478
WEIGHTS AND MEASURES
THIS subject may be best divided for convenience of reference into three parts:—I. Scientific, including the facts and data usually needed for scientific reference; II. Historical, including the principles of research and results in ancient metrology; and III. Commercial, including the weights and measures of modern countries as used in commerce.
I. Scientific.
A unit of length is the distance between two points defined by some natural or artificial standard, or a multiple of that. For instance, in Britain the unit of the yard is defined by the distance between two parallel lines on gold studs sunk in a bar of bronze, when at 62° F., which bar is preserved in the Standards Office. There are other units, such as the inch, foot, mile, &c.; but, as these are aliquot parts or multiples of the yard, there is no separate standard provided for them. A unit is an abstract quantity, represented by a certain standard, and more or less perfectly by copies of the standard.
A unit of mass is the matter of a standard of mass, or a multiple of that. For instance, in Britain the unit of the pound is defined by a piece of platinum preserved in the Standards Office.
A unit of weight is the attractive force exerted between a unit of mass and some given body at a fixed distance,—this force being the weight of the unit in relation to the given body, or any other body of equal mass.[1] Usually the given body is the earth, and the distance a radius of the earth. For instance, the unit of weight in Britain is the attraction between the earth and the standard pound when that is placed at sea-level at London, in a vacuum. For astronomical comparisons the unit of mass is the sun, and a unit of weight is not needed.
Standards of length are all defined on metal bars at present in civilized countries. Various natural standards have been proposed, such as the length of the polar diameter of the earth (inch), the circumference of the earth (metre) in a given longitude, a pendulum vibrating in one second at a fixed distance from the earth, a wave of light emitted by an incandescent gas, &c. But the difficulty of ascertaining the exact value of these lengths prevents any material standard being based upon them with the amount of accuracy that actual measurements, to be taken from the standard, require. A natural standard is therefore only a matter of sentiment.
Standards of length are of two types, the defining points being either at a certain part of two parallel lines engraven in one plane (a line-standard), or else points on two parallel surfaces, which can only be observed by contact (an end-standard). The first type is always used for accurate purposes. Units of surface are always directly related to standards of length, without any separate standards. Volume is either determined by the lineal dimensions of a space or a solid, or, for accurate purposes, by the mass of water contained in a volume at a given temperature, which again is measured either by liquid measure, or, more accurately, by weight. The standard of volume in Britain is a hollow cylinder of bronze, with a plate glass cover, when at 62° (gallon), legally defined as 277·274 cubic inches, or containing 10 pounds of water at 62°F.
Comparisons.—Lengths nearly equal are compared accurately by fixing two micrometer microscopes with their axes parallel, and at the required distance apart, on a massive support which will not quickly vary with temperature; then the two lengths to be compared, e.g., the standard yard and another, are alternately placed beneath the microscopes, and their lengths observed several times. The error of a single observation in the Standards Department is stated to be a 100,000th of an inch. For fractional lengths a divided bar is required, the accuracy of which is ascertained by a shorter measure, which can be compared with successive sections of the whole length by micrometers. For ordinary purposes, where not less than ·001 inch is to be observed, measures may be placed in contact if one is divided on the edge, and the comparison made with a magnifier. In large field-work the ends of a measure are transferred vertically to the ground by a small transit instrument or theodolite. End-measures between surfaces are read by means of a pair of contact pieces bearing line marks, the value of which is ascertained separately, or by a second end-measure; if both measures bear a line for observation, reversals then give the value of each measure.
Volumes are always most accurately defined by their weight of water, as weighing can be more accurately done than measuring. If the volume is hollow, it may be filled with water and closed with a sheet of plate glass, or if solid the body may be weighed in water and out, the difference giving the weight of its volume of water. Unfortunately the relation between water-weight and absolute volume is not yet accurately known. Volumes of liquid are similarly ascertained by their weight. Volumes of gas are measured in a graduated glass vessel inverted over a liquid, or for commercial purposes by some form of registering flow-meter.
Masses are compared by the Balance (q.v.), which may be made to indicate a 100,000,000th of the mass. They may also be estimated, not by their attractive force being balanced by an equal mass, but by the elasticity of a spring; this, which is the only true weighing-machine showing weight and not mass, is useful for rough purposes, owing to its quick indication; the most accurate form probably is that with angular readings.[2]
Temperature and the Atmosphere.—All the serious difficulties of weighing and measuring result from these causes, the effects of which and their corrections we will briefly notice. In measurement, since all bodies expand by heat, the temperature at which any measure or standard bar represents the abstract unit requires to be accurately stated and observed, the accuracy of optical observation being about equal to 1100 of a degree F. of expansion in a standard. Great accuracy is therefore needed in the manufacture and reading of thermometers, and care that the standard and the thermometer shall be at the same temperature. Another method is to attach a parallel bar of very expansible metal to one end of the standard, and read its length on the standard at the other end; this ensures a more thorough uniformity of mean temperature between the standard and the heat-measurer. The most accurate method is by immersing the measures in a liquid, of which the temperature is read by several thermometers; but this is scarcely needful unless high or low temperatures are required to ascertain the rate of expansion. A room with thick walls, double windows, and the temperature regulated by a gas stove is practically sufficiently equable for comparisons.
The temperature adopted for the standards is not the
- ↑ The word weight has in common use two meanings,—(1) the force exerted between the earth and a body, and (2) a mass which is weighed against other bodies. In scientific use, however, weight means only a property of matter by which it is most convenient to compare the relative amounts of masses.
- ↑ See Nature, xxx. 205.
