2 y (c 



Mr. Ivory on the Theory of the Astronomical Refractio7is. 391 



the first and greatest ; and the denominator of that term is 

 to be expanded. Thus we obtain 



rf.86=sin9. «(!+«). ^ r ,-^~, .- 



1_ f* dx dd.c-^'^^jx) 



2 y ~7coFr+i7^ * f^^ 



'dx.c-^.i^x^ 

 {cosH + 2ix)f 



In order to estimate the relative magnitude of the several 

 parts of this formula we must find the numerical values of the 

 quantities « and i. If >j stands for the refraction at 45° of 

 altitude, determined very exactly from many astronomical 

 observations, we shall have 



a = ))(l-2i + 2>}), 



as will readily appear from the formula according to Cassini's 

 method given in $ 1. MM. Biot and Arago have ascertained 

 the value of « with great exactness in a different way, by 

 means of experiments on the gases with the prism. In some 

 of the best attempts to determine a, the refractions at 45° of 

 altitude, being reduced to the barometer 29*6 and to the tem- 

 perature 50° Fahr., are as follows: ;/ 



Dr. Brinkley 57'4.2 



DeLambre 57*58 



Bessel, Tab. Reg 57-55 



Experiments of MM. Biot and Arago 57*65 



Mean 57*55 



It appears that Bessel's determination has the best claim to 

 be preferred : but as it differs very little from De Lambre's 

 result, which is adopted in the paper of 1823, the same value 

 will be retained in the calculations which follow. According 

 to De Lambre, the value of a is 60"*616* at the temperature 

 0° centigrade, and the barometric pressure 0™*76: wherefore, 

 when the temperature is 50° Fahrenheit, and the pressure 30 

 inches (= 0'^'762), we shall have 



" = «»•"•"' 760j?0018 X --^ = ''"■"■■ 



"*" 480 



• Tableaux CAronomiques, pvbliees par le Bureau des Longitudes de 

 France. 



