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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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maailman ja kaiken käsittäväksi yhteydeksi. Jos Sinä olisit ottanut
keisarin maailman ja purppuraviitan, niin olisit perustanut koko
maailman käsittävän valtakunnan ja antanut maailmanrauhan. Sillä
kutka hallitsisivat ihmisiä, jos eivät ne, joilla on vallassaan heidän
omatuntonsa ja käsissään heidän leipänsä? Me olemme ottaneet
keisarin miekan, ja ottamalla sen olemme tietysti hylänneet Sinut ja
lähteneet seuraamaan häntä. Oi, menee vielä vuosisatoja vapaan
järjen rivoudessa, heidän tieteilyssään ja antropofagiassa, sillä kun
he ovat alkaneet rakentaa Baabelin torniansa ilman meitä, niin he
päätyvät antropofagiaan. Mutta juuri silloin peto mateleekin
luoksemme ja nuolee jalkojamme ja vuodattaa niille silmistään
verikyyneliä. Ja me istuudumme pedon selkään ja kohotamme
maljan ja siihen on kirjoitettu: 'Salaisuus!' Ja silloin, mutta vasta
silloin alkaa ihmiselle rauhan ja onnen valtakunta. Sinä ylpeilet
valituillasi, mutta Sinulla on vain valittusi, jotavastoin me
rauhoitamme kaikki. Ja vielä muutakin: kuinka monet noista
valituista, samoinkuin voimakkaista, joista voisi tulla valittuja, lopulta
ovatkaan väsyneet Sinua odottaessaan ja ovat siirtäneet sekä vielä
siirtävät henkensä voiman ja sydämensä hehkun toiselle vainiolle ja
lopettavat siten, että nostavat Sinua vastaan vapaan lippunsa. Mutta
tämän lipun olet Sinä itse nostanut. Meillä sen sijaan kaikista tulee
onnellisia, eivätkä he enää kapinoi eivätkä tuhoa toisiaan, kuten
Sinun vapautesi aikana kaikkialla tapahtui. Oi, me saamme heidät
vakuutetuiksi siitä, että heistä vasta silloin tulee vapaita, kun he
luopuvat vapaudestaan meidän hyväksemme ja alistuvat meidän
valtaamme. Ja mitä, olemmeko silloin oikeassa vai valehtelemmeko?
He itse tulevat vakuutetuiksi siitä, että olemme oikeassa, sillä he
muistavat, millaisiin orjuuden ja levottomuuden kauhuihin heidät
saattoi Sinun vapautesi. Vapaus, vapaa henki ja tiede johtavat heidät
semmoisiin rotkoihin ja asettavat heidän eteensä sellaisia ihmeitä ja

ratkaisemattomia salaisuuksia, että toiset heistä, alistumattomat ja
hurjat, tuhoavat itsensä, toiset, jotka ovat alistumattomia, mutta
vähävoimaisia, tuhoavat toisensa, ja jäljelläolevat, vähäväkiset ja
onnettomat, matelevat jalkojemme juureen ja parkuvat meille: 'Niin,
te olitte oikeassa, teillä yksin oli hallussanne Hänen salaisuutensa, ja
me palaamme teidän luoksenne, pelastakaa meidät meiltä
itseltämme.' Kun he saavat meiltä leipää, niin he tietysti selvästi
näkevät, että me otamme heiltä heidän omaa, heidän omin käsin
hankkimaansa leipää jakaaksemme niitä heille itselleen, mitään
ihmettä tekemättä, he näkevät, että me emme ole muuttaneet kiviä
leiviksi, mutta totisesti he paljon enemmän kuin leivästä iloitsevat
siitä, että saavat sen meidän käsistämme! Sillä kovin hyvästi he
muistavat, että ennen, ilman meitä, leivät heidän käsissään
muuttuivat vain kiviksi, mutta kun he palasivat meidän luoksemme,
niin kivetkin heidän käsissään muuttuivat leiviksi. Suuren, suuren
arvon he antavat sille, mitä merkitsee alistuminen kerta kaikkiaan!
Niin kauan kuin ihmiset eivät ymmärrä tätä, he ovat onnettomat.
Kuka on kaikkein enimmän vaikuttanut siihen, että he eivät tätä
ymmärrä? Kuka on hajoittanut lauman ja päästänyt sen kulkemaan
tuntemattomia teitä? Mutta lauma kootaan yhteen uudelleen ja se
alistuu taas ja nyt jo ainaiseksi. Silloin me annamme heille heikkojen
olentojen hiljaisen, nöyrän onnen, ja heikoiksi olennoiksihan heidät
on luotu. Oi, me saamme viimein heidät vakuutetuiksi siitä, että ei
pidä ylpeillä, mutta Sinä koroitit heidät ja opetit siten ylpeilemään; me
todistamme heille, että he ovat heikkoja, että he ovat vain
lapsiraukkoja, mutta että lapsen onni on suloisin kaikista. He tulevat
aroiksi ja he alkavat katsoa meihin sekä painautua meidän turviimme
peloissaan niinkuin linnunpoikaset emoansa vastaan. He
ihmettelevät ja pelkäävät meitä ja ylpeilevät siitä, että me olemme
niin voimakkaat ja ylpeät, että olemme voineet taltuttaa niin hurjan

