Full download Sensors and Transducers 3rd ed Edition Ian Sinclair pdf docx

Download the full version of the ebook now at ebookultra.com
Sensors and Transducers 3rd ed Edition Ian
Sinclair
https://ebookultra.com/download/sensors-and-
transducers-3rd-ed-edition-ian-sinclair/
Explore and download more ebook at https://ebookultra.com

Recommended digital products (PDF, EPUB, MOBI) that
you can download immediately if you are interested.
SENSORS AND TRANSDUCERS 2nd Edition D. Patranabis
https://ebookultra.com/download/sensors-and-transducers-2nd-edition-d-
patranabis/
ebookultra.com
Measured Tones 3rd ed Edition Ian Johnston
https://ebookultra.com/download/measured-tones-3rd-ed-edition-ian-
johnston/
ebookultra.com
Build and Upgrade Your Own PC Third Edition Build Your Own
Ian Sinclair
https://ebookultra.com/download/build-and-upgrade-your-own-pc-third-
edition-build-your-own-ian-sinclair/
ebookultra.com
The lymphoid neoplasms 3rd ed Edition Ian Magrath
https://ebookultra.com/download/the-lymphoid-neoplasms-3rd-ed-edition-
ian-magrath/
ebookultra.com

In Situ Hybridization Protocols 3rd Edition Ian A. Darby
(Ed.)
https://ebookultra.com/download/in-situ-hybridization-protocols-3rd-
edition-ian-a-darby-ed/
ebookultra.com
Digital Communications 3rd Edition Ian Glover
https://ebookultra.com/download/digital-communications-3rd-edition-
ian-glover/
ebookultra.com
Java Cookbook 3rd Edition Ian F. Darwin
https://ebookultra.com/download/java-cookbook-3rd-edition-ian-f-
darwin/
ebookultra.com
Galois theory 3rd Edition Ian N. Stewart
https://ebookultra.com/download/galois-theory-3rd-edition-ian-n-
stewart/
ebookultra.com
Practical RF Handbook 3rd Edition Ian Hickman
https://ebookultra.com/download/practical-rf-handbook-3rd-edition-ian-
hickman/
ebookultra.com

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.

Other documents randomly have
different content

CHAPTER VII.
After Mr Darnley the elder had finished his unpleasant colloquy
with his son, and had seen his daughters walk out together; though
at the time he had not any suspicion of their intentions, yet he began
to be suspicious that some intercourse might be carried on thus
clandestinely with the prohibited fair one of Smatterton. He then
sought for his son, whom he found in the dining-room with a book
spread open before him, but apparently little occupied with the
contents of the volume. With a dry and careless air, the father
addressed the young man:
“Where are your sisters, Robert?”
“They are gone out to take their morning’s walk, sir,” replied the
son.
“And where are they gone?” said the elder gentleman, with greater
emphasis and asperity than was usual with him.
To an interrogation thus suspiciously addressed to him, the young
gentleman did not feel inclined to give a very explicit and satisfactory
answer. There is frequently a great difficulty in managing replies to
some questions, which force, as it were, an unpleasant answer, or
an untruth. It is hard and ungenerous to ask such questions, and
when people of any delicacy of feeling find that they have by any
unintentional impertinence proposed a question of this nature, they
will immediately, and with as good a grace as possible, waive
pressing for an answer. But in the present case, the question was
put for the very express purpose of extorting reluctant information.
And the younger Darnley did not feel himself at all inclined to give an
answer, or to tell a falsehood. He therefore remained silent and
looked again upon his book, considering that the recent discussion
between himself and his father was sufficient to account for a little
sulkiness and gloom.

The father became now more suspicious, and he repeated his
question with greater earnestness, and he said in an angry tone, “I
ask you, Sir, where your sisters are gone. Why do you not answer
me?”
Then the young man was angry in his turn, and he replied, “I am
not in the habit, Sir, of interrogating my sisters as to the direction in
which they may please to walk.”
Now as Mr Darnley the elder was not quite so much aware of the
angriness of his own tones as he was of the sharpness of the
answer, his suspicions were still farther corroborated, and he said,
“You know that they are gone to Smatterton.”
Robert Darnley was again silent, and though his father repeated
the assertion in a variety of modes, he gave no answer to it. Mr
Darnley the elder, then in a most angry mood, set out to walk to
Smatterton, that he might convince himself of the truth of his
suspicions.
In the course of his walk, Mr Darnley was interrupted and delayed
by meeting with Sir George Aimwell and Colonel Crop. People who
are not mightily gifted with any great flow of words are sometimes as
tedious as professed and notorious praters. For though they do not
convey much information, and do not utter any great quantity of
words, yet if they have not much to do, and are at a loss for the
passing of their time, they will sometimes stand dribbling out
monosyllables for half an hour together and more too. Thus did the
two troublesome ones above named most mercilessly and
remorselessly pounce on the rector of Neverden.
The baronet and the colonel were on foot, walking slowly in a
direction opposite to that in which the rector was walking. When the
clergyman saw the two gentlemen, he felt himself necessitated to lay
aside the frowning look of the angry father, and to assume a more
gracious and courtier-like smile. And when the two distinguished
characters met the reverend gentleman bearing smiles upon his
countenance, which smiles were manifestly designed to signify how
great was the delight which he felt in meeting the said gentlemen,

