MAGNETTCAL OBSERVATIONS IN IRELAND. 
159 
lines, corresponding to a difference of half a degree of dip, is 50*7 
geographical miles. 
The lines of dip and of horizontal intensity being known, the 
lines of total intensity may be deduced. For if / denote the 
total intensity, h its horizontal component, and 5 the dip, as 
before, 
h — f cos 8; 
and differentiating, and dividing by the equation itself, 
f~ l df— hr 1 d h + tan 8 sin F t/8. (I.) 
Now, if the values of x and y for the lines of dip and of ho¬ 
rizontal intensity be denoted by x^y and y^y $(hy and if 
x^ and y ^ be the corresponding quantities for the lines of 
total intensity, 
d 8 = a x^ — by^ 
d h = a x (h) - h 7/ (h) (II.) 
<U = ® - v (fi ^ V (fy 
in which a = (p — ju, y ) cos A, b — A — A y (E.); p, and A being 
the longitude and latitude of any assumed station, and and A / 
those of Dublin. Substituting these values in (I.), it becomes 
/ 1 (a 5y (/) ) — h 1 (ax^ b y^y) 
+ tan 8 sin F (ax^ — by 
(III.) 
But as a and b are entirely independent, their coefficients must 
be, separately, equal, and we have 
f~ x x^jt) = h 1 x^ + tan 8 sin F x^ 
= h ~'y<.h) + tan 8 sin Vy w 
(IV.) 
so that the values of x^ y^ ^ are found when those of x^ x^ 
y[K) vq) are known ' 
Let the second members of the preceding equations (IV.) be 
denoted, for abridgement, by P and Q, then 
X^ ^ — t COS W — / P, 
y (f) = t sin w = /Q; 
in which w is the inclination of the line of total intensity to 
