MAGNETIC FORCE IN IRELAND. 205 



that disturbing actions of a local nature are exerted on a much 

 larger scale. Whether the earth's magnetic force be an inherent 

 property, and the resultant of the forces of all its parts, or whether 

 it be simply the effect of thermo-electric currents produced by 

 the heating action of the sun, the result must in either case be 

 greatly modified by the configuration of a country, and by the 

 nature of its superficial strata. If this view be just, the greatest 

 irregularities should prevail in those parts of the earth in which 

 the uniformity of surface is broken by hill and valley, and where 

 the strata have been rent and contorted by the uplifting of moun- 

 tain chains. In Ireland, accordingly, we should expect to find 

 much greater anomalies in the direction and intensity of the mag- 

 netic force than in the plains of central Europe ; and it must be, 

 consequently, in the same degree more difficult to arrive at general 

 results. 



The only mode of escaping from these difficulties was to eeek 

 the general result of the entire series of observations, as to the po- 

 sition of the isodynamic and isoclinal lines ; and to combine the 

 partial results in such a manner that their deviations whether 

 local, temporary, or casual should have the least influence on the 

 final conclusion. Such is the object of the following computations. 



Let A and fi denote the latitude and longitude 

 of any place at which an observation has been made, 

 Ao and fi the latitude and longitude of the station 

 which is chosen as the origin of the coordinates ; 

 then the position of the former place may be fixed 

 with reference to the latter in terms of these quan- 

 tities. For let P be the pole of the earth, M and 

 the two places, PM and PO their meridians, 

 and MQ a great circle passing through Jfand per- 

 pendicular to PO. It is obvious that the position 

 of M will be determined by the rectangular sphe- 

 rical coordinates, OQ and QJ/. Now in the right-angled triangle 

 MPQ, we have 



tan PQ = tan PM cos P, sin MQ = sin PM sin P ; 

 or, denoting the co-ordinates OQ and QM by a and 0, 



cot (A + a) = cot A cos (n - no] 



(A) 

 sin /3 = cos A sin (ju - /*,). 



