of Terrestrial Magnetism. 351 



The following calculations will show the order of magnitude 

 of the vertical currents required to produce a sensible effect 

 on the magnetic needle. But, in the first place, we may esti- 

 mate the intensity of the displacement-current, consistent 

 with electrostatic observations. The numbers given in the 

 following quotation from Sir Wm. Thomson* may serve as a 

 basis : — " Even in fair weather the intensity of the electric 

 force in the air near the earth's surface is perpetually fluctua- 

 ting. The speaker had often observed it, especially during 

 calms or very light breezes from the east, varying from forty 

 Daniell's elements per foot to three or four times that amount 

 during a few minutes." 



We may then take '01 volt per centimetre in a second as a 



variation not unfrequently occurring. Reduced to C.Gr.S. 



units, this gives 10 G as the rate of variation of displacement. 



de I 

 The current intensity C is measured by -j I ^ttv 2 , where v 



is the velocity of light ; and for — we put, as just found, 10 6 . 



We thus obtain C = 10 -16 nearly. This means that the total 

 current through a surface of a million square kilometres, is 

 equal to unity. Charges such as described by Sir William 

 Thomson, if occurring simultaneously over a surface of 600 

 miles square, would thus be equivalent to a unit current. 

 If occurring over an area about 20 per cent, larger than 

 Ireland, therefore, the current would be equivalent to one 

 ampere. 



Let us ask next how large the current through an area 

 like that of Ireland would have to be in order to show itself 

 in magnetic observations. A deflection of one minute of arc 

 in the declination, if recurring periodically, would no doubt 

 show itself, This means, in our latitudes, a force of 5 x 10 ~ 5 

 C.G.S. Assuming, for simplicity's sake, the surface to be a 

 circular disk of radius 16 x 10 6 , we get 400 units of current, 

 or 4000 amperes ; which is 4000 times stronger than the 

 displacement- currents observed by Sir William Thomson. 

 We may then leave out of account the variations of electri- 

 fication on the earth's surface ; for although the conditions 

 are somewhat more favourable over larger surfaces, and espe- 

 cially near the equator, the possible effects seem to me always 

 to fall outside the observable limits. It is difficult to estimate 

 the possible values of actual discharge, especially in the polar 

 or equatorial regions. It must therefore be one of our first- 

 objects to find out whether the line-integral of magnetic force 

 does or does not vanish when taken round a closed curve 



* Reprints of Papers on Electrostatics and Magnetism, xvi. p. 219. 



