MAGNETIC FORCE IN IRELAND. 215 



very widely with moderate variations in the values of X( h ^ xy w , (5 ), 

 i/(s), on which it depends ; or, in other words, that a small error in 

 the position of the lines of dip, or of horizontal intensity, will entail 

 a very great one in that of the lines of total force. Thus, if we 

 were to take for the lines of dip those inferred from the observa- 

 tions of the year 1835 alone, we should find 



P = + -0001051. Q = - -0000455, 



tan w = - -4329, w = - 23 25' ; 



a result differing by more than 10 from the former. In these 

 latitudes, therefore, very great accuracy is necessary in the deter- 

 mination of the lines of dip and of horizontal force before we can 

 make, in this manner, even an approximation to the direction of 

 the lines of total force. For these reasons the results of the direct 

 method, to which we now proceed, seem to be deserving of more 

 confidence. 



In the calculation of the isodynamic lines from the results of 

 observation by the statical method, we shall take the number of 

 observations at each station to represent the weight of the result ; 

 we have in this manner 



Limerick, .... weight = 4, 

 Armagh, ..." =2, 



Youghal, .... =2; 



the weight of each of the other determinations being unity. 

 The following are the results of the computation : 



S(wa*) = 178390, S(waV) = + 38216, 8(wb v ) = 96066, 



8(wac) = + 13-3229, S(wbc) = - 2'2448. 

 The final equations therefore are 



178390* + 38216^ = + 13-3229, 

 38216* + 96066y = - 2-2448 ; 

 from which we obtain, by elimination, 



x = + -00008711, y = - -00005802. 



