RHYTHM 



of the widest generalizations of physics can 

 carry us, and before we attempt to go further, 

 we may fitly present in a single view the con- 

 clusions reached in this and in the preceding 

 chapter. 



We observed first that the three departments 

 of abstract-concrete science are alike concerned 

 with the investigation of the general laws of 

 force as manifested in the motions of matter. 

 By an analysis of the widest propositions which 

 these sciences can furnish, concerning the move- 

 ments of masses and molecules, we arrived at 

 the axiom that every manifestation of force 

 must be preceded and followed by an equiva- 

 lent manifestation. We saw that this axiom is 

 involved, alike in every special theorem with 

 which each physical inquiry sets out, and in the 

 general theorem of the uniformitv of law and 

 the universality of causation with which all phy- 

 sical inquiries must equally set out. We saw 

 next that this axiom gives rise to three corolla- 

 ries which, as expressing truths that transcend 

 the sphere of any single science, belong to that 

 transcendental region of knowledge which we 

 have assigned to philosophy. By our first cor- 

 ollary it appeared that any given mode of mo- 

 tion may be metamorphosed into several other 

 modes ; so that, when we contemplate such a 

 complex system of motions as that presented by 

 the various aggregations of matter upon the 

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