HYPOTHESES OF DYNAMICS. 13 



the greatest of all dynamical laws, the conservation of energy ? This law may be 

 proved, by the aid of the second and third laws of motion, to hold in the case of any sys- 

 tem of particles which is neither giving energy to, nor receiving energy from, external 

 bodies, provided the stresses between the particles may be regarded as acting in the lines 

 joining them and as being functions of their distances, as for example in the case of 

 gravitational, electrical and magnetic attractions. It has also been proved by experiment 

 to hold in a very large number of cases in which the laws of the forces acting are 

 unknown, the energy disappearing in one form, and the energy appearing simultaneously 

 in another form, being measured. One immediate deduction from it, that it is impossible 

 to construct a machine which will do more work for us than we do upon it, has been so 

 abundantly verified by experience that " the perpetual motion " has come to occupy in 

 physics the same position as circle-squaring in mathematics, the philosopher's stone in 

 chemistry, and the elixir vitœ in physiology. An immense number of other deductions 

 from it have been verified by experiment, and no deduction properly drawn from it has 

 been found inconsistent with fact. The evidence of all kinds in its favour is so over- 

 whelming that no doubt is now entertained of its being applicable to all natural forces ; 

 and accordingly either this law itself or some law from which it may be derived is 

 universally treated as being axiomatic. It would seem, therefore, that the formally 

 recognized hypotheses of dynamics should either include this law or give it by deduction. 



Several writers have held, at any rate indirectly, that the law of the conservation of 

 energy may be deduced from the second law of motion. They have not usually said so in 

 so many words, but they have made statements involving the possibility of this deduction. 

 Thus Grarnett says ' : "In order to lose our faith in the principle of the conservation of 

 energy, we must give up our belief in the fundamental principles of dynamics expressed 

 in the laws of motion." He therefore holds that this law involves no hypothesis addi- 

 tional to those of the laws of motion. For if it did we must lose faith in the conservation 

 of energy on losing faith in the additional hypothesis, even though we retained our belief 

 in the laws of motion. It would follow that the law of conservation, involving no addi- 

 tional hypothesis must be capable of deduction from the laws of motion. Garnett does 

 not state, in the paper from which the above quotation is made, from which law, or in 

 what way, the deduction may be made. But in another work ' he asserts that a certain 

 statement made by Newton in his comments on the laws of motion, which, owing to the 

 form he gave it, is often referred to as his second interpretation of the third law of motion, 

 " is nothing more nor less than the enunciation of the great principle of the conservation of 

 energy;" ' and as we shall see, this is equivalent to the a.sisertiou that the law of the con- 

 servation of energy may be deduced from the second law of motion alone. 



This statement* of Newton's is translated by Thomson and Tait' in the following 



' Ency. Brit., 9th Ed., Art. Dynamics. 



* Elementary Dynamics, 1886, p. 47. 



■'' For evidence tliat Garnelt may not have meant what he seems to say in this passage, see his Elementary 

 Treatise on Heat (1878) , p. 169. 



*"Si iBStimetur agentis actio es ejus vi et velocitate conjunctim; et similiter resistentis reactio œstimetur 

 conjunctim ex ejus pariium aingidarum velocitatibus et viribua resistendi ab earum attritione, cclia:-sione, pondère 

 et acceleratione oriundis; erunt actio et reactio, in omni instrumentorum usu, sibi iuvicem semper œquales." 

 (Principia : Scholium to Axiomata). 



^ Treatise on Natural Philosophy, Vol. I. Part I. (1870), 'i 263. 