they could not of course for a moment imagine that he should be
very glad to part with those whom he appeared so happy to meet.
Therefore the unpaid and the half-paid made at the rector, what is
called a dead set. They fairly and completely stopped him; stopped
him as completely as a couple of footpads, one on one side of him
and the other on the other. They did not indeed demand his money
or threaten his life, but they demanded his time, which was to him at
that moment as valuable as his money, and they put in danger his
politeness, which was as dear to him as life.
The first salutations were soon paid, acknowledged, and returned.
Then the interrupters stood still looking at Mr Darnley and at each
other; and then Mr Darnley having nothing more to say, and fancying
that his friends by their silence were similarly situated, made a slight
movement, as if indicating an intention of taking leave. But his good
friends were not disposed to give him leave; and the worthy baronet
then began a short speech by saying, “Oh, Mr Darnley, have you had
your newspaper this morning?”
Mr Darnley replied very politely, “I have, Sir George.”
Then the baronet asked: “Is there anything new?”
Then Mr Darnley said, “Nothing, Sir George.”
And then Sir George was silent again; and then Mr Darnley, after a
little interval, made another move. Then Colonel Crop took up the
tale and said, “The papers are very dull now.”
To which Mr Darnley suitably and assentingly replied; “Very:”—
thinking perhaps at the same time that Colonel Crop was as dull as
any of them.
Once more Mr Darnley was in hopes of getting away from his
tormenting detainers; but the excellent magistrate thinking that it was
now his turn to speak, directed himself again to the impatient rector,
saying, “What remarkably mild weather it is for the time of year.”
“Remarkably mild;” replied Mr Darnley.
Thus did the cruel ones, unmindful of the inconvenience to which
they put the poor man, detain him a most unreasonable length of

time with an unconnected and uninteresting succession of idle
common-places, interlarded with long intervals of insipid silence. So
long as he stood still silently looking at them, so long did they hold
their tongues, but whenever the poor man shewed symptoms of
moving, they stopped him by some unmeaning gabble. So does a
wantonly cruel cat play with a poor innocent mouse which she
suffers for a moment to escape from her claws, and leaves
unmolested while it is motionless; but, as soon as it moves a limb in
signal of departure, down comes her merciless paw upon it again.
At length however when the worthy baronet and his friend were
tired of their own laziness, they suffered the persecuted divine to
escape from them; for after having detained him an unreasonable
length of time, and that for no purpose whatever, the considerate
baronet very coolly said: “Well, Mr Darnley, perhaps we are detaining
you: good morning.”
“Good morning,” said Colonel Crop; and so also said Mr Darnley.
It was now absolutely impossible for the rector of Neverden to
overtake his daughters before they should arrive at Smatterton
parsonage, if that were the object of their excursion, and nothing
remained for him but the prospect of meeting them on their return,
and the satisfaction which he might have in reproving them for their
implied disobedience.
The delay which he had experienced by no means softened his
asperity or abated his anger; and when at a little distance before
him, just at the entrance of the village of Smatterton, he saw his
three daughters in deep and apparently interesting conversation
approaching him, and not perceiving him in consequence of the
interest which they seemed to take in the subject of their
conversation, he concluded of course that they had been at the
rectory at Smatterton contrary to his known will and inclination.
They were within reach of his voice before they saw him; and
when they heard him address them, they lifted up their faces and
were astonished into silence, and surprised into apparent confusion.
It was merely the unexpectedness of the meeting that confused

