218 ON THE ISOGONAL LINES IN IRELAND. 



ments, in the reports above referred to ; such a discussion serving 

 to complete the Magnetic Survey, so far as Ireland is concerned, 

 and to furnish a formula for the Magnetic Declination at any point 

 in the island whose position is known. 



The following is the mode of doing this : 



If S denote the magnetic declination at any place ; S that at 

 some near station which is taken as the origin of co-ordinates ; 

 and x and y the actual distances (in geographical miles) between 

 them, measured on the parallel of latitude and on the meridian, 

 respectively or the co-ordinates of position of the former station 

 referred to the latter as an origin ; the relation of these quantities 

 is expressed approximately by the equation 



in which M and N represent the increase of declination correspond- 

 ing to each geographical mile of distance in the two directions. If 

 A and /j. denote the latitude and longitude of the former station, 

 A and [i those of the latter, 



y = A-A , x = OU-M O ) cos A. 



It is evident, that if X and y be treated as variable, S being 

 constant, the preceding equation is that of the locus of all the 

 points of given declination. It is that of a right line, making the 

 angle with the meridian, 



and the increase of declination corresponding to each geographical 

 mile of distance, in a direction perpendicular to this line, is 



It is evident then that, to obtain the values J/"and N, obser- 

 vation must give the values of the declination at three, or more, 

 stations. The observations of Sir James Boss were taken at 

 twelve stations, well distributed throughout the island ; and as they 

 were all made during the months of October and November, 1838, 

 no correction is required to reduce them to a common epoch. For 

 convenience of reference, they are here extracted from Colonel 



