DETERMINATION OF ASTRONOMICAL REFRACTION. 85 



7. Errors of Graduation of the Circle. 



The errors of graduation of the circle, used in obtaining 

 the observations, have never been adequately determined. 

 A cursory examination of certain records found in the 

 Observatory books seemed to indicate that the errors 

 were not large, and that the circle is a fairly accurate one. 

 In this connection no corrections have been applied to the 

 observations used in this investigation. If circumstances 

 permit, it is intended to examine the circles of this instru- 

 ment. The results may form the subject of a future com- 

 munication to the Society. 



8. Reduction of the Observations. 



The first operation was to take the mean of the four 

 micrometer readings and apply the result to the reading of 

 the pointer, hence the complete circle reading denoted by 

 C in the tabular form prepared for the computation. The 

 errors of runs of the micrometers were taken several times 

 during the evening's work, but these never became appreci- 

 able. From the values of O the quantity Y can now be 

 formed. The terms 8' and X being deduced from the 

 declinations, see equations (3) and (4). All numerical 

 work was checked, either by duplication or by differences 

 in some cases. 



The calculated refractions were obtained by computation 

 from the tables, adopting the height of the barometer and 

 temperature of the air for a stated time. To correct these 

 quantities for the state of the air at the time of observa- 

 tion, a table was prepared, from which the corrections 

 could be easily interpolated. 



The following examples give the reductions in the case 

 of the two stars 975 and 317. The same form was used 

 for all pairs without exception. 



