18 APPLIED MECHANICS 
direction of its motion. Hence if just for an instant the whole body 
be made to revolve about O, the directions of the motions of A and B 
will be unaltered. 
‘Again, since A and B are definite points on a rigid body, they must 
remain at the fixed distance AB from one another. Hence the com- 
ponents of the velocities of A and B along AB must be equal, that is, 
V, cos a= Vz cos B, where V, and Vy are the velocities of A and B 
respectively in the directions in which they are actually moving. An 
inspection of Fig. 15 shows that cos a=sin OAB, and cos f = sin OBA, 
therefore V, sin OAB= Vz sin OBA, or 
V,_ sin OBA monies OA 
V, sin OAB’ which is equal to OB ° 
: ; Vv, _ OA 
But if the body be made to revolve for an instant about O, then v.-OB' 
B 
Hence, for the instant, the motions of A and B are unaltered by making 
the body revolve about the point O. 
The point O is called the instantaneous centre or virtual centre of the 
body for the position shown. The instantaneous centre is continually 
changing, except for a body which has rotary motion only. The locus of 
the instantaneous centre is called a centrode. A line through the instan- 
taneous centre perpendicular to the plane of motion is an émstantaneous 
axis, and the locus of the instantaneous axis is a surface called an axode. 
23. Force.—Force is any cause which tends to move a body which is 
at rest, or which tends to change the motion of a moving body. 
A force is completely specified when its magnitude, its direction, and 
a point in its line of action are given. 
A force may be completely specified graphically on paper. Thus, a 
line ab (Fig. 16) has a length which, measured with a certain scale, 
represents the magnitude of the force, the direction of this line re- 
presents the direction of the force, and a point 
O is given as a point in the line of action of the wi 
force. The line along which the force. acts will getty 
obviously be the line OX drawn through O parallel 
to ab. The force may act from O to X or from X OT est a 
to O, and this may be fixed by an arrow-head placed x 
on the line ab. The arrow-head determines the Fic. 16. 
sense of the force. The sense may also be fixed by 
the order in which the letters a and 6 at the extremities of the line are 
stated ; thus a force ab would be a force acting in the direction ab from 
a to 6, while a force 6a would be one acting in the direction da from 
b toa, . ; 
24. Mass and Weight.—The mass of a body is the quantity of 
matter which it contains. The weight of a body is the force of attraction 
which the earth exerts\on it. The mass of a body is proportional to its 
weight. The weight of a body is, however, slightly different at different 
parts of the earth’s surface. 
25. Engineer's Units of Force and Mass.—In engineering calcula- 
tions the unit of force is the attraction which the earth exerts in the 
latitude of London on a certain standard piece of platinum, and the unit 
is called the pound or pound weight. The unit of mass is taken as the 
