382 Mr. J. J. Waterston on the Integral of Gravitation, 



It is impossible to imagine an infinite attribute belonging to a 

 finite entity. It is therefore in space that the energy that con- 

 tributes the power of gravitation exists, and the element of matter 

 merely gives to it a centripetal direction. 



This, as a consequent of the law of gravitation, seems notewor- 

 thy from it probably being applicable to molecular forces gene- 

 rally. It favours the idea that the function of the material ele- 

 ment is to give direction to a living force that pervades space. 



This is further discussed in § l-l-. 



. . §^- 



The law of Gravitation with respect to the element of radial 



space. 



This law is usually defined with reference to a constant element 

 of time ; the increment of velocity generated being proportional 

 to the increment of time — whatever the direction or velocity of 

 the motion — and inversely as the square of the central distance. 

 If we view it with reference to a constant element of radial space, 

 we find that the increment of square velocity generated by the 

 force of gravitation is proportional to decrement of radial distance, 

 and inversely as square of central distance. This holds what- 

 ever the velocity or direction of the motion, whatever the orbit 

 of the projectile. 



Thus each element of radial distance has associated with it a 

 fixed element of mechanical force, to be given to or taken from 

 all bodies traversing it ; whatever may be the direction of their 

 motion or the time taken to pass through it. A weight attached 

 to clockwork may take a day to descend through one foot, and 

 the same weight falling freely from a height may take only 

 ■j-y'jj(jth of a second to pass through the same foot, yet the me- 

 chanical force communicated in each case is the same. 



§4. 

 The mutual gravitation of two bodies developes mechanical force 

 in each of them inversely proportional to its mass. 



Suppose two bodies to descend towards each other by their 

 mutual gravitation, their common centre of gravity being at rest. 

 At any time before they meet, their acquired velocities being ex- 

 amined will be found inversely as their masses, which assume as 

 1 to 10. Suppose them removed to the earth's surface and 

 each projected up a vertical with their acquired velocities respect- 

 ively : the smaller body rises 100 times the height ascended by 

 the larger, and thus in again descending would be able to per- 

 form ten times the work. 



Although in ordinary parlance the action and reaction of these 

 two attracting bodies are equal according to Newton's third law, 



