316 STAFF COMMANDER EVANS AND. ME. A. SMITH ON THE MAGNETIC 
effect of the sphere is to increase the quadrantal deviation ; if in the starboard or port 
quadrant, it will decrease the quadrantal deviation. 
If we have two spheres, one on each side and at the level of the compass, a =90°, 
y=90°, j3=0° and 180°, whence 
X=l+M, 
3M 
1+M' 
1 + 
(?)' 
nearly. 
Hence we get the following for the effect of two such spheres according to the 
number of semidiameters which their centres are distant from the centre of the compass. 
r. 
e. 
D. 
2 V 
•333 
19 30 
3 P 
•107 
6 10 
4 p 
•046 
2 40 
bp 
•023 
1 20 
Hence also we find the distance of the spheres required to correct any given qua- 
drantal deviation 2, 
Ant 
~3 x 
As we have supposed — ^-=1, the deviation which two balls of iron of the usual 
1 +T X 
kind will correct will be one or two per cent, less than the above. 
When the sphere is in either of the diagonal planes, a=45°, |3=45°, or a= — 45°, 
/3=135°, 
2=0, and 
or (S is the same as the 2 when the sphere is in a principal plane. This We should of 
course anticipate. 
M 
From the expression 33= — 3 cos a cos y tan 0, we see that in the northern hemisphere, 
if the sphere be below and before, or above and abaft the compass, we have a + semi- 
circular deviation ; if above and before, or below and abaft, a — semicircular deviation. 
Spherical Shell. 
The effect, if the compass be exterior to the shell, will be precisely the same as that 
of a sphere if for M we substitute 
M 
( i+ H 
ti 
1 + Airx -f 
4 8/ 
