kind of geometrical drawings or plans; and for the perfect knowledge and economical working of a mineral district, it is essential that the subterranean relations of all the strata should be correctly known and expressed in an intelligible form:-1st. The original order of stratification; 2nd. The amount of dislocation by fracture; 3rd. The changes of the surface produced by denudation; and all these can be intelligibly and simultaneously expressed by models. "The deceptive appearances frequently caused by faults or fractures are represented by dissecting and making the models moveable in the direction of those faults, so that the strata may be restored to their original position, and again shifted or dislocated. The still further difficulties which arise from the denudation of the upper portion of the dislocated strata, can be adequately expressed only by the solid fac-similes of nature which models afford*. A topographical model, intended solely to represent the surface of the country, without aiming at conveying a knowledge of its internal stratification, is easily constructed, as follows, from the data given on a correct plan. Trace the outline on paper, and paste the tracing on a level board. By means of pincers fix wires into the board at the principal stations, and at the points remarkable for their elevation, or serving to give the position of the leading features. With nippers cut off the wires to the proper height, as ascertained by a vertical scale applied at their side. With fine modelling clay fill up the spaces between the wires, and give the true form and elevation to the intervening surface, by reference to a hill-sketch in horizontal contours. * Proceedings of Geol. Soc., DR. BUCKLAND'S Address, 1841, page 474. When the model is finished, a mould of it in plaster of Paris is prepared in the common way, and when the mould has been completely dried by the heat of the sun or fire, plaster casts may be taken from it. To harden the surface of the plaster in the mould and casts, they are covered with two or three coats of drying oil. If it be required to write, or trace outline, on the casts, they are prepared to receive the ink or colour, by a wash of isinglass or glue sizing, applied when quite hot. In almost all cases of topographical modelling on small scales, it is necessary to exaggerate the vertical scale, in order to convey to the observer the same appearance as that presented by nature. Under any circumstances of observation, owing to the small elevation of the eye, mountains and hills appear in profile, with the horizontal distances more or less fore-shortened, and consequently apparently diminished, their elevation suffering no apparent diminution from the same cause. When examining a model, on the contrary, the eye is so much above it, that a degree of fore-shortening takes place with respect to the vertical, and none with respect to the horizontal distances; an impression therefore is conveyed different from that which nature presents to us. Mount Etna clearly illustrates the proposition, that the effect, on our senses, of extension in height is exaggerated in nature. The base of the mountain is about 87 miles in circumference, and its height 10,874 feet, or about 2 miles. Its profile, in a model made in true proportion, would present an elevation equal only to one fourteenth part of its base; such a model, unless on a very large scale, would not recall to our minds the impressions caused by a sight of its bold features and high relief. The exaggeration to be given to the vertical distances, depends on the proportion which the model bears to nature. If the scale be very small (say 1 inch to a mile, orth of the actual size), the height may be doubled; with a scale of 6 inches to a mile, orth of the actual size, the height may be increased by one-half, and so on in proportion, the exaggeration diminishing as the scale increases. The relation must depend also on the nature of the country, a low undulating country requiring more exaggeration than a mountainous and rugged district. On a small scale this exaggeration is absolutely necessary in order to represent the small features, which would otherwise become microscopic objects. 238 CHAPTER IX. LEVELLING WITH THE MOUNTAIN BAROMETER. EXPERIENCE having once clearly demonstrated that, in a barometer carried successively to different elevations above the level of the sea, the height of the mercurial column diminished as the elevation increased, the application of the barometer to the mensuration of altitude readily suggested itself*. Experiment further determined the law, that, when the elevation increases in an arithmetical ratio, the weight or density of the atmosphere, and consequently the height of the mercurial column, diminish in a geometrical ratio. If to this be added a knowledge of the real altitude which corresponds to any given height of the mercurial column, (or to any given density of the atmosphere,) the relative altitudes of different stations may be deduced from observations made at each station, by means of the barometer, on the varied pressure of the atmosphere, under the same conditions of temperature. There are various experiments by which the real altitude which corresponds to any given height of the mercury may be deduced; the readiest is that founded on the known specific gravity of air, with respect to the whole pressure of the atmosphere on the surface of the earth. The investigation is thus given by Huttonf:— "Because the terms of an arithmetical series are proportional to the logarithms of the terms of a geometrical * BIOT's Traité de Physique, book ii., chap. 5. series, different altitudes above the earth's surface, are as the logarithms of the densities, or of the weights of air, at those altitudes. So that, if D denote the density at the altitude A, and d denote the density at the altitude a; then A being as the log. of D, and a as the log. of d, D d. the diff. of alt. A - a will be as the log. D-log.d, or log. And if A=0, or D the density at the surface of the earth; D then any altitude a above the surface A is as the log. of Asssume h so that a = h × log., when h will be of one constant value for all altitudes; and, to determine that value, let a case be taken in which we know the altitude a corresponding to a known density d; as, for instance, take a=1 foot, or 1 inch, or some small altitude; then, because the density D may be measured by the pressure of the atmosphere, or the uniform column of 27600 feet, when the temperature is 55°; therefore 27600 feet will denote the density D at the lower place, and 27599 the less den sity dat 1 foot above it; consequently 1h x log. =h × (log. 27600 – log. 27599). Performing the operation, 27600 27599 feet nearly, which gives, for any altitude in general, this theorem, viz.: |