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the objections themselves which ignorance opposed to Torricelli's immortal discovery of the weight of our atmosphere. But more than a century elapsed before the improvements in mechanics had completely adapted the machine to that purpose, and experiment combined with observation had ascertained the proper corrections. Barometers of various constructions are now made quite portable, and which indicate with the utmost precision the height of the mercurial column supported by the pressure of the atmosphere. The air which invests our globe, being a fluid extremely compressible, must have its lower portions always rendered denser by the weight of the incumbent mass. To discover the law that connects the densities with the heights in the atmosphere, it is only requisite, therefore, to apply the fact which experiment has established,—that the elasticity counterbalancing the pressure is exactly proportioned to the density. The elasticity of the air at any point of elevation, is hence measured by a column possessing the same uniform density, with a certain constant altitude. Let AB denote the height of this equiponderant column, and the perpendicular BI its density; and suppose the mass of air below to be distinguished into numerous strata, having each the same thickness BC. It is evident that the weight of the minute stratum at B will be expressed by BC; whence AB is to AC, or BI to CK, as the pressure at B to the augmented pressure at C, and therefore the density at C is denoted by CK. Again, having joined IC,
and drawn KD parallel, BI: CK :: BC : CD ; and consequently CD will, on the same scale of density, express the weight of the stratum at C. Hence, AC is to AD, as CK to DL, or as the density at C is to that at D. It thus appears, that, repeating this process, the densities BI, CK, DL, &c. of the successive strata form a continued geometrical progression. But the same relation will evidently obtain at equal though sensible intervals. Thus, the density of the atmosphere is reduced nearly to one half, for every 3% miles of perpendicular ascent. At 7 miles in height, the corresponding density is one-fourth; at 10% miles, one-eighth; and at 14 miles, onesixteenth. The difference of altitude between two points in the atmosphere, is hence proportional to the difference of the logarithms of the corresponding densities or vertical pressures. But the heights of mountains may be computed from barometrical measurement to any degree of exactness, by a simple numerical approximation. Since AB, AC, AD, &c. are continued proportionals, it follows that AB; BC : : AB+AC+AD, &c.; BC+CD+DE, &c. or BH. Let n denote the number of secAn example will elucidate the whole process. In August 1775, General Roy observed the barometer on Caernarvon Quay at 30.091 inches, the attached thermometer being 15°.7, and the detached 15°.6 centigrade, while on the Peak of Snowdon the barometer stood at 26.409, the attached thermometer marking 10°.0, and the detached 8°.8. Here, twice the difference of the attached thermometers is 11°.4, which multiplied into .00264 gives .030, for the correction of the upper barometer. Next, 30.091 + 26.439 : 30.091 - 26.439, or 56.530: 3.652: : 52000 : 3359. Again, twice the sum of the degrees marked on the detached thermometers is 48.8, which multiplied into 3.359 gives 164; wherefore, the true height of Snowdon above the Quay of Caernarvon is 3359-1-164, or 3533 feet. The correction for centrifugal force is only 7 feet more.
tions or strata contained in the mass of air, and ; (AB+AH)
will nearly express the sum of the progression AB, AC, AD, &c.; wherefore, AB+AH : BH:: 2AB: nBC, or the absolute difference of altitude. The height AB of the equiponderant column, reduced to the temperature of freezing water, is nearly 26,000 feet; and hence this general rule,_As the sum of the mercurial columns is to their difference, so is the constant number 52,000 to the approximate height. This number is the more easily remembered, from the division of the year into weeks. Two corrections depending on the variation of temperature are besides required. I. Mercury expands about the 5,000th part of its bulk, for each degree of the centigrade scale; and hence the small addition to the upper column will be found, by removing the decimal point four places to the left, and multiplying by twice the difference between the degrees of the attached thermometers. 2. But the correction afterwards applied to the principal computation is of more consequence. Air has its volume increased by one 250th part, for each degree of heat on the same scale. If, therefore, the approximate height, having its decimal point shifted back three places, be multiplied by twice the sum of the degrees on the detached thermometers, the product will give the addition to be made. If it were worth while to allow for the effect of centrifugal force in diminishing the pressure of the aërial column, this will be easily done before the last multiplication takes place, by adding to twice the degrees on the detached thermometers the fifth part of the inean temperature corresponding to the latitude.
