DIURNAL VARIATION OF TERRESTRIAL MAGNETISM. 
171 
We can satisfy equation (3) by assuming R to be made up of two or four terms, 
according as we treat of the diurnal or semidiurnal variations. Remembering that 
by the fundamental equation 
Ism 9 d\ 2 
+ Id sin e 7w + n ’ n+1 ) = °’ 
we find the terms which are introduced by the inclination of the magnetic axis to lie 
for the diurnal variation 
-fy-R-f sin (2X +1 — a) — ^R 3 ° sin (t — a), 
and for the semidiurnal variation 
-fy-R,/ sin (3X + 2i —a) + fR , 1 —j^R'g) sin (X + 2^ —a). 
The additional terms are therefore, restoring the constant factor, 
-O = — [TAfy/ sin (f + X — ai)— f Afy' 2 sin (t'— X—a^ + hAA,^ 3 sin(2f + X — a,) 
+ fyfyfy — A, (sin 2d —X — a 2 )] npeC tan .(12). 
Here tan (f> represents the angle between the magnetic and geographical axes 
(tan cf> = 0 - 202), and t' has been introduced to represent the local time \ + t. The 
functions xjj are the tessera! functions, so that 
fy° = f cos 2 0—j, xfj'z = f sin 6 (5 cos 2 $—1), ify = sin 9, 
\jj 2 2 = 3 sin 2 6 , \jj 2 =15 sin 3 9. 
Equations (12) show that if the inclination of the magnetic axis be taken into account, 
the diurnal variations do not entirely depend on local time. A barometric variation 
of a certain period is accompanied by a magnetic variation of the same period, as is 
obvious; but if the lines of equal magnetic potential in the diurnal variation are 
drawn as in my previous communication, a barometric variation represented by 
rp/ cos a-t results in a magnetic potential containing terms 
fyt-d -1 cos(o--l)X; fy+d -1 cos(cr-l) X ; ifyV* 1 cos (cr+1) ; fy + y +1 cos (cr+1) X. 
These equipotential lines and their coincident stream lines revolve with velocities 
crco/cr— 1 and crw/(cr+l) round the earth, co being its angular velocity, and in this way 
variations proportional to cos at are produced. 
In order to estimate the magnitude of these terms, consider the diurnal variation, 
the normal term of which has been found to be equal to -fAfyf, cos (t — u.). 
Along a meridian circle for which X is either 0 or 7r, the additional terms are, 
putting Aj equal to unity, for X = 0 
sin 2 9 —yo (3 cos 2 0—1)] cos (t — a) = -fy- (1 — 3 cos 29) cos (t — ot). 
z 2 
