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Inertial Navigation Systems with Geodetic Applications 2nd Edition Christopher Jekeli
Inertial Navigation Systems with Geodetic Applications
2nd Edition Christopher Jekeli Digital Instant Download
Author(s): Christopher Jekeli
ISBN(s): 9783110784329, 3110784327
Edition: 2
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Year: 2023
Language: english
Christopher Jekeli
Inertial Navigation Systems with Geodetic Applications
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Christopher Jekeli
Inertial Navigation
Systems with Geodetic
Applications
2nd Edition
Author
Dr. Christopher Jekeli
School of Earth Sciences
Division of Geodetic Science
Ohio State University
275 Mendenhall Laboratory
125 South Oval Mall
Columbus OH 43210
United States of America
christopher.jekeli@gmail.com
ISBN 978-3-11-078421-3
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Library of Congress Control Number: 2022951986
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To Roberta
Inertial Navigation Systems with Geodetic Applications 2nd Edition Christopher Jekeli
PREFACE
It is amazing that gyros perform as well as they do.
Wallace E. Vander Velde, M.I.T., 1983.
The quote above is a beautiful expression and tribute to the engineering triumph in the
latter half of the twentieth century of the mechanical gyroscope that is an integral part
of the traditional inertial navigation system (INS). In today’s technological age of lasers
and digital electronics, having also benefited inertial sensors, high performance is al-
most expected; yet the most accurate navigation and guidance systems still rely on the
mechanical predecessors of the modern optical gyro. On the other hand, robustness,
reliability, efficiency, and, above all, cost-effectiveness belong to the new generation of
sensors and open the opportunity for increased utility and wider application in com-
mercial, industrial, and scientific endeavors. Concurrent with the technological innova-
tions came new analytical tools, specifically the Kalman filter, that is tailor-made for
the analysis, calibration, and integration of the inertial navigation system. In the last
two decades, the Global Positioning System (GPS) has come to dominate the wide range
of positioning and navigation applications, but the new inertial sensor technology has
enabled a continuing and growing utilization of these marvelous instruments and has
motivated a revival from a number of different perspectives, the geodetic one in the
present case, especially in regard to their integration with GPS.
Geodesy, the science of the measurement and determination of the Earth’s sur-
face, now routinely relies on the exquisite accuracy extractable from GPS, but equally
recognizes the advantages and opportunities afforded by including INS in several ap-
plications. Although the present book is ultimately dedicated to this goal, it should
prove to be of equal value to non-geodesists who desire a thorough understanding of
the mathematics behind the INS and its general use for precision navigation and posi-
tioning. In particular, an attempt is made with this book to join the principles of iner-
tial technology and estimation theory that applies not only to an understanding of the
dynamics of the sensors and their errors, but to the integration of INS with other sys-
tems such as GPS. The text is written by a geodesist who loves the application of math-
ematics and believes that an appreciation of these topics comes best with illustrative
formulas that are derived from first principles. As such, considerable effort is devoted
to establishing preliminary concepts in coordinate systems, linear differential equa-
tions, and stochastic processes, which can also be found readily in other eminent
texts, but whose inclusion makes the present text essentially self-contained. With the
mathematical details, and occasional numerical considerations, it is also hoped that
the reader will obtain an appreciation for Vander Velde’s statement, above, that may
well be extended to the navigation system and further to its entire technological de-
velopment – the achievements in inertial technology are truly amazing.
The text assumes that the reader is fluent in the differential and integral calculus,
as well as the basic vector and matrix algebras. Undergraduate courses in calculus,
https://doi.org/10.1515/9783110784329-202
including the traditional advanced calculus, and linear algebra are, therefore, prerequi-
sites to this text. Further minimal background in complex variables, differential equa-
tions, and numerical and statistical analyses, though not essential, would provide the
reader with additional mathematical maturity to fully benefit from the material. The
book may be used as a text for a college semester course at the senior or graduate level.
Although mathematical derivations are given in detail, the old adage that mathematics
is not a spectator sport should be followed by serious readers.
This text would not have materialized without the significant inspiration derived
from my colleagues while working at the Air Force and at the Ohio State University. I
would like to thank, in particular (affiliations are not necessarily current): Warren
Heller, Jim White, Jacob Goldstein, Robert Shipp (TASC); Triveni Upadhyay, Jorge Gal-
dos (Mayflower Communications, Inc.); David Gleason, Gerald Shaw (Air Force Geo-
physics Laboratory); Jim Huddle (Litton Guidance and Control, Inc.); Alyson Brown
(NAVSYS Corp.); Klaus-Peter Schwarz (University of Calgary); Clyde Goad, Burkhard
Schaffrin, Ren Da, Jin Wang, Jay Kwon (Ohio State University). In addition, several
outstanding lecture notes by W. Vander Velde and A. Willsky (both at M.I.T.) have mo-
tivated key aspects of the mathematical understanding embodied in this text.
C. Jekeli
Columbus, Ohio; July 2000
VIII PREFACE
Preface to the Second Edition
The first two decades of the twenty-first century have witnessed an incredible ad-
vance in technology, not least in the area of geographic positioning and navigation,
made possible by Global Navigation Satellite Systems, of which GPS is still the leading
workhorse. Advancements in inertial instrument technology have focused on con-
sumer and industrial applications, with the development of miniature, robust, inex-
pensive, and power-thrifty, though less accurate, solid-state devices. Still, in the
meantime, the much more accurate inertial measurement units (IMUs) for precision
navigation have not lost ground and continue to serve in aiding satellite navigation
and geodetic kinematic positioning. Of course, the essential physical principles of in-
ertial devices have not changed and with this second edition, most of the changes,
while always an improvement over the previous edition, are more cosmetic than
transformative. The emphasis, as before, is on presenting a comprehensive treatment
of how gyroscopes and accelerometers function and how their data are used in a
number of high-end applications in geodesy. The more significant revisions from the
first edition include, firstly, a new section on miniature vibratory gyroscopes. Al-
though these are not yet ready for precision IMUs, their principle of operation differs
notably from their cousins that are based on angular momentum or the Sagnac effect.
Second, the chapters on the statistical estimation now have a mathematically more
rigorous notation, which makes a clearer distinction between a random variable and
its realized value. Third, the numerical example illustrating the extended Kalman fil-
ter and smoother has been enhanced with more explicit details. Finally, a number of
updates are included in areas that have seen significant changes, specifically coordinate
reference systems, GPS (also other GNSSs are mentioned), and scalar moving-base gra-
vimetry. This second edition also enabled the correction of numerous typographical, as
well, as a few conceptual errors in the overall text of the previous version.
This work would not have ensued without the encouragement of the publisher, and
certainly not without the undying support of my loving wife, to whom it is dedicated.
C. Jekeli
Brunswick, Maine; November 2022
https://doi.org/10.1515/9783110784329-203
Inertial Navigation Systems with Geodetic Applications 2nd Edition Christopher Jekeli
Abstract
This book covers all aspects of inertial navigation systems (INS), including the sensor
technology and the estimation of instrument errors, as well as their integration with
Global Navigation Satellite Systems, specifically the Global Positioning System (GPS)
for geodetic applications. The text is of interest to geodesists, including surveyors,
mappers, and photogrammetrists; to engineers in aviation, navigation, guidance,
transportation, and robotics; and to scientists involved in aerogeophysics and remote
sensing. The most recent developments are covered in this second edition that also
features an updated treatment of the classical material.
– Detailed mathematical derivations of the principles of measurement and data
processing of inertial measurement units for both stabilized and strapdown
systems.
– Complete treatment of the error dynamics from a statistical viewpoint, including
the Kalman filter.
– A self-contained description of GPS with emphasis on kinematic applications.
– Key concepts supported by illustrations and numerical examples.
Christopher Jekeli is Professor Emeritus at the Ohio State University,
where he has taught courses in geometric and physical geodesy, as well as
inertial navigation systems. His extensively published research focused on
Earth’s gravity field for geodetic applications.
https://doi.org/10.1515/9783110784329-204
Inertial Navigation Systems with Geodetic Applications 2nd Edition Christopher Jekeli
Contents
PREFACE VII
Preface to the Second Edition IX
Abstract XI
1 Coordinate Frames and Transformations 1
1.1 Introduction 1
1.2 Coordinate Frames 3
1.2.1 Inertial Frame 3
1.2.2 Earth-Centered–Earth-Fixed Frame 6
1.2.3 Navigation Frame 7
1.3 Transformations 10
1.3.1 Direction Cosines 10
1.3.2 Euler Angles 12
1.3.3 Quaternions 15
1.3.4 Axial Vectors 20
1.3.5 Angular Rates 21
1.4 Differential Equation of the Transformation 22
1.5 Specific Coordinate Transformations 24
1.6 Fourier Transforms 29
2 Ordinary Differential Equations 33
2.1 Introduction 33
2.2 Linear Differential Equations 34
2.3 General Solution of Linear Differential Equations 36
2.3.1 Homogeneous Solution 37
2.3.1.1 An Example 41
2.3.1.2 Fundamental Set of Solutions 42
2.3.2 Particular Solution 44
2.3.2.1 The Example, Continued 46
2.4 Numerical Methods 47
2.4.1 Runge–Kutta Methods 48
2.4.2 Numerical Integration of Functions 54
3 Inertial Measurement Units 55
3.1 Introduction 55
3.2 Gyroscopes 57
3.2.1 Mechanical Gyroscope 59
3.2.1.1 The SDF Gyro 61
3.2.1.1.1 Principal Error Terms 69
3.2.1.2 The TDF Gyro 71
3.2.2 Optical Gyroscopes 76
3.2.2.1 The Ring Laser Gyro 78
3.2.2.1.1 RLG Error Sources 82
3.2.2.2 The Fiber-Optic Gyro 86
3.2.2.2.1 FOG Error Sources 91
3.2.3 MEMS Gyroscopes 91
3.2.3.1 The Dynamics of MEMS Vibratory Gyroscopes 93
3.2.3.2 MEMS Gyroscope Error Sources 102
3.3 Accelerometers 103
3.3.1 Accelerations in Non-inertial Frames 106
3.3.2 Force-Rebalance Dynamics 108
3.3.3 Pendulous Accelerometer Examples 111
3.3.4 Vibrating Element Dynamics 114
3.3.5 Error Sources 116
4 Inertial Navigation System 118
4.1 Introduction 118
4.2 Mechanizations 120
4.2.1 Space-Stabilized Mechanization 122
4.2.2 Local-Level Mechanization 123
4.2.2.1 Schuler Tuning 124
4.2.2.2 Wander-Azimuth Mechanization 127
4.2.3 Strapdown Mechanization 128
4.2.3.1 Numerical Determination of the Transformation Matrix 131
4.2.3.1.1 A Second-Order Algorithm 132
4.2.3.1.2 A Third-Order Algorithm 136
4.2.3.2 Specializations 140
4.3 Navigation Equations 141
4.3.1 A Unified Approach 143
4.3.2 Navigation Equations in the i-Frame 144
4.3.3 Navigation Equations in the e-Frame 145
4.3.4 Navigation Equations in the n-Frame 145
4.3.5 Navigation Equations in the w-Frame 150
4.3.6 Numerical Integration of Navigation Equations 154
5 System Error Dynamics 159
5.1 Introduction 159
5.2 Simplified Analysis 160
5.3 Linearized Error Equations 168
5.3.1 Error Dynamics Equations in the i-Frame 172
XIV Contents
5.3.2 Error Dynamics Equations in the e-Frame 172
5.3.3 Error Dynamics Equations in the n-Frame 174
5.4 Approximate Analysis 179
5.4.1 Effects of Accelerometer and Gyro Errors 181
5.4.2 Vertical Velocity and Position Error Effects 183
5.4.3 Essential Error Modes 184
6 Stochastic Processes and Error Models 188
6.1 Introduction 188
6.2 Probability Theory 188
6.2.1 Gaussian Distribution 194
6.3 Stochastic Processes 195
6.3.1 Covariance Functions 197
6.3.2 Power Spectral Density 199
6.3.3 Ergodic Processes 200
6.4 White Noise 202
6.5 Stochastic Error Models 205
6.5.1 Random Constant 206
6.5.2 Random Walk 207
6.5.3 Gauss–Markov Model 208
6.6 Gravity Models 212
6.6.1 The Normal Gravity Field 212
6.6.2 Deterministic Gravity Models 216
6.6.3 Stochastic Gravity Models 219
6.7 Examples of IMU Error Processes 222
7 Linear Estimation 224
7.1 Introduction 224
7.2 Bayesian Estimation 226
7.2.1 Optimal Estimation Criteria 227
7.2.2 Estimation with Observations 229
7.2.2.1 The A Posteriori Probability Density Function 231
7.2.2.2 The A Posteriori Estimate and Covariance 233
7.3 The Discrete Kalman Filter 236
7.3.1 The Observation Model 237
7.3.2 Optimal State Vector Estimation 238
7.3.2.1 Prediction 241
7.3.2.2 Filtering 242
7.3.2.3 Smoothing 244
7.4 The Discrete Linear Dynamics Model 250
7.5 Modifications 254
7.5.1 Augmented State Vector 254
Contents XV
7.5.2 Closed-Loop Estimation 256
7.6 A Simple Example 258
7.7 The Continuous Kalman Filter 264
7.7.1 Covariance Function 268
7.7.2 Solution to Matrix Ricatti Equation 270
7.7.2.1 Constant Coefficient Matrices 270
7.7.2.2 No System Process Noise 272
7.7.2.3 No Observations 272
8 INS Initialization and Alignment 274
8.1 Introduction 274
8.2 Coarse Alignment 276
8.3 Fine Alignment and Calibration 280
8.3.1 Acceleration Observations 281
8.3.2 Velocity and Azimuth Observations 283
8.3.3 Kinematic Alignment 289
9 The Global Positioning System (GPS) 293
9.1 Introduction 293
9.2 The Global Positioning System 297
9.2.1 Clocks and Time 297
9.2.2 The GPS Signals 299
9.2.3 The GPS Receiver 302
9.3 The GPS Observables 305
9.4 GPS Errors 308
9.5 Combinations of Observations 313
9.5.1 Dual-Frequency Pseudorange and Phase 314
9.5.2 Single and Double Differences 318
9.6 Kinematic Positioning 322
9.6.1 The Dynamics Model 324
9.6.2 The Observation Equations 327
9.6.2.1 Single-Receiver Case 328
9.6.2.2 Multiple-Receiver Case 333
10 Geodetic Application 336
10.1 Introduction 336
10.2 The Inertial Survey System 338
10.2.1 Historical Developments 338
10.2.2 Estimation Methods 341
10.2.2.1 Models and Observations 341
10.2.2.2 Parameter Estimation 344
10.2.3 Typical Results 346
XVI Contents
10.3 GPS/INS Integration 348
10.3.1 Integration Modes 350
10.3.1.1 Decentralized Integration 351
10.3.1.2 Centralized Integration 356
10.3.2 Cycle Ambiguity Determination 360
10.4 Moving-Base Gravimetry 362
10.4.1 Gravitation from Inertial Positioning 366
10.4.2 Gravitation from Accelerometry 370
10.4.2.1 Scalar Gravimetry 373
10.4.2.2 Vector Gravimetry 379
References 385
Index 395
Contents XVII
Inertial Navigation Systems with Geodetic Applications 2nd Edition Christopher Jekeli
1 Coordinate Frames and Transformations
1.1 Introduction
When describing locations of points on or near the Earth’s surface, we most naturally
turn to a system of coordinates. Although one could imagine devising a relational or
synthetic data base to describe the whereabouts of objects and places, it is of necessity
that we assign an algebraic system of coordinates if we wish to go beyond mere loca-
tion information and obtain measures of distance, area, volume, and direction. And,
likewise with navigation, we need to define a coordinate system in which we can mea-
sure our progress and easily determine our course and destination. There are several
coordinate systems from which to choose. Each has its own unique utility depending
on the particular application in a particular discipline. In geodesy we deal with deter-
mining positions, or the mathematics of map projections, or the navigation of a vehi-
cle, or its guidance along a predefined path. Specific coordinate systems must be
defined in each case.
