26 APPLIED MECHANICS 
If the amount of turning is given as m revolutions, then the distance _ 
through which P acts is 2rRn, and the work done is 2rPRn, or 27Tn. 
43. Rate of Work—Horse-power.—The working power of any 
agent depends on the amount of work which it can do in a given time. 
Watt found that a good working horse could do 33,000 foot-pounds of 
work in one minute, and he introduced this as the unit for measuring 
the working power of steam-engines. A steam-engine or any working 
agent is said to be of one horse-power when it can do 33,000 foot-pounds 
of work in one minute, or 550 foot-pounds in one second. 
Evidently the simple rule for finding the horse-power of any working 
agent or the horse-power transmitted by any piece of machinery is to 
divide the number of foot-pounds of work done or transmitted per minute 
by 33,000, or horse-power equals work per second divided by 550. 
Horse-power is a measure of the rate of doing or transmitting 
work. 
44, Electrical Units and their Mechanical Equivalents,—The 
electromotive force, or electric pressure of an electric current, is measured 
in volts, and the strength of the current, or the rate of flow of the 
electricity across a section of the conductor, is measured in amperes. The 
power of a current of 1 ampere at an electrical pressure of | volt is called a 
watt, Volts x ampéres= watts. 1 horse-power = 746 watts. 1 kilowatt 
= 1000 watts. 1 electrical unit or 1 Board of Trade unit = 1000 watt-hours. 
45, Machines.—For the purposes of this Article a machine may be 
defined as a contrivance for overcoming a force applied at one point by 
means of another force applied at another point. In books on mechanics 
it used to be the practice to call the former force the weight and the 
latter force the power, but since the force to be overcome is not necessarily 
that of gravity, it is better to call it the resistance, and since the term 
power is used in connection with rate of work, it is better to use the term 
effort instead of power when referring to the driving force in a machine. 
In this Article the effort will be denoted by P, and the resistance by W. 
The points at which the effort and re- 
sistance act may be called the driving point 
and working point respectively. 
In machines when the driving point 
moves through a definite distance, say a, 
the working point moves through another 
definite distance, say 6, and in many ma- 
chines the ratio of a to bis constant. In other 
machines the ratio of a to 0 is different for 
different positions of the driving and working 
points. In a simple wheel and axle (Fig. 24), 
for example, the displacement of P will bear a constant ratio to the 
displacement of W, whereas in a toggle joint (Fig. 25) the ratio of the 
displacement of P to that of W will be different for different positions 
of the parts of the machine. 
In a machine in which the displacement of the driving point bears a 
constant ratio to the displacement of the working point, this ratio (a/b) 
is called the velocity ratio of the machine. In a machine in which this 
ratio is variable, the velocity ratio of the machine for any given positions 
of its parts is the ratio of the displacement of the driving point to the 
Fig. 24 Fig. 25: 
