120 A. TAXAKADATE. 



. dY flX 



ax oi/ 



which in polar co-ordinates becomes 



1 / OY ,., 1 OX \ 



or replacing X, Y by Hcosrî and Hsino, we have 



i ( OH . . , „ , nd TT • > , 



v: = -p < -^ -sHio + Hcoso— H sino to- ç 



4- K ( i)<f d(f ^ 



— 1 ---, coso — Hsino — ^ [ 



cos (f \ 0/ 9/ J) 



in terms of the ol)served elements. The ellipticity of the meri- 

 dian arc is neglected as its correction falls within the errors of 

 oljservations at present. If the rectangular components, in- 

 stead of the declination, dip and horizontal force, be expanded 

 in different powers of dißerential longitude and latitude the 

 calculation becomes much simpler. The differences of rectangular 

 components in Tables XII and XIII give sufficiently close 

 approximation of the differential coefficients as was found by 

 actual trial. The currents found by the above formula are given 

 in Table XVIII and Map 8. 



By way of comparison, the current densities are calcu- 

 lated for Austria and Great Britain. Map 9 gives the lines 

 of equal vertical currents obtained from the expressions of 

 magnetic elements in Austria given by Prof. Liznar, and Map 9a 

 the same for Great Britain obtained from the data given by 

 Profs. Riicker and Thorpe. In the latter, two systems of lines 

 are given ; the dotted lines are those calculated by taking dif- 

 ferences of rectangular components computed from elements in 

 Tables III, YI and IX in Vol. 188 of the Philosophical Trans- 

 actions of the Eoval Societv of London : those lines are not 



