284 
the center through all places around it, for 
moving bodies which are in those places. 
The vis acceleratrix as thus described re- 
minds us of the conception of the strength 
of a field of force. 
This analysis of the concept of force 
surely does not promote a clear apprehen- 
sion of it. The only one of the distinctions 
which have been made which seems to be 
worth retaining is that between the vis 
impressa, or action, and the vis motrix im- 
pressa, the one being force in its general 
or conceptual sense, the other the same 
force when given a measure or value. This 
distinction was clearly in Newton’s mind 
and appears in the enunciation of the Laws 
of Motion. In the First Law the departure 
of a body from its state of rest or of uni- 
form motion is ascribed to the vis im- 
pressa; that is, to force in general, without 
any specification as to its measure or even 
any declaration that it can be measured. 
In the Second Law the change of momen- 
tum is said to be proportional to the vis 
motriz impressa; that is, to force that is 
measured so that a proportionality to some- 
thing else can be predicated of it. As has 
already been stated, Newton declared of 
this vis motriz in the special case of gravi- 
tation that it is known, or measured, by the 
force opposite to it and equal to it, by 
which the fall of the body, or, in the gen- 
eral case, the motion of the body, can be 
prevented. In the Third Law the force is 
called actio. This is the alternative word 
used in the definition of the vis impressa, 
as an equivalent for force in its general 
sense. The word in this sense is consist- 
ently used in the enunciation of the Third 
Law, in which forces are not considered as 
measured, but merely as compared by the 
condition of equality. From the examples 
of action and reaction which Newton gives 
(the finger pressed against a stone; the 
horse drawing a stone by a rope and drawn 
SCIENCE 
[N.S. Vou. XXXV. No. 895 
back equally toward the stone, because of 
the stretching of the rope and its exertion 
of equal forces at its two ends) it is plain 
that Newton conceived of forces in the way 
which is familiar to all of us, as the pushes 
and pulls which can be perceived by our 
motor sense, and as the causes of motions. 
He goes on to say that by these actions 
there are caused equal changes, not of 
velocity, but of momentum, so that the 
changes of velocity are inversely as the 
bodies (corporibus). In this way, without 
measuring forces, there is introduced the 
method of comparing masses. 
It is difficult to perceive in these many 
definitions and declarations exactly what 
Newton’s conception was of force, of the 
unit in which it is measured and of its 
relation to mass. After careful considera- 
tion of all that I can find in the ‘‘Prin- 
cipia’’ bearing on the question I am con- 
vineed that Newton viewed the concept of 
force as a primary one, or one directly 
given by intuition, and that he thought of 
the motions of bodies caused by these forces 
as connected quantitatively with them by 
the experimental relation embodied in the 
Second Law. Since Newton does not use 
a system of units, and states most of his 
laws and theorems in terms of proportions, 
the priority of force to mass, in the order 
of their apprehension, is not clearly pre- 
sented. 
In the matter of measuring a force he 
clearly asserts that a vis motrix is meas- 
ured by the force which will counteract it 
and keep the body to which it is applied at 
rest, and the force thus used can hardly be 
other than a force measured statically ; but 
his frequent insistence on the measure of 
vis motric by the momentum which it 
causes shows that he had a conception also 
of the dynamical measure of foree. He 
further supplies the measurement of mass 
as a fundamental quantity which is needed 
