HERMANN VON HELMHOLTZ 



nised by Newton ; and in the language of the present 

 day m v (mass into speed) is the quantity of motion 

 or momentum, and m v 2 (mass into square of speed) 

 is twice the kinetic energy. 



From a consideration of the principles of the lever, 

 the pulley and the inclined plane, came the definition 

 of work as the product of the quantity of a force into 

 the minute movement of a material point measured in 

 the direction of the force. This led to the establish- 

 ment of the principle of virtual velocities according 

 to which any material system is in equilibrium only 

 when for every virtual or infinitely small movement 

 compatible with the connections of the points, the 

 work of the entire system is equal to zero. From 

 Galileo's doctrine of inertia, and the enunciation of 

 Newton's three laws of motion, a basis was formed for 

 theoretical dynamics. The more important of these 

 laws in the present connection are the first and second. 

 The first asserts that every body continues in a state 

 of rest or of uniform motion in a straight line, unless 

 compelled to change that state by the action of some 

 external force ; in other words, it expresses the prin- 

 ciple of inertia. Force may be defined as that which 

 changes or tends to change the state of rest or motion 

 of a body, and force is measured by the change of 

 momentum it produces in a unit of time. In the idea 

 of momentum, the quantity of matter moved (mass) 

 is taken into account as well as the rate at which it 

 travels. This leads to the second law. Rate of 



