136 Count Paul de Saint-Robert on a Barometrical Formula 



Height above the level of 

 the sea. 



Sky partially clear. 



Sky cloudy. 



From 



To 



Calculated 



average height 



for a decline 



of 1°. 



Difference 

 between cal- 

 culated and 

 observed 

 height. 



Calculated 



average height 



for a decline 



ofl°. 



Difference 

 between cal- 

 culated and 

 observed 

 height. 



feet. 



feet. 



feet. 



feet. 



feet. 



feet. 







1,000 



140 



+ 1 



222 









2,000 



162 



+ 2 



230 









3,000 



182 



4- 6 



237 



+3 





4,000 



196 



+ 1 



244 



+2 





5,000 



207 



- 4 



249 



-6 





6,000 



219 



-11 









7,000 



231 



-12 









8,000 



242 



-12 









9,000 



253 



-10 









10,000 



264 



_ 8 









11,000 



275 



- 4 









12,000 



286 













13,000 



296 



+ 3 









14,000 



306 



+ 6 









15,000 



315 



+ 7 









16,000 



323 



+ 9 









17,000 



331 



+ 9 









18,000 



339 



+ 9 









19,000 



346 



+ 9 









20,000 



353 



+ 7 









21,000 



358 



+ 3 









22,000 



368 



+ 10 









23,000 



372 



+ 4 









24,000 



378 



+ 1 









25,000 



382 



- 4 









26,000 



386 



-10 









27,000 



391 



-13 









28,000 



394 



-19 









29,000 



398 



-25 









30,000 



404 



-24 







Further experiments may render it necessary to add other 

 terms to the equation representing the law of decrement. In 

 order to preserve more generality to that expression, I will 

 assume the equation 



z=a(t -t)-b{t *-t*)+c{t s -t 3 )+kc. . . (1) 



as representing the law of decrement of heat. 



This being premised, we shall proceed to find the barometrical 

 formula arising from it. 



If p be the pressure of the air of the density p at any height a? 

 where the gravity is g> it is well known that the equation of equi- 

 librium of a column of air is 



dp = —gpdx. 



Moreover p is linked to p by the relation 



p = hpt, 



