DIURNAL VARIATIONS OF TERRESTRIAL MAGNETISM. 
19 
the variations in the Northern and Southern hemispheres. The summer and winter 
data are, of course, widely different, though the Northern summer bears considerable 
resemblance to the Southern winter, and vice versa. 'The mean, \ (Summer + Winter), 
was taken to represent the part of the phenomenon common to both seasons—it is, 
indeed, as would be expected, nearly symmetrical about the equator—-while the semi¬ 
difference, \ (Summer —Winter), represents the variable, seasonal part of the 
phenomenon, which is anti-symmetrical about the equator. As will appear, the 
solstitial mean agrees very closely, in many respects, with the equinoctial mean, 
showing that a large part of the variation continues almost uniformly throughout the 
year. Even the residuals are very similar in the two cases. 
These three sets of group means were taken separately for the years 1902 and 1905, 
and are to be found in Tables III. (a), (/3), (y). For the sake of completeness the 
equinoctial semi-differences, \ (Spring —Autumn), were also examined (cf Table III. ($)), 
but only for the mean of 1902 and 1905, as this set is less important than the others. 
It need hardly be pointed out that this analysis of the data can be immediately adapted 
so as to give the result for any single season, \ (Summer + Winter)— f- (Summer 
— Winter), for instance, giving the winter analysis alone. 
In the investigation of these tables of group means, the aim kept always in view 
has been that of reproducing the broad features by as simple a mathematical 
representation as possible, considering, first of all, potential functions depending solely 
on local time. The residuals are discussed later, in connection with the question as 
to whether there are important terms varying with the longitude (§27). 
On examination it became clear that the nearly constant, “ annual ” part of 
the phenomenon, corresponding to the equinoctial and solstitial group means of 
Tables III. (a) and II. (/3), can be represented with fair accuracy by a single harmonic 
function for each periodic term, as far as regards the West force variations. The 
seasonal portions (Tables III. (y) and III. ($)) can, for the same component of force, be 
represented in each case by two such functions. These harmonic functions, depending 
on local time only, agreed in type with the main terms in Schuster’s and Fritsche’s 
analyses, so far as the three investigations are comparable. 
If the diurnal magnetic variations have a potential, the North force variations must 
be deducible from the potential function which represents the West force data. In 
Table III. the calculated values are given both for the West and North force varia¬ 
tions, using the functions chosen to represent the West force data alone. The 
agreement with the observed values may be considered satisfactory in the latter case, 
but it is not nearly so good for the North force variations. Perhaps the local 
irregularities in the data will account for the discrepancy, at any rate in the case of 
the three components of shorter period (12, 8, and 6 hours). The residuals for the 
24-hour component are very systematic, however, and could not be accounted for by 
a mere change in the amplitude of the potential function derived from the West force 
variations (cf. § 4). Possibly the two sets of data could be more nearly represented 
i) 2 
