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Sensors and Transducers 3rd ed Edition Ian Sinclair
Digital Instant Download
Author(s): Ian Sinclair
ISBN(s): 9780750649322, 0750649321
Edition: 3rd ed
File Details: PDF, 1.54 MB
Year: 2001
Language: english

Sensors and
Transducers
Third edition
Ian R. Sinclair
OXFORD AUCKLAND BOSTON JOHANNESBURG MELBOURNE NEW DELHI

Newnes
An imprint of Butterworth-Heinemann
Linacre House, Jordan Hill, Oxford OX2 8DP
225 Wildwood Avenue, Woburn, MA 01801-2041
A division of Reed Educational and Professional Publishing Ltd
A member of the Reed Elsevier plc group
First published by BSP Professional Books 1988
Reprinted by Butterworth-Heinemann 1991
Second edition published by Butterworth-Heinemann 1992
Third edition 2001
# I. R. Sinclair 1988, 1992, 2001
All rights reserved. No part of this publication
may be reproduced in any material form (including
photocopying or storing in any medium by electronic
means and whether or not transiently or incidentally
to some other use of this publication) without the
written permission of the copyright holder except
in accordance with the provisions of the Copyright,
Designs and Patents Act 1988 or under the terms of a
licence issued by the Copyright Licensing Agency Ltd,
90 Tottenham Court Road, London, England W1P 9HE.
Applications for the copyright holder's written permission
to reproduce any part of this publication should be addressed
to the publishers
British Library Cataloguing in Publication Data
A catalogue record for this book is available from the British Library
ISBN 0 7506 4932 1
Typeset by David Gregson Associates, Beccles, Su¡olk
Printed and bound in Great Britain

Contents
Preface to Third Edition vii
Preface to First Edition ix
Introduction xi
1 Strain and pressure 1
2 Position, direction, distance and motion 21
3 Light and associated radiation 53
4 Temperature sensors and thermal transducers 87
5 Sound, infrasound and ultrasound 116
6 Solids, liquids and gases 142
7 Environmental sensors 170
8 Other sensing methods 197
9 Instrumentation techniques 206
10 Switch principles 233
11 Switch mechanisms 248
12 Signal-carrying switches 270
Appendix A: Suppliers of sensors and transducers 290
Appendix B: Glossary of terms 293
Index 296

Preface to Third Edition
This third edition of Sensors and Transducers has been thoroughly revised to
take account of the ever-increasing role of these components and of im-
provements in design. New tables of properties and illustrations have also
been added. The topic of switches and switching actions has also been
added because so many types of sensor are intended ultimately to provide a
switching action.
Ian Sinclair

Preface to First Edition
The purpose of this book is to explain and illustrate the use of sensors and
transducers associated with electronic circuits. The steady spread of elec-
tronic circuits into all aspects of life, but particularly into all aspects of
control technology, has greatly increased the importance of sensors which
can detect, as electrical signals, changes in various physical quantities. In
addition, the conversion by transducers of physical quantities into electronic
signals and vice versa has become an important part of electronics.
Because of this, the range of possible sensors and transducers is by now
very large, and most textbooks that are concerned with the interfaces
between electronic circuits and other devices tend to deal only with a few
types of sensors for speci¢c purposes. In this book, you will ¢nd described a
very large range of devices, some used industrially, some domestically,
some employed in teaching to illustrate e¡ects, some used only in research
laboratories. The important point is that the reader will ¢nd reference to a
very wide range of devices, much more than it would be possible to present
in a more specialized text.
In addition, I have assumed that the physical principles of each sensor or
transducer will not necessarily be familiar. To be useful, a book of this kind
should be accessible to a wide range of users, and since the correct use of
sensors and transducers often depends critically on an understanding of the
physical principles involved, these principles have been explained in as
much depth as is needed. I have made the reasonable assumption that elec-
trical principles will not be required to be explained in such depth as the
principles of, for example, relative humidity. In order for the book to be as
serviceable as possible to as many readers as possible, the use of mathematics
has been avoided unless absolutely essential to the understanding of a
device. I have taken here as my guide the remark by Lord Kelvin that if
he needed to use mathematics to explain something it was probably

because he didn't really understand it. The text should prove useful to
anyone who encounters sensors and transducers, whether from the point of
view of speci¢cation, design, servicing, or education.
I am most grateful to RS Components for much useful and well-organized
information, and to Bernard Watson, of BSP Professional Books, for advice
and encouragement.
Ian Sinclair
April 1988
x PREFACE TO FIRST EDITION

Introduction
A sensor is a device that detects or measures a physical quantity, and in this
book the types of sensors that we are concerned with are the types whose
output is electrical. The opposite device is an actuator, which converts a
signal (usually electrical) to some action, usually mechanical. A transducer
is a device that converts energy from one form into another, and here we
are concerned only with the transducers in which one form of energy is elec-
trical. Actuators and sensors are therefore forms of transducers, and in this
book we shall deal with actuators under the heading of transducers.
The di¡erences between sensors and transducers are often very slight. A
sensor performs a transducing action, and the transducer must necessarily
sense some physical quantity. The di¡erence lies in the e¤ciency of energy
conversion. The purpose of a sensor is to detect and measure, and whether
its e¤ciency is 5% or 0.1% is almost immaterial, provided the ¢gure is
known. A transducer, by contrast, is intended to convert energy, and its e¤-
ciency is important, though in some cases it may not be high. Linearity of
response, de¢ned by plotting the output against the input, is likely to be
important for a sensor, but of much less signi¢cance for a transducer. By
contrast, e¤ciency of conversion is important for a transducer but not for a
sensor. The basic principles that apply to one, however, must apply to the
other, so that the descriptions that appear in this book will apply equally
to sensors and to transducers.
. Switches appear in this book both as transducers/sensors in their own
right, since any electrical switch is a mechanical^electrical transducer,
and also because switch action is such an important part of the action of
many types of sensors and transducers.
Classi¢cation of sensors is conventionally by the conversion principle, the
quantity being measured, the technology used, or the application. The

organization of this book is, in general, by the physical quantity that is
sensed or converted. This is not a perfect form of organization, but no form
is, because there are many `one-o¡' devices that sense or convert for some
unique purpose, and these have to be gathered together in an `assortment'
chapter. Nevertheless, by grouping devices according to the sensed
quantity, it is much easier for the reader to ¢nd the information that is
needed, and that is the guiding principle for this book. In addition, some of
the devices that are dealt with early in the book are those which form part
of other sensing or transducing systems that appear later. This avoids
having to repeat a description, or refer forward for a description.
Among the types of energy that can be sensed are those classed as radiant,
mechanical, gravitational, electrical, thermal, and magnetic. If we
consider the large number of principles that can be used in the design of
sensors and transducers, some 350 to date, it is obvious that not all are of
equal importance. By limiting the scope of this book to sensors and transdu-
cers with electrical/electronic inputs or outputs of the six forms listed
above, we can reduce this number to a more manageable level.
Several points should be noted at this stage, to avoid much tedious repeti-
tion in the main body of the book. One is that a fair number of physical
e¡ects are sensed or measured, but have no requirement for transducers ^
we do not, for example, generate electricity from earthquake shocks
though we certainly want to sense them. A second point is that the output
from a sensor, including the output from electronic circuits connected to
the sensor, needs to be proportional in some way to the e¡ect that is being
sensed, or at least to bear some simple mathematical relationship to the
quantity. This means that if the output is to be used for measurements,
then some form of calibration can be carried out. It also implies that the
equation that connects the electrical output with the input that is being
sensed contains various constants such as mass, length, resistance and so
on. If any of these quantities is varied at any time, then recalibration of the
equipment will be necessary.
Sensors can be classed as active or passive. An active or self-generating
sensor is one that can generate a signal without the need for any external
power supply. Examples include photovoltaic cells, thermocouples and
piezoelectric devices. The more common passive sensors need an external
source of energy, which for the devices featured in this book will be electri-
cal. These operate by modulating the voltage or current of a supply.
Another class of passive sensors, sometimes called modi¢ers, use the same
type of energy at the output as at the input. Typical of these types is a
diaphragm used to convert the pressure or velocity oscillations of sound
waves into movements of a solid sheet.
Another point that we need to be clear about is the meaning of resolution as
applied to a sensor. The resolution of a sensor measures its ability to detect
a change in the sensed quantity, and is usually quoted in terms of the
smallest change that can be detected. In some cases, resolution is virtually
xii INTRODUCTION

in¢nite, meaning that a small change in the sensed quantity will cause a
small change in the electrical output, and these changes can be detected to
the limits of our measuring capabilities. For other sensors, particularly
when digital methods are used, there is a de¢nite limit to the size of change
that can be either detected or converted.
It is important to note that very few sensing methods provide a digital
output directly, and most digital outputs are obtained by converting from
analogue quantities. This implies that the limits of resolution are deter-
mined by the analogue to digital conversion circuits rather than by the
sensor itself. Where a choice of sensing methods exists, a method that
causes a change of frequency of an oscillator is to be preferred. This is
because frequency is a quantity that lends itself very easily to digital
handling methods with no need for other analogue to digital conversion
methods.
The sensing of any quantity is liable to error, and the errors can be static
or dynamic. A static error is the type of error that is caused by reading
problems, such as the parallax of a needle on a meter scale, which causes
the apparent reading to vary according to the position of the observer's
eye. Another error of this type is the interpolation error, which arises when
a needle is positioned between two marks on a scale, and the user has to
make a guess as to the amount signi¢ed by this position. The amount of an
interpolation error is least when the scale is linear. One distinct advantage
of digital readouts is that neither parallax nor interpolation errors exist,
though this should not be taken to mean that errors corresponding to inter-
polation errors are not present. For example, if a digital display operates to
three places of decimals, the user has no way of knowing if a reading
should be 1.2255 because this will be shown as 1.225, and a slight increase
in the measured quantity will change the reading to 1.226.
The other form of error is dynamic, and a typical error of this type is a dif-
ference between the quantity as it really is and the amount that is
measured, caused by the loading of the measuring instrument itself. A
familiar example of this is the false voltage reading measured across a
high-resistance potential divider with a voltmeter whose input resistance is
not high enough. All forms of sensors are liable to dynamic errors if they
are used only for sensing, and to both dynamic and static errors if they are
used for measurement.
Since the development of microprocessors, a new breed of sensors has
been developed, termed intelligent or smart sensors. This type of system uses
a miniature sensor that is integrated on a single chip with a processor.
Strictly speaking, this is a monolithic integrated sensor to distinguish it
from the hybrid type in which the sensor and the processor are fabricated
on the same substrate but not on the same chip. This book is
concerned mainly with sensor and transducer principles rather than with
the details of signal processing. The advantages of such integration
methods include:
INTRODUCTION xiii

. Improved signal-to-noise ratio
. improved linearity and frequency response
. improved reliability.
Finally, two measurable quantities can be quoted in connection with any
sensor or transducer. These are responsivity and detectivity, and although
the names are not necessarily used by the manufacturer of any given
device, the ¢gures are normally quoted in one form or another. The respon-
sivity is:
output signal
input signal
which will be a measure of transducing e¤ciency if the two signals are in
comparable units (both in watts, for example), but which is normally
expressed with very di¡erent units for the two signals. The detectivity is
de¢ned as:
S=N of output signal
size of output signal
where S/N has its usual electrical meaning of signal to noise ratio. This
latter de¢nition can be reworked as:
responsivity
output noise signal
if this makes it easier to measure.
xiv INTRODUCTION

