Hypotheses of Dynamics. 261 



I need not enter into a criticism of the discussion of this 

 example, the conclusion being quite sufficient for my purpose. 

 " By the consideration of instances/'' Prof. Lodge says, " we 

 have thus been led to the induction that energy can be trans- 

 mitted without obvious change of form by substances with 

 infinite properties, e. g. by an incompressible solid ; all mole- 

 cular processes being either non-existent or being ignored ; 

 but that with ordinary matter there is always some percentage 

 of obvious transformation, though we may apparently have 

 all grades of it from complete to very small." This is of 

 course partial, but not complete transformation. " Thinking 

 of these impact cases alone, it might appear as if I had 

 been overhasty in saying that the whole of energy must be 

 transformed when it is transferred*. Yet observe that it has 

 to pass through the intermediate condition. A row of ivory 

 balls in contact has another thrown against one end, and from 

 the other end one leaps off. The energy has been transmitted 

 through the row r somewhat as it is transmitted through the 

 compressed strata of two impinging rods. Yet if the elastic 

 connexions of every stratum are attended to, and if these be 

 regarded as massless, 1 think it will be found that all the 

 transmitted kinetic has really passed through a momentary 

 existence as potential." Thus, in order to uphold the com- 

 plete transformation of kinetic energy during transference, it 

 is found necessary to assume the rods to consist of strata 

 alternately massive and massless. Similarly, in order to make 

 good the complete transformation of potential energy it would 

 be necessary (as in the former example) to assume the rods to 

 consist of strata alternately rigid and elastic. " The fact of 

 necessary transformation," he continues, " is not so obvious 

 when you come to look into some of these special cases ; but 

 I would refer once more to the proof given at the beginning 

 of Part IV., which seems to me conclusive as to essential 

 fact." Prof. Lodge therefore finds it difficult to make the 

 accuracy of his thesis obvious in such examples, and falls back 

 upon the general demonstration, which, as shown above, even 

 if it be admitted without criticism, proves only partial trans- 

 formation. " The difficulty arises because when an elastic 

 body is struck (say a massive molecule with a massless spiral 

 spring connexion) it begins to move a little directly the spring- 

 is the least compressed, and is moving half speed when the 

 spring is fully compressed." In my paper (p. 140) I pointed 

 out this " difficulty " as standing in the way of the doctrine 



* See footnote f to p. 259. 