them, but the rector thought their silence was from the conviction of
their guilt.
“And so, young ladies, you have, in despite of your father’s
authority, been paying a visit to Smatterton rectory! And pray let me
ask you, what is your motive for this act of rebellion?”
Now the young ladies mentally pleaded not guilty to the
accusation, and they gave voice also to the plea, saying: “Indeed,
Sir, we have not been at the rectory.”
“But have you not seen Miss Primrose?”
“We have,” replied the eldest. “We have seen Miss Primrose, but
we have not been paying her a visit. Our meeting was accidental.”
The young lady did not say that there was intention in the
accident; and if there be a fault in that omission, we are humbly of
opinion that at least one half of the blame rests upon Mr Darnley
himself, for assuming such magnificent airs and playing the great
bashaw in his family. We could write a long dissertation on this
subject, but whether such dissertation would be read is doubtful.
As when the above reply was given to Mr Darnley by his daughter
he stood in mute astonishment for a while, an opportunity was thus
afforded for the young lady to continue, and to endeavour to divert
for a moment her father’s thoughts from Penelope, and to direct
them to poor Fitzpatrick. Miss Darnley therefore said:
“And we met Miss Primrose, Sir, as she was coming from a visit of
consolation to a poor old man, of whom we have often heard you
speak?”
Mr Darnley in an instant understood to whom the allusion was
made, and he exclaimed: “Bless me! Is poor old Fitzpatrick living still,
and in Smatterton?”
Seeing how completely and pleasantly the current of her father’s
thoughts was changed by this recollection, Miss Darnley proceeded
to give a full and abundant relation of all the particulars of the poor
man’s case, and the illness of the grand-daughter.

Mr Darnley was moved at the narration, and he said, “I will go and
see the poor man and his grand-child.”
Miss Darnley then directed her father to the cottage, and with her
sisters returned to Neverden. They were all three much pleased that
their father’s attention was thus directed, and they entertained some
hopes that good might result from his accidental meeting with
Penelope, which they anticipated, as they had not many minutes
back parted with her at the door of the poor man’s cottage. And
when they arrived at Neverden, they told their brother all that had
passed, and he also was pleased, and he anticipated favourable
results from the meeting.
In the mean time, Mr Darnley the elder found his way to
Fitzpatrick’s cottage; and as he entered the wretched abode, his
feelings were shocked at the sight of such miserable destitution as
appeared in the lower apartment. Scarcely could he believe that
such a place could be the abode of human beings; and he could not
help thinking, that though there was not in Neverden so splendid a
building at Smatterton castle, yet at the same time there was not a
hovel so miserable as that in which he was then standing. He felt
compassion for the poor man who was destined to close his life in so
desolate an abode, and he thought of the service which that poor
man had rendered to him.
As Mr Darnley had entered the cottage with gentle step, as fearing
to disturb the sick, those who were above were not aware of his
presence till he entered the upper room. And when he was there,
though Miss Primrose herself was before him, and though his anger
had been strongly excited against her, he thought not of the offence
or the offender. His attention was first arrested by the sight of the
poor old man, who was standing by his grand-daughter’s bed side,
and trembling with age and infirmity. There was not in the
countenance of the poor man any expression of grief or sympathy;
his eye, expressive of no emotion or even consciousness, rested
coldly on his grand-daughter; and as Mr Darnley entered the room,
the old man just turned his face towards the visitor, and no otherwise
altered his position or expressed any sense of a stranger’s
presence.

Penelope was leaning over the bed on which the sick girl lay, and
was endeavouring to soothe her with kind words, and to persuade
her to take some slight nourishment. And when the patient saw Mr
Darnley, she started with astonishment, which led Miss Primrose to
look towards the door of the apartment. Penelope was the only one
of the three who at that moment knew Mr Darnley; for the old man
had forgotten him, and the poor girl had never known him.
The young lady was much moved at the sight of Mr Darnley; and
she was preparing to rise to pay her respects to the gentleman. She
could not rise very quickly, for her left arm was supporting the sick
girl’s head, and Penelope was unwilling to withdraw that support
hastily. Mr Darnley saw this, and signified by the moving of his hand,
and by a gentle whisper, that he would not have the sick one
disturbed. Then he came near and took the old man’s hand, which
was yielded placidly and wonderingly. But when Mr Darnley spoke to
him and called him by name, the old man’s recollection returned, and
the light of intelligence came into his looks.
“Have you no recollection of me, Fitzpatrick?” said Mr Darnley.
“Oh yes, Sir,” replied the old man; “I do recollect you now. But it is
a long time since I have seen you, Sir.”
Then Fitzpatrick pointed to the poor girl, and said to Mr Darnley:
“There’s a sight, Sir, for an old man. You remember my boy; he was
at one time likely to do well in the world; but he was carried off by a
fever in the prime of life, and there lies his only child.”
The old man was going to say more, but his feelings prevented his
utterance. And Mr Darnley spoke kindly to him, and gave him
assurance that he should not want, but that every comfort should be
given him to cheer his declining days.
“You are good, Sir, very good; but I shall not long stand in need of
any comforts. This good young lady, Sir, has been very kind to us
both.”
By this time Penelope had gently and gradually disengaged her
arm from supporting the head of the poor girl; and Mr Darnley
addressed himself to the exhausted and almost expiring patient. But

