Table Of ContentSHIP MAGNETISM
and the Magnetic Compass
F. G. MERRIFIELD
Extra Master, M.I.N.
Principal Lecturer, Department of Navigation,
Welsh College of Advanced Technology
PERGAMON PRESS
OXFORD • LONDON • NEW YORK • PARIS
1963
PERGAMON PRESS LTD.
Headington Hill Hall, Oxford
4 &5 Fitzroy Square, London, W. 1
PERGAMON PRESS INC.
122 East 55th Street, New Tork 22, N.T.
GAUTHIER-VILLARS
55 Quai des Grands-Augustins, Paris 6
PERGAMON PRESS G.m.b.H.
Kaiserstrasse 75, Frankfurt am Main
Copyright
©
1963
Pergamon Press Ltd.
Library of Congress Card Number: 62-19267
Set in 10 on 12 pt. Baskerville and Printed in Great Britain by
ADLARD & SON, BARTHOLOMEW PRESS, DORKING
PREFACE
IN this book an endeavour has been made to meet the demand for
a concise course of practical interest and utility. The text as a
whole is based on lecture notes which have been used for a con
siderable time in the preparation of candidates for the ordinary
M.o.T. examinations in Magnetism and Deviations of the Mag
netic Compass and the needs of such candidates have been kept
particularly in mind in the presentation of the subject.
Very careful consideration has been given to the scope of the
book which it is hoped will be sufficient to stimulate an interest
in what, to date, has been looked upon by some as black magic.
Emphasis has been placed on the distinction between the devia
tion itself and what causes the deviation. The special features of
the book are numerous worked examples for exercise at the ends
of the chapters. By means of these examples, it should be possible
for the student to test his grasp of the principles and processes
given in the text and later, when in a position of authority, to
detect defects, if any, in the compensation of the magnetic com
passes and, moreover, remedy these defects rather than tolerate
an inefficient compass.
The author is deeply indebted to his colleague Captain W.
Burger, M.Sc, who has given invaluable service and advice in the
preparation of the MS., also to Captain J. H. Clough-Smith,
B.Sc, F.I.N., for many valuable suggestions made by him in all
stages of the work.
Thanks and acknowledgement are due to the Hydrographic
Department of the Admiralty for permission to reproduce charts
showing values of magnetic elements, also to Messrs. Kelvin &
Hughes (Marine) Ltd. for generously supplying photoprints of the
"Kelvin Hughes Deflector" and "Bealls Compass Deviascope"
and their approval of the reproduction of these.
Cardiff. F. G. MERRIFIELD
vii
CHAPTER I
MAGNETOMETRY (1)
Unit Pole and Law of Inverse Squares
Before proceeding to the study of magnetism of ships and the
deviation of the magnetic compass produced by this magnetism,
it is desirable to look a little way into the magnitude of the forces
involved and the manner in which these forces act.
The elementary law that "Like poles repel and Unlike poles
attract" is well known, but to obtain a measure of these forces
of attraction and repulsion we must first agree on what is meant
by the ''strength" of a magnetic pole.
Unit Pole
A pole is said to have a strength of one unit if it attracts (or
repels) another pole of the same strength with a force of one dyne
when placed at a distance of one centimetre from it (in air).
Note that this force is mutual.
If one pole has a strength of 2 units and is placed at a distance
of 1 cm from another pole of strength 1 unit, then the mutual force
of attraction or repulsion is 2 dynes.
So long as the distance apart is kept at 1 cm, the force will
always be the product of the respective pole strengths. Thus:
Force = m± X m% dynes
where mi and m% are the respective pole strengths and the distance
between them is 1 cm.
In general, when energy emanates from a point source, this
energy diminishes or falls off as the square of the distance.
2 SHIP MAGNETISM AND THE MAGNETIC COMPASS
Law of Inverse Squares
If it were possible to isolate two magnetic poles, the force each
exerts on the other would vary
(i) directly as the product of their pole strengths, and
(ii) inversely as the square of their distance apart, thus:
_ m± X m2 ,
r orce = dynes
d*
This equation assumes that air or some other non-magnetic
substance is the medium in which the poles are situated.
EXAMPLES
1. Two N poles, each of strength 20 units, are placed 5 cm apart.
Find the force each exerts on the other.
Force =f= =16 dynes (repulsion)
52
2. At what distance should a N pole of strength 16 units be
placed from another of strength 25 units to repel it with a force
of 4 dynes ?
A 16 x 25
d2 = l^x 25 = 1(X)
4
d = vToo =
10 cm
3. A N pole A of strength 20 units is placed 30 cm E magnetic
of another N pole B of strength 80 units. On the line joining their
poles is a short magnetic needle which lies in the magnetic meri
dian.
Find the distance from pole A to this needle.
Let the distance from A to the needle = x cm, and
the distance from B to the needle = y cm.
MAGNETOMETRY (1) 3
^ . .. 30cm ♦-
Fig. 1
Hence
x + y = 30 (I)
Also let the pole strength of the small needle be m units, then
force on the N pole due to
A 20m -
A — —— dynes
x2
and force on the N pole due to
B — —— dynes
These forces must be equal since the needle lies in the magnetic
meridian. So:
20m _ 80m
(II)
yii
Divide each by 20m
x2 yl
y 2 = 4^2
Take the square root
y = 2x
Substitute this value in Equation (I).
x + 2x = 30
3x = 30
x= 10,
so pole A is 10 cm from the needle.
