The barometer applied to the measuring of iiltitudes.—The secondary character of the barometer, namely, as an instrument for measuring accessible heights or depths, was first proposed by Pascal and Descar tes, and succeeding philosophers have been at great pains to ascertain the pro. portion between the fall of the barometer and the height to which it is carried ; as Halle, Mariotte, Shockburgh, Rey, and more especially by De Luc, who has given a critical and historical detail of most of the attempts that have at different times been made for applying the motion of the mercury in the barometer to the mea surement of accessible heights And for this purpose serves the portable barome ter already described, which should be made with all the accuracy possible. Va rious rules have been liven, by the writers on this subject, for computing the height ascended from the given fall of the mer cury in the tube of the barometer, the most accurate of wh ch was that of Dr. Halley, till it was rendered much more accurate by the indefatigable researches of De Luc, by introducing into it the cor rections of the columns of mercury and air, on account of heat. 'Plus rule is as 111 follows: viz. 10000 x log. of -- is the al titude in fathoms, in the mean tempera ture of 31° ; and for every degree of the thermometer above that, the result must be increased by so many times its 435th part, and diminished when below it : in which theorem M denotes the length of the column of mercury in the barometer tube at the bottom, and in that at the top of the hill, or other eminence ; which lengths may be expressed in any one and the same sort of measures, whether feet, or inches, or tenths, &c. and either Eng lish, or French, or of any other nation ; but the result is always in fathoms, of six English feet each. The following rules must be attended to.
1. Observe the height of the barome ter at the bottom of any height or depth proposed to be measured ; together with the temperature of the mercury, by means of the thermometer attached to the baro meter, and also the temperature of the air in the shade, by another thermometer which is detached from the barometer.
2. Let the same thing be done also at the top of the said height or depth, and as near to the same time with the former as may be.- And letthose altitudes of mer cury be reduced to the same temperature, if' it be thought necessary, by correcting either the one or the other, viz. augment ing the height of the mercury in the colder temperature, or diminishing that in the warmer, by its 9600th part for every degree of difference between the two ; and the altitudes of mercury so cor rected are what are denoted by M and m, in the algebraic formula above.
3. Take out the common logarithms of the two heights of mercury, so corrected, and subtract the less from the greater, cutting off from the right-hand side of the remainder three places for decimals ; so shall those in the left be fathoms in whole numbers, the tables of logarithms being understood to be such as have seven places of decimals.
4. Correct the number last found, for the difference of the temperature of the air, as follows : viz. take half the sum of the two temperatures of the air, shewn by the detached thermometers, for the mean one ; and for every degree which this differs from the standard tempera ture of 31°, take so many times the 435th part of the fathoms above found, and add them, if the mean temperature be more than 31°, but subtract them, if it be below 31°; so shall the sum or difference be the true altitude in fathoms, or, being multi plied by 6, it will give the true altitude in English feet.
Er. 1. Let the state of the barometers and thermometers be as follows, to find the altitude ; viz.
Thermometers. . Barometers. detached. attached.
57 57 29.68 lower 42 43 25.28 upper mean 4gildif 14 As 9600 : 14 : : 29.68 :.04 cor. 04 logs.
mean 491 M ..-- 29.64 - 4718782 stand. 31 m = 25.28 - 4027771 dif. Thf As 435 : 18i:: 691.011 _: 29.388 29.388 the altitude 5720.399 fath.
sought is Z. or 4322.394 feet.
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Ex. 2. To find the altitude of a hill, when the state of the barometer and thermometer, as observed at the bottom and top of it, is as follows ; viz.
Barometers.
I detached. attached.
35 41 29.45 31 38 26.82 mean n lif. 3 As 9600 : 3 : : 29.45 : .01 .01 logs.
mean 33 M = 29.44 - 4689378 stand.31 m = 26.82 - 4284588 dif. 2 As 435 404.7F) : 1.86 1.86 the altitude c4u6.65 fathotns.
sought is Z or 2439.93 feet.
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The mean height of the barometer in London upon an average of two observa tions in every day in the year, kept at the house of the Royal Society for many years past, it 29.88 ; the medium tempera ture,or height of the thermometer,accord ing to the same, being 58°. But the medi um height, at the surface of the sea, ac cording to Sir Geo. Shuckburgh, is 30.04 inches, the heat of the barometer being 55°, and of the air 62°. See l'sl,meTtcs.