she was unable to make any audible reply to Mr Darnley’s enquiries,
but her lips moved and there was a hectic flush which lasted only for
a moment, and was succeeded by a paleness more livid than before.
She turned her eyes tearfully and gratefully towards Penelope, and
thus corroborated by her looks what the old man had said of the
kindness of their gentle benefactor.
Mr Darnley now felt himself compelled to speak to Miss Primrose;
and, considering the habitual haughtiness of his manner and the
unfriendly feelings which he had entertained towards her, he spoke
with great gentleness. He enquired how long the poor people had
been in that miserable abode, and he asked if there was anything
which he could do for their assistance. And Penelope thanked him
with as much grateful energy of expression as though the kindness
were offered to herself, and she added:
“It is but little, Sir, that they want, and that little we can easily
supply them with. But I wish I could as easily soothe the poor girl’s
mind. She reproaches herself so bitterly, and will hear no
consolation.”
Penelope said this in a low and gentle tone. She was hardly aware
that the patient heard her, till poor Ellen’s voice interrupted her, and
the sick one spoke audibly and distinctly, and said, “I am happy
now.”
At hearing this, Mr Darnley and Penelope turned hastily round,
and they caught a glimpse of an expiring smile, and they heard the
unchecked breath rush through the pale lips of the sufferer, and then
poor Ellen’s earthly sorrows were at an end.

CHAPTER VIII.
It was mentioned in the preceding chapter, that Sir George
Aimwell and Colonel Crop most inopportunely met and detained Mr
Darnley. This worthy couple, after leaving the rector of Neverden to
pursue his walk, lounged lazily towards Neverden Hall, and entered
into wise and knowing consultation concerning the commission with
which the colonel fancied himself entrusted, as relating to Miss
Glossop.
The worthy baronet thought and said, that if Lord Spoonbill had
any serious intention of marrying Miss Glossop, it would be far more
suitable that his lordship should make his personal appearance, and
offer his hand regularly and orderly.
“Certainly,” said the colonel, “certainly; but you know that his
lordship is peculiarly situated.”
Whether the colonel had any meaning, when he said that Lord
Spoonbill was peculiarly situated, we cannot say, but there is in
general a very great and comprehensive meaning in that phrase. If,
for instance, a man is looking for a piece of preferment, or is in any
way dependent on the powers that be, or the powers that may be,
and if he is requested to give a vote on any occasion according to
his own views or opinions, he is very ready to say that he wishes
well to that person or object for whom the vote is solicited, but that it
is not in his power to vote as he wishes, because he is peculiarly
situated. In short, wherever a man’s interest interferes with his duty
or conscience, and the principle of selfish interest is stronger than
duty or conscience, then it is that he is peculiarly situated.
Now the Right Honorable Lord Spoonbill was a man of title and
high rank, and his associates were of a select and superfine
description; if therefore he fixed his affections on a lady in a humbler
sphere, or less distinguished society, he could not make advances
regularly and honorably, because he was peculiarly situated.

To the remark of Colonel Crop, that Lord Spoonbill was peculiarly
situated, the worthy magistrate of Neverden Hall considerately
replied:
“Clearly so, I am perfectly aware of it: but still you must
acknowledge that it would have been more correct if his lordship had
communicated his intentions to Arabella without the intervention of a
third person. However, I will not say or do anything that shall be the
means of preventing the poor girl from having a good establishment
in life. I know that these high people have very peculiar notions.”
Then the gallant colonel launched forth right liberally in praise of
Lord Spoonbill, and well he might, seeing that not only was he
indebted to his lordship for access to a most excellent table, but he
was also under obligation to him for the distinction and consideration
derived from such noble patronage and countenance.
“I suppose,” continued the baronet, “that it must be a private
marriage?”
“No doubt,” replied the colonel; “for his lordship is entirely
dependent on the Earl his father, and it would be a serious affair to
act in direct and open opposition to his will.”
“Exactly so,” answered the magistrate; “but when the marriage has
taken place, and the Earl sees that opposition must be fruitless, and
especially when he is introduced to the young lady, then he will think
more calmly on the subject. Well, it will be a fine match for Arabella.
Her father little thought when he sent her to Neverden what good
luck was in store for her. I think I will not write to her father about the
affair, but let him be taken by surprise.”
At this step in the consultation the interruption of the dinner-bell
put a stop to the discussion, and the two gentlemen soon found
themselves pleasantly engaged in paying an unequivocal and
practical homage to the culinary talents of the baronet’s cook.
Colonel Crop was unusually attentive to Miss Glossop, and the
young lady in return was most politely attentive to Colonel Crop. But
Lady Aimwell was not so very polite to Colonel Crop as was her
general custom; for her ladyship had been mightily displeased with

