164 
MR. ARTHUR SCHUSTER ON THE 
variations have their origin therefore in different layers, which may to some extent 
oscillate independently. Though we shall find that the facts may be reconciled with 
the simpler supposition of one united oscillation of the whole shell of air, there are 
certain difficulties which are most easily explained by assuming possible differences 
in phase and amplitude between the upper and lower layers. If the two oscillations 
are quite independent, the conducting power depending on the now unknown 
amplitude of the periodic motion cannot he calculated, but must still be large, unless 
the amplitude reaches a higher order of magnitude than we have any reason to 
assume. 
The mathematical analysis is simple so long as we take the electric conductivity of 
the air to be uniform and constant; hut the great ionisation which the theory 
demands requires some explanation, and solar radiation suggests itself as a possible 
cause. Hence we might expect an increased conducting power in summer and in 
daytime as compared with that found during winter and at night. Observation shows, 
indeed, that the amplitude of the magnetic variation is considerably greater in 
summer than in winter, and we know that the needle is at comparative rest during 
the night. The variable conducting power depending on the position of the sun helps 
us also to overcome a difficulty which at first sight would appear to exclude the 
possibility of any close connexion between the barometric and magnetic variations ; 
the difficulty is presented by the fact that the change in atmospheric pressure is 
mainly semidiurnal, while the greater portion of the magnetic change is diurnal. 
This may to some extent be explained by the mathematical calculation, which shows 
that the flow of air giving a 24diourly variation of barometric pressure is more 
effective in causing a magnetic variation than the corresponding 12-bourly variation, 
but the whole difference cannot be accounted for in this manner. If, however, the 
conductivity of air is greater during the day than during the night, it may be proved 
that the 12-hourly variation of the barometer produces an appreciable periodicity of 
24 hours in the magnetic change, while there is no sensible increase in the 12-hourly 
magnetic change due to the 24-hourly period of the barometer. The complete 
solution of the mathematical problem for the case of a conducting power proportional 
to the cosine of the angle of incidence of the sun’s rqys is given in Part II. But even 
this extension of the theory is insufficient to explain entirely the observed increased 
amplitude of the magnetic variation during summer. We are, therefore, driven to 
assume either that the atmospheric oscillation of the upper layer is greater in summer 
than in winter and is to that extent independent of the oscillation of the lower layers, 
or that the ionising power of solar radiation is in some degree accumulative and that 
atmospheric conductivity is therefore not completely determined by the position of 
the sun at the time. The increased amplitude at times when sunspots are frequent 
is explained by an increased conductivity corresponding to an increase in solar 
activity. All indications, therefore, point to the sun as the source of ionisation, and 
ultra-violet radiation seems to be the most plausible cause. 
