Manchester Memoirs, Vol. xlvi. (1902), No. 10. n 



velocity, the motion is double ; with twice the velocity it 

 is quadruple." To make this definition 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.''* 



Although Galilei had long before demonstrated that 

 the spaces described by heavy bodies from the beginning 

 of their descent are as the squares of the times, and as the 

 squares of the velocities acquired in falling through those 

 spaces, yet the significance of this law in relation to the 

 moving force of bodies was entirely overlooked until 

 Leibnitz made the announcement, in 1686, that the force 

 of a body in motion, by the free action of gravity, is as 

 the square of the velocity. To this measure of moving 

 force Leibnitz applied the term vis viva, or living force. 



That Newton failed to recognise that the spaces 

 through which a body moved by the free action of gravity 

 were a measure of moving force, is seen in the scholium 

 to his third law of motion, wherein it is stated that," When 

 a body is falling, the uniform force of its gravity acting 

 equally, impresses, in equal particles of time, equal forces 

 upon that body, and therefore generates equal velocities ; 

 and in the whole time impresses a whole force and 

 generates a whole velocity proportional to the time." 

 Maclaurin, the pensioned defender of the Newtonian 

 philosophy, also states that, " When a body is projected 

 upwards with a double velocity, the uniform impulses 

 must be continued for a double time, to be able to destroy 

 the motion of the body ; and hence it arises that the body, 

 by setting out with a double velocity, and ascending for a 

 double time, must arise to a quadruple height before its 



* Newton's Priiicipia, Def. 2, Law 2. 