the announcement which she had recently received from her right
worshipful lord and master. In proportion, however, to Lady Aimwell’s
lack of courtesy, was the redundance and superabundance of Miss
Glossop’s politeness and vivacity; so that ere the cloth was removed,
her ladyship was in a complete fit of the sullens, and took it into her
head to have the head-ache, and expressed her intention of retiring
immediately.
Miss Glossop, as in duty bound, attended her discourteous
relative, and was in full expectation of hearing a long dismal lecture
all about propriety and all that sort of thing. There are two sorts of
people that do not like to be lectured—those that do not understand
the subject on which they are lectured, and those that do understand
it. For such as know all that can be said, do not mightily desire to
hear it all over again; and such as know nothing about it, care
nothing about it; and if there be a few in an intermediate class who
know a little about the matter, they do not in general desire to have
their little knowledge increased by lecturing. When Mr Martin’s Act
about cruelty to animals was passed, not a word was said about
lecturing. This was a great omission.
But fortunately for Arabella Glossop, it so happened that Lady
Aimwell was too far gone in ill humour even to administer a lecturing
to her high-minded relative. Her ladyship merely, in a pettish tone,
said, “I beg, madam, that I may not detain you from more agreeable
company.”
Miss Glossop, who knew that time would be lost if she should
enter upon any discussion, readily took her aunt at her word, and
politely wishing her good night, returned to the company more
agreeable to herself.
It is not known by what arguments, or with what eloquence, the
gallant colonel convinced and assured Miss Glossop of the
supposed fact of Lord Spoonbill’s tender affection and high regard
for her; nor is there any record of the readiness or reluctance with
which the young lady believed it all; it is only known that in the
absence of Lady Aimwell, which gave the colonel an opportunity of
executing his commission, Miss Glossop was put in possession of

the important information, and that she was delighted at the thought
of marrying the son of an Earl, especially such a charming man as
Lord Spoonbill.
It should however be mentioned, that Miss Glossop never heard,
or even suspected, that Colonel Crop was commissioned with any
more humiliating proposals. And though there might be something
suspicious, and not altogether accurate, in this proxy courtship, yet
the young lady pardoned it all under the consideration that Lord
Spoonbill was peculiarly situated.
Very pleasing were the anticipations of Miss Glossop in looking
forward to the possession of a mansion so splendid as Smatterton
Castle. Very readily did Miss Glossop dismiss from her mind all
thoughts of tenderness for the poor lieutenant, and very readily did
she renounce all design on the heart of Robert Darnley, leaving that
in the undisturbed possession of Miss Primrose.
Colonel Crop had no sooner fulfilled his commission, than he
immediately betook himself to the gratifying employment of
communicating his success to Lord Spoonbill, in the full expectation
of receiving his lordship’s most hearty thanks for the pains that he
had taken, and the dexterity with which he had conducted the
negociation.
It was too great a task for the gallant colonel to write a whole letter
on the very evening of his return from Neverden Hall to Smatterton
Castle; he therefore began the letter in the evening, resolving to
finish it on the morning of the following day.
Just as the gallant officer had concluded the writing of his
despatches, and was preparing to fold and seal his important
communication, the successor of the crafty Nick Muggins brought
letters to Smatterton Castle. One of these letters concerned Colonel
Crop and the business of which he had just been writing. The
colonel, seeing the hand-writing of his respected patron and
employer, had sense and sagacity enough to open and read that
letter before he sealed and sent off his own.

It is astonishing to observe what wonderful sagacity some people
possess, who are by no means regarded by the rest of the world as
conjurors. Colonel Crop, to an ordinary observer, would have
appeared a very stupid kind of man, and by no means addicted to
the exercise of the reasoning powers. But notwithstanding this his
habitual and constitutional obtuseness, he had the wisdom to reason
so far as to conclude that he might as well read Lord Spoonbill’s
letter to him before he sent off his letter to Lord Spoonbill.
The letter, which Colonel Crop now opened, was as follows:
“Dear Crop,
“I find by a letter from my old maiden cousin addressed to
the Countess, that the young lady’s father is not in such
flourishing circumstances as he represents himself, and if
Darnley has deserted her also, I think that I may now have
her on my own terms. However, if Aimwell makes a fuss
about the matter, let the negociation go on as if for marriage.
Only of course you will represent that it is absolutely
indispensable that the marriage must be private, and must be
kept a secret for some time. Bring her up to town with you as
soon as possible, giving me a day’s notice of your journey.
“Yours ever,
Spoonbill.”
Now the conduct which Lord Spoonbill recommended Colonel
Crop to pursue on this occasion, was villanous, mean, and
treacherous. But the right honorable one knew that the gallant officer
would not disoblige a good friend; and the colonel himself, though he
might perhaps have had some slight objection to be used as an
instrument of treachery, was peculiarly situated. For he knew not
where else he should find so good a table and such superb claret, at
so slight a cost as at the houses of Lord Smatterton. Besides, it was
not (he reasoned) his fault, if Lord Spoonbill should deceive the
young lady.
It is very likely that Colonel Crop, under other circumstances,
would not have lent himself to negociations of this nature; but as it

