DIURNAL VARIATION OF TERRESTRIAL MAGNETISM. 
169 
diurnal term, the calculated amplitude of the magnetic potential would be increased 
considerably more than is required to bring it into harmony with the semidiurnal 
term, because not only is tbe amplitude of the term of the barometric variation in 
sin 6 increased, but the additional term gives rise to a magnetic potential which is of 
the same degree and type and more than doubles the effect of the first term. 
Very little importance, however, can be attached to this calculation, which depends 
to a great extent on the last entry of the foregoing table; but enough has been said 
to show that our present knowledge of the 24-hourly variation of the barometric 
pressure is very uncertain, and that a term of the third degree in its expression is 
likely to diminish materially the discrepancy between the electric conductivity of the 
atmosphere as derived from the diurnal and semidiurnal periods. 
5. We must next turn our attention to several corrections which modify the 
calculated values without, however, introducing material changes. The observed 
magnetic variations have been treated as if they were wholly due to outside causes, 
although it was shown in my previous communication that an appreciable portion of 
it was an effect of electric currents induced inside the earth by tbe varying potential 
itself. What we observe is the resultant of the original outside effect and its 
concomitant induced inside effect. To explain the absence of time lag of the induced 
variation it was necessary to assume a good conductivity of an inner core and small 
conductivity of the outer shell. An estimate may be made of the radius of the 
conducting core. If the outer potential is represented by VLr n a~'\ where a is the 
radius of the earth, and the inner potential is an estimate of k may be 
obtained by the fact that if the inner conductivity is sufficiently great the vertical 
force is entirely destroyed at the surface of the inner core. If this has a radius r 0 , 
it follows that nr 0 n a~ n and {n + 1) K')' 0 ~ n ~ 1 a n+1 must have equal values, or that 
k = nr 2n+1 /(n + 1) a 2n+1 . 
The resultant potential at the surface of the earth is, therefore, 
If this expression is multiplied by n, we obtain the vertical force calculated from 
the horizontal force on the supposition that the whole effect comes from the outside. 
The observed vertical force, on the other hand, is 
nil [1 — (r 0 /a) 2n+1 ]. 
The previous result showed that the actual vertical force was about half the 
calculated one, the principal term being that due to n = 2. We find in this way 
{n/af. 
The thickness of the outer non-conducting crust would thus appear to be about 
1000 kilometres, and cannot, therefore, be connected with the layer having a thickness 
VOL. CCVIII.—A. Z 
