366 KRETZ. 



of arc of a great circle. If then we change formulae (6) to 

 read 



and, as before 





r,r,,= ^rr' + ]{^^1S- T,)r^V^ 



we obtain probable errors which make a direct comparison pos- 

 sible, and which enable us to assign relative weights to the re- 

 sulting positions for 1875. This is what I have done through- 

 out, and all probable errors are computed by the above expres- 

 sions. It should be mentioned here, however, that, for right 

 ascensions, the values obtained by the above formulae must be 

 multiplied by sec o, in order to make them applicable to the 

 position of the star ; for evidently the formulae give the probable 

 error in equatorial seconds for both coordinates. This I have 

 done for all of my stars, and the probable errors in right ascen- 

 sion found in the succeeding tables are therefore in terms of 

 seconds of arc of a small circle of declination passing through 

 the star in question. 



(26) 



