8 



Herman Schultz, 



whereas the true value of ju, always must make r somewhat too great. 

 Consequently I think it most satisfactory to compute r for both these hypo- 

 theses, as in this manner two limits at least are obtained, between which 

 the true value of the quantity sought must lie. The computation of the 

 errors on these principles has given the following numbers, where the ob- 

 jects are divided in 3 groups according to the 5 classes of brightness here 

 adopted, and all the media employed are supposed to have approximately 

 the same weight. 



Probable Errors in the Results of One Evening. 



(Aa'.CW). 



Class 









Prob. 



Error. 



of 



Brightness. 







2e\ Cos 2 J 









fj, = true 

 value. 



ft,— I. 



1 and 2 



37 



101 



l s 1788 



0*092 



5 073 



3 



98 



221 



2,5122 



0,096 



0,072 



4 and 5 



86 



198 



4,2166 



0,130 



0,099 



Probable 



Errors in 



the Results of One 



Evening. 















Class 









Prob. 



Error. 



of 



Brightness. 















In 





fi — true 

 value. 





1 and 2 



37 



100 



87"41 



0"79 



0"63 



3 



95 



217 



287,87 



1,03 



0,78 



4 and 5 



86 



197 



429,36 



1,32 



1,00 



As I presuppose that my observations are free from sensible constant 

 errors of an instrumental nature, and as the probable errors here given 

 are not based upon the deviations of single observations from the medium 

 of the corresponding evening but are deduced from the deviations between 

 the media of the different nights; they ought, I conceive, to give on an 

 average a very fair idea of the real errors of the positions. Small con- 

 stant differences will no doubt often be found between definitive positions 

 by different observers, but I am fully convinced, that the indications of 

 greater personal equations, which have been found in nebular observations, 

 depend more on instrumental circumstances than on the observer's person. 



