364 KRETZ. 



As J//q and a^ are not independently determined the correct- 

 ness of the last formula is not immediately evident. It is, how- 

 ever, easily proved. For we have 



- ^^^^ - (1875- 7i) ^^ [by equation (4)] 



-(1875-7;) ^cD\ 



+ A ^2 ([c/?] -(1875- ?;)[/] Q) 



+ ■■• 1 



and since the i?'s are independent, and the probable error of B^ 

 is r^ I \/pi, we get for the probable error of «jg^g 



+A'-iM[C/?]-(i875-7;)[/]C,)2 



+ . 



= f7pfc^2|M[^^]^-2[C/)][/](i875-7'o)[/c'] 

 + C/]'[/^^'](i875-7;)2| 



= ^+(x875-r„).^^ 

 = rr2+(i875-7;)2r^2 



remembering that 



[/C] = o and [/C^] = [C/?]. 



In applying the above formulae to a special case, I invariably 

 proceeded as follows (the explanation is again confined to right 

 ascension ; it applies equally to declination, however) : 



(24) 



