Srorion IIL., 1895. [85] Trans. R. S.C. 
VI.—On the Hypotheses of Abstract Dynamics. 
By Prof. J. G. MacGreeor, D.Se., Dalhousie College, Halifax, N.S. 
(Read May, 1895.) 
In a paper which I had the honour of communicating to the Royal 
Society in 1892' I endeavoured to express in as precise, complete and 
simple a form as possible the hypotheses ordinarily employed in abstract 
dynamics. They were found to be as follows : 
(1) The Law of Force (Newton's Second Law of Motion).—Relatively 
to any dynamical reference system, the acceleration produced in a particle 
by a force is proportional to the force, and has the same direction. 
(2) The Law of Stress—Natural forces may be considered to be 
attractions or repulsions whose magnitudes vary solely with the distance 
of the particles between which they act. 
The usual mode of expressing the hypotheses, viz., in terms of force, 
was adhered to, partly because of its being usual, and partly because of 
its advantages from an educational standpoint. It was not maintained 
that this mode was logically superior to other modes, e. g., to the expres- 
sion of the hypotheses in terms of energy ; it was simply held that if 
Newton’s Second Law be adopted as one of the hypotheses, the above 
Law of Stress forms a simple, complete, and independent expression of 
the others. 
The form in which the second hypothesis is given, although suited 
to the discussion of all problems in which bodies are regarded as consist- 
ing of particles acting on one another at greater or smaller distances, is 
not suited to the discussion of elastic solids and fluids when they are 
treated as continuous bodies whose elements exert forces on contiguous 
elements across their surfaces of separation, or to the discussion of what 
are apparently cases of action at a distance, on the assumption that the 
apparent action at a distance is really due to action through an elastic 
medium. 
The discussion of elastic solids has been carried out both by means 
of the conception of action at a distance and by means of contact action ; 
but the results obtained are discordant. As, therefore, it has not been 
found possible to carry out entirely satisfactory crucial experiments, it 
would appear that it must be regarded as an unsettled question which 
of the two methods is to be preferred. Nevertheless it has been held by 
Mr. Love that the molecular hypothesis ought to be discarded.  “ Even,” 
he says, ‘‘if the experimental evidence were all fairly interpretable in 

IMrans. Hos... vol. -x., sec. lil. D. 9. 
