CHAP, iv.] APPLICATIONS OF COMPRESSED AIH. 85 



very simple calculation, therefore, which would consist in deducing 

 for each millimetre of difference in the barometric height a corre- 

 sponding difference of 10 n "5, in altitude, is not applicable, or at least 

 is only approximate for very small heights. 



The strata of air, in fact, in proportion as we go higher, diminish 

 in density, precisely because the pressures which they undergo are less 

 and less considerable. Halley and Newton discovered the law of 

 this variation, and showed that if the heights follow an arithmetical 

 progression, the pressures vary in geometrical progression. Besides, 

 the temperature starting from a certain height, diminishes progressively 

 with the altitude, and from this there follows an increase of density 

 which must also be taken into account. Lastly, the hygrometric 

 state, or the quantity of vapour contained in the air has also an in- 

 fluence on the pressure. 



The problem is therefore much more complex than it appeared at 

 first, and the formula that Laplace has given is not so simple that we 

 can describe it here. Let us only state that it is necessary to 

 observe at the lower station and the higher one simultaneously ; first, 

 the height of the barometer ; secondly, the temperature of the instru- 

 ment itself, given by the thermometer fixed to it ; thirdly, the tem- 

 perature of the surrounding air, by the detached thermometer ; and 

 lastly, the temperature of evaporation by the wet bulb. The hour at 

 which the observation is made should also be noted. 



These four series of measures taken, it is possible to deduce the 

 differences of altitude of the two stations. It is necessary as much 

 as possible to avoid accidental variations, to make the observations 

 of which we have just spoken. If the two stations are at some 

 distance from each other, the observations should be made simul- 

 taneously, or if that is not possible, care must be taken to repeat them 

 at the station at which they were begun, in order to ascertain how far 

 during the interval the elements may have changed. In every case 

 it is preferable to make the observations at different times and to 

 calculate the required altitude each time. By taking the mean of the 

 results, a closer approximation to a precise result will be obtained. 



The formula supposes that the pressure and temperature vary with 

 the height according to certain laws, which are approximately exact 

 only for small differences of elevation in the atmosphere. When 

 they are applied to determine the height of the atmosphere itself 



