cury in the cistern would be equally diminished in ascending through equal 

 heights. Thus, if the pressure produced by an ascent of 10 feet were equiva- 

 lent to the weight of one inch of mercury, then the column would fall one inch 

 in ascending that height. It would fall two inches in ascending 20 feet, three 

 in ascending 30 feet, and so on. To find, therefore, the perpendicular height 

 of ths barometer at any time above its .position, at any other time, it would be 

 only necessary to observe the difference between the altitude of the mercury 

 in both cases, and to allow 10 feet for every inch of mercury in that difference ; 

 and a similar process would be applicable if an inch of mercury corresponded 

 to any other number of feet. 



But this explanation proceeds on the supposition that in ascending through 

 equal heights, the barometer leaves equal weights of air below it. Suppose 

 in ascending 10 feet the mercury is observed to fall the hundredth of an inch, 

 then it follows, that the air left below the barometer in such an ascent has a 

 weight equal to the one hundredth of an inch of mercury. Now. in ascending 

 the next ten feet, the air which occupies that space having a less weight above 

 it will be less compressed, and, consequently, within that height of 10 feet 

 there will be contained a less quantity of air than was contained in the first 10 

 feet immediately below it. In this second ascent the mercury will, therefore, 

 fall, not the hundredth of an inch, but a quantity as much less than the hun- 

 dredth of an inch as the quantity of air contained in the second 10 feet of 

 height is less than the quantity of air that is contained in the first 10 feet of 

 height. In like manner, in ascending the next ten feet a still less quantity of 

 air will be left below the instrument, and the mercury will fall in a proportion- 

 ally less degree. If the only cause affecting density of the air were com- 

 pression produced by the weight of the incumbent atmosphere, it would be 

 easy to find the rule by which a change of altitude might be inferred from an 

 observed change of pressure. Such a rule has been determined, and is capa- 

 ble of being expressed in the language of mathematics, although it is not of a 

 nature which admits of explanation in a more elementary and popular form. 

 But there are other causes affecting the relation of the pressure to the altitude 

 which must be taken into account. The density of any stratum of air is not only 

 affected by the weight of the incumbent atmosphere, but also by the temperature 

 of the stratum itself. If any cause increase this temperature the stratum will 

 expand, and, with a less density, will support the same incumbent pressure. If, 

 on the contrary, any cause produce, a diminution of temperature, the stratum 

 will contract, and acquire a greater density under the same pressure. In the 

 one case, therefore, a change of elevation which would be necessary to pro- 

 duce a given change in the height of the barometer, would be greater than 

 that computed on theoretical principles, and in the other case the change would 

 be less. The temperature, therefore, forms an essential clement in the calcu- 

 lation of heights by the barometer. 



A rule or formulary has been deduced, partly from established theory, and 

 partly from observed effects, by which the change of elevation may be deduced 

 from observations made on the barometer and thermometer. To apply that 

 rule, it is necessary to know. 1st, the latitude of the places of observation ; 2d, 

 the height of the barometer and thermometer at the higher station. By arith- 

 metical computation the difference of the levels of the two stations may then 

 be calculated. The formulary does not admit of being explained without the 

 use of mathematical language. 



It has been already stated, that the atmospheric pressure at the surface of 

 the earth is capable of supporting a column of water 34 feet in height. It fol- 

 lows, therefore, that if our atmosphere were condensed to such a degree that 

 its specific gravity would be equal to that of water, its height would be 34 



