HELMHOLTZ IN BERLIN 



measured by the product of its force into its velocity, 

 and if similarly the counter activity of the resistance 

 be measured by the velocities of its several parts 

 multiplied into their several forces, whether these 

 arise from friction, cohesion, weight or acceleration, 

 activity and counter activity in all combinations of 

 machines will be equal and opposite.' In overcoming 

 resistance, as when work is spent in altering the 

 shape of a body, work is done against the elastic 

 forces of the body worked against, and, according to 

 Newton's statement, the amount of work spent, or 

 the rate of spending work in distorting the body, is 

 equal to the amount of work done or the rate of 

 doing work against the elastic forces. The work is 

 stored up in the distorted body as potential energy. 

 Suppose, again, work is expended in a body where 

 there is no resistance from friction, cohesion or 

 weight, it will be spent in overcoming the inertia of 

 a body and increasing its velocity, that is to say, the 

 kinetic energy of the body increases. In such a case 

 the 'rate at which work is spent is measured by the 

 product of the momentum into the acceleration in the 

 direction of the motion.' We know that when 

 work is done against friction, an amount of heat is 

 produced exactly proportional to the amount of work 

 expended. In Newton's day, this had not been 

 experimentally proved ; otherwise Newton would 

 probably have definitely formulated the law of the 

 conservation of energy. As Professor Tait says 

 45 



