CHARACTER OF THE ARMOUR-PLATED SHIPS OF THE ROYAL NAVY. 265 
Observations of horizontal force, for the purpose of ascertaining the diminution of the 
mean directive force, have now become part of the regular series of observations made 
in ships in which its determination is of importance, and formulae and graphic methods, 
for the purpose of deducing from them the proportion of the mean value of the directive 
force to North to the earth’s horizontal force, are given in the ‘ Admiralty Manual.’ 
Another error of the greatest importance, which has been brought into prominence 
in the modern class of iron -built ships, is the “ heeling error.” 
The deviations obtained by the usual process of swinging are for a vessel in an upright 
position. It is found by experience that, as the vessel heels over, the north end of the 
compass-needle is drawn either to the weather or lee side, generally in the northern 
hemisphere to the former, and the deviation so produced when the ship’s head 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 
particularly if the period of each roll approximates to the period of oscillation of the 
compass, it produces a swinging of the compass-needle which may make the compass 
for the time useless for steering. 
This error had been known to exist, and its amount had even been measured in the 
case of Her Majesty’s ships Eecruit (1846), Bloodhound (1847), Sharpshooter (1848), 
and in various cases recorded by the Liverpool Compass Committee (1855-61); but no 
method had been proposed for determining this error by observations made with the 
ship upright, and considerable obscurity was even supposed to rest on the causes and 
law of this deviation. The application of Poisson’s formulae has entirely removed the 
obscurity, and furnishes an easy method of determining the heeling error by observations 
of vertical force made on one or more directions of the ship’s head. These observations 
have likewise now become a regular part of the complete series of magnetic observations 
made in the principal iron ships of Her Majesty’s Navy. 
Fortunately the mechanical correction of this error, when its amount is ascertained, is 
not difficult, and as the correction does not affect the deviation when the ship is upright, 
its application is free from some of the objections which exist to the mechanical correc- 
tion of the ordinary deviation. 
The importance of being thus able to detect the heeling error by observations of a 
simple kind made with the ship upright is great, and this is perhaps one of the most 
practically useful of the immediate results of the application of mathematical formulae 
to this subject. 
Besides these, which may be called the direct results of the additional observations 
now made, and of the application to them of the mathematical formulae, there are some 
other results of the use of the formulae which have a practical value as well as a theo- 
retical interest. 
Among these is the separation into their constituent parts of the several coefficients, 
so as to indicate the particular arrangements of the iron from which each arises. This 
is not only of great theoretical interest, but is of considerable practical importance in 
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