178 
MR. ARTHUR SCHUSTER ON THE 
been shown to be insufficient to produce appreciable effects, and we are therefore 
driven to look upon electromagnetic induction as being the only possible cause of the 
observed effects, the earth’s magnetism and atmospheric circulation being the active 
agents. Assuming as most probable that atmospheric circulation is symmetrical north 
and south of the equator, the character of the magnetic variation shows that the 
effective component of terrestrial magnetism has opposite signs in the two hemi¬ 
spheres; it must therefore be the vertical component which is active. We next put 
the question: What must be the atmospheric circulation which under the action of 
the vertical magnetic force produces periodical magnetic effects equal to those actually 
observed ? Taking the average for the complete year, the leading terms of the 
variable magnetic potential are n 2 x cos (X-K) and Hy cos 2 (X + £), the amplitude of the 
diurnal term being equal to about eight times the amplitude of the semidiurnal one. 
Calculation shows that fl, 1 may be produced by a quasi-tidal atmospheric flow having 
as velocity potential either i/zfl cos (X + ^) or i/y 1 cos (X + t), while the semidiurnal term 
may be produced by a flow having a velocity potential \fj 2 2 cos 2(X + £) or xp 4 2 cos 2(X+£). 
But these velocity potentials are exactly what is required for the atmospheric waves 
causing the daily changes of barometric pressure. The semidiurnal term of the 
pressure change is the one least affected by local conditions, and its distribution over 
the earth’s surface is therefore accurately known. It is found that xp 2 is small 
compared with xp.f. As regards the diurnal term having an amplitude at the equator 
of only one-third of the semidiurnal one, it varies somewhat irregularly and the 
relative importance of xp t l and xpg 1 is not well ascertained. Assuming the barometric 
variation to be wholly due to il/fl cos (X + t) and xp 2 2 cos 2 (X + t), we may deduce the 
magnetic variation and compare it with the observed changes. This has been the 
course of the investigation in the preceding paragraphs. It is found that the 
calculated magnetic variations have a phase which lags behind the observed one by 
about If hours, and this lag is slightly less for the diurnal term, but the difference is 
insignificant in view of the uncertainties of the data. The amplitude of the calculated 
diurnal term is about 2f times as great as that of the semidiurnal one, while obser¬ 
vation gives, as has already been stated, a ratio of 8 for the two terms. But if part 
of the barometric variation is due to a term xp : )—and there is some evidence that this 
is the case—agreement in the ratio of the two terms may be secured. There is, 
however, a further cause tending to increase the semidiurnal magnetic variation. In 
order to explain, on the basis of our theory, the difference in the magnetic changes 
between summer and winter, we must assume that the conductivity of the atmosphere 
is greater in that hemisphere which is more directly under the influence of the solar 
rays. Assuming that the electric conductivity is proportional to 1 + cos co, where co is 
the angle measured on the celestial sphere between the sun and the point considered, 
the calculated semidiurnal term reaches a value which is 4 - 7 times as great as that of 
the diurnal term, so that the term xp 2 is now called upon to a much smaller extent 
for making up the deficiency in the diurnal term. The supposed inequalities of 
