Terrestrial Refraction. 561 



of the ith arc ; and let &>/ be the angle between the successive 

 chords whose lengths are L;_i and L z (i = l, 2, . . . . 8). 



Then we have, since the angles and coi' are all small, 

 and a>i=di, 



(Oi _ A4>i-l — (^1 ' + <°2 + + <»' * - 1) + #i 



/< " ' Li 



o) t - = 2, o)j , (do) 



v>i=r {A*-ft-««-if. • • (^6) 



We liave also 



0i = £^ and L t - = £(,-, . . . (37) 



where A 2( £i represents the first differences of the refractions 

 A</>;> as already considered in § 5. The approximate values 

 of €{ are then given by 



By means of these formulae we find the following values 

 for €i : — 



Table VI. (Values for e*.) 



00* e 'l' e 2- e 3- 6 4-- 6 5« 6 B- 6 T- 6 8- 



90° -500 -521 -529 -533 '537 -542 -547 -552 



89 30' -500 -512 -519 -524 -529 535 -541 '547 



89 -500 -509 -515 -521 -526 -532 -538 -545 



85 -500 -507 -512 -518 "524 -531 -537 -544 



80 -500 -506 -513 -518 -524 -530 -537 544 



60 -500 -504 -512 -517 -523 -531 -536 -543 



The refraction correction for an instrumental observation 

 made on the ground is thus given by the product of the 

 appropriate value of e* and the corresponding value of A<£, 

 in Table II. 



