MR. IVORY ON THE THEORY OF ASTRONOMICAL REFRACTIONS. 215 



•0873930 C7 = -151186 



•0748672 Cc) = •204491 



•0446024 Cji = -193076 



•0209241 Ci3 = -142381 



•OO8I714 Ci5 = -087220 



•0027438 Ci7 = ^046149 



•0008096 Ci9 = -021658 



•0002133 €21 = -009187 



-0000511 €23 = -003569 



-0000105 €25 = -001290. 



As the value of / is not fixed with the same certainty as that of X, the coefficients 

 of Q2 have not been multiplied by/; the intention of which is to make it more easy 

 to determine a variation of the refraction, viz 1/ X Q2, answering to ^/ any variation 

 ofy that good observations may require. 



The part of the horizontal refraction depending on Q2 is 



2 a ( 1 + «) ^ „ 



-5- X /-r^ X 0-919534 = 148"-51. 



If we integrate the original expression of Q2 from x = to x = ess, e being 1, we shall 

 have 



-gXcc{l+u)xJ ^7^^=^ -9- T^y— 1^2^/2- 2>/-148 63. 



It thus appears that the error is less than 0"-12 ; for the exact integral from x = 

 to X = m = 10, is less than the second number, and greater than the first on account 

 of the terms of the series left out. 



The next point that should engage attention is to find the value of /' x Q3. In 

 the present state of our knowledge of the phenomena of the atmosphere, it seems im- 

 possible to determine/' by experiments. The probability is, that it is much less than 



/ or -g- ; and as the integral Q3 is inconsiderable except within a degree or two above 



the horizon, and even at such low altitudes is not great ; it follows that the part of 

 the refraction depending on/ Q3 will only be sensible, if at all, when a star is distant 

 88° or more from the zenith. At present the probability is, that there is no other way 

 of ascertaining the value of/ but by good observed refractions at great distances 

 from the zenith ; which observations are neither numerous nor easily collected. From 

 the uncertainty of the term /' X Q3, it cannot be estimated in constructing a table of 

 mean refractions, which must therefore be deduced entirely from the other three 

 terms, as in the paper of 1823. In this manner has the table in this paper been com- 

 puted, by means of the formulas now to be explained. But the term/ Q3 will after- 



