THE COMPASS-NEEDLE ON THE DEVIATIONS OE THE COMPASS. 
171 
The coefficient of the sextantal terms having cos 3 
« + «' 
2 
as a factor is zero if 
«+«' 
= 30 
o 
9 
or if the ends of the needles be at equal angular distances on each side of the point of 
30°, It is therefore zero if one pair of needles be 15° from the diameter, the other at 
45° from the diameter, which is the usual construction of the Admiralty Standard com- 
pass. 
In each case it will be seen that the semicircular deviation is increased by the length 
of the needle in the proportion of 
J-i-s 42- J- 
These results hold good if, instead of one magnetic particle, any number of magnetic 
particles or of magnets act on the compass. 
If we go back to equation (I.), and if, instead of finding the effect of a single magnetic 
particle on two or four needles, we inquire into the effect of two equal magnetic particles 
at equal distances from the compass, but in different azimuths and on a single 
needle, we find the force to tmm the needle to be 
4Mmpcos(^'— 
/t . 3 15 2 
I ^"^8 2 ‘ 1 " 8 t ' — ' 
' ' roa — 
w. 
. (4.) 
The coefficient of the sextantal deviation having cos 3 — for a factor is zero if 
^'—^"=60°; so that two similar bar magnets placed similarly with reference to a 
single-needle compass, but at azimuths differing 60° from each other, wiU produce a 
semicircular de\iation, but no sextantal deviation. 
If the point M, instead of being in the plane of the needle, be at a height h above it, 
b being now the distance from the centre of the needle, of the projection of M on the 
horizontal plane : — 
The force to turn a needle of length 2a about its centre 
2M.mah 
^ 3 a%'^ / • VI , 15 
-*- + 8 (62 + A2)2 y-*- 8’{b^ + hy 
The equation shows that for a given semicircular deviation the sextantal deviation 
produced by a magnet raised above, or depressed below the level of the compass, is less 
than that produced by a magnet in the same horizontal plane in the proportion of 
*2 . 1 
in which b' is the horizontal distance of the magnet in the same horizontal plane. But 
inasmuch as in order to produce the same semicircular deviation we must have 
b 1 
2 B 2 
