336 THE MECHANICAL EQUIVALENT OF HEAT. 



This definition not only corresponds perfectly with facts, 

 but it accords as far as possible with that which already ex- 

 ists ; for, as I shall show, it contains by implication the con- 

 ception of force as met with in the higher mechanics, and re- 

 ferred to above by II. 



If a mass M, originally at rest, while traversing the effect- 

 ive space s, under the influence and in the direction of the 

 pressure jp, acquires the velocity c, we haveps^Mc 8 . Since, 

 however, every production of motion implies the existence of 

 a pressure (or of a pull) and an effective space, and also the 

 exhaustion of one at least of these factors, the effective space, 

 it follows that motion can never come into existence except 

 at the cost of this product, >s=Mc 2 . And this it is which 

 for shortness I call " force." 



The connection between expenditure and performance (in 

 other words, the exhaustion of force in producing its effect) 

 presents itself in the simplest form in the phenomena of grav- 

 itation. The necessary condition of every falling motion is 

 that the centre of gravity of the two* masses concerned in it 

 (that is, of the earth and of the falling weight) should ap- 

 proach each other. But in the case of the falling together of 

 the two masses, the approach of their centres of gravity 

 reaches its natural limit, and hence the production of a fall- 

 ing movement is thus bound up with an expenditure, namely, 

 with the exhaustion of the given falling-space, and thereby 

 also of the product of that space into the attraction. The 

 falling down of a weight upon the earth is a process of me- 

 chanical combination ; and just as in combustion the capacity 

 of performance (that is, the condition of the development of 

 heat) ceases when the act of combination comes to an end, so 

 also the production of motion ceases when the weight has 

 fallen to its lowest position. The weight, when lying on the 

 solid ground, is, like the carbonic acid formed in combustion, 

 nothing but a caput mortuum. The affinity, whether mechan- 

 ical or chemical, is still there after the union just as much as 