Chapter 1
Strain and pressure
1.1 Mechanical strain
The words stress and strain are often confused in everyday life, and a clear
de¢nition is essential at this point. Strain is the result of stress, and is
de¢ned as the fractional change of the dimensions of an object. By fractional
change, I mean that the change of dimension is divided by the original
dimension, so that in terms of length, for example, the strain is the change
of length divided by the original length. This is a quantity that is a pure
number, one length divided by another, having no physical dimensions.
Strain can be de¢ned for area or for volume measurements in a similar
way as change divided by original quantity. For example, area strain is
change of area divided by original area, and volume strain is change of
volume divided by original volume.
A stress, by contrast, is a force divided by an area. As applied to a wire or a
bar in tension or compression, for example, the tensile (pulling) stress is the
applied force divided by the area over which it is applied, which will be the
area of cross section of the wire or bar. For materials such as liquids or gases
which can be compressed uniformly in all dimensions, the bulk stress is the
force per unit area, which is identical to the pressure applied, and the strain
is the change of volume divided by the original volume. The most common
strain transducers are for tensile mechanical strain. The measurement of
strain allows the amount of stress to be calculated through a knowledge of
the elastic modulus. The de¢nition of any type of elastic modulus is stress/
strain (which has the units of stress, since strain has no physical units), and
the most commonly used elastic moduli are the linear Young's modulus, the
shear (twisting) modulus, and the (pressure) bulk modulus.
For small amounts of strain, the strain is proportional to stress, and an
elastic modulus is a quantity that expresses the ratio stress/strain in the

2 SENSORS AND TRANSDUCERS
elastic region, i.e. the portion of the stress^strain graph that is linear. For
example, Young's modulus is the ratio tensile stress/tensile strain, typically
measured for a material in the form of a wire (Figure 1.1). The classic
form of measurement, still used in school demonstrations, uses a long pair
of wires, one loaded, the other carrying a vernier scale.
Sensing tensile strain involves the measurement of very small changes of
length of a sample. This is complicated by the e¡ect of changes of tempera-
ture, which produce expansion or contraction. For the changes of around
0^30
C that we encounter in atmospheric temperature, the expansion or
contraction of length will be about the same size as the changes caused by
large amounts of stress. Any system for sensing and measuring strain must
therefore be designed in such a way that temperature e¡ects can be compen-
sated for. The principles used to sense linear or area strain are piezoresistive
and piezoelectric.
The commonest form of strain measurement uses resistive strain gauges.
A resistive strain gauge consists of a conducting material in the form of a
Figure 1.1 The classic method of measuring tensile stress and strain for a wire.

thin wire or strip which is attached ¢rmly to the material in which strain is
to be detected. This material might be the wall of a building, a turbine
blade, part of a bridge, anything in which excessive stress could signal
impending trouble. The fastening of the resistive material is usually by
means of epoxy resins (such as `Araldite'), since these materials are
extremely strong and are electrical insulators. The strain gauge strip will
then be connected as part of a resistance bridge circuit (Figure 1.2). This is
an example of the piezoresistive principle, because the change of resistance
is due to the deformation of the crystal structure of the material used for
sensing.
The e¡ects of temperature can be minimized by using another identical
unstrained strain gauge in the bridge as a comparison. This is necessary
not only because the material under investigation will change dimensions
as a result of temperature changes, but because the resistance of the strain
gauge element itself will vary. By using two identical gauges, one
unstrained, in the bridge circuit, these changes can be balanced against
each other, leaving only the change that is due to strain. The sensitivity of
this type of gauge, often called the piezoresistive gauge, is measured in terms
of the gauge factor. This is de¢ned as the fractional change of resistance
divided by the change of strain, and is typically about 2 for a metal wire
gauge and about 100 for a semiconductor type.
STRAIN AND PRESSURE 3
Figure 1.2 Strain gauge use. (a) Physical form of a strain gauge. (b) A bridge
circuit for strain gauge use. By using an active (strained) and a passive (unstrained)
gauge in one arm of the bridge, temperature e¡ects can be compensated if both
gauges are identically a¡ected by temperature. The two gauges are usually side by
side but with only one fastened to the strained surface.

The change of resistance of a gauge constructed using conventional wire
elements (typically thin Nichrome wire) will be very small, as the gauge
factor ¢gures above indicate. Since the resistance of a wire is proportional
to its length, the fractional change of resistance will be equal to the frac-
tional change of length, so that changes of less than 0.1% need to be
detected. Since the resistance of the wire element is small, i.e., of the order
of an ohm or less, the actual change of resistance is likely to be very small
compared to the resistance of connections in the circuit, and this can make
measurements very uncertain when small strains have to be measured.
The use of a semiconductor strip in place of a metal wire makes measure-
ment much easier, because the resistance of such a strip can be considerably
greater, and so the changes in resistance can be correspondingly greater.
Except for applications in which the temperature of the element is high
(for example, gas-turbine blades), the semiconductor type of strain gauge
is preferred. Fastening is as for the metal type, and the semiconductor
material is surface passivated ^ protected from atmospheric contamination
by a layer of oxidation on the surface. This latter point can be important,
because if the atmosphere around the gauge element removes the oxide
layer, then the readings of the gauge will be a¡ected by chemical factors as
well as by strain, and measurements will no longer be reliable.
Piezoelectric strain gauges are useful where the strain is of short duration,
or rapidly changing in value. A piezoelectric material is a crystal whose
ions move in an asymmetrical way when the crystal is strained, so that an
EMF is generated between two faces of the crystal (Figure 1.3). The EMF
can be very large, of the order of several kV for a heavily strained crystal,
Figure 1.3 Piezoelectric crystal principles. The crystal shape is not cubic, but the
directions of the e¡ects are most easily shown on a cube. The maximum electric
e¡ect is obtained across faces whose directions are at right angles to the faces on
which the force is applied. The third axis is called the optical axis because light
passing through the crystal in this direction will be most strongly a¡ected by polari-
zation (see Chapter 3).

so that the gauge can be sensitive, but the output impedance is very high
and usually capacitive. Figure 1.4 illustrates the electrical equivalent
circuit, and Figure 1.5 shows the response around the main resonant fre-
quencies for a quartz crystal. The output of a piezoelectric strain gauge is
not DC, so this type of gauge is not useful for detecting slow changes, and
its main application is for acceleration sensing (see Chapter 2).
Two major problems of strain gauge elements of any type are hysteresis
and creep. Hysteresis means that a graph of resistance change plotted
against length change does not follow the same path of decreasing stress as
for increasing stress (Figure 1.6). Unless the gauge is over-stretched, this
e¡ect should be small, of the order of 0.025% of normal readings at the
Figure 1.4 The equivalent circuit of a crystal. This corresponds to a series
resonant circuit with very high inductance, low capacitance and almost negligible
resistance.
Figure 1.5 The electrical characteristics of a typical quartz crystal.

most. Overstretching of a strain gauge will cause a large increase in hyster-
esis, and, if excessive, will cause the gauge to show a permanent change of
length, making it useless until it can be recalibrated. The other problem,
creep, refers to a gradual change in the length of the gauge element which
does not correspond to any change of strain in the material that is being
measured. This also should be very small, of the order of 0.025% of normal
readings. Both hysteresis and creep are non-linear e¡ects which can never
be eliminated but which can be reduced by careful choice of the strain
gauge element material. Both hysteresis and creep increase noticeably as
the operating temperature of the gauge is raised.
LOAD CELLS
Load cells are used in electronic weighing systems. A load cell is a force
transducer that converts force or weight into an electrical signal. Basically,
the load cell uses a set of strain gauges, usually four connected as a Wheat-
stone-bridge circuit. The output of the bridge circuit is a voltage that is pro-
portional to the force on the load cell. This output can be processed
directly, or digitized for processing.
1.2 Interferometry
Laser interferometry is another method of strain measurement that
presents considerable advantages, not least in sensitivity. Though the prin-
ciples of the method are quite ancient, its practical use had to wait until
suitable lasers and associated equipment had been developed, along with
practicable electronic methods of reading the results. Before we can look at
Figure 1.6 The hysteresis e¡ect on a strain gauge, greatly exaggerated. The graph
is linear for increasing strain, but does not take the same path when the strain is
decreasing. This results in the gauge having permanently changed resistance when
the strain is removed.

what is involved in a laser interferometer strain gauge, we need to under-
stand the basis of wave interference and why it is so di¤cult to achieve
with light.
All waves exhibit interference (Figure 1.7). When two waves meet and
are in phase (peaks of the same sign coinciding), then the result is a wave
of greater amplitude, a reinforced wave. This is called constructive interfer-
ence. If the waves are in opposite phase when they meet, then the sum of
the two waves is zero, or a very small amplitude of wave, and this is destruc-
tive interference. The change from constructive to destructive interference
therefore occurs for a change of phase of one wave relative to another of
half a cycle. If the waves are emitted from two sources, then a movement
of one source by a distance equal to half a wavelength will be enough to
change the interference from constructive to destructive or vice versa.
If the waves that are used have a short wavelength, then the distance of
half a wavelength can be very short, making this an extremely sensitive
measurement of change of distance.
The wavelength of red light is about 700 nm, i.e., 10 7
m or 10 4
mm, so
that a shift of half this distance between two red light sources could be
expected to cause the change between fully constructive and fully destruc-
tive interference ^ in practice we could detect a considerably smaller
change than this maximum amount.
This method would have been used much earlier if it were not for the
problem of coherence. Interference is possible only if the waves that are
interfering are continuous over a su¤ciently long period. Conventional
Figure 1.7 Wave interference. When waves meet and are in phase (a), the ampli-
tudes add so that the resultant wave has a larger amplitude. If the waves are in
antiphase (b), then the resultant is zero or a wave of small amplitude.

light generators, however, do not emit waves continuously. In a light source
such as a ¢lament bulb or a £uorescent tube, each atom emits a pulse of
light radiation, losing energy in the process, and then stops emitting until
it has regained energy. The light is therefore the sum of all the pulses from
the individual atoms, rather than a continuous wave. This makes it imposs-
ible to obtain any interference e¡ects between two separate normal sources
of light, and the only way that light interference can normally be demon-
strated using such sources is by using light that has passed through a
pinhole to interfere with its own re£ection, with a very small light path dif-
ference.
The laser has completely changed all this. The laser gives a beam in
which all the atoms that contribute light are oscillating in synchronization;
this type of light beam is called coherent. Coherent light can exhibit interfer-
ence e¡ects very easily, and has a further advantage of being very easy to
obtain in accurately parallel beams from a laser. The interferometer makes
use of both of these properties as illustrated in Figure 1.8.
Figure 1.8 Principles of wave interferometry. The set-up of laser and glass plates is
shown in (a). The glass plates will pass some light and re£ect some, so that both the
re£ector and the screen will receive some light from the laser beam. In addition,
the light re£ected from the re£ector will also strike the screen, causing an interfer-
ence pattern (b). For a movement of half of one wavelength of the re£ector, the
pattern will move a distance equal to the distance between bands on the screen.

