PROCEEDINGS. 
585 
body has two kinds of motion; a motion of translation and a whirling 
motion. We also see bodies change their forms while moving, and this 
occurs even among the heavenly bodies, as is shown when a comet ap¬ 
proaches the sun and recedes from it. Again, in order to make the ques¬ 
tion simple, we leave out of consideration the whirling motions of bodies 
and their changes of form, and to do this we imagine the moving body to 
be infinitely small, and call it a particle. This particle we adopt as the 
unit of matter. Assuming this simple body to be uniformly changing its 
velocity under the action of causes which we designate as forces, we have 
the proportion, 
<P 
v_ 
T ' 
Let F be the unit of force, or a force which acting on a unit of matter 
during the unit of time produces a unit of velocity; then for a uniform 
force we have 1 
v 
If the force be variable we have 
dv d 2 s 
9 = at = 
Force appears, therefore, as a secondary idea, or as a function of the three 
fundamental conceptions of matter, space, and time. It is true that this 
process teaches us nothing concerning the nature of force, and I know of 
no method that does; but from the preceding simple equations can be 
deduced the whole theory of rational mechanics. We are able to study 
the modes under which forces act, and in some cases to deduce the laws 
of their action, but all these results are to be controlled by accurate obser¬ 
vation and measurement. Thus it is very natural to extend the New¬ 
tonian law of gravitation to the stellar universe, but such an extension 
should be tested by observation, and the reasons for the universal ex¬ 
tension of the simple law that controls our solar system should be care¬ 
fully examined. 
The notion of force is one that we acquire fronj our earliest experiences, 
such as lifting bodies, putting them in motion, or resisting their motions. 
Let us examine some of the phrases that are in common use; and first the 
“ centrifugal force.” The equations of motion of a particle for rectangular 
coordinates are 
d 2 x Fy d 2 z 
dt 2 ~ dt 2 ~ dt 2 ~ Z ’ 
in which t is the independent variable. The phrase “ centrifugal force ” 
75—Bull. Phil. Soc., Wash., Vol. 11. 
