94 ROYAL SOCIETY OF CANADA 
may be considered to be continuous, their elements exerting forces only 
on neighbouring elements at surfaces of contact. 
(2) The Law of Force (Newton's Second Law of Motion).—Relatively 
to any dynamical reference system, the acceleration produced in a body 
by a force is proportional to the force, and has the same direction. 
(3) The Law of Stress.—The stresses called into play by a strain are 
such that their components at any point are proportional to the rates of 
increase, with respect to the corresponding strain components respectively, 
of a function of the strain components at the point. 
Il. In Casts OF ACTION AT A DISTANCE. 
(1) The Law of the Constitution of Bodies.—Bodies may be considered ~ 
to consist of particles exerting forces upon one another at a distance. 
(2) The Law of Force.—As above. 
(3) The Law of Stress.—The stresses between the particles of a sys- 
tem are proportional to the rates of increase, with respect to the distances 
of the particles between which they act respectively, of a function of the 
distances of all the pairs of particles of the system, and of these distances 
between which stresses act. 
The Law of Stress usually employed in cases of action at a distance, 
however, is as follows: The stresses between the particles of a system are 
functions of the distances of the pairs of particles between which they 
act respectively, and of such distances only ; and this hypothesis differs 
from the one given above, which is both necessary and sufficient for the 
deduction of the law of the conservation of energy, by involving in addi- 
tion the hypothesis of the physical independence of stresses, viz., that the 
stress between any pair of particles of a system does not depend in any 
way upon the other particles of the system. 
It seems to have escaped the notice of the opponents of the molecular 
mode of treating elastic bodies that those who have used it have made 
this additional assumption. Love’ sums up their objections as follows : 
“The opponents of the theory urge against it, firstly, that it rests on a 
hypothesis possibly doubtful; secondly, that this hypothesis has been 
incorrectly worked out ; thirdly, that it contradicts the results of experi- 
ment ; and, lastly, that the known laws of energy lead to results which 
are certainly true, whether the molecular hypothesis be correct or no, 
and these laws are sufficient to serve as a basis for theory.” There is 
here no distinction between the molecular conception itself and the 
assumptions which have been made in applying it. It is not pointed out 
that the logical content of the assumptions made by those who have 
applied it is greater than that of the assumptions used in employing the 
contact-action conception, and that, therefore, the deductions from it 

1 “Treatise on the Theory of Elasticity,” vol. i., p. 15. 
