260 Introduction to the Seventh Section 



This comparison seems to confirm that the manner of re- 

 ducing the observations which has been employed, is correct 

 as far as the accidental errors of observation will allow to per- 

 ceive it; the remaining differences of the four independent 

 determinations of each star are either not greater than would 

 be expected, or nowhere so regular as to prove the neglecting 

 of any constantly acting error: I believe, therefore, that it may 

 be assumed that the polar distances of the stars observed with 

 Reichenbach's meridian circle, and computed agreeably to this 

 investigation, vary, like the right ascensions, in both positions 

 of the instrument and in both passages only on account of 

 contingent errors, from each other : the separate investigation 

 of each individual correction seems to justify the hope that not 

 only agreement, but likewise correctness, has been obtained 

 within narrow limits. 



It now only remains to reduce the refraction and its changes 

 to the true Fahrenheit's thermometer. The refraction is found 

 for48°*75 of Schafrinsky's thermometer =§. 1*004624, where g 

 signifies the number taken from the table in the Fundamenta 

 Astronomice : it follows from the 3d article and the supposed 

 influence of the temperature on the mercury of the barometer, 

 that the difference of two refractions for the readings t and r t 

 of the exterior and the centesimal degrees r' and t/, of the in- 

 terior thermometer is = 



r i + ioj 



1 + lOw 



1+(t-50)k 1 +«■/»» l+(r-50>i 



where m is by supposition =0*00018484, and n has been 

 found =0*00194653. Let g(l+y) signify the true refraction 

 for 48°*75 Fahr., and 1 : 1 +§ the ratio of the densities of the 

 air at the points of boiling and freezing, as they must be as- 

 sumed for representing as exactly as possible the changes of 

 refraction : I suppose besides, agreeably to the accurate experi- 

 ments of Messrs. Dulong and Petit, the ratio of the densities 

 of mercury =55'5 : 56'5, and for the brass of the scale of the 

 barometer 537 : 538. Then the true refraction will be = 



. \( _t \5550ti° v 35700 +t' l 80+ f . 16-75 



^ '^ \ 333-28/ 5550 +t X 53700+10 X f80+ e .(/-32)* 



If we put/=0*997039T — 0°*538 as found in article 2, we 

 have for t = 48°*75, /=48°*06765; therefore the refraction 

 observed at that temperature 



\.i\r\A.KOA m , \5550+lO 53700+r' J80+ ? . 1675 

 g.l*004624 = ? (l +y) E go+7 >< 53755+10 X iSo-fU^ ' 



This equation maybe abridged by pulling t'= §(,/— 80 o, 067), 



which 



