500 Mr. Lubbock on the Heat of Vapours 



sin { 1 132"-8 e + 639"-9 e 3 + 220"'4 e 6 



+ 60"'5 e 1 + 17'"8 e 9 + 5"-5 <?" + &c.} 



At the horizon e = 1, and this portion of the horizontal refraction 

 = 2076"-9. 

 The second term in the refraction is 



3 sin 6 a. t 2 a:* d ca 



' (cos 2 6 

 3 . 4 ^Ta sin 6 #" 2 * 2 { 1 - e 9 + e z z} 2 e 3 d 





 d x 



{\ -e* 

 3 . 4 VT sin d .r" 2 ^ 2 g 3 d to 



/ 

 2 v 2 



Suppose d w contains any term 



-2s? 2 



3 . 4- V7" sin . f . .... 



d.88=-- - A n (l-z} n (\ 



|] _22g 9 + {5z 2 -2z}e 4 -&c.j^ 

 Neglecting the higher powers of c 



3.4 A/Tct sin fl g 3 f 2 . 1 A l x" 3 2.1 A% x"* 2 . 1 A a x 1 

 \ 2.3.4 3.4.5 4.5.6 



[2] 

 With the same constants as before, y = 1-5, H= *54378 



1 ../ ~f/3 Q ~\ A r-"4 O 1 // 

 . 1 y/| . . <b A /J i .t * />< 



[2] 



= l"-5 sin e 3 . 



This term thus amounts to only l"-5 at the horizon ; according 

 to Mr. Ivory it does not amount to more than l". 



Hence, finally, the refraction is expressed by the following 

 series : 



Ref. = sin 9 {1132"- 8 e + 638"-4 e 3 + 220"-4 e 5 



+ 60"'5 e 1 + l7"-8 e 9 + 5"-5 e 11 + &c.} 



