DIURNAL VARIATION OF TERRESTRIAL MAGNETISM. 
173 
If we take the current sheets to be of finite thickness e, and p denotes conductivity 
referred to unit volume, we must write 
^TTCtKOe 
tan e = -- r — . 
2n+ 1 
If pe has the value previously determined by the semidiurnal variation, I calculate 
a retardation of 1 hour for the semidiurnal and about lb hours for the diurnal term. 
The amplitude would be reduced by about 14 per cent. There are various causes, 
notably the inequalities of conductivity, tending to diminish the retardation, so that 
we may consider that self-induction would not cause a shift of phase amounting to 
more than an hour, but it is in the opposite direction to that indicated by the 
observations, if the barometric and magnetic oscillations are due to identical causes. 
10. It is known that the air contains an excess of positive electricity, and the 
question might be raised whether the oscillations of the atmosphere do not 
convectively produce direct magnetic effects. If E be the total quantity of electricity 
contained in a vertical column of unit cross section, and V, the velocity of air in that 
column, supposed to be uniform, the total current in the atmosphere across a vertical 
area of unit width is EY, and the magnetic force at the surface of the earth is of 
the order of magnitude 27 tEV. The quantity E must be equal and opposite to the 
surface electrification of the earth, which itself is equal to F/iw 2 , where v is the 
velocity of light, and F the normal fall of potential, which we may put equal to 
1 volt per centimetre, or to 10\ The magnetic force has therefore a magnitude 
of order 5'8V x 10 -14 . If the velocity potential of the atmospheric oscillation is 
A^/sinc r(\ + t), the velocity in the two cases considered is greatest at the equator, 
where its maximum rises to crAxfj//a, which for the diurnal and semidiurnal change is 
A Ja and 6A 2 /a respectively. It follows from the numerical values given in (8) that 
the maximum equatorial velocities are 10 and 30 centims. per second respectively. 
The magnetic forces due to such velocities are quite insignificant. In the literature 
referring to the subject we frequently find it suggested that magnetic disturbances 
are due to moving masses of electrified air, some writers even going so far as to say 
that this has been proved ; it may be demonstrated, on the contrary, that the assumed 
cause is insufficient. For horizontal air currents this has just been demonstrated, 
and the effects of ascending or descending currents are still less efficient. If a column 
of air of cylindrical shape having as base a circle of radius r rises or falls with 
velocity Y, and it is imagined as an extreme case that the column extends indefinitely 
in both directions, the magnetic force at the boundary is 27rrEY, where E is the 
electric density. At the surface of the earth the ionisation is such that the free 
electric charges of each kind amount to about 1 electrostatic unit per cubic metre. 
Let us assume one kind to be suppressed altogether, so that this number represents 
the electric volume density, or in electromagnetic measure 0'33 x 10 -16 . If r be 
1 kilometre, and the velocity that of an express train, or 30 metres a second, the 
