130 On the Xuiih Polar Distances 



ilifFerences. A clifFerenco of y-^ of an inch, in the two barome- 

 ters, is equivalent to about 0",38 h) tlie constant of refraction; 

 and 2° difference in the two thermometers, is equivalent to 

 about O'jS-t : the sum is 0",62. A discordance to this amount 

 is not very unlikely. 



But no real source of error arises from this cause, when the 

 constants of refraction are determined by help of the respective 

 barometers and thermometers; as has been done by Dr. 

 Brinkley and M. Bessel. Mr. Pond has not made public any 

 determination of his constant ; but as he has so steadily ad- 

 hered to Dr. Bradley's table of refraction, there cannot be a 

 doubt that he has satisfied himself by his own observations, as 

 to the constant from which that table is deduced: and in fact 

 it appears, by a recent comparison of the Dublin and Green- 

 >vich North Polar distances, that the constant used in each of 

 those places is really the same ; although in consequence, as is 

 liighly probable, of the discordances of the meteorological in-. 

 Struments, they appear to differ by 0",6S ; that used by Mr. 

 Pond being 5 7", 04, and Dr. Brinkley's being 5 7", 72. 



Dr. Brinkley and M. Bessel make nearly the same allow- 

 ance for change of temperature. Mr. Pond, having adopted 

 Bradley's table, of course differs considerably from them. But 

 this does not affect the comparisons here made ; because the 

 three catalogues may be all considered as made within a few 

 degrees of the mean temperature. It is very difficult to esti- 

 mate precisely the discordances resulting fi'om using at Dublin 

 the interior thermometer, and at Konigsberg the exterior. It 

 is however reasonable to suppose they are not great. Admit- 

 ting, then, that the two catalogues may be assimilated to each 

 other, by using the constants of refraction above stated, it re- 

 mains to account for an error apparently so great as 0",6 in 

 the constant as determined at each place. If we consider the 

 manner in which this element is deduced, we shall easily see 

 that 0",6 can by no means be considered as a great error. 



Let us suppose the constant of refraction =1' 4-SZ-, ^k being 

 very small : that is, suppose we have determined the constant 

 = k nearly. Then if, with this constant, p be the co-latitude 

 determined by stars near the Pole, and y the co-latitude by stars 

 at a considerable distance from the Pole, ik-^'^^-, n beinff a 



n ° 



number depending on the tangents of the zenith distances. 



For determining/*', stars lower than 76° or 77° Z. D. ought 

 not to be used, on account of the imperfection of the theory of 

 refraction. The stars used are generally between 60° and 75° 

 Z. D. ; and the value of n cannot salcly be so great as unity. 



In 



