DIURNAL VARIATION OF TERRESTRIAL MAGNETISM. 
167 
with the principal terms of that variation as observed when the average annual value 
is considered and the seasonal changes are disregarded. 
3. It remains to be seen whether the calculated variation agrees as regards phase 
and can be made to coincide in magnitude by a reasonable value of the conductivity 
and thickness of the effective layers of the atmosphere. 
For this purpose we first obtain a value for the constants A 1 and A 2 . If Bp be the 
variation of the pressure p, and da the corresponding change of the density a, we 
have 
Bp _ da _ dxfj 
p a v 2 dt ’ 
where xfj is the velocity potential and v the velocity of sound. Under the assumption 
that the whole atmosphere oscillates equally in all its layers, Bp/p will be the same at 
every point of a vertical line, and we may, therefore, determine its value at the surface 
of the earth. 
According to Hann (‘ Meteorologie,’ p. 189), the diurnal change of the barometer at 
the equator, measured in millimetres, is represented by 
0-3 sin (X + t) + 0-92 sin (2 (X + t) + 156°}. 
If this expression be denoted by Bj), we must assign the value of 760 to p to bring 
the units into harmony. 
It follows that at the equator 
^ = [-0-3 cos (X + t) + 0-46 cos {2 (\ + t) +156°}] NU/2tt^ . . . (7). 
The numerical value of NU/2 p is 6'281 x 10 1 " (N = 86400; v 2 = ll'05x 10 s ), or 
98 '5a, where a is the radius of the earth. 
The constants A x and A 2 of the velocity potential in (6) are, therefore, determined by 
ttAj = 0 - 3 x 98 - 5a = 29 - 6«, and 7 tA 2 = 0‘153 x 98'5a = 15*lc* . . (8). 
We ultimately get for the calculated magnetic potential 
n/a = [11-8 cos (X + t) -4-6 cos 2 (X + t-102°)] pe C, 
or, introducing the value of C and restoring the term containing the latitude, 
n/a = [7'89i//.> cos (X + t—180°) + 3*07cos 2 (X + t—l02°)\pe . . (9). 
The principal terms of the diurnal and semidiurnal variations of magnetic force, 
abstraction being made of seasonal changes, were found in my previous communication 
to be 
1 0 6 n/a = 89 xfj 2 ' cos (\ + £—156°) + lfl6i//, 2 cos 2 (X-M-74-5 0 ) . . (10). 
If we compare the phases, we find that the magnetic potential calculated from the 