Light from a small laser is passed to a set of semi-re£ecting glass plates
and some of the light is re£ected onto a screen. The rest of the light is
aimed at a re£ector, so that the re£ected beam will return to the glass
plates and also be re£ected to the screen. Now this creates an interference
pattern between the light that has been re£ected from the outward beam
and the light that has been re£ected from the returning beam. If the
distant re£ector moves by one quarter of a wavelength of light, the light
path of the beam to and from the re£ector will change by half a wavelength,
and the interference will change between constructive and destructive.
Since this is a light beam, this implies that the illumination on the screen
will change between bright and dark. A photocell can measure this
change, and by connecting the photocell through an ampli¢er to a digital
counter, the number of quarter wavelengths of movement of the distant
re£ector can be measured electronically.
The interferometer is often much too sensitive for many purposes. For
example, the e¡ect of changing temperatures is not easy to compensate for,
though this can be done by using elaborate light paths in which the two
interfering beams have travelled equal distances, one in line with the stress
and the other in a path at right angles. An advantage of this method is
that no physical connection is made between the points whose distance is
being measured; there is no wire or semiconductor strip joining the points;
the main body of the interferometer is in one place and the re£ector in
another. The distance between the main part of the device and the
re£ector is not ¢xed, the only restraint being that the distance must not
exceed the coherence distance for the laser. This is the average distance over
which the light remains coherent, and is usually at least several metres for
a laser source.
1.3 Fibre optic methods
Developments in the manufacture and use of optical ¢bres have led to these
devices being used in the measurement of distance changes. The optical
¢bre (Figure 1.9) is composed of glass layers and has a lower refractive
index for the outer layer than for the inner. This has the e¡ect of trapping
a light beam inside the ¢bre because of the total internal re£ection e¡ect
(Figure 1.10). When a light ray passes straight down a ¢bre, the number of
internal re£ections will be small, but if the ¢bre is bent, then the number of
re£ections will be considerably increased, and this leads to an increase in
the distance travelled by the light, causing a change in the time needed,
and hence to a change in the phase.
This change of phase can be used to detect small movements by using the
type of arrangement shown in Figure 1.11. The two jaws will, as they
move together, force the optical ¢bre to take up a corrugated shape in
which the light beam in the ¢bre will be re£ected many times. The extra

distance travelled by the beam will cause a delay that can be detected by
interferometry, using a second beam from an unchanged ¢bre. The sensor
must be calibrated over its whole range, because there is no simple relation-
ship between the amount of movement and the amount by which the light
is delayed.
Figure 1.9 Optical ¢bre construction. The optical ¢bre is not a single material but
a coaxial arrangement of transparent glass or (less usefully) plastics. The materials
are di¡erent and refract light to di¡erent extents (refractivity) so that any light ray
striking the junction between the materials is re£ected back and so trapped inside
the ¢bre.
Figure 1.10 Total internal re£ection. When a ray of light passes from an optically
dense (highly refractive) material into a less dense material, its path is refracted
away from the original direction (a) and more in line with the surface. At some
angle (b), the refracted beam will travel parallel to the surface, and at glancing
angles (c), the beam is completely re£ected. The use of two types of glass in an
optical ¢bre ensures that the surface is always between the same two materials, and
the outer glass is less refractive than the inner so as to ensure re£ection.

1.4 Pressure gauges
Pressure in a liquid or a gas is de¢ned as the force acting per unit area of
surface. This has the same units as mechanical stress, and for a solid
material, the force/area quantity is always termed stress rather than
pressure. For a solid, the amount of stress would be calculated, either from
knowledge of force and area of cross-section, or from the amount of strain.
Where the stress is exerted on a wire or girder, the direct calculation of
stress may be possible, but since strain can be measured by electronic
methods, it is usually easier to make use of the relationship shown in Table
1.1.
Young's modulus is a quantity that is known for each material, or which
can be measured for a sample of material. The stress is stated in units of
Figure 1.11 Using optical ¢bres to detect small distance changes. The movement
of the jam distorts one ¢bre, forcing the light paths to take many more re£ections
and thus increasing the length of the total light path. An interference pattern can
be obtained by comparing this to light from a ¢bre that is not distorted, and the
movement of the pattern corresponds to the distortion of one ¢bre. The sensitivity
is not so great as that of direct interferometry, and the use of ¢bres makes the
method more generally useful, particularly in dark liquids or other surroundings
where light beams could not normally penetrate.

N/m2
(newton per square metre), and is normally a large quantity. When
pressure in a liquid or gas is quoted, the units of N/m2
can also be termed
pascals (Pa). Since the pascal or N/m2
is a small unit, it is more usual to
work with kilo-pascals (kPa), equal to 1000 Pa. For example, the `normal'
pressure of the atmosphere is 101.3 kPa.
The measurement of pressure in liquids and gases covers two distinct
ranges. Pressure in liquids usually implies pressures greater than
atmospheric pressure, and the methods that are used to measure pressures
of this type are similar for both liquids and gases. For gases, however, it
may be necessary also to measure pressures lower than atmospheric
pressure, in some cases very much lower than atmospheric pressure. Such
measurements are more specialized and employ quite di¡erent methods.
We shall look ¢rst at the higher range of pressures in both gases and liquids.
The pressure sensors for atmospheric pressure or higher can make use of
both indirect and direct e¡ects. The indirect e¡ects rely on the action of
the pressure to cause displacement of a diaphragm, a piston or other
device, so that an electronic measurement or sensing of the displacement
will bear some relationship to the pressure. The best-known principle is
that of the aneroid barometer, illustrated in Figure 1.12. The diaphragm is
acted on by the pressure that is to be measured on one side, and a constant
(usually lower) pressure on the other side. In the domestic version of the
barometer, the movement of the diaphragm is sensed by a system of levers
which provide a pointer display of pressure.
For electronic measurement, the diaphragm can act on any displacement
transducer and one well-suited type is the capacitive type, illustrated in
Figure 1.13. The diaphragm is insulated from the ¢xed backplate, and the
capacitance between the diaphragm and the backplate forms part of the
resonant circuit of an oscillator. Reducing the spacing between the
diaphragm and the backplate will increase the capacitance, in accordance
with the formula shown in Figure 1.13(b), and so reduce the resonant
Table 1.1 Stress, strain and the elastic constants of Young's modulus and the bulk
modulus.
Stress ˆ strain Young's modulus (for tensile stress)
Example: If measured strain is 0.001 and the Young's modulus for the
material is 20 1010
N/m2
then stress is: 20 1010
0.001 ˆ 20 107
n/m2
For bulk stress use:
Stress ˆ strain bulk modulus
with volume stress ˆ
change of volume
original volume

Figure 1.12 The aneroid barometer principle. The domestic barometer uses an
aneroid capsule with a low pressure inside the sealed capsule. Changes of external
pressure cause the diaphragm to move, and in the domestic barometer these
movements are ampli¢ed by a set of levers.
Figure 1.13 The aneroid capsule (a) arranged for pressure measurement. This is
an inside-out arrangement as compared to the domestic barometer. The pressure to
be measured is applied inside the capsule, with atmospheric air or some constant
pressure applied outside. The movement of the diaphragm alters the capacitance
between the diaphragm and a ¢xed plate, and this change of capacitance can be
sensed electronically. The formula relating capacitance to spacing is shown in (b).

frequency of the oscillator. This provides a very sensitive detection system,
and one which is fairly easy to calibrate.
Although the thin metal corrugated diaphragm makes the device suitable
only for detecting pressures of about atmospheric pressure, the use of a
thicker diaphragm, even a thick steel plate, can permit the method to be
used with very much higher pressures. For such pressure levels, the sensor
can be made in the form of a small plug that can be screwed or welded
into a container. The smaller the cross-section of the plug the better when
high pressures are to be sensed, since the absolute amount of force is the
product of the pressure and the area of cross-section. The materials used
for the pressure-sensing plate or diaphragm will also have to be chosen to
suit the gas or liquid whose pressure is to be measured. For most purposes,
stainless steel is suitable, but some very corrosive liquids or gases will
require the use of more inert metals, even to the extent of using platinum
or palladium.
When a ferromagnetic diaphragm can be used, one very convenient
sensing e¡ect is variable reluctance, as illustrated in principle in Figure
1.14. The variable-reluctance type of pressure gauge is normally used for
fairly large pressure di¡erences, and obviously cannot be used where dia-
phragms of more inert material are required. The method can also be used
for gases, and for a range of pressures either higher or lower than atmo-
spheric pressure.
The aneroid barometer capsule is just one version of a manometer that
uses the e¡ect of pressure on elastic materials. Another very common form
is the coiled £attened tube, as illustrated in Figure 1.15, which responds to
a change of pressure inside the tube (or outside it) by coiling or uncoiling.
This type of sensor can be manufactured for various ranges of pressure
simply by using di¡erent materials and thicknesses of tubing, so that this
method can be used for both small and large pressure changes. The main
drawback as far as electronics is concerned is the conversion from the
Figure 1.14 Using a variable reluctance type of sensing system. The movement of
the diaphragm causes considerable changes in the reluctance of the magnetic path,
and so in the inductance of the coil.

coiling/uncoiling of the tube into electronic signals, and one common
solution is to couple the manometer to a potentiometer.
Another transducing method uses a piezoelectric crystal, usually of
barium titanate, to sense either displacement of a diaphragm connected to
a crystal, or pressure directly on the crystal itself. As explained earlier, this
is applicable more to short duration changes than to steady quantities. For
a very few gases, it may be possible to expose the piezoelectric crystal to
the gas directly, so that the piezoelectric voltage is proportional to the
pressure (change) on the crystal. For measurements on liquids and on
corrosive gases, it is better to use indirect pressure, with a plate exposed to
the pressure which transmits it to the crystal, as in Figure 1.16. This type
of sensor has the advantage of being totally passive, with no need for a
power supply to an oscillator and no complications of frequency measure-
ment. Only a high input impedance voltmeter or operational ampli¢er is
needed as an indicator, and if the sensor is used for switching purposes, the
output from the crystal can be applied directly to a FET op-amp.
Piezoresistive, piezoelectric, and capacitive pressure gauges can be fabri-
cated very conveniently using semiconductor techniques. Figure 1.17 illus-
trates the principle of a piezoresistive pressure gauge constructed on a
silicon base by oxidizing the silicon (to form an insulator) and then deposit-
Figure 1.15 The £attened-tube form of a pressure sensor.
Figure 1.16 Using a piezoelectric crystal detector coupled to a diaphragm for
sensing pressure changes.

ing the piezoresistive elements and the metal connections. Piezoelectric and
capacitive pressure-sensing units can be created using the same methods.
1.5 Low gas pressures
The measurement of low gas pressures is a much more specialized subject.
Pressures that are only slightly lower than the atmospheric pressure of
around 100 kPa can be sensed with the same types of devices as have been
described for high pressures. These methods become quite useless, however,
when the pressures that need to be measured are very low, in the range
usually described as `vacuum'. Pressure sensors and transducers for this
range are more often known as vacuum gauges, and many are still cali-
brated in the older units of millimetres of mercury of pressure. The conver-
sion is that 1 mm of mercury is equal to 133.3 Pa. The high-vacuum region
is generally taken to mean pressures of 10 3
mm, of the order of 0.1 Pa,
although methods for measuring vacuum pressures generally work in the
region from about 1 mm (133.3 Pa) down. Of some 20 methods used for
vacuum measurement, the most important are the Pirani gauge for the
pressures in the region 1 mm to 10 3
mm (about 133 Pa to 0.13 Pa), and
the ion gauge for signi¢cantly lower pressures down to about 10 9
mm, or
1.3 10 7
Pa. A selection of measuring methods is illustrated in Table 1.2.
. All vacuum gauge heads need recalibration when a head is replaced.
The Pirani gauge, named after its inventor, uses the principle that the
thermal conductivity of gases decreases in proportion to applied pressure
for a wide range of low pressures. The gauge (Figure 1.18) uses a hot wire
element, and another wire as sensor. The temperature of the sensor wire is
deduced from its resistance, and it is made part of a resistance measuring
Figure 1.17 A piezoresistive semiconductor pressure gauge element.

