and on Astronomical Refractions. 505 



3 m 



1.2 



= ! _ c *' c -*' + # c **' c- 2 ' 1 '- ^ C 3 ''' c-- 3 ' 1 ' 



+ i . 2 . a sc< 



€ 1? = c"' c-*' - 2 h< c 2 "' C - 2 ^' + ?-^ c 3l ''c-^' 

 dr 1.2 



+ 1TTT3 c c ~ &c - 



The first part of the refraction is given by the expression 



l5* 



a (1 + a) sin 5 



o '/cos 2 + 2 *"' #' 

 Let 



/cos' 

 



?♦*}- 



[_ 2i 



, n cos 2 -. 2 2; d z 



n x' — z 2 - — - — r, — d x = 



2z' n 



/^ c" wj/ d^ 2/ r c 



/ ^cos 9 + 2i' ^ ~~ ^2l! VnJ 



At the horizon cos = 0, 2' = 



k CV3 



c d^ 





-%< , V'< 



c- z ~dz = 



This part of the horizontal refraction 



«(!+«) ^* J", *' 2A'c 2 *' 3*V°c 3k ' 4?N*c* v 

 = 711 I ^ + 1.2Vy - l.2.3Vt + & ' 



«(!+«) </ 



v * r 1 2 a 



. L3^ 3^ _J_ 2 _^__ 



+ 2.4.6^ + 2.4 J + 1.2. 2'' +1.2. 3 



2.3.5^ /2 „^5_ &2/ 23/ i3 .. 



\/2 2.4 V^22 V 2 1 . 2 



+ ^3 2.2 J 1.2^/3" 1.2.3^/F 



