same in different countries. In Britain 62° F. has been adopted since the revision of the standards in 1822, as being a convenient average temperature for work; but, as it is purely a temperature of convenience, the rather higher point of 68° F. would be better. In any case an aliquot part of the thermal unit from freezing to boiling of water should be adopted; 62° is 16 and 68° is 15 of this interval. Whether a much higher temperature would not be more conducive to accuracy is a question; 92°, or 13 of the thermal unit, would be so near the temperature of the observer's skin and breath that measures and balances could be approached with less production of error; and such a heat does not at all hinder accurate observing. The French temperature of 32° F. for standards has abandoned all other considerations in favour of readily fixing the temperature in practice by melting ice. This is a ready means of regulation, but a point so far from ordinary working temperatures has two great disadvantages: the observer's warmth produces more error, and the corrections for all observations not iced are so large that the rates of expansion require to be known very accurately for every substance employed. For water their standard temperature is 39°.2 F., when it is at its maximum density; this has the advantage that the density varies less with temperature than at any other point, but it is very doubtful if this is much used for actual work.
No substance expands uniformly with temperature, most materials expanding more rapidly at higher temperatures. The expansion of rods of the following metals, of 100 inches long, is given in decimals of an inch for the 90° from 32° to 122° F. (0 to 50° C.), and from 122° to 212° F. (50° to 100° C.):[1]—
| Platinum. | Platino- iridium. |
Steel. | Iron. | Bronze. | Brass. | Zinc. | |
| 32° to 122° | .0445 | .0435 | .0536 | .0591 | .0876 | .0915 | .1469 |
| 122° to 212° | .0471 | .0454 | .0574 | .0637 | .0927 | .0964 | .1437 |
But variations of 3 or 4 per cent. may easily be found in the rates of different specimens apparently alike; hence the individual expansion of every important measure needs to be ascertained.
Weighing is complicated by being done in a dense and variable atmosphere, unless—as in the most refined work—the whole balance is placed in a vacuum. When in the air all bodies placed in the balance must, for accurate purposes, have their volume known; and the weight of an equal volume of such air as they are weighed in must be added to their apparent weight to get their true weight. The weight of air displaced by a pound of the following materials is given in grains, at temperature 62° F., barometer 30 inches,—also with barometer 29 inches (temperature 62°), and with temperature 32° (barometer 30 inches), to illustrate the variation[2] (allowing for contraction of the material as well):—
| Platinum. | Brass. | Gilt Bronze. |
Iron, with Lead Adjustment. |
Quartz. | Glass. | Water. | |
| Sp. Gr. | 21.157 | 8.143 | 8.283 | 7.127 | 2.650 | 2.518 | 1.000 |
| 62°, 30 | .403 | 1.047 | 1.029 | 1.196 | 3.217 | 3.385 | 8.523 |
| 62°, 29 | .390 | 1.012 | .995 | 1.156 | 3.110 | 3.272 | 8.240 |
| 32°, 30 | .429 | 1.112 | 1.093 | 1.271 | 3.422 | 3.600 | 9.056 |
The above is for London at sea-level; but where the force of gravity is less 30 inches height of mercury will weigh less, and will therefore balance a less weight of air; the air allowance must therefore be less for 30 inches of mercury barometer in lower latitudes and greater heights over sea-level. The change, for instance, in the allowance of air equal to the brass pound will make it, instead of 1.047 grains, become 1.046 when 15,000 feet above the sea, or 10° S. of London. Hence this reduction need rarely be noticed. The composition of the air also varies, and most seriously in the amount of aqueous vapour; the above is ordinary air, but if quite dry the 1.047 grains would become 1.052 grains; the change in carbonic acid is quite immaterial, unless in very close rooms, so that it may be concluded that the moisture of the air is the main point to be noted, after its temperature and pressure,—small errors in any of these three data making far more difference than any other compensation that can be made in the weight of air.
The more complex allowances for the expansion of water in glass, brass, or other vessels we need not enter on here; the principles are simple, but the data require to be accurately determined for the material in question. The expansion of water is, however, so often in question, especially for taking specific gravities, that it is here given. A constant volume which contains or displaces 10,000 grains of water at 62° will contain[3]—
| At | 32° F. (0° C.), | 10,009.84 | grains. | At | 62° F. (1623° C.), | 10,000.00 | grains. |
| At„ | 39°.2 F. (4° C.), | 10,011.20 | grains.„ | At„ | 68° F. (20° C.), | 9,993.76 | grains.„ |
| At„ | 50° F. (10° C.), | 10,008.89 | grains.„ | At„ | 86° F. (30° C.), | 9,968.76 | grains.„ |
Hence if a specific gravity is observed at any of these temperatures it must be × the corresponding weight ÷ 10,000 to reduce it to a comparison with water at 62°; the expansion of the body observed is another question altogether, and must be compensated also.
The weight of a cubic inch, or other linearly measured volume, of water is not yet very accurately known. The observations have been made by weighing closed hollow metal cases in and out of water (thus obtaining the weight of an equal volume of water), and then gauging the size of the case with exactitude. Cubes, cylinders, and spheres have been employed. The results are:[4]—
| Cubic Inch at 62° F. |
Cubic Foot at 62° F. |
Cubic Decimetre at 4° C. | ||||||
| Grains. | Ounces. | Grammes. | ||||||
| 1795 |
|
252.603 | 997.70 | 1000.000 | ||||
| 1797 |
|
252.724 | 998.18 | 1000.480 | ||||
| 1821 | ||||||||
| 1825 | 252.678 | 998.00 | 1000.296 | |||||
| 1830 |
|
252.515 | 997.35 | 999.653 | ||||
| 1841 |
|
252.600 | 997.69 | 999.989 | ||||
National Standards and Copies.—Having now noticed the principles and constants involved, we will consider the British and metric standards, the only ones now used in scientific work.
The imperial standard yard is a bronze bar 38 inches long, 1 inch square; the defining lines, 36 inches apart, are cut on gold studs, sunk in holes, so that their surface passes through the axis of the bar. Thus flexure does not tend to tip the engraved surfaces nearer or farther apart. This bar when in use rests on a lever frame, which supports it at 8 points, 4.78 inches apart, on rollers which divide the pressure exactly equally.[5] This standard is in actual use for all important comparisons at the Standards Office. Four copies, which are all equal to it, within 16° of temperature, are deposited in other places in case of injury or loss of the standard. The standard pound is a thick disk of platinum about 116 inches across, and 1 inch high, with a shallow groove around it near the top. Four copies are deposited with the above copies of the yard. For public use there are a series of end-standards exposed on the outer wall of Greenwich observatory; and a length of 100 feet, and another of 66 feet (1 chain), marked on brass
- ↑ Computed from Fizeau, Ann. Bur. Long., 1878.
- ↑ Computed from Chisholm, Weighing and Measuring, 1877, p. 162; also see p. 158.
- ↑ Computed from Report of Standards Department, 1883.
- ↑ Computed from Chisholm, op. cit., p. 112.
- ↑ See Chisholm, op. cit., pp. 188, 189. For less refined purposes measuring bars should be supported on two points, 21 per cent, of the whole length from the ends. This equalizes the strains in the curves, and makes a minimum distortion.
