26 PHYSICS. " 
little, or no time at all; in the latter the action takes place incessantly with- 
out a conceivable instant in which the force does not exert its influence. 
Every momentary force imparts to a material point upon which it operates 
an equable motion; every continuous force operates in producing an 
accelerated or retarded motion. 
The following may be adduced as fundam ental propositions in Dynamics, 
consequently not derived ad priori, but the results of experience. They are 
modifications of the well known Newtonian laws of motion. 
1. A moving material point continues in a state of rectilineal and equable 
motion, until affected by some other influencing force. 
2. Two forces acting momentarily, are as the velocities which they com- 
municate to the same material point in the same instant of time. 
3. A moving body loses just as much motion as it communicates to ano- 
ther body ; that is, action and reaction are equal and opposite. 
a. Equable Motion. 
As a material point or body, in a condition of equable motion, traverses 
equal spaces in equal times, the spaces traversed in different times are as 
these times. If, therefore, s be the space traversed in a time, ¢, and s’ that 
traversed in a time, t’, then s:s’::t:t/; and if t/ one second, s’ is the 
velocity, c, of the body; thus s = ct, c = = and _ Thus in equable 
motion the space described equals the product of the time by the velocity ; 
the velocity equals the space divided by the time; and the time equals the 
space divided by the velocity. 
If a body be acted upon by two momentary forces in different directions, 
the direction and velocity of the motion will take place as the diagonal of 
the parallelogram of forces. Representing the velocities of the forces by c 
and v, and the included angle by a, then the velocity attained, 7 = 
parallelogram of velocities. From this it may readily be shown how much 
a body loses in velocity by moving with a given velocity against a fixed 
obstruction, and from it, it also follows, that an equably moving body which 
enters in the direction of the tangent upon a curve, must move in it with 
undiminished velocity. 
b. Varying Motion. 
It has been already observed that varying motion may be uniformly so 
or not. ‘Taking first into consideration the uniformly accelerated motion 
of a body, the velocity after the expiration of any period of time (the final 
velocity) may easily be determined. In this case the velocity increases 
equably in equal times. If, therefore, G be the velocity at the expiration 
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