PHYSICS. 5) 
MECHANICS, 
A. Tue Sratics or Souw Boonies. 
a. General Ideas. 
When two or more forces, acting in different directions upon the same 
body, are so adjusted as completely to neutralize each other, no change 
being produced in the body, the body is said to be in equilibrium, or the 
forces are said to hold each other in equilibrium. Statics investigates the 
conditions of equilibrium in bodies, being divisible into three sections, 
according to the three different states of aggregations: statics of solids— 
Geostatics; statics of liquids—Hydrostatics ; and statics of gases—Aero- 
statics. The laws of the motions produced, when, among the different forces, 
the laws of equilibrium are not satisfied, are investigated by Dynamics. 
This, also, is divisible into dynamics of solids—Geodynamics ; dynamics of 
liquids—Hydrodynamics, or Hydraulics; and dynamics of gases—Aero- 
dynamics, or Pneumatics. 
A point acted upon by a single force must move in the direction of the 
force and likewise, in a straight line. Equal forces are those which, when 
acting in diametrically opposite directions, neutralize each other completely. 
Two equal forces acting in the same direction are equal to twice the amount 
of one of them acting in this direction: several forces, even though unequal, 
act, in the same dixection, as a single one equal to their sum. This is called 
the resultant. Resultants acting in precisely opposite directions, neutralize 
each other either entirely, when equal, or partially, when unequal: in the 
first case there is equilibrium, in the second there is motion, in the direction 
of the greater resultant. If the forces act at an angle with each other, 
motion is in a direction between them, obeying a mean force, the resultant 
of the different lateral forces. The magnitude and direction of this mean 
force is known from a law called the parallelogram of forces, explained by 
pl. 16, fig. 1. Let the lines AB, AC represent the direction and intensity 
of two forces, acting at the same instant on the body A. Completing a 
parallelogram from the angle BAC, and its sides, AB and AC; DA, the 
diagonal of the parallelogram, ABDC, will represent the direction and inten- 
sity of the force, which, if acting alone upon the point A, would produce the 
same effect upon it as the two simultaneous forces BA andCA. Ifa lateral 
force be supposed capable of urging the point A as far as B in a certain 
time, and another Jateral force be capable of carrying it to C in the same 
time, the two together will carry it from A to D. 
In a manner similar to the preceding, by which two forces may be consi- 
dered as one, one force may be separated into two, of which it may be 
considered the resultant. The problem then becomes, to determine the 
intensity and direction of two forces, which, acting upon a body at a given 
angle, shall produce the same effect as the single given force. Suppose, for 
instance, that in pl. 16, fig. 2, the force AC act upon the body A, and it be 
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