MAGNETIC FORCE IN IRELAND. 209 



and dividing, we have 



tan u = -. ; (H) 



.A. 



by which the direction of the isodjnamic line is determined. Again, 

 squaring and adding, 



B*', (I) 



which gives the rate of increase of the force in the* normal direction. 

 The lines of absolute intensity, and of dip, will be obtained by a 

 similar process, the only difference being in the values of the 

 second members of the equation (F) . 



Before we can apply these formulas to the investigation of the 

 lines of horizontal intensity, it is necessary to assign the weights 

 due to each equation of condition, or to the determination which it 

 involves. We shall assume, accordingly, that the weights of the 

 values of (h - /*), recorded in the preceding Table, are measured by 

 the number of separate comparisons from which they have been 

 deduced,* and we shall have, on this principle, 



Limerick, . . . weight = 12, 

 Markree, ... 3, 



Armagh, ... 2, 



the weights of each of the other determinations being represented 

 by unity. 



The values of a, b, and c being <:iven in Table VII., we may 

 now proceed to calculate the coefficients of the equations (Q-). "VVe 

 find, 



(?ra 2 ) = 257431, S(wab) = + 49169, (#) = 116509, 



S(tcac) = - 23-598, S(icbc) = + 35-644. 

 And the equations are 



257431 x + 49169 y = - 23-598, 

 49169 x + 116509 y = 4- 35-644 ; 



* For a more correct method of estimating the weights of observed results, th< 

 reader is referred to the Report on the Magnetic Isoclinal and iBodynamic lines in t!i- 

 British Islands, Eighth Report of the British Attociation for the Adfattcemt*tofSctrcr, 

 p. 95, &c. 



P 



