INTRODUCTION. 



UNITS OF MEASUREMENT. DIMENSIONAL AND 

 CONVERSION FORMULAE. 



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 depend 

 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 1760 yards or 5280 feet. The numerical 

 factor evidently becomes 8800 and 26400, 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 (addi- 

 tive) magnitude. 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, — density, tem- 

 perature 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 

 vdth 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. Simphcity should regulate the choice, — 

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

 and 2nd, physically, in permitting as straightforward and simple definition as 



