HYPSOMETRY (Greek, Theight-measure ment"), the art of determining differences of elevation on the earth's surface. Three dis tinct modes of procedure may be adopted for measuring a given difference in level. The first and most accurate of these consists in running a aline of between the two stations whose difference in height is to be determined. This operation is conducted as follows: Let A, B and C be any three points on the earth's surface, such that the difference in level be tween any two of 'them is not more than a few feet; and let us suppose that B lies between A and C, and that it is not more than a few hun dred feet distant from either of them. A pre cise spirit level is set up at B, so that its tele scope is higher than either A or C. A gradu ated staff is then held in a vertical position upon the point A, and the observer at the level determines, by looking through the telescope, which division of the staff is of precisely the same height as the cross-hairs of his instru ment. If the height of A is known, we have merely to add to it the known length of the graduated staff, from the ground up to the vision that has been observed, in order to as certain the exact height of the cross-hairs of the level. The staff is next carried forward to the point C and a second observation of the same kind is made upon it at this point. The height above the ground of the division that is here found to be on a level with the instru ment is then subtracted from the known height of the cross-hairs in the telescope and the re sult is the height of the point C. The instru ment is then carried forward to a point, D, situ ated beyond C, and the altitude of a still more remote point, E, is determined in the same manner, by observing the graduated staff at C and at E, and then calculating the height of E from the known height of C, as determined by the preceding operation. A chain of ob servations of this sort is called a aline of lev els," and it is obvious that the difference of ele vation of any two points whatever may be de termined with great precision by running such a line from one of them. to the other.
The labor and expense of joining two dis tant points by a line of precise levels are often prohibitively great; and hence when a high order of accuracy is not essential, trigonomet ric or barometric methods are used instead. In determining the height of a mountain (for example) by the trigonometric method, a con veniently situated station is selected, from which the summit of the' mountain can be well seen and the horizontal distance from this sta tion to the vertical line passing through the summit of the mountain is first determined by any of the methods used by surveyors for de termining the distance of an inaccessible ob ject. The apparent angular elevation of the mountain is next observed; that is, the angle included between the horizontal plane through the station and the line joining the station to the top of the mountain is measured. If the earth were flat and devoid of any atmosphere, these data would enable us to compute the height of the mountain with considerable pre cision. For the vertical height of the moun tain above the station. and its horizontal dis tance from the and the line joining the station to its summit, would constitute the three sides of a right-angled triangle; and the base of this triangle being known, as well as one of the adjacent angles, its vertical height (that is, the height of the mountain above the observing station), could be easily calculated by the ordinary rules of trigonometry. In the actual case, however, the problem is compli cated by the curvature of the earth's surface and by the refraction effects due to the pres ence of the atmosphere. Corrections can be easily applied for the curvature, since that is constant in ahy given spot, and its value is well known. The refraction effects, however, are variable from time to time, according to at mospheric conditions; and it is impossible to determine them, at any given moment, with a precision sufficient to enable the trigonometric method to compete, in accuracy, with the method of leveling already described.