12 APPLIED MECHANICS 
The most convenient method of drawing any of the cycloidal curves 
is the transparent templet method. Let AB (Fig. 11) be the directing 
line or circle, and CDP the rolling circle. The directing line or circle is 
to.be drawn on the drawing paper, and the rolling circle is to be drawn 
on a piece of tracing paper or thin transparent celluloid, Mark the 
tracing point P by a short radial line cutting the circle, and also by a 
small needle hole. Place the tracing paper 
on the drawing paper so that the directing 
line and the rolling circle touch one another 
at P. Place a needle through the tracing 
paper and into the drawing paper at P. 
Turn the tracing paper round until the 
rolling circle cuts the directing line at a 
near point Q,. Transfer the needle from 
P to Q,, and turn the tracing paper until ¥1c. 11. 
the rolling circle touches the directing 
line at Q,. The tracing point will now have moved from P to P,. 
Mark the drawing paper at P, with a needle-pointed pencil. Again 
turn the tracing paper until the rolling circle cuts the directing line at 
another near point Q,. Transfer the needle from Q, to Q,, and turn the 
tracing paper until the rolling circle touches the directing line at Q,. 
The tracing point will now have moved to P,. Mark the drawing paper 
at P,. Continuing the process, any number of points on the required 
curve may be obtained, and these points may then be joined by a fair 
curve. 
13. Scalar and Vector Quantities.—Certain quantities, such as the 
weight of a body, the volume of a body, a sum of money, the energy 
stored in a moving body, can be denoted by numbers representing their 
magnitudes in terms of suitable units. For example, a body may weigh 
5 lbs., the energy of a moving body may be 205 foot-pounds. All such 
quantities are called scalar quantities. 
Other magnitudes, such as velocity, acceleration, force, involve the 
idea of direction as well as magnitude, and they cannot be completely 
defined by numbers. There must also be descriptions defining their 
directions. For example, a velocity may be 10 feet per second in a 
direction from south to north. All such quantities are called vector 
quantities. 
A vector quantity may be represented by a straight line, which is 
called a vector. The length of the vector represents the B 
magnitude of the quantity, and the direction of the line 
represents the direction of the quantity. A line AB (Fig. 12) Se f- 
represents a vector quantity whose magnitude is the length <A 
AB, measured with a certain scale, and whose direction is yy, 19, 
parallel to AB. It is necessary to distinguish between the 
direction AB and the direction BA, the one being opposite to that 
of the other. This distinction is the sense of the direction, and may 
be given by the order in which the letters on the line are mentioned 
in referring to the line. An arrow-head placed on the vector is 
the best way of showing the sense of the direction. A vector 
with an arrow-head on it may be referred to by using a single letter, 
as P. 
