*THE POPULAR SCIENCE MONTHLY.*

difference of height, required. Before the barometer readings can be used, this must be reduced to the *same* temperature—usually 32º F.

Various formulæ have been computed by eminent mathematicians and physicists for calculating the difference of height between two points. These formulæ depend on certain assumptions which, however, can not be considered as rigidly true. The most important of these assumptions is that the atmosphere may be supposed to be in a state of statical equilibrium. But owing to the changes constantly taking place, due to differences of temperature, humidity, winds, etc., this assumption can not be considered correct. The result will therefore be only an approximation to the truth. Assuming, however, a statical equilibrium of the atmosphere, a formula can easily be deduced from known principles. For this purpose we must first ascertain the weight of a cubic inch of air and a cubic inch of mercury at a certain temperature and pressure, and in a given latitude, say 45º. Then, by Boyle and Mariotte's law, connecting the weight of a gas and the pressure, the formula can be obtained for determining the height required. There are several elaborate formulæ used for this purpose. These include terms for altitude, latitude, temperature, and humidity. A correction for altitude is theoretically necessary owing to the diminution in the force of gravity—and, therefore, a decrease in the weight of bodies—with increased distance from the center of the earth, but this correction is comparatively very small, and may, for all practical purposes, be neglected. For the same reason a correction for latitude is mathematically required, owing to the spheroidal figure of the earth; but this, too, is very small, and may be safely neglected. The correction for temperature of the *air* is, however, very important. This term is easily computed. It is obtained—for the Fahrenheit scale—by deducting 64 from the sum of the observed temperatures at the upper and lower stations, dividing the difference by 900, and adding unity to the result. A correction for humidity of the air is also necessary; but it is doubtful whether it is desirable to complicate the formula by a correction for atmospheric moisture, the laws of which are so imperfectly understood.

In all the barometric formulæ which have been proposed the first term is constant, and common to all. It is known as the "barometric coefficient," and is 5·744*m**a*, where *m* is the "weight of a cubic inch of mercury at the sea level in latitude 45º at 30º F. when the barometer reads 29·92 inches," and a the weight of a cubic inch of dry air under the same conditions of latitude, temperature, and pressure. Various values of this constant have