276 
STAFF COMMANDER EVANS AND MR. A. SMITH ON THE MAGNETIC 
creases the directive force, — e diminishes it; but as — e always exceeds -\-a, the result 
is a diminution on the whole. 
The expression for X in terms of a and e is 
X = l + 
a + e 
The tabulated values of X are obtained by comparing the terms of vibration of a hori- 
zontal needle vibrated in the position of the compass in the ship and also on shore; 
X does not change with a change of geographical position. 
The determination of 3) and X gives us the means of determining the two parts a and 
e, and also the two parts of which D is composed, separately ; and these are accordingly 
tabulated. 
The preceding are the only coefficients which affect the compass when the ship is 
upright ; but when the ship heels over, new disturbing forces are called into play, caused 
by arrangements of soft or hard iron of one or other of the following types: — 
Fig. 5. 
— e represents, as before, the transverse soft iron, which will evidently, as the ship heels 
over, produce a force to windward, or the high side of the ship, on the north end of the 
needle. If the rods -\-7c and — k represent soft iron, then -| -k gives a force acting down- 
wards on the north end of the needle, which, as the ship heels, becomes a force to wind- 
ward ; — k a force acting upwards, which, as the ship heels, becomes a force to leeward. 
The permanent magnetism of the ship will generally act downwards if the compass is 
over the end which has been South in building, upwards if over the end which has been 
North in building. The amount of the two forces may be ascertained by vibrating a 
dipping-needle on shore and in the ship with her head in certain positions. The pro- 
portion of the mean vertical force on board to the vertical force on shore is denoted by 
the coefficient p, which is tabulated for those ships in which the observations have been 
made. 
From the values of 3) and X we obtain by a simple formula, viz. ^3) + 1^ tan 6 1°, 
the “ heeling coefficient to windward,” or the deviation to windward caused, when the 
ship’s head is N. or S. by compass, by an angle of heel of 1°. When this coefficient has 
a negative sign it indicates a deviation to leeward. The values of the heeling coefficient 
so deduced are tabulated. The value changes with a change of geographical position. 
From the values of p, 3) and X we may also determine how much of the heeling error 
arises from the transverse soft iron represented in the figures 3, 4 & 5, and how 
