174 
MR. ARTHUR SCHUSTER ON THE 
magnetic effect would be 6‘3 x HU 8 C.G.S. This is insignificant and leaves a good 
margin for a greater sectional area of the ascending current, especially if it is 
remembered that both our assumed velocity and the volume charges are many times 
greater than is allowable. Magnetic effects due to the motion of electrified air must 
therefore be ruled out as effective causes of either regular or irregular magnetic 
changes. 
11. The daily variation of the magnetic forces includes a strong seasonal term, the 
amplitudes being greater in summer than in winter. In order to explain this term 
according to the theory advocated, it is necessary to assume a greater electric 
conductivity of the atmosphere in summer than in winter, or an oscillation of greater 
amplitude, which is not, however, indicated by the barometric changes. That the 
conductivity depends on the position of the sun, and may therefore vary with the 
season, is suggested by the relation in phase between the diurnal and semidiurnal 
terms, these terms combining together so as to leave the needle comparatively 
quiescent during the night. Reserving the possible causes of the conductivity and 
its dependence on solar position for further discussion, we may complete the theoretical 
investigation l:> 3 r introducing a variable conductivity. The simplest supposition to 
make will be that the conducting power in any small volume is proportional to the 
cosine of the angle between the vertical and the line drawn to the sun, or, in other 
words, proportional to the cosine of the angle, measured at the centre of the earth on 
the celestial sphere, between the sun and the small volume considered. This angle 
(w) is expressed in spherical co-ordinates by 
cos co = sin S cos 9 + sin 6 cos S cos X.(13), 
where X is the longitude measured from the meridian passing through the sun, and 9 
is measured from the pole, § representing the sun’s declination. To put the assumed 
law of conductivity into mathematical form, we write 
p = po + p i cos co. 
If p l = p^ the conductivity would be zero at a point opposed to the sun, and this 
is the highest admissible value of p x . In order to keep our investigation as general 
as possible, I write 
p = p 0 (l+y' cos 9 + y sin 9 cos X), 
where y and y may have any assigned values. The solution of our problem is 
obtained if we can find values of S and R satisfying the equations 
p cot 9 ^ 
dX 
-P cos e TW 
f/S dR ) 
^ cl9 sin 9cl\ | 
L 
dS _ cm | 
^ sin 9 d\ d9 J 
(14). 
R 
will now give directly the current function which hitherto was denoted by p 0 R. 