was, he could not well help himself. It is also very probable that, if
Lord Spoonbill had not been dependent on his father, he would not
have used such indirect and circuitous negociation, and he might
perhaps have made honorable proposals instead of making those
which were dishonorable. The Society for the Suppression of Vice is
perfectly aware that narrowness of circumstances is the great cause
of most of the sins of which mortals are guilty; and therefore that
venerable society wisely directs its attention and investigations to the
poorer classes. The nobility never sell apples on Sunday, the nobility
never shave for a penny on Sunday morning. And all those countless
abominations, at which that excellent society lifts up its pious eyes,
are the sins arising from narrowness of circumstances and
dependence of situation.
When Colonel Crop had read Lord Spoonbill’s letter, he forthwith
proceeded to make such additions to his own letter as the
circumstances of the case required; and if the colonel had not been
an indolent man, and desirous of affecting a very laconic species of
writing, he most surely would, in the letter which he wrote on this
occasion, have led his right honorable employer to suspect an error
of apprehension, and a mistake in the person.
Lord Spoonbill very readily accounted for what appeared to him as
the ready compliance of Penelope, by referring it to the
circumstances of the desertion of Robert Darnley, and the perplexed
condition of her father’s affairs. His lordship also took it into his head
that Mr Primrose had designedly misrepresented the condition of his
property, and therefore his lordship affected to be mightily angry with
him, and to think that it would be but a proper and suitable retaliation
to deceive the unwary daughter.
This was a curious mode of reasoning, but a very slight shadow of
apology will serve to satisfy a gentleman of such habits and pursuits
as the heir apparent to the earldom of Smatterton. Besides, if a man
is resolved on an act of treachery and meanness at all events, what
signifies the strength or weakness of the apology which he makes to
himself? The most logical apology is no excuse to the world, and the
most illogical is a very good one to himself.

CHAPTER IX.
When a lady of such temperament as Lady Aimwell takes upon
herself the trouble of going into a fit of the sullens, though she may in
the first instance be speechless and even resolve not to open her
lips upon the subject of her wrath, or to utter any expressions of
anger against the object of her indignation, yet she finds at the last
that there is no other mode of getting rid of the oppressive burden
than by throwing it off in words. In like manner, also, when two
gentlemen quarrel about any subject, whether it be geology, or
theology, and they cannot convince one another, then they are angry
and sulky, and they treat one another with what they call silent
contempt, and yet they make a mighty noise and a great trumpeting
about the silence of their contempt. So again, when an author who
has written the best possible book on any subject, and another
author reviews that same book and proves by most ingenious
argument that it is utterly worthless, the writer of the book runs about
among the circle of his acquaintance foaming at the mouth to shew
how cool he is, and dinning every one’s ears with the noise that he
makes in proclaiming his silent contempt of the scrub who has
criticized him. And what else can he do? Who is to know anything of
the existence of silent contempt unless it be advertized? We have
heard the phrase, “proclaiming silence;” it has its origin perhaps in
this silence of contempt, which by the way seems to be rather a
contempt of silence.
If the reader does not by this time understand the state of mind in
which Lady Aimwell was, on the occasion referred to, he must be
obtuse; if he does not pity Arabella Glossop, he must be inhuman
and unfeeling.
On the morning which followed Colonel Crop’s last mentioned visit
to Neverden Hall, Lady Aimwell took her seat in the drawing-room as
usual, and spread before her eyes the accustomed Stackhouse. But
her ladyship found it difficult to command her attention, and to find

room in her mind for any other thoughts than those which related to
Arabella Glossop. And the young lady as usual made her
appearance. At her entering the apartment Lady Aimwell lifted her
eyes and fixed them frowningly on the young lady.
It is not pleasant to be frowned at, even though it be but by an
automaton. There is in the human mind, especially in the minds of
the young, a love of cheerfulness, and this principle was exceedingly
strong in Arabella Glossop.
Lady Aimwell had never been very courteous to this gay-spirited
young woman, and yet her ladyship expected, or seemed to expect,
that Miss Glossop ought to be most especially courteous to her. Lady
Aimwell made herself as repulsive as she possibly could to Miss
Glossop, and then with a most diverting simplicity expressed her
wonderment that the young lady should seem so readily to avoid her
company. Lady Aimwell had certain obsolete notions of decorum,
and divers crotchets about propriety which she had learned from her
grandmother’s sampler, and curiously did she profess herself
astonished that the hoydenish daughter of a successful attorney
should not have the same starched notions and the same precise
formality.
It has been said that Lady Aimwell looked frowningly upon Miss
Glossop, as soon as the young lady entered the drawing-room. But
Miss Glossop, with all her rudeness and vulgarity, was not so rude or
vulgar as to return the frown. On the contrary, she very kindly asked
her ladyship if she had recovered from her yesterday’s indisposition.
The question was asked very civilly, and with the most conciliating
intonation of voice; but it was answered with great incivility and with
a most sneering cadence.
“You care much about my health,” replied Lady Aimwell.
To this no reply was made; and Miss Glossop, seeing that her
ladyship was in an ill-humour, thought it best to let that humour take
its course. But as the young lady had no very great desire to
undergo a dissertation on propriety, she was preparing to leave the
room. Thereupon Lady Aimwell was roused to greater volubility; and,
closing the great book with a great noise, she said, “It is very

