SURVEY OF THE BRITISH ISLES FOR THE EPOCH JANUARY I, 1886. 235 
district, it will be understood that the values appropriate to any station are throughout 
properly weighted. The lueans of the latitudes, longitudes, and declinations deter¬ 
mined the central station of the district and the declination at that station (Sq )- If 
was then assumed, if V and X' be the district coordinates of a station, i.e., the 
differences between its latitude and longitude and those of the central station, 
that the declination is connected with these quantities by the linear equation— 
8 = Sq “b xl -j- y\. 
Two ecpiations of condition were then formed by adding the equations thus 
obtained—(l), for all stations to the north of the central station ; (2), for all stations 
to the east of it, and dividing by the number of stations employed, each multiplied by 
its proper weight. 
By solving these for x and y, the rates of change of the Declination per degree 
of latitude and longitude respectively were obtained.'^" 
To test this method, it was applied in the case of the Dips to the whole of Scotland. 
This portion of Great Britain furnished a severe test, as from the irregularity of 
its form it is not particularly well adapted for the application of the method of 
equations of condition. The calculation was also made by the method of least squares. 
Both calculations were repeated twice, viz., with and without the inclusion of Soa and 
Canna, at which the local disturbance is very coiisirdeable. The central station was 
not that given by the mean latitude and longitude, but that obtained from Welsh’s 
Dip observations, viz., lat. 5G° 48' N. ; long. 4° 19' W. In this particular again, the 
conditions of the selected example were unfavourable to the method of ecjuations 
of condition. 
In the following Table, u is the angle made by the lines of equal Inclination with 
the geographical meridian, r is the change in Inclination (expressed in minutes) per 
geographical mile, measured at right angles to the isoclinals, and 0^ is the Dip at the 
central station ;— 
0,;. 
u. 
Including Soa and Canna . . | 
Least squares. 
Equations of condition 
0 t 
71 9-7 
71 9T 
67 23 
68 7 
0'625 
0-670 
Excluding Soa and Canna . . | 
Least squares. 
Equations of condition 
71 8-0 
71 7-8 
72 49 
72 42 
0-.595 
0-609 
* A plan very similar to that above described was employer! by Dr. van Rijckevorsel in working up 
tbe results of bis survey of tbe Indian Archipelago (‘ Magnetiscbe Opnemiug van den Indiscben 
Arcbipel in de Jaren 1874-77, gedaan door Dr. van Rijckevorsel.’ Amsterdam, J. Muller, 1879). 
2 
H 
2 
