15 



generally used these standards for the measurement of the magnitudes of 

 quantities but rather multiples or submultiples of them. For instance, for very 

 small quantities the micron (/i) or one-millionth of a meter is often used. The 

 following table 8 gives some of the systems proposed, all built upon the funda- 

 mental standards already described. The centimeter-gram-second (cm-g-sec or 

 cgs) system proposed by Kelvin is the only one generally accepted. 



Part 2. — Some proposed systems of units 



Further, the choice of a set of fundamental physical quantities to form the 

 basis of a system does not necessarily determine how that system shall be used 

 in measurements. In fact, upon any sufficient set of fundamental quantities, a 

 great many different systems of units may be built. The electrostatic and elec- 

 tromagnetic systems are really systems of electric quantities rather than units. 

 They were based upon the relationships F —QQ /Kr 2 and mm'/ pr 2 , respec- 

 tively. Systems of units built upon a chosen set of fundamental physical quan- 

 tities may differ in two ways: (1) the units chosen for the fundamental 

 quantities may be different; (2) the defining equations by which the system is 

 built may be different. 



The electrostatic system generally used is based on the centimeter, gram, 

 second, and dielectric constant of a vacuum. Other systems have appeared, 

 differing from this in the first way — for instance using the foot, grain, and 

 second in place of the centimeter, gram, and second. A system differing from 

 it in the second way is that of Heaviside which introduces the factor 4-tt at 

 different places than is usual in the equations. There are similarly several 

 systems of electromagnetic units in use. 



Gaussian systems. — "The complexity of the interrelations of the units is 

 increased by the fact that not one of the systems is used as a whole, consistently 

 for all electromagnetic quantities. The 'systems' at present used are therefore 

 combinations of certain of the systems of units." 



Some writers 9 on the theory of electricity prefer to use what is called a 

 Gaussian system, a combination of electrostatic units for purely electrical quan- 

 tities and electromagnetic units for magnetic quantities. There are two such 

 Gaussian systems in vogue — one a combination of cgs electrostatic and cgs elec- 

 tromagnetic systems, and the other a combination of the two corresponding 

 Heaviside systems. 



When a Gaussian system is used, caution is necessary when an equation 

 contains both electric and magnetic quantities. A factor expressing the ratio 

 between the electrostatic and electromagnetic units of one of the quantities 

 has to be introduced. This factor is the first or second power of c, the number 



8 Circular 60 of the National Bureau of Standards, Electric Units and Standards, 1916. 

 The subsequent matter in this introduction is based upon this circular. 



9 For example, A. G. Webster, Theory of electricity and magnetism, 1897; J. H. Jeans, 

 Electricity and magnetism, 1911; H. A. Lorentz, the theory of electrons, 1909; and 

 O. W. Richardson, The electron theory of matter, 1914. 



SMITHSONIAN PHYSICAL TABLES 



