299] MEASUREMENT AND UNITS. 375 



commercial units of length and mass in this country are the foot and the 

 pound, and corresponding to these there is a system of dynamical units. 

 There is however another important respect in which this system differs 

 from the c. G.s. system, and that is in respect of the unit of force. The 

 unit of force employed by British engineers is statical, it is the force that 

 must be applied to support a body whose mass is one pound. This involves 

 a change in the measurement of force. Instead of saying, as we have in 

 Article 75, that the force acting on a body of mass m and producing an 

 acceleration / is measured by the product of the numbers m, /, we should 

 have to say that the measure of the force is the product of the numbers m, f, 

 and a constant coefficient. The coefficient is then the reciprocal of the 

 numerical measure of the acceleration due to gravity in terms of the unit 

 of length employed (the foot). This constant is accordingly l/(32'2). Thus 

 the equation which we write P = mf, where P is the force producing accele- 

 ration / in a body of mass m, could be written in these units P = (mlg}f, 

 where g is the said constant*. In the system of units we are now de- 

 scribing certain measures of quantities of work and power have received 

 special names. 



The unit of work is the foot-pound, it is the work done by a force which 

 would support a body of mass one pound acting through a displacement of 

 one foot. The potential energy of a body which weighs m pounds raised 

 to a height h above the Earth's surface is mh foot-pounds. According to 

 Article 149 this is 'the measure of the " potential energy of the body in the 

 field of the Earth's gravitation." 



The unit of power employed in the same system is the horse-power. It 

 is the power of an agent which does 33000 foot-pounds of work per minute. 



The units of the system here described are called "gravitation units" 

 because the quantities expressed by the units at any place depend on the 

 local numerical value of the acceleration due to gravity. They are unsuited 

 to the general expression of dynamical equations, which are required to hold 

 without modification not merely for relatively small bodies at a place on 

 the Earth's surface but for bodies of any size in any place. 



* It does not tend to simplicity that the writers who use these units also use 

 the word "weight" for the quantity we call "mass," and the letter W where we 

 use m, and thus they write the above equation P=(W/g)f. In the notation of 

 Article 281 this would be a valid equation in c. o. s. units, or in any units in 

 which the unit force produces unit acceleration in unit mass, but all the letters 

 except/ would have different meanings. Much confusion has thus been produced. 