Table 1.2 Vacuum gauge types and approximate pressure limits.
Gauge type Pressure range (Pa)
Diaphragm 105
to 10 2
Manometer 105
to 10 3
Pressure balance 1 to 105
Radioactive ionization gauge 10 2
to 105
Compression gauge 10 6
to 103
Viscosity gauge 10 6
to 103
Pirani gauge 10 3
to 104
Thermomolecular gauge 10 7
to 10 1
Penning gauge 10 7
to 10 1
Cold-cathode magnetron gauge 10 8
to 10 2
Hot-cathode ionization gauge 10 5
to 1
High-pressure ionization gauge 10 4
to 10
Hot cathode gauge 10 7
to 10 2
Modulator gauge 10 8
to 10 2
Suppressor gauge 10 9
to 10 2
Extractor gauge 10 10
to 10 2
Bent beam gauge 10 11
to 10 2
Hot-cathode magnetron gauge 10 11
to 10 2
Figure 1.18 The Pirani gauge. One ¢lament is heated, and the other is used as a
sensor of temperature by measuring its resistance. As the pressure in the air sur-
rounding the ¢laments is decreased, the amount of heat conducted between the
¢laments drops, and the change in resistance of the cold ¢lament is proportional to
the change in pressure.

bridge circuit identical to that used for resistive strain gauges. As the gas
pressure around the wires is lowered, less heat will be conducted through
the gas, and so the temperature of the sensor wire will drop, since the
amount of heat transmitted by convection is negligible (because of the
arrangement of the wires) and the amount radiated is also very small
because of the comparatively low temperature of the `hot' wire. Commer-
cially available Pirani gauges, such as those from Leybold, are robust, easy
to use, fairly accurate, and are not damaged if switched on at normal air
pressures. They can be obtained calibrated for various pressure ranges,
each with a range (high/low) of around 104
.
1.6 Ionization gauges
For very low pressure, or high vacuum, measurement, some form of ioniza-
tion gauge is invariably used. There are many gauges of this type, but the
principles are much the same and the di¡erences are easily understood
when the principles are grasped. The ionization gauge operates by using a
stream of electrons to ionize a sample of the remaining gas in the space in
which the pressure is being measured. The positive gas ions are then
attracted to a negatively charged electrode, and the amount of current
carried by these ions is measured. Since the number of ions per unit
volume depends on the number of atoms per unit volume, and this latter
¢gure depends on pressure, the reading of ion current should be reasonably
proportional to gas pressure. The proportionality is fairly constant for a
¢xed geometry of the gauge (Figure 1.19) and for a constant level of
electron emission. The range of the gauge is to about 10 7
mm (0.013 Pa),
which is about the pressure used in pumping transmitting radio valves and
specialized cathode ray tubes.
The most serious problem in using an ionization gauge is that it requires
electron emission into a space that is not a perfect vacuum. The type of
electron emitter that is used in the hot-cathode or Bayard^Alpert gauge is
invariably a tungsten ¢lament. If this is heated at any time when the gas
pressure is too high (above 10 3
mm, 133 Pa), then the ¢lament will be
adversely a¡ected. If, as is usual, the gas whose pressure is being reduced is
air, the operation of the ¢lament at these pressures will result in oxidation,
which will impair electron emission or result in the total burnout of the
¢lament. If hot-cathode ionization gauges are used, as they nearly always
are, in conjunction with other gauges, usually Pirani gauges, then it should
be possible to interlock the supplies so that the ionization gauge cannot be
turned on until the pressure as indicated by the other gauge, is su¤ciently
low. If this can be done, then the ionization gauge can have a long and
useful life. A spare gauge head should always be held in stock, however, in
case of ¢lament damage, because tungsten ¢laments are delicate,
particularly when at full working temperature. Each gauge head will

need to be calibrated if precise measurements of low pressure are
required.
A common variation on the ionization method is the Penning gauge, which
uses electron emission from a point (a cold-cathode emitter). This avoids
cathode damage from oxidation and from £uorine, and the same
advantage is claimed for ionization gauges that use thoria-coated iridium
(ThOIr) cathodes. A tungsten ¢lament is not poisoned by halogen gases,
and is preferred for applications that involve £uorine, chlorine or iodine
gases.
Other variants on the ionization gauge arise because a simple electron
beam in a con¢ned space is not necessarily a very e¤cient means of
ionizing the residual gas in that space, because only the atoms in the path
of the beam can be a¡ected. If the electron beam is taken through a longer
path, more atoms can be bombarded, and more ions generated from a
given volume of gas, and so the sensitivity of the device is greatly
increased. The usual scheme is to use a magnetic ¢eld to convert the
normal straight path of the electron beam into a spiral path that can be of
Figure 1.19 The simplest form of an ionization gauge. The grid is a loosely wound
spiral of wire surrounding the ¢lament, and exerts little control on the electron
stream. With a constant high current of electrons to the anode, positive ions from
the remaining gas are attracted to the grid and the resulting grid current is
measured and taken as proportional to gas pressure.

a much greater total length. This is the magnetron principle, used in the
magnetron tube to generate microwave frequencies by spinning electrons
into a circular path that just touches a metal cavity, so that the cavity
resonates and so modulates the electron beam.
The much greater sensitivity that can be obtained in this way is bought at
the price of having another parameter, the magnetic ¢eld £ux density, that
will have to be controlled in order to ensure that correct calibration is main-
tained. The magnetic ¢eld is usually applied by means of a permanent
magnet, so that day-to-day calibration is good, but since all permanent
magnets lose ¢eld strength over a long period, the calibration should be
checked annually. Gauges of this type can be used down to very low
pressures, of the order of 10 11
Pa.
. On the other end of the pressure range, a radioactive material can be used
as a source of ionization, and this allows measurements up to much
higher ranges of pressure, typically up to 105
Pa.
1.7 Transducer use
The devices that have been described are predominantly used as sensors,
because with a few exceptions, their e¤ciency of conversion is very low
and to achieve transducer use requires the electrical signals to be
ampli¢ed. The piezoelectric device used for pressure sensing is also a useful
transducer, and can be used in either direction. Transducer use of piezoelec-
tric crystals is mainly con¢ned to the conversion between pressure waves in
a liquid or gas and electrical AC signals, and this use is described in detail
in Chapter 5. The conversion of energy from an electrical form into stress
can be achieved by the magnetically cored solenoid, as illustrated in Figure
1.20. A current £owing in the coil creates a magnetic ¢eld, and the core
will move so as to make the magnetic £ux path as short as possible. The
amount of force can be large, so that stress can be exerted (causing strain)
on a solid material. If the core of the solenoid is mechanically connected to
a diaphragm, then the force exerted by the core can be used to apply
pressure to a gas or a liquid. In general, though, there are few applications
for electronic transducers for strain or pressure and the predominant use of
devices in this class is as sensors.
Figure 1.20 The solenoid, which is a current-to-mechanical stress transducer.

Chapter 2
Position, direction, distance
and motion
2.1 Position
Position, as applied in measurement, invariably means position relative to
some point that may be the Earth's north pole, the starting point of the
motion of an object, or any other convenient reference point. Methods of
determining position make use of distance and direction (angle) informa-
tion, so that a position can be speci¢ed either by using rectangular
(Cartesian) co-ordinates (Figure 2.1) or by polar co-ordinates (Figure 2.2).
Position on £at surfaces, or even on the surface of the Earth, can be
speci¢ed using two dimensions, but for air navigational purposes three-
dimensional co-ordinates are required. For industrial purposes, positions
are usually con¢ned within a small space (for example, the position of a
robot tug) and it may be possible to specify position with a single number,
such as the distance travelled along a rail.
In this chapter we shall look at the methods that are used to measure
direction and distance so that position can be established either for large-
or small-scale ranges of movement. There are two types of distance
sensing: the sensing of distance to some ¢xed point, and the sensing of
distance moved, which are di¡erent both in principle and in the methods
that have to be used. The methods that are applied for small-scale sensing
of position appear at ¢rst glance to be very di¡erent, but they are in fact
very similar in principle.
Since position is related to distance (the di¡erence between two
positions), velocity (rate of change of position) and acceleration (rate of
change of velocity), we shall look at sensors for these quantities also. Rota-
tional movement is also included because it is very often the only
movement in a system and requires rather di¡erent methods. In addition,

of course, the rotation of a wheel is often a useful measurement of linear
distance moved.
2.2 Direction
The sensing of direction on the Earth's surface can be achieved by observing
Figure 2.1 The Cartesian co-ordinate system. This uses measurements in two
directions at right angles to each other as reference axes, and the position of a point
is plotted by ¢nding its distance from each axis. For a three-dimensional location,
three axes, labelled x, y and z, can be used. The ¢gure also shows the conversion of
two-dimensional Cartesian co-ordinates to polar form.
Figure 2.2 Polar co-ordinates make use of a ¢xed point and direction. The
distance from the ¢xed point, and the angle between this line and the ¢xed
direction, are used to establish a two-dimensional position. For a three-dimensional
location, an additional angle is used. The ¢gure also shows conversion of two-dimen-
sional polar co-ordinates to Cartesian.

and measuring the apparent direction of distant stars, by using the Earth's
magnetic ¢eld, by making use of the properties of gyroscopes, or by radio
methods, the most modern of which are satellite direction-¢nders.
Starting with the most ancient method, observation of stars, otherwise
known as Celestial navigation, depends on making precise angle measure-
ments. The basic (two-dimensional) requirements are a time measurement
and tables of data. For example, a sextant can be used to measure the angle
of a known star above the horizon, a precise clock (a chronometer) that can
be read to the nearest second (one second error corresponds to about 1
4
nautical mile in distance) is used to keep Greenwich mean time, and a
copy of a databook such as the `Nautical Almanac' will allow you to ¢nd
your position from these readings.
The simplest form of celestial navigation is the observation of local noon.
The sextant is used to measure the angle of the sun above the horizon at
local noon, and the Almanac will ¢nd the latitude corresponding to this
angle value. By referring to the chronometer you can ¢nd the di¡erence
between local noon and Greenwich noon, and so ¢nd, using the Almanac,
the longitude. The latitude and longitude ¢gures establish your position.
Navigation by the local noon method is simple, but it is not necessarily
always available, and although it has been the mainstay of navigation
methods in the past, it was superseded several centuries ago by true
celestial navigation, which relies on making a number of observations on
known stars. The advantage of using stars is that you do not have to wait
for a time corresponding to local noon. The process is summarized in
Table 2.1.
The traditional compass uses the e¡ect of the Earth's magnetic ¢eld on a
small magnetized needle that is freely suspended so that the needle points
along the line of the ¢eld, in the direction of magnetic north and south.
The qualifying word `magnetic' is important here. The magnetic north
pole of the Earth does not coincide with the geographical north pole, nor is
it a ¢xed point. Any direction that is found by use of a magnetic form of
POSITION, DIRECTION, DISTANCE AND MOTION 23
Table 2.1 A true celestial navigation method.
. For each of several identi®ed stars, measure the altitude of a star and the
Greenwich time.
. Calculate the position of the star at the time of your observation, using
the Almanac.
. From this position calculation, calculate for each star you have observed
what altitude and azimuth (direction) you should have observed.
. Compare each measured altitude with each calculated altitude to give
a ®gure of offset.
. Plot each offset on a chart as a line of position.
. Find your true position as the point where several lines of position cross.

