Section III., 1892. [ 3 ] Trans. Roy. Soc. Canada. 



I. — On the FandamctiUd Hi/potheses of Abstract Dynamics. — Presidential Address} 

 By Prof. J. G-. MacG-regor, D.Sc, Dalhousie College, Halifax, N.S. 



(Read May, 1892.) 



On accouut of the variety of the scientific interests represented in this Section, 1 have 

 had some difficulty in selecting a subject for the address, with which, owing to your 

 haying done me the honour to elect me President for the year, it is my duty to open the 

 session. I venture to hope, however, that the subject 1 have chosen, the fundamental 

 hypotheses of abstract dynamics, may be one which will be of interest to you all. 

 For the mathematician comes into contact with these hypotheses in the application of his 

 subject, and the natural philosopher, the astronomer, the chemist and the engineer must 

 discuss them when they investigate the security of the foundations of their different 

 departments of science. 



The term Abstract Dynamics has been differently used by different writers. I use 

 it to-day as denoting that portion of dynamics which treats of the general laws held to 

 apply to all natural forces and as excluding that portion, often called Physical Dynamics, 

 which treats of the laws of particular forces. I wish therefore to discuss in some respects 

 the fundamental principles or axioms involved in the general laws which either have 

 been proved, or are generally assumed, to hold with regard to all the forces of nature. 



Dynamical writers employ a great variety of axioms, including Newton's laws of 

 motion, Galileo's law of the physical independence of forces, D'Alembert's Principle, 

 the principle of moments, the principle of the transmissibility of force, the principle of 

 virtual velocities, the impossibility of the perpetual motion, and others too numerous 

 to mention. Of these, all but one either are merely transformations of Newton's laws, 

 or are readily deducible from them, while that one, the impossibility of the perpetual 

 motion, is frequently held to be deducible from them also. Thus Newton's laws may be 

 taken as being a statement of the formally recognized axioms of dynamics. What I 

 have to say with regard to them will apply at once to axioms which are cither these 

 laws in other forms or deductions from them. 



The Laws of Motion may be regarded either as constituting a definition of force or as 

 being statements about force, force in the latter case being regarded as a familiar concep- 

 tion. If they be regarded as forming a definition of force, it is at once clear that the con- 

 ception of force thus obtained is different from the ordinary conception. Thus according 

 to the first law we recognize a body as being free from the action of force, by its having 



' Through tlie lamented death of the Secretary of the Section the manuscript of this address was lost. I 

 liave rewritten it by the aid of rough notes and of an abstract published in Science, vol. xx, 1892, p.71. — In rewriting 

 it I have made a few modifications suggested by the criticisms of Prof. Hoskinsand Mr. B. T. Dixon {Science, vol. 

 XX, pp. 122 and 149). 



