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ure at 61o.2, and the Modern French at 32°, it is necessary, before comparing observations taken with the three barometers, to reduce them to the same temperature, so as to neutralise the inequalities arising from the expansion of the scales by heat.
52. Correction for Height. - In comparing barometric observations at different places, we must take account of their respective heights above the sea ; for as we rise above the level of the sea, a portion of the atmosphere is left behind, and the pressure being thereby diminished, the height of the column is less. Hence an addition requires to be made proportional to the height of each station above mean sea-level. This addition is technically called “correction for height.” The amount of this correction is determined by the height of the place above the sea; the atmospheric pressure and temperature at the time ; and the distance from the centre of gravity of the earth, which is known from the latitude and height above the sea.
53. The correction for decrease of gravitation at the high station, as compared with the force of gravity at sea-level, is small, amounting only to about 0.001 inch per 400 feet.
54. Since the force of gravity is diminished in proportion to the square of the distance from the centre of gravity, the rate of its decrease with the height varies in different latitudes. Places at the equator being farther from the earth's centre than places at the poles, it follows that the force of gravity diminishes at a less rapid rate as we ascend at the equator than it does at the poles. Now, since at the equator gravity diminishes least rapidly with the height, the air of the atmosphere will at any given height weigh more there than anywhere else on the globe at the same height as compared with what it would do at sea-level. Hence to bring it to the average, a subtraction requires to be made at the equator, which diminishes in amount as we proceed towards the poles, till it falls to zero at latitude 45°, where the mean rate of decrease of gravity with the height is attained. For higher latitudes an addition is required which constantly increases
till it reaches the maximum at the poles. This correction is also small, being, for 1000 feet, less than 0.001 inch in Great Britain, and less than 0.003 inch at the equator and at the poles.
55. Since air is denser when the pressure is 30 inches than when it is 28 inches, the correction for height will be considerably greater in the one case than in the other. And again, since air is denser at 32° than at 60°, the correction for height is greater at 32° than at 60°. A column of air 87.51 English feet in height balances one-tenth of an inch of mercury (0.100 inch), when the mean temperature is 32°, and the pressure at the base of the column 30.000 inches. The coefficient expressing the expansion of air by heat, as determined by Gay-Lussac, is 0.0021 of its bulk for one degree Fahrenheit. Hence, if the temperature be raised to 50°, the height of the column of air necessary to balance one-tenth of an inch of mercury will be 91.01 feet,—that is, the raising of the temperature from 32° to 50° has pushed the air up 31 feet above places at a height of 871 feet; and the atmospheric pressure being thus increased by the weight of the 3! feet raised above them, and consequently pressing on them, the correction for height becomes less. Let H be the height in feet of a column of air at the given temperature required to balance 1 inch of mercury; f the height of the place above sea-level; h' the reading of the barometer reduced to 32°, and h the height of the barometer at the sea-level, thenThe correction for height
56. Table IV. gives the corrections for heights computed from the constants of Laplace's formula, the barometric coefficient being 60,345.51 English feet, and the coefficient for expansion of moist air 0.004; the correction for decrease of gravity on a vertical (par. 53) being included. The table gives the corrections for heights up to 1000 feet, and for every 10 degrees of temperature from 0° to 90°. The normal
height of the barometer has been assumed to be 30 inches in constructing the table.
57. It will be observed that the numbers for which corrections are given in the table begin at 10, and run thus, 10, 20, 30, &c. The corrections for the digits are obtained from those for 10, 20, 30, &c., by simply shifting the decimal point one place to the right; and for the intermediate numhers by adding the correction for the digits to those for the even tens. Example : At a temperature of 50° and at a height of 388 feet the correction will be,
58. Up to 500 or 600 feet, and when the pressure at sealevel is about 30 inches, the table may be considered sufficiently accurate as it stands : but for greater heights, and when the pressure at sea - level differs materially from 30 inches, the figures require some alteration.