compass must therefore be corrected for true north if high accuracy is
required. The size and direction of this correction can be obtained from
tables of magnetic constants (the magnetic elements) that are published for
the use of navigators. The drift speed and direction of the magnetic north
pole can be predicted to some extent, and the predictions are close enough
to be useful in fairly precise navigation in large areas on the Earth's surface.
For electronic sensing of direction from the Earth's magnetic ¢eld, it is
possible to use a magnetic needle fastened to the shaft of a servo-generator,
but this type of mechanical transducer is rarely used now that Hall-e¡ect
sensors are available. The Hall e¡ect is an example of the action of a
magnetic e¡ect on moving charged particles, such as electrons or holes,
and it was the way in which hole movement in metals and semiconductors
was ¢rst proved. The principle is a comparatively simple one, but for most
materials, detecting the e¡ect requires very precise measurements.
The principle is illustrated in Figure 2.3. If we imagine a slab of material
carrying current from left to right, this current, if it were carried entirely
by electrons, would consist of a £ow of electrons from right to left. Now for
a current and a magnetic ¢eld in the directions shown, the force on the
conductor will be upwards, and this force is exerted on the particles that
carry the current, the electrons. There should therefore be more electrons
Figure 2.3 The Hall e¡ect. Hall showed that the force of a magnetic ¢eld on a
current carrier was exerted on the carriers, and would cause de£ection. The de£ec-
tion leads to a di¡erence in voltage across the material, which is very small for a
metal because of the high speeds of the carriers, but much larger for a semiconduc-
tor.

on the top surface than on the bottom surface, causing a voltage di¡erence,
the Hall voltage, between the top and bottom of the slab. Since the
electrons are negatively charged, the top of the slab is negative and the
bottom positive. If the main carriers are holes, the voltage direction is
reversed.
The Hall voltage is very small in good conductors, because the particles
move so rapidly that there is not enough time to de£ect a substantial
number in this way unless a very large magnetic ¢eld is used. In semicon-
ductor materials, however, the particles move more slowly, and the Hall
voltages can be quite substantial, enough to produce an easily measurable
voltage for relatively small magnetic ¢elds such as the horizontal
component of the Earth's ¢eld. Small slabs of semiconductor are used for
the measurement of magnetic ¢elds in Hall-e¡ect £uxmeters and in elec-
tronic compasses. A constant current is passed through the slab, and the
voltage between the faces is set to zero in the absence of a magnetic ¢eld.
With a ¢eld present, the voltage is proportional to the size of the ¢eld, but
the practical di¤culty is in determining direction.
The direction of maximum ¢eld strength is in a line drawn between the
magnetic north and south poles, but because the Earth is (reasonably
exactly) a sphere, such a line, except at the equator, is usually directed
into the Earth's surface, and the angle to the horizontal is known as the
angle of dip (Figure 2.4). The conventional magnetic compass needle gets
around this problem by being pivoted and held so that it can move only in
a horizontal plane, and this is also the solution for the Hall-e¡ect detector.
A precision electronic compass uses a servomotor to rotate the Hall slab
under the control of a discriminator circuit which will halt the servomotor
in the direction of maximum ¢eld strength with one face of the Hall slab
positive. By using an analogue to digital converter for angular rotation, the
direction can be read out in degrees, minutes and seconds. The advantages
of this system are that the e¡ects of bearing friction that plague a conven-
tional compass are eliminated, and the reading is not dependent on a
human estimate of where a needle is placed relative to a scale. Many con-
ventional needle compasses are immersed in spirit, and the refractivity of
the liquid causes estimates of needle position to be very imprecise, unless
the scale is backed by a mirror in order that parallax can be avoided by
placing the eye so that the needle and its re£ection coincide.
The global nature of the Earth's magnetic ¢eld makes it particularly
convenient for sensing direction, but the irregular variations in the ¢eld
cause problems, and other methods are needed for more precise direction-
¢nding, particularly over small regions. Magnetic compasses served the
Navy well in the days of wooden ships, and when iron (later, steel) construc-
tion replaced wood, magnetic compasses could still be used provided that
the deviation between true magnetic north and apparent north (distorted
by the magnetic material in the ship) could be calculated and allowed for,
using deviation tables. By the early part of the 20th century, it was found

that the magnetization of a warship could be a¡ected by ¢ring guns or by
steering the same course for a long period, and that deviation tables could
not be relied upon to correct for these alterations. Submarines provided
even greater di¤culties because of their use of electric motors, and also
because the interior is almost completely shielded by ferrous metal from
the Earth's ¢eld.
This led in 1910 to the development of the Anschu
« tz gyrocompass. The
principle is that a spinning £ywheel has directional inertia, meaning that it
resists any attempt to alter the direction of its axis. If the £ywheel is
suspended so that the framework around it can move in any direction
without exerting a force on the £ywheel, then if the axis of the £ywheel has
been set in a known position, such as true north, this direction will be main-
tained for as long as the £ywheel spins.
The early Anschu
« tz models were disturbed by the rolling motion of a ship,
and a modi¢ed model appeared in 1912. This compass model was super-
seded, in 1913, by the Sperry type of gyrocompass. Full acceptance of gyro-
compasses did not occur until errors caused by the ships' movement could
be eliminated. Suspension frameworks were developed from the old-
fashioned gimbals that were used for ships' compasses, and the wartime
Figure 2.4 The angle of dip shows the actual direction of the Earth's ¢eld, which
in the northern hemisphere is always into the surface of the Earth.

gyrocompasses maintained the rotation of the spinning wheel by means of
compressed air jets.
Gyrocompass design was considerably improved for use in air navigation
in World War II. The gyrocompass has no inherent electrical output,
however, and it is not a simple matter to obtain an electrical output
without placing any loading on the gyro wheel. Laser gyroscopes making
use of rotating light beams have been developed, but are extremely special-
ized and beyond the scope of this book. In addition, gyroscopes are not
used to any extent in small-scale direction ¢nding for industrial applica-
tions.
Radio has been used for navigational purposes for a long time, in the form
of radio beacons that are used in much the same way as light beacons were
used in the past. The classical method of using a radio beacon is illustrated
in Figure 2.5 and consists of a receiver that can accept inputs from two
aerials, one a circular coil that can be rotated and the other a vertical
whip. The signal from the coil aerial is at maximum when the axis of the
coil is in line with the transmitter, and the phase of this maximum signal
will be either in phase with the signal from the vertical whip aerial or in
antiphase, depending on whether the beacon transmitter is ahead or astern
of the coil. By using a phase-sensitive receiver that indicates when the
phases are identical, the position of maximum signal ahead can be found,
and this will be the direction of the radio beacon.
Figure 2.5 The radio direction-¢nder principle. The output from the vertical
aerial is obtained from the electrostatic ¢eld of the wave, and does not depend on
direction. The magnetic portion of the wave will induce signals in a coil, but the
phase of these signals depends on the direction of the transmitter. By combining the
signals from the two aerials, and turning the coil, the direction of the transmitter
can be found as the direction of maximum signal.

The form of radio direction-¢nding that dated from the early part of the
20th century was considerably improved by Watson-Watt, who also
invented radar. The original Watson-Watt system used multiple-channel
reception with two dipoles, arranged to sense directions at right angles to
each other and a single whip aerial connected to separate receivers. A later
improvement used a single channel, and modern methods make use of
digital signal processing to establish direction much more precisely.
Satellite direction-¢nding is an extension of these older systems and
depends on the supply of geostationary satellites. A geostationary satellite is
one whose angular rotation is identical to that of the Earth, so that as the
Earth rotates the satellite is always in the same position relative to the
surface of the planet. The navigation satellites are equipped with transpon-
ders that will re-radiate a coded received signal. At the surface, a vessel
can send out a suitably coded signal and measure the time needed for the
response. By signalling to two satellites in di¡erent positions, the position
on the Earth's surface can be established very precisely ^ the precision
depends on the frequency that is used, and this is generally in the millimetre
range.
2.3 Distance measurement ± large scale
The predominant method of measuring distance to a target point on a large
scale is based on wave re£ection of the type used in radar or sonar. The
principle is that a pulse of a few waves is sent out from a transmitter,
re£ected back from some distant object and detected by a receiver when it
returns. Since the speed of the waves is known, the distance of the re£ector
can be calculated from the time that elapses between sending and
receiving. This time can be very short, of the order of microseconds or less,
so that the duration of the wave pulse must also be very short, a small
fraction of the time that is to be measured. Both radar and sonar rely
heavily on electronic methods for generating the waveforms and measuring
the times, and although we generally associate radar with comparatively
long distances, we should remember that radar intruder alarms are
available whose range is measured in metres rather than in kilometres.
Figure 2.6 shows a block diagram of a radar system for distance measure-
ment, such as would form the basis of an aircraft altimeter. A sonar system
for water depth would take the same general form, but with di¡erent trans-
ducers (see Chapter 5). The important di¡erence is in wave speeds;
3 108
m/s for radio waves in air, but only 1.5 103
m/s for sound waves
in sea-water.
Where radar or sonar is used to provide target movement indications, the
time measurements will be used to provide a display on a cathode ray
tube, but for altimeters or depth indications, the time can be digitally
measured and the ¢gure for distance displayed. Before the use of radar alti-

meters, the only method available was barometric, measuring the air
pressure by an aneroid capsule and using the approximate ¢gure of
3800 Pa change of pressure per kilometre of altitude. The air pressure,
however, alters with other factors such as humidity, wind-speed and tem-
perature, so that pressure altimeters are notoriously unreliable. Even if
such an altimeter were to give a precise reading, the height that it
measures will either be height above sea-level or the height relative to the
altitude of the place in which the altimeter was set, rather than true
height. It is, in fact, remarkable that air travel ever became a reality with
such a crude method of height measurement.
Position measurement on a smaller scale (e.g. factory £oor scale) can
make use of simpler methods, particularly if the movement is con¢ned in
some way, such as by rails or by the popular method of making a robot
trolley follow buried wires or painted lines. For con¢ned motions on rails
or over wires, the distance from a starting point may be the only measure-
ment that is needed, but it is more likely that the movement is two-
dimensional. Over small areas of a few square metres, an arti¢cially
generated magnetic ¢eld can be used along with magnetic sensors of the
types already described. Radio beacon methods, using very low power
transmitters, are also useful, and ultrasonic beacons can be used; although
problems arise if there are strong re£ections from hard surfaces. For a full
Figure 2.6 The block diagram for a simple radar system. The time required for a
pulse of microwave signal to travel to the target and back is displayed in the form
of a distance on a cathode ray tube. The transmitter and receiver share the same
aerial, using a TR/ATR (transmit/anti-transmit) stage to short-circuit the receiver
while the transmitted pulse is present.

discussion of the methods as distinct from the sensors, the reader should
consult a text on robotics.
2.4 Distance travelled
The sensing of distance travelled, as distinct from distance from a ¢xed
reference point, can make use of a variety of sensors. In this case, we shall
start with the sensors for short distance movements, because for motion
over large distances the distance travelled will generally be calculated by
comparing position measurements rather than directly. Sensors for small
distances can make use of resistive, capacitive or inductive transducers in
addition to the use of interferometers (see Chapter 1) and the millimetre-
wave radar methods that have been covered earlier. The methods that are
described here are all applicable to distances in the range of a few milli-
metres to a few centimetres. Beyond this range the use of radar methods
becomes much more attractive.
A simple system of distance sensing is the use of a linear (in the mech-
anical sense) potentiometer (Figure 2.7). The moving object is connected
to the slider of the potentiometer, so that each position along the axis will
correspond to a di¡erent output from the slider contact ^ either AC or DC
can be used since only amplitude needs to be measured. The output can be
displayed on a meter, converted to digital signals to operate a counter, or
used in conjunction with voltage level sensing circuits to trigger some
action when the object reaches some set position. The main objections to
this potentiometric method are: that the range of movement is limited by
the size of potentiometers that are available (although purpose-built poten-
tiometers can be used), and that the friction of the potentiometer is an
obstacle to the movement. The precision that can be obtained depends on
how linear (in the electrical sense) the winding can be made, and 0.1%
should be obtainable with reasonable ease.
Figure 2.7 A sensor for linear displacement in the form of a linear potentiometer.
The advantage of this type of sensor is that the output can be a steady DC or AC
voltage that changes when the displacement changes.

