17, 18] The Fundamental Conceptions of Electrostatics 15 



a mere number, so that we cannot neglect the factor 7 when equating 

 physical dimensions on the two sides of the equation. 



f*0> 



So also in the formula F= (3) 



we can and do choose our unit of charge in such a way that the numerical 

 value of c is unity, so that the numerical equation becomes 



but we must remember that the factor c still retains its physical dimensions. 

 Electricity is something entirely apart from mass, length and time, and it 

 follows that we ought to treat the dimensions of equation (3), by introducing 

 a new unit of electricity E and saying that c is of the dimensions of a force 

 divided by E 2 /r* and therefore of dimensions 



If, however, we compare dimensions in equation (4), neglecting to take 

 account of the physical dimensions of the suppressed factor c, it appears as 

 though a charge of electricity can be expressed in terms of the units of 

 mass, length and time, just as it might appear from equation (2) as though 

 a mass could be expressed in terms of the units of length and time. The 

 apparent dimensions of a charge of electricity are now 



M*L*T~* .................................... (5). 



It will be readily understood that these dimensions are merely apparent 

 and not in any way real, when it is stated that other systems of units are 

 also in use, and that the apparent physical dimensions of a charge of 

 electricity are found to be different in the different systems of units. The 

 systems which we have just described, in which the unit is defined as 

 the charge which makes c numerically equal to unity in equation (3), is 

 known as the Electrostatic system of units. 



There will be different electrostatic systems of units corresponding to 

 different units of length, mass and time. In the C.G.S. system these units 

 are taken to be the centimetre, gramme and second. In passing from one 

 system of units to another the unit of electricity will change as if it were 

 a physical quantity having dimensions M^L%T~ l , so long as we hold to the 

 agreement that equation (4) is to be numerically true. i.e. so long as the 

 units remain electrostatic. This gives a certain importance to the apparent 

 dimensions of the unit of electricity, as expressed in formula (5). 