We will be concerned primarily with the Cartesian, or rectangular, coordinates,
whose axes are mutually orthogonal by definition, but this triad of axes, as shown in
Figure 1.1, may assume a variety of orientations in space. The axes of any coordinate
system are designated here generally in numerical order as the 1-axis, the 2-axis, and
the 3-axis. Each system of axes is defined to be right-handed in the sense that a 90
coun-
terclockwise (positive) rotation about the 1-axis, as viewed along the 1-axis toward the
origin, rotates the 2-axis into the 3-axis. Also, a 90
rotation about the 2-axis rotates the
3-axis into the 1-axis; and a 90
rotation about the 3-axis rotates the 1-axis into the 2-axis.
We will denote the set of Cartesian coordinates by a lowercase subscripted letter,
such as xj, j = 1, 2, 3. The corresponding bold letter, x, will denote a vector with xj as
1
2
3
x
x1
x3
e1
e2
e3
x2
Figure 1.1: Cartesian coordinates of vector, x, and unit vectors, ej.
https://doi.org/10.1515/9783110784329-001
components (see Figure 1.1). Also shown in Figure 1.1 is a set of special vectors, called
unit vectors, denoted by ej, j = 1, 2, 3. Each unit vector has only one non-zero component,
namely the jth component equals 1; that is, ej is directed along its respective axis and has
unit length.
The vector representation of x as an ordered triplet of coordinates is
x =
x1
x2
x3
0
B
@
1
C
A. (1:1)
Or, using the unit vectors, we may also write
x = x1e1 + x2e2 + x3e3, (1:2)
where it is clear that the coordinates, xj, are the orthogonal projections of x onto the
respective axes. It is assumed that the reader is familiar with vector (and matrix) alge-
bra, including the usual operations of addition, subtraction, and multiplication (scalar
or dot product, vector, or cross product as well as matrix multiplication and inver-
sion). For a review of these algebras, see, e.g., (Lang 1971).
Before proceeding, a few additional introductory remarks are in order. The geo-
detic/astronomic conventional usage of the terms coordinate system and coordinate
frame will be followed (Moritz and Mueller 1987). The system includes the conventions
and physical theories, or their approximations and models, that are used to define the
triad of coordinate axes; while a frame denotes the accessible realization of the sys-
tem through a set of points whose coordinates are monumented or otherwise observ-
able. The general principles and methodologies of determining a coordinate (or,
reference) system are beyond the scope of this text, and it is enough to know for pres-
ent purposes that each set of coordinate axes is well-defined and accessible and repre-
sents a coordinate frame. In the navigation literature reference is often made to frames
instead of systems, a convention also adhered to in this text, where we will understand
that for each frame there is a system in the background.
The frames that we will deal with are either global or local in extent, where the
“extent” is largely defined by the application and the accuracies desired. The global Car-
tesian coordinates are tied either to the rotating Earth or to the celestial sphere (“fixed”
stars); the local Cartesian coordinates are defined by local directions, such as north,
east, and down. In addition, we consider curvilinear coordinates as alternative descrip-
tors of points in space – we do not use these to characterize the intrinsic properties of
surfaces (or space) which is perhaps their more pertinent mathematical (differential
geometric) application; rather, their use is motivated by the fact that our motions and
positions are generally close to being on a spherical or ellipsoidal surface. These coordi-
nates are still three-dimensional and serve mostly to facilitate computations and deriva-
tions, besides having their own historical significance. The curvilinear coordinates are
2 1 Coordinate Frames and Transformations
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“I love you,” he whispered. “Monimé, I love you.”
“Men have said that to me before,” she answered, “and there was
one man whom I believed.... We built the house of our life upon that
foundation, but it fell to ruins all the same. Soon he ceased to tell
me that he loved me.”
“You are a married woman then?” he asked.
“Yes,” she said.
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left him.”
“Why?” he asked.
“Because we disliked one another. It seemed to me altogether
wrong that a man and a woman totally out of sympathy with one
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selling my pictures.”
“Were there any children?” he asked.
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remained with him. Like flowers, they hide many a sepulchre.”
“It was brave of you to go,” he said.
“I felt it to be a woman’s right,” she declared, spreading her hands
in a gesture of conviction. “Since then I have been a wanderer. I’ve
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“And what about the future?” he asked.
“My dear,” she smiled, “the future is a veil of fog that only lifts for
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For some time they talked; but at length when the little band of
musicians, whose songs had formed a distant accompaniment to
their thoughts, had gone their way, and the sound of the sea alone
traversed the silence, she suggested that he should bring down his
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“The proprietress tells me she has heard you playing in your
room,” she smiled. “She described it as très agréable mais un peu
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Jim was not very willing to comply, for he had been termed a
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His companion, however, was so insistent that he was obliged to
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overcoming a feeling of shyness, and presently he passed into a
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left him, and soon his fine voice was strong enough to be heard in
the hotel, so that the proprietress and some of her guests came tip-
toeing out and stood listening near the open door, the light from the
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shadows across the gravel and on to the encircling palms.
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It was a song which told of a silent, enchanted city built by
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couch, and kissed the mouth of the sleeper....
When he had ended the song there was a moment of silence
before Monimé turned to him. “Do you mean to tell me,” she
exclaimed, “that you have to earn your living at the mines when you
can write verses like that?”
“Oh, it’s only doggerel,” he laughed, “and I cribbed most of the
music from things I’d heard.”
“Have you got the poem written down?” she asked.
“No, I’ve lost my only copy,” he answered. “I stuffed it into a hole
in the woodwork of my berth on a certain tramp steamer, to keep
the cockroaches from coming out. I never could get used to
cockroaches.”
“Jim,” she said, taking his hands in hers, “you are wasting your
life.”
“I am living for the first time to-night,” he replied.
It was midnight when at length they ascended the stairs to their
rooms, but there was on his part a mere pretence of bidding good-
night at their doors. He knew well enough that presently he would
attempt to renew their wonderful romance upon the balcony which
connected their two rooms; but for the moment the serene
inscrutability of her face baffled him. She neither made advance
towards him, nor retreat from him. She seemed, mentally, to be
standing her ground, undisturbed, unmoved. The wisdom of the
ages was in her eyes, and the smile of precognition was on her lips.
In love, man is so simple, woman so wise. Man blunders along,
taking his chance as to whether he shall find favour or give offence;
woman alone knows when the great moment has come, that
moment when the time and the place and the person are plaited into
the perfect pattern. Some women betray that knowledge in their
agitation; some are made shy by the revelation; some, again, have
the imperturbable confidence of their intuition, and these last alone
are the celestials, the daughters of Aphrodite, the children of Isis
and Hathor.
In his room Jim sat for awhile upon the side of his bed, trying to
fathom the unfathomable meaning of her expression. His brain was
full of her—her hair black as the Egyptian darkness, her eyes grey as
the twilight, and her flesh like the alabaster of the Mokattam Hills.
There was such modesty, such reserve in her bearing, and yet with
these qualities there went a kind of confidence, a self-assurance,
which he could not define. In her presence he became aware of the
shortcomings of his own sex, rather than of his mastery; yet at the
same time he was conscious of an overwhelming intensification of
his manhood.
At last, a cigarette as his excuse, he stepped out on to the
balcony, and for some moments stood looking out to sea. When he
took courage to turn towards her window he found that though the
light in the room was still burning, the shutters were closed; and
thus he remained, staring at the green woodwork for what seemed
an interminable time.
He was about to go back disconsolately to his room when the light
was extinguished, and the shutters were quietly pushed open. Who
shall say whether she knew that Jim was standing in silence upon
the balcony, or whether, being prepared for her bed, she now merely
opened the windows that the cool of the night might bring her
refreshing sleep? Woman is wise: she knows if the hour be meet.
Chapter IV: BEDOUIN LOVE
Jim awoke next morning with the feeling that he had come back
to earth from heaven. The events of the night before seemed to
belong to a world of enchantment, and had no relation to the keen,
practical sunlight which now struck into his room through the open
windows, nor to the cool sea breeze which waved the curtains to
and fro, nor yet to the vivid blue sea and the clean-cut rocks which
came into sight as he sat up in bed.
“In the next room,” he mused to himself, “sleeps a woman who in
the darkness was to me the gateway of my dreams, but who in this
bright sunlight will be again only a capable, pretty creature and an
amusing companion. Night, after all, is woman’s kingdom, and in it
she is mistress of all the magic arts of enchantment, she becomes
greater than herself; but day belongs to man. How, then, shall I
greet her?—for my very soul seemed surrendered to her a few hours
ago, yet now I find myself still master of my destiny.”
Like an artist who steps back to view his picture, or like a poet
who measures up his dream, he allowed his mind to take stock of
his emotions. When her head had been thrown back upon the
pillows, and the white column of her throat could be seen in the dim
light of the moon against the black confusion of her hair, it had
seemed to him that the marks of the chisel of the Divine Artist were
impressed upon the alabaster of her flesh. It was as though, gazing
down at her beauty, his eyes had been opened and he had beheld
the handicraft of Paradise.
