502 
PROFESSOR A. SCHUSTER ON THE DIURNAL 
The result'will not hold, of course, if conduction in the Earth’s crust takes place 
chiefly at some distance below the surface, as in that case the vertical force due to the 
induced currents will not tend to become equal to the vertical force due to the 
primary variation. For a bad conductivity we shall always have a resultant vertical 
force sensibly equal to the primary force. If the conductivity increases, the resultant 
will have a different phase from the primary variation, tending towards a difference 
of 45°, if the conductivity is uniform. If the conductivity is not uniform, a maximum 
difference of phase will be reached, which, if the conductivity is still further increased, 
diminishes indefinitely. 
VI. The Magnetic Potential on the Surface of the Earth. 
As it seemed interesting to trace the equipotential lines on the surface of the Earth 
as far as they depend on tlie diurnal variation, I have calculated the potential from 
the equations [A] and [BJ. 
It is necessary, for this purpose, to compute the tesseral harmonics for definite 
points on the Earth’s surface. It would seem most natural to choose these points, so 
that they lie on equidistant circles of latitudes, but as tables"”" exist for the zonal 
harmonics in terms of the cosine of the colatitude, I have selected values of these 
cosines so that the corresponding angles should differ as nearly as possible by 10°. 
The values of u and jx — cos u, for which the potential is computed on the Northern 
hemisphere, are given in Table XXIV., u being the colatitude. 
Table XXIV. 
li = cosu= *98 *94 ’87 
u= 11° 29' 19^57' 29° 32' 
•77 -64 -50 -34 *17 
39° 39' 50° 12' 60° 00' 70° 07' 80° 13' 
•00 
90° 00' 
Symmetrical circles of latitude were taken on the Southern hemisphere. 
Taking from Mr. Glaisher’s Table the values of corresponding to each of the 
above values of /r, we obtain the differential coefficients of zonal harmonics by a 
successive application of the formula 
(tPi _ (/V- o 
dfX (IfM 
= (2^ - 1) P,_,. 
The first and second difterential coefficients thus calculated are given in Tables 
XXV. and XXVI. 
* ‘Report of the Rritish Association ’ (Sheffield, 1879). 
