( 515 ) 



Out of the curves, indicating according to the above numbers 

 the daily vibration of earth-current and magnetic component, is 

 evident : 



that this vibration for them corresponds; 



that the direction of the earth-current is such that it can be regarded 

 as causing the variations of the magnetic comj)onent ; 



further : that the magnetic component is retarded with respect to the 

 earth-current and finally ; 



that the ratio of the amplitudes of corresponding vibrations decreases 

 with the duration of that vibration, so that those of the earth-currerit 

 are relatively larger ivith a shorter duration. 



The chief maximum in the afternoon is reached by the earth- 

 current about an hour and a half earlier, the chief maximum at 

 night about two liours earlier. 



The secondary vibration in the evening-hours is for the earth- 

 current much stronger. 



It is an indication to apply here the harmonic analysis and to 

 employ for it the formula 



A-=. An sin n{t -\- c,,). 



The results of the harmonic analysis confirm in full w^hat the 

 mere observation taught us. 



Especially the increase of the earth-current as the duration of the 

 corresponding variation of the earth-magnetism becomes shorter is very 

 distinctly expressed. 



This dependence can be pretty accurately expressed by the following 

 formula. 



Let the amplitude of the magnetic component be M ; the duration 

 expressed in days T, and the amplitude of the earth-current A., then 



= ''^Yi. 



TM 



The values in the above column "calc" (on the next page) have been 

 computed with the aid of this formula. 



Yet not much value must be attached to that correspondence, as 

 the higher terms of the harmonic analysis are very untrustworthy 

 on account of the inaccuracy of the hourvalues employed. 



The difference of phase increases regularly as far as the 5*^^ term, 

 and then drops again to the value it had for the ^^^ term; but the 

 phase dififerences found for the higher terms deserve little confidence. 



I have been successful in obtaining a confirmation of a part of 

 these results with the aid of the cable Batavia— Billiton. The four 

 months March — June 1906 gave for the nightly course proper results. 



3Ö 



Proceedings Royal Acad. Amsterdam. Vol. X. 



