INTRODUCTION 



UNITS OF MEASUREMENT 



The quantitative measure of anything is expressed by two factors — one, 

 a certain definite amount of the kind of physical quantity measured, called the 

 unit ; the other, the number of times this unit is taken. A distance is stated 

 as 5 meters. The purpose in such a statement is to convey an idea of this dis- 

 tance in terms of some familiar or standard unit distance. Similarly quantity 

 of matter is referred to as so many grams ; of time, as so many seconds, or 

 minutes, or hours. 



The numerical factor definitive of the magnitude of any quantity must de- 

 pend on the size of the unit in terms of which the quantity is measured. For 

 example, let the magnitude factor be 5 for a certain distance when the mile is 

 used as the unit of measurement. A mile equals 1,760 yards or 5,280 feet. The 

 numerical factor evidently becomes 8,800 and 26,400, respectively, when the 

 yard or the foot is used as the unit. Hence, to obtain the magnitude factor for 

 a quantity in terms of a new unit, multiply the old magnitude factor by the ratio 

 of the magnitudes of the old and new units ; that is, by the number of the new 

 units required to make one of the old. 



The different kinds of quantities measured by physicists fall fairly definitely 

 into two classes. In one class the magnitudes may be called extensive, in the 

 other, intensive. To decide to which class a quantity belongs, it is often helpful 

 to note the effect of the addition of two equal quantities of the kind in question. 

 If twice the quantity results, then the quantity has extensive (additive) mag- 

 nitude. For instance, two pieces of platinum, each weighing 5 grams, added 

 together weigh 10 grams; on the other hand, the addition of one piece of 

 platinum at 100° C to another at 100° C does not result in a system at 200° C. 

 Volume, entropy, energy may be taken as typical of extensive magnitudes ; 

 density, temperature and magnetic permeability, of intensive magnitudes. 



The measurement of quantities having extensive magnitude is a compara- 

 tively direct process. Those having intensive magnitude must be correlated 

 with phenomena which may be measured extensively. In the case of tempera- 

 ture, a typical quantity with intensive magnitude, various methods of measure- 

 ment have been devised, such as the correlation of magnitudes of temperature 

 with the varying lengths of a thread of mercury. 



Fundamental units. — It is desirable that the fewest possible fundamental 

 unit quantities should be chosen. Simplicity should regulate the choice — 

 simplicity first, psychologically, in that they should be easy to grasp mentally, 

 and second, physically, in permitting as straightforward and simple definition 

 as possible of the complex relationships involving them. Further, it seems de- 

 sirable that the units should be extensive in nature. It has been found possible 

 to express all measurable physical quantities in terms of five such units : first, 

 geometrical considerations — length, surface, etc. — lead to the need of a length ; 

 second, kinematical considerations — velocity, acceleration, etc. — introduce 

 time; third, mechanics — treating of masses instead of immaterial points — in- 



SMITHS0NIAN PHYSICAL TABLES 1 



