24 



indeed made by Sir James Ross ; but they have only lately 

 been given to the public in a Memoir by Lieut.-Colonel Sabine, 

 on the lines of Magnetic Declination in the Atlantic* In 

 this Memoir, the observations referred to are combined with 

 a large mass of other materials, and the position of the iso- 

 gonal lines inferred from the whole by a graphical process. 

 The Irish portion of these observations is, however, so dis- 

 tinct, and so complete in itself, that it seemed to me desirable 

 that they should be discussed by the same method which had 

 already been applied to the observations of the other two ele- 

 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 Decli- 

 nation 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-ordi- 

 nates ; 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 corres- 

 ponding to each geographical mile of distance in the two di- 

 rections. If A and fi denote the latitude and longitude of the 

 former station, A and fi those of the latter, 



y = A-A oS x = (ji - ja ) cos A. 



" It is evident, that if x and y be treated as variable, t? 

 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, 



* Philosophical Transactions, 1849, Part ii. 



