69.] FORCE. 39 



accurate appliances for comparing the weights of different 

 bodies at the same place, the idea suggests itself of selecting 

 as unit force the weight of a certain standard mass. 



In the metric gravitation system the weight of a kilogramme 

 has been selected as unit force ; in the British gravitation sys- 

 tem, the weight of a pound is the unit force. 



68. There are two serious objections to the gravitation system of 

 measuring force, one of a practical nature, the other theoretical. The 

 former is that the words " kilogramme " and " pound " are thus used in two 

 different meanings, sometimes, and more correctly, as denoting a mass, 

 sometimes as denoting a force. Wherever an ambiguity might arise 

 from this double use, the word "mass" or "weight" must be added. 



The other objection is more serious. The weight of a body, and 

 hence the gravitation unit of force, is not a constant quantity ; it changes 

 from place to place as it depends on the value of g, the acceleration of 

 gravity. 



For, the weight W of any mass m being the force with which this 

 mass is attracted by the earth, we have 



W= mg, 



where g is the acceleration produced by the earth's attraction. Now it 

 is known from experiment that this acceleration varies from place to 

 place ; according to the law of gravitation, it is inversely proportional 

 to the square of the distance from the centre of the earth. 



The weight of a body is therefore a meaningless term unless the place 

 be specified where the body is situated, and the value of g at that place 

 be given. 



It is true, however, that the value of g for different points on the 

 earth's surface varies but little, so that for most practical purposes 

 the gravitation system is accurate enough. 



In the equations of theoretical dynamics, in particular in kinetics, the 

 use of absolute units is always understood. In statics, however, where 

 we are mainly concerned with the ratios of forces and not with their 

 absolute values, gravitation units will generally be used in the present 

 work in view of the practical applications. 



69. The numerical relation between the absolute and gravita- 

 tion measures of force is expressed by the equations 



