38 
additional argument by means of an equation which is 
severely criticised by Mr. Chambers. It seemed to me that 
the variable part of the potential at different places can be 
approximately expressed by the product of a function of the 
local time into a function of the latitude, and I consequently 
took— 
v/a=-TU (1) 
where T is a function of the local time t, and U a function 
of the colatitude ; a being the radius of the earth. From 
(1) we can derive — 
Ysina = U^, X = T-— (2) 
at du ^ ' 
as explained in my paper. 
Mr. Chambers expresses his opinion that these results 
“ have a most delusive appearance of generality.” But 
where, may I ask, is the delusion ? 
I have clearly expressed the assumptions on which (1) 
depends, I have, as far as I know, correctly deduced equations 
(2) from (1), and, as results of a mathematical investigation, 
are not generally called ‘‘delusive” unless there is some 
blunder either in the statement of the assumptions or in the 
analytical deductions, I shall briefly restate my reasons for 
taking (1) as an approximate expression for the potential. 
The equation depends in the first place on the observed 
fact, that, except perhaps in high latitudes, the diurnal 
variations of terrestrial magnetism in each circle of latitude 
are nearl}^ the same for a given local time, so that we may 
take the time variation at any place to be equal to the longi- 
tude variation at the same time. I need not enter into the 
question raised by Mr. Chambers whether this is, or is not, 
true in high latitudes, because it is not necessary that equa- 
tion (1) should hold over the whole surface of the earth, as 
long as the equations (2) are applied to those parts only for 
which (1) holds. I have only used the equations in regions 
