186 The Rev. Dr. Robinson on the Constant of Refraction. 



41 

 The terms /3, 7, and 8 have nearly the ratio — X tang* 6, and therefore the 



Or 



convergence ceases when the fraction =: 1 ; or below 85°. Near that limit several 

 of the higher terms are equal with opposite signs, and therefore (Lacroix, III. 

 p. 160) I retain half the two last, which I find give at 85° the same results as a 



much more extended development, including all affected with ¥ and — ~- 6. 



This expression may be put into the form given by Brinkley, certainly the 

 most convenient with which I am acquainted, 



B, = fiX tang 6 — c ; 



the last of which quantities can be tabulated with the argument zenith distance, 

 and is, in most cases, independent of the barometer and thermometer. 



Their influence is, when necessary, easily allowed for : if a unit of air at 50° 



become l-\- e(t — 50) at f, the quantity - must be multiplied by this factor, 



Or 



and that of fi or b divided by it, from which we deduce the change of c for 

 temperature, 



D = e (^ - 50°) X[a' + p- 2q' - 3q" - 7], 

 which is always small from the absence of a, the largest of the terms. 



this was unnecessary. Assuming Bessel's jj. to be 67" .524, and Ivory's 58".496, my table, when 

 changed for these values, gives at their normal circumstances, 



The diflference obviously depending on some slight difference between the values of jj. and those 

 used in computing the tables. It is equally evident, that to the zenith distance of 85 the results of 

 the three formulae are identical for all practical purposes. 



