o/'Bessel's Astronomical Observations. 261 



which is not much different from the truth, and has little in- 

 fluence: we then have 



and hence the true change of refraction = 



... ; 0-9998266 l80-f e . 16-75 9998266 I80+ e 16-75 _ \ 



.?( +V) l+m'(/-50) X l80-j- e (/-32) l+« t </'_50)-l80+ € (/ ; -32)J 



where ?m' = 0*000089557. 



If 1 -\-tj be denominated from this equation by the equation 

 ( 1 ), the change of refraction will be 



( 1 180 -\- ? . 1606765 1 



= g.l0044492| r+OT , (/ _ 50) . l80+c . (/ - 3 2) ~ &C - } 



The same is by observation substituting jT for t 



= g. 0*9960353 < i+(/_ 50)0-000 10248 x l+(/- 50)00019497 ~~ c c ' j 



These two equations give 



1+^=1-003282 probable error = +0-00061 



§ = 0-36438— (/+/, — 100)0-000000501 +0-0016. 



The latter is therefore almost independent of the tempe- 

 rature of the observations ; indeed g may without hesitation be 

 assumed =0*36438, as the mean temperature of all observa- 

 tions will be nearly =50°. If we suppose that the mean 

 humidity of the air is nearly the mean between dryness and 

 saturation, it will be seen from article 3 that this determina- 

 tion is in near accordance with that found by Gay-Lussac. 



In order to satisfy as nearly as possible the observations at 

 Konigsburg, the refraction derived fromBrad ley's observations 

 must be multiplied by 1-003282 ; but this change, small as it is, 

 would perhaps not be necessary if we had a more accurate 

 knowledge of the meteorological instruments used by Bradley; 

 his thermometer was in melting snow at 33° to 33^°, and ac- 

 cordingly I assumed that it was 1°*25 too high; but I am in- 

 debted to Prof. Tralles for the communication, that melting 

 snow when already mixed with water always gives the freezing 

 point too high, so that the correction applied to the thermo- 

 meter becomes doubtful; but without this correction the new 

 refractions would hardly differ from the former ones. 



[To be continued.] 



XLIV. On 



