152 
FIFTH REPORT- 1835. 
(throughout the limited area of the present district of observa¬ 
tion) be assumed to be proportional to the distance, measured in 
a direction perpendicular to the line of equal force, or of equal 
dip. Accordingly, if u be the angle which the line of equal ho¬ 
rizontal intensity passing through O makes with the meridian of 
the place, the difference of the intensities at the two stations will 
be proportional to p, or 
h — h i — rp; 
h and h t being the horizontal intensities at the two stations, and 
r a constant coefficient which determines the rate of increase. 
Substituting, then, for p its value (C), and making 
r cos u = x, r sin u = y, (D) 
we have 
{[x — ft y ) cos A . x — (A — A y ) y — h — h / (E) 
The equations of condition deduced from the observations of 
total intensity, and of dip, will be of a similar form; and the 
coefficients of the unknown quantities, in the first member of the 
equations, will be the same. 
The station chosen for the origin of the coordinates is Dublin, 
and it is obvious that there will be as many equations of con¬ 
dition as there are other places of observation. The coefficients 
of these equations are given in the following table. The first, 
second, and third columns contain the place of observation, its 
latitude and its longitude*. The numbers in the fourth and 
fifth columns are the differences of latitude and longitude, (esti¬ 
mated in minutes of latitude,) of the place of observation and 
Dublin, or the values of (A — A y ) and (fx — (x,) cos A ; and the 
numbers in the three remaining columns are the corresponding 
differences of dip , of horizontal intensity , and of total intensity , 
which form the second members of the equations. The dip 
having been observed at Dublin in each of the two years (1834 
and 1835), the differences of dip are obtained by subtracting 
that belonging to the year in which the observation was made 
at the other station. 
* The latitudes and longitudes of some of the more important stations have 
been kindly furnished by the officers of the Ordnance survey. The remainder 
have been taken from Arrowsmith's map of Ireland. 
