412 Count Paul de Saint-Robert on Atmospheric Refraction. 



When the upper station is on the surface of the ground, the 



factor ( — J must be augmented in order to take into account 



the attraction of the portion of the earth which is elevated above 

 the level of the lower station. According to Poisson*, we must 

 substitute for it the expression 



/0 



or approximately 



f?> 



5/r— r c 



1_ i 



The same remark is applicable to f — J , when the lower station 



is on the surface of the ground. 



In ordinary cases the variation of gravity may be neglected, 

 but then the coefficient A should be somewhat increased, for 

 instance about -^q, similarly to what is done in the ordinary 

 barometrical formula. 



When the degree of moisture of the air at the two stations 

 has not been ascertained, we may use the very simple formula 



# = A 



H -H 



/„ * t 



increasing somewhat the constant A in order to include the cor- 

 rection for the effect of moisture. An increase of 20^0 wouM 

 correspond to a pressure of vapour at the upper and lower sta- 

 tion of 7*5 °f the respective atmospheric pressure. 



The value of the coefficient A, including both corrections (va- 

 riation of gravity and presence of moisture), would thus become 



A= 5 8' 8 in metrical measure, 

 A=107"2 in English measure. 



III. Atmospheric Refraction. 



It is known that if the earth's surface were a plane, and the 

 air consequently disposed in plane and parallel strata, the effect 

 of the atmosphere upon a ray of light passing through it would 

 depend only upon the density of the air at the two ends of the 



* Traite de Mecanique, vol. i. No. 255; vol. ii. No. 629. 



