584 
PHILOSOPHICAL SOCIETY OF WASHINGTON. 
planets and the stars. Men are so constituted that theories for the expla¬ 
nation of these motions and changes will soon be formed. Thus we find 
in the oldest hooks that have come down to us very complete and dog¬ 
matic accounts of the construction of the universe. The slow growth of 
science has overturned one after another of these explanations until we 
have come to look with distrust upon elaborate theories that cannot be 
tested by observation or reduced to truths that may be considered axio¬ 
matic. The history of astronomy gives a good example of such changes of 
opinion. The study of this science presents to observers the motions of 
bodies in a manner that cannot fail to excite their curiosity. From the 
study of the motions of bodies has come the science of rational mechanics. 
It deals with questions in a purely mathematical form, and its funda¬ 
mental conceptions are matter, space, and time. It is not necessary to 
undertake the definition of these conceptions. The only satisfactory 
method seems to be that every one shall determine them for himself. 
We assume that they are quantities that can be measured, and proceed to 
consider the motions of a body. Among the first things we notice are 
differences in the rates of motion ; this gives us the idea of velocity. Our 
first step in such investigation is always to simplify the conditions, and 
here we begin by considering motions that are uniform and rectilinear. 
In this case we measure velocity by comparing the ratio of the observed 
spaces to that of the observed times. Thus we have 
v : V: 
v 
FX 
T 
X S 
In order to make measurements we must adopt units of space, time, and 
velocity. If we make 
£=1, T= 1, F=l, 
we have for uniform motion 
If the motion be variable we have for the instant t, by the usual, method 
of proceeding to the limit, 
ds 
Observation shows that the same body has different velocities at differ¬ 
ent times, and we infer a cause for this change. We notice that a large 
