MR. IVORY ON THE THEORY OF ASTRONOMICAL REFRACTIONS. 221 



// log- 



— ei9 X 13-334, 1 '12498 



— e2i X 7*427, 0-87080 



-e23x 3-480, 0-54158 I 



The amount of this expression at the horizon, or when e = 1, is /' X 62"- 1, almost 

 the same with/' X 62"-4, which, as is shown in § 9, is the limit of the integral when 

 it is extended from x = to a? = oo. It is thus proved that the error of the series is 

 of no account. This part of the refraction cannot be computed because f is un- 

 known. But although the precise value oif is uncertain, it is probably very consider- 



2 



ably less than/, or -5-; so that the effect on the refraction cannot exceed a few 



seconds even at the horizon. We shall be better able to form a just notion with 

 respect to this point, when the Theoretical Table in this paper is compared with ob- 

 servations. 



13. It remains to investigate the corrections that must be made in the practical 

 application for the deviations indicated by the meteorological instruments from the 

 mean constants used in constructing the table. 



For this purpose we have 



^ ^ = sm ^ X \^ X S, 

 S = Qo + xQi-/Q2, 



cos fl 1 - g** 



a. 



i 



The quantities e and X depend only upon a and i: a varies both with the barometer 

 and thermometer, and i, with the thermometer only : the quantity/ does not seem 

 liable to change in our climate. Admitting that the prefix d refers only to variations 

 of the barometer and thermometer, we shall have 



S^H-.rf.$^ = sm^X-^7ff^x|(l+--^-7-j.S 



+ de dS 

 e de 



^•^Q.} 



Now 



