DIURNAL VARIATIONS OF TERRESTRIAL MAGNETISM. 
7 
a year of abnormally high solar and magnetic activity,* so that the data were not 
typical, though this is no drawback so far as the investigation is self-contained. The 
first part of the discussion dealt with the determination of a potential function 
which, on differentiation, yields as close a representation as possible of the observed 
variations in the North and West components of force. It was provisionally assumed 
that such a potential function exists, and that it is symmetrical with respect to the 
earth’s axis and remains constant in its relation to the sun as the earth revolves— i.e., 
that the variations depend solely on local time. Moreover, since the number of 
stations from which data were used was small, it was necessary to assume symmetry 
also with respect to the equatorial plane. Thus the Northern winter variations 
were taken to represent! the variations, at corresponding Southern latitudes, 
contemporaneous with the observed Northern summer variations.^ The period of 
the year to which the calculations apply is consequently a half-year centred at either 
solstice. 
If such a potential function exists, data from the above four stations should suffice 
to indicate its main features, although the area of the earth’s surface from which 
they are drawn is somewhat limited. It is desirable to have more stations, however, 
both in order to test the validity of the assumption, and to evaluate the function 
more exactly. Walker states that the observed variations indicate the presence 
of important harmonics not depending solely on local time ; the new data of this 
paper do not give much support to this conclusion, but they agree with Fritsche’s 
results in suggesting that an appreciable part of the variations at an)^ one station 
is local and peculiar to the place. If data from only a few observatories are 
used it is nearly always possible to represent them closely by including a sufficient 
number of tesseral harmonics in the potential function ; but from the above it is clear 
that only the main terms are likely to have significance as indicative of variations 
which are world-wide. For this reason it would now seem that Schuster’s analysis 
of his data was unnecessarily elaborate, but at the time there was no previous 
experience to serve as a guide, and it was probably best to risk going too far in this 
direction, rather than to fall short of what the data might yield. Only the more 
important terms, however, which agree with those considered in this paper, were 
discussed. They are reproduced (in the notation of § 9) in Table D, p. 25, for com¬ 
parison with other determinations by Fritsche and the present author. The various 
investigations give results which agree fairly well as regards the phase angles, and in 
the relative orders of magnitude of the various amplitude-coefficients. The absolute 
* Wolfer’s sunspot number for this year was 139, a value which has been approached only on one 
other known occasion, viz., in 1848, when the sunspot number was 124. 
t With suitable changes of sign in certain components. 
| This was done only for the first two components of periods 24 and 12 hours. The seasonal terms 
were not considered in the case of the 8-hour and 6-hour components, for which the mean of summer and 
winter was taken to apply to each hemisphere alike. 
