———$ —_—-  —-— ——— 
OOO 
MAGNETIC INCLINATION AT GOTTINGEN. 639 
m the product of the magnetic moment of the needle into the 
total intensity of the magnetic force of the earth, gravity being 
taken as the unit of the accelerating forces. 
g the weight of the needle multiplied into the distance of the 
centre of gravity from the axis of rotation. 
ce the small angle between the straight line joining the extre- 
mities of the needle and its magnetic axis, being positive when 
the latter is to the right, the needle being imagined to be lying 
flat with its marked face uppermost. 
Q the angle between the line joining the extremities of the 
needle, and a line from the axis of rotation to the centre of gra- 
vity, commencing from the first-named line, and counted from 
left to right in the same position of the needle as in c. 
0 the directive force. 
If we resolve the magnetic force of the earth into a vertical 
and a horizontal portion, we obtain from the vertical portion, 
m sinicos (L + c) 
as the moment of rotation, taken as positive in the sense of L 
increasing ; and from the horizontal portion, 
— mcosi(V — V°)sin(L + ¢). 
The effect of gravity is the moment 
gcos (L + Q). 
As L expresses the position of equilibrium, the sum of these 
three moments = 0, whence we obtain the leading equation, 
— sinicos (L + ce) + cos? cos(V — V°) sin (L + ce) 
=f .(L + Q). 
If we write in the sum of the three moments L + 2 instead 
of L, we obtain the moment of rotation which exists with a de- 
flection z from the position of equilibrium ; if we develope this 
expression into two parts with the factors cos z and sin 2, the 
first disappears by virtue of the leading equation, and the second 
becomes = —ésinz. Thus we have for 6 the general formula 
$= msinisin (L + c) + mcosicos (V — V°) (cos (L + C) 
+ gsin(L + Q). 
We find from hence, for the three chief cases,— 
1. For V-= ¥", 
sin (L + ¢ — i) =1 cos (L + Q) 
VOL. III, PART XII, 20 
