DIURNAL VARIATION OF TERRESTRIAL MAGNETISM. ' 
181 
the variation of declination as characteristic, Dr. Chree’s formula for the semidiurnal 
term, leaving out the annual variation, is : 
SD = 1-82 [1 + 0-137 sin (2«+271°)], 
where t is measured from the beginning of January and each month counts as 
30 degrees. Tire corresponding term in the barometric formula is, according 
to Hann, # 
S p = 0-988 [1 + 0-061 sin (2* + 293‘4)], 
but if I understand the formula correctly, the time here is counted from the middle 
of January. To make the equations correspond, we must therefore diminish the 
angle in the last equation by 30 degrees, reducing it to 263"4 degrees, in close agree¬ 
ment with that given by Chree, the phase angle for the equinox being 265 degrees. 
The maxima of horizontal force occur, however, a fortnight later, so that too much 
value should not be given to this agreement; the effect in amplitude is only about 
half for the barometric variation ; but questions of conductivity may affect this ratio. 
A remarkable feature distinguishing the barometric change is the maximum which 
takes place simultaneously in both hemispheres early in January when the earth is in 
perihelion. According to the theory here discussed, a corresponding annual inequality 
should show itself in the magnetic variation, though the effect would be partially 
masked in the northern hemisphere by the changes of conductivity, and could only 
be ascertained by a comparison of the annual terms in the two hemispheres. We 
should expect the difference between winter and summer to be more marked in the 
southern hemisphere, because there the effects of conductivity would act in the same 
direction as the effects of diminished distance from the sun. It is much to be desired 
that some systematic attempt should be made to investigate the lunar influence on 
the magnetic changes, for we possess at present only the vaguest information as to 
how the different components of magnetic force are affected. It is quite possible 
that the effects may depend on a tidal disturbance of the upper regions of the 
atmosphere. If so, we may expect to get a valuable test of our theory by their 
investigation. 
13. We are now prepared to discuss the magnitude of the conductivity required 
in order that the proposed theory should be tenable. If equations (9) and (10) are 
compared with each other, and the correction discussed in § 5 be applied, we find 
from the semi-diurnal term 
pe = 3 x 10 -6 . 
The first question which arises is the value to be assigned to e. Observations of 
the aurora borealis conducted by the Danish expedition under the late Mr. Paulsen 
have led to the conclusion that the arc of these luminosities is generally at a height 
* ‘Met. Zeitschrift,’ 1898, vol. XV., p. 381. 
