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There is no need of presenting the views 
of Archimedes or of Stevinus, whose work 
was exclusively in statics and who used the 
concept of force given us by our muscular 
or motor sense, and measured forces by 
weights. The views of Galileo, however, 
are interesting as showing how far one can 
go in dynamics without using the concept 
of mass. 
Galileo examined the problem of the 
motion of a body acted on by a constant 
foree. The only constant force of which 
he could dispose was the weight of a body, 
or a component of its weight, and he ac- 
cordingly was limited in his studies to the 
examination of the laws of falling bodies. 
Owing to the relation of proportionality 
between the weight of a body and its mass, 
this limitation in a way simplified the prob- 
lem, while at the same time it made it more 
difficult to develop a complete doctrine of 
force and motion. By the famous experi- 
ment at the Leaning Tower Galileo satis- 
fied himself that he could study any falling 
body as a type, and that the conclusions 
which he would reach from that study 
would apply to all. His attention was 
therefore directed almost wholly to the 
consideration of the motion of the falling 
body, while the question of the relation 
between the motion and the weight of the 
body was disregarded. The result of this 
was that he developed the laws of linear 
motion with constant acceleration, and 
numerous consequences of those laws, 
chiefly relating to motion down inclined 
planes, with really wonderful complete- 
ness, and was led in the course of his 
thought to a full appreciation and state- 
ment of the principle of inertia, while yet 
he did not, in this part of his work, attain 
to any useful conception of the relation of 
force to mass. He makes it clear that the 
conception of force which is sufficient for 
his purposes is that with which he was 
SCIENCE 
[N.S. Vou. XXXV. No. 895 
familiar from his study of statics. He 
says, in speaking about the ‘‘tendency’’ of 
a body to fall down inclined planes of the 
same height, that ‘‘It is clear that the tend- 
ency of a body to fall is as great as the 
resistance or the least force which suffices 
to prevent its falling and to keep the body 
at rest.’’ In fact Galileo thought of the 
weight of a body, with which he was 
familiar from common experience, as a 
force which moved the body, and assuming 
that the weight was unchanged during 
motion his experiments demonstrated what 
kind of motion such a constant force will 
set up and maintain. 
In the very interesting discussion which 
Galileo gives of the forces exerted by the 
collision of one body against another, he 
approaches nearer than in other parts of 
his discourse to an appreciation of mass as 
a characteristic of a moving body. He 
speaks in one place of the falling body 
being a composite of weight and velocity, 
and his discussion of the impulse applied 
by such a falling body to another on which 
it falls shows that he was very near the 
concept of momentum; but there is no real 
precision in his statements. 
We now turn to Newton to get the full 
doctrine of the relations of force and mo- 
tion. It will be clear to any one who 
examines the introductory parts of the 
““Prineipia,’’ that Newton did not under- 
take in that book to present a systematic 
treatise on dynamics. He merely blocks 
out a rough set of definitions and postu- 
lates, in a very uncritical way, which are 
sufficient to enable him to go on as 
promptly as possible to the real task which 
was before him. A striking instance of 
this uncritical attitude of mind is found 
in Definition I., in which he says, ‘‘Quan- 
tity of matter is its measure derived from 
its density and volume jointly.’’ This 
quantity of matter thus defined he names 
