102 Prof. A. W. Riicker on Vertical Earth-Air 



components at the points on latitudes 52° and 58° respectively. 

 The integral was calculated by quadrature, graphic methods 

 being employed. 



To give an idea of the relative magnitudes of the terms, I 

 append the following data : — 



6N 52 +18a+f 6 ^/ / =l-00896-0-06864-0-00152 



■VxdV=V 



= 0-93880. 



The constant C was taken = 11119320 cm., so that the 

 work done in this part of the circuit is 1*04387 x 10 7 ergs. 



Treating the other parts of the circuit in the same way, the 

 four quantities, the algebraical sum of which is the work done 

 in completing the circuit, are : — 



(1-04388 + 017082 - 1-00637 -0-20902) X 10 7 = - 6*9 X 10 3 ergs. 



Dividing by 47r, we find that the total current within the 

 circuit is —550 C.G.S. units, and, since the area is 2*13 x 10 5 

 square kilometres, this amounts to —0*026 ampere per 

 square kilometre. The negative sign indicates that the 

 current flows downwards. 



A similar calculation carried out with respect to the ft 

 circuit, of which the greatest extension is East and West, 

 and the area is 1*77 x 10 5 square kilometres, indicates a 

 current of only —0*004 ampere per square kilometre. 



(2) The First Survey 1891 Curves. 



When the 1886 curves are reduced to the Epoch Jan. 1, 

 1891, by methods which are fully described in the account of 

 the later survey, the results obtained from the a and ft cir- 

 cuits are —0*045 and — 0'030 ampere per square kilometre 

 respectively. It would at first sight appear as though the 

 fact that these values are larger than those calculated for 

 Jan. 1, 1886, might be due to errors introduced by the assumed 

 values of the secular change ; but, as will immediately be 

 seen, they are not larger than those obtained by another 

 method, which this cause of error does not affect. 



(3) The Second Survey 1891 Curves. 



Treated in exactly the same way as the last, these give 

 values of about the same magnitude but of opposite signs ; 

 viz. for the a circuit +0*016, and for the ft circuit + 0*020 

 ampere per square kilometre. Thus two different methods of 

 calculating the same quantity lead to very different results, 

 which point to the conclusion that the apparent effects of the 



