SURVEY OF THE BRITISH ISLES FOR THE EPOCH JANUARY 1, 1886. 77 
In the first place then, we take as the error of a Decimation, the difference from 
the mean of the values obtained at the same station at an interval so small that the 
secular correction is not involved {i.e., a few hours or days), when both the geographical 
and magnetic meridians are determined independently. 
The error of a Force observation is taken as half the difference between the two 
independent values, calculated as above described. 
Lastly, the error of a Dip observation is half the difference between the results given 
with needles 1 and 2. In the case of the last two, it is evident that both quantities 
may be affected with small errors which are not thus detected, such as , that due 
to uncertainty as to temperature, in the case of the Forces, and errors of setting in 
the magnetic meridian, in that of the Dips. 
Taking, however, these quantities and treating them as though all the results in 
each group were measures of the same quantity, we get the following values of the 
probable error ;— 
Nnmber of observations. 
Pi-obable error. 
Declination .... 
97-5 
0'-699 
Horizontal Force . 
196 
0-00028 (M.U.) 
Dip. 
190 
O'-15 
In this Table, we count each double observation as one. The fraction, in the case 
of the Declination, is due to the fact that, at some stations, an odd number of 
observations was made. 
It is useful to analyse the observations still further. In so doing, we have generally 
treated Scotland as a whole. During our earlier tours we observed together, and 
sometimes one observer would take the geographical and the other the magnetic 
meridian, one would observe the deflection and the other the time of vibration. It is, 
therefore, difficult to separate the results. In England and Ireland we always observed 
apart; and, with the exception of a short tour in 1886, when Dr. Thorpe used Dip Circle 
No. 74, we always used different instruments. The mean values of the quantities are 
taken irrespective of sign, so that they indicate the average value whether positive or 
negative. 
The definitions of the quantities used as tests, are given on p. 70. The symbol dS 
indicates the mean error of the element. 