And when, in his ardour, he had had the feeling of not knowing
what next to do nor what words to utter, her silencing loveliness had
baffled him, so it seemed, because her body was stamped with the
seal of the Infinite and fashioned in the likeness of God. True, she
was but imperfect woman; yet the art of the Lord of Arts had
created her, and, by the magic of the night, he had found her rich in
the inimitable craftsmanship of heaven.
He had seen the glory of heaven in her eyes. He had heard the
voice of all the ages in her voice. In the touch of her lips there had
been the rapture of the spheres, and the gods of the firmament had
seemed to ride out upon the tide of her breath.
But was it she whom he had wanted when he held her pinioned in
his arms? He could not say. It seemed more reasonable to suppose
that through her he was looking towards the splendour which his
soul sought. She was but the necromancy by which he had carried
earth up to heaven; she was the magic by which he had brought
heaven down to the earth. She had been the door of his dreams, the
portal of the sky; and through her he had made his incursion into
the kingdom beyond the stars.
“It was only an illusion,” he said, as he stood at the window,
invigorated by the breeze. “We are actually almost strangers. I don’t
know anything about her, and she knows little of me. It was the
magic of the night employed by scheming Nature for her one
unchanging purpose; and all that happened in the darkness will be
forgotten in the sunlight. We shall meet as friends.”
To some extent he was right, for when at mid-morning she came
down to the blazing beach and seated herself by his side in the
shade of the rocks, she greeted him quietly and serenely, with
neither embarrassment nor familiarity.
“Are you going to bathe this morning?” he asked her, and on her
replying in the affirmative, he told her that he thought he was well
enough to do so, too. At this she showed some concern, but he
reminded her that the water, at any rate near the shore, was warm
to the touch and was hardly likely to do him harm.
The little sandy bay, flanked by rocks which projected into the sea,
was the site of a number of bathing huts and tents used by the
Europeans who lived in the surrounding villas and bungalows. The
breakers rolled in upon this golden crescent, continuously driven
forward by the prevalent north-west wind; but at one side a barrier
of low, shelving rocks formed a small lagoon where the water was
peaceful, and one might look down to the bottom, ten or twelve feet
below the surface, and see the brilliant shells and seaweeds almost
as clearly as though they were in the open air. So strong was the
summer sunlight that every object and every plant at the bottom
cast its shadow sharply upon the sparkling bed; and the passage of
little wandering fishes was marked by corresponding shadows which
moved over the fairyland below.
It was not long before Jim and Monimé were swimming side by
side across this small lagoon to the encircling wall of rocks, and soon
they had clambered on to them and had seated themselves where
the surf rushed towards them from the open azure sea on the one
side, drenching them with cool spray, and on the other side the low
cliffs and rocks, surmounted by the clustered palms, were reflected
in the still water. Here they sunned themselves and talked; and from
time to time, when the heat became too great, they dived down
together with open eyes into the cool, brilliant depths, gliding
amongst the coloured sea-plants, grimacing at one another as they
scrambled for some conspicuous pebble or shell, and rising again to
the surface in a cloud of bubbles.
It was a joyous, exhilarating, agile occupation, far removed from
the enchantments of the darkness; and the glitter of sun and sea
effectually diminished the lure of the night’s witchery.
“You know,” said Jim, suddenly looking at his companion, as they
lay basking upon the spray-splashed rocks, “I can hardly believe last
night was anything but a dream.”
“Let us pretend that it was,” she answered. She pointed down into
the translucent water. “Life is like that,” she said. “We dive down into
those wonderful depths when the glare of actuality is too great, and
we see all the pretty shells down there; and then we have to come
up to the surface again, or we should drown.”
“I see,” he replied; “I was just a passing fancy of yours.”
She answered him gravely. “Women in that respect are not so
different to men. Judge me by yourself.”
“Oh, but there’s a world of difference,” he said, chilled by her
words. “I am simply a vagabond, a wandering Bedouin, here to-day
and over the hills and far away to-morrow.”
“I am also a wanderer,” she smiled. “We are both free beings who
have broken away from the beaten path. We both earn our living,
and claim our independence.”
“Yet the difference is this,” he reminded her, “that the world will
shrug its shoulders at my actions, but will condemn yours.”
She made an impatient gesture. “Oh, that threadbare truism!” she
said. “I have turned my back on the world, and I don’t care what it
thinks. I act according to my principles, and in this sort of thing the
first principle is very simple. If a woman is a thoughtful, responsible
being, earning her own living, and able to lead her own life without
being in the slightest degree dependent on the man of her choice, or
on any other living soul, she is entitled to respond to the call of
nature at that precious and rare moment when her heart tells her to
do so. There should be no such thing as a different law for the man
and for the woman: there should only be a different law for the self-
supporting and the dependent. The sin is when a woman is a
parasite.”
With that she took a header into the water, and he watched her
gliding amidst the swaying tendrils of the sea-plants, like a sinuous
mermaiden.
When she rose to the surface once more he dived in, and swam
over to her, his face emerging but a few inches from hers. “Do you
love me?” he asked, smiling amongst the bubbles.
“No, I hate you,” she replied, striking out towards the shore.
“Why?” he called after her.
“Because you haven’t the sense to leave well alone,” she said, and
thereat she dived once more, nor came to the surface again until
she had reached shallow water.
At luncheon she met him with an ambiguous smile upon her lips;
but finding that he was not eating his food with much appetite, she
at once became motherly and solicitous, refused to allow him to eat
the salad, offered to cut up the meat for him, and directed the
waiter to bring some toast in place of the over-fresh roll which he
was about to break. At the conclusion of the meal she ordered him
to take a siesta in his room, and in this he was glad enough to obey
her, for he was certainly tired.
When he woke up, an hour or so later, and presently went out on
to the balcony, he saw her standing in her room, contemplating her
painting materials.
“May I come in?” he asked.
She nodded. “Have you had a good sleep?” she inquired. “Sit
down and talk to me. I have a feeling of loneliness this afternoon.
I’m not in a mood to paint; yet I suppose I must, or I shall run short
of money.”
He went to her side and put his hands upon her shoulders,
drawing her to him; but she pushed him away from her, with averted
face.
“I said ‘sit down,’” she repeated.
Jim was abashed. “You’re very difficult,” he told her. “I think that
under the circumstances I’d better go. I don’t know where I am with
you.”
“You haven’t tried to find out,” she answered. “You’re quite
capable of understanding me: I should never have let you come into
my life at all if I had not been certain that you had it in you to
understand.”
“Tact is not my strong point,” he said. “I’m just a man.”
“Nonsense!” she replied. “Don’t belittle yourself.”
He was puzzled. “Why, what’s wrong with men?”
“Their refusal to study women,” she answered.
She was not in a communicative mood, and would not be drawn
into argument. He was left, thus, with a disconcerting sense of
frustration, bordering on annoyance. It seemed evident to him that
yesterday, by some secret conjunction of the planets, so to speak,
their destinies had met together in one sentient hour of sympathy;
but that now they had sprung apart once more, and he knew not
what stars in their courses would bring back to him the ripe and
mystic moment.
An appalling loneliness descended like a cloud upon him, and he
was conscious that she too, was experiencing the same feeling. It
was the lot, he supposed, of all persons who were born with the
Bedouin temperament; and he accepted it with resignation.
At length she conducted him—or did he lead her?—down to the
verandah of the hotel; and now she had her paints with her, and
occupied herself in making some colour-notes of the brilliant sea
which stretched before them, and of the golden rocks and vivid
green palms. Jim, meanwhile, read an English newspaper, some
weeks old, which he had chanced upon in the salon; but from time
to time he sat back in his chair and watched her as she worked, his
admiration manifesting itself in his eyes.
“What are you staring at?” she asked him, presently.
“I was admiring the way you handle your paints,” he replied.
“You’re a real artist.”
“The fact that a woman paints,” she remarked, “does not mean
that she is an artist, any more than the fact that she talks means
that she is a thinker. To be an artist requires two things, firstly, that
you have something to express, and, only secondly, that you know
technically how to express it. It is the point of view, the angle of
vision, that counts; and in fact one can say that primarily one must
live an art.”
He nodded. He wondered whether the events of the previous
night were but the living of her art; and the thought engendered a
kind of mild bitterness which led him to give her measure for
measure. “I know what you mean so well,” he said, “because I
happen to have the talent to put things into nice metre and rhyme;
but it is the subject matter that really counts, and that’s where I feel
my stuff is so flat. Sometimes I am obliged to seek experience to
help me.”
“You must let me see some of these poems,” she said, pursuing
the theme no further.
He shook his head. “They are only doggerel, like the one I sang
last night,” he laughed. “They are as shallow as my heart.”
She resumed her painting and he his reading; but his mind was
not following the movement of his eyes.
He was thinking how little he understood his companion. She was
clearly a woman of strong views, one who had taken her life into her
own hands and was facing the world with reliant courage. In fact, it
might be said of her that she was the sort of woman who would not
be turned from what she knew to be right by any qualms of guilty
conscience. He smiled to himself at the epigram, and again allowed
his thoughts to speculate upon her alluring personality.
He found at length, however, that the matter was beyond him;
and presently he turned to his reading once more.
It was while he was so engaged that suddenly he sat up in his
chair, gazing with amazement at the printed page before him.
“Great Scott!” he whispered, pronouncing the words slowly and
capaciously. There was a crazy look of astonishment upon his face.
“What’s the matter?” she asked, glancing at him, but unable to tell
from the whimsical expression of his mouth and eyes what manner
of news had taken his attention.
He looked at her as though he did not see her. Then he read once
more the words, which seemed to dance before him, and again
stared through her into the distance of his breathless thoughts.
“News that concerns you?” she asked.
He nodded, holding his hand to his forehead.
“Bad news?”
“Yes,” he answered, as though speaking in a dream. “Very bad ...
wonderful!”
She could not help smiling, and her intuition quickly jumped to the
truth. “Somebody has died and left you some money?” she
suggested.
He uttered an almost hysterical laugh. “I’m free!” he cried. “Free! I
shall never have to go back to the mines.”
He sprang to his feet, folding the newspaper, and crushing it in his
hand.
“Don’t go and faint again,” she said, quietly.
He laughed loudly, and a moment later was hastening into the
hotel. He snatched his hat from a peg in the hall, and hurried out
through the dusty little garden at the front of the building, and so
into the afternoon glare of the main road. Here he hailed a carriage,
and, telling the driver to take him to the Eastern Exchange Telegraph
office, sat back on the jolting seat, and directed his eyes once more
to the Agony Column of the newspaper. The incredible message read
thus:
James Champernowne Tundering-West, heir to the late
Stephen Tundering-West, of the Manor, Eversfield,
Oxon, is requested to communicate with Messrs.
Browne  Beadle, 135a, Lincoln’s Inn Fields, London.
His uncle was dead, then, and the two sons, his unknown cousins,
must have predeceased him or died with him! He had never for one
moment thought of himself as a possible heir to the little property;
and heaven knows how long it might have been before he would
have had knowledge of his good fortune had he not chanced upon
this old newspaper.
Arrived at his destination, he despatched a cablegram to the
solicitors, notifying them that he would come to England by the first
possible boat. Then he drove on to Cook’s office in the heart of the
city, which he reached not long before it closed; and here, after
some anxious delay, he was told that a berth, just returned by its
prospective occupant, was available on a French liner sailing for
Marseilles that night at eleven o’clock. This he secured without
hesitation, and so went galloping back towards the hotel as the sun
went down.
In the open road, between the city and the hotel another carriage
passed him in which Monimé was sitting, on her way to dine with
some friends, of whom she had spoken to him. He waved to her, and
both she and he called their drivers to a halt. Then, hastening across
to her, he told her excitedly that he was sailing for England that
night.
“You see, I’ve inherited some property,” be explained. “I must go
and claim it at once.”
Her face was inscrutable, but there was no light of happiness in it.
“I’m sorry it has come to an end so soon,” she cried.
“What?” he cried, and it was evident that he was not listening to
her. “You’ve been wonderful to me. We mustn’t lose sight of each
other. This thing has got to go on and on for ever.”
He hardly knew what he was saying. An hour ago she had been
almost the main factor in his existence. Now she was but a fragment
of a life he was setting behind him. It was almost as though she
were fading into a memory before his very eyes. He was, as it were,
looking through her at an amazing picture which was unfolding itself
beyond. The yellow walls of the houses, the sea, the palms, the
sunset, were dissolving; and in their stead he was staring at the
green fields of England, at the timbered walls of an old manor-house
last seen when he was a boy, at the grey stone church amongst the
ilex-trees and the moss-covered tombstones.