An alternative that is sometimes more attractive, but often less practical,
is the use of a capacitive sensor. This can take the form of a metal plate
located on the moving object and moving between two ¢xed plates that are
electrically isolated from it. The type of circuit arrangement is illustrated
in Figure 2.8, showing that the ¢xed plates are connected to a transformer
winding so that AC signals in opposite phase can be applied. The signal at
the moveable plate will then have a phase and amplitude that depends on
its position, and this signal can be processed by a phase-sensitive detector
to give a DC voltage that is proportional to the distance from one ¢xed
plate. Because the capacitance between plates is inversely proportional to
plate spacing, this method is practicable only for very short distances, and
is at its most useful for distances of a millimetre or less.
An alternative physical arrangement of the plates is shown in Figure 2.9,
in which the spacing of the ¢xed plates relative to the moving plate is small
and constant, but the movement of the moving plate alters the area that is
common to the moving plate and a ¢xed plate. This method has the
advantage that an insulator can be used between the moving plate and the
¢xed plates, and that the measurable distances can be greater, since the sen-
sitivity depends on the plate areas rather than on variable spacing.
The most commonly used methods for sensing distance travelled on the
small scale, however, depend on induction. The basic principle of
induction methods is illustrated in Figure 2.10, in which two ¢xed coils
enclose a moving ferromagnetic core. If one coil is supplied with an AC
signal, then the amplitude and phase of a signal from the second coil
depends on the position of the ferromagnetic core relative to the coils. The
amplitude of signal, plotted against distance from one coil, varies as shown
Figure 2.8 The capacitor plate sensor in one of its forms. A change in the position
of the moving plate will cause the voltage between this plate and the centre tap of
the transformer to change phase, and this phase change can be convened into a DC
output from the phase-sensitive detector.

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in the windows—the cold air has condensed and frozen the water
breathed out from our lungs, and snow has been known to fall in a
ball-room when a cold current of air was admitted.
People are sometimes apt to think that if the sun were very hot,
glaciers, and such icy masses, would diminish; but we think after
what has been said respecting the power of the sun’s rays to
evaporate water, all will see that the contrary is the fact. Without
sun-heat we should have no cloud, and as clouds give us rain and
snow and ice and glacier, we must come quickly to the conclusion
that glaciers and snow are the direct results of the heat of the sun.
The “light” rays of the sun do not penetrate snow, and that is why
our eyes are so affected in snowy regions. The poor Jeannette
sufferers a short time since were blinded by reflected light, and dark
spectacles are worn on all Alpine expeditions. The invisible rays, as
we have said, dissolve the ice into rivers.
The atmosphere produces clouds by expansion of vapour, which
chills or cools it, and it descends as rain. To prove that expansion
cools air is easy by experiment, but if we have no apparatus we
must make use of our mouths. In the body the breath is warm, as
we can assure ourselves by opening our mouths wide and breathing
upon our hands. But close the mouth and blow the same breath
outwards through a very small aperture. It is in a slight degree
compressed as it issues from the lips, and expanding again in the
atmosphere feels colder. Air compressed into a machine and
permitted to escape will form ice.

Fig. 717.—Cumulus cloud.
Water is present in clouds which assume very fantastic and beautiful
forms. We know nothing more enjoyable than to sit watching the
masses of cumuli on a fine afternoon. The grand masses built up like
the Alps appear to be actual mountains, and yet we know they are
but vapour floating in the air, and presently to meet with clouds of
an opposite disposition, and produce a thunderstorm with torrents of
rain. Those who will devote a few minutes every day to the steady
examination of clouds, will not be disappointed. They give us all the
grandeur of terrestrial scenery. Mountains, plains, white “fleecy
seas,” upon which tiny cloudlets float, and low upon the imaginary
yet apparent horizon, rise other clouds and mimic mountains far and
farther away in never-ending distance.
A pretty, light, feathery cloud, with curling tips and fibres, is known
as cirrus, and exists at a very great elevation. Gay-Lussac went up in
a balloon 23,000 feet, and even at that height the cirri was far above
him in space. We can readily understand that at such an extreme
elevation they must be very cold, and they are supposed to consist
of tiny particles of ice. Such clouds as these are very frequently
observed at night, as cirro-cumulus around the moon, and a
yellowish halo, apparent to all observers, is thought to be coloured
by the icy particles of the lofty cirrus. The beautiful and varied

phenomena of perihelia, etc., are due also to the snowy or icy flakes
of the cirri and cirri-cumuli, caused by the refraction of light from the
frozen particles. These cirri clouds are indicative of changeable
weather as “Mares’ tail” skies, and long wisps of cloud, foretelling
storm.
The cirro-cumulus is the true “mackerel” sky, and is formed by the
cirri falling a little and breaking off into small pieces of cumulus,
which is a summer (day) cloud generally, and appears in the
beautifully massive and rounded forms so familiar. The stratus is, as
its name implies, a cloudy layer formed like strata of rock. It is
generally observable at night and in the winter. It often appears
suddenly in the sky consequent upon diminished pressure or a rapid
fall of temperature. It is low-lying cloud sometimes, and at night
forms fogs.
Fig. 718.—Cirrus cloud.
The cirro-stratus is perceived in long parallel lines, and indicates
rain; when made-up rows of little curved clouds it is a certain
prophet of storm, and when viewed as haze is also indicative of rain
or snow. “Mock-suns” and halos are often observed in the cirro-
stratus.

The nimbus is the rain-cloud, or condition of a cloud in which rain
falls from it. It is upon this rain-cloud we can perceive the rainbow,
and on no other cloud, but otherwise only in the sky.
We have now seen the varieties of cloud and their common origin
with fogs and mists, which differ from them only in the elevation at
which they come into existence, according to the condition of the
atmosphere.
The uses of clouds are many and varied. Their first and most
apparent use seems to be the collection and distribution of rain upon
the earth. But besides this, they shelter us from the too great heat
of the sun, and check the evaporation at night. Supposing we had
no clouds we should have no rain. If we had no rain the earth would
dry up, and the globe would appear as the side of the moon appears
—a waterless desert. The invisible vapour in the atmosphere will
produce cloud, but the moon can have no atmosphere in that sense.
Vapour will also absorb heat, and intercept the sun’s heat rays,
acting much as clouds do in preventing radiation and great changes
of temperature.33
All animals and plants depend upon moisture in the atmosphere as
much as upon the varying degrees of warmth. A dry east wind
effects us all prejudicially; warm, soft airs influence us again in other
ways. Air will be found drier as a rule in continents than in islands or
maritime districts, and this will account for the clearness of the sky
in continental regions. Fogs and mists arise when the air is what is
termed saturated with moisture, and colder than the earth or waters
upon it. So the celebrated and dangerous fogbanks of Newfoundland
arise from the warm water of the Gulf Stream, which is higher in
temperature than the air already saturated. And the same effect is
produced when a warm wind blows against a cold mountain; the air
is cooled, and condenses in cloud.
The cooling of the breath by the exterior air is exemplified in winter
when we can perceive the vapour issuing from our mouths as we
speak.

Fig. 719.—Storm clouds.
Rain, Snow, and Dew.
Rain is produced by the condensation of vapour. “Vesicular vapours,
or minute globules of water filled with air,” compose the clouds, and
at last these vesicles form drops, and get heavy enough to come to
the ground. Perhaps they are not sufficiently heavy to do so, and
then they are absorbed or resolved into vapour again before they
can get so far, because the lower strata of air are not yet saturated,
and can therefore contain more moisture.
On the other hand, we may experience rain from a cloudless sky.
This is no very uncommon case, and occurs in consequence of the
disturbance of the upper strata when warm and cold currents come
into collision and condense the vapours.
Rain is very unequally distributed. We shall find that the region of
calms, which we mentioned in a former page, is also the zone of the
greatest amount of rain. The heated air rises and falls back again,
there being little or no wind to carry it away. The rainy season,
therefore, sets in when a place enters the zone of calms. Equatorial
districts have two rainy seasons, as they enter twice a year into the
region of calms, but most places have only a wet and dry season,
while north and south of the calm region we find rainless districts, or
zones tempered by the trade winds, which are dry winds.

But if we suppose—as indeed is the case in South America—that
these dry winds happen to come in contact with a cool mountain,
the moisture of the air is precipitated in rain. In Australia, on the
contrary, we have portions of land actually burnt up for want of rain,
because the mountain chain breaks the clouds, so to speak, on a
limited corner of the island, while the interior is parched. The winds
also coming over India from the Bay of Bengal discharge clouds and
rain in the Himalayan slopes. So we perceive that the situation of
mountain chains have much to do with the rain-fall, and of necessity,
therefore, with the vegetation and fertility of the land. This is
another noticeable link in the great chain of Nature.
Fig. 720.—Meteorological Observatory, Pic du Midi.
Perhaps it may now be understood why westerly and south-westerly
winds bring rain upon our islands, and why the counties such as
Westmoreland and Cumberland and those in Wales receive more rain
than any other part of the United Kingdom. Seathwaite, so well
known to tourists in the lake district, has the proud position of the
wettest place in these islands. We find that when the westerly wind
sets in it has come across the warm Atlantic water and become

laden with moisture, which, when chilled by the mountains, is
precipitated as rain.
The amount of rain that falls in the United Kingdom is carefully
measured by rain-gauges, some of which are extremely simple. The
water is caught in a funnel-mouthed tube, and measured in a
measuring glass every four-and-twenty hours. Thereby we can tell
the annual rainfall in any given district, whether it be twenty inches
or a hundred. One inch of rain actually means one hundred tons of
water falling upon one acre of land. Therefore, if the annual report
of rainfall (including all moisture) be twenty inches, we have an
aggregate of 2,000 tons of water upon every acre of surface within
the district. Twenty inches is a very low estimate. Some places have
an annual rainfall of forty or fifty inches. In Cumberland we find 165
inches has been recorded! If we then multiply these last figures we
get the enormous quantity of 16,500 tons of water upon every acre
of land in the district in one year. It is reported from India that in the
Khasia Hills the average is 610 inches, which must be the maximum
rainfall in the world. At other places, in the north-west provinces, the
fall is only seven inches. Sometimes in tropical rains we find fifteen
inches of rain in a day, and that has been exceeded.
We can now judge of the enormous amount of moisture carried up
by the sun and dispersed over the earth in rain, which swells our
brooks and rivers, cleanses the air of its impurities, supplies our
springs, carries with it into the sea lime from the rocks for the shells
of marine animals, and then leaving its salts, is again evaporated to
form clouds, which discharge the fresh water continually upon the
earth in a never-ceasing rotation.
Snow.
“We all know what Snow is,” you will say, perhaps. Well, then, will
any ordinary young reader tell me what he knows about snow? “It
falls from the sky in white flakes,” says one. “It’s frozen rain,”
remarks another. “Why, snow is snow,” says a third. “There’s nothing
like it; it’s white rain-water frozen.”

