340 On Hypsometrical Measurements. [No. 4. 



60 metres. And Poisson has shewn # that the force of gravity at 

 the height z above the mean level of the sea is — 



-j 1 — J 2 J — > >; force of gravity at the sea level ; 



(V 2 p/ r ) 



where p' is the density of that part of the eartli above the mean 



level of the sea, and p the mean density of the earth. Hence the 



weight of a litre of dry air - at the level of the sea, in latitude 



45° under a pressure of 29.9218 inches is — 



-4- \ (l— 1.32— ^ (l— .0026257 cos 97° 40' 28" \ I 



1.2934963 



1.2934963 



= L2930586. 



1.00033847 

 Now, if we take the standard height of the English barome- 

 ter as 30 inches, we have for the weight under that pressure at 

 32° Faht. ;— 



in. in. gr. gr. 



As 29.9218: 30:: 1.2930586: 1.296438. 



gr. 



But the weight of a litre of mercury is 13596, and hence, — 



1296438 1 

 D = = ,t 



13596 10487.2 



in. 



and since 30 = 2.5 feet and M =0.43429448, we have,— 



B 2.5 * 10487.2 



L = ea • === 60369.15 feet. 



D. M 0-43429448 



4. a, or the co-efficient of the dilatation of the air has usually been 

 taken from the experiments of Gay Lussac, who found the expansion 

 between the freezing and boiling point of water to be 0.375 of its 

 volume at 32° Faht. ; Kudberg found 0.3648 ; Magnus 0.365508 ; 



* Poisson, Traite de Mecanique, torn. ii. p. 629. 



1.2930586 1 1 



f Under a pressure of 29.9218 in., D = = , or part of 



13596 10516.46 472 



2.49304 



itself less than Bessel's value ; and L = = 60369.15 feet as above. 



DM 



