INTRODUCTION. 



UNITS OF MEASUREMENT AND CONVERSION FORMULA. 



Units. — The quantitative measure of anything is a number which expresses the 

 ratio of the magnitude of the thing to the magnitude of some other thing of the 

 same kind. In order that the number expressing the measure may be intelligi- 

 ble, the magnitude of the thing used for comparison must be known. This leads 

 to the conventional choice of certain magnitudes as units of measurement, and 

 any other magnitude is then simply expressed by a number which tells how many 

 magnitudes equal to the unit of the same kind of magnitude it contains. For 

 example, the distance between two places may be stated as a certain number of 

 miles or of yards or of feet. In the first case, the mile is assumed as a known 

 distance ; in the second, the yard, and in the third, the foot. What is sought for 

 in the statement is to convey an idea of the distance by describing it in terms of 

 distances which are either familiar or easily referred to for comparison. Similarly 

 quantities of matter are referred to as so many tons or pounds or grains and so 

 forth, and intervals of time as a number of hours or minutes or seconds. Gen- 

 erally in ordinary affairs such statements appeal to experience ; but, whether this 

 be so or not, the statement must involve some magnitude as a fundamental quan- 

 tity, and this must be of such a character that, if it is not known, it can be readily 

 referred to. We become familiar with the length of a mile by walking over dis- 

 tances expressed in miles, with the length of a yard or a foot by examining a yard 

 or a foot measure and comparing it with something easily referred to, — say our 

 own height, the length of our foot or step, — and similarly for quantities of other 

 kinds. This leads us to be able to form a mental picture of such magnitudes 

 when the numbers expressing them are stated, and hence to follow intelligently 

 descriptions of the results of scientific work. The possession of copies of the 

 units enables us by proper comparisons to find the magnitude-numbers express- 

 ing physical quantities for ourselves. The numbers descriptive of any quan- 

 tity must depend on the intrinsic magnitude of the unit in terms of which it is 

 described. Thus a mile is 1760 yards, or 5280 feet, and hence when a mile is 

 taken as the unit the magnitude-number for the distance is i, when a yard is taken 

 as the unit the magnitude-number is 1760, and when afoot is taken it is 5280. 

 Thus, to obtain the magnitude-number for a quantity in terms of a new unit when 

 it is already known in terms of another we have to multiply the old magnitude- 

 number by the ratio of the intrinsic values of the old and new units ; that is, by 

 the number of the new units required to make one of the old. 



