OF ARTS AND SCIENCES. 



291 



from them the refraction as given by Bessel. These residuals are 

 arranged in groups in Tables XI. and XII. Each group extends over 

 10', its central point being given in the first columns. Table XI. 

 gives the number of residuals contained in each group, and Table XII. 

 their mean value. The corresponding number of the series is given at 

 the top of each column. The measures of the upper and lower limbs 

 of the sun are combined, as there seems to be no systematic difference 

 between them. Series 7 is omitted, since there is an error in the num- 

 ber of turns of the micrometer screw, or in the number of minutes in 

 the observed times. 



The results of these two tables are combined in Table XIII. The 

 successive columns give the altitude, the corresponding refraction 

 according to Bessel, the total number of observations of the sun, and 

 of a Bootts. The next two columns are derived from Table XII., and 

 give the means of the residuals contained in that table relating to the 

 sun, and the means of those relating to a Bootis. 



TABLE XII. — Mean Residuals. 



