14 Electrostatics Physical Principles [OH. i 



The Unit of Electricity. 



17. The law of Coulomb supplies us with a convenient unit in which 

 to measure electric charges. 



The unit of mass, the pound or gramme, is a purely arbitrary unit, and 

 all quantities of mass are measured simply by comparison with this unit, 

 The same is true of the unit of space. If it were possible to keep a charge 

 of electricity unimpaired through all time we might take an arbitrary charge 

 of electricity as standard, and measure all charges by comparison with this 

 one standard charge, in the way suggested in 8. As it is not possible to do 

 this, we find it convenient to measure electricity with reference to the units 

 of mass, length and time of which we are already in possession, and Coulomb's 

 Law enables us to do this. We define as the unit charge a charge such that 

 when two unit charges are placed one on each of two small particles at 

 a distance of a centimetre apart, the force of repulsion between the particles 

 is one dyne. With this definition it is clear that the quantity c in the 

 formula (1) becomes equal to unity, so long as the C.G.S. system of units 

 is used. 



In a similar way, if the mass of a body did not remain constant, we might 

 have to define the unit of mass with reference to those of time and length 

 by saying that a mass is a unit mass provided that two such masses, placed at 

 a unit distance apart, produce in each other an acceleration of a centimetre 

 per second per second. In this case we should have the gravitational 

 acceleration f given by an equation of the form 



and this equation would determine the unit of mass. 



18. Physical dimensions. If the unit of mass were determined by 

 equation (2), m would appear to have the dimensions of an acceleration 

 multiplied by the square of a distance, and therefore dimensions 



As a matter of fact, however, we know that mass is something entirely apart 

 from length and time, except in so far as it is connected with them through 

 the law of gravitation. The complete gravitational acceleration is given by 



m 



-*> 



where 7 is the so-called " gravitation constant." 



By our proposed definition of unit mass we should have made the value 

 of 7 numerically equal to unity ; but its physical dimensions are not those of 



