MAGNETIC FORCE IN IRELAND. 213 



and yy) be the corresponding quantities for the lines of total 

 intensity, 



(II.) 



df=ax (f) -by (f] , 



in which a = (fjt - /K O ) cos A, b = A - A ; /* and A being the longitude 

 and latitude of any assumed station, and /i and A those of Dub- 

 lin. Substituting these values in (I.), it becomes 



tan S sin 



But as a and 6 are entirely independent, their coefficients must be 

 separately equal, and we have 



- l x = k~ l xh + tan S sin 



tan 5 sin l'y (6 ) ; 



so that the values of #(/) and^(/) are found when those of #(*), &(&), 

 y (h }, ya) are known. 



Let the second members of equations (IV.) be denoted, for 

 abridgment, by P and Q, then 



X( f ] = tcOBW =/P, 



2/(/) = ^ sin ; =/Q ; 



in which w is the incKnation of the line of total intensity to the 

 meridian, and t the coefficient which determines the rate of increase. 

 Dividing the latter by the former, there is 



tan w = -p . (V.) 



And squaring and adding, 



t=/SJ I Tw. (Vi.) 



From the preceding formulas it appears that the direction of the 

 isodynamic line at any point is dependent on the values of /i and of c 

 at that point, so that these lines will not be parallel, even though tlie 

 lines of dip and of horizontal intensity should be so. The devia- 

 tions, however, will not be considerable within the limits of Ire- 



