168 
MR ARTHUR SCHUSTER ON THE 
barometric variation lags behind the observed one by an amount which is 1 hour and 
36 minutes for the diurnal and 1 hour and 50 minutes for the semidiurnal variation, 
showing a remarkably close agreement in the two terms. As regards amplitude, we 
can establish agreement by adjusting the value of pe, but the same value ought to 
satisfy both terms, which is not the case, pe being 3‘63x 10 -6 if calculated from the 
12-hourly variation, and ll'3x 10~ 6 if calculated from the 24-hourly variation. 
4. The tacit assumption has been made that the barometric variation is distributed 
over the surface of the earth according to the simplest harmonic term consistent with 
each period, so that for the diurnal variation the amplitude would be proportional to 
the cosine of the latitude, and for the semidiurnal variation to the square of the 
cosine. 
The experimental data show, however, that there are other terms to be considered, 
and for the semidiurnal variation Dr. Adolf Schmidt has obtained the best agreement 
by introducing the harmonic of the fourth degree, having an amplitude which at the 
equator would amount to the twelfth part of the whole effect. The amplitude of the 
second term in Equation 9 would consequently be reduced to 3'07 x = 2'814, and 
a higher harmonic would be introduced; but the experimental evaluation of these 
higher terms in the magnetic variation is too uncertain to be taken account of at 
present, their effect in any case being small. As regards the 24-hourly variation, its 
dependence on latitude has not been clearly established. The term, as commonly 
observed, is much affected by local circumstances, and Hann takes therefore the 
observation on board ship to represent the true phenomenon so far as it depends on 
the atmosphere as a whole. While greater consistency is thus gained, the observations 
on board ship cannot lay claim to the same accuracy as those taken on land, and, as 
the figures show, considerable uncertainty still prevails. In the following table the 
values given by Hann are collected together :— 
Latitude. 
Amplitude in 
millimetres. 
Latitude. 
Amplitude in 
millimetres. 
o 
4-5 
0-262 
0 
33-8 
0-148 
11*1 
0-265 
35-9 
0-140 
15-8 
0-268 
37 
0-342 
23 
0-115 
40-7 
1-85 
These numbers do not follow any very simple law and can only be very partially 
represented by an expression varying as the cosine of the latitude. The rapid 
increase in the amplitude at latitudes of about 40° suggests the presence of the third 
harmonic, and treating tine figures by the method of least squares we are led to an 
expression 
Sp = 0’49 sin #—0*33 {f sin 6 (5 cos 2 0—1)}. 
If this equation were to represent correctly the distribution in latitude of the 
