Mr. Ivory on the Theory of the Agronomical Refractions. 507 



separate these terms from the rest, representing their sum by 

 the symbol V (3). These things being attended to, we have, 

 in the first place, this formula for computing ^, viz. 



log . tan i> - log . sec . 9 + 19'20678'tO — 20 : <? = tan ~. 



Next, reducing the arcs to seconds, 



?iii±^=726"'687: 

 V5z 



n 



sm 



+ ^ 

 + ell 



+ e^^ 



e X 726-687, 



X 597-280, 



X 



X 



X 



X 



X 



401-638, 



219-674, 



96-012, 



31-513, 



5-728, 



V (fi) = sin 9 X { 



V(9). 



15 



e 



19 



,21 



log. 



2'86134.72 



2-7761772 

 2-6038343 

 2-3417796 

 1-9823255 

 1-4984866 

 0-7580287 



log. 



0-1710 



+ e 



+ e 



+ e' 



+ e^ 



X 1-483, 



X 2-129, 0-3282 



X 1-337, 0-1266 



X 0-649, —1-8122 



0-270, -1-4307 



0-102, -1-0072 



When 9 = 87°, V (9) is zero ; and if this function be com- 

 puted for every succeeding half-degree, the quantity answer- 

 ing to any intermediate value of 5 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 <? = 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. 



[To be continued.] 



