SURVEY OF THE BRITISH ISLES FOR THE EPOCH JANUARY I, 1886. 79 
We have analysed the dips in a somewhat different way. 
If one needle tends to give a slightly higher or lower result than the other, the 
mean value of the difference of the results, always taken in the same order—viz., dip 
given by Needle 1, minus dip given by Needle 2~ought to give the bias or measure of 
the difference due to imperfections in their construction. If this cpiantity be sub¬ 
tracted from the difference of the results in each observation, we get the error of 
experiment, which is the difference due to imperfection in observing and correcting. 
The mean of the last quantities, taken without reference to sign, is the mean error of 
experiment. 
Thus, if we take the difference as positive when Needle 1 is the higher, out of 
23 stations in Ireland at which observations were made with the same instrument (74), 
it was positive at 15 and negative at 8. The mean of all the differences showed that, 
on the average. Needle 1 gave results 0'’31 higher, and Needle 2 results 0''31 lower, 
than the mean of the two needles ; so that there is evidence of a bias which would 
make Needle 1 give results 0'‘6 higher than Needle 2. That this number is worthy of 
credit is shown by the close agreement of the values obtained with the same instru¬ 
ment in England, and by the practical identity of all the numbers obtained for Dip 
Circle 83 in England, Scotland, and Ireland. 
The axles of the needles of Dip Circle No. 74 appear to have undergone some slight 
alteration between the end of 1885 and the beginning of 1886, but there seems no 
doubt that since that date Needles No. 1 in the two instruments have read about 0''3 
and 0''2 respectively above the mean of the two needles. 
The following Table gives a summary of the results :— 
Instrument 74. 
i 
Number of stations, with 
difference. 
Bias. 
Ob.servers. 
Upper sign. Needle 1. 
Lower sign, Needle 2. 
Positive. 
Negative. 
Scotland . 
T., R., and L. 
18 
31 
+ 0-25 
England . 
T. 
8 
2 
+ 0-25 1 
R. 
24 
12 
+ 0-33 
Ireland 
R. 
15 
8 
-b 0-31 
