363 



variation, and to separate it into an external and an internal part. ^) 

 The notation is the same as tiiat of Steinkk. Instead of the 

 notation used by Fritschk in accordance with (Gauss) where 



y n = CD 

 — — 2 Pn 



m=7i 



Pn ^= -2" (q COS 771 k A- h sin m ).) P , 



. n u n 



X representing the geoigraphical longitude, V the potential, and R 

 the radius of the earth, the functions P„ differing from the spherical 

 harmonics only by a numerical factor, we put: 



[ a'« (cos m A -|- f") for the external field. 

 j.4"' {cosmX + (g -+- «)'") .' .. internal field. 



^"' cos m / -|- A"' sin 7ii X 



5. In Tab. Ill c = — and a for each term represent the ratio 



a 



of amplitudes and the phase difference between those parts that 



correspond to the internal and external fields. 



In the first column are given the values calculated for two 

 limiting values of the specific resistance, in the second our i-esults, 

 in the third column the results of Fritsche's first calculation, in 

 the fourth those deduced from his last publication. (The first and 

 third column are taken from Steiner for the sake of comparison). 



A comparison of the values show's that the newly calculated 

 values are more regular than those of Fritsche, a fact especially 

 demonstrated by the agreement between summer and winter. 



With the exception of P\, P\ and P\ the ratio c is situated 

 between the limits calculated from theory, somewhat closer however 

 to that corresponding to the smallest q. 



The phasedifference « is negative for the first four terms, positive 

 for the other ones; all differences are smaller than those resulting 

 from theory, but approaching to the limit corresponding to the 

 smallest resistance. 



The regularities in the terms of higher order are in favirur of 

 Schuster's idea, but the fact that the principal terms P\ and P\ 

 do not correspond (o the theory indicates, that the cause of the 

 diurnal variation certainly cannot be asciibed to nothing else but 

 a system of currents exterior to the earth and currents within the 

 earth induced by the former system. 



1) Some details of this research, which will be trented more at length in a 

 thesis for the doctorate, are given in the foregoing communication. For the potential 

 from which part of the horizontal forces is to be deduced we took {{:^x -\- ^v). 



24* 



