DIURNAL VARIATION OF TERRESTRIAL MAGNETISM. 
177 
The main terms of the magnetic potentials ft 2 * and ft 3 2 are now each affected b) r 
both the diurnal and semidiurnal barometric variation, and their relative amplitudes 
may differ considerably from those calculated on the assumption of a uniform con¬ 
ductivity. If y has its maximum value, which is unity, we have for these two terms, 
neglecting an unimportant difference of phase, and leaving out common factors, 
<V = - Aj +—A a = 21-0-, 
2 5 1 105 2 tt’ 
ft , 2 = 
32 
8 
A 2 + —A,= 47-. 
105 2 315 7r 
The 24-hourly variation of terrestrial magnetism now takes the lead and as regards 
westerly force is now 47 times as great as the semidiurnal variation, but the latter is 
still too great for complete agreement with the facts, the observational ratio being 8’8. 
This remaining discrepancy is not decisive against the accuracy of the assigned cause 
in view of the uncertainty which attaches to the 24-hourly term in the barometric 
variation as explained in § 4, and the considerations brought forward in the following 
paragraph. There is the theoretical possibility of a further increase in the diurnal 
term through a velocity proportional to P 3 °; the motion specified by this potential 
would give a barometric oscillation determined by the time of some definite meridian, 
and though observations seem to indicate the existence of part of the oscillation being 
of this nature, it is not likely that it is sufficiently great to produce a marked magnetic 
effect. 
12. A general review of the argument, even at the risk of repeating a portion of 
what has already been said, may be appropriate, and is necessary to show how we are 
naturally led to the theory here proposed. It will also serve to introduce the 
consideration of the remaining difficulties and of the possibility of accounting for 
the amount of ionisation necessary to explain the magnitude of the observed 
effects. 
Our object is to explain the cause of the periodic changes of the terrestrial magnetic 
forces in so far as they depend on the position of the sun. The diurnal changes may 
be represented as being governed by a magnetic potential ft composed of terms of the 
form ft/ cos o-(X-H), where f 1 / is a surface harmonic; the observed vertical forces 
show, as proved in my previous communication, that vve must seek the cause of the 
variation outside the earth’s surface. Electric currents circulating in our atmosphere 
and having a current function made up of terms which are respectively proportional 
to ft/ produce the required effect, and we are justified in assuming this—the simplest 
explanation—to be also the correct one until it is shown to lead to contradictions. 
The maintenance of the electric currents necessarily requires an electromotive force, 
and their closed lines of flow dispose of any theory which would seek this force in a 
static distribution of potential. Electric charges carried along by air currents have 
VOL. CCVIII.—A. 2 A 
