ON THE CONSERVATION OF FORCE 197 



power of velocity or, what is the same thing, the ins 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 circum- 

 stances, to as great a height as possible. 3 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. 95, 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 and of friction. Neither 

 does it increase, but it continually 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 winding up the clock, and are uncoiled 

 by the working of the clock. To coil up the spring we con- 

 sume the force of the arm ; this has to overcome the resisting 

 elastic force of the spring as we wind it up, just as in the 

 clock we have to overcome the force of gravity which the 

 weight exerts. The coiled spring can, however, perform 

 work; it gradually expends this acquired capability in driv- 

 ing the clockwork. 



If I stretch a crossbow and afterwards let it go, the 

 stretched string moves the arrow; it imparts to it force in 

 the form of velocity. To stretch the cord my arm must 

 work for a few seconds ; this work is imparted to the arrow 



8 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 fhe velocity at the end of the first second of a freely falling body. 



