tube is bent through 45° the readings are only increased in the ratio of 7 to 5. The wheel barometer of Dr R. Hooke, and the steel-yard barometer, endeavour to magnify the oscillation of the mercury column by means of a float resting on the surface of the mercury in the cistern; the motion of the float due to any alteration in the level of the mercury being rendered apparent by a change in the position of the wheel or steel-yard. The pendant barometer of G. Amontons, invented in 1695, consists of a funnel-shaped tube, which is hung vertically with the wide end downwards and closed in at the upper end. The tube contains mercury which adjusts itself in the tube so that the length of the column balances the atmospheric pressure. The instability of this instrument is obvious, for any jar would cause the mercury to leave the tube.
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| Fig. 1. Siphon Barometer. | Fig. 2. Cistern Barometer. |
The Siphon Barometer (fig. 1) consists of a tube bent in the form of a siphon, and is of the same diameter throughout. A graduated scale passes along the whole length of the tube, and the height of the barometer is ascertained by taking the difference of the readings of the upper and lower limbs respectively. This instrument may also be read by bringing the zero-point of the graduated scale to the level of the surface of the lower limb by means of a screw, and reading off the height at once from the surface of the upper limb. This barometer requires no correction for errors of capillarity or capacity. Since, however, impurities are contracted by the mercury in the lower limb, which is usually in open contact with the air, the satisfactory working of the instrument comes soon to be seriously interfered with.
Fig. 2 shows the Cistern Barometer in its essential and simplest form. This barometer is subject to two kinds of error, the one arising from capillarity, and the other from changes in the level of the surface of the cistern as the mercury rises and falls in the tube, the latter being technically called the error of capacity. If a glass tube of small bore be plunged into a vessel containing mercury, it will be observed that the level of the mercury in the tube is not in the line of that of the mercury in the vessel, but somewhat below it, and that the surface is convex. The capillary depression is inversely proportional to the diameter of the tube. In standard barometers, the tube is about an inch in diameter, and the error due to capillarity is less than ·001 of an inch. Since capillarity depresses the height of the column, cistern barometers require an addition to be made to the observed height, in order to give the true pressure, the amount depending, of course, on the diameter of the tube.
The error of capacity arises in this way. The height of the barometer is the perpendicular distance between the surface of the mercury in the cistern and the upper surface of the mercurial column. Now, when the barometer falls from 30 to 29 inches, an inch of mercury must flow out of the tube and pass into the cistern, thus raising the cistern level; and, on the other hand, when the barometer rises, mercury must flow out of the cistern into the tube, thus lowering the level of the mercury in the cistern. Since the scales of barometers are usually engraved on their brass cases, which are fixed (and, consequently, the zero-point from which the scale is graduated is also fixed), it follows that, from the incessant changes in the level of the cistern, the readings would be sometimes too high and sometimes too low, if no provision were made against this source of error.
A simple way of correcting the error of capacity is—to ascertain (1) the neutral point of the instrument, or that height at which the zero of the scale is exactly at the height of the surface of the cistern, and (2) the rate of error as the barometer rises or falls above this point, and then apply a correction proportional to this rate. The instrument in which the error of capacity is satisfactorily (indeed, entirely) got rid of is Fortin’s Barometer. Fig. 3 shows how this is effected. The upper part Fortin’s Barometer.of the cistern is formed of a glass cylinder, through which the level of the mercury may be seen. The bottom is made like a bag, of flexible leather, against which a screw works. At the top of the interior of the cistern is a small piece of ivory, the point of which coincides with the zero of the scale. By means of the screw, which acts on the flexible cistern bottom, the level of the mercury can be raised or depressed so as to bring the ivory point exactly to the surface of the mercury in the cistern. In some barometers the cistern is fixed, and the ivory point is brought to the level of the mercury in the cistern by raising or depressing the scale.
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| Fig. 3.—Fortin’s Barometer. |
In constructing the best barometers three materials are employed, viz.:—(1) brass, for the case, on which the scale is engraved; (2) glass, for the tube containing the mercury; and (3) the mercury itself. It is evident that if the coefficient of expansion of mercury and brass were the same, the height of the mercury as indicated by the brass scale would be the true height of the mercurial column. But this is not the case, the coefficient of expansion for mercury being considerably greater than that for brass. The result is that if a barometer stand at 30 in. when the temperature of the whole instrument, mercury and brass, is 32°, it will no longer stand at 30 in. if the temperature be raised to 69°; in fact, it will then stand at 30·1 in. This increase in the Corrections of the barometer reading. height of the column by the tenth of an inch is not due to any increase of pressure, but altogether to the greater expansion of the mercury at the higher temperature, as compared with the expansion of the brass case with the engraved scale by which the height is measured. In order, therefore, to compare with each other with exactness barometric observations made at different temperatures, it is necessary to reduce them to the heights at which they would stand at some uniform temperature. The temperature to which such observations are reduced is 32° Fahr. or 0° cent.
If English units be used (Fahrenheit degrees and inches), this correction is given by the formula x＝−H·09T − 2·561000; in the centigrade-centimetre system the correction is ·0001614 HT (H being the observed height and T the observed temperature). Devices have been invented which determine these corrections mechanically, and hence obviate the necessity of applying the above formula, or of referring to tables in which these corrections for any height of the column and any temperature are given.
The standard temperature of the English yard being 62° and not 32°, it will be found in working out the corrections from the above formula that the temperature of no correction is not 32° but 28·5°. If the scale be engraved on the glass tube, or if the instrument be furnished with a glass scale or with a wooden scale, different corrections are required. These may be worked out from the above formula by substituting for the coefficient of the expansion of brass that of glass, which is assumed to be 0·00000498, or that of wood, which is assumed to be 0. Wood, however, should not be used, its expansion with temperature being unsteady, as well as uncertain.
If the brass scale be attached to a wooden frame and be free to move up and down the frame, as is the case with many siphon barometers, the corrections for brass scales are to be used, since the zero-point of the scale is brought to the level of the lower limb; but if the brass scale be fixed to a wooden frame, the corrections for brass scales are only applicable provided the zero of the scale be fixed at (or nearly at) the zero line of the column, and be free to expand upwards. In siphon barometers, with which an observation is made from two readings on the scale, the
