Manchester Memoirs, Vol. liii. (1909), No. 115. 



XIII. On the Moving Force of Terrestrial and Celestial 

 Bodies in relation to the Attraction of Gravitation. 



By Henry Wilde, D.Sc, D.C.L., F.R.S. 



Received and read March sjrd, igog. 



1. In the course of a lecture which I delivered before 

 the Society in 1902, " On the Evolution of the Mental 

 Facuhies in relation to some Fundamental Principles of 

 Motion," prominence was given to the historic controversy 

 respecting the measure of moving force of terrestrial bodies 

 which has exercised the minds of distinguished men of 

 science and learning for more than two centuries, 



2. The proposition was enunciated by Descartes in 

 his Prmcipia^ " That when a part of matter is moved 

 with double the quickness of another, and that other is 

 twice the size of the former, there is just precisely as much 

 motion, but no more, in the less body as in the greater." 

 Forty years later Newton adopted in his Principia 

 Descartes' definition of the quantity of motion in a 

 moving body in substantially the same terms as follows : — 

 " The quantity of motion is the measure of the same 

 arising from the velocity and quantity of matter con- 

 jointly. The motion of the whole is the sum of the 

 motion of all its parts ; and therefore in a body double in 

 quantity with equal velocity the motion is double ; with 

 twice the velocity it is quadruple." To make this defini- 

 tion more explicit, Newton states under his second law, 

 " if any force generates a motion, a double force will 

 generate double the motion, a triple force triple the 

 motion, whether that force be impressed altogether and at 

 once, or gradually and successively. 



* '^ Principia Philosophia'," Pars. 2, § XXXVI., 1643. 

 April 8th, igog. 