Fig. 721.—Crystals of snow.
The last answer we received is the nearest of all. Snow is not snow,
paradoxical as that sounds. Snow is Ice! Flakes of snow are ice-
crystals—white, because reflecting light. In the section of Mineralogy
we mentioned crystals, which are certain definite shapes assumed
by all substances, and we gave many examples of them. Just as
alum crystallizes and rock crystal assumes varied and beautiful
forms, so ice crystallizes into six-rayed stars.
It is to Professor Tyndall that the world is chiefly indebted for the
descriptions of snow crystals and ice flowers. In his work upon “Heat
as a Mode of Motion,” this charming writer shows us the structure of
ice flowers. He describes a snow shower as a “shower of frozen
flowers.” “When snow is produced in calm air,” he says, “the icy
particles build themselves into stellar shapes, each star possessing
six rays.” We annex some drawings of snow crystals, which are,
indeed, wonderfully made. Hear Professor Tyndall once again:—
“Let us imagine the eye gifted with a microscopic power sufficient to
enable us to see the molecules which compose those starry crystals:
to observe the solid nucleus formed and floating in the air; to see it
drawing towards it its allied atoms, and these arranging themselves
as if they moved to music, and ended by rendering that music
concrete.” This “six-rayed star” is typical of lake ice also.

Fig. 722.—Ice crystal.
Snow sometimes reaches us in a partly melted condition; under
these circumstances it is called sleet, and snow being much lighter
than rain (ice is lighter than water), it descends less directly, and
represents about one-tenth the depth of the rain-fall. The use of
snow in warming the earth is universally acknowledged, and as it is
such a bad conductor, a man in a snow hut will soon become
unpleasantly warm.
Fig. 723.—Ice crystal.
Ice is only water in another form, and snow is ice; and it is the air in
the snow that gives it warming properties. These are all simple facts,
which any one by observation and careful reading and study may

soon ascertain for himself. We have another frozen fall of water from
the clouds—viz., hail, which may possibly be the development of
sleet.
Hail is formed by the falling rain being frozen in its descent, or when
different currents meet in the atmosphere. A hail-storm is
accompanied with a rushing sound, as if the hail-stones were
striking against each other. They are very destructive, and actual hail
showers occur in summer more frequently than in winter, and a
peculiarity noticeable with regard to hail is its infrequent occurrence
during the night.
Records of destructive hail storms are plentiful. The hail assumes a
great size, weighing sometimes as much as two ounces, and
measuring several inches round. Thunder and lightning are very
frequent accompaniments of hail showers.
Dew is moisture of the atmosphere deposited on a cool surface—
another form of condensation, in fact. Cold water in a tumbler will
produce a “dew” upon the outside of the glass when carried into a
warm atmosphere. Such is the dew upon the grass. It is produced
by the air depositing moisture as it becomes colder after a warm day
when much vapour was absorbed. Warm air can hold more water
than cold air, and, the saturation point being reached, the excess
falls as dew at the dew (or saturation) point. We have previously
remarked that one use of clouds was to prevent rapid radiation of
heat which they keep below. Under these circumstances—viz., when
a night is cloudy—we shall find much less dew upon the grass than
when a night has been quite clear, because the heat has left the
atmosphere for the higher regions, and has then been kept down by
the clouds; but on a clear night the air has become cooled rapidly by
radiation, and having arrived at saturation point, condensation takes
place.
Dew does not fall, it is deposited; and may be more or less
according to circumstances, for shelter impedes the radiation, and

some objects radiate less heat than others. Hence some objects will
be covered with dew and others scarcely wetted.
When the temperature of the air is very low,—down to freezing
point,—the particles of moisture become frozen, and appear as hoar-
frost upon the ground. Thus dew and hoar-frost are the same thing
under different atmospheric conditions, as are water and ice and
vapour.
We have now come round again almost to whence we started. We
have seen the land and water, and the parts that water, in its various
forms, plays upon the land, and its effects in the air as rain, etc. We
have noticed the winds and air currents as well as the ocean and its
currents. We know what becomes of rain and how it is produced,
and how the sea works upon the shore, and how clouds benefit us.
There are besides some less common phenomena which we will now
proceed to examine.

CHAPTER XLIX.
PHYSICAL GEOGRAPHY. METEOROLOGY
(continued).
ATMOSPHERIC PHENOMENA—THUNDER AND LIGHTNING—AURORA
BOREALIS—THE RAINBOW—MOCK SUNS AND MOCK-MOONS—
HALOS—FATA MORGANA—REFLECTION AND REFRACTION—
MIRAGE—SPECTRE OF THE BROCKEN.
There are a great number of interesting, and to inhabitants of these
islands uncommon,—perhaps we might say fortunately uncommon,
—phenomena, which overtake the traveller in other countries. We
have referred to whirlwinds and tornados, and will now mention two
phenomena connected with these storms. There is the water-spout,
for instance, and sand-pillars in the desert, which are whirled up by
these winds in spiral columns of water and sand respectively. The
tiny whirlwind at cross-roads, which picks up straws and leaves, is
the common appearance of whirling or crossing currents of air.

Fig. 724.—The Waterspout.
Waterspouts, when they are permitted to come near a ship at sea,
or when they break upon land, which is seldom, are very
destructive. The waterspout is begun generally by the agitation of
the sea, and the cloud above drops to meet the water, which at last
unites with it, and then the column of whirling liquid, tremendously
disturbed at the base, advances with the prevailing wind. Its course
is frequently changed, and ships within its influence would be
speedily wrecked. The only way to save the vessel is to fire a cannon
ball through the column and break it.

Fig. 725.—Thunderstorm and shower of ashes from Vesuvius.
A waterspout once devastated a district in the Hartz mountains of
Saxony. “A long tube of vapour descended to the earth, and several
times was drawn upward again; but at last it reached the ground,
and travelled along at the rate of four-and-a-half miles in eight
minutes, destroying everything in its way.”
On another occasion at Carcassonne in 1826, “a reddish column was
seen descending to the ground, and a young man was caught up by
it and dashed against a rock.” His death was instantaneous.
The cause of these whirling winds is supposed to be in the action of
vertical currents of air which ascend heated, and return rapidly as
cold air. The “waterspouts,” etc., are quickly formed. The tornado is
a monster whirlwind like a waterspout in form, and advances at a
tremendous rate—eastward as a rule. It moves in leaps and bounds,
passing over some portions of the ground and descending again.

The current of air is directed to the centre; the cyclone, as
mentioned, has a spiral or rotatory movement.
Thunder and lightning have been, to some extent, described under
the head of Electricity, but some observations may also be
introduced here, as storms of that nature appertain to meteorology
distinctly.
Electricity is always present in the atmosphere, and arises from
evaporation and condensation as well as from plants. As the air
becomes moist, the intensity of the so-called “fluid” increases, and
more in winter than in summer. Clear skies are positively electric,
and when large, heavy clouds are perceived in process of formation
in a sky up to that time clear, a storm is almost certain to follow.
These “thunder clouds,” in which a quantity of electricity exists,
attract or repel each other respectively. The cloud attracts the
opposite kind of electricity to that within it; and when at last a
tremendous amount has been stored up in the cloud and in the air,
or in another cloud, the different kinds seek each other, and
lightning is the result, accompanied by a reverberation and
commotion of the air strata, called thunder.
Lightning most frequently darts from cloud to cloud, but often strikes
the ground, whereon and in which are good conductors, such as wet
trees, metals, running water, etc. The “electric fluid” assumes
different forms—“forked,” “sheet,” and “globular.” The second is
perhaps the most familiar to us, and the third kind is the least
known of all. There are many well-authenticated instances on record
in which lightning with the form and appearance of fireballs has
entered or struck houses and ships.
“Fulgarites” are vitreous tubes formed in sandy soils by the lightning
in search of subterranean water-courses, for running water is a great
conductor of electricity.34 The fire-ball form of lightning has been
known to enter a school-house where a number of children were,
and to singe the garments of some, killing others. The ball passed
out through a pane of glass, in which it bored a hole, breaking every

other pane, however, in its transit. Another instance occurred in
which the lightning ran about the floor of a room, and descending
the stairs, exploded without doing any injury.
Lightning, like the electric current of the laboratory, will not always
set fire even to inflammable objects. An electric spark can be passed
through gunpowder without setting fire to it, and lightning will often
shatter the object without firing it. Death by lightning is
instantaneous, and in all probability quite painless; for we may argue
from analogy, that as those who have been rendered insensible by
lightning have had no remembrance of seeing the flash which strikes
so instantaneously, nor of hearing thunder after it, it is
instantaneous in its effects. Besides, the natural attitude is
preserved, and the face is usually peaceful and limbs uncontorted
after death by lightning.
There are some curious electrical phenomena, such as St. Elmo’s
Fire, already noticed under Electricity; and in some parts of America,
in very hot weather, such a light is perceived to issue from trees as
the fire glides through the forest. Many instances are on record
concerning the luminosity of pointed sticks, and even of the tails and
manes of horses in certain conditions of the atmosphere, and of the
universal power of electricity and its pervading influence in nature.
The benefits conferred by thunderstorms in purifying the air, and in
the production of ozone and nitric acid, are very great, and apart
from the magnificent phenomena exhibited, are well worth our
attention, though beyond our reach.

Fig. 726.—Aurora Borealis.
Terrestrial magnetism, however, is still more puzzling in its action
than is electricity, and the study of the needle, its destination,
inclination, and intensity, which are marked upon charts, just as are
the weather reports of the Times, is an interesting one. These
magnetic maps are termed the charts of Isoclinic and Isodynamic
lines. The declination of the magnetic needle from the true north is
its deviation from that point, and the “inclination” is its dip towards
the horizon. The line of its direction being known as the magnetic

meridian, its divergence from this line constitutes its declination.
There are places where it does not deviate, and these, in direction
north and south, are called lines of “no variation.” There are also
places in the equatorial regions where the needle does not “dip.” The
line connecting such places is termed the Magnetic Equator, and
north or south of this the needle dips respectively to north or south
in degrees coinciding with the distance from the equator.
The earth, then, acts as a magnet, and attracts the needle, but the
magnetic poles are not identical with the terrestrial poles. The north
magnetic pole was reached in 1831 by Sir James Ross, when the dip
was only one minute less than 90°, and the south magnetic pole was
very nearly reached also by him in 1840. The magnetic equator
passes between these two points.
Fig. 727.—Paraselenæ, or mock moons.

It is to magnetic atmospherical disturbance that the aurora is due.
These northern (or southern) phenomena are extremely brilliant and
diversified. In temperate regions the aurora does not present such
grand forms as in the extreme north. There the spectacle is
astonishingly beautiful. The sky at first clouds over, and mist is
developed. Humboldt has eloquently described the aurora borealis,
and the beautiful changes of light, the constant movement, flashes,
etc., denoting a “magnetic” storm, as electrical discharges indicate
an electric storm, although the area affected by the former is far
more extensive than that of the latter, and there is no thunder
accompanying the magnetic storm, with the production of which the
electricity of the earth is unassociated. To the continuous flow of this
electricity the aurora is due, and the flashes are only the electric
current descending towards the earth. But the true reason of the
phenomena may have to be yet discovered, for nothing absolutely
certain is known as to the origin of the aurora.
Amongst the numerous effects of refraction and reflection of light
the Rainbow is most common and the most beautiful. If we hold a
chandelier “drop” in the sunlight, we shall see a brilliant
representation of the rainbow on the wall or on the carpet. The
three colours—red, yellow, and blue—mingle or shade away into
seven—red, orange, green, blue, yellow, indigo, and violet. These
colours are all found in the rainbow.

Fig. 728.—Parhelia, or mock suns.
The colour of the atmosphere—the usual blue tint of the sky—arises
from the blue rays of the spectrum being reflected more than the
rest by the aerial particles, and the less vapour the bluer the sky,
because the vapour gives it a whitish or misty tint. At sunset and
sunrise the sky is red or yellow, like gold, or of crimson hue. This is
because the sun’s rays have so much farther to come to us at
sunrise or sunset, as you will readily perceive if you draw a line from
the sun to the sides and then to the top of the arc of the heavens.
The blue rays are thus lost in space, while red and yellow, which
travel so much faster than blue, are transmitted to the eye, not
giving the air time to absorb them.