tuhatmiljoonaisen lauman. He vapisevat heikkoina meidän
vihaamme, heidän mielensä tulee araksi, heidän silmänsä tulevat
herkkäkyynelisiksi kuin lasten ja naisten, mutta yhtä helposti he
myös meidän viittauksestamme siirtyvät iloitsemaan ja nauramaan,
valoisaan riemuun ja onnelliseen lapsen lauleluun. Niin, me
pakotamme heidät tekemään työtä, mutta työstä vapaina hetkinä me
järjestämme heidän elämänsä lasten leikiksi, jossa lasten laulut
kaikuvat, jossa laulellaan kuorossa ja tanssitaan viattomia tansseja.
Oi, me sallimme heidän tehdä syntiäkin, he ovat heikkoja ja
voimattomia, ja he rakastavat meitä kuin lapset sen tähden, että me
sallimme heidän tehdä syntiä. Me sanomme heille, että jokainen
synti annetaan anteeksi, jos se on tehty meidän luvallamme; me
sallimme heidän tehdä syntiä sen tähden, että me rakastamme heitä,
ja rangaistukset näistä synneistä me, olkoon menneeksi, otamme
päällemme. Me otamme ne päällemme, ja he jumaloivat meitä
hyväntekijöinään, jotka ovat Jumalan edessä ottaneet kantaakseen
heidän syntinsä. Eivätkä he salaa mitään meiltä. Me sallimme tai
kiellämme heitä elämästä vaimojensa ja rakastajattariensa kanssa,
heillä saa olla tai ei saa olla lapsia, — aina sen mukaan, miten
kuuliaisia he ovat, —- ja ilolla ja riemulla he alistuvat tahtoomme,
Omantuntonsa kiduttavimmat salaisuudet — kaikki, kaikki he
ilmoittavat meille, ja me ratkaisemme kaiken, ja he luottavat ilomielin
ratkaisuumme, sillä se vapauttaa heidät persoonallisen ja vapaan
ratkaisun suuresta huolesta ja kauheista tuskista, joita he nykyisin
saavat kärsiä. Ja kaikista tulee onnellisia, kaikista miljoonista
olennoista, paitsi niistä sadoistatuhansista, jotka heitä hallitsevat.
Sillä vain meistä, joiden suojeltavana on salaisuus, tulee onnettomia.
Tulee olemaan tuhansia miljoonia onnellisia lapsia ja satatuhatta
marttyyria, jotka ovat ottaneet kantaakseen hyvän ja pahan
tietämisen kirouksen. Hiljaa he kuolevat, hiljaa sammuvat Sinun

nimeesi ja haudan tuolla puolen saavat osakseen vain kuoleman.
Mutta me säilytämme salaisuuden ja heidän onnekseen
houkuttelemme heitä taivaallisella ja iankaikkisella palkinnolla. Sillä
jos toisessa maailmassa olisi jotakin olemassa, niin se ei tietenkään
olisi heidän kaltaisiaan varten. Sanotaan ja ennustetaan, että Sinä
tulet ja voitat uudelleen, tulet valittujesi kanssa, ylpeittesi ja
voimakkaittesi kanssa, mutta me sanomme, että he ovat pelastaneet
ainoastaan itsensä, kun taas me olemme pelastaneet kaikki.
Sanotaan, että pedon selässä istuva ja käsissään salaisuutta pitävä
portto saatetaan häpeään, että vähäväkiset taas nousevat kapinaan,
että purppuraviitta reväistään ja hänen 'inhoittava' ruumiinsa
paljastetaan. Mutta silloin minä nousen ja osoitan Sinulle tuhansia
miljoonia onnellisia lapsia, jotka eivät ole tunteneet syntiä. Ja me,
jotka heidän onnensa tähden olemme ottaneet kantaaksemme
heidän syntinsä, me astumme eteesi ja sanomme: 'Tuomitse meidät,
jos voit ja uskallat.' Tiedä, että minä en pelkää Sinua. Tiedä, että
minäkin olen ollut erämaassa, että minäkin olen elättänyt henkeäni
heinäsirkoilla ja juurilla, että minäkin olen siunannut vapautta, jolla
Sinä olet onnellistuttanut ihmiset, minäkin valmistauduin kuulumaan
Sinun valittujesi joukkoon, niiden joukkoon, jotka ovat voimakkaat ja
mahtavat ja palavat halusta 'täyttää lukumäärän'. Mutta minä tulin
järkiini enkä tahtonut palvella mielettömyyttä. Minä käännyin takaisin
ja liityin niiden joukkoon, jotka paransivat Sinun sankaritekosi. Minä
menin pois ylpeitten parista ja palasin nöyrien luo näiden
kuolevaisten onnen tähden. Se, mitä minä puhun Sinulle, toteutuu, ja
meidän valtakuntamme rakentuu. Toistan Sinulle, jo huomenna Sinä
saat nähdä tämän kuuliaisen lauman, joka minun ensimmäisestä
viittauksestani syöksyy kasaamaan hiiliä Sinun roviotasi varten, jolla
minä poltan Sinut sen tähden, että tulit meitä häiritsemään. Sillä Sinä

olet paremmin kuin kukaan muu ansainnut roviomme. Huomenna
poltan Sinut. Dixi.»
Ivan pysähtyi. Hän oli kiihtynyt puhuessaan ja puhui innostuneesti.
Lopetettuaan hän äkkiä alkoi hymyillä.
Aljoša, joka oli kuunnellut häntä ääneti, mutta lopulta hyvin
kiihtyneenä monta kertaa koettanut keskeyttää veljensä puheen,
vaikka nähtävästi oli hillinnyt itsensä, alkoi äkkiä puhua aivan kuin
olisi riuhtaissut itsensä irti:
— Mutta… tämä on järjettömyyttä! — huudahti hän punastuen. —
Sinun runoelmasi on ylistys Jeesukselle, eikä herjaus… niinkuin sinä
sen tahdoit. Ja kuka uskoo puhettasi vapaudesta? Noinko, noinko se
on ymmärrettävä! Tämmöinenkö on oikeauskoisuuden käsitys…
Tämä on Rooma, eikä Roomakaan kokonaisuudessaan, tämä on
valhetta, — tätä ovat huonoimmat katolilaisista, inkvisiittorit,
jesuiitat!… Eikä ollenkaan voi olla olemassakaan niin
mielikuvituksellista henkilöä kuin sinun inkvisiittorisi. Mitä ihmisten
syntejä he ottavat kantaakseen? Mitä salaisuuden säilyttäjiä ovat
nuo, jotka ovat ottaneet päällensä jonkinmoisen kirouksen ihmisten
onnen tähden? Milloin niitä on nähty? Me tiedämme jesuiitat, heistä
puhutaan pahaa, mutta ovatko he sellaisia kuin sinä kuvaat? He ovat
aivan muuta, kokonaan muuta… He ovat yksinkertaisesti Rooman
armeija tulevaa koko maailman käsittävää maallista valtakuntaa
varten, jonka hallitsijana on keisari — Rooman ylipappi… siinä on
koko ihanne, mutta ilman mitään salaisuuksia ja ylevää murhetta…
Kaikkein yksinkertaisinta vallanhimoa, likaisten maallisten
hyvyyksien tavoittelua, orjuuttamisen halua… jonkinmoista tulevaa
maaorjuutta, niin että he ovat isäntiä… siinä koko heidän

