VARIATION OF TERRESTRIAL MAGNETISM. 
505 
Introducing these quantities in the equations for the potential, and taking proper 
account of the change of sign of p, in the Southern hemisphere, I have obtained 
Table XXVII., in which the potentials are given for 24 equidistant meridian circles. 
In order to reproduce the daily variations, we must imagine the whole system of 
equipotential lines to revolve round the Earth from East to West; the time for which 
the potential is given is mean noon for the zero meridian. It will be remembered 
that the equations for the potential have been derived from the mean summer values 
in the Northern, and mean winter values in the Southern hemisphere. If we want 
to get a symmetrical potential in both hemispheres, we must take the average varia¬ 
tion for the whole year, or, what comes to the same thing, we ma.y in Table XXVII. 
write down the mean values for two corresponding circles of latitude, one in each 
hemisphere. This has been done in Table XXVIIL, where the values are only given 
for the Northern hemisphere. The mean equipotential lines for the year are drawn 
in fig. 12. If we imagine the variable part of the magnetic force to be produced by 
a system of surface currents in a conducting sphere concentric with the Earth, and 
surrounding it, we may, if the potential is known, calculate the distribution of the 
lines of flow. 
If the magnetic surface potential is of the form H,;, when fl,; is a harmonic of degree n, 
the current function (f)„ is given by 
AttcP,, = — 
so that the lines of flow are the same as the equipotential lines. This is no longer 
true when the magnetic potential is made up of a number of terms corresponding to 
harmonics of different degrees, for the factor (2n + l)[[n 1) will vary for different 
terms, and the resultant current function will therefore no longer be proportional to 
the resultant magnetic potential. 
In our own case, taking the mean values for the whole year, the series begins with 
11 . 2 , fh© factor (2?r -j- l)l{n + 1) will vary, therefore, only between 5/3 and 2. We 
may then, as an approximation, still take the ecjuipotential lines to give us the general 
form of the lines of flow. We conclude that we may imagine the daily variation 
of the Earth’s magnetic force to be produced by a system of electric currents in a 
sphere surrounding the Earth, in which the lines of flow are roughly represented in 
fig. 12, the direction being such that at longitude 60° East the flow is away from the 
equator. 
* Maxwell, ‘ Electricity and Magnetism,’ vol. 2, p. 281. 
MDCCCLXXXIX. — A. 3 t 
