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directors of magnetical observatories were to reduce their 
observations so as to give us changes in the components of 
force directed towards the geographical north and west 
ratlier than, as is customary, changes in horizontal force 
and declination. In all reductions such as I have attempted, 
and indeed in all comparisons of the results obtained at 
different stations, what interests us most is the two com- 
ponents of force resolved along two definite directions like 
north and west, and not the components of force resolved 
as at present in directions changing sometimes rapidly from 
place to place. 
It may ultimately appear that some variations of terres- 
trial magnetism are expressed most simply according to a 
system of large and small circles, having the points of in- 
tersection of the magnetic axis with the surface of the earth 
as poles ; but the present system seems to me quite arbitrary, 
and until we know more accurately the position of the 
magnetic axis, the latitude and -longitude circles seem to me 
to be the only possible lines of reference for the magnetic 
forces. 
Supposing we have, by expansion in spherical harmonics, 
obtained the distribution of potential, representing some 
periodic variation we wish to investigate, we may easily, 
should it be considered desirable, obtain such a distribution 
of electric currents on any sphere concentric with the earth’s 
surface, inside or outside as the case may be, which might 
cause the observed variation. Such a representation would 
always be instructive, although the actual currents causing 
the disturbance may be distributed in a very different manner 
if they have any vertical components. The simplest plan 
would be, in the first place, to take the sphere on which we 
draw the currents close to the earth’s surface, either just 
outside or just inside, according to the result obtained for 
the vertical force. 
If the magnetic potential is distributed over the earth’s 
