74 REPORT—1885. 
We possess now so much more information on the mean value of the 
terrestrial elements at different places, that, it seems to me, a repetition 
of the calculations of Gauss would lead to valuable results. Such a cal- 
culation would not only be of theoretical importance. For we might in 
this way detect many points of interest, as, for instance, where if anywhere 
masses of iron are present near the surface of the earth in sufficient 
quantity to affect the magnetic elements. At such places we should ex- 
pect the harmonic analysis to give correct results only if extended toa 
large number of terms, so that if we confine ourselves, like Gauss, to four 
or five terms only, and find considerable differences between the calculated 
and observed values at some part of the earth’s surface, we should have 
our attention specially directed to that part. 
It is only by a reduction such as that of Gauss that we shall be able 
to find out where we require further observations, and where a multiplica- 
tion of observations is unnecessary. 
It would be very desirable if we could extend the analysis of spherical 
harmonics to the daily variation of the elements and to magnetic dis- 
turbances generally. But it seems to me that if, as is likely, these changes 
are due to electric currents either above or below the earth’s surface but 
near it, the analysis would have to be carried to a large number of terms 
before it would yield satisfactory resulis. But this, of course, isa matter 
which the actual calculation only can settle, and we ought therefore, at 
any rate, to make the attempt to apply the method of Gauss to the daily 
variation. With our present knowledge of that variation at different 
places of the earth’s surfaces, there ought to be no difficulty in finding 
out whether five or six terms are sufficient to represent it, taking ac- 
count, of course, also of those terms which have their origin outside the 
earth. 
Some observations of Sabine made near the magnetic pole! seem to 
point to the fact that part of the diurnal variation is due to a vertical 
component of an electric current crossing tbe earth’s surface. Whether 
such a vertical component exists can be determined without difficulty, for 
we can actually measure it by taking the line integral of magnetic force 
at a given time over a closed curve on the earth’s surface. 
I should like, therefore, to propose to the Committee to find out, in the 
first place, what determinations of the magnetic elemerts ought to be 
taken account of in the reductions. In countries where we possess a great 
number of accurate data, it would seem only an increase of labour to take 
account of all of them. On the other hand, where we possess few 
measurements we should in all probability have to use even approximate 
determinations. It is a point for the Committee to decide whether we 
ought to take the places which are to be included in the calculation spread 
as evenly as possible over the earth’s surface, or whether a preponderance 
should be given to places near the magnetic poles or at other places of 
special importance. Also whether the more accurate observations ought 
to be weighed. Should the Committee approve of these reductions, it 
would be well to ask at the next meeting of the Association for a suflicient 
grant to engage the assistance of one or two computers. 
I should like in conclusion to submit a few observations respecting 
the remarks made by Professor Balfour Stewart and Sir Henry Lefroy. 
The function of the Committee seems to me to be a double one. In the 
' See Encyclopedia Britannica—Terrestrial Magnetism (art. Meteorology). 