hommansa. Kenties he eivät usko Jumalaankaan. Sinun kärsivä
inkvisiittorisi on pelkkä mielikuvituksen tuote…
— Seis, seis, — nauroi Ivan, — sinäpä vasta tulistuit.
Mielikuvituksen tuote, sanot sinä. Olkoon vain! Tietysti se on
kuvittelua. Sallihan kuitenkin: luuletko sinä todellakin, että koko
viimeisten vuosisatojen katolinen liike tosiaankin on vain pyrkimystä
valtaan yksistään likaisten hyvyyksien tähden? Eiköhän vain isä
Paísi opettane sinulle tuommoisia?
— Ei, ei, isä Paísi päinvastoin kerran puhui jotakin samaan
suuntaan kuin sinä… mutta tietysti toista, aivan toista, — puuttui
Aljoša äkkiä puheeseen.
— Arvokas tiedonanto, vaikka sanotkin sen olleen »aivan toista».
Minä kysynkin sinulta juuri sitä, miksi sinun jesuiittasi ja inkvisiittorisi
ovat liittyneet yhteen vain kurjien aineellisten etujen takia. Miksi
heidän joukossaan ei voi sattumalta olla ainoatakaan marttyyria, jota
kiduttaa suuri murhe ja joka rakastaa ihmiskuntaa? Näetkö: otaksu,
että löytyy vaikkapa vain yksi ainoa kaikkien näiden vain aineellisia
ja saastaisia hyvyyksiä tavoittelevien joukosta, — vaikkapa vain yksi
ainoa sellainen kuin minun inkvisiittorivanhukseni, joka itse on syönyt
juuria erämaassa ja riehunut voittaakseen lihansa, jotta tulisi
vapaaksi ja onnelliseksi, mutta joka on samalla koko elämänsä ajan
rakastanut ihmiskuntaa ja äkkiä nähnyt kaiken sekä huomannut, että
ei ole suuri moraalinen autuus saavuttaa tahdon täydellisyys
varmistuakseen samaan aikaan siitä, että miljoonat muut Jumalan
luomat olennot ovat vain pilkaksi syntyneet eivätkä koskaan jaksa
tulla toimeen vapautensa kanssa, että kurjista kapinoitsijoista ei
koskaan tule jättiläisiä, jotka saavat tornin valmiiksi, että suuri
idealisti ei unelmoinut harmoniastaan tämmöisiä hanhia varten.

Ymmärrettyään kaiken tämän hän kääntyi takaisin ja liittyi… järkeviin
ihmisiin. Eikö tämmöistä todellakaan olisi voinut tapahtua?
— Kehen liittyi, mihin järkeviin ihmisiin? — huudahti Aljoša
melkein kiivastuneena. — Ei ole heillä mitään sellaista järkeä eikä
mitään sellaisia salaisuuksia… On ainoastaan jumalattomuutta, siinä
on heidän koko salaisuutensa. Sinun inkvisiittorisi ei usko Jumalaan,
siinä on koko hänen salaisuutensa!
— Vaikkapa niinkin! Vihdoinkin sinä sen huomasit. Tosiaankin asia
on niin, siinä tosiaankin on koko salaisuus, mutta eikö se ole
kärsimystä esimerkiksi hänenkaltaiselleen ihmiselle, joka on
tuhlannut koko elämänsä sankaritekoon erämaassa eikä ole voinut
parantua rakkaudestaan ihmiskuntaan? Elämänsä ehtoolla hän tulee
selvästi vakuutetuksi siitä, että ainoastaan suuren, peloittavan
hengen aivoitukset voisivat saada edes jossakin määrin siedettävän
järjestyksen toimeen vähäväkisten kapinoitsijoiden, noiden
»viimeistelemättömien, pilkaksi luotujen koe-olentojen» elämässä. Ja
tultuaan tästä vakuutetuksi hän näkee, että on kuljettava viisaan
hengen, kuoleman ja hävityksen kauhean hengen, osoittamaa
suuntaa ja sitä varten hyväksyttävä valhe ja petos sekä johdettava
tietoisesti ihmisiä kuolemaan ja hävitykseen pettäen samalla heitä
kaiken aikaa matkan kestäessä, jotta he eivät mitenkään tulisi
huomanneeksi, mihin heitä viedään, niin että nämä kurjat soaistut
edes matkalla pitäisivät itseään onnellisina. Ja huomaa, tämä on
petosta Hänen nimeensä, jonka ihanteeseen vanhus koko elämänsä
ajan oli niin intohimoisesti uskonut! Eikö tämä ole onnettomuutta? Ja
joskin vain yksi ainoa tämmöinen olisi joutunut koko tuon »vain
saastaisten hyvyyksien takia valtaa himoitsevan» armeijan
etunenään, — niin eikö tuo yksi tuollainen jo ole kylliksi, jotta siitä
syntyisi murhenäytelmä? Eikä siinä kyllin: riittää jo yksikin

