resulting from Observations made in Eight Balloon- Ascents, 137 



t being the absolute temperature of the air, and h a constant. 

 Hence we have the equation 



7 dp doc 



p * t 



whose integral will give the relation between the pressure p and 

 the temperature t, when x is known in functions of /. 

 By equation (1) we have 



dx= —adt + Zbt dt-2>cf dt— &c, 

 and therefore 



9 P * 

 Integrating, we shall find 



7 O 



— log p = a\ogt—2bt + 7rc£ 2 -H&c. -f constant : 

 9 & 



the logarithms are hyperbolic. 



Continuing to denote by p and t the pressure and the abso- 

 lute temperature at the lower station, we have for determining 

 the constant the equation 



h ^ 



-logj9 = alog/ — 2bt + o^o 2 + &c.+ constant. 

 9 * 



Thence 



^logJ= fl log|-2S(< o -0+| e (<o s -< 8 ) + &c. . (2) 



Now as we can determine the parameter a by the observed 

 temperatures t and / at the lower and upper stations, we deduce 

 from equation (1) 



a =^+^ o + 0- C ^f 3 -&c; 



substituting which in (2), we derive 



Wf 8p L° kgi 



+ te-,* <hc3!t£=£ \ +k i . (3) 

 L 3 log^ J 



for the barometrical formula. 



According to Mr. Glaisher's results, the value of the parame- 

 ters c, d, &c. must be very small. Limiting ourselves then to 



