128 
It is, then, to circumpolar and equatorial observations 
that we must look for an answer, and as the point is of 
importance, steps ought to be taken to settle it. Accurate 
and uniform observations over a limited area will be more 
valuable than less uniform observations over a more ex- 
tended area. Two or three declination magnetographs 
distributed over the northern frontier of India, together 
with one additional vertical force instrument in Central 
India, would, I believe, when taken together with the 
Madras and Bombay observations, give definite results in 
the course of one year, and the instruments might then 
become available for other work. 
The following calculation, however, seems to justify us in 
neglecting, until we have more definite information, the 
vertical discharges through the earth. 
In the first place, it is necessary to draw attention to the 
fact that, as concerns the subject of discussion, everything 
that holds for any set of observations taken over the earth’s 
surface at any particular time, must also be true of the 
average values taken over a certain period of time, and 
hence we may deal with the averages which give us the 
daily variations exactly in the same manner as we should 
deal with the whole components of force at any particular 
time. All we assume is, that no part of the mean magnetic 
force is due to vertical currents crossing the earth’s surface. 
Suppose the periodic forces on which the diurnal variation 
depends to be expressed all over the earth in terms of longi- 
tude, latitude, and the time of a given meridian. Obser- 
vation tells us, that all over a given circle of latitude we 
may take the variation to be very nearly the same, for a 
given local time ; that is to say, we may write— 
dt ~ dX’ dt ~ dx’ 
where X and Y are the components of force towards the 
geographical north and west respectively, and X is the longi- 
