402 Count Paul de Saint-Robert on the Measurement 



of the results to which it leads with those observed ; but I think 

 it was never confirmed by direct observations of the density of 

 the successive strata of the atmosphere ; nor do I think that it 

 has been used heretofore in the formula for the measurement of 

 heights by the barometer. 



I. Constitution of the Atmosphere. 



The condition of any stratum of the atmosphere depends upon 

 five quantities — namely, the temperature /, the pressure p, the 

 elasticity «r of the aqueous vapour, the density p, and the dis- 

 tance r from the earth's centre. These quantities are linked 

 together by two equations ; of which the first is the equation of 

 equilibrium, 



dp=—gpdr, (1) 



expressing that the decrement of pressure in ascending from the 

 distance r to the distance r-\-dr is equal to the weight of the 

 column of air included between r and r-\-dr. 

 The second is the equation of dilatability , 



P_ 

 Po 



t /p-m*T\ 



t\p - m «rj> ' ' ■' ' ' W 



1 — 771 being the ratio of the density of vapour to that of the air 

 at the same temperature and pressure (according to Gay-Lussac 

 m=f ); which equation embodies the laws of Mariotte, Gay- 

 Lussac, and Dalton. The temperature is reckoned from the 

 absolute zero (493°*2 F. below the melting-point of ice). 



Now if we could have, either by experiment or by theory, two 

 other relations among the five quantities above mentioned, the 

 first four, which are the physical elements of the aerial strata, 

 would be determinable in function of the altitude alone; thus 

 the physical constitution of the atmosphere would be entirely 

 known. Were we to neglect the vapour mixed with the air, 

 then only one relation, either theoretical or experimental, added 

 to the two first, would be sufficient to determine the condition 

 of the atmosphere. 



The knowledge of these required relations can be experiment- 

 ally obtained by balloon-ascents, when the barometer, the ther- 

 mometer, and the hygrometer are observed simultaneously in a 

 great number of strata successively traversed, without any need 

 of knowing the elevation. In fact with the values of p, t, and 

 bt thence resulting, we can deduce for every stratum the density 

 p by means of equation (2) ; then by (1), if the observations are 

 numerous enough, we can by the method of quadratures obtain 



