4 
Mr . Christie on the effects of temperature on 
To obtain the equation requisite for this purpose, take the 
centre of the needle as the origin of the rectangular co-ordi- 
nates, the axis of the x’s being in the magnetic meridian. 
Let X and y be the co-ordinates to the south pole of the 
needle, x being measured towards the north, andjy towards 
the west : also, let r be the distance of either pole of the 
needle from its centre ; p the distance of the poles of each of 
the magnets from their respective centres ; and R the distance 
between the centre of the needle and the centre of either 
magnet. For the sake of expressing clearly and concisely 
the distances between the poles of the needle and those of 
the magnets, we will indicate these points as follow ; 
5, the south pole of the needle ; that is, the pole which, when 
the needle is freely suspended, points towards the north; 
n , the north pole of the needle ; 
a ^ , the south pole of the magnet which is to the north of the 
needle ; that is, its pole nearest to the centre of the needle ; 
^ , the north pole of the same magnet, or its pole which is 
furthest from the needle's centre ; 
^ , the south pole of the south magnet, or that pole which is 
furthest from the centre of the needle ; 
u , the north pole of the same magnet, or that pole which is 
"s’ 
nearest to the centre of the needle. 
Now resolve the terrestrial magnetic force acting on the 
north arm of the needle, in the line of the dip, into two ; one 
horizontal or in the direction x, and the other vertical : and 
let the horizontal force be M. Also, let the force with which 
a pole of the needle is repelled from the pole of the same 
name of either magnet, or attracted towards that of a con- 
