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: 
<<‘ Tf § denote the magnetic declination at any place; 8, 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 
o-6,=Mx+ Ny, 
in which M and N represent the increase of declination corres- 
ponding to each geographical mile of distance in the two di- 
rections. If) and » denote the latitude and longitude of the 
former station, \, and yu, those of the latter, 
y=A-Ao» = T=("- Hy) COSA. 
‘It is evident, that ifx and y be treated as variable, 6 
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. 
