Arbitrary and Absolute Units

The method of measuring a quantity, q [Q], is thus resolved into two parts: (1) the selection of a suitable unit [Q], and (2) the determination of q, the number of times which this unit is contained in the quantity to be measured. The second part is a matter for experimental determination, and has been considered in the preceding chapter. We proceed to consider the first part more closely.

The selection of [Q] is, and must be, entirely arbitrary - that is, at the discretion of the particular observer who is making the measurement. It is, however, generally wished by an observer that his numerical results should be understood and capable of verification by others who have not the advantage of using his apparatus, and to secure this he must be able so to define the unit he selects that it can be reproduced in other places and at other times, or compared with the units used by other observers. This tends to the general adoption on the part of scientific men of common standards of length, mass, and time, although agreement on this point is not quite so general as could be wished. There are, however, two well-recognised standards of length¹: viz. (1) the British standard yard, which is the length at 62°F. between two marks on the gold plugs of a bronze bar in the Standards Office; and (2) the standard metre as kept in the French Archives, which is equivalent to 39.37079 British inches. Any observer in measuring a length adopts the one or the other as he pleases. All graduated instruments for measuring lengths have been compared either directly or indirectly with one of these standards. If great accuracy in length measurement is required a direct comparison must be obtained between the scale used and the standard This can be done by sending the instrument to be used to the Standards Office of the Board of Trade.

There are likewise two well-recognised standards of mass, viz. (1) the British standard pound, a certain mass of platinum kept in the Standards Office; and (2) the kilogramme des Archives, a mass of platinum kept in the French Archives, originally selected as the mass of one thousandth part of a cubic metre of pure water at 4°C. One or other of these standards, or a simple fraction or multiple of one of them, is generally selected as a unit in which to measure masses by any observer making mass measurements. The kilogramme and the pound were carefully compared by the late Professor W. H. Miller; one pound is equivalent to 0.453593 kilogramme.

With respect to the unit of time there is no such divergence, as the second is generally adopted as the unit of time for scientific measurement. The second is 1/86400 of the mean solar day, and is therefore easily reproducible as long as the mean solar day remains of its present length.

These units of length, mass, and time are perfectly arbitrary. We might in the same way, in order to measure any other physical quantity whatever, select arbitrarily a unit quantity of the same kind, and make use of it just as we select the standard pound as a unit of mass and use it. Thus to measure a force we might select a unit of force, say the force of gravity upon a particular body at a particular place, and express forces in terms of it. This is the gravitation method of measuring forces which is often adopted in practice. It is not quite so arbitrary as it might have been, for the body generally selected as being the body upon which, at Lat. 45°, gravity exerts the unit force is either the standard pound or the standard gramme, whereas some other body quite unrelated to the mass standards might have been chosen. In this respect the gallon, as a unit of measurement of volume, is a better example of arbitrariness. It contains ten pounds of water at a certain temperature.

We may mention here, as additional examples of arbitrary units, the degree as a unit of angular measurement, the thermometric degree as the unit of measurement of temperature, the calorie as a unit of quantity of heat, the standard atmosphere, or atmo, as a unit of measurement of fluid pressure, Snow Harris's unit jar for quantities of electricity, and the B.A. unit of electrical resistance.

1	See Maxwell's Heat, chap. iv. The British Standards are now kept at the Standards Office at the Board of Trade, Westminster, in accordance with the ' Weights and Measures Act,' 1878.