APPENDIX I 

 THE AMPERE-OHM SYSTEM OF UNITS 



THE ampere and the ohm can be now considered as two 

 arbitrary fundamental units established by an international 

 agreement. Their values can be reproduced to a fraction of a 

 per cent according to detailed specifications adopted by practically 

 all civilized nations. These two units, together with the centi- 

 meter and the second, permit the determination of the values of 

 all other electric and magnetic quantities. The units of mass and 

 of temperature do not enter explicitly into the formulae, but are 

 contained in the legal definition of the ampere and of the ohm. 

 The dimension of resistance can be expressed through those of 

 power and current, according to the equation P=I 2 R, but it 

 is more convenient to consider the dimension of R as fundamental 

 in order to avoid the explicit use of the dimension of mass [M]. 



For the engineer there is no more a need of using the electro- 

 static or the electromagnetic units; for him there is but one 

 ampere-ohm system, which is neither electrostatic nor electro- 

 magnetic. The ampere has npt only a magnitude, but a physical 

 dimension as well, a dimension which with our present knowledge 

 is fundamental, that is, it cannot be reduced to a combination 

 of the dimensions of length, time, and mass (or energy). Let 

 the dimensions of current be denoted by [I] and that of resistance 

 by [R] ; let the dimensions of length and time be denoted by the 

 commonly recognized symbols [L] and [T]- The magnitudes and 

 the dimensions of the important magnetic units are expressed 

 through these four, as is shown in the following table. For the 

 expressions of the electric and the electrostatic quantities in the 

 ampere-ohm system see the author's " Electric Circuit." 



Other units of more convenient magnitude are easily created 

 by multiplying the above-tabulated units by powers of 10, or 

 by adding prefixes milli-, micro-, kilo-, mega-, etc. 



A study of the physical dimensions of the magnetic quantities 



262 



