ON TERRESTRIAL MAGXETISM AN'D ATMOSPHERIC ELECTRICITV. 755 



[X = force to north ; Y = force to west ; \ = longitude measured eastward.] 

 If Y sin 6 be expanded in a .series of surface liarmonics tlie potential V will be 

 obtained immediately in a similar series ; but somewhat ditiicult complications 

 arise when V is to be obtained from the ."-eries for X. This difficulty completely 

 disappears in the method here propo.«ed, for X being expressed in a series of 

 circular function, we may integrate with respect to 6 without chaiifjing the nature 

 of the series. The process to be employed may be summed up as follows : — 

 Express both X and Y in the form — 



X = X,, + X| cos X + Xo cos 2X + ... 



+ X/ sin X + X./ sin 2X+ . . . 



Y = Y, cos X + Y, cos 2X + . . . 



+ Y,' sin X + Y.j' sin 2X + ... 



and further express X, and Y„ in Fourier's cosine series for even and in the slve 

 series for o- odd. If Y is then calculated by either of the equations (7) and the 

 substitutions, or (5) or (6) of the corresponding equations are performed, the 

 potential will be expressed in a series of spherical harmonics. The values of X 

 and Y are not known in the polar region, but must be obtained by interpolation. 

 The term iw^erpolation is the appropriate one because the value of X^ and Y/ are 

 known at the poles, vanishing there except for Yj. Al'^o the first o- ditlereutial 

 coefficients of X^ and the tirst o- — 1 differential coefficients of Y, will vanish at 

 the same points. The value of Y^ and Y/ is very approximately known at the 

 poles from previous investigations, and also its first differential coefficients will 

 vanish. 



I have not taken account of the possibility of earth currents traveiving the 

 surface of the earth in sufficient intensity to affect magnetic forces. The investi- 

 gations of Adolph Schmidt have shown how the problem must be treated wlien 

 their influence has to be taken into consideration. The general method of 

 expansion here suggested will remain the same. 



On Magnetic Ohf^frvations at Funafuti. Bij Captain E. "W. 

 Creak, R.N., F.R.S. 



•4. On the Relations between the Variations in the Earth Currents, the 

 Electric Currents from the Atmosphere, arid the Magnetic Perturbations. 

 By Selim Lemstrom. 



The paper contains an historical slcetch of the observations and researches 

 made on the earth currents by Laniont, Airy, Wild, Blavier, and others. The author 

 describes the method employed by him for measuring the electromotive force of 

 the electric currents coming from the atmosphere, and gives the evidence of the 

 fact that the variations of earth currents occur a short time (five minutes) before 

 the magnetic perturbations, and that the former are more numerous than the 

 latter. From the observations in Sodankyla it is, however, proved that all 

 magnetic perturbations are not preceded by variations in the earth currents, but 

 that these probably are caused by electrical currents from the atmosphere to the 

 earth, or vice versa. 



The proofs of that conclusion are : (1) That the magnetic perturbations in polar 

 regions have a contrary direction to those in more southern countries; (2) That at 

 the times of auroras the electrical curreut from the atmosphere varies much, and 

 must exert on magnetic instruments a marked influence depending on their position, 

 relative to the space within which this current is moving. It follows from this that 

 we cannot find the causes of the magnetic variations, or, rather, perturbations, 

 before we have mvestigated the earth currents and the electrical currents in the 

 atmosphere. 



The author's experience showa that we must seek the key to these relations in 



3c 2 



