346 LORD WROTTESLEY ON THE PERIODICAL OBSERVATION OF STARS 
In the case of the four binary stars, to which an asterisk is attached in the Tables, 
the means, both of the positions and the distances, given in this table are obtained 
by employing the assigned or arbitrary weights, as before described. 
In deference to the objections which may be urged to this mode of reduction, I 
had originally intended to use the common arithmetical mean in all these cases ; but 
out of fifty-four means of positions computed strictly by the usual formulae, and com- 
pared with means obtained as last described, and also with the arithmetical means 
of the same quantities, it was found that the mean obtained by using the arbitrary 
weights differed only in thirteen cases more than 9' from the strict mean, and that 
in eight out of the thirteen cases, the result was rendered more erroneous by using 
the arithmetical mean, instead of the mean derived from the use of arbitrary weights : 
there were seven cases out of the fifty-four in which the computed and arbitrary 
weights gave precisely the same result. 
