=42. Method of Calculating Heights by the Barometer.=--The pressure of the atmosphere being measured by the barometer, it is evident that as the instrument is carried up a high mountain or elevated in a balloon, the length of the column must decrease as the atmospheric pressure decreases, in consequence of a stratum of air being left below. The pressure of air arises from its weight, or the attraction of gravitation upon it, and therefore the quantity of air below the barometer cistern cannot influence the height of the column. Hence it follows that a certain relation must exist between the difference of the barometric pressure at the foot and at the top of a hill or other elevation, and the difference of the absolute heights above the sea. Theoretical investigation, abundantly confirmed by practical results, has determined that the strata of air decrease in density in a geometrical proportion, while the elevations increase in an arithmetical one. Hence we have a method of determining differences of level, by observations made on the density of the air by means of the barometer. It is beyond our purpose to explain in detail the principles upon which this method is founded, or to give its mathematical investigation. We append Tables, which will be useful to practical persons,--surveyors, engineers, travellers, tourists, &c.,--who may carry a barometer as a travelling companion. Table I. is calculated from the formula, height in feet = 60,200 (log. 29.922 - log. B) + 925; where 29.922 is the mean atmospheric pressure at 32 deg. F., and the mean sea-level in latitude 45 deg.; and B is any other barometric pressure; the 925 being added to avoid minus signs in the Table. Table II. contains the correction necessary for the mean temperature of the stratum of air between the stations of observation; and is computed from Regnault's co-efficient for the expansion of air, which is .002036 of its volume at 32 deg. for each degree above that temperature. Table III. is the correction due to the difference of gravitation in any other latitude, and is found from the formula, _x_ = 1 + .00265 cos. 2 lat. Table IV. is to correct for the diminution of gravity in ascending from the sea-level. To use these Tables: The barometer readings at the upper and lower stations having been corrected and reduced to temperature 32 deg. F., take out from Table I. the numbers opposite the corrected readings, and subtract the lower from the upper. Multiply this difference successively by the factors found in Tables II. and III. The factor from Table III. may be neglected unless precision is desired. Finally, add the correction taken from Table IV. TABLE I. _Approximate Height due to Barometric Pressure._