unaccountable, Miss Glossop, that you have so great a dislike to me
that you take every opportunity to avoid me.”
At hearing this Miss Glossop returned, and would have made
something of a reply, but Lady Aimwell prevented her by continuing
the oration.
“I cannot imagine what I can have done or said to make you dislike
me so much. I have never said anything to you but for your good.
But young people now-a-days think themselves so prodigiously wise,
that they will not condescend to be advised. I know that when I was
a young woman, if any one had taken so much pains with me as I
have with you, I should have been grateful for it, instead of turning
my back upon my best friends.”
All this was what is called too bad. It was villanously tedious and
generally untrue. Lady Aimwell could very well imagine what it was
rendered her company unacceptable to Miss Glossop; nor could her
ladyship think it very likely that all which she had been pleased to
say for the good of the young lady, should be considered by her as
really pleasant and agreeable. And in good truth we really believe
that, though what had been said by Lady Aimwell might, by a little
ingenuity, be interpreted as being said for the young lady’s good, yet
the principal motive which urged her ladyship to say all this, was the
gratification of her own ill humour and the indulgence of her own
spleen. And when the wife of the exemplary magistrate of Neverden
Hall said, that had any one in her younger days so administered the
tediousness of snarling exhortation, she should have been grateful
for it, we are of opinion that imagination had usurped the throne of
memory, or that invention had taken the place of veracity. For, unless
Lady Aimwell had greatly changed since the days of her youth, or
unless we have grossly misapprehended the character of her mind,
we are of opinion that she would not have borne so patiently, as Miss
Glossop did, the tediousness of prosy exhortation.
To all that Lady Aimwell was pleased to remark as touching the
ingratitude of Miss Glossop and the degeneracy of the present
generation of juvenile spinsters, the belectured young lady only
replied, and that most meekly, “I am sure, Lady Aimwell, I never had

the slightest intention of treating you disrespectfully. As you were
unwell last night, and as I thought you did not seem quite recovered
this morning, I could not do otherwise than enquire after your health.”
“Not quite recovered!” echoed Lady Aimwell, with great briskness
of tone and peculiar sharpness of manner—“Not quite recovered!
So, I suppose you mean to insinuate that I was out of humour? Yes,
yes, I understand what you mean by not quite recovered.”
At this remark, Miss Glossop smiled inwardly, but she took
especial care not to manifest any outward and visible signs of mirth,
lest she might provoke her ladyship to exercise some inconvenient
mode of retaliation. Nor, on the other hand, could the young lady so
far attempt the mask of hypocrisy as expressly and explicitly to
disavow all thought and suspicion of ill-humour on the part of Lady
Aimwell. Being however somewhat indignant at the pertinacity with
which her ladyship kept up the hostility, and thinking that a little
semblance of opposition would be better than a placid and
unyielding acquiescence in the gratuitous accusations and
assumptions of her ladyship, Miss Glossop, with some degree of her
natural tartness, replied:
“I think, Lady Aimwell, that you are treating me very ill to put an
unfavourable construction on everything I say or do; I am sure I have
not the slightest wish to behave disrespectfully to you; but you will
not give me leave to pay you ordinary civilities without
misinterpreting them.”
Now her ladyship knew that there was truth in this, therefore,
fearing that she might be worsted in a regular argument, she thought
it advisable to change the mode of attack, and, instead of continuing
the discussion in that line, Lady Aimwell replied, “You may talk as
long as you please, Miss Glossop, but nobody can make me believe
that your conduct towards Lord Spoonbill the other day was at all
becoming, or even decent.”
This was a repetition of a former attack, and as in the first instance
this attack had driven the young lady to passionate weeping, Lady
Aimwell was in expectation that a renewal of it would produce a
renewal of the young lady’s sobs and tears. But in this calculation