tämmöinen etunenässä kulkeva tekemään sen, että koko Rooman
asiasta kaikkine armeijoineen ja jesuiittoineen löytyy lopulta
todellinen johtava aate, tämän asian korkein aate. Minä sanon
sinulle suoraan uskovani lujasti, että tämä ainoa ihminen ei koskaan
ole puuttunut liikkeen johdossa olevien keskuudesta. Kukapa tietää,
kenties Rooman ylipappien joukossakin on sattunut olemaan näitä
ainoita. Kukapa tietää, kenties tuo kirottu ukko, joka niin
itsepintaisesti omalla tavallaan rakastaa ihmiskuntaa, on nytkin
olemassa kokonaisena joukkona monia tuollaisia ainoita ukkoja eikä
ollenkaan satunnaisesti, vaan on olemassa sopimuksena, salaisena
liittona, joka jo ammoin on perustettu salaisuuden suojelemista
varten, sen suojelemiseksi onnettomilta ja heikoilta ihmisiltä, jotta
heistä tehtäisiin onnellisia. Tämä on ehdottomasti olemassa ja on
niin oleva. Mielessäni väikkyy, niinkuin myös vapaamuurareilla olisi
jotakin tämän salaisuuden tapaista pohjanaan, ja siksipä katolilaiset
niin vihaavat vapaamuurareita, kun näkevät heissä kilpailijoita,
aatteen yhteyden pirstoamista, silloin kun pitäisi olla yksi lauma ja
yksi paimen… Muuten puolustaessani ajatustani minä olen kuin
tekijä, joka ei ole kestänyt kritiikkiäsi. Riittää tästä.
— Kenties sinä itse olet vapaamuurari! — pääsi äkkiä Aljošan
suusta.
— Sinä et usko Jumalaan, — lisäsi hän, nyt jo hyvin murheellisena.
Sitäpaitsi hänestä näytti, kuin veli olisi katsonut häntä ivaten. —
Miten sinun runoelmasi loppuu? — kysyi hän äkkiä katsellen
maahan. —
Vai onko se jo lopussa?
— Aikomukseni oli lopettaa se näin: kun inkvisiittori on vaiennut,
niin hän odottaa jonkin aikaa, että Vanki vastaisi hänelle. Hänestä on
vaikeata Hänen vaitiolonsa. Hän oli nähnyt, kuinka Vanki koko ajan

oli kuunnellut häntä katsellen läpitunkevasti ja hiljaa suoraan hänen
silmiinsä ja nähtävästi tahtomatta väittää mitään vastaan. Ukko olisi
tahtonut, että toinen olisi sanonut hänelle jotakin, vaikkapa
katkeraakin ja peloittavaa. Mutta Hän lähestyy äkkiä ääneti vanhusta
ja suutelee hiljaa hänen verettömiä yhdeksänkymmenvuotiaita
huuliaan. Siinä on koko vastaus. Ukko hätkähtää. Hänen huuliensa
reunat hieman nytkähtävät; hän menee ovelle, avaa sen ja sanoo
Hänelle: »Mene, äläkä tule enää… älä tule ollenkaan… milloinkaan,
milloinkaan!» Ja hän päästää Hänet »kaupungin tummille toreille».
Vanki poistuu.
— Entä ukko?
— Suudelma polttaa hänen sydäntään, mutta ukko pitää entisen
aatteensa.
— Ja sinä yhdessä hänen kanssaan, sinä myös? — huudahti
Aljoša surullisesti. Ivan alkoi nauraa.
— Tämähän on pötyä, Aljoša, tämähän on vain järjettömän
ylioppilaan järjetön runoelma, ylioppilaan, joka ei koskaan ole
kirjoittanut kahta säettäkään. Miksi sinä otat sen niin vakavasti?
Etköhän vain luule, että matkustan nyt suoraan sinne, jesuiittain luo,
yhtyäkseni niitten ihmisten joukkoon, jotka parantavat Hänen
sankaritekoaan? Herra Jumala, mitä se minuun kuuluu! Minähän
sanoin sinulle: kunhan vain pääsen jotenkuten kolmenkymmenen
vuoden ikään asti, niin sitten — pikari lattiaan!
— Entä tahmeat lehdet ja rakkaat haudat ja sininen taivas ja
armas nainen! Kuinka sinä aiot elää, kuinka rakastaa niitä? —
huudahti Aljoša surullisesti. — Onko se mahdollista, kun on
tuommoinen helvetti rinnassa ja päässä? Ei, sinä menet pois juuri

sitä varten, että yhtyisit heihin… tai jos ei ole niin, niin sinä surmaat
itse itsesi, sinä et jaksa sietää tätä!
— On olemassa sellainen voima, joka kestää kaiken! — lausui
Ivan kylmästi naurahtaen.
— Mikä voima?
— Karamazovin voima… Karamazovien alhaisuuden voima.
— Siis hukkua irstailuun, kuolettaa sielunsa turmeluksessa, niinkö,
niinkö?
— Ehkäpä niinkin… vaikka kolmenkymmenen vuoden ikään
mennessä kenties voin sen välttääkin, mutta sitten…
— Kuinka vältät? Miten vältät? Se on mahdotonta, kun on sellaiset
ajatukset kuin sinulla.
— Taaskin Karamazovien tavalla.
— Niinkö, että »kaikki on luvallista»? Kaikki on luvallista, niinkö,
niinkö?
Ivan rypisti kulmiaan ja tuli äkkiä omituisen kalpeaksi.
— Ahaa, sinä tartuit eiliseen pikku sanaan, joka niin loukkasi
Miusovia… ja joka sai veli Dmitrin niin naiivilla tavalla hyökkäämään
esiin ja toistamaan sen, — naurahti hän vääristäen suutaan. —
Olkoon niinkin: »kaikki on luvallista», jos kerran sana on tullut
sanotuksi. Minä pysyn siinä. Eikä myöskään Mitjkan sanontatapa ole
hullumpi.
Aljoša katseli häntä ääneti.

