and the Conservation of Energy. 141 



trations, because the air, the spring, the bullet, which are 

 treated as simple bodies, must be regarded as complex systems 

 between the parts of which transferences of energy are oc- 

 curring. When we make a more intimate study of such 

 instances from the point of view of contact-action, we must, 

 as Prof. Lodge points out, regard bodies as consisting of 

 particles connected by a medium possessing some property of 

 the nature of elasticity. If we assume the particles to be 

 rigid they can, of course, have kinetic energy only. If the 

 medium be assumed to have no inertia, its elements can have 

 potential energy only. Hence if both assumptions be made, 

 transference of energy between the particles and the medium 

 must involve complete transformation, while transference 

 from element to element of the medium must occur 

 without transformation. If, however, both the particles and 

 the medium be assumed to have both inertia and elasticity, 

 the transference of energy will, in general, it seems to me, 

 involve only partial transformation, whether it occur between 

 the elements of the medium or between the particles and the 

 medium. When, therefore, Prof. Lodge states that " a bullet 

 fired upwards gradually transfers its undissipated energy to 

 the gravitation medium, transforming it at the same time into 

 potential," he seems to me to assume that the bullet is rigid 

 and that the medium is without inertia. 



Prof. Lodge states finally that " energy cannot be trans- 

 formed without being transferred," but he gives no demon- 

 stration of this proposition. I find it difficult to reconcile 

 with this statement one of his illustrations : — " A perfectly 

 elastic bounding ball has all its energy transformed into 

 potential at the middle of every period of contact with the 

 obstacle from which it rebounds." Immediately after con- 

 tact has ceased all its energy is kinetic, for apparently vibra- 

 tions are excluded by hypothesis. The energy has thus been 

 completely transformed without transference from the ball. 

 It may, of course, be held that the ball must be regarded as 

 a system of particles connected by an elastic medium. But 

 in that case, what has been said of the ball, as a whole, is true 

 of the particles in contact with the obstacle, if they are as- 

 sumed to be elastic, or, if not, of the elements of the medium 

 in contact with them, provided the medium be assumed to 

 have inertia. After the middle of the period of contact, they 

 do work on the elements of the medium beyond them. 2so 

 work is done on them. They, therefore, lose energy and 

 gain none. Yet after contact is over they possess kinetic 

 energy. Whence has it come, if not through transform;;! ion 

 of their own potential energy ? That energy cannot be trans- 



