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mutually consistent. Galileo’s experiments 
on falling bodies are then the direct ex- 
perimental proof in a limited case of the 
proportionality between the force which 
acts on a body, measured at any one place 
by a weight, and the acceleration imparted 
to the body. Newton’s Second Law is a 
statement of Galileo’s discovery, with this 
addition, that the acceleration imparted by 
a force is not the same for all bodies, but 
depends upon a certain characteristic of 
the body. This characteristic, the mass of 
the body, first calls for recognition at this 
point. In the view I have taken the mass 
is the factor of proportion between the 
force which acts on a body and the accel- 
eration which it imparts to the body. 
Since we can measure forces by compari- 
son with a standard force, we can also 
measure masses by the aid of properly 
instituted experiments. Whether we meas- 
ure masses in this way or not, and it turns 
out to be not a satisfactory way to do it, 
we at least get from this relation between 
force, of which we have a concept, and 
motion, of which we have a concept, an 
adequate working concept of mass. Force 
is the primary concept and mass is a de- 
rived concept. 
Now owing to the permanency of masses 
of matter it is convenient to construct our 
system of units with a mass as one of the 
fundamental units. We are able to do this 
and to compare one mass with another 
chosen as standard, without going through 
the operation of measuring forces, by 
utilizing the principle embodied in New- 
ton’s Third Law. This law asserts that 
bodies which interact, that is, which exert 
forees on each other, exert equal forces, 
and thus, if the bodies are free to move, 
their acceleration will be inversely as their 
masses. By observation of the accelera- 
tions of two mutually interacting bodies 
we may thus compare their masses, and so 
SCIENCE 
[N.S. Vou. XXXV. No. 895 
construct a set or scale of masses, and use 
these masses and their accelerations to 
measure forces. Thus while the concept of 
force is primary in the order of thought, 
we may make the unit of mass funda- 
mental in the development of a system of 
units. 
The point upon which I wish to insist is 
that both reason and the history of me- 
chanies show that the foundation of the 
science is the purely intuitional concept of 
force which is shared by every intelligent 
being, and that this intuitional concept is 
not only accurate so far as it goes, but ade- 
quate to serve as the foundation of a great 
science. No use of the concept of force in 
the theories of physics has ever violated in 
any particular this original and intui- 
tional concept of it. Even the brilliant en- 
deavor of Hertz to found all the principles 
of dynamics upon the three concepts of 
time, space and mass can not escape the 
criticism that the concept of mass is mean- 
ingless to us unless it is given to us by our 
experience of the inertia of matter when 
we exert force upon it. Once that concept 
is attained it may be used, as Hertz so 
beautifully used it, in the logical upbuild- 
ing of a system of dynamics. Perhaps my 
contention will be made clearer if we con- 
sider briefly the question whether it would 
be possible for us to construct our present 
system of dynamics if we were disembod- 
ied spirits, gifted with the means of ob- 
serving spaces, times and colors, but with- 
out the sensation of force. We could see 
colored volumes, sometimes moving with 
constant velocity, sometimes with varying 
velocity, and we could ascribe the changing 
velocity to the action of a force. We 
further could connect the force with the 
moving volume by setting it equal to the 
acceleration multiplied by some factor 
which we might name the mass. This 
equation would contain two unknown and 