— Minä, veliseni, ajattelin lähtiessäni, että omistan tässä
maailmassa edes sinut, — lausui äkkiä Ivan odottamattoman
tunteellisesti, — mutta nyt näen, ettei sinunkaan sydämessäsi ole
sijaa minulle, rakas erakkoni. Tunnuslauselmaa »kaikki on luvallista»
minä en hylkää, no, senpä takia sinä hylkäät minut, niinkö, niinkö?
Aljoša nousi, astui hänen luokseen ja suuteli ääneti ja hiljaa hänen
huuliaan.
— Kirjallista varkautta! — huudahti Ivan äkkiä riemastuen. —
Tämän sinä olet varastanut minun runoelmastani! Kiitos kuitenkin.
Nouse, Aljoša, menkäämme, jo on aika niin minun kuin sinunkin.
He lähtivät ulos, mutta pysähtyivät ravintolan ovelle.
— Tiedätkö mitä, Aljoša, — lausui Ivan lujalla äänellä, — jos
minusta todellakin on tahmeitten lehtien harrastajaksi, niin minä
rakastan niitä ainoastaan sinua muistellen. Minulle riittää se, että
sinä olet täällä jossakin, enkä minä menetä elämänhaluani. Riittääkö
tämä sinulle? Jos tahdot, niin pidä tätä vaikkapa rakkauden
tunnustuksena. Mutta nyt mene sinä oikealle, minä menen
vasemmalle, riittää jo, kuuletko, riittää. Toisin sanoen, jos minä
huomenna en matkustaisikaan pois (luullakseni lähden varmasti) ja
me vielä sattuisimme jotenkuten tapaamaan toisemme, niin kaikista
näistä aiheista älä puhu kanssani enää sanaakaan. Pyydän sitä
hartaasti. Äläkä myöskään veli Dmitristä, pyydän sitä erityisesti, älä
edes aloita koskaan enää keskustelua kanssani, — lisäsi hän äkkiä
ärtyisästi, — kaikki on pohjaan asti pengottua, kaikki on loppuun
puhuttua, eikö niin? Minä puolestani lupaan sinulle myöskin tämän
yhden asian: kun kolmenkymmenen iässä mieleni tekee »paiskata
pikari maahan», niin minä tulen vielä kerran keskustelemaan sinun
kanssasi, olitpa missä tahansa… tulen vaikkapa Amerikasta, tiedä

se. Tulen vartavasten. Tulee olemaan sangen mielenkiintoista
nähdäkin sinut siihen aikaan: millainen mahdatkaan silloin olla?
Jokseenkin juhlallinen lupaus, kuten huomaat. Mutta nyt luultavasti
todellakin sanomme toisillemme jäähyväiset noin seitsemäksi tai
kymmeneksi vuodeksi. No, mene nyt tuon Pater Seraphicus -
ystäväsi luo, hänhän on kuolemaisillaan; jos hän kuolee
poissaollessasi, niin kenties vielä suutut minuun siitä, että olen
viivyttänyt sinua. Näkemiin, suutele minua vielä kerta, kas niin, ja
mene…
Ivan käännähti äkkiä ja meni tiehensä katsomatta enää taakseen.
Se oli samanlaista kuin veli Dmitrin lähtö eilen Aljošan luota, vaikka
eilinen lähtö oli kokonaan toisenluontoinen. Tämä omituinen pikku
havainto lennähti kuin nuoli läpi Aljošan surullisen mielen, surullisen
ja murheellisen tällä hetkellä. Hän odotti vähän aikaa katsellen
veljensä jälkeen. Jostakin syystä hän äkkiä pani merkille, että veli
Ivan kulkee omituisesti heiluen ja että hänen oikea olkapäänsä,
takaapäin katsoen, näyttää olevan alempana kuin vasen. Tätä hän ei
ollut koskaan aikaisemmin huomannut. Mutta äkkiä hänkin kääntyi
ympäri ja lähti miltei juoksujalkaa luostaria kohti. Oli jo tullut
melkoisen pimeä, ja häntä melkein peloitti; hänessä kasvoi jotakin
uutta, johon hän ei olisi voinut antaa vastausta. Alkoi kuten eilenkin
taas tuulla, ja ikivanhat hongat hänen ympärillään alkoivat surullisesti
humista, kun hän saapui erakkomajoja ympäröivään metsikköön.
Hän melkein juoksi. »Pater Seraphicus» — mistä hän sai tuon nimen
— mistä? — välähti Aljošan päässä. — Ivan, Ivan-raukka, milloin
taas saankaan sinut nähdä… Tuossa on erakkomajakin, hyvä
Jumala! Niin, niin, hänpä juuri, tämä Pater Seraphicus, häneltäpä
pelastus tuleekin… häneltä ja ainaiseksi!

Myöhemmin hän suuresti hämmästellen muisteli muutaman kerran
elämänsä aikana, kuinka hän oli saattanut äkkiä erottuaan Ivanista
niin täydelleen unohtaa veljensä Dmitrin, jonka hän aamulla vain
muutamaa tuntia aikaisemmin oli päättänyt ehdottomasti etsiä
käsiinsä, samoinkuin hän oli päättänyt olla poistumatta, ennenkuin
olisi sen tehnyt, vaikkapa olisi täytynyt olla sinä yönä palaamatta
luostariin.
6.
Vielä sangen epäselvää toistaiseksi
Erottuaan Aljošasta Ivan Fjodorovitš lähti kotiinsa Fjodor
Pavlovitšin taloon. Mutta omituista, hänet valtasi äkkiä sietämätön
kaiho, ja, se oli tässä tärkeintä, tuo kaiho kasvoi kasvamistaan joka
askelella, sikäli kuin hän lähestyi taloa. Kaiho itsessään ei ollut
omituista, vaan se, että Ivan Fjodorovitš ei mitenkään voinut
määritellä, mitä hän kaihosi. Hän oli tuntenut kaihon mielessään
usein ennenkin, eikä ollut kumma, että se oli vallannut hänet nyt
tämmöisenä hetkenä, kun hän valmistautui jo huomenna äkillisesti
katkaisemaan kaiken sen, mikä oli houkutellut hänet tänne, ja
uudelleen tekemään jyrkän käänteen toiseen suuntaan sekä
astumaan uudelle, aivan tuntemattomalle tielle, taaskin aivan yksin
niinkuin ennenkin, paljon toivoen, mutta tietämättä mitä, paljon, kovin
paljon odottaen elämältä, mutta osaamatta itse määritellä mitään,
odotuksiinsa enemmän kuin toiveisiinkaan nähden. Ja kuitenkin tällä
hetkellä, vaikka hänen sielussaan oli todellakin uuden ja
tuntemattoman kaiho, häntä kiusasi aivan toinen asia. »Eiköhän vain

