246 KINETIC THEORIES OF GRAVITATION. 



inversely as the square of the central distance. If we view it with ref- 

 erence to a constant element of radial space, w'e 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 dis- 

 tance. This holds whatever the velocity or direction of the motion, 

 whatever the orbit of the projectile . . . ." 



"Section 4. The mutual gravitation of two bodies develops mechan- 

 ical force in each of them inversely proportional to its mass. Suppose 

 two bodies to descend toward each other by their mutual gravitation, 

 their common center of gravity being at rest. At any time before they 

 meet, their acquired velocities being examined will be found inversely 

 as their masses 5 which assume as one to ten. Suppose them removed 

 to the earth's surface, and each projected up a vertical with their ac- 

 quired velocities res|)ectively : the smaller body rises 100 limes the 

 height ascended by the larger, and thus in again descending would be 

 able to perform ten times the work . . . ."* 



After some other propositions and discussions, not specially bearing 

 on the present inquiry, Mr. Waterston gives a general statement of 

 results as follows : " Even if we had not those proofs of the existence 

 of a universal medium that the undulatory theory of light supplies, it 

 would be well to admit the existence of media to which ordinary matter 

 may be assumed to be entirely subordinate in all their potential rela- 

 tions, so as to give order to our ideas in tracing out the dynamical 

 sequence of nature. It would be taking too narrow a view if we limited 

 the function of the luminiferous fether to the conveying of i^hysical 

 pulses only. The atmosphere also conveys physical pulses, but that is 

 the least important of its functions in the economy of nature. There is 

 nothing that should hinder us attributing to the media concerned in 

 the radiation of heat and light the higher functions of electric polarity 

 and gravitation. The special dynamic arrangements by which this is 

 effected may ever elude research, but as there is no limit to the vis viva 

 which such media may conserve in their minutest parts, so there is no 

 physical impossibility in that vis viva being suddenly transferred to the 

 molecules of ordinary matter in the proportions and sequence required 

 to carry out the order and system of nature. The fundamental princi- 

 ple of action in such media must be in accordance with elastic impact, 

 for upon that the dynamic theory of heat and conservation of force rests 

 as a foundation. The statical and dynamical characteristics of gravita- 

 tion and transfusion of force have also been shown to conform to it, so 

 that all the forces that hold the molecules of bodies together must also 

 be in subjection to it." t 



From the above it would aj)pear that the writer in previously afiirming 

 the integral of gravitation to be a function of space, intendsd rather the 

 content of space, or the dynamic medium supposed to occupy- it. Th-^ 



* Loco citat., p. 332. t Loco citat., p. 344. 



