11^2 



(t) 'Vhe former readily appears from the equation 

 lk = ~ art. 1, 



For since the temperature decreases as we ascend, it fol- 

 lows that the satne density takes place at a distance from the 

 surface greater than in the case of an uniform temperature. 

 Now the only variable quantity in OC is f, therefore OC re- 

 maining the same, OP is increased, and consequently R 

 diminished, therefore refraction ory R is greater in the case 

 of uniform temperature than in the actual state of the atmos- 

 phere. 



(2) By the annexed observed refractions of a Lyrie, below 

 the pole, it will appear that the actual refraction is greater 

 than would take place, did the density of the air decrease 

 uniformly. 



The mean of these 42 observations of « Lyrae below the 

 pole gives the refraction at the zenith distance 87° 42' 1(/' = 

 17' ?b",5, the mean of the heights of the barom. =: 29,50, 

 and the mean of the heights of the therm. = 55'',0. 



These heights of the barom. and therm, give, (vid. art. 11.) 



!^ = 59",50 and , ^ ., i = 3,803. Hence if the 



density of the air decreases uniformly, 



