The New Student's Reference Work/Measurement

Measurement consists essentially in the comparison of one quantity with another. Thus the measurement of a length, which is one of the simplest of all measurements, consists in determining how many times greater or less the given length is than some other given length which we agree to take as a unit. In like manner an interval of time is measured by comparing it with the interval which we employ as a unit, namely, the mean solar day. Evidently, therefore, it is possible to measure a quantity without understanding much about that quantity. No intelligent measurement, however, can be made unless one understands just what quantities are necessary to define the quantity about to be measured. The position of a point in space is intelligently measured only when we know that three definite and independent co-ordinates are required to locate the point and have determined the numerical values of these three co-ordinates. To measure the kinetic energy of a body in translation we must know how many units of mass there are in the body and with how many units of speed it is moving. Thus also we may accurately and definitely measure the acceleration of gravity at various points on the earth's surface, and yet not know the explanation of gravitation.

Practically all the quantities involved in physical science and engineering can be measured in terms of three quantities: a length, a time and a mass. The units of these three quantities are therefore called the fundamental units.

The standard of length, except in English and American commerce, is the meter; the standard of time the mean solar day; and the standard of mass the kilogram. (See Earth, Kilogram and Meter.) Units are founded upon standards, but they often differ in size from standards and may be chosen of a size which, for any particular purpose, is most convenient. Thus, in physics the centimeter or hundredth of a meter is most frequently employed; and in astronomy the second (1/86,400 of a day) is frequently a very convenient unit of time, though often the year (or 365 days roughly speaking) is more convenient.

No physical measurements can be carried out with absolute accuracy. Every comparison is affected with error to some extent. Even the standard meter at Paris, which is correct by definition, may be changing its length owing to crystallization. The rate of rotation of the earth is probably diminishing (and hence the length of the mean solar day increasing) owing to tidal friction. Even if comparisons could be made with perfect accuracy, the final measurement would be affected with error. On the other hand, the precision of modern measurement almost surpasses belief. Michelson, for instance, has succeeded in making a comparison of the standard meter with a wave-length of cadmium light in which the error does not exceed about one part in 2,000,000. Two masses may be compared with even greater accuracy. See Everett's Units and Physical Constants.