DIURNAL VARIATION OF TERRESTRIAL MAGNETISM. 
201 
The tables which follow give the calculated values of p / and q n r , and therefore 
solve the problem as far as terms of the fourth order in y and y. It will be noticed 
that for unity, which is the highest admissible value of y and y', all the factors 
involving higher powers than the first are so small that their effect falls much below 
anything that observation is capable of showing. Hence the approximate calculation 
given in Part I. is sufficient for all practical purposes. 
Restoring constant factors, we may summarise the result of the previous investiga¬ 
tion as follows :— 
1. Notation. 
Q/ denotes the tessera! function sin' 7 9 cPP^/fZ/T 7 , where P„ is the zonal harmonic of 
degree n, and 9 the colatitude. 
C measured upwards denotes the vertical magnetic force of the earth’s permanent 
field at the geographical pole. 
e is the thickness of the conducting atmospheric shell. 
p is the conductivity, which is supposed to be variable and depending on 6 and the 
local time X + t, according to the relation p = p t) [1 + "/ cos 9 + y sin 6 cos (X + t)], where 
y and y' are constant. 
A/Q/ cos {<x(X + t) — a] is the velocity potential of the flow of air. 
2. Conclusion. 
The current function R of electric flow induced under the action of the vertical 
force C cos 0 in the oscillating shell of air is then expressed as a sum 
R 
A/GVpo 
t p/Q/ sin (o-(X + £) —a}+ $ p/Q/ sin (cr (\ + t) + a} 
<7 = 0 <7 = 1 
In order to obtain the magnetic potential of the variation caused by the flow of 
air, a factor — 477 (n + l)/(2?i + 1) has to be applied. 
The factors p/ and q/ are given in the tables (including terms of the fourth order 
of y and y') for the velocity potentials 
A'iQ' = A\ sin 9 cos {(X + £) — «} 
and 
A 2 2 Q 2 3 = 3A 2 2 sin 2 9 cos [2 (X + £) — a}. 
2 D 
VOL. CCVIII.-A 
