88 REPORT—1862. 
method is unfamiliar ; but for general use there seems to be no form supe- 
rior-to the usual form of Napier’s diagram. 
Part III. contains the practical application to this subject of mathematical 
formule derived from the fundamental equations deduced by Poisson from 
Coulomb’s theory of magnetism. This part was published separately in the 
year 1851, and afterwards as a Supplement to the “ Practical Rules ” in 1855. 
At that time it was considered sufficient to use approximate formule, going 
as far only as terms involving the first powers of the coefficients of deviation. 
The very large deviations found in iron-plated ships of war rendering it 
desirable to use in certain cases the exact instead of the approximate formule, 
this part has been re-written. 
It may be desirable to give here some account of these formule. 
Poisson’s equations are derived from the hypothesis that the magnetism 
of the ship, except so far as it is permanent, is transient induced magnetism, 
the intensity of which is proportional to the intensity of the inducing force, 
and that the length of the compass-needle is infinitesimal compared to the 
distance of the nearest iron. 
On this hypothesis the deviation of the compass is represented ewactly by 
one or other of the following formule :— 
sin 5=@ cos +B sin 2/+€ cos 2/4 B sin (22'+6)+€ cos (22'+6) .. (1) 
t sat sin £+€ cos €4+B sin 2 + € cos 22 (2) 
aO=7 +38 cos —C ain 24D cos PTE an BE Se 
in which 8 represents the deviation, Z the ‘ correct magnetic course,” 2! the 
“ compass course ;” Q, 3B, & are coefficients depending solely on the soft iron 
of the ship ; 34 and € coefficients each consisting of two parts, one part a co- 
efficient depending on the soft iron and multiplied by the tangent of the dip, 
the other part a coefficient depending on the hard iron and multiplied by the 
reciprocal of the earth’s horizontal force at the place, and by a factor, Y? 
generally a little greater than unity, and depending on the softiron. In 
these equations the sign+ indicates an easterly, —a westerly deviation of the 
north point of the compass. 
If the coefficients are so small that their squares and products may be 
neglected, the first equation may be put under the form 
S=A+B sin 2'+C cos Z'+-D sin 22'4+E cos 22!.... 6. eee eee (3) 
in which it will be observed that the coefficients are now expressed in are, the 
Roman letters being nearly the arcs of which the German letters are the sines. 
When the deviations do not exceed 20°, this equation is sufficiently exact. 
As the subject with which we are now dealing cannot be understood or 
followed without distinctly apprehending the meaning of the several parts of 
this expression, we do not apologise for pausing to explain them. 
The term A is what is called the “ constant part of the deviation.” <A real 
value of A can only be caused by soft iron unsymmetrically arranged with 
reference to the compass. 
It will easily be seen that such an arrangement of horizontal soft iron rods, 
such as that in figure 1, 
eS 
Fig. 1. 
© 
would give a positive value of A, and no other term in the deviation. 
