230 TRANSFORMATION AND EQUIVALENCE OF FORCES. 



and to certain other energies which they initiate; or else 

 nothing must become something and something must be- 

 come nothing. The alternatives are, to deny the persistence 

 of force, or to admit that every physical and psychical 

 change is generated by certain antecedent forces, and that 

 from given amounts of such forces neither more nor less of 

 such physical and psychical changes can result. And since 

 the persistence of force, being a datum of conscious- 

 ness, cannot be denied, its unavoidable corollary must be 

 accepted. This corollary cannot indeed be made 



more certain by accumulating illustrations. The truth as 

 arrived at deductively, cannot be inductively confirmed. 

 For every one of such facts as those above detailed, is estab- 

 lished only through the indirect assumption of that persist- 

 ence of force, from which it really follows as a direct conse- 

 quence. The most exact proof of correlation and equiva- 

 lence which it is possible to reach by experimental inquiry, 

 is that based on measurement of the forces expended and the 

 forces produced. But, as was shown in the last chapter, any 

 such process of measurement implies the use of some unit of 

 force which is assumed to remain constant; and for this as- 

 sumption there can be no warrant but that it is a corollary 

 from the persistence of force. How then can any reasoning- 

 based on this corollary, prove the equally direct corollary 

 that when a given quantity of force ceases to exist under one 

 form, an equal quantity must come into existence under 

 some other form or forms ? Clearly the d priori truth ex- 

 pressed in this last corollary, cannot be more firmly estab- 

 lished by any d posteriori proofs which the first corollary 

 helps us to. 



" What then," it may be asked, " is the use of these in- 

 vestigations by which transformation and equivalence of 

 forces is sought to be established as an inductive truth? 

 Surely it will not be alleged that they are useless. Yet if 

 the correlation cannot be made more certain by them than 

 it is already, does not their uselessness necessarily follow? " 