vastenmielisyys isänkotia kohtaan?» ajatteli hän itsekseen. »Siltä se
tuntuu, niin vastenmieliseksi on paikka käynyt, ja vaikka viimeisen
kerran tänään astun tuon iljettävän kynnyksen yli, niin se on sittenkin
vastenmielistä»… Mutta ei, ei se ole sitäkään. Eiköhän tätä
surumielisyyttä liene aiheuttanut jäähyväisten sanominen Aljošalle ja
keskustelu hänen kanssaan: »Niin monta vuotta olin puhumatta
mitään koko maailmalle enkä pitänyt sitä puheeni arvoisena, ja
yhtäkkiä laskettelin semmoisen määrän pötyä.» Tämä saattoi
tosiaankin olla nuoren kokemattomuuden ja nuoren turhamaisuuden
harmia sen johdosta, että ei ollut osannut sopivasti tuoda esille
sanottavaansa, vieläpä sellaiselle olennolle kuin Aljoša, johon
nähden hänellä sydämessään epäilemättä oli suuria toiveita. Tietysti
oli tässä sitäkin, nimittäin harmia, ja sitä täytyikin olla ehdottomasti,
mutta ei tämä surumielisyys ollut sitäkään, se oli jotakin muuta.
»Mieli on niin alakuloinen, että ihan inhoittaa, mutta en kykene
määrittelemään mitä tahdon. Olisikohan parasta olla kokonaan
ajattelematta»…
Ivan Fjodorovitš koetti »olla ajattelematta», mutta siitäkään ei ollut
apua. Pääasia oli, että tämä alakuloisuus oli siitä harmillinen ja
ärsytti mielen sillä, että se oli laadultaan tilapäinen ja ikäänkuin aivan
ulkonainen, sen tunsi. Jossakin seisoi ja törrötti jokin olento tai esine
samaan tapaan kuin joskus jokin törröttää silmän edessä eikä sitä
pitkään aikaan huomaa, kun on työssä tai keskustelee innokkaasti,
mutta ilmeisesti kuitenkin tuntee olevansa äreä ja melkein kiusattu,
kunnes vihdoin hoksaa poistaa näkyvistä tuon kelvottoman esineen,
joka usein on aivan tyhjänpäiväinen ja naurettava, jokin esine, jota ei
ole muistettu panna paikoilleen, lattialle pudonnut liina, kaappiin
panematta jäänyt kirja t.m.s. Viimein Ivan Fjodorovitš saapui erittäin
pahalla tuulella ja ärtyneenä isänsä talon luo ja äkkiä, noin
viidentoista askelen päässä siitä, hän katsahdettuaan portille heti

ymmärsi, mikä häntä oli niin kiusannut ja tehnyt hänen mielensä
levottomaksi.
Penkillä portin luona istui ja vilvoitteli itseään illan ilmassa lakeija
Smerdjakov, ja Ivan Fjodorovitš ymmärsi heti luotuaan katseen
häneen, että hänen sielussaankin oli istunut lakeija Smerdjakov ja
että juuri tätä miestä hän ei voinut sietää. Kaikki ympärillä kirkastui ja
selkeni. Äsken jo, kun Aljoša oli kertonut kohtauksestaan
Smerdjakovin kanssa, oli jotakin synkkää ja vastenmielistä äkkiä
tunkeutunut hänen sydämeensä ja saanut siinä vihan nousemaan.
Sitten keskustelun kuluessa oli Smerdjakov joksikin aikaa unohtunut,
mutta jäänyt kuitenkin hänen sieluunsa, ja heti Ivan Fjodorovitšin
erottua Aljošasta ja lähdettyä yksin kotiin oli unhoon jäänyt tunne
äkkiä taas alkanut nopeasti nousta pinnalle. »Voiko todellakin tuo
ala-arvoinen lurjus siinä määrin häiritä rauhaani!» ajatteli hän tuntien
sietämätöntä vihaa.
Seikka oli semmoinen, että Ivan Fjodorovitšille tämä mies oli
todellakin tullut hyvin vastenmieliseksi viime aikoina ja varsinkin
aivan viime päivinä. Hän oli itsekin alkanut huomata tämän melkein
vihankaltaisen tunteen kasvamisen tuota olentoa kohtaan. Kenties
oli tämän vihan kehittymisprosessi saanut niin kärjistyneen muodon
juuri sen tähden, että alussa, kun Ivan Fjodorovitš juuri oli tullut
luoksemme, asiat olivat olleet aivan toisin. Silloin oli Ivan Fjodorovitš
tuntenut jonkinmoista erikoista osanottoa Smerdjakovia kohtaan,
vieläpä pitänyt häntä hyvin omalaatuisena. Itse hän oli totuttanut
tämän kanssaan puhelemaan, vaikka aina ihmettelikin hänen
järkensä eräänlaista sotkuisuutta, tai paremmin sanoen eräänlaista
levottomuutta, eikä käsittänyt, mikä saattoi niin alituisesti ja
poistamattomasti herättää levottomuutta »tässä mietiskelijässä». He
puhuivat myös filosofisista kysymyksistä ja siitäkin, miksi valo loisti

