The third general method of elevations on the earth's surface depends upon the fact that the atmosphere possesses weight, so that its pressure diminishes as we pass up ward. The difference in depth of two given points below the surface of the sea can be de termined with a good deal of precision by not ing the hydrostatic pressures at the two points. If these pressures are expressed in pounds per square foot and their difference is divided by the weight, in pounds, of a cubic foot of the water, the quotient will he the difference in depth of the two points, expressed in feet. The same general principle applies to the determina tion of the differences of elevation in the at mosphere, only in this case the problem is far less simple in its actual application, because the air, instead of having a practically constant density as water has, is very elastic and com pressible and very sensitive to changes of tem perature.• The observations, therefore, have to be combined by means of a formula which will take these facts into account, so far as possible. In determining differences of height by this method (which is called "barometric hypsom etryp), the difference in atmospheric pressure at the two points that are to be compared is usually determined by means of barometric readings, though the boiling-point method, to which reference will presently be made, is also used. The mercurial barometer gives the most accurate results, but the aneroid form is so much more convenient to manipulate and trans port that it is commonlypreferred for ordinary work. (See BAROMETER). When the differ ence of elevation between two given stations is to be determined, it is preferable to make the' barometric observations at both places simul taneously, simultaneous observations of the at mospheric temperature being also taken. This implies the co-operation of two observers and the possession of two sets of instruments; and hence it is not always feasible. When the work is carried out by a single observer, or with a single set of instruments, the observations should be made first at Station A, then at Sta tion B and finally at Station A again; the average readings at Station A, both of baro metric pressure and of temperature, being adopted as the definite observations at that sta tion. In this way the effects of variations of temperature and pressure are eliminated as far as possible. If h is the average reading of the barometer at the lower station, in inches, and H is the reading of the barometer at the upper station, also in inches, and if f and t' are the temperatures observed at the two stations, on the Fahrenheit scale, then the difference in height between the two stations, as expressed in feet, is approximately (log h—log H) X 60,158.6X (1
900 In place of the barometer, an instrument called a is sometimes used for determining the difference in barometric pres sure between the two Stations. The hypsom eter is essentially an instrument for determin ing the boiling point of water with a consider able degree of precision. Water, which at the normal atmospheric pressure boils at F. boils at a lower temperature on the tops of mountains, where the atmospheric pressure is less. The change in the boiling point is ap proximately 1° F. for every 511 feet of ascent; though this relation is not exact. In the practical application of the method, the boiling point is observed, on the mountain top, by an accurate thermometer which should be graduated as fine as fiftieths of a degree on the Fahrenheit scale. The difference between the temperature so obtained and 212° F. is then multiplied by the constant factor 511 and added to n (n —1) where n is the difference in tem perature, and the result is the desired estimate of the height of the mountain above the sea. This procedure, it will be seen, assumes that at the time the observation is made, the atmos pheric pressure at the sea-level has its normal (or average) value, so that water would boil there at 212° F. precisely. This condition will seldom be more than approximately fulfilled, and hence the method by boiling points, as usu ally carried out, is more uncertain than the barometric method as described above. The thermometric method is very convenient, how ever, and for this reason it is in strong favor among travelers and explorers, who usually are content with a more or less rough approxima tion to the height to be measured. The method is capable of being refined further than has here been indicated; but when more accurate results are desired than are obtainable by the process as described above, it is better to make use of simultaneous readings of the barometer and thermometer, at the two stations to be compared. (See SURVEYING), Consult John son, 'Theory and Practice of Surveying' (17th ed., rewritten by L. S. Smith, New York 1913).