122 Proceedings of the Royal Society 
I. The motion of a body is uniform if no force act on it. 
II. Change of motion is proportional to the force producing it, 
and takes place in the direction in which the force is exerted. 
From this it follows at once, that force is measured by the rate 
of change of motion it produces ; in other words, by the product of 
the mass, and the acceleration of its velocity.. 
This, combined with purely geometric ideas as to motion in the 
abstract, leads directly to the parallelogram of forces, and through 
it to the subjects of the Statics and Kinetics of a single particle. 
In order to extend our investigations to a hody^ or a system of 
bodies, we require the additional law, 
III. To every action there is an equal and opposite reaction. 
Newton shows that there are two ways in which this action may 
be measured, the third law being true for either. These lead to 
two classes of important dynamical theorems. 
(a) Mutual pressures, tensions of rods and cords, attractions, 
stresses in solids or liquids, &c. &c., form one class of Actions and 
Eeactions. We have thus, as immediate consequences, “Conser- 
vation of Momentum,” and “ Conservation of Areas.” From this 
point of view, we have also the general statement, by what is 
commonly called “ D’Alembert’s Principle,” of the equations of 
equilibrium and motion, and therefore the mathematical expres- 
sion of the circumstances of any dynamical problem. 
(&) But Newton goes farther, and points out another kind of action 
and reaction, ruled by the third law. His words are, — si cestime- 
tur agentis actio ex ejus vi et velocitate conjunctim, et similiter resis- 
tentis reactio cestimetur conjunctim ex ejus partium singularum veloci- 
tatihus et virihus resistendi ah earum attritione, coheesione, fonder e.^ et 
acceleratione oriundis ; erunt actio ^reactio ..... sihi invicem 
semfer cequales. The Actio here spoken of, the product of a force 
by the rate of motion of its point of application, is now known as the 
rate of doing work, or the horse-power of the prime mover. We notice 
amongst the various forms of the corresponding Eeactio, the rate of 
losing work by the resistances, such as friction, cohesion, and weight ; 
but we also have as a reaction, the resistance due to the acceleration 
of the various parts of the system ; and in this statement (made by^ 
