IN WOOD-BUILT AND IRON-BUILT SHIPS. 
61 
sums of the deviations in the two groups are to be taken: one is to be subtracted 
from the other, and the remainder is to be divided by 32. The quotient is the mean 
deviation. This is to be compared with the Means of Polar-Magnet-Deviations at the 
foot of the columns of the Table. Two adjacent Tabular Means being found, one^ 
greater and one less than the mean deviation just obtained, and the values of modulus, 
corresponding to those two tabular means being noted, there is no difficulty in find- 
ing by interpolation the value of modulus corresponding to the mean deviation just 
obtained. This is the “Approximate Modulus.” 
8. By use of the approximate neutral position, the angle of apparent azimuth from 
the neutral position will be formed for every observation. Using this as the argu- 
ment of Azimuth in the Table, the Polar-Magnet-Deviation is to be taken out for 
every observation with two tabular values of Modulus, one greater and one less than 
the approximate modulus just found. Between these, the Polar-Magnet-Deviation 
will be interpolated for the approximate modulus ; and thus the Tabular Polar- 
Magnet-Deviation corresponding to the Approximate Modulus will be obtained for 
every observation. 
9. Subtracting this Tabular Polar-Magnet-Deviation algebraically from theObserved 
Deviation, the residual quantity will consist of Quadrantal Deviation, of the small cor- 
rection and of errors of observation. Neglecting the two last mentioned, a pretty 
accurate estimate of the coefficient of quadrantal deviation may be got by omitting 
the values for Op, 8p, 16p, 24p, and dividing the sum of each group of seven numbers 
by 5 ; the quotient will be the coefficient, or the Quadrantal Deviation for 4P, 12p, 20p, 
28P. The conversion of this coefficient into abstract number (radius =1) gives the 
numerical coefficient P. 
2 
10. The angle g X coefficient of quadrantal deviation X sine of twice the approxi- 
mate starboard angle is to be subtracted from the approximate starboard angle to 
give the “'True Starboard Angle.” And the approximate modulus is to be multiplied by 
p 
l-pgX cosine of twice the approximate starboard angle to give the “True Modulus.” 
1 1 . The Headward Modulus = True Modulus X cosine True Starboard Angle ; and 
the Starboard Modulus = True Modulus x sineTrue Starboard Angle. As the modulus 
is the proportion of the disturbing force to the terrestrial horizontal force (slightly 
diminished everywhere in the same proportion), we must, for the exhibition of the 
absolute values of the disturbing forces, multiply these quantities by the terrestrial 
horizontal force. Then (referring to the statements at the commencement of this 
paper for the results of theory) we shall have. 
Headward Modulus X Terrestrial Horizontal Force=H-l-N X Terrestrial Vertical Force, 
Starboard Modulus X Terrestrial Horizontal Force=S, 
where H and S are the forces of the ship’s subpermanent magnetism in the head- 
ward and starboard directions ; andN is a constant peculiar to the ship, depending 
