MR. IVORY ON THE THEORY OF ASTRONOMICAL REFRACTIONS. 



217 



When = 87°, V {&) is zero ; and if this function be computed for every succeeding 

 half-degree, the quantity answering to any intermediate value of will be found by 

 an easy interpolation. Such is the intention of the following Table ; by the help of 

 which any refraction from the zenith to the horizon may be computed by a series of 

 the simplest form, and consisting of no more than seven terms. 



If e = 1, the result will be the horizontal refraction, viz. 



2078"-53 — 5"-97 = 2072"-56, 



which is almost exactly the same with 2072"-46, the quantity before computed in 

 § 10 by a very different method. 



12. We next proceed to inquire into the influence which the term multiplied hyf, 

 before omitted, may have on the refractions. 



Investigation of the integral Q3. 



The expression of this integral is, 



y'*^ edx ( «■* \ 



which is a negative quantity, as appears from the valuation of it in § 9 : it will there- 

 fore contribute to distinctness if its sign be changed, in which case it will be thus 



MDCCCXXXVIII. 2 p 



