ch. ii.] RHYTHM. 311 



matter. By an analysis of the widest propositions which 

 these sciences can furnish, concerning the movements of 

 masses and molecules, we arrived at the axiom that every 

 manifestation of force must be preceded and followed by an 

 equivalent 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 uniformity 

 of law and the universality of causation with which all 

 physical inquiries must equally set out. We saw next that 

 this axiom gives rise to three corollaries 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 corollary it appeared 

 that any given mode of motion 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 suriace of our earth, it 

 becomes legitimate to inquire from what antecedent form of 

 energy proceeded all these motions. This inquiry we shall 

 make in due season. By our second corollary it appeared 

 that where motion results from the composition of two or 

 more forces, it must always take place in the line of least 

 resistance ; but that the difficulty of calculating or predicting 

 this resultant line must increase very rapidly with each 

 addition to the number of forces which are concerned in 

 producing it. 



Our third corollary has given us glimpses of a truth, which, 

 though less immediately obvious, is equally necessary and 

 equally important with any of the foregoing. We have seen 

 that, in the hypothetical case of a single moving body in an 

 otherwise empty universe, the direction of motion would be 

 in a straight line, and the velocity would be uniform. In the 

 hypothetical case of a single pair of mutually attracting 

 bodies moving in independent directions in an otherwise 

 empty universe, the motion would be rhythmical both in 



