394 
Mr. Christie on the magnetism of 
to the west of the needle, or in longitude 180 ° ; and in south 
latitude, as in the observed deviations in Tables A and B, 
and that its upper edge revolves from east to west. Take 
the centre of the needle as the origin of the rectangular co- 
ordinates, the axis x being horizontal, and towards the west, 
that of z upwards, in the direction of the magnetic axis. We 
will indicate the north end of the magnetic particle, in the 
V 
centre of the needle, on which the iron is supposed to act, by 
N, its south end by S ; the north end of the line joining the 
poles in the plate by v, its south end by cr, its centre by y. 
Let the co-ordinates to the centre of this line be a, b ; to its 
north end a„ b,; to its south end a^, b„; and let i]/ be the 
angle which this line makes with a line passing through its 
centre, and parallel to the axis z. Also let r be half the 
length of the magnetic particle in the centre of the needle. 
Since the effect of any force to turn the particle SN will 
be the same, whether it be supposed to act on N in a given 
direction, or on S in the contrary one, we may refer the 
action of the mass of the iron, and likewise the actions of its 
poles, wholly to the end S. Calling then m, the magnetic 
force of the earth acting in the direction of the dip ; F the 
force of the mass of the iron, and/ that of one of its poles on 
S, at the unity of distance ; also the sum of all the forces on 
S resolved in the directions x and Zy X and Z, we shall have 
1 
(s7» Ny') 
+ + Nf?) (sT3 N^')} J 
X 
am -1- F. l^-pS ^t±S] 
' \ Sy3 / 
/'b b -\- r 
+ /• (“sT" + T77’ 
b — r 5 _L r \ 
<r o- ' ^ 
So-3 J 
z 
