160 
FIFTH REPORT.- 1835. 
the meridian, and t the coefficient which determines the rate of 
increase. Dividing the latter by the former, there is 
O' v 
tan w = p-, (V.) 
and, squaring and adding, 
t=fVW+Qr. (VI.) 
From the preceding formulas it appears that the direction of 
the isodynamic line at any point is dependent on the values of h 
and of £ at that point, so that these lines will not he parallel, 
even though the lines of dip and of horizontal intensity should 
be so. The deviations, however, will not be considerable within 
the limits of Ireland ; and for our present purpose it will be 
enough to seek the mean direction of the lines, and the mean 
rate of increase in the direction perpendicular to them. We 
must therefore employ in the preceding formulae the values of/, 
h } and 5, corresponding to the mean point of the island, or the 
point whose latitude and longitude are 53° 25' and 7° 55'*, and 
for which therefore 
A — A = 4 ? , g — i a / = 100'. 
Xow it has been already found that 
if — — ‘0001633, — T - *3239, 
y (A ) = + -0003748, y {l) = - ‘4950; 
and substituting these values in the formulae 
s h — (p* f 4 /) cos A x^ (A — Ay) y^y 
h hj = (a J a i/ cos A x^ (A * Ay) y ^ ; 
we find S — Bj = 2 1'*4, h — h l = — *0113. Consequently, 
8 = 71° 24 J 4, h = ‘9282, and/= 1*0295. 
We have now the numerical values of all the quantities which 
enter the formulae 
P = h~ l x^ + tan 5 sin V x^y 
Q = h- 1 y (k) + tan c sin l'y (}) ; 
and we find on substitution, 
P = -f *0001042, Q = — *0000242. 
Introducing these values in (Y.) and (YI.), 
tan iv = — *2322, iv = — 13° 4 ( , t — *0001102. 
* This point corresponds, almost exactly, to the town of Athlone. 
