ELECTRICAL AND MAGNETIC DERIVED UNITS. 587 



of the change of the intensity of gravity ; the mass of a body, 

 on the contrary, is an invariable quantity wherever it may be 

 placed. 



It is easy to see what is the ratio between these two units ; 

 the formula p = mg, in which m represents the mass of a body, 

 and / its weight in a place where the acceleration of gravity is g, 

 shows that if the mass of a body is unity, its weight will impart 

 to it an acceleration equal to g, and is equivalent to g times the 

 unit of force as defined above, the acceleration being expressed as 

 a function of the length taken as fundamental unit. 



Thus, if we take the metre and the mass of the kilogramme as 



units, the unit of force is - - kilogramme, or about 100 grammes. 



9'oi 



With the kilogramme as unit of force, the unit of mass is that ol 

 a body weighing 9*81 kilogrammes. 



606. ELECTRICAL AND MAGNETIC DERIVED UNITS. The most 

 important electrical magnitudes are the quantity of electricity, the 

 strength of the electrical field, the potential or the electromotive force, 

 the capacity, the strength of the current, the resistance, etc. We have, 

 in like manner, for the magnetic units the quantity of magnetism, 

 the intensity of the magnetic field, the magnetic strength of a shell, etc. 

 All these magnitudes are connected by the ratios which define them, 

 and if one is given the others follow from it. 



In order to have an absolute system, the quantity which serves 

 as the starting-point must be measured directly in mechanical units. 

 Thus, the quantity of electricity might be defined by Coulomb's 

 law (7), or the quantity of magnetism by the corresponding law 

 (293), or again the strength of the current, by Ampere's electro- 

 dynamical law (473). Out of this arise three systems of absolute 

 measure, which are independent, and incompatible, in which the 

 various units are differently connected with the fundamental units, 

 and to which the names electrostatic system, electromagnetic system, 

 and electro dynamic system have been given. 



There is no theoretical reason for preferring one system to the 

 others ; two of them, however, possess a greater practical importance : 

 these are the electrostatic and electromagnetic systems. The units 

 of the electrodynamic system only differ, moreover, by a numerical 

 factor from the corresponding electromagnetic units, and their 

 applications are less simple. We shall restrict ourselves to the 

 first two ; and shall represent the quantities measured in electrostatic 

 units by small letters, and expressions of the same magnitude in 

 the electromagnetic system by capitals. 



