26 
MR. GEORGE W. M^ALKER ON THE MAGNETIC RE-SURVEY OE THE 
isomagnetics, and hence the obvious step is to determine the best linear forms which 
do coiiform to a potential. This is very readily determined from the independent 
reductions of the geographical components. 
Having obtained the best potential solution giving linear isomagnetics for each 
district, we try to find a potential solution for the whole region. We might expect 
to have to proceed to non-linear isomagnetics (still satisfying a potential) but in the 
event it appeared that no adequate improved agreement with the observed values 
could be 80 obtained. 
Accm’dingly I have adopted the magnetic potential giving linear isomagnetics for 
N, W and V and the best agreement with observation as representing the terrestrial 
lines due to remote causes, and the difierences between the observed and the 
calculated values are taken as the “ disturbing forces.” These latter may or may not 
have a potential. 
The procedure differs from Rucker and Thorpe’s in that I have made the terrestrial 
lines conform to a potential, and that I found no adequate grounds in the data to 
justify the introduction of higher powers than squares in the potential. 
We may now return to the main argument. 
If we have set out the co-ordinates of the stations in a district and the corresponding 
observed values of the element, say, N, we might proceed by the method of least 
squares to find the best linear form. But I am satisfied that Rucker’s method of 
“ equations of condition ” is quite adequate and much simpler. 
Let 
A|j and 4 represent the mean co-ordinates, and 
A\, A/ represent the differences for the station, 
Nf, represent the mean values of the element, and 
AN represent the difference for the station. 
We then take all the stations to North (or South) of and sum AX, A/, and AN, 
we thus get 
2iAN = a2( + AX) + 62A4 
Again, take all stations to East (or West) of 4 and sum A/, AX, and AN, we get 
another equation 
SgAN = AX + 62 (+ A^). 
Solving these for a and h we get 
N = Ny-f a AX-f/o A/ 
as the best linear solution given by tlie observations. 
The results for the different districts and different components are set out in 
Table V. 
