CHARACTER Of THE ARMOUR-PLATED SHIPS OE THE ROYAL NAVY. 313 
extends half the breadth of the ship abaft the compass , it will diminish the quadrantal 
deviation. 
When — | y—{rf —y)^m }» 
or when the armour-plating extends a little less than half the breadth abaft the compass, 
its effect on the quadrantal deviation vanishes, and when the distance is less than that 
last mentioned, it increases the quadrantal deviation. 
If the central part of a beam be cut out, and if y and y' be the transverse coordinates, 
r, r' the distances of its outer and inner extremities from the compass, 
«=2*s{=£+^}. 
Hence if such a beam be near the compass so that it will increase the directive 
force and diminish the quadrantal deviation ; if distant it will have the opposite effect. 
A vertical rod, z being the vertical coordinate of the upper, z 1 of the lower end, x and 
y being the horizontal coordinates, will produce 
c —%Sx (k—ptj ’ 
k =*S ^“3 * 
The effect which is of most interest is that of k, as it affects the heeling error. 
If z be negative, z 1 positive, or if the upper end of the beam be above and the lower 
end below the level of the compass, we see that k will be negative, and will in general 
diminish the heeliug error. 
If the rod be a short one of length n, 
here k will be +, as 
£> JL 
r<*/3’ 
or, in other words, if the centre of the rod be within the cone traced out by a line 
through the compass, making an angle of 54° 45' with the vertical, k will be positive, 
and the force of the rod will act downwards and increase the heeling error. On the 
other hand, if the centre of the rod be without the cone, k will be negative, and the 
force will act upwards and decrease the heeling error. 
Hence we see that in all cases, except when the compass is raised very much above 
the upper part of the armour-plates, the effect of armour-plating will be to diminish the 
heeling error. 
2u 2 
