HELMHOLTZ IN BERLIN 



change of momentum is proportional to the impressed 

 force, and takes place in the direction in which the 

 force acts. Then we have the third law, that to 

 every action there is always an equal and opposite 

 reaction. 



Greater precision is introduced by adopting the 

 Gaussian notion of unit force. If a unit of force 

 act for a unit of time upon a unit of mass, the 

 velocity of the mass will be changed, and the total 

 acceleration will be unity in the direction of the 

 force. Further, in accordance with Newton's Second 

 Law, the magnitude and direction of this total 

 acceleration will be the same whether the body is 

 originally at rest or in motion. Again, when any 

 number of forces act on a body, the acceleration 

 due to each force is the same in direction and magni- 

 tude as if the others had not been in action. 1 



It was about this stage that Huygens, Leibnitz, 

 and the Bernoullis contributed to the discussion, 

 but their arguments were often of a metaphysical 

 character. 



Half the product of the mass of a particle into 

 the square of its speed is its kinetic energy. A 

 material system may have any number of such par- 

 ticles, and the sum of the individual kinetic energies 

 will become the kinetic energy of the system. 

 Further, any increase in the kinetic energy of a 

 material system in passing from one configuration 



1 Clerk Maxwell, Matter and Motion, p. 42. London, 1876. 

 239 



