30 FOKCE AKD THE LAWS OF MOTION 



This gives us a means of comparing the masses of any two 

 bodies. In every country a certain mass is taken as standard, and 

 the mass of any other body is then compared with this standard, or 

 with a copy of it, and in this way we get a knowledge of the actual 

 mass of a body. For instance, in saying that the mass of a body 

 is n pounds we mean that its mass (or weight) is equal to n times 

 the mass (or weight) of a certain standard body kept at London. 



22. Measurement of force. The weight of a unit mass is a 

 force which may conveniently be taken to represent a unit force, 

 and if this is done all other forces may be compared with this 

 force. Thus a force of m pounds weight will mean a force m times 

 as great as the weight of the standard pound. 



This unit of force, however, is convenient rather than scientific, 

 since it varies when the mass is moved about from place to place 

 on the earth's surface. A unit pound mass will weigh more at 

 London than at Washington ; for instance, it will be found to 

 extend or compress the spring of a spring balance more at London 

 than at Washington, so that if the pound weight is taken as unit 

 of force, we must remember that the unit of force is different at 

 different parts of the earth's surface, and that a force of m pounds 

 weight at London will be different from a force of m pounds 

 weight at Washington. 



For this reason a second unit of force is generally used for 

 scientific purposes. This is called the absolute unit of force, and 

 is chosen so as to be independent of position on the earth's surface. 

 The second unit of force is defined to be one which produces unit 

 acceleration in unit mass, whereas the former unit produced an 

 acceleration equal to the value of gravity at the point. Thus, if g is 

 the value of gravity, i.e. the acceleration of a body falling freely in 

 a vacuum, the practical unit equals g times the absolute unit. 



If unit force produces unit acceleration in unit mass, a force P 



P 



will produce in mass m an acceleration Hence, denoting the 



m 



acceleration by /, we have the fundamental equation 



P = mf, (10) 



