Electric Currents in the United Kingdom. 101 



(4) The mean terrestrial curves for Jan. 1, 1891, deduced 

 from (2) and (3). These will be called the mean 1891 curves. 



(5) Lastly, the true isomagnetic curves deduced from the 

 results at all the 882 stations fur the epoch Jan. 1, 1891. 

 These will be called the (rue 1891 curves. 



(1) The 1886 Curves. 



The advantage of using the calculated terrestrial curves is 

 that they can be carried across the sea from England to 

 Ireland, or extended a few miles from the coast by extra- 

 polation. The area included can therefore be made as large 

 as possible. On the other hand, the method of obtaining 

 these curves is such that the errors in their positions will 

 probably be greatest near the boundaries of the land area 

 over which the survey was carried. In order therefore that 

 such errors might affect different calculations as differently as 

 possible, it was determined to take two circuits, which should 

 have their greatest extensions N. and S., and E. and W. 

 respectively. They will be called the a and (3 circuits. 



The a circuit was bounded by long. 2° W., lat. 58° N., 

 long. 7° W. and lat. 52° N. 



The /3 current was bounded by long. 1° W., lat. 55° N., 

 long. 9° W. and lat. 52° N. 



In the published account of the 1886 survey (loc. cit. 

 p. 322), the values of the declination (S) and horizontal force 

 (H) are given for all points within the United Kingdom 

 denned by the intersection of whole degrees of latitude and 

 lono-itude. From these the northerly components of the 

 force (H cos 8) were calculated for all such points on the lines 

 of latitude, and the westerly components (H sin 8) for all 

 such points on the lines of longitude which bounded the 

 circuits. 



The method of calculating the line-integral of the force 

 may best be shown by an example, for which we may select 

 long. 2° W. between lat. 52° and 58°. 



Let C be the number of cm. in a degree of latitude, 

 and N the northerly component of the force. Assume that 

 N = N 52 + ^ / + #, where a is a constant, V = l — 52, and x is a 

 small variable. 



Let W be the work done as the unit pole moves due North 



from lat. 52° to lat. 58°. 



Then r™ f 6 



W = C NdZ=C{N 52 x6+18a+ \ xdl'\. 



J 52 Jo 



The value of a was found from the values of the northerly 