“I must go on and pack at once,” he said, standing first on one leg
and then on the other. “You’re sure to be back before I leave. You
can get away by ten, can’t you?”
He wrung her hand effusively, and hurried to his carriage, from
which, standing up, he waved his hat wildly to her as they drove off
in opposite directions.
But when the clock struck ten there was no sign of Monimé and a
few minutes later the hotel porter, who was to accompany him to
the harbour, began to urge him to delay his departure no longer.
Being somewhat flurried, he thought to himself that he would write
her a farewell letter from the steamer, and give it to the porter to
carry back with him.
But by the time he had found his cabin and seen to his baggage,
the siren was blowing, and the porter in alarm was hurrying down
the gangway.
“I’ll write or cable from Marseilles,” he said to himself. “I don’t
suppose she cares a rap about me: the whole thing was due to our
romantic surroundings. But still one would be a fool to lose sight of a
real woman like that.... I wish I knew her name.”
Chapter V: THE SQUIRE OF
EVERSFIELD
The art of life is very largely the art of burying bones. That is the
science of mental economy. When a man is confronted with a
problem which he cannot solve; when, so to speak, Fate presents
him with a bone which he cannot crack, sometimes, without intent,
he slinks away with it and, like a dog, buries it, in the undefined
hope that at a later date he may unearth it and find it then more
manageable.
Even so, during the sea voyage, Jim unconsciously buried the
bewildering thought of Monimé. He was a careless fellow, very
reprehensible, having no actual harm in him, yet bearing a record
pock-marked, so to speak, with the sins of omission. He was one of
the world’s tramps by nature; and now once more he was out upon
the high road, and the lights of the city wherein he had slept had
faded behind him as he wandered onwards into another sunrise. It is
true that he wrote her a long and intense letter upon the day after
his departure, and that he posted this upon his arrival at Marseilles;
but his brain, by then full of other things, conjured up no clear vision
of her, and his heart sent forth no impassioned message with the
written word. He had been deeply stirred by her, but also he had
been baffled; and, as in the case of a dream, he made no effort to
retain the sweetness of the memory.
On the morning of his arrival he called at the office of the
solicitors who had inserted the advertisement, and was not a little
startled to find himself greeted with that kind of obsequiousness
which he had supposed to have vanished from Lincoln’s Inn fifty
years ago.
The little pink-and-white man who was the senior partner, and
whose name was Beadle, rubbed his hands together as though he
were washing them, and actually walked backwards for some paces
in front of his visitor, bowing him into a shabby leather chair which
stood beside the large, imposing desk.
“I hope,” he crooned, when Jim had established his identity, “that
we may still have the duty, and pleasure, of serving you, sir, as we
have served your uncle and your grandfather.”
“I hope so,” replied Jim. “I suppose you know all the ins and outs
of the family affairs.”
Mr. Beadle smilingly directed the young man’s attention to a
number of black tin boxes stacked in the corner of the room. “The
Tundering-West documents for the last two hundred years,” he
declared, blowing his breath through his teeth, an action which
served him for laughter.
Jim had a vision of legal formalities and lawyers’ rigmaroles—
things which he had always detested; and the passing thought
contributed to the growing dislike he felt for the harmless, but
sycophantic, Mr. Beadle.
“Well, first of all,” he said, “tell me what my inheritance consists
of, and what sort of income I’ve got.”
Mr. Beadle explained that the little property comprised some two
hundred acres, most of which were rented; the score of houses and
cottages which constituted the tiny little village; the small but
comfortable manor-house; and twenty thousand pounds of invested
capital. This was better than Jim had expected, and his pleasure was
manifest by the broad smile upon his tanned face.
“You see, you will have quite a comfortable income in a small
way,” the solicitor told him. “I do not think that your duties will
embarrass you. You will find your tenants very respectful and
deferential country-people, who will give you little bother; and your
obligations as landlord will be very easily discharged.”
“They’re a bit behind the times, eh?” suggested Jim.
“Ah, my dear sir,” said Mr. Beadle, “I am thankful to say that there
are still some parts of the English countryside where a gentleman
may live in comfort, and where the people keep their place.”
Jim was astonished by the remark, for he had believed such
sentiments to be entombed in the novels of long ago. “Poor old
England!” he murmured. “We’re a comic race, aren’t we, Mr. Beetle?”
“‘Beadle,’” the little old man corrected him; and “Sorry!” said Jim.
They spoke later of the tragedies which had thus brought the
inheritance out of the direct line, and hereat came the conventional
sighs from Mr. Beadle, as forced as his laughter. Jim was told how
his cousin, Mark, had died in India of pneumonia, and how his uncle
and the remaining son, James, having gone to the Lakes that the old
gentleman might recover his equanimity, were both drowned in a
sudden squall while sailing at a considerable distance from the
shore. The bodies were recovered and brought to Eversfield for
burial; and very solemnly the solicitor produced a photograph of the
memorial tablet which had been set up in the church.
“Some day, I trust a very long time hence, your own mural tablet
will be set up there,” he said, after Jim had handed back the
photograph in silence. “‘Nihil enim semper floret; ætas succedit
ætati,’ as the good Cicero says.”
“Quite so,” said Jim.
“It has all been a terrible blow to me,” sighed Mr. Beadle. “The late
Mr. Tundering-West treated me quite as a personal friend.”
“Did he really?” Jim was going to be rude, but checked himself. He
felt an extraordinary hostility to this well-meaning but servile little
personage. “I shall go down there to-morrow,” he remarked, as he
rose to take his departure, “and I’ll probably have the house
thoroughly renovated before I go into it.”
“I don’t think you will find much that requires alteration,” Mr.
Beadle assured him, his hand raised in a gesture of deprecation.
“Hasty changes are always undesirable; and, when you have grown
into the spirit of the place I think you will find that you have a duty
to the past.” He checked himself, and bowed. “I trust you will not
mind an old man giving you that advice,” he murmured, as they
shook hands. He bowed so low that it appeared to be a complete
physical collapse.
On the following day Jim motored to Eversfield in a hired open car.
He could with greater ease have gone by train to Oxford, and could
have driven over in a fly; but he wanted to have the pleasure of
spending some of his new money, and, moreover, a fifty-mile drive
through the fair lands of Berkshire and Oxfordshire in the radiance of
a summer’s day appealed to his imagination. Nor was he
disappointed. He acknowledged the beauties of the land of his birth
with whole-hearted pleasure; and his eyes, weary with long gazing
upon leaden skies and burning sands, were soothed in a manner
beyond scope of words by the green fields, the soft foliage of the
trees, and grey skies of a hot, hazy morning. It is true that the roads
were extremely dusty, and that his face and clothes were soon
thickly powdered; but, as the chauffeur had provided him with a pair
of motoring glasses, he was not troubled in this respect.
The little hamlet of Eversfield lay seemingly asleep in its hollow
amidst the richly timbered hills, as, at midday, he drove up to the
grey stone gates of his future home. Here was the narrow village
green just as he had last seen it when he was a boy: on one side of
the lane which opened on to it were these imposing gates; on the
other side were the little church and moss-covered gravestones
leaning at all angles, as though the dead were whispering together
deferentially at the entrance of the manor. Upon the green were the
old stocks, and the stump and worn steps of the ancient cross; and
behind them stood the thatched cottages backed by the stately
elms.
“I suppose in years to come,” he thought, “I shall be walking
through these gates to the church on Sundays, followed by the lady
of my choice and half-a-dozen children; and the villagers will nudge
one another and say ‘Here comes Squire and all his little squirrels.’ ...
Good Lord!”
The exclamation was due to the sudden feeling that he had
walked into a trap, that he had been caught by immemorial society,
and would soon be forced to conform to its ways; and, as the car
passed in at the gates of the manor, he had, for a moment, a desire
to jump out and run for his life.
A short, straight drive, flanked by clipped box-trees, led to the
main door of the timbered Tudor house; and here the new owner,
dusty, and somewhat untidily dressed, was received by the gardener
and his buxom wife, who had both grown grey in his uncle’s service.
The man held his cap in his hand, and touched his wrinkled forehead
with his finger a number of times, painfully anxious to find favour;
while his wife curtseyed to him at least thrice.
“Are you the gardener?—what is your name?” Jim asked briskly,
feeling almost as awkward as the man he addressed, but determined
to go through the ordeal with honour.
“Peter, sir,” said the gardener. “Peter Longarm, sir. I rec’lect you,
sir, when you was no more’n so ’igh, I do.”
“Why, of course,” Jim replied. “I remember you now. You’re the
fellow who told my uncle when I broke the glass of the forcing
frame.”
The old man looked sheepish. “I ’ad to do my dooty, sir,” he said.
“I ask your pardon.”
“Duty,” Jim thought to himself. “I’m beginning to know that word.
I wonder what it really means.” He turned to the woman. “Now,
please go and open the doors of all the rooms, and then leave me to
walk through the house by myself.” He wanted to be alone to realize
his new possession and to dream his dream of future ease. Mrs.
Longarm eyed him nervously for a moment before obeying his
instructions; she told her husband afterwards, with tears in her eyes,
that she felt as though she were surrendering the house to a cut-
throat foreigner.
As he wandered, presently, from room to room he was at first
overpowered by the feeling that he was intruding upon the privacy
of some sort of family life which he did not understand. His uncle’s
wife had been dead for three or four years, but there were still many
traces of her influence: the drawing-room, for example, was
furnished in a style which called to his mind faded pictures of
feminine tea-parties. Here was the old piano upon which the good
lady must have tinkled the songs of which the music still lay in the
cabinet near by—songs such as My Mother Bids Me Bind My Hair,
and Ah, Welladay my Poor Heart. And here was the little sewing-
table where had doubtless rested the silks and needles for her
embroidery. Perhaps it was she who had chosen the gilt-framed
engravings upon the walls—the depressed picture of “Hagar and
Ishmael in the Wilderness;” a youthful portrait of Alexandra, Princess
of Wales; “Jacob weeping over Joseph’s coat;” the sprightly
“Hawking Party,” and so forth.
Looking around, he experienced a sensation of mingled mirth and
awe, and he hoped that the ghost of his aunt would not haunt him
when he laid sacrilegious and violent hands upon these things, as at
first he intended to do. The chintzes appeared to be of more recent
date; but these, too, would have to go, for, as a pattern, he detested
sprays of red roses tied with blue ribbons.
The dining-room, hall and staircase, being panelled and hung with
family portraits, were impressive in their conveyance of a sense of
many generations; and the hereditary library, if sombre, was
interesting. Jim was very fond of old books, and he stood there for
some time taking the calf-bound volumes from the shelves, and
turning over the ancient pages. But, the morning-room, with its red-
covered chairs, its mahogany sideboard, and its sham Chinese vases,
was distressing. Yet here, as in the drawing-room, there was a
chaste and awful solemnity, from which he shrank, as a
conscientious Don Juan might shrink at a lady’s prie-Dieu.
The larger bedrooms upstairs, with their mahogany wardrobes and
heavy chests of drawers full of clothes, and cupboards full of boots
and hats, were startling in their association with their late tenants.
On a table beside his uncle’s bed there lay a recent novel, which Jim
himself had also just read: it constituted a gruesome link between
the living and the dead. He glanced about him and through the
window, down the drive, almost expecting to see the apparitions of
his relatives stalking up from the family vault in the churchyard to
see what he was about. His uncle would probably think him a
dreadful scallawag, for the old gentleman had been an accredited
pillar of Church and State, with, so the cupboards testified, a mania
for collecting the top hats he had worn on Sundays or when in town.
He had been a model of propriety, and the monumental stone, the
photograph of which he had seen at the solicitors, stated that he
had “nobly upheld the traditions of his race.”
Jim felt depressed, and presently went out into the garden which
was ablaze with flowers; and here, after a late meal of sandwiches,
eaten upon an ornamental stone bench, his spirits revived, for the
manor and its setting formed a very beautiful picture. If only he
could get rid of all those hats and clothes and old photographs!
A sudden idea occurred to him: he would go and find the padre,
and tell him to take these things for the poor of the parish. They
must be got rid of at once, even though every man in the village be
obliged to wear a top hat. They must all be gone before he came
here again, or he would never bring himself to live in the house at
all! He hurried down the drive, asked Peter Longarm at the lodge to
point out the vicarage to him, and thereafter hastened on his errand.
Near the church, however, and at a point where a gap in the trees
revealed a distant view of the dreaming, huddled spires of Oxford,
flanked by the lonely tower of Magdalen College, he met with a
white-bearded clergyman whom he presumed to be the vicar, and at
once accosted him.