This mode of approximation may be deemed sufficiently near, for any heights which occur in this island; but greater accuracy is attained by assuming intermediate measures. To illustrate this, I shall select another example. At the very period when General Roy was making his barometrical observations at home, Sir George Shuckburgh Evelyn found the barometer to stand at 24.167 on the summit of the Mole, an insulated mountain near Geneva, the attached and detached thermometers indicating 14°.4 and 13°4, while they marked 16°.3 and 17°.4 at a cabin below and only 672 feet above the lake, the altitude of the barometer at this station being 28.132. Now, 3.8x.0024=.009, and 24.167+009=24.176; the arithmetical mean between which and 28.132 is 26.154; and hence, separately, 50.330: 1.978:: 52000: 2044, and 54.286 : 1.978:: 52000: 1895. Wherefore, joining these two parts, 2044+ 1895, or 3939 expresses the approximate height. The final correction is 61.6x3.939–243, or 254 feet, if allowance be made for the effect of centrifugal force, and consequently the Mole has its summit elevated 4865 feet above the lake of Geneva, and 6063 above the level of the sea.
In general, let A and A + nb denote the correct lengths of the columns of mercury at the upper and the lower stations; the approximate height of the mountain will be expressed by
If n were assumed a large number, the result would approach to the accuracy of a logarithmic computation, though such an extreme degree of precision will be scarcely ever wanted. To expedite the calculation of heights from barometrical observations, I have now caused Mr Cary, optician in London, to make for sale a sliding-rule, of an easy and commodious construction. That small instrument, which should be accompanied with a barometer of the lightest and most portable kind, will be found very useful to mineralogical travellers who have occasion to explore mountainous tracts. Nothing could tend more to correct our ideas of physical geography, than to have the principal heights in all countries measured, at least with some tolerable degree of precision. But the elevation of any place above the sea may be ascertained very nearly, from the comparison of even very distant barometrical observations, especially during the steadiness of the fine season in the happier climates. In the summer of 1814, Engelhardt and Par, rot, two Prussian travellers, by a series of fifty-one barometrical observations, made along the distance of 711 miles, from the Caspian to the Black Sea, ascertained the former to be 334 English feet below the level of the latter, which completely oversets the supposition of any subterranean communication existing between those seas. By the same mode may be traced a profile or vertical section, that shall exhibit at one glance the great features of a country. As a specimen, I have combined and reduced the sections which the celebrated philosophic traveller Humboldt has given of the continent of America, running in a twisted direction from Acapulco to Vera Cruz, and connecting the Pacific with the Atlantic Ocean.
A AcAPULco. f Venta de Chalco.
a Peregrino. g St Martin.
B CHILPANSINGO. E LA PUEBLA DE Los ANGELEs. b Mescala. - h El Pinal.
c Tepecuacuilco. i Perote.
d Puente de Istla. k Cruz Blanca. C CUERNAVACA. F XALAPA.
e La Cruz del Marques. G WERA CRUz. D Mexico.
The divided scale expresses the horizontal distance in miles, while the parallels, on a much larger scale, mark the elevation in feet. This profile is really composed of four successive sections, which are distinguished by opposite shadings. The survey proceeded first along the road from Acapulco to Mexico, thence to Puebla de los Angeles, next to Cruz Blanca, and finally to Vera Cruz. These several directions and distances are expressed in the ground plan. An attempt is likewise made in this profile, to convey some idea of the geological structure of the external crust: Limestone is represented by straight lines slightly inclined from the horizontal position. Basalt, by straight lines slightly reclined from the perpendicular. Porphyry, by waved lines somewhat reclined. Granite, by confused hatches. Amygdaloid, by confused points.
But the easiest way of estimating within moderate limits the elevation of a country, is founded on the difference between the standard and the actual mean temperature as indicated by deep wells or copious and shaded springs. Professor Mayer