60 



declination both at the star and at the polar point, and the 

 latter also affects the subpolar observation ; hence, caUing 

 the tabular refraction fxv, and the difference between it and 

 the observed c?r, we have for each observation the equation 

 of condition 



dB. = dfi |v — v' — 2pJ —dfiX^; 

 combining which by minimum squares, the value of rf/u for that 

 star is obtained. If the values of it at different zenith dis- 

 tances are equal, or differ only by what may reasonably be 

 considered error of observation, then it may be also inferred, 

 that the formula correctly assigns the refraction through 

 the range of zenith distance included by the observations. 



Dr. R. then gives details respecting the mural circle 

 which he used, the permanence of its microscopes as to r«», 

 and the mode of obtaining its index correction, and the cor- 

 rection of its divisions. When the stars are spectra, he 

 bisects the yellow near the green, and remarks that the fluc- 

 tuations of irregular refraction are often of considerable 

 duration. Tlie hygrometric state of the air does not seem to 

 produce any effect, and he shews that the external thermo- 

 meter is to be used at his observatory. The details of ob- 

 servation are then given for seventeen stars, from 77° 10' to 

 84° 56' zen. dist., of which there are 317 subpolar obser- 

 vations. 



If a southern star be determined at a place when it 

 passes near the zenith, so that its place may be assumed 

 as free from error of refraction, the value oi djx is multiplied 

 by a much larger factor. This advantage, however, is more 

 than balanced by the uncertainty caused by the difference of 

 instruments and local circumstances at the two observatories ; 

 but Dr. R. has given the result of such a trial. He used 

 the declinations of Mr. Johnson, (St. Helena Catalogue,) and, 

 in many instances, those of Mr. Henderson at the Cape, and 

 by 241 observations from 77° 53' to 84° 40' he found for fi 

 57*586 ; but conceives the result obtained from the northern 



