34:0 H. Jacoby — Determination of the Division 



The difference, therefore, is : 



=r (maximum) — =r (minimum) = — — r — 



The formula obtained by Lorentzen for computing P m is, allow- 

 ing for the difference of notation (Astr. Nach., 3134, Eq. 15) : 



1 2, . 2m. 

 _ = - 5 ( w _l) + _(n- W 



which agrees with equation (2) just obtained. But Lorentzen's 

 value for the weight of a quantity he calls d, which equals the 

 excess of the true average space of scale A over the true aver- 

 age space of scale B, is not quite exact. In our notation this 



excess is — K , and as we have seen, it is equal to : 



— 5 (the sum of all the parentheses in Table I). 



We have also seen that the sum of all the parentheses in any 

 horizontal line of Table I, has for the square of its mean error 

 the quantity : 



268 



And, as there are 2?i—l horizontal lines, the sum of the whole 

 table has for the square of its mean error : 



2(2n — \)88 



Therefore the square of the mean error of d is : 



2(2?i— 1) 



and the weight of d, ee being taken as unity, is : 



n* 



which may be written : 



2(2^—1) 



n 



7-T 



n 



Lorentzen gets for the same quantity the slightly incorrect 

 value : 



In Table II, which will be given further on, are contained 

 the maximum and minimum weights obtained in Gill's method 

 for various values of n. The table is computed by means of 

 equations (3) and (4). When n is an even number, the maxi- 

 mum weight applies to the middle line of the scale ; and when 



