been found, depending on the values assumed for m and a. Arago and Biot found ma 10,467. This makes the "barometric coefficient" 60,122·4 feet. Raymond's value, namely 60,158·6 feet, was found by comparing the values given by the formulae with the results of actual leveling with a spirit level. His observations were, however, few in number, and, although his coefficient is frequently used, it is probably the least accurate of all the determinations. In Laplace's formula, Raymond's constant is used. Babinet used the constant 60,334, and in Baily's formula the constant is 60,346. In Williamson's formulæ the constant is 60,384, which is the value found by Regnault, and is probably the most accurate of all. Sometimes the coefficient in the formula is given as 10,000 fathoms, which is roughly correct.
We will now consider the errors underlying the barometric measurement of heights, which render the method inapplicable in cases where great accuracy is required. The most important of these sources of error is probably that due to what is called the "barometric gradient," a term frequently used in meteorological reports. Taking three points at which the barometric pressure is, the same, if the atmosphere was in a state of statical equilibrium these points would lie on the same level plane. But usually this plane is not level, but inclined, and the inclination of the plane is termed the "barometric gradient." For a number of points the surface on which they lie would not be a plane at all, but an undulating surface. These surfaces for different heights are never parallel, and frequently slope in opposite directions. Allowance can not be fully made for this disturbing cause, but the error can, to some extent, be eliminated by making a number of simultaneous observations at the two stations, and taking the mean of the results.
Another cause of error is due to variations in the temperature of the air. It is generally assumed that the mean temperature of the column of air between two stations, one vertically over the other, is the mean of the temperatures at the upper and lower stations, but this is not always the case. The error may be partially eliminated by making observations at intermediate stations, but can not be entirely overcome. High winds also cause a variation in the height of the barometer.
In addition to the errors mentioned, there are, of course, errors of observation, and instrumental errors. The former may be caused by imperfect adjustment of the zero point, and erroneous reading of the mercury on the scale. These errors are, however, usually small, and may with care be neglected. The instrumental errors are due chiefly to imperfect graduation of the scales of the barometer and attached thermometer, the impurity of the mer-
