I 



Astronomical and Nautical Collections. 37 1 



and r = =^ f-^ - s + ^+^^ -^±l. + t^ 

 dips \ mps ps 4 Iddr ps J 



- n^ i-L^ - s + J^ + i^ - -^ + ^ ^ = zH 



64ps \ mps ps ^ 2ps ps ) 64ps 



\ mps 4ps I6ps 8ps ps ) ^\ps \ mps 



5v- \ 

 ~s + ). By substituting these values, we obtain the 



16ps J 



, / 2.85275 1 N 2 , oonfl w 3 , 576 

 equation ps = vr + I — — s) r^ + 2306 — r + 



\ S Ai &s ss 



(^-s+5450!^y. 



With this formula, we may proceed to calculate the refraction 

 for the case v = .1, that is, for an altitude of 5° 44' 21", which 

 will be allowed to be as low as can possibly be required for any 

 accurate observations. Assuming then r — .0026, we have r^ = 

 .000 006 76, r3 = .000 000 017 576, and r* =: .000 000 000 0457 ; 

 also s = .99500, s" = .9900, and s^ ~ .9850, and the equation 

 becomes p = .00026130 + .00001610 + .00000411 + .00000157 

 + [.000 00 1 50] r= .000 28458, so that .0026 is too much by about 

 ^J"0, and r = .00259, which may be called certain to the last 

 figure, giving 8' 54".2, a result probably very near the truth in 

 the actual mean state of the atmosphere. 



B. Mr. Ivory's tables are constructed upon the hypothesis 



y s= .75z + .25z'^ ; hence ^= ^ = .75 + 5z, ^ =; 4^ = :^ 

 * dz dr ar 



S3 HjLy and f ' = — ; the equation then becomes p = — 



2ps 2j}S dr s 



+ (2.85275 - Jl $s) — + 2012 v !l + 503 (4.7055 + 7055 v^ 



2 ss s^ 



—, and assuming again il = .0026130, — = .000 006 8276, ?L 

 s* s s' «■* 



= .000 000 01784, and — - .000 000 000 0467, we have p = 



