90 REPORT—1862. 
might be either increased, or diminished, or left unaltered, according as the 
effect of the longitudinal and the transverse iron preponderated. We may, 
therefore, by observing the effect on the directive force, as well as on the 
quadrantal deviation, ascertain how much of the latter is caused by fore-and- 
aft iron, how much by transverse iron. 
This explanation of the coefficients will probably be sufficient for the 
purposes of this Report, and we now revert to Part III. of the ‘ Manual.’ 
The principal object of this part is to find the means of computing A, B, 
C, D, E, from the deviations observed or derived by Napier’s curve for a 
certain number (8, 16, or 32) equidistant points. This is easily done by 
formule founded on the method of least squares ; and the method is made of 
ready application by tabular forms and tables given in this part. 
The direct computation of the exact coefficients A, 3, €, B, € by the 
method of least squares would be a matter of very great labour; but they 
are easily derived to terms of the 3rd order inclusive from the approximate 
coefficients A, B, C, D, E by formule which are given for the first time in 
this part. 
There are two other coefficients, the knowledge of which is of great 
importance, but which can only be derived from observations of force, viz. d, 
or the ratio of the mean force to north at the place of the compass to the 
earth’s horizontal force, and p, the ratio of the mean vertical force at the 
same place to the earth’s vertical force. 
One of the most important errors in the modern iron-built and iron- 
plated vessels is the heeling error, The deviations obtained by the usual pro- 
cess of swinging are for a vessel on an even keel. It is found by experience 
that as the vessel heels to one or other side, the north point of the compass 
is drawn either to the weather or lee side, generally the former; and the 
deviation so produced, when the ship’s course is near north or south, often 
exceeds the angle of heel. This not only produces a deviation which may 
cause a serious error in the ship’s course, but if the ship is rolling, and par- 
ticularly if the period of each roll approximates to the period of oscillation of 
the compass, produces a swinging of the compass-needle, which may amount 
to many times the angle of heel, and make the compass for the time useless 
for steering. 
This is a part of the deviation which has been involved in some obscurity. 
Mr. Airy, in a paper in the ‘ Transactions of the Institution of Naval 
Architects, vol. i. p. 107 (1860), says that the disturbance produced by 
heeling has not been well observed, and its correction has not yet been 
reduced to easy laws; and that the effect of heeling is the only part of the 
magnetic disturbance in regard to which the practical correction of the com- 
pass is really at fault ; and the Reports of the Liverpool Compass Committee 
refer to it as one of the most perplexing parts of the subject. It therefore 
appeared to us desirable to deduce from Poisson’s formule, expressions for the 
alteration of the coefficients introduced by the inclination of the ship. This 
has been done in the ‘Manual,’ and the result is, we think, to remove entirely 
the obscurity which rested on the subject. The effect of the heeling error is, 
as might have been anticipated, to leave unaltered the coefficients which 
depend on fore-and-aft action, viz. B and D, to alter C, and to give a value 
to A and EK. The latter appear to be, except when the compass is near 
either extremity of the vessel, of small amount. The alteration of C is the 
only one which is important. The formule show that it consists of two 
parts, which are caused by arrangements of iron, such as that in the follow- 
‘ing figure, in which the vertical line represents iron permanently magnetized, 
