40 
the expansion will vanish. There is, in fact, no question at 
all in this part of my w'ork of an expansion of the potential 
into a series, for we can deal with the complete expression 
as it stands, and it would simply have been absurd on my 
part to have tested the formulse by taking, as Mr. Chambers 
suggests, ‘'only the single-wave element of the observed 
variations, which have the full day for their period, or the 
similar elements which have half a day for their period.” 
I cannot help thinking that Mr. Chambers would have saved 
himself considerable trouble in his criticisms, had he remem- 
bered the fact that any function of two spherical co-ordinates 
can be expanded into spherical harmonics, and that, there- 
fore, the values of the potential on a sphere, as, indeed, on 
any closed surface, can be chosen arbitrarily and are not 
subject to any conditions. 
In the second part of my paper, I stated that the following 
set of equations seemed to me to give the chief characteristics 
of the diurnal variation ■ 
where X, Y, Z are respectively the forces on a north pole 
directed towards the north, the west, and vertically down- 
wards. I described some of the principal points of the equa- 
stated, for instance, that the equations “give us the phase of 
the vertical force to be the same for each hemisphere.” The 
whole context showed that I meant, namely, that the phase 
is the same within the same hemisphere. Mr. Chambers, 
however, takes me to mean that the phase is the same in the 
northern as in the southern hemisphere, and on the strength 
of this interpretation, triumphantly proves me to be ignorant 
of the fact that sin2i6 is negative when n is greater than 
90^. There is^ however, one cuiious point which Mr. 
tions in a sentence which I admit was badly expressed. I 
