ON THE CONSERVATION OF FORCE. 293 



from a to M, and does not stop there, but ascends to b, in oppo- 

 sition to the action of gravity, is only to be sought in its velocity. 

 The velocity which it has acquired in moving from the height 

 A a is capable of again raising it to an equal height, B b. The 

 velocity of the moving mass, M, is thus capable of raising this 

 mass; that is to say, in the language of mechanics, of perform- 

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

 a velocity to the suspended weight by a blow. 



Prom this we learn further how to measure the working 

 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 b, 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 im- 

 parted to the pendulum is not lost in these oscillations, provided 

 we may leave out of consideration the influence of the resistance 

 of the air and of friction. Neither does it increase, but it con- 

 tinually changes the form of its manifestation. 



Let us now pass to other mechanical forces, those of elastic 

 bodies. Instead of the weights which drive our clocks, we find 

 in time-pieces and in watches, steel springs which are coiled in 



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 fdling body. 