ensimmäisenä päivänä, vaikka aurinko, kuu ja tähdet luotiin vasta
neljäntenä päivänä, ja kuinka tämä on ymmärrettävä; mutta Ivan
Fjodorovitš tuli pian vakuutetuksi siitä, että ei ollut ollenkaan
kysymys auringosta, kuusta eikä tähdistä, että aurinko, kuu ja tähdet
tosin ovat mielenkiintoinen asia, mutta Smerdjakoville täysin
toisarvoinen, ja että hän tahtoo jotakin aivan muuta. Oli miten oli, niin
joka tapauksessa alkoi näkyä ja yhä selvemmin tulla esille rajaton ja
samalla loukattu itserakkaus. Ivan Fjodorovitšia tämä ei ollenkaan
miellyttänyt. Siitä alkoi hänen vastenmielisyytensä. Myöhemmin
alkoivat talossa sotkuiset olot, ilmestyi Grušenjka, alkoi juttu veli
Dmitrin kanssa, tuli huolia, — he puhelivat tästäkin, mutta vaikka
Smerdjakov puhui siitä aina hyvin kiihtyneenä, niin ei taaskaan
mitenkään voinut päästä selville, mitä hän itse siinä oikeastaan
tahtoi. Täytyi suorastaan ihmetellä joittenkin hänen toivomustensa
epäjohdonmukaisuutta ja sotkuisuutta, kun ne tahtomatta tulivat
esille; ne olivat aina epäselviä. Smerdjakov kyseli myötäänsä, teki
jonkinmoisia ilmeisesti harkittuja syrjäkysymyksiä, mutta mitä varten
— sitä hän ei selittänyt, ja tavallisesti hän juuri kiihkeimmin
kysellessään yhtäkkiä vaikeni tai siirtyi aivan muihin asioihin. Mutta
pääasia, mikä viimein lopullisesti suututti Ivan Fjodorovitšin ja
synnytti hänessä niin suuren vastenmielisyyden, — oli jonkinmoinen
iljettävä ja erikoislaatuinen tuttavallisuus, jota Smerdjakov alkoi
selvästi osoittaa häntä kohtaan, sitä selvemmin, kuta pitemmälle
aika kului. Ei niin, että hän olisi ottanut itselleen vapauden olla
epäkohtelias, päinvastoin hän puhui aivan erinomaisen
kunnioittavasti, mutta asiat kehittyivät kuitenkin sellaisiksi, että
Smerdjakov ilmeisesti alkoi, ties mistä syystä, pitää lopulta itseään
jossakin suhteessa solidaarisena Ivan Fjodorovitšin kanssa, puhui
aina semmoisella tavalla, kuin heidän kahden välillä olisi jo jotakin
sovittua ja ikäänkuin salaista, jotakin, mikä joskus oli lausuttu heidän

kummankin puolelta ja minkä vain he molemmat tiesivät, mutta mikä
muille heidän ympärillään liikkuville kuolevaisille oli suorastaan
käsittämätöntä. Ivan Fjodorovitš ei tällöin kuitenkaan pitkään aikaan
ymmärtänyt tätä hänessä kasvavan vastenmielisyyden todellista
syytä, vaan pääsi aivan viime aikoina selville, mistä tässä oli
kysymys. Tuntien halveksimista ja vihastusta hän aikoi kulkea
Smerdjakovin ohi ääneti ja tähän katsomatta pikkuportille, mutta
Smerdjakov nousi penkiltä, ja yksistään jo tästä liikkeestä Ivan
Fjodorovitš heti arvasi miehen haluavan erityisesti keskustella hänen
kanssaan. Ivan Fjodorovitš katsahti häneen ja pysähtyi, ja se, että
hän näin yhtäkkiä pysähtyi eikä mennyt ohi, kuten oli tahtonut juuri
hetkinen sitten, suututti häntä niin, että hän vapisi. Vihoissaan ja
inhoten hän katseli Smerdjakovin riutuneita kuohilaankasvoja, hänen
sileiksi kammattuja ohimoitaan ja pöyhistettyä pientä hiustöyhtöään.
Smerdjakovin vasen, hiukan siristetty silmä vilkutti ja nauroi aivan
kuin olisi sanonut: »Mitä sinä menet, ethän pääse kuitenkaan ohi,
näethän, että meillä kahdella älykkäällä miehellä on keskenämme
puhuttavaa.» Ivan Fjodorovitš vapisi.
»Pois, heittiö, olenko minä sinun toverisi, hölmö!» oli vähältä
lennähtää hänen suustaan, mutta hänen suureksi ihmetyksekseen
kieli lausuikin aivan toista:
— Nukkuuko isä vai onko hän herännyt? — lausui hän hiljaa ja
nöyrästi, odottamatta itsekään sellaista, ja kävi äkkiä, niinikään aivan
odottamatta, istumaan penkille. Hetkiseksi hänet valtasi melkeinpä
pelko, hän muisti sen myöhemmin. Smerdjakov seisoi vastapäätä
häntä kädet selän takana ja katseli häntä varmasti, miltei ankarasti.
— Vielä nukkuu, — lausui hän kiirehtimättä (»Itse, näes, alkoi
ensimmäisenä puhua, enkä minä.») — Ihmettelen minä teitä, herra,

