272 STAFF COMMANDER EVANS AND MR. A. SMITH ON THE MAGNETIC 
rods being imaginary, that they exercise no action on one another, a , b , and c will produce 
a force to head 
=aX+bY+cZ ; 
so d , e, and /will produce a force to starboard 
=dK+eY+fZ, 
and g , h, and k will produce a force to nadir 
=#X+AY+£Z. 
By comparing these results with Poisson’s formulae, we see that for the effect of the 
soft iron of the ship, however complicated its arrangement may be, we may substitute 
the nine soft iron rods. 
The quantities P, Q, E in the general equations may be conveniently represented by 
three bar-magnets, placed in fixed positions in the ship ; P attracting the north end of the 
compass-needle to the head, Q to starboard, and E to nadir. 
Very simple considerations will show us that the two rods a and e will increase the 
directive power on the needle in the proportion of l + ~7y~ : 1? and that the other seven 
rods, as well as the permanent forces P, Q, E, will not affect the mean directive force. 
Simple considerations will also show that a and e will produce a deviation, 
^sin2£=Dsin2£ 
nearly. Like considerations will show that c and P will produce a deviation, 
C - Z ^T sin £ = ^ tan 0 + ~ ^ sin £'=B sin £'. 
Also that f and Q will produce a deviation, 
/Z + Q. y. ( f QA y. ^ y. 
cos ^ tan^-f-g ) cos £'=C cos 
The other less important terms, as well as the heeling error, may be obtained in the 
same manner. 
DISCUSSION OF THE TABLES. 
At the risk of some repetition it may be convenient to give here a brief explanation 
of the quantities tabulated. 
The first five quantities, A, B, C, D, E, are the “approximate coefficients” which 
give the deviation of the compass on every course by means of the expression 
S = A+ B sin £ + C cos £ + D sin 2£ + E cos 2£, 
in which & is the deviation, the azimuth of the ship’s head measured eastward from 
the direction of the disturbed needle, A, B, C, D, E being expressed in degrees and 
minutes. 
This expression is sufficiently accurate for deviations not exceeding 20° ; for larger 
deviations, the exact expression for the deviation given in the preceding part of the 