the baronet’s lady reckoned wrong. The conversation which Miss
Glossop had had the preceding evening with Colonel Crop, and the
bright prospects which lay before her, of rank and opulence and
luxury and homage, rendered an allusion of this nature rather
agreeable than otherwise. Instead therefore of yielding, as before, to
the down-rushing tear and the passionate sobbing, the possible
countess replied with spirit and vivacity, “Lord Spoonbill is as well
qualified to judge of propriety as any one. And if I said or did
anything disrespectful to his lordship, it is his concern.”
In this reply we by no means vindicate Miss Glossop; we rather
think that she was much to blame; for young men are not such good
judges of propriety as old ladies; and it is not to be supposed, that if
a pretty-looking young woman, as Miss Glossop certainly was,
should behave with impertinent forwardness towards so gay and
gallant a young gentleman as Lord Spoonbill, that his lordship would
reprove her, and administer a wholesome lesson on the subject of
decorum.
Lady Aimwell was precisely of our opinion on this point, and
answered accordingly, “Miss Glossop, are you a downright
simpleton? Or what do you mean by such language? Nothing could
be better amusement for Lord Spoonbill, than to see you make a fool
of yourself.”
Here Lady Aimwell had clearly the advantage of Miss Glossop. It
was indeed true, that Lord Spoonbill had been mightily amused with
seeing the ridiculous and fantastic airs which the young lady shewed
off at the castle. But though Lady Aimwell was right, the young lady
thought she was wrong. And from what Miss Glossop had heard on
the preceding evening from Colonel Crop, there was not in her mind
the remotest suspicion that Lord Spoonbill had regarded her
demeanour with any other feeling than that of approbation.
Several times was Miss Glossop on the very brink of exultingly
avowing to her ladyship what had been said by Colonel Crop
concerning the approbation which that discriminating judge of
propriety Lord Spoonbill had been pleased to express of herself. But
as frequently she checked herself, since she thought that the mode

in which Lord Spoonbill had conveyed to her his approbation and
admiration were not quite according to the etiquette of Lady
Aimwell’s grandmother’s sampler.
The inward consciousness however that Lord Spoonbill was
graciously disposed towards her, gave her unusual calmness and
composure, so that she could patiently bear much of the rebuke that
was addressed to her by Lady Aimwell.
But at last came the grand, decisive, interrogatory, which referred
to Colonel Crop’s negociation. Now we cannot approve Lady
Aimwell’s conduct in leaving her young friend exposed to such
negociation; for it was very obvious, that on the preceding evening
her ladyship had retired early, because she was displeased with the
visible symptoms of Colonel Crop’s extraordinary attention to the
young lady. With an exulting and almost triumphing confidence did
Lady Aimwell say, “Now, pray, Miss Glossop, may I take the liberty to
ask, did your friend Colonel Crop deliver any message to you from
your favorite Lord Spoonbill?”
There was a sneer in the phraseology of this question, there was
also a still stronger expression of contempt in the tone and cadence
of it. And thereat Miss Glossop coloured, not blushed merely with
maiden diffidence and modesty, but coloured with mighty and
puissant indignation at the question, at the language in which it was
conveyed, and at the tone in which it was uttered. The
consciousness that she was destined to a high rank in society, and
that she was honored with the approbation of so great a man as Lord
Spoonbill, gave her an additional confidence, and increased her
natural pertness, and she replied, “If your ladyship must know, I can
tell you that Colonel Crop did deliver a message to me from Lord
Spoonbill. What that message was, your ladyship may know
hereafter.”
At this reply Lady Aimwell was struck with tenfold astonishment.
And we will here do her ladyship the justice to acknowledge, that
whatever might be the spirit of her endeavours, they were certainly
directed with a view to the young lady’s good. For Lady Aimwell,
though not the brightest woman in the world, could easily see that a

Welcome to our website – the ideal destination for book lovers and
knowledge seekers. With a mission to inspire endlessly, we offer a
vast collection of books, ranging from classic literary works to
specialized publications, self-development books, and children's
literature. Each book is a new journey of discovery, expanding
knowledge and enriching the soul of the reade
Our website is not just a platform for buying books, but a bridge
connecting readers to the timeless values of culture and wisdom. With
an elegant, user-friendly interface and an intelligent search system,
we are committed to providing a quick and convenient shopping
experience. Additionally, our special promotions and home delivery
services ensure that you save time and fully enjoy the joy of reading.
Let us accompany you on the journey of exploring knowledge and
personal growth!
ebookultra.com

Full download Sensors and Transducers 3rd ed Edition Ian Sinclair pdf docx

More Related Content

Similar to Full download Sensors and Transducers 3rd ed Edition Ian Sinclair pdf docx (20)

Recently uploaded (20)

Full download Sensors and Transducers 3rd ed Edition Ian Sinclair pdf docx