12 AKSEL S. STEEN. TERRESTRIAL MAGNETISM. [NORW. POL. EXP. 
then approximately, provided the intervals are of about equal length, 
1 2 Se 2 her Gy ek 
ate _,, bh — = = By» ote. 
2? 
and the circle readings 
St ts and 6, , te and a, , ont Ms and 6, , ete. 
may be considered to be simultaneous for both positions of the needle. For 
each such combination, a value is obtained for the error of collimation, 
2(m—1) values in all. If these values be indicated by c¢,, ¢,, ¢,, ete. 
we have 
a+ _ 4 
> 1 
Gi; eaniie Sa lal i 
a, b, + bs 
C, — 5 
a, + a; b 
a 2 
C, — 5 
a Bias ar bn 
; 5 
Cim—1) = cy Se 
and the mean error of collimation 
pice Ore uO sab Gye Seyenie teete ee + Cr m—1) 
= 2(n—1) 
By this formula I have calculated the error of collimation from the series 
of observations (noted when the disturbance was not very great) for cases 
in which the difference in time 
amt ants pop Bm Bn ts 
ms 2) 
2 — Gm +1 
was less than 1 minute. The results obtained are given in the following 
table. 