“Excuse me,” he said, ingratiatingly, barring his way. “Would you
care to have some old hats?—I mean of course, would your flock like
to wear them?—Top hats, you know, and old boots, too, if you want
them.”
The elderly gentleman was annoyed, and, with a curt “No thank
you, not to-day,” proceeded on his way. Jim, however, called after
him, coaxingly: “They are quite good hats really; they only want
brushing.”
At this the man of God stopped and turned, looking at Jim’s
somewhat dusty figure with wonderment. “Do I understand that you
are selling old hats?” he asked, endeavouring to speak politely.
Jim rushed feverishly into explanation. “No, I want to get rid of
them,” he gabbled; “I want to get rid of all sorts of things—hats,
coats, trousers, dressing-gowns, shirts, vests, boots, slippers, old
photographs, umbrellas ...” He paused for breath, inwardly laughing.
Very slowly and deliberately the clergyman adjusted his eyeglasses
low down upon his nose, and stared at Jim. “Young man,” he said,
“is this a jest at my expense?”
“Good Lord, no!” Jim answered. “I’m in deadly earnest. I can’t
possibly live in the house with all these things. You will help me,
won’t you? How would it be if you came over to-morrow and cleared
them all out, and then had a meeting or something, and gave them
as prizes to the regular church-goers?”
“I don’t know what you are talking about,” the clergyman
responded, gently but firmly pushing him aside. “Good-day!”
Jim stared at him as he walked. “You are the vicar, aren’t you?” he
asked.
“No, I’m not,” the other replied somewhat sharply, over his
shoulder; “I’m the President of Magdalen.”
Jim uttered an exclamation of impatience, and hastened on to the
Vicarage.
The servant who appeared in response to his knock, was about to
ask him his name, when the vicar, an old man with a clean-shaven,
kindly face, and grey hair, happened to cross the hall.
“Yes, what is it, what is it?” he asked, coming to the door, while
the maid retired.
“Are you the vicar?” Jim asked, beginning more cautiously.
“I am,” the other responded.
“You really are? Well I want to ask you about some old clothes.
I....”
The vicar held up his hand. “No, I have none to sell you,” he said
smiling sadly. “I wear mine out.”
Jim laughed aloud. “First I’m thought to be selling them, and now
you think I’m buying them,” he exclaimed. “We certainly are a nation
of shop-keepers.”
The vicar was puzzled. “I don’t understand. What is it you want?”
“I have a lot of hats and old clothes I want to get rid of. I thought
you might like them.”
The clergyman bowed stiffly. “It is very kind of you,” he said
frigidly. “My stipend, I admit, is small, but I am not yet reduced to
the necessity of wearing a stranger’s cast-off clothing.”
“Oh, I didn’t mean that,” Jim hastily explained. “And they’re not
mine: they belonged to my late relatives. I am just coming to live at
the manor, and I thought the poor of the parish would....”
The vicar interrupted him. “I beg your pardon. Are you ...?” He
hesitated, incredulous.
“Yes, I’m the new Tundering-West,” Jim told him.
The other held out his hands. “Well, well!” he cried. “And I
thought you were....” He hesitated.
“The old clothes man,” laughed Jim.
“Oh, very droll!” the vicar smiled, shaking him warmly by the
hand. “How ridiculous of me! Do come in, my dear sir!”
Jim followed him into the drawing-room, and here he found a little
old lady, who was introduced to him as Miss Proudfoote, and a florid,
middle-aged man with a waxed moustache, who looked like a
sergeant-major, and proved to be Dr. Spooner, the local medical
man. They had evidently been lunching at the Vicarage, and were
now drinking the post-prandial concoction which the English believe
to be coffee. They both greeted him with a sort of deference, which
however, did not conceal their curiosity.
During the next ten minutes Jim heard a great deal of his “poor
dear uncle” and his unfortunate cousins. The tragedy of their deaths,
it seemed, had cast the profoundest gloom over the village; but it
was a case of “the King is dead; long live the King!” and all three of
his new acquaintances appeared to be anxious to pay him every
respect.
Dr. Spooner asked him from what part of England he had just
come, and the news that he had been living abroad and had not
visited the land of his birth for many years caused a sensation. The
thought occurred to him that he ought not to mention Egypt, or any
other land which had recently known him as Jim Easton; for any
such revelations might bring discredit upon him, and he wished to
start his life at Eversfield without any handicap. He therefore spoke
only of California, referring to it casually as a country where he had
resided.
Miss Proudfoote turned to the vicar. “Is it not extraordinary,” she
said, “how many of our young men shoulder what Mr. Kipling calls
‘the white man’s burden’ and go forth to live amongst the heathen?”
Her geography was evidently at fault, but out of consideration for
her years and her sex, no correction was forthcoming. “I suppose,”
she proceeded, “you met with our missionaries out there? It is
wonderful what a great work the Church Missionary Society is doing
all over the world.”
The Doctor here had the hardihood to interpose. “Oh, but
California is a part of the United States of America ...” he ventured.
“How foolish of me!—of course,” smiled the old lady. “The
Americans are quite an educated people. I met an American traveller
once in Oxford: a pleasant spoken young man he seemed, so far as
I could understand what he said.”
“Yes,” remarked the vicar, “America can no longer be called ‘the
common sewer of England,’ as it was when I was a boy.”
Jim stared from one to the other in amazement. “But America is
the largest and most progressive part of the Anglo-Saxon race,” he
protested. “They are already ahead of us in many ways.”
Miss Proudfoote was shocked, and she showed it. “It is evident
that you do not know England,” she replied, coldly.
“I mean,” he emphasized, “it always seems to me a fine thought
that England can never die, because she will live again over there;
and then she’ll have another lease of life in Australia; and so on.
This England here may die, but the English will go on for ever and
ever, it seems to me. And wherever their home may be,” he added,
laughing, “they’ll always think it ‘God’s own country,’ and think
themselves the chosen people.”
Miss Proudfoote looked anxiously at him, hoping that there was
some good in him. “I trust,” she said, “that it is now your intention
to settle down?”
“Yes,” he replied. “I fancy my wanderings are over.”
“Heaven has placed you in a very responsible position,” she said,
gazing earnestly at him. “I am sure our best wishes will be with you
in your duties.”
“Yes, indeed,” sighed the vicar, whose name, as Jim had just
ascertained, was Glenning. “Are you a married man, may I ask?”
“Oh no,” Jim replied.
Miss Proudfoote patted his arm. “We shall have to find you a wife,”
she smiled.
Jim was aghast, and hastily changed the subject. “Now about the
old clothes,” he began.
Mr. Glenning coloured, slightly. “What an absurd error for me to
have made,” he said. “Now, tell me, what is it you wish me to do?”
“I’m going back to London to-day,” Jim explained, “and I want
you, while I am away, to go through all my uncle’s things, and give
away to the poor everything you think I shall not want. Just use your
own judgment.”
“It will be a melancholy duty,” he replied.
“I’m sure it will,” the new Squire answered, “but, I tell you frankly,
anything useless I find here when I return I shall burn.”
The vicar raised his hands; the doctor sniffed; and Miss
Proudfoote looked at the stranger indignantly.
“That is rather hasty, is it not?” she asked, tremulously.
Jim felt awkward. He had made a bad impression, and he knew it.
“You see,” he tried to explain, “my uncle died so suddenly and the
place is littered with his things. All I want to keep is the furniture,
and the silver, and the books, and that sort of thing, but I will see to
that myself.”
Miss Proudfoote turned away suddenly and Jim, to his horror, saw
her raise a handkerchief to her eyes. He could have kicked himself.
He wished the floor would open and engulf him. He looked in
despair at the two men.
“You know I haven’t seen my uncle since I was a boy,” he
stammered. “I am a complete stranger.”
“He was our very dear friend,” said Mr. Glenning.
Chapter VI: SETTLING DOWN
While the congregation in the little church at Eversfield was
singing the last hymn of the morning service the October sun passed
from behind an extensive bank of cloud, and its rays shot down
through the plain glass window upon the figure of a young woman,
whose sudden and surprising illumination instantly attracted many
pairs of eyes to her. She looked, and knew it, like a little angel as
she stood in this shaft of brilliance, hymn-book in hand, singing the
well-known words in a voice which enhanced their ancient
sweetness; and the vicar, from his place at the side of the small
chancel, fixed his gaze upon her with an expression of such saintly
beatitude upon his face as to be almost idiotic.
Her name was Dorothy Darling; but her mother, who here stood
beside her in the shadow under the wall, called her Dolly, and rightly
congratulated herself upon having chosen for her only baby, twenty-
three years ago, a name of which the diminutive was so appropriate
to the now grown woman.
In the sunshine the girl’s soft, fair hair looked like a puff of gold,
and her skin like coral; and the play of light and shade accentuated
the pretty lines of her figure, so that they were by no means lost
under the folds of her smart little frock. Her large, soft eyes were as
innocent as they were blue, and never a glance betrayed the fact
that she was singing for the direct benefit of the new Squire, whose
head and shoulders appeared above the carved wooden walls of the
sort of loose-box which was his family pew.
The miniature church, though dating from the twelfth century, still
retained the features by which it had been transformed and
modernized in the obsequious days of Walpole and the first of the
Georges. The pews for the “gentry” were boxed in, and each was
fitted with its door; but the walls of Jim’s pew were higher than the
others and its area bigger. At the back of the church there were the
open seats for the villagers and persons of vulgar birth; but the
woodwork here was not carved, save with the occasional initials of
lads long since passed out of memory.
At the sides of the chancel were set the mural tablets which
recorded the genealogical lustres of dead Tundering-Wests, back to
the day when a certain Captain of Horse had obtained a grant of the
manor from the Commonwealth, in lieu of his devastated estate in
Devon, and, with admirable tact, had married the daughter of the
exiled Royalist owner. Around the whitewashed walls of the small
nave large wooden boards were hung, upon which were painted the
arms and quarterings of the successive Squires and their spouses;
and above the chancel arch the royal Georgian escutcheon was
displayed in still vivid colours.
The church, indeed, was a tiny monument to all that glory of caste
which its Divine Founder abhorred, and which the aforesaid
Roundhead, misapprehending the unalterable character of his fellow-
countrymen, had apparently fought in his own day to suppress.
When the hymn was finished, the blessing spoken, and Mr.
Glenning gone into the vestry behind the organ, this traditional
distinction between the classes was emphasized by the behaviour of
the little congregation. Nobody of the meaner sort moved towards
the sunlit doorway until Jim, looking extraordinarily embarrassed,
had marched down the aisle and had passed out into the autumnal
scurry of falling leaves, followed closely by Mrs. and Miss Darling, Mr.
Merrivall of Rose Cottage, Dr. and Mrs. Spooner, and old Miss
Proudfoote of the Grange; and, when these were gone, way had still
to be made for young Farmer Hopkins and his wife, Farmer
Cartwright and his idiot son, and the other families of local standing.
Outside, in the keen October air, Jim paused under the ancient
ilex-tree, and turned to bid good-morning to the Darlings. Dolly had
interested and attracted him during these three months since he
took up his residence at the manor; but he had been so much
occupied in settling himself into his new home that he had not given
her all the attention he felt was her due, now that the shaft of
sunlight in the church had revealed her to him in the palpable charm
of her maidenhood.
He greeted her, therefore, with cheery ardour, as though she were
a new discovery, and walked beside her and her mother down the
path which wound between the moss-covered gravestones, and out
into the lane under the rustling elms. A great change had come over
him since he had returned to England: he had become in some ways
more normal, and the quiet, simple life of an English village had, as
it were, taken much of the exotic colour out of his thoughts. In the
romantic East he had looked for romance, but here in the domestic
West his mind had turned towards domesticity. His poetic
imagination was temporarily blunted; and whereas in Alexandria he
had responded eagerly to the enchantments of hour and place, in
Eversfield he was readily satisfied with a more rational aspect of life.
He turned to the mother. “What a little picture your daughter
looked, singing that hymn in the sunlight,” he remarked, with
enthusiasm.
Mrs. Darling sighed. Twenty years ago she, too, had been a little
picture; but, so she thought to herself, she had had more character
in her face than Dolly, and less softness. Outwardly her little girl took
after that scamp of a father of hers, whose innocent blue eyes and
boyish face had won him more frequent successes than his
continence could handle.
“Yes,” she replied, evasively, “that is Dolly’s favourite hymn.... She
has a nice little voice.”
“Delightful!” said Jim. “I didn’t know hymns could sound so
beautiful!”
Dolly looked at him as our great-grandmothers must have looked
when they said, “Fie!”
“Aren’t you a regular church-goer?” she asked, gazing up at him
with childlike eyes.
