troduces matter with the need of a fundamental unit of mass ; fourth, electrical, 

 and fifth, thermal considerations require two more such quantities. The dis- 

 covery of new classes of phenomena may require further additions. 



As to the first three fundamental quantities, simplicity and good use sanction 

 the choice of a length, L, a time interval, T, and a mass, M. For the measure- 

 ment of electrical quantities, good use has sanctioned two fundamental quan- 

 tities — the dielectric constant, K, the basis of the "electrostatic" system, and 

 the magnetic permeability, n, the basis of the "electromagnetic" system. Be- 

 sides these two systems involving electrical considerations, there is in common 

 use a third one called the "absolute" system, which will be referred to later. 

 For the fifth, or thermal fundamental unit, temperature is generally chosen. 1 



Derived units. — Having selected the fundamental or basic units — namely, 

 a measure of length, of time, of mass, of permeability or of the dielectric 

 constant, and of temperature — it remains to express all other units for physical 

 quantities in terms of these. Units depending on powers greater than unity of 

 the basic units are called "derived units." Thus, the unit volume is the volume 

 of a cube having each edge a unit of length. Suppose that the capacity of some 

 volume is expressed in terms of the foot as fundamental unit and the volume 

 number is wanted when the yard is taken as the unit. The yard is three times 

 as long as the foot and therefore the volume of a cube whose edge is a yard is 

 3x3x3 times as great as that whose edge is a foot. Thus the given volume 

 will contain only 1/27 as many units of volume when the yard is the unit of 

 length as it will contain when the foot is the unit. To transform from the foot 

 as old unit to the yard as new unit, the old volume number must be multiplied 

 by 1/27, or by the ratio of the magnitude of the old to that of the new unit of 

 volume. This is the same rule as already given, but it is usually more con- 

 venient to express the transformations in terms of the fundamental units 

 directly. In the present case, since, with the method of measurement here 

 adopted, a volume number is the cube of a length number, the ratio of two units 

 of volume is the cube of the ratio of the intrinsic values of the two units of 

 length. Hence, if / is the ratio of the magnitude of the old to that of the new 

 unit of length, the ratio of the corresponding units of volume is / 3 . Similarly 

 the ratio of two units of area would be I 2 , and so on for other quantities. 



CONVERSION FACTORS AND DIMENSIONAL FORMULAE 



For the ratio of length, mass, time, temperature, dielectric constant, and 

 permeability units the small bracketed letters, [/], [m], [t], [8], [k], and [/a] 

 will be adopted. These symbols will always represent simple numbers, but the 

 magnitude of the number will depend on the relative magnitudes of the units 

 the ratios of which they represent. When the values of the numbers represented 

 by these small bracketed letters as well as the powers of them involved in any 

 particular unit are known, the factor for the transformation is at once obtained. 

 Thus, in the above example, the value of / was 1/3, and the power involved 

 in the expression for volume was 3 ; hence the factor for transforming from 

 cubic feet to cubic yards was I 3 or 1/3 3 or 1/27 These factors will be called 

 conversion factors. 



1 Because of its greater psychological and physical simplicity, and the desirability that 

 the unit chosen should have extensive magnitude, it has been proposed to choose as the 

 fourth fundamental quantity a quantity of electrical charge, e. The standard units of electri- 

 cal charge would then be the electronic charge. For thermal needs, entropy has been pro- 

 posed. While not generally so psychologically easy to grasp as temperature, entropy is of 

 fundamental importance in thermodynamics and has extensive magnitude. (Tolman, R. C, 

 The measurable quantities of physics, Phys. Rev., vol. 9, p. 237, 1917.) 



SMITHSONIAN PHYSICAL TABLES 



