176 WORK 



Thus, for configurations near to P, we may neglect these latter 

 terms altogether, and write the equation in the form 



(C&TT/~\ 

 - ) may be either positive or negative. 

 ^ IP 

 If it is positive, then W W P is positive whatever the value of 



x, so that the potential energy W in every configuration near to 

 P is greater than that in configuration P. In other words, W 7 is a 

 minimum at P. 



So also if / - - J is negative, W W P is negative for all small 



\ x /P 

 values of x, and we find that W is a maximum at P. 



148. Suppose now that the system is placed at rest in some con- 

 figuration near to P. This configuration is not one of equilibrium, 

 so that the system cannot remain at rest. To determine the direc- 

 tion in which it begins to move, we^need only notice that as the 

 system moves it acquires kinetic energy, and as this must, by 

 143, be acquired at the expense of its potential energy, we see 

 that the system will begin to move in such a direction that its 

 potential energy will be diminished. 



A glance at equation (42) will show whether this direction is 



towards or away from P. We see that if ( ) is positive, the 



\ x IP 

 value of a? must decrease, so that the motion will be towards P, 



/3 2 W\ 

 whatever the value of x. Similarly, if ( - J is negative, the 



\ d* IP 

 value of x z must increase, so that the motion will be always away 



from P. 



We have now seen that if the system is placed in a con- 

 figuration adjacent to P, the question of whether the motion 

 which ensues is towards or away from P does not depend on the 

 configuration in which the system is placed, but depends on the 



* t& W \ 



Slgn of 



