DIURNAL VARIATION OF TERRESTRIAL MAGNETISM. 
185 
another place that the energy involved in a great magnetic storm is so considerable 
that we can only think of the earth’s rotational energy as the source from which it 
ultimately is drawn. The earth can only act through its magnetisation in combination 
with the circulation of the atmosphere, so that magnetic storms may be considered to 
be only highly magnified and sudden changes in the intensity of electric currents 
circulating under the action of electric forces which are always present. 
Those currents only are discussed in this communication which produce periodic 
variations in the magnetic elements, but there are also electromotive forces giving rise 
to current functions which are expressed by zonal harmonics and cannot under 
ordinary circumstances be observed, though any variation of conductivity between 
summer and winter would produce an annual period. 
One further consequence of the theory deserves to be noticed. The electric currents 
indicated by our theory are sufficiently large to produce a sensible heating effect in 
the low-pressure regions through which they circulate. They will protect, therefore, 
the outer sheets of the atmosphere from falling to the extremely low temperatures 
which sometimes have been assumed to exist there, .and they may help to form the 
isothermal layer which balloon observations have proved to exist at a height of about 
50,000 feet. 
Enough has been said to show the importance of the questions on which further 
investigation of the diurnal variation must give valuable information. If the 
fundamental ideas underlying the present enquiry stand the test of further research, 
we are in possession of a powerful method which will enable us to trace the cosmical 
causes which affect the ionisation of the upper regions of the atmosphere and which 
act apparently in sympathy with periodic effects showing themselves on and near the 
surface of the sun. It should be our endeavour to put the theory itself to a more 
accurate test than can at present be done. The most promising line of attack seems 
to me to be the investigation of the diurnal variation near the equator, where, as 
explained in § 6, it should not only vary with local time, but possess a term depending 
on the time of the meridian which passes through the magnetic axis. An exact 
determination of lunar effects would also, as has already been pointed out, serve as 
a valuable test of the theory. 
PART II. 
The problem to be solved may be stated thus : a spherical shell of fluid is animated 
by a quasi-tidal motion and is under the influence of magnetic forces of which only 
the vertical components are considered. It is required to find the magnetic effect of 
the induced currents if the motion is subject to a velocity potential if// cos <x (X-M — a), 
where xp/ is a surface harmonic, X the longitude measured from some standard 
meridian towards the east, and t is the local time of that meridian. The conductivity 
p of the fluid is not necessarily uniform, but we take it to be expressible in the form 
p = p 0 + pi cos 0+p 2 sin 6 cos (X-K), 
2 B 
VOL. ccvm.— A. 
