ON THE CONSERVATION OF FORCE. 335 



You see here that the reason why the weight, when it 

 comes from a to M, and does not stop there, but ascends 

 to 6, in opposition to the action of gravity, is only to be 

 sought in its velocity. The velocity which it has ac- 

 quired in moving from the height A a is capable of again 

 raising it to an equal height, B 6. The velocity of the 

 moving mass, M, is thus capable of raising this mass ; 

 that is to say, in the language of mechanics, of performing 

 work. This would also be the case if we had imparted 

 such a velocity to the suspended weight by a blow. 



From this we learn further how to measure the workin g 

 power of velocity or, what is the same thing, the vis 

 viva of the moving mass. It is equal to the work, 

 expressed in foot pounds, which the same mass can 

 exert after its velocity has been used to raise it, under 

 the most favourable circumstances, to as great a height 

 as possible. 1 This does not depend on the direction of 

 the velocity; for if we swing a weight attached to a 

 thread in a circle, we can even change a downward 

 motion into an upward one. 



The motion of the pendulum shows us very distinctly 

 how the forms of working power hitherto considered 

 that of a raised weight and that of a moving mass may 

 merge into one another. In the points a and 6, Fig. 43, 

 the mass has no velocity ; at the point M it has fallen as 

 far as possible, but possesses velocity. As the weight goes 

 from a to m the work of the raised weight is changed into 

 vis viva ; as the weight goes further from m to b the vis 

 viva is changed into the work of a raised weight. Thus the 

 work which the arm originally imparted to the pendulum 

 is not lost in these oscillations, provided we may leave out 

 of consideration the influence of the resistance of the air 



1 The measure of vis viva in theoretical mechanics is half the product of 

 the weight into the square of the velocity. To reduce it to the technical 

 measure of the work we must divide it by the intensity of gravity ; that 

 is, by the velocity at the end of the first second of a freely falling body. 



