Dr. J. Croll on the Transformation of Gravity. 245 



gives 20 foot-pounds ; and when the ground is reached the 

 potential energy is gone ; for although the force of gravity is 

 not diminished; yet the potential energy is consumed, there 

 being now no space through which the force can act. Kinetic 

 energy thus generated being measured by the mass of the 

 stone multiplied by the half-square of its velocity, the sum of 

 the potential and the kinetic energies must therefore always 

 remain constant. When the stone reaches the ground it is in 

 possession of the 100 foot-pounds of energy in the form of 

 motion. When it was halfway down it possessed 50 foot- 

 pounds in the kinetic form of motion, and another 50 foot- 

 pounds in the potential form ; for, having another 50 feet to 

 fall, its potential energy was 1 x 50 = 50 foot-pounds. 



This mode of viewing the matter, it is perfectly true, com- 

 pletely meets the mathematical and mechanical conditions of 

 the problem ; but for this very reason it seems to me to hide 

 somewhat the real physical nature of the process. 



On a former occasion* I briefly endeavoured to show that 

 the fundamental objection to this mode of explanation is that 

 it makes space a form of energy, whereas, when we analyze 

 the process properly, we find that time and space can, in the 

 very nature of things, be nothing more than conditions. 

 The object of the present paper is to discuss more fully this 

 objection. 



Time and space are but conditions in the process of trans- 

 formation. — Space and time are conditions, but conditions 

 absolutely necessary, to the transformation of potential energy 

 into kinetic and of kinetic energy into potential ; but they 

 themselves cannot be forms of energy. But if it be true that 

 the mere force of gravity or tendency of the stone to fall to 

 the ground is not the potential energy, but that this potential 

 energy is the force x the space through which it can act, 

 then space must become a form of potential energy. This is 

 evident ; for the potential energy in this case consists of two 

 factors, one of which is the space through which the force 

 acts. It thus becomes just as much a form of energy as the 

 other factor, viz. the force. 



The reason why this mode of explanation fulfils the mathe- 

 matical conditions of conservation is obvious. Space, like 

 time, being a condition absolutely essential to the transforma- 

 tion of potential energy into kinetic, it follows that, no matter 

 how much potential energy may be in the raised stone, no 

 transformation can possibly take place if the space condition 

 is not supplied, and the amount of transformation will just be in 

 proportion to the space supplied. The stone maybe raised to 

 * Phil. Ma?. December 1807. 



