HYPOTHESES OF DYNAMICS. 17 



is not the law of the present ; and it is because the law of conservation in its ordinary 

 form is widely assumed in dynamical investigation to be so completely verified as to have 

 become axiomatic, that 1 have taken the possibility of its deduction as the test of the 

 sufficiency of the laws of motion. 



Helmholtz showed in his celebrated memoir on the Conservation of Force,' that the de- 

 duction of the law of the conservation of energy in its ordinary form maybe "based on either 

 of two maxims, either on the maxim that it is not possible by any combination whatever 

 of natural bodies to derive an unlimited amount of mechanical force, or on the assumption 

 that all actions in nature can be ultimately referred to attractive or repulsive forces, the 

 intensity of which depends solely upon the distances between the points by which the 

 forces are exerted." It may also be deduced, as is well known, from the axiom that the 

 work done during any change of configuration of a system of particles acted upon by 

 natural forces depends only upon the changes in the positions of the particles and not 

 upon the velocities with which or the i^aths by which they have moved from the old 

 positions to the new. The first of these hypotheses is the assertion of the impossibility 

 of "the perpetual motion," the second is the assertion that natural forces may be regarded 

 as central forces, the third may be referred to as asserting that natural forces are conserva- 

 tive forces. In addition we may adopt the law of the conservation of energy itself as a 

 fundamental hypothesis, on the ground that it " is always acquiring additional credibility 

 from the constantly increasing number of deductions which have been drawn from it, 

 and which are found in all cases to be verified by experiment." - 



To reach a conclusion as to which of these hypotheses is best fitted for adoption as a 

 fourth law of motion, a knowledge of their relations to the three laws already widely 

 adopted is obviously of importance. I shall consider them individually therefore from 

 this point of view. 



Taking the last mentioned hypothesis first, the law of the conservation of energy it- 

 self, we have seen that it may be derived from the second law of motion together with the 

 assumption of the conservatism of natural forces, The hypothesis of which this law, if 

 made a law of motion, would bo the expression, would thu.s include the hypothesis of the 

 second law, and the second law would thus have to be rejected as logically superfluous. 

 The third law would thus become meaningless ; and the new law having been expressed 

 in terms of energy, the third law woi^ld have to be replaced by a law of the transference 

 of energy between particles. The adoption of this hypothesis would therefore render a 

 complete readjustment of our fundamental hypotheses logically necessary. It may per- 

 haps be desirable to make this readjustment, to adopt, as Tait^ suggests, the laws of the 

 conservation and the transformation of energy as our dynamical axioms, and thus to 

 banish the conception of force to the limbo of once useful things. But this course has 

 educational disadvantages. For in accordance with the sound educational maxim that 

 we should proceed from the known to the unknown, it would seem to be better to start 

 from the sense-given idea of force rather than from the derivative idea of energy. Until there- 

 fore it has been shown that the adoption of the laws of energy as fundamental hypotheses 



' See Taylor's Scientific Memoirs,— Nat. Pliil., 1853, p. 114. 

 - Maxwell : Matter and Motion, Art. Ixxiii. 

 ^ Ency. Brit, 9th Ed., Art. Mechanics, ? 299. 



Sec. Ill, 1892, 3. 



