

 rising of the piston. 



