3+2 Introduction to the Seventh Section 



division, the latter being taken out of the table in article I. 

 If two verniers only have been read off, the difference between 

 two verniers and four is to be applied besides ; by the curve 

 which I have drawn, and the mean difference of the two pairs 

 of verniers, which in the 6th section of this work was found 

 = l"*26, I have made a table of this difference, which, with 

 the table of the corrections for flexure and imperfect division, 

 is to be found at the end of this Introduction. To the places 

 of the pole, derived from observations of the two pole stars, is 

 to be added, in the Eastern position of the circle — 0"*25 

 Western + 1 "'18 



The polar distances thereby obtained are cleared from re- 

 fraction by the formula 



„1 nno.ooof b y 555 °+ 10 y 537QO+A A, 180+16.75-0,36438 u 

 §.1,00^-02^333,28 * 5550+t' 53700-j-lO^ ^ 1 80+ (/- 32)0,36438' 

 where g,A,\ refer to the table in the Fundamenta Astrotiomiec, 

 and b signifies the true height of the barometer in Paris lines. 

 t and f the readings of the interior centesimal and exterior 

 Fahrenheit thermometer. For facilitating this computation 

 I give below tables in which I have assumed for £.1,003282 

 the form a. tang, zenith distance ; they contain log. « as far 

 as zenith distance 80° : but I hope to continue it to the hori- 

 zon as soon as Dr. Argelander's observations have been more 

 accurately investigated. 



It is probable in itself, that every observatory does not want 

 a peculiar table of refraction, except perhaps for very small 

 altitudes; and this is likewise now confirmed by the close 

 agreement of my new determination with the former one. 

 But it may be doubted whether the place where the exterior 

 thermometer is fixed, does not give rise to a mean difference 

 between the temperature which it shows and the real tempera- 

 ture of the air : in order to investigate this, I placed a second 

 thermometer at the distance of six inches from the building, 

 and perfectly exposed to the wind, which I have compared 

 these six months with Schafrinsky's, which is attached at the 

 same height to a side shutter of the observatory; but, to my 

 great surprise, I have never perceived a sensible difference, 

 and therefore I now believe that a difference of refraction in 

 different observatories arising from this cause is not much to 

 be feared. 



Applying these refractions to the Kimigsburg observations, 

 there remain irregularities, the amount of which I have deter- 

 mined in the 3d article, deducting the one taking place for 

 the zenith, which is 0"*7126, there will remain that probable 

 error of a single observation at which one would arrive by 



the 



