14 J. G. MacGREGOE on THE 



words : — " If the activity of an agent be measured by its amount and its velocity conjoint- 

 ly ; and if similarly, the counter-activity of the resistance be measured by the velocities 

 of its several parts and their several amounts conjointly, whether these arise from friction, 

 cohesion, weight or acceleration ; — activity and counter-activity, in all combinations of 

 machines, will be equal and opposite." They have also given the following paraphrase 

 of it in modern dynamical terms : ' — " Work done on any system of bodies has its equiva- 

 lent iu work done against friction, molecular forces, or gravity, if there be no acceleration ; 

 but if there be acceleration, part of the work is expended in overcoming the resistance to 

 acceleration, and the additional kiuetic energy developed is equivalent to the work so 

 spent," — a paraphrase which would be closer to the original, it seems to me, if the last 

 clause were omitted. With regard to this statement, the same authors point out - that it 

 may be expressed analytically in the following equation : 



in which the symbols have their usual meanings. " Here," they say, " the first member 

 is composed of Newton's Adiones Agentium ; with his Reacliones Resislenliiim so far as 

 friction, gravity and molecular forces are concerned, substracted : and the second consists 

 of the portion of the Reactiones due to acceleration." Now this equation, as is well known, 

 and as may be seen in the passage cited above, is obtained directly from the second law 

 of motion without the use of any other dynamical hypothesis. Hence Newton's state- 

 ment may be deduced from the second law alone, and if it be " nothing more nor less than 

 the enunciation of the great principle of the conservation of energy," that principle must 

 also be capable of deduction from the second law. 



We must therefore consider whether or Dot G-arnett's assertion as to this statement is 

 correct. Before doing so, however, we may observe that other writers make similar 

 though more guarded assertions. Thus Tait'' says Newton's statement " has been shown 

 to require comparatively little addition to make it a complete enunciation of the conserva- 

 tion of energy," and, " what Newton really wanted was to know what becomes of work 

 which is spent in friction." Maxwell ' says : " That this statement of Newton's implicit- 

 ly contains nearly the whole doctrine of energy was first pointed out by Thomson and 

 Tait," which, though doubtless expressing his own opinion, is somewhat stronger than 

 the statement of the authors he quotes, who say that "the foundation of the abstract 

 theory of energy is laid by Newton in an admirably compact and distinct manner in the 

 sentence of his scholium already quoted," '^ and that this sentence " points out the modern 

 principles of work and energy.'"' Besaut' says : "This passage really shadows forth the 

 principle of energy in its modern form, and indeed states the principle as far as it could be 

 stated at the time when the Principia was written. It was not until Count Eumford began 

 to make observations, and to draw inferences from his observations, followed by 



' Treatise on Natural Philosophy, Vol. I., Part I., (1879) I 269. 



■■' Ibid., ? 293. 



■' Properties of Matter (1885), p. 104, and Recent Advances in Physical Science (1878), p. 38. 



* Matter and Motion, A rt. xcvi. 



'' Treatise on Natural Philosophy, Vol. I., Part I., I 208. 



<" Ibid., ? 242. 



'Dynamics (1885), p. 49. 



