DIURNAL VARIATIONS OF TERRESTRIAL MAGNETISM. 
67 
§ 26. Discussion of the Phases of the Magnetic Variations. 
The explanation of the phases of the magnetic variations is, perhaps, the most 
difficult part of the present problem. The data to be reconciled are as follows. The 
various annual harmonics in the solar and lunar diurnal magnetic variations are 
approximately in agreement amongst themselves, the time factors being approxi¬ 
mately as below, in the two cases 
(98) 
(Solar) 
— cos (nt + 25°), 
(99) 
(Lunar) 
— cos (nt + 7 8°). 
Neglecting self-induction and the small terms p m ~ n (§ 22), the theory of § 22 
indicates that the velocity potentials of the atmospheric oscillations responsible for 
these magnetic variations should have the same phase, the negative sign in (68) and 
the negative sign of C (cf 47, 51, 68) neutralizing one another. 
If the simple relation (31) holds good between the pressure variation and atmo¬ 
spheric velocity potential, the time factors in the pressure variations corresponding to 
(98) and (99) should be 
(100) (Solar) sin (2t — 155°), 
(101) (Lunar) sin (2t — 102°). 
The factor n is here written as 2, since the fundamental pressure changes appear 
to be semi-diurnal. 
The observed pressure variations at the earth’s surface (§§ 19, 20) have the time 
factors 
(102) (Solar) sin (2t+ 154°) = sin (2^ — 206°), 
(103) (Lunar) sin (2t+ 65°) = sin (2t — 295°). 
There is consequently no kind of agreement between the observed and calculated 
pressure variations in the lunar diurnal case. In the solar case the two variations 
agree better, but it must be remembered that the observed phase diminishes with 
height to a considerable extent (90 degrees or possibly more —cf (91)), so that the 
agreement between (100) and (102) would not hold good if the latter had represented 
the pressure variation as it is supposed to exist in the upper atmosphere, viz., 
approximately 
(Solar) sin (2£ —296°). 
K 2 
(104) 