“Can’t say I am,” he answered, with a quick laugh. “I’m new to all
this, you know. I’ve knocked about all over the world since I left
school. But, I say!—that family pew, and the respectful villagers!—
they give me the hump!”
“Oh, I think it is charming, perfectly charming,” said Mrs. Darling.
“Well,” he replied, “I expect I’ll get used to it. I suppose this sort
of life grows on one: in some ways I’m beginning to have a sort of
settled feeling already.”
They were walking away from the gates of the Manor, which rose
opposite the ivy-covered church, and were approaching the
picturesque little cottage where the Darlings lived. Jim paused, and
as he did so Dolly experienced a sudden sense of disappointment.
She had hoped that he would accompany them to their door, and
she had intended then to entice him through it, and to show him
over their pretty rooms and round the flower-garden and the
orchard. Until now they had only occasionally met, and their
exchanges of conversational trivialities had been carried on in the
lane, or at the door of the church, or outside the cottage which
served as the post-office. He seemed to be a difficult man to take
hold of; and during the last few weeks, since her mind had begun to
be so disastrously full of the thought of him, she had felt ridiculously
frustrated in her attempts to develop their friendship. Frustration, of
course, is woman’s destiny, which meets her at every turn; but in
youth it sometimes serves as her incentive.
“Won’t you come in and see our little home?” she asked. “It’s
rather a treasure.”
He shook his head. “I’m afraid I can’t,” he replied. “I promised to
go round my place with the gardener this morning. He’ll be waiting
for me now. But, I say, what about dinner to-night? Won’t you both
dine with me?” He was feeling reckless.
Dolly’s heart leapt, and, in a flash, she had selected the dress she
would put on, and had considered whether she should wear the little
diamond pendant or the sham pearls.
“We shall be delighted,” murmured Mrs. Darling. “Eh, Dolly?”
The girl looked doubtful. “I don’t know that we ought to to-night,”
she answered. “We had half promised to drive over to a sort of
sacred concert affair in Oxford.”
“Oh, don’t disappoint me,” said Jim. “I’ve got the house almost
shipshape now; I’d like you to see it.”
Dolly did not require really to be pressed; and soon the young
man was striding homewards down the lane, wondering why it had
taken him three months to realize that this girl was perfectly
adorable; while she, on her part, was pinching Mrs. Darling’s arm
and saying: “Oh, mother dear, doesn’t he look delightfully wicked!”
“Yes, he seems a nice, sardonic fellow,” her mother remarked
grimly, as they entered their house. “Why did you begin by saying
we were engaged to-night? It’s the first I’ve heard of it.”
Dolly smiled. “Oh, I made that up, because I thought you were
too prompt in accepting. He’ll want us all the more if we are stand-
offish. Men are like that.”
Mrs. Darling sniffed. She was a lazy, plump, and rather languid
little woman; and sometimes she grew impatient at her daughter’s
ingenious method of dealing with these sorts of situations. She
herself had grown more direct in her Yea and Nay: perhaps at the
age of forty-five she was a little tired of dissimulation. The world had
treated her scurvily; and, having a settled grievance, she was
inclined now to take whatever pleasant things were to be had for the
asking, without any subtle manœuvering for position.
Her husband had left her when Dolly was five years old, and, so
far as she knew, he was now dead. For several years she had
bravely maintained herself in a tiny Kensington flat by writing social
and theatrical articles for pretentious papers. She had been a
purveyor of gossip, a tattle-monger, a dealer in bibble-babble; and
she had carried on her trade with an increasing inclination to yawn
over it, and a growing consciousness of her daughter’s contempt,
until the editors who had supported her became aware that her
heart was not in her work, and five years ago gave her her congé.
Then, with a temporary display of energy, she had followed Dolly’s
cultured advice, and had established a little business off Sloane
Square, which she called “The Purple Shop.” Here she sold purple
cushions and lamp-shades, poppy-heads dipped in purple paint,
poetry-books in purple covers, sketches by Bakst in purple frames,
lengths of purple damask, and so forth. But purple went out of
fashion, and her once very considerable profits sank to the vanishing
point. She introduced other colours, and softer shades of mauve and
lilac. She sold a doll which had mauve hair and naughty black eyes;
she took in a stock of bottled new potatoes tinged with a harmless
purple liquid, and presented them to the jaded world of fashion as
Pommes de terre pourpres de Tyr; she even sold brilliant bath-robes
for bored bachelors, with coloured soap to match.
A financial crash followed, and, after a few months spent in
dodging her creditors, she heard of this little cottage at Eversfield,
and fled to it with her daughter, leaving no address. She was in
receipt of a small annual allowance from the estate of a deceased
brother, and this she supplemented by writing the monthly fashion
article in one of the journals devoted to the world, the flesh and the
devil. She wrote under the nom-de-plume of “Countess X”; and her
material was obtained by a monthly visit to London and a tour of the
leading modistes.
For eighteen months now she had lain low in this nook of the
Midlands where Time stood still, and gradually she had ceased to
dread the visit of the postman, and had begun to take a languid
interest in the cottage. The colour purple no longer set her fat knees
knocking together, and lately she had been able even to look up
some of her old friends in London and to greet them with the sad,
brave smile of a wronged woman.
To Dolly, however, the enforced seclusion had been a sore trial,
and there were times when her pretty eyes were red with weeping.
She had been utterly bored by the purposeless existence she was
called upon to lead; but now the arrival of the new Squire at the
manor, which had hardly seen its previous owner during the last year
of his life, had aroused her from her sorrows and had set her heart
in a flutter. She liked his strange, swarthy face and his moody eyes,
and thought he looked artistic and even intellectual; and she liked
his obvious embarrassment at the deference paid to him in this little
kingdom which he had inherited.
She spent the afternoon, therefore, in a condition of pleasurable
excitement, stitching at the dress she was going to wear and making
certain alterations to the shape of the neck.
While she plied her needle, Mrs. Darling sat at the low window
overlooking the orchard, and scribbled her monthly article upon a
writing-pad resting on her knee. “Here is a charming little conceit I
chanced upon in Bond Street t’other day,” she wrote. “It is really a
tub-time frock; but its success in the drawing-room is likely to be
immediate. Organdy ruchings of moonlight blue, and a soupçon of
jet cabochons on the corsage. It is named ‘Hopes in turmoil.’” And
again, “I noticed, too, a crisp little trotteur frock, with a nipped-in
waist-line hesitating behind a moyenage girdle of beige velours
delaine. They have called it ‘Cupid’s Teeth.’ Oh, very snappy, I assure
you, my dears!”
She smiled lazily as she wrote, but once she sighed so heavily that
her daughter asked her if anything were amiss.
“No,” she replied. “I was only just wondering whether anybody in
their senses could understand the nonsense I am writing. The
editor’s orders are to make the thing sound French: I should lose my
job if I wrote in plain English.”
“Oh dear,” sighed Dolly, “how tedious all that sort of thing seems!
I wonder that you can bother with it.”
“I’ve got to,” her mother answered, with irritation. “I shan’t be
able to give it up till you are married and off my hands.”
“Yes, so you are always telling me,” said Dolly; and therewith their
silence was renewed.
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Inertial Navigation Systems with Geodetic Applications 2nd Edition Christopher Jekeli

  • 1. Inertial Navigation Systems with Geodetic Applications 2nd Edition Christopher Jekeli - PDF Download (2025) https://ebookultra.com/download/inertial-navigation-systems-with- geodetic-applications-2nd-edition-christopher-jekeli/ Visit ebookultra.com today to download the complete set of ebooks or textbooks
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  • 5. Inertial Navigation Systems with Geodetic Applications 2nd Edition Christopher Jekeli Digital Instant Download Author(s): Christopher Jekeli ISBN(s): 9783110784329, 3110784327 Edition: 2 File Details: PDF, 14.17 MB Year: 2023 Language: english
  • 6. Christopher Jekeli Inertial Navigation Systems with Geodetic Applications
  • 7. Also of Interest Flugnavigation. Grundlagen, Mathematik, Kartenkunde, leistungsbasierte Navigation . Auflage Wieland Richter,  ISBN ----, e-ISBN ---- Vehicle Technology. Technical Foundations of Current and Future Motor Vehicles Dieter Schramm, Benjamin Hesse, Niko Maas and Michael Unterreiner,  ISBN ----, e-ISBN ---- Geophysical Modelling of the Polar Motion Christian Bizouard,  ISBN ----, e-ISBN ---- Fahrdynamik. Regelung für Elektrofahrzeuge mit Einzelradantrieben Martin Schünemann,  ISBN ----, e-ISBN ----
  • 8. Christopher Jekeli Inertial Navigation Systems with Geodetic Applications 2nd Edition
  • 9. Author Dr. Christopher Jekeli School of Earth Sciences Division of Geodetic Science Ohio State University 275 Mendenhall Laboratory 125 South Oval Mall Columbus OH 43210 United States of America christopher.jekeli@gmail.com ISBN 978-3-11-078421-3 e-ISBN (PDF) 978-3-11-078432-9 e-ISBN (EPUB) 978-3-11-078439-8 Library of Congress Control Number: 2022951986 Bibliographic information published by the Deutsche Nationalbibliothek The Deutsche Nationalbibliothek lists this publication in the Deutsche Nationalbibliografie; detailed bibliographic data are available on the internet at http://dnb.dnb.de. © 2023 Walter de Gruyter GmbH, Berlin/Boston Cover image: Chor muang/iStock/Getty Images Plus Typesetting: Integra Software Services Pvt. Ltd. Printing and binding: CPI books GmbH, Leck www.degruyter.com
  • 12. PREFACE It is amazing that gyros perform as well as they do. Wallace E. Vander Velde, M.I.T., 1983. The quote above is a beautiful expression and tribute to the engineering triumph in the latter half of the twentieth century of the mechanical gyroscope that is an integral part of the traditional inertial navigation system (INS). In today’s technological age of lasers and digital electronics, having also benefited inertial sensors, high performance is al- most expected; yet the most accurate navigation and guidance systems still rely on the mechanical predecessors of the modern optical gyro. On the other hand, robustness, reliability, efficiency, and, above all, cost-effectiveness belong to the new generation of sensors and open the opportunity for increased utility and wider application in com- mercial, industrial, and scientific endeavors. Concurrent with the technological innova- tions came new analytical tools, specifically the Kalman filter, that is tailor-made for the analysis, calibration, and integration of the inertial navigation system. In the last two decades, the Global Positioning System (GPS) has come to dominate the wide range of positioning and navigation applications, but the new inertial sensor technology has enabled a continuing and growing utilization of these marvelous instruments and has motivated a revival from a number of different perspectives, the geodetic one in the present case, especially in regard to their integration with GPS. Geodesy, the science of the measurement and determination of the Earth’s sur- face, now routinely relies on the exquisite accuracy extractable from GPS, but equally recognizes the advantages and opportunities afforded by including INS in several ap- plications. Although the present book is ultimately dedicated to this goal, it should prove to be of equal value to non-geodesists who desire a thorough understanding of the mathematics behind the INS and its general use for precision navigation and posi- tioning. In particular, an attempt is made with this book to join the principles of iner- tial technology and estimation theory that applies not only to an understanding of the dynamics of the sensors and their errors, but to the integration of INS with other sys- tems such as GPS. The text is written by a geodesist who loves the application of math- ematics and believes that an appreciation of these topics comes best with illustrative formulas that are derived from first principles. As such, considerable effort is devoted to establishing preliminary concepts in coordinate systems, linear differential equa- tions, and stochastic processes, which can also be found readily in other eminent texts, but whose inclusion makes the present text essentially self-contained. With the mathematical details, and occasional numerical considerations, it is also hoped that the reader will obtain an appreciation for Vander Velde’s statement, above, that may well be extended to the navigation system and further to its entire technological de- velopment – the achievements in inertial technology are truly amazing. The text assumes that the reader is fluent in the differential and integral calculus, as well as the basic vector and matrix algebras. Undergraduate courses in calculus, https://doi.org/10.1515/9783110784329-202
  • 13. including the traditional advanced calculus, and linear algebra are, therefore, prerequi- sites to this text. Further minimal background in complex variables, differential equa- tions, and numerical and statistical analyses, though not essential, would provide the reader with additional mathematical maturity to fully benefit from the material. The book may be used as a text for a college semester course at the senior or graduate level. Although mathematical derivations are given in detail, the old adage that mathematics is not a spectator sport should be followed by serious readers. This text would not have materialized without the significant inspiration derived from my colleagues while working at the Air Force and at the Ohio State University. I would like to thank, in particular (affiliations are not necessarily current): Warren Heller, Jim White, Jacob Goldstein, Robert Shipp (TASC); Triveni Upadhyay, Jorge Gal- dos (Mayflower Communications, Inc.); David Gleason, Gerald Shaw (Air Force Geo- physics Laboratory); Jim Huddle (Litton Guidance and Control, Inc.); Alyson Brown (NAVSYS Corp.); Klaus-Peter Schwarz (University of Calgary); Clyde Goad, Burkhard Schaffrin, Ren Da, Jin Wang, Jay Kwon (Ohio State University). In addition, several outstanding lecture notes by W. Vander Velde and A. Willsky (both at M.I.T.) have mo- tivated key aspects of the mathematical understanding embodied in this text. C. Jekeli Columbus, Ohio; July 2000 VIII PREFACE
