with reference to the Measure and Transfer of Force. 335 



element of matter is determined by the inverse square distance 

 of that element fi'om another : precisely as if an emanative influ- 

 ence had issued fi'om each as a centre and become diluted as it 

 became diflFiised through an augmenting spherical smface. 



2. An impulse that accumulates square velocity on an element 

 in motion in a ratio combined of the rate at ^hich its distance 

 from the central element diminishes, and of the amount of sta- 

 tical impulse due to that distance, and to the number of elements 

 to which the impulse is directed. This defines its dynamical 

 or force-producing magnitude. 



8. An impulse operating exactly in the direction of and towards 

 the distant material element. 



4. An impulse cumulative to an apparently illimitable extent, 

 according to the number of the distant collocated elements of 

 matter : e. g., at the earth^s surface an element of matter in pass- 

 ing — in any direction and with any velocity — through a foot 

 vertical, has given to it 64 feet of square velocity. At the surface 

 of the Sim, a foot vertical contributes 1800 feet square velocity. 



5. An impulse, that, so far as observation extends, although 

 dependent on matter at a distance, is uninfluenced by intervening 

 matter. 



6. An impulse that is not diminished by the velocity with 

 which a body moves in the direction in which it operates. 



Two of these characteristics, the fifth and sixth, are physical 

 paradoxes of the same degree as the marvel in the wave theoiy 

 of light, that the medium or media that convey the impressions 

 of heat and hght, although acting and acted upon by the ele- 

 ments of bodies, presents no resistance to the planetary motions. 



The sixth has been put to the test by Laplace while seeking to 

 account for the secvdar inequality of the moon. Mr. Adams 

 having lately found the treatment of this subject defective, it 

 might be worth while to examine analytically the influence that 

 an infinitesimal divergence from the law of gravitation in the 

 case of bodies approaching or receding from each other would 

 have on the planetaiy motions, so as to be prepared to recognize 

 its accumulated effects through geological periods of time. The 

 tendency of first diff"erentials of an elliptic orbit seems to be mo- 

 tion of apses in the direction of the motion of the planet ; dimi- 

 nution of the major axis, and the minor axis unchanged ; ellipses 

 thus tending towards circles with fixed diameters. The chief 

 question is as to the moon's motion being so delicate a test of the 

 divergence as Laplace has deduced from his analysis. 



The quantity of motion in a body is proportional to the square 

 of its velocity. 

 Motion as a physical entity is a combination of two quantitative 



