SPHERE OF MAGNETIC MATERIAL IN A UNIFORM FIELD. 171 



possible size of the effect on the Earth of the Largest of sun-spot areas, endowed with what he considers 

 the largest magnetic moment reasonably attributable. The resulting disturbance is only of the order of 

 nnnr f the range of large magnetic storms at Greenwich, and Dr. SCHUSTER thus reaches much the same 

 conclusion as Lord KELVIN. Just, however, as in KELVIN'S case, I think it would be unwise at present to 

 pass a final judgment. It must also be remembered that magnetic disturbances are of varied forms and 

 sizes. Even if we wore justified in concluding that large movements of, say, lOOOy in H cannot be due 

 to direct magnetic action from the Sun, it is still conceivable that the comparatively small but outstanding 

 movements which often precede by several hours the largest movements of a disturbance may represent 

 such direct action. I have thus thought it worth while to make a few mathematical calculations as to 

 what might be expected to happen if direct action took place. The Sun's distance being so great compared 

 to the Earth's diameter, the field due to the Sun's action at any instant may be treated as constant 

 throughout an element of space large enough to contain the Earth and her atmosphere. The presence of 

 tho Earth modifies the field, and thus leads to variations in the disturbing force experienced at different 

 parts of her surface. The problem is not strictly a statical one, as the disturbing forces do not remain 

 constant. Rapid, however, as magnetic changes may seem when recorded by ordinary slow-running 

 magnetographs, they arc usually infinitely slow as compared to the changes which occur in wireless 

 telegraphy. Even the sudden commencements of storms, as we have seen, consist of changes persistent in 

 one direction for several minutes, the rate of change being usually less than lOy per minute. There is 

 thus reason to think that whilst the treatment of the problem as a statical one involves departures from 

 actual conditions, the results ought not to suffer so much from this limitation as to be unworthy of 

 consideration. A complete treatment ought of course to regard the Earth as a conductor of electricity. 

 Earth currents, we know, have diurnal, annual and irregular variations, and there can be no doubt that 

 a relationship exists between these currents and the phenomena of terrestrial magnetism. Our knowledge 

 at present, however, as regards Earth currents, is exceedingly limited. Even close to the surface but few 

 reliable observations have been made, and what depths the currents may extend to, or what the electrical 

 resistance of the several strata is, we do not know. The fact that the greater portion of the Earth's 

 surface is sea may be a most important consideration. We are thus almost perforce obliged to confine 

 ourselves to the statical problem, which will now be considered. 



87. It must be admitted that our direct knowledge of the Earth's magnetic quality is very slight. 

 There are few surface materials which are appreciably magnetic, and how the Earth comes to be a magnet 

 is a mystery. A magnet however it must be unless there is something absolutely wrong in the application 

 of the Gaussian analysis. According to that analysis, the source of the Earth's magnetism is almost 

 entirely internal, and the potential, to a rough first approximation, is that due to a solid sphere or internal 

 spherical shell uniformly magnetised. The natural inference is that the Earth's magnetic quality is, to 

 a first approximation, a function only of the distance r from the centre. We shall first consider the 

 simplest case, viz., that of a sphere of uniform permeability /* and radius a. Let F denote the strength of 

 the field in the absence of the sphere, and let r and be polar co-ordinates, being measured from the 

 diameter which coincides with the direction of the field F. On the introduction of the sphere the field in 

 the medium outside it, supposed of unit permeability, is given by 



V = -Fr cos 0+ >^y <?. cos 6 (1). 



ii i k > ._ x ' 



In the figure, APA' is a section through the centre of the sphere, A'A being the diameter parallel to 

 the direction of the field F. 



z 2 