— lisäsi hän vaiti oltuaan ja loi keimaillen silmänsä alas, työnsi
oikean jalkansa eteenpäin ja keikutteli kiiltonahkaisen patiinin
kärkeä.
— Miksi sinä minua ihmettelet? — lausui Ivan Fjodorovitš
katkonaisesti ja kylmästi koettaen kaikin voimin hillitä itseään ja
ymmärsi äkkiä inhoa tuntien, että häntä vaivasi mitä voimakkain
uteliaisuus ja että hän ei millään ehdolla lähde tästä, ennenkuin on
saanut sen tyydytetyksi.
— Miksi te, herra, ette lähde Tšermašnjaan? — sanoi Smerdjakov
heittäen äkkiä häneen silmäyksen ja hymyillen tuttavallisesti. »Miksi
minä hymyilin, se täytyy hänen itsensä ymmärtää, jos on älykäs
mies», näytti hänen siristetty vasen silmänsä sanovan.
— Miksi minun pitäisi mennä Tšermašnjaan? — sanoi Ivan
Fjodorovitš ihmeissään.
Smerdjakov oli taas jonkin aikaa vaiti.
— Itse Fjodor Pavlovitškin pyysi teitä niin hartaasti, — lausui hän
viimein kiirehtimättä ja aivan kuin pitäen itsekin omaa vastaustaan
vähäarvoisena: »mainitsen, näes, toisarvoisen verukkeen, vain
sanoakseni jotakin».
— Äh, piru, puhu selvemmin, mitä sinä tahdot? — huudahti
vihdoin kiukuissaan Ivan Fjodorovitš, jonka nöyryys muuttui
tylyydeksi.
Smerdjakov siirsi oikean jalan vasemman viereen, ojentautui
suoremmaksi, mutta katseli edelleen yhtä rauhallisesti ja samalla
tavoin hymyillen.

— Mitään olennaista ei ole… muuten vain, puhuakseni…
Syntyi taas äänettömyys… He olivat vaiti melkein minuutin ajan.
Ivan Fjodorovitš tiesi, että hänen olisi pitänyt heti nousta ja
suuttua, mutta Smerdjakov seisoi hänen edessään ja näytti
odottavan:
»Minäpä katson, suututko sinä vai etkö?» Siltä ainakin tuntui
Ivan Fjodorovitšista. Viimein hän heilautti ruumistaan noustakseen.
Smerdjakov aivan kuin käytti hyväkseen otollista hetkeä.
— Minun asemani on kauhea, Ivan Fjodorovitš, en edes tiedä,
kuinka auttaisin itseäni, — lausui hän äkkiä selvästi ja lujasti ja
huokaisi lausuessaan viimeisiä sanoja. Ivan Fjodorovitš istuutui taas
heti.
— Molemmat ovat mielettömiä, molemmat ovat ihan kuin pikku
lapsia, — jatkoi Smerdjakov. — Minä puhun teidän isästänne ja
teidän veljestänne Dmitri Fjodorovitšista. Nyt he nousevat, Fjodor
Pavlovitš nimittäin, ja alkavat heti joka hetki ahdistaa minua: »Eikö
hän ole tullut? Miksi ei ole tullut?» — Ja tätä menoa sydänyöhön asti
ja jälkeen sydänyönkin. Mutta jos Agrafena Aleksandrovna ei tule
(sillä he kenties eivät ensinkään koskaan aiokaan tulla), niin
huomisaamuna taas käyvät minun kimppuuni: »Miksi ei ole tullut?
Minkätähden ei tullut, milloin tulee?» — Ikäänkuin minä tässä jollakin
tavoin olisin heidän edessään syyllinen. Toiselta puolen taas on
semmoinen juttu, että heti kun alkaa hämärtää, ja jo ennenkin sitä,
teidän veljenne ilmestyy ase kädessä läheisyyteeni: »Katsokin,
senkin lurjus, liemenkeittäjä: jos päästät huomaamatta hänet
menemään etkä ilmoita minulle, että hän on tullut, — niin tapan sinut
ennen muita.» Yö kuluu, aamulla hekin samoin kuin Fjodor Pavlovitš
alkavat kiusaamalla kiusata minua: »Miksi ei tullut, tuleeko kohta»,

— aivan kuin taaskin minä olisin heidänkin edessään syyllinen
siihen, että heidän neitinsä ei ole näyttäytynyt. Ja siinä määrin he
kumpikin joka päivä ja joka hetki suuttuvat yhä enemmän, että
toisinaan pelosta olen ollut vähältä riistää itse hengen itseltäni. Minä,
herra, en luota heihin.
— Mitäs menit sotkeutumaan asiaan? Miksi aloit viedä tietoja
Dmitri
Fjodorovitšille? — lausui Ivan Fjodorovitš ärtyisästi.
— Ettäkö minä olisin sotkeutunut asiaan? Minä en ole puuttunut
siihen ensinkään, jos tahdotte tietää aivan täsmälleen. Minä olen
koko ajan alusta asti pitänyt suuni kiinni enkä ole uskaltanut sanoa
vastaan, mutta he itse ovat määränneet minut palvelijakseen —
nöyrimmäksi palvelijakseen. Mutta he eivät siitä lähtien osaa
puhuakaan kuin: »Tapan sinut, lurjuksen, jos et pidä silmällä!»
Luulen varmasti, herra, että huomenna minulle sattuu pitkä
lankeaminen.
— Mikä pitkä lankeaminen?
— Semmoinen pitkä kohtaus, harvinaisen pitkä. Jatkuu muutamia
tunteja, tai kenties päivän ja toisenkin. Kerran se kesti minulla kolme
päivää, minä putosin silloin vinniltä. Lakkaa puistattamasta, mutta
sitten alkaa taas; enkä minä kaikkina noina kolmena päivänä
päässyt järkiini. Fjodor Pavlovitš lähettivät silloin hakemaan
Herzenstuben, täkäläisen tohtorin, tämä pani jäitä päälaelle ja käytti
vielä erästä ainetta… Olisin voinut kuolla.
— Mutta sanotaanhan, että kaatuvataudista ei voi edeltäpäin
tietää, millä hetkellä se tulee. Kuinka sinä siis sanot, että se tulee

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