  • 14. Preface to the Second Edition The first two decades of the twenty-first century have witnessed an incredible ad- vance in technology, not least in the area of geographic positioning and navigation, made possible by Global Navigation Satellite Systems, of which GPS is still the leading workhorse. Advancements in inertial instrument technology have focused on con- sumer and industrial applications, with the development of miniature, robust, inex- pensive, and power-thrifty, though less accurate, solid-state devices. Still, in the meantime, the much more accurate inertial measurement units (IMUs) for precision navigation have not lost ground and continue to serve in aiding satellite navigation and geodetic kinematic positioning. Of course, the essential physical principles of in- ertial devices have not changed and with this second edition, most of the changes, while always an improvement over the previous edition, are more cosmetic than transformative. The emphasis, as before, is on presenting a comprehensive treatment of how gyroscopes and accelerometers function and how their data are used in a number of high-end applications in geodesy. The more significant revisions from the first edition include, firstly, a new section on miniature vibratory gyroscopes. Al- though these are not yet ready for precision IMUs, their principle of operation differs notably from their cousins that are based on angular momentum or the Sagnac effect. Second, the chapters on the statistical estimation now have a mathematically more rigorous notation, which makes a clearer distinction between a random variable and its realized value. Third, the numerical example illustrating the extended Kalman fil- ter and smoother has been enhanced with more explicit details. Finally, a number of updates are included in areas that have seen significant changes, specifically coordinate reference systems, GPS (also other GNSSs are mentioned), and scalar moving-base gra- vimetry. This second edition also enabled the correction of numerous typographical, as well, as a few conceptual errors in the overall text of the previous version. This work would not have ensued without the encouragement of the publisher, and certainly not without the undying support of my loving wife, to whom it is dedicated. C. Jekeli Brunswick, Maine; November 2022 https://doi.org/10.1515/9783110784329-203
  • 16. Abstract This book covers all aspects of inertial navigation systems (INS), including the sensor technology and the estimation of instrument errors, as well as their integration with Global Navigation Satellite Systems, specifically the Global Positioning System (GPS) for geodetic applications. The text is of interest to geodesists, including surveyors, mappers, and photogrammetrists; to engineers in aviation, navigation, guidance, transportation, and robotics; and to scientists involved in aerogeophysics and remote sensing. The most recent developments are covered in this second edition that also features an updated treatment of the classical material. – Detailed mathematical derivations of the principles of measurement and data processing of inertial measurement units for both stabilized and strapdown systems. – Complete treatment of the error dynamics from a statistical viewpoint, including the Kalman filter. – A self-contained description of GPS with emphasis on kinematic applications. – Key concepts supported by illustrations and numerical examples. Christopher Jekeli is Professor Emeritus at the Ohio State University, where he has taught courses in geometric and physical geodesy, as well as inertial navigation systems. His extensively published research focused on Earth’s gravity field for geodetic applications. https://doi.org/10.1515/9783110784329-204
  • 18. Contents PREFACE VII Preface to the Second Edition IX Abstract XI 1 Coordinate Frames and Transformations 1 1.1 Introduction 1 1.2 Coordinate Frames 3 1.2.1 Inertial Frame 3 1.2.2 Earth-Centered–Earth-Fixed Frame 6 1.2.3 Navigation Frame 7 1.3 Transformations 10 1.3.1 Direction Cosines 10 1.3.2 Euler Angles 12 1.3.3 Quaternions 15 1.3.4 Axial Vectors 20 1.3.5 Angular Rates 21 1.4 Differential Equation of the Transformation 22 1.5 Specific Coordinate Transformations 24 1.6 Fourier Transforms 29 2 Ordinary Differential Equations 33 2.1 Introduction 33 2.2 Linear Differential Equations 34 2.3 General Solution of Linear Differential Equations 36 2.3.1 Homogeneous Solution 37 2.3.1.1 An Example 41 2.3.1.2 Fundamental Set of Solutions 42 2.3.2 Particular Solution 44 2.3.2.1 The Example, Continued 46 2.4 Numerical Methods 47 2.4.1 Runge–Kutta Methods 48 2.4.2 Numerical Integration of Functions 54 3 Inertial Measurement Units 55 3.1 Introduction 55 3.2 Gyroscopes 57 3.2.1 Mechanical Gyroscope 59 3.2.1.1 The SDF Gyro 61
  • 19. 3.2.1.1.1 Principal Error Terms 69 3.2.1.2 The TDF Gyro 71 3.2.2 Optical Gyroscopes 76 3.2.2.1 The Ring Laser Gyro 78 3.2.2.1.1 RLG Error Sources 82 3.2.2.2 The Fiber-Optic Gyro 86 3.2.2.2.1 FOG Error Sources 91 3.2.3 MEMS Gyroscopes 91 3.2.3.1 The Dynamics of MEMS Vibratory Gyroscopes 93 3.2.3.2 MEMS Gyroscope Error Sources 102 3.3 Accelerometers 103 3.3.1 Accelerations in Non-inertial Frames 106 3.3.2 Force-Rebalance Dynamics 108 3.3.3 Pendulous Accelerometer Examples 111 3.3.4 Vibrating Element Dynamics 114 3.3.5 Error Sources 116 4 Inertial Navigation System 118 4.1 Introduction 118 4.2 Mechanizations 120 4.2.1 Space-Stabilized Mechanization 122 4.2.2 Local-Level Mechanization 123 4.2.2.1 Schuler Tuning 124 4.2.2.2 Wander-Azimuth Mechanization 127 4.2.3 Strapdown Mechanization 128 4.2.3.1 Numerical Determination of the Transformation Matrix 131 4.2.3.1.1 A Second-Order Algorithm 132 4.2.3.1.2 A Third-Order Algorithm 136 4.2.3.2 Specializations 140 4.3 Navigation Equations 141 4.3.1 A Unified Approach 143 4.3.2 Navigation Equations in the i-Frame 144 4.3.3 Navigation Equations in the e-Frame 145 4.3.4 Navigation Equations in the n-Frame 145 4.3.5 Navigation Equations in the w-Frame 150 4.3.6 Numerical Integration of Navigation Equations 154 5 System Error Dynamics 159 5.1 Introduction 159 5.2 Simplified Analysis 160 5.3 Linearized Error Equations 168 5.3.1 Error Dynamics Equations in the i-Frame 172 XIV Contents
  • 20. 5.3.2 Error Dynamics Equations in the e-Frame 172 5.3.3 Error Dynamics Equations in the n-Frame 174 5.4 Approximate Analysis 179 5.4.1 Effects of Accelerometer and Gyro Errors 181 5.4.2 Vertical Velocity and Position Error Effects 183 5.4.3 Essential Error Modes 184 6 Stochastic Processes and Error Models 188 6.1 Introduction 188 6.2 Probability Theory 188 6.2.1 Gaussian Distribution 194 6.3 Stochastic Processes 195 6.3.1 Covariance Functions 197 6.3.2 Power Spectral Density 199 6.3.3 Ergodic Processes 200 6.4 White Noise 202 6.5 Stochastic Error Models 205 6.5.1 Random Constant 206 6.5.2 Random Walk 207 6.5.3 Gauss–Markov Model 208 6.6 Gravity Models 212 6.6.1 The Normal Gravity Field 212 6.6.2 Deterministic Gravity Models 216 6.6.3 Stochastic Gravity Models 219 6.7 Examples of IMU Error Processes 222 7 Linear Estimation 224 7.1 Introduction 224 7.2 Bayesian Estimation 226 7.2.1 Optimal Estimation Criteria 227 7.2.2 Estimation with Observations 229 7.2.2.1 The A Posteriori Probability Density Function 231 7.2.2.2 The A Posteriori Estimate and Covariance 233 7.3 The Discrete Kalman Filter 236 7.3.1 The Observation Model 237 7.3.2 Optimal State Vector Estimation 238 7.3.2.1 Prediction 241 7.3.2.2 Filtering 242 7.3.2.3 Smoothing 244 7.4 The Discrete Linear Dynamics Model 250 7.5 Modifications 254 7.5.1 Augmented State Vector 254 Contents XV
  • 21. 7.5.2 Closed-Loop Estimation 256 7.6 A Simple Example 258 7.7 The Continuous Kalman Filter 264 7.7.1 Covariance Function 268 7.7.2 Solution to Matrix Ricatti Equation 270 7.7.2.1 Constant Coefficient Matrices 270 7.7.2.2 No System Process Noise 272 7.7.2.3 No Observations 272 8 INS Initialization and Alignment 274 8.1 Introduction 274 8.2 Coarse Alignment 276 8.3 Fine Alignment and Calibration 280 8.3.1 Acceleration Observations 281 8.3.2 Velocity and Azimuth Observations 283 8.3.3 Kinematic Alignment 289 9 The Global Positioning System (GPS) 293 9.1 Introduction 293 9.2 The Global Positioning System 297 9.2.1 Clocks and Time 297 9.2.2 The GPS Signals 299 9.2.3 The GPS Receiver 302 9.3 The GPS Observables 305 9.4 GPS Errors 308 9.5 Combinations of Observations 313 9.5.1 Dual-Frequency Pseudorange and Phase 314 9.5.2 Single and Double Differences 318 9.6 Kinematic Positioning 322 9.6.1 The Dynamics Model 324 9.6.2 The Observation Equations 327 9.6.2.1 Single-Receiver Case 328 9.6.2.2 Multiple-Receiver Case 333 10 Geodetic Application 336 10.1 Introduction 336 10.2 The Inertial Survey System 338 10.2.1 Historical Developments 338 10.2.2 Estimation Methods 341 10.2.2.1 Models and Observations 341 10.2.2.2 Parameter Estimation 344 10.2.3 Typical Results 346 XVI Contents
  • 22. 10.3 GPS/INS Integration 348 10.3.1 Integration Modes 350 10.3.1.1 Decentralized Integration 351 10.3.1.2 Centralized Integration 356 10.3.2 Cycle Ambiguity Determination 360 10.4 Moving-Base Gravimetry 362 10.4.1 Gravitation from Inertial Positioning 366 10.4.2 Gravitation from Accelerometry 370 10.4.2.1 Scalar Gravimetry 373 10.4.2.2 Vector Gravimetry 379 References 385 Index 395 Contents XVII
  • 24. 1 Coordinate Frames and Transformations 1.1 Introduction When describing locations of points on or near the Earth’s surface, we most naturally turn to a system of coordinates. Although one could imagine devising a relational or synthetic data base to describe the whereabouts of objects and places, it is of necessity that we assign an algebraic system of coordinates if we wish to go beyond mere loca- tion information and obtain measures of distance, area, volume, and direction. And, likewise with navigation, we need to define a coordinate system in which we can mea- sure our progress and easily determine our course and destination. There are several coordinate systems from which to choose. Each has its own unique utility depending on the particular application in a particular discipline. In geodesy we deal with deter- mining positions, or the mathematics of map projections, or the navigation of a vehi- cle, or its guidance along a predefined path. Specific coordinate systems must be defined in each case. We will be concerned primarily with the Cartesian, or rectangular, coordinates, whose axes are mutually orthogonal by definition, but this triad of axes, as shown in Figure 1.1, may assume a variety of orientations in space. The axes of any coordinate system are designated here generally in numerical order as the 1-axis, the 2-axis, and the 3-axis. Each system of axes is defined to be right-handed in the sense that a 90 coun- terclockwise (positive) rotation about the 1-axis, as viewed along the 1-axis toward the origin, rotates the 2-axis into the 3-axis. Also, a 90 rotation about the 2-axis rotates the 3-axis into the 1-axis; and a 90 rotation about the 3-axis rotates the 1-axis into the 2-axis. We will denote the set of Cartesian coordinates by a lowercase subscripted letter, such as xj, j = 1, 2, 3. The corresponding bold letter, x, will denote a vector with xj as 1 2 3 x x1 x3 e1 e2 e3 x2 Figure 1.1: Cartesian coordinates of vector, x, and unit vectors, ej. https://doi.org/10.1515/9783110784329-001
  • 25. components (see Figure 1.1). Also shown in Figure 1.1 is a set of special vectors, called unit vectors, denoted by ej, j = 1, 2, 3. Each unit vector has only one non-zero component, namely the jth component equals 1; that is, ej is directed along its respective axis and has unit length. The vector representation of x as an ordered triplet of coordinates is x = x1 x2 x3 0 B @ 1 C A. (1:1) Or, using the unit vectors, we may also write x = x1e1 + x2e2 + x3e3, (1:2) where it is clear that the coordinates, xj, are the orthogonal projections of x onto the respective axes. It is assumed that the reader is familiar with vector (and matrix) alge- bra, including the usual operations of addition, subtraction, and multiplication (scalar or dot product, vector, or cross product as well as matrix multiplication and inver- sion). For a review of these algebras, see, e.g., (Lang 1971). Before proceeding, a few additional introductory remarks are in order. The geo- detic/astronomic conventional usage of the terms coordinate system and coordinate frame will be followed (Moritz and Mueller 1987). The system includes the conventions and physical theories, or their approximations and models, that are used to define the triad of coordinate axes; while a frame denotes the accessible realization of the sys- tem through a set of points whose coordinates are monumented or otherwise observ- able. The general principles and methodologies of determining a coordinate (or, reference) system are beyond the scope of this text, and it is enough to know for pres- ent purposes that each set of coordinate axes is well-defined and accessible and repre- sents a coordinate frame. In the navigation literature reference is often made to frames instead of systems, a convention also adhered to in this text, where we will understand that for each frame there is a system in the background. The frames that we will deal with are either global or local in extent, where the “extent” is largely defined by the application and the accuracies desired. The global Car- tesian coordinates are tied either to the rotating Earth or to the celestial sphere (“fixed” stars); the local Cartesian coordinates are defined by local directions, such as north, east, and down. In addition, we consider curvilinear coordinates as alternative descrip- tors of points in space – we do not use these to characterize the intrinsic properties of surfaces (or space) which is perhaps their more pertinent mathematical (differential geometric) application; rather, their use is motivated by the fact that our motions and positions are generally close to being on a spherical or ellipsoidal surface. These coordi- nates are still three-dimensional and serve mostly to facilitate computations and deriva- tions, besides having their own historical significance. The curvilinear coordinates are 2 1 Coordinate Frames and Transformations
  • 26. Other documents randomly have different content
  • 27. “I love you,” he whispered. “Monimé, I love you.” “Men have said that to me before,” she answered, “and there was one man whom I believed.... We built the house of our life upon that foundation, but it fell to ruins all the same. Soon he ceased to tell me that he loved me.” “You are a married woman then?” he asked. “Yes,” she said. “Tell me who you are,” he begged. She shook her head. “No,” she replied. “I have no name. I have left him.” “Why?” he asked. “Because we disliked one another. It seemed to me altogether wrong that a man and a woman totally out of sympathy with one another should continue to live together. So I made my exit. I live by selling my pictures.” “Were there any children?” he asked. “No,” she answered. “If there had been, I suppose I should have remained with him. Like flowers, they hide many a sepulchre.” “It was brave of you to go,” he said. “I felt it to be a woman’s right,” she declared, spreading her hands in a gesture of conviction. “Since then I have been a wanderer. I’ve had some hours of happiness, some of loneliness, but always there has been my independence to cheer me, and the knowledge that I have been faithful to my sex, and have not misled others by the usual shams and pretences of the disillusioned wife.” “And what about the future?” he asked. “My dear,” she smiled, “the future is a veil of fog that only lifts for the passage of a soul. When I am about to die I will tell you of my future. But now, while I am in the midst of life, only the present counts.”