4 SHIP MAGNETISM AND THE MAGNETIC COMPASS
4. Four S poles are at the corners of a square ABCD of side
3-5 cm. A, B and C have pole strengths of 20 units each, D is 5
units.
Find the resultant of the forces that these poles exert on a
unit N pole placed at the centre of the square.
A2o B20
/
D5
-3-5cm *~
Fig. 2
Consider the poles A and C; they are equidistant from the
centre, their forces on the unit pole are equal and opposite, hence
their effects cancel each other.
To find the effects of poles B and D we must know the diagonal
of the square which is y3-52 + 3-52 or 5 cm, so each pole is
2-5 cm from the centre.
Force due to
20 x 1
B = :
2-52
and due to
D = ——■—- dynes
2-52 y
So resultant force is
20 --5 __ J5^
= 2-4 dynes towards B
T52 ^25
MAGNETOMETRY (1) 5
5. Two N poles lie on an E-W line, 20 cm apart; A is 25 units
and B 35 units. Find the resultant of their forces on a S pole C
of strength 30 units which is 12 cm from A and 15 cm from B.
So far the forces involved have been along the same straight
line. When they are inclined to one another the resultant is found
by applying the principle of the Parallelogram of Forces. A
graphical solution will generally give a result accurate enough to
be acceptable.
Fig. 3
ABC is drawn carefully to scale to indicate the relative positions
of the poles.
Attractive force
. 25 x 30 _ .
A on Cn = -~— = 5- 02 dynes
12
2
Attractive force
„ 35 x 30 .
B on Cn — —-—- — 4-7n Ad ynes
152 *
The force parallelogram can be built up on the original tri
angle by making CX to scale to represent 5-2 and CT to represent
4-7. Completing the parallelogram, the diagonal C£ measures
6 SHIP MAGNETISM AND THE MAGNETIC COMPASS
7 units; hence the resultant force is 7 dynes, acting in a direction
inclined 45° (<£CT) to the line joining CB.
EXERCISES. I.
1. Calculate the force between magnetic poles of strength 60 and 90 units
when placed 10 cm apart.
2. Two N poles repel one another with a force of 2-4 dynes when their
distance apart is 2 cm. What will be their distance apart when the force is
4-8 dynes? Find also their repulsive force when their distance is 4 cm.
3. AN pole of strength 16 units is placed 45 cm E magnetic from a N pole
of strength 9 units. At what point between them will a small compass
needle point north magnetic ?
4. Four N poles, A 10 units, B 20 units, C 10 units and D 50 units, are at
the corners of a square ABCD of side 7 cm. Find their resultant force on a
unit pole at the centre of the square.
5. AN pole of 50 units has another N pole of 40 units 20 cm due E magnetic
of it. Find their resultant force on a S pole of 30 units, 16 cm from the first
pole and 12 cm from the second.
6. AS pole of strength 50 units is situated in line with the N-S axis of a
magnet at a distance of 25 cm from its centre. If the length of the magnet
is 10 cm and its pole strength 20 units, find the force on the S pole.
7. Find the force on the magnetic pole of strength 20 units, situated at a
distance of 20 cm from each pole of a magnet whose length is 20 cm and
pole strength 20 units.
Field Strength, Moment, Long and Short Magnet,
Restoring Couple
Field Strength (F)
The Field Strength of a magnet at a given point is the force, in
dynes, that the magnet exerts on a unit Npole placed at that point.
This force is generally expressed in oersteds, so one oersted simply
means a force of one dyne per unit pole.
EXAMPLE
6. Find the field strength of a bar magnet 20 cm long with a
pole strength of 50 units at a point 20 cm from its centre in line
with the N-S axis.
Imagine a unit pole P 10 cm from one pole of the magnet and
30 cm from the other.
MAGNETOMETRY (1) 7
, , P
1? Nl •
-«- 10cm---*-
-* 30cm *-
Fig. 4
Force exerted by
TNV = 50— x __l = 0n- 5 *dAy ne
102
Force exerted by
^ = °-°
S = 56 dynC
Resultant force or field strength (F) = 0-444 oersted.
The same result would be obtained at the corresponding point
Pi on the other side of NS.
Note that if the force on a unit pole at P is 0-444 dyne then the
force on a pole of m units at P would be 0-444 X m dynes.
Hence the force exerted by a magnet on any pole placed in the
field is the product of the strength of that pole and the field
strength of the magnet at that point.
Force (f) = Field Strength (F) x Pole Strength (m).
EXAMPLE
7. What force does the earth's magnetic field exert on the N end
of a compass needle of pole strength 100 units at Cardiff where
the horizontal field strength of the earth's magnetic field is 0-2
oersted ?
Force (/) = 0-2 X 100 = 20 dynes, which is equivalent to
about one-fiftieth of a gram weight.
Magnetic Moment
In the example above, on finding field strength, the length
of the magnet NS was an important factor. Try the same example
using 10 cm as the length of NS instead of 20 cm. The result
should be about 0-14 oersted, indicating that the length as well
