[•] 



500 Mr. Lubbock on the Heat of Vapours 



= sin { ll32"-8 e + 639"'9 e 3 + 220"'4 £ 5 



+ 60"\5 <? T + 17'"8 e 9 + 5'{'5 e u + &c.} 



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

 = 2076"-9. 

 The second term in the refraction is 



3 sin 6 a t* x 2 d co 



2 (cos 2 + 2ix)% 



3.4>\ / 7*s'mex" 2 z <2 {1 -e 2 + e 2 *} 2 * 3 ^^ 



d x 



2 V2/{1 - e 2 + 2e 2 s} 2 



3 . 4 V i u sin x m z 2 e 3 d 



d x 



dz 



2 V 2 a;" 



+ {5z 2 -2z} e 4 -&c.\ 



suppose d oo contains any term 



A n (x"-x) n dx 



X" -X=r- X !, (l -«)(!•+ e 2 *) 



{'- 



2** s 



d.§0 = - 



3.4 V g « si 



sin y <r 



Wn+2 



^^ 4,(1 -*) w + e 2 s) w s 2 e 3 d 



2 ^2 .z" 



] -22^ 2 +{5z 2 -22}^ 4 - 

 Neglecting the higher powers of e 



■} 



3.4 V i a sin Q e 3 f2. 1 A x x" 3 2.1 A 2 x" 4 2 . 1 A 



M 



3.4.5 4.5.6 



[2] 

 1-5, H- -54378 



+ 



4.5.6 



2 ^2^" L 2.3.4 



+ Scc.j> 



With the same constants as before, y 



n . A _f2. l^" 3 , 2.1^ 2 

 3 6= -[1-3861838] sin flgM 2t3 ) 4 + 3<4 " 



= - 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 1". 



Hence, finally, the refraction is expressed by the following 

 series : — 



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



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



[2] 