If you go under water and look at the sun it will appear very fiery
indeed, and we may likewise imagine that fiery crimson rays, which
betoken atmospherical disturbance, very often are due to the
moisture through which they are transmitted. Wet and storm
frequently succeed a crimson sunset, which betokens much moisture
in the air. The sun is similarly seen through the steam issuing from
an engine, and the colours vary according to the density of the
steam in its stages of condensation.
Fig. 729.—Mirage at sea.
Vapour, we know, is invisible and transparent, but when it has been
condensed into rain-drops, and the sun is shining, if we stand with
our backs to the sun we see what we call the rainbow, because a ray
of light entering the drop is reflected, and as all rays are not of equal
refrangibility, the light, which is composed of three simple rays, is
divided and reflected into those and the complementary colours.
When the sun is at the horizon, the rainbow, to an observer on the
earth (but not on a mountain), will appear to be a semi-circle. The
higher the sun rises the lower is the centre of the rainbow. So we
can never see rainbows at noon in summer because the sun is too
high. A second rainbow is not uncommon, the second reflection

producing the colours in a different order. The colours in the
“original” range from violet to red; in the “copy” they extend from
red to violet. “Rainbows” are often visible in the spray of waterfalls
and fountains.
Halos are frequently observed surrounding the moon, and then we
are apt to prognosticate rain.
“The nearer the wane
The farther the rain,”
is an old couplet referring to the appearance of the moon, and is
supposed to foreshadow the weather by the size of the halo, which
is caused, as we know, by the existence of vesicular vapour in the
atmosphere.
Mock Suns, or parhelia, and mock-moons, or paraselenæ, are
continually observed in cold climates, where the tiny ice particles are
so abundant in the air. These phenomena were recognized by the
ancients, and halos round the sun can be observed by means of
darkened glasses. We annex an illustration of a mock sun and moon
seen on the continent of Europe. Readers of Mr. Whymper’s
“Scrambles in the Alps” will remember the gorgeous, and to the
guides mysterious, fog-bow or sun-bow seen as the survivors of the
first and most fatal ascent of the Matterhorn in 1865 were
tremblingly pursuing their descent over the upper rocks of that
mountain.
The Mirage, or Fata Morgana, is a very curious but sufficiently
common phenomena, and in the Asiatic and African plains it is
frequently observed. When the weather is calm and the ground hot,
the Egyptian landscape appears like a lake, and the houses look like
islands in the midst of a widely-spreading expanse of water. This
causes the mirage, which is the result of evaporation, while the
different temperatures of the air strata cause an unequal reflection
and refraction of light, which give rise to the mirage. Travellers are

frequently deceived, but the camels will not quicken their usual pace
until they scent water.
The Fata Morgana and the inverted images of ships seen at sea are
not uncommon on European coasts. Between Sicily and Italy this
effect is seen in the Sea of Reggio with fine effect. Palaces, towers,
fertile plains, with cattle grazing on them, are seen, with many other
terrestrial objects, upon the sea—the palaces of the Fairy Morgana.
The inverted images of ships are frequently perceived as shown in
the illustration (fig. 729), and many most extraordinary but perfectly
authentic tales have been related concerning the reflection and
refraction of persons and objects in the sky and on land, when no
human beings nor any of the actual objects were within the range of
vision.
It will be well to explain this phenomenon, and the diagrams will
materially assist us in so doing, for the appearances are certainly
startling when realized for the first time. The Spectre of the Brocken
we see mimics our movements, and we can understand it. But when
apparently solid buildings appear where no buildings have been
erected,—when we see—as has been perceived—soldiers riding
across a mountain by a path, or ledge, perfectly inaccessible to
human beings even on foot, we hesitate, and think there is
something uncanny in the sight. Let us now endeavour to explain
the mirage.
Suppose that in the annexed diagram the space enclosed between
the letters a, b, c, d, be a glass vessel full of water. The ship is below
the horizon, the eye being situated at e—the glass vessel of course
representing the atmosphere charged with moisture. The eye at e
will perceive the top of the mast of the ship, s, and we may imagine
a line drawn from e to s. Then put a (short focus) convex lens at a
just above this (imaginary) line, and a concave one, b, just over it.
Through the former an inverted ship will be seen, and an erect one
through the latter at s′ and s″ respectively. We now have the effect
in the air just as reproduced in nature by the difference in
temperature in air strata, which cause it to act like a concave lens

Fig. 730.—Explanation of
Mirage.
Fig. 731.—The Mirage.
when the density of the water diminishes towards the centre, and
like a convex lens when it is increased.
This can be proved by heating the air
(by hot irons) above the glass vessel
filled with oil, and the effects will be
just the same as through the lenses.
Dr. Wollaston obtained the mirage by
using a clear syrup,—about one-third
of the vessel full,—and filling it with
water. The gradual mingling of these
fluids will produce the phenomenon. The illustration in the margin
(fig. 731) shows us the rays proceeding from the ship’s hull, and
refracted into the line reaching the eye, above the line proceeding
from the mast, so the ship appears hull uppermost; the rays cross at
x. But if they did not cross before they reach the eye, the image
would appear as at s´ p´ in an erect position.
The Spectre of the Brocken arises from
a different cause. Such appearances
are only shadows,—projected on thin
clouds or dense vapours at sunrise, or
when the sun’s rays are directed
horizontally,—for of course vertical
rays will throw the shadow on the
ground on to the zenith. Balloons are
also reflected thus, and much interest
has been caused by the appearance of a twin balloon, until the aerial
voyagers have discovered the cheat by seeing the shadowy aeronaut
imitating their actions, and the second balloon has been discovered
to be an airy nothing.

CHAPTER L.
PHYSICAL GEOGRAPHY. CLIMATOLOGY.
WEATHER, CLIMATE, AND TEMPERATURE—ISOTHERMAL LINES—
ISOBARS, WEATHER FORECASTS, AND SIGNS OF THE SKY.
It is usually considered a sign of a paucity of ideas when one begins
a conversation about the “weather,” but there can be no doubt that
there is no more interesting question in social life at certain times as
to whether it will or will not rain. Our outdoor amusements are all
dependent upon weather, and a little cloud may throw a deep
shadow over all our pleasure if we neglect to bring out an umbrella,
or to carry a waterproof. We are never independent of what we term
the “capricious” climate, but in reality the laws of “the Weather,”
though so imperfectly understood, are fixed and invariable, and if we
could read the signs in the sky and learn the condition of the
atmosphere, we might leave the “prayers for rain” and “for fine
weather” out of the Church service, for then we should understand
that unless miracles are performed for us the laws of Nature can in
no wise be altered.
Of late years weather forecasts (not prophecies) have come before
us in our newspapers after the manner instituted by the late Admiral
Fitzroy, whose name has become a household word in England. But
at the commencement of the Christian era and before that time the
signs of the heavens and the behaviour of animals and birds were
noted with reference to changes of weather. If we read Virgil we
shall find numerous references to these portents, and the translation
usually quoted will furnish us with information which must be as true
nowadays as it was in Virgil’s time, for wild animals do not change
their habits. Speaking of wet weather in the Georgics the poet
wrote:—

“The wary crane foresees it first, and sails
Above the storm, and leaves the hollow vales;
The cow looks up, and from afar can find
The change of heaven, and sniffs it in the wind;
The swallow skims the river’s watery face,
The frogs renew the croaks of their loquacious race;
The careful ant her secret cell forsakes,
And draws her eggs along the narrow tracks;
Huge flocks of rising rooks forsake their food,
And, crying, seek the shelter of the wood.
The owls, that mark the setting sun, declare
A starlight evening and a morning fair.”
We might quote further selections respecting the signs in the heaven
and earth mentioned, but the foregoing verses will be sufficient to
illustrate our position, and to show us that weather forecasting is, at
any rate, as old as the Christian era.
The moon is generally supposed to influence the weather—a
“Saturday’s Moon” being particularly objectionable, or when she
appears anew at some hours after midnight thus—
“When first the moon appears, if then she shrouds
Her silver crescent, tipped with sable clouds,
Conclude she bodes a tempest on the main,
And brews for fields impetuous floods of rain.”

Fig. 732.—In the northern Seas.
Weather permitting, we can go out and study the clouds as
described in the foregoing chapters, or consult the barometer, and
see which way the wind blows. The child will tell us that a high
“glass” means fine weather, and a low barometer indicates rain, but
this is only relatively true. A high glass may be falling, a low glass
may be rising. A sudden fall or a sudden rise are indicative of bad,
windy weather, or a short-lived fine period. The glass may rise with a
northerly wind, and rain will supervene, so careful observation is
necessary before one can obtain even a superficial knowledge of the
weather. (See subsequent observations on “Weather.”)
The Americans telegraph the results of their observations of coming
storms across the Continent, corrected by the signs noticed and
recorded by vessels arriving in New York. Thus they are frequently
very accurate; steady application and observation at Sandy Hook
must give them a great deal of useful information for the “forecasts.”
The word Climate is derived from the Greek klima, a slope; and thus
at a glance we perceive how the aspect it presents to the rays of the
sun in the earth’s revolutions, must affect the “climate” of a country.
Of course the position of any portion, the elevation and locality of

the mountains, have also a share with the soil, winds, rains, and
sea-board, in determining the climate of any region. Many points
have already been touched upon in former chapters. Temperature,
moisture, and vegetation are the chief natural features which
determine climate, and we must find out the position of the land
with reference to the sun first, to ascertain the climate.
The more vertical the sun is the hotter the atmosphere, for the rays
strike directly upon the earth, which radiates the warmth received.
These heat rays are, as we know, invisible. The hottest portion of
the earth must be at the equator for the sun is overhead, and the
rays beat down directly upon the earth. The sun is also nearer than
when at the horizon, and less rays are absorbed by the atmosphere.
The longer the day the greater the heat.
Fig. 733.—In the southern steppes.
Temperature is registered by observation of the thermometer, and
the distribution of heat is represented upon a chart across which
lines are drawn at places of equal temperature. These lines are
called “isothermal.” There are also terms to denote equal winter

temperature and the average summer heat—isochimines and
isotheres respectively.
Temperature decreases as we ascend from, and increases as we
descend into, the earth. This fact proves that the air is not warmed
by the sun’s heat, but by radiation from the ground. As we ascend
we reach the line of perpetual snow, which varies in different parts
of the globe. In the tropics it extends from 15,000 to 18,000 feet;
but it varies even in places of the same latitude, according as the
towns are inland or on the coast, as in the Pyrenees and Caucasus,
where there is a difference of three thousand feet in the snow limit.
The line of the snow limit, as a rule, gets lower as we journey from
the equator to the poles. Exception will be found in the Himâlaya,
where the snow line is higher on the northern side, in consequence
of the existence of the Thibetan tableland, which causes a higher
temperature than that existing upon the abrupt southern slope.
Countries, therefore, though in the same latitude, may have different
climates according to the elevation of the land.
The proximity to the sea is another reason for climatic difference.
Water takes some time to become warm, but when it has once
become so it will not readily part with its heat. The Gulf Stream, with
its warm current beating along our shores, gives us a high
temperature and a moist climate—a very different condition to
Newfoundland or Nova Scotia, which are in much the same latitude
as England and Ireland. By the sea the climate is more uniform, and
the extremes of heat and cold are not so distant. We send invalids to
the seaside to save them the effects of such violent changes.
Winters are milder and summers cooler by the sea.
We can readily understand how such circumstances affect the
vegetation, and places which in winter may enjoy a mild and genial
climate (comparatively speaking), may have a cold summer. Ferns
may flourish in winter out of doors, but wheat will not ripen in the
autumn owing to the want of heat.

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