Latitudes of Montjouy and Barcelona, 251 



formula; and thus all the tables of refraction, for greater 

 zenith distances than 74°, are to a certain degree empirical. 

 The method suggested by M. Laplace causes the French tables 

 to be less so than others, and as far as 80° they may be em- 

 ployed without considerable error; but at the distance of 82J°, 

 which is that of ^ Ursae Majoris, the errors may be estimated at 

 from 4" to 5'. The recent researches of MM. Brinkley and 

 Groombridge show that it is rare at that distance to obtain even 

 the mean results of different observers in accordance with each 

 other. 



We thus perceive that the discrepancy of the latitude derived 

 from the passages of this star below the pole was produced by 

 irregularity of refraction, combined with errors arising from 

 the double nature of the star. Perhaps we might add the pos- 

 sibility of error in the direction of the telescope, occasioned by 

 the dispersion of light in the atmosphere : were the whole of 

 the image of a star constantly visible, this dispersion would 

 occasion no error, for the centre of the dispersed rays would still 

 be the true centre of the object ; but in the supposition that a 

 part of the rays might be intercepted, either by being absorbed 

 by the vapours with which the horizon is charged, or by the 

 manner in which the field of view of the telescope may be illu- 

 minated, the apparent centre of the image would no longer be 

 the real centre of the object. The numerous experiments of 

 M. Arago on this subject show, that in certain cases this dis- 

 placement of the apparent centre takes place to an amount 

 which is very sensible. 



The latitude deduced from the passages above the pole of ^ 

 Ursae Majoris presents no anomaly ; here no irregularity of re- 

 fraction interfered, and the other sources of error appear in 

 great measure to have compensated each other, since the result 

 is comprised within those hmits of difference which are found 

 to exist between the other stars observed to the north of the 

 zenith. 



The latitude resulting from the passages below the pole of 

 ct Draconis manifests also the influence of the irregularity of 

 refraction at low altitudes ; it is in defect about 3", an error in 

 the same sense as in the case of ^ Ursae Majoris. 



Under these circumstances, the part which should be taken 



