and on Astronomical Refractions. 473 



But Mr. Ivory afterwards neglects the terms depending upon 

 ,/', f", &c, so that he virtually assumes 



l + "*' , ,(, s ('° s J )* , > I 





2 

 Mr. Ivory makes the constant y = — -, p. 197 9 so that 



- = [9'8908555] - 1 - + [9*3467875] ^ 



P 9 



s 



_ g g' d a' 



g § 2 



(•+f) 



• * Pi 1 "/) i 9 



= [0*9635418] log ^j + [0*3582881] A — -M 



9' g 



*(l+«fl)(l-/) lofr j _ l 2A(l+«t)/ / 1 _ _| 



r v r? 



(for 50° Fahr. at the lower station. 



As we cannot make direct observations of the temperature and 

 density of the highest regions of the atmosphere, it becomes very 

 important to avail of all indirect means of investigation. The pro- 

 blem of Astronomical Refractions furnishes us with valuable data 

 in this respect, and any hypothesis relative to the state of the atmo- 

 sphere which will not satisfy the known phenomena of refraction, 

 must of course be discarded. In any investigation of this kind it 

 is indispensable to employ a formula for z in terms of the density 

 consistent with the hypothesis, which may be made respecting the 

 decrement of temperature ; it is equally indispensable to carry the 

 integral which affords the amount of refraction through limits which 

 are in conformity with the same supposition. 



* a iu = (T in Mr. Ivory's notation. In this page;? is the pressure and o is the density 

 at the earth's surface. 



[To be continued.] 





