1858.] On Hypsometrical Measurements. 839 



Now (g), which depends on the variation of gravity between the 

 equator and the poles, has the form — 



(^) = 1 — \ n cos. 2 A. 

 where n is J- times the ratio of the centrifugal force to gravity at 

 the equator, diminished by the ellipticity of the earth. Slightly 

 different values have been deduced by different philosophers for the 

 value of %,* but with Bessel we may adopt — 



in = 0.0026257; 

 and consequently we have 



(jg) = 1 — 0.0026257 cos. 2 A. 

 3. The constant L is the most important, and depends on the den- 

 sity of the air in terms of that of mercury ; thus, B being the 

 standard height of the barometer at the level of the sea in lati- 

 tude 45° ; D, the density of air under the pressure B of mercury in 

 terms of the density of mercury, and M the modulus of the common 



logarithms— 



B 



L = . 



D M 



Bessel, in determining the value of L, has derived it from the 



experiments of Arago and Biot on the weight of air, whence he finds 



1 

 D = . 



10466.8 



Bitter, however, has shewn that according to Eegnault's experi- 

 ments, the weight of a litre of air containing the average amount 

 of 0.0004 of its volume of carbonic acid and under a pressure of 

 760 mm. of mercury is 1.2934963 gramme.f Now the latitude of 

 the college in Paris is 48° 50' 14", and the height above the sea is 



1 



* If for the ratio of the centrifugal force to gravity we adopt the value , 



289.4 

 1 5 11 



and Bessel's value of the ellipticity we haven = — ° = 



299.15 2 289.4 299.15 



0.0052964, or|» = 0.0026482 ; Laplace, Gauss and Littrow used for § n the 

 Value 0.002845 ; Poisson (Traite de Mecanique 2nd ed.) give3 § n = 0.002588 ; 

 Sabine from his pendulum experiments infers that § n = 0.0025914 ; and Baily 

 (Mem. Ast. Soc. vol. vii. p. 94) gives .0025659. 



t Memoires de la Societc de Physique de Greneve, torn. hi. p. 361. 



