Mr. Ivory on the Theory of the Astronomical llefractions. 93 



/' X sin^x -i- . X Qo =/' xsin 9 X <^ e-^ X 35-324, 1-54807 



+ ^9 X 51-529, 1-71205 

 + ei»x 32-476, 1-51156 

 + e^^x 1-809, 0-25755 

 -e^^X 16*205, 1-20965 

 —gi^X 18-588, 1-26925 

 -e^^x 13-334, 1-12498 

 -e'^^x 7-427, 0-87080 

 — e^X 3-480, 0-54158 \. 



The amount of this expression at the horizon, or when e = \, 

 is/'x62"-l, ahnost the same with /" x 62"-4, which, as is 

 shown in § 9, is the limit of the integral when it is extended 

 from :r = to .r = co. It is thus proved that the error of 

 the series is of no account. This part of the refraction can- 

 not be computed because f is unknown. But although the 

 precise value of y is uncertain, it is probably very consider- 



2 

 ably less than_^ or — ; 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 

 observations. 



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 



8s = sin»x!5ii+f) ^S, 

 V 5i 



_S = Q0 + AQ1-/Q2, 



V 5i e 



cos 9 1— e^ ' 



a 

 A = — . 



I 



The quantities e and X depend only upon « and /: a varies 

 both with the barometer and thermometer, and z, with the 

 thermometer only : the quantity f 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 



