DIURNAL VARIATIONS OF TERRESTRIAL MAGNETISM. 
9 
§ 3. Fritsche’s Investigations of the Solar Diurnal Magnetic Variations. 
Fritsche’s investigations of the solar diurnal magnetic variations are works of 
considerable magnitude and numerical detail, and are contained in three papers of 
1902, 1905, and 1913.* In the first paper a Gaussian potential function is determined 
to represent as closely as possible the variations in the North and West components 
of force at 27 stations. The function was determined separately for the summer and 
winter half-years. It was not necessary to assume symmetry about the equator, as 
Schuster had done, since Fritsche’s stations included five in the Southern hemi¬ 
sphere ; the assumption that the variations depend only on local time was, however, 
retained. The use of a much larger number of stations was in itself an improve¬ 
ment, but this was attained, in Fritsche’s case, by throwing over an important 
consideration to which Schuster rightly gave much weight, viz., that the data 
should all relate to the same epoch. Fritsche’s data are drawn from series of 
observations extending in some cases only over a few months, and in others over 
several years, and their epochs range from 1841 to 1896. They are consequently far 
from homogeneous, both on account of the eleven-year cycle in the magnetic 
activity of the earth, and probably also because of varying degrees of observational 
accuracy. 
Of the 27 stations, nine were North of latitude 60° N., thirteen lay between 0° 
and 60° N., while the remaining five extended from 0“ to 60° S. After deducing his 
potential functions from the North and West force data taken together, using the 
method of least squares,! Fritsche made an elaborate numerical comparison of the 
calculated and observed variations. The best agreement was found for the ten 
Northern observatories lying between the tropical circle and 60° N. ; it was less good 
for the tropical and Southern stations, and very bad for the nine stations above 
60° N. latitude. The last circumstance is perhaps not unnatural, owing to the 
divergence of the magnetic from the geographical poles of the earth. So long as the 
analysis of the magnetic variation is based on the assumption that they depend 
solely on local time, it seems best to use data only from stations between ±60° 
latitude. All the other investigations described here conform to this rule, and 
Fritsche himself decided later that it was desirable to exclude the nine polar 
stations and to re-calculate the potential function from the remaining 18 obser¬ 
vatories. This work is described in his 1913 paper. The 18 sets of data, combined 
* Fritsche, St. Petersburg, 1902, Riga, 1905, and Riga, 1913. The second paper, so far as it deals 
with the daily variation, is in the nature of an appendix to the first, and need not be separately 
considered. 
t The 27 stations were combined into six groups, and the mean diurnal inequalities in each element 
were computed from those for the separate stations in each group. These mean inequalities (in the form 
of 24 hourly values) were harmonically analysed, and the Fourier coefficients were then treated by the 
method of least squares so as to fit a potential function to them as closely as possible. Two of the six 
groups included the stations North of 60° N. 
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