59. (1.) For Temperature. The temperature strictly is not the temperature of the higher station, nor the temperature at sea-level, but the mean of the two; that is, the mean temperature of the whole stratum of air from the higher station down to sea-level. Since the temperature falls one degree for about every 300 feet of elevation, the temperature of the air will require to be increased 1° for every 600 feet the higher station is above the sea. Thus, suppose the temperature of a place 1200 feet in height to be 48°, in calculating the correction we should add 2° to it, thus making it 50°.
60. (2.) For Low Pressures at Sea-level. When the barometric reading reduced to 32° and sea-level would be less than 30 inches, the correction is too large ; and if greater, the correction is too small. To compensate for this error a column of “Differences " is added to the table, giving the amounts to be added to or taken from the corrections for each inch which the pressure at sea-level falls short of or exceeds 30 inches. With these modifications the table may be extended to include heights of 2000 feet where great accuracy is not required, or where it is not possible to be attained. But in reducing to sea-level the mean barometric observations made at high situations during a number of years, and where consequently the mean temperature of the air is closely approximated to, the more accurate methods of reducing barometric observations to sea-level given in Guyot's admirable Meteorological and Physical Tables,' which ought to be in every practical meteorologist's hands, should be adopted.
61. E.cample showing the Reduction of the Barometer to 32° and Sea-level. --At Edinburgh, during June 1867, the mean daily height of the barometer was 29.820 inches, the attached thermometer 61°.7, and the mean temperature of the air 56o.6, the height of barometer above mean sea-level being 270 feet.
Reduced to 32°,
Correction for height, 270 feet, air being 569.6 (Table IV., 7.291
Hence, if the Edinburgh observations during June 1867 had been made at sea-level, and the temperature remained at 32°, the mean barometric height for the month would have been 30.023 instead of 29.820.
62. Barometric Measurement of Heights.—It would be out of place here to give the more exact formulæ for determining heights by means of barometric observations, since to be of any value it would require to be accompanied by series of tables quite beyond the scope of an elementary treatise. Table IV. may be used for the determination of heights with sufficient accuracy for general purposes, and it may be easily enlarged so as to include all places and heights in Great Britain. A double set of observations made simultaneously is necessary -one at the place whose height it is required to determine,
and the other at the level of the sea, or at a place whose height is known, and as near the former place as possible. At each place the height of the barometer, the attached thermometer, and the temperature of the air in shade require to be observed. The problem is made simpler by reducing both barometers to 32°. To take a simple case :-Suppose the barometer at the lower station, or at the sea-level when reduced to 32°, to be 30.000 inches, and temperature of the air 51°; and the barometer at the higher station 29.510 inches, and temperature of the air 49o. The mean of the two temperatures being 50°, and the difference of the barometers .490 inch, we shall find, if we cast our eye down the column of the temperature of 50°, that .490 inch stands opposite 450 feet : the height is therefore 450 feet above the sea. where simultaneous observations cannot be had at the sealevel, the height may be determined from observations made at some known height above the sea, with which, being reduced to sea-level, the observations at the higher place may be compared.
63. Variations of the Barometer.—The variations observed in the pressure of the air may be divided into two classes— viz., periodical and irregular; the periodical variations recurring at regular intervals, whilst the irregular variations observe no stated times. The most marked of the periodical variations is the daily variation, the regularity of which in the tropics is so remarkable that, according to Humboldt, the hour may be ascertained from the height of the barometer without an error of more than 15 or 17 minutes on the average. This horary oscillation of the barometer is masked in Great Britain by the frequent fluctuations to which the atmosphere is subjected in these regions. It may, however, be detected by taking the means of a series of hourly observations conducted for some time. The results show two maxima occurring from 9 to 11 A.M. and from 9 to 11 P.M., and two minima occurring from 3 to 5 A.M. and from 3 to 5 P.M. 64. At Calcutta, where, as in other tropical climates, the