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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 Parrot, 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 VERA CRUz.

-D MExico.

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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

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of Göttingen, from a comparison of distant observations on the surface of the globe, proposed a formula, which, with a slight modification, appears to exhibit correctly the temperature of any place at the level of the sea. Let 4 denote the latitude; and 29 cosp", or 14% suvers 24, B will express, in degrees of the centigrade scale, the medium heat on the coast. But the gradations of climate are more easily conceived by help of a geometrical diagram. From the centre C, draw straight lines to the several degrees of the qua- **** - |-------------------- a 1–1 – 1

drant, and cutting is “: “75-'73"aa"; i. the interior semi- circle; then the radius CA denoting 29°, the perpendiculars from the points of section will intercept segments proportional to the mean temperature expressed on DE.

The higher regions are invariably colder than the plains; and I have been able, after a delicate and patient research, to fix the law which connects the decrease of temperature with the altitude. If B and b denote the barometric pressure at the

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lower and upper stations; then will (#–4) 25 express,

on the centigrade scale, the diminution of heat in ascent. Hence, for any given latitude, that precise point of elevation

may be found, at which eternal frost prevails. Put a = +

l and t = the standard temperature; then -— a ) 25=t, or

a" + .04 ta = 1, which quadratic equation being resolved, gives the relative elasticity of the air at the limit of congelation, whence the corresponding height is determined. From these data the following table has been calculated.

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This table will facilitate the approximation to the altitude of any place, which is inferred either from its mean temperature or its depth below the boundary of perpetual congelation. The decrements of heat at equal ascents are not altogether uniform, but advance more rapidly in the higher regions of the atmosphere. At moderate elevations, however, it will be sufficiently near the truth, to assume the law of equable progression, allowing in this climate one degree of cold by Fahrenheit's scale for every ninety yards of ascent, and for every hundred yards in the tropical regions. Thus, the temperatures of the Crawley and Black springs on the ridge of the Pentland hills, were observed by Mr Jardine, where they first issue from the ground, to be 46°.2 and 45°; which, compared with the standard temperature at the same parallel of latitude, would give 567 and 891 feet of elevation above the sea. The real heights found by levelling were respectively 564 and 882; a coincidence most surprising and satisfactory.— This ready mode of estimation claims especially the attention of agriculturists. Dr Francis Buchanan informs me, that he found the temperature of a spring at Chitlong, in the Lesser Valley of Népal, to be 14°.7 centigrade. But the mean temperature in the parallel of 27°38' being 229.8, the density of the atmosphere corresponding to difference 8°.1, is .8510, which gives 4500 feet for the corrected altitude. From other observations of the same accurate traveller, we may conclude that Kathmandre, the capital of Népal, is elevated about 2780 feet above the level of the sea. I found myself the temperature of the celebrated fountain of Vaucluse, which gushes with such volume as to form almost immediately a respectable river, to be 13° centigrade, or 2° less than what corresponds to its latitude or 430 55'. It may hence be inferred, that Vaucluse is 1080 feet above the level of the Mediterranean. The rule stated above for computing the measurements by the barometer, seems to give results somewhat less, on the whole, than those which are obtained from geometrical observations. It would ensure greater accuracy, perhaps, to view the approximate height as answering to a temperature one degree under the point of congelation; and consequently, in applying the last correction, to add unit to the indi

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