240 Prof. J. G. MacGregor on Abstract Dynamics and 



that obviously any operation Which increases the surface-ten- 

 sion of the film separating a rj gu id from its own vapour will 

 also raise the boiling-point, for \ v hen T is increased, a greater 

 vapour-pressure vr within a bubble will be required in order 

 to enable it to expand against a given external pressure. 

 This prediction of the theory appears to be in accordance with 

 the observed facts. 



XXI v. jT/ie Hypotheses of Abstract Dynamics and the ques- 

 tion oft.Jie number of the Elastic Constants. By Prof. J. G. 

 MacG-Rbgob, D.Sc, Dalhousie College, Halifax, JST.S, * 



IN a for m er paper f an attempt was made to formulate the 

 hypotheses employed in Abstract Dynamics, when bodies 

 are considered as consisting of particles exerting forces upon 

 one anoth( 3r a t a distance. As these may be expressed in 

 various w; lYS , Newton's Second Law of Motion, owing to its 

 very general employment, was selected as one of them, and it 

 was sought to determine what others are required in order to 

 establish bioth the equations of motion and the law of the 

 conservation of energy. It was shown that the following 

 independent assumptions are both necessary and sufficient for 

 this purpose, viz., (a) the Third Law in its wide sense, i. e., as 

 asse/fting that action and reaction are not only equal and 

 opposite but also in the same straight line, and (/>) the law 

 of the conservation of natural forces, i. e., that natural forces 

 are such that the work done during any change of the con- 

 figuration of a system depends only upon the initial and final 

 configurations, or that £ (Xdx + Ydy + Zdz) is a complete 

 differential. Both (a) and (b) are assertions about natural 

 forces, (a) referring to magnitude, direction, and action-line, 

 and (6) to magnitude. They may be combined in one by 

 noting that when (a) holds, S(X^-f Ydy + Zdz) becomes 

 SSc?5, where S is the stress between any pair of particles 

 and s their distance from one another, and that the condition 

 that S&ds shall be a complete differential is that each S shall 

 be a function of all the s's, or in more precise terms, that the 

 stresses between the various pairs of particles shall be propor- 

 tional to the rates of change, with respect to the corresponding 

 distances respectively, of a function of the distances of all the 

 pairs of particles of the system. 



Thus the requisite hypotheses reduce to two, viz., (1) the 



* An abstract (with some additions) of a paper read before the Royal 

 Society of Canada. Communicated by the Author, 

 t Trans. Roy. Soc. Canada, vol. x. sec. iii. (1892) p. 3. 



