LEVEL AND LEVELING (ante). Custom has established the measurement of absolute levels from the average surface of The ocean—the mean between high and low water—as the zero level; when reckoned from any other zero level, they are relative levels. Leveling, or finding the difference between the levels of two or more points, is designated by the term hypsometry in geodesy. There are three principal and independ ent methods of leveling. The first depends upon the fact that the surfaces of fluids at rest are perpendicular to the direction of the force of gravity; upon this is based the common level. In the second method, trigonometrical leveling, we must know, first, the zenith distance,"or the angle between the zenith of the station and the object whose height we wish to find (making a correction for the effect of refraction), and, second, the horizontal distance from the station to the object, determined usually by triarTultt tion. In accurate work a careful adjustment of the theodolite, the instrument used in this method, is necessary. Local attraction sometimes causes a deflection of the plumb line, thus affecting measurements of zenith distance. Atmospheric refraction is a inure important element of uncertainty, for which reason the horizontal distance should not exceed 12 or 15 miles. The coefficient of refraction is irregular, and varies with the temperature and pressure of the atmosphere; it is most steady and nearest its minimum between 10 A.M. and 2 P.M. From the above data, the difference in level is easily calcu
lated. The weight of the atmosphere bearing upon a unit of surface diminishes in a geo metrical progression as the heights increase in an arithmetical progression; therefore, by the third method, heights are determined with the barometer. Physicists have con structed numerous formula; embodying the law of Mariotte, and introducing corrections for temperature, expansion of the air, and the effect of latitude and height upon the action of gravity. It is believed that considerable accuracy can be attained by this method, particularly if the annual means of temperature and pressure for the stations whose dif ference in level it is desired to find are substituted in the formula. Aneroid barometers have been graduated to indicate heights up to 12,000 Or 16,000 ft.; they give only approximate results. If a delkate apparatus for determining the boiling-point of water be used, the corresponding heights taken from a table will give the reading of the barometer at that point, so that the instrument itself can be dispensed with. This depends upon the fact that the boiling-point of water decreases as the pressure of the atmosphere becomes less.