INTRODUCTION. 



XXXV 



NUMERICALLY DIFFERENT SYSTEMS OF UNITS. 



The fundamental physical quantities which form the basis of a system for 

 measurements have been chosen and the fundamental standards selected and 

 made. Custom has not however generally used these standards for the meas- 

 urement 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 ^ gives some of the systems pro- 

 posed, all built upon the fundamental standards already described. The centi- 

 meter-gram-second (cm-g-sec. or c.g.s.) system proposed by Kelvin is the only 



one generally accepted. 



Table |. 



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"^ and mm'/fJLr^, respec- 

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

 tities may differ in two ways: (i) the units chosen for the fundamental quanti- 

 ties 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 47r 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. 



^ Circular 60 of the Bureau of Standards, Electric Units and Standards, 1916. The subse- 

 quent matter in this introduction is based upon this circular. 