  • 28. For some time they talked; but at length when the little band of musicians, whose songs had formed a distant accompaniment to their thoughts, had gone their way, and the sound of the sea alone traversed the silence, she suggested that he should bring down his guitar and play to her. “The proprietress tells me she has heard you playing in your room,” she smiled. “She described it as très agréable mais un peu mélancolique.” Jim was not very willing to comply, for he had been termed a howling jackal at the mines, and, indeed, he had once been obliged to black a man’s eye for throwing something at him. He had no wish to fight anybody to-night. His companion, however, was so insistent that he was obliged to fetch the instrument and to sing to her. The darkness aided him in overcoming a feeling of shyness, and presently he passed into a mood which was conducive to song. He sang at first in quiet tones, and his fingers struck so lightly upon the strings that sometimes the rich chords were lost in the murmur of the surf. From sad old negro melodies he passed to curious chanties of the sea, and thence to the wistful music of the Italian peasants; and as he sang his diffidence left him, and soon his fine voice was strong enough to be heard in the hotel, so that the proprietress and some of her guests came tip- toeing out and stood listening near the open door, the light from the passage illuminating their motionless figures and casting their black shadows across the gravel and on to the encircling palms. “Listen,” said Jim, at length. “I’ll sing you some verses I made up when I was in Ceylon.” It was a song which told of a silent, enchanted city built by ancient kings upon the shores of an uncharted sea, where there were pavilions of white marble whose pinnacles shot up to the stars, seeming to touch the Milky Way, and whose domes were so lofty that at moonrise their silver orbs were still tinged with the gold of the sunset. It told how here, upon a bed of crystal, there slept a
  • 29. woman whose hair was as dark as the wrath of heaven, whose breast was as white as the snowclad mountain-tops, and whose lips were as red as sin; and how, upon a hot, still night there came a lost mariner to these shores, who passed up through the deserted streets of the city, and ascended a thousand stairs to the crystal couch, and kissed the mouth of the sleeper.... When he had ended the song there was a moment of silence before Monimé turned to him. “Do you mean to tell me,” she exclaimed, “that you have to earn your living at the mines when you can write verses like that?” “Oh, it’s only doggerel,” he laughed, “and I cribbed most of the music from things I’d heard.” “Have you got the poem written down?” she asked. “No, I’ve lost my only copy,” he answered. “I stuffed it into a hole in the woodwork of my berth on a certain tramp steamer, to keep the cockroaches from coming out. I never could get used to cockroaches.” “Jim,” she said, taking his hands in hers, “you are wasting your life.” “I am living for the first time to-night,” he replied. It was midnight when at length they ascended the stairs to their rooms, but there was on his part a mere pretence of bidding good- night at their doors. He knew well enough that presently he would attempt to renew their wonderful romance upon the balcony which connected their two rooms; but for the moment the serene inscrutability of her face baffled him. She neither made advance towards him, nor retreat from him. She seemed, mentally, to be standing her ground, undisturbed, unmoved. The wisdom of the ages was in her eyes, and the smile of precognition was on her lips. In love, man is so simple, woman so wise. Man blunders along, taking his chance as to whether he shall find favour or give offence; woman alone knows when the great moment has come, that
  • 30. moment when the time and the place and the person are plaited into the perfect pattern. Some women betray that knowledge in their agitation; some are made shy by the revelation; some, again, have the imperturbable confidence of their intuition, and these last alone are the celestials, the daughters of Aphrodite, the children of Isis and Hathor. In his room Jim sat for awhile upon the side of his bed, trying to fathom the unfathomable meaning of her expression. His brain was full of her—her hair black as the Egyptian darkness, her eyes grey as the twilight, and her flesh like the alabaster of the Mokattam Hills. There was such modesty, such reserve in her bearing, and yet with these qualities there went a kind of confidence, a self-assurance, which he could not define. In her presence he became aware of the shortcomings of his own sex, rather than of his mastery; yet at the same time he was conscious of an overwhelming intensification of his manhood. At last, a cigarette as his excuse, he stepped out on to the balcony, and for some moments stood looking out to sea. When he took courage to turn towards her window he found that though the light in the room was still burning, the shutters were closed; and thus he remained, staring at the green woodwork for what seemed an interminable time. He was about to go back disconsolately to his room when the light was extinguished, and the shutters were quietly pushed open. Who shall say whether she knew that Jim was standing in silence upon the balcony, or whether, being prepared for her bed, she now merely opened the windows that the cool of the night might bring her refreshing sleep? Woman is wise: she knows if the hour be meet.
  • 31. Chapter IV: BEDOUIN LOVE Jim awoke next morning with the feeling that he had come back to earth from heaven. The events of the night before seemed to belong to a world of enchantment, and had no relation to the keen, practical sunlight which now struck into his room through the open windows, nor to the cool sea breeze which waved the curtains to and fro, nor yet to the vivid blue sea and the clean-cut rocks which came into sight as he sat up in bed. “In the next room,” he mused to himself, “sleeps a woman who in the darkness was to me the gateway of my dreams, but who in this bright sunlight will be again only a capable, pretty creature and an amusing companion. Night, after all, is woman’s kingdom, and in it she is mistress of all the magic arts of enchantment, she becomes greater than herself; but day belongs to man. How, then, shall I greet her?—for my very soul seemed surrendered to her a few hours ago, yet now I find myself still master of my destiny.” Like an artist who steps back to view his picture, or like a poet who measures up his dream, he allowed his mind to take stock of his emotions. When her head had been thrown back upon the pillows, and the white column of her throat could be seen in the dim light of the moon against the black confusion of her hair, it had seemed to him that the marks of the chisel of the Divine Artist were impressed upon the alabaster of her flesh. It was as though, gazing down at her beauty, his eyes had been opened and he had beheld the handicraft of Paradise. And when, in his ardour, he had had the feeling of not knowing what next to do nor what words to utter, her silencing loveliness had baffled him, so it seemed, because her body was stamped with the seal of the Infinite and fashioned in the likeness of God. True, she was but imperfect woman; yet the art of the Lord of Arts had
  • 32. created her, and, by the magic of the night, he had found her rich in the inimitable craftsmanship of heaven. He had seen the glory of heaven in her eyes. He had heard the voice of all the ages in her voice. In the touch of her lips there had been the rapture of the spheres, and the gods of the firmament had seemed to ride out upon the tide of her breath. But was it she whom he had wanted when he held her pinioned in his arms? He could not say. It seemed more reasonable to suppose that through her he was looking towards the splendour which his soul sought. She was but the necromancy by which he had carried earth up to heaven; she was the magic by which he had brought heaven down to the earth. She had been the door of his dreams, the portal of the sky; and through her he had made his incursion into the kingdom beyond the stars. “It was only an illusion,” he said, as he stood at the window, invigorated by the breeze. “We are actually almost strangers. I don’t know anything about her, and she knows little of me. It was the magic of the night employed by scheming Nature for her one unchanging purpose; and all that happened in the darkness will be forgotten in the sunlight. We shall meet as friends.” To some extent he was right, for when at mid-morning she came down to the blazing beach and seated herself by his side in the shade of the rocks, she greeted him quietly and serenely, with neither embarrassment nor familiarity. “Are you going to bathe this morning?” he asked her, and on her replying in the affirmative, he told her that he thought he was well enough to do so, too. At this she showed some concern, but he reminded her that the water, at any rate near the shore, was warm to the touch and was hardly likely to do him harm. The little sandy bay, flanked by rocks which projected into the sea, was the site of a number of bathing huts and tents used by the Europeans who lived in the surrounding villas and bungalows. The breakers rolled in upon this golden crescent, continuously driven
  • 33. forward by the prevalent north-west wind; but at one side a barrier of low, shelving rocks formed a small lagoon where the water was peaceful, and one might look down to the bottom, ten or twelve feet below the surface, and see the brilliant shells and seaweeds almost as clearly as though they were in the open air. So strong was the summer sunlight that every object and every plant at the bottom cast its shadow sharply upon the sparkling bed; and the passage of little wandering fishes was marked by corresponding shadows which moved over the fairyland below. It was not long before Jim and Monimé were swimming side by side across this small lagoon to the encircling wall of rocks, and soon they had clambered on to them and had seated themselves where the surf rushed towards them from the open azure sea on the one side, drenching them with cool spray, and on the other side the low cliffs and rocks, surmounted by the clustered palms, were reflected in the still water. Here they sunned themselves and talked; and from time to time, when the heat became too great, they dived down together with open eyes into the cool, brilliant depths, gliding amongst the coloured sea-plants, grimacing at one another as they scrambled for some conspicuous pebble or shell, and rising again to the surface in a cloud of bubbles. It was a joyous, exhilarating, agile occupation, far removed from the enchantments of the darkness; and the glitter of sun and sea effectually diminished the lure of the night’s witchery. “You know,” said Jim, suddenly looking at his companion, as they lay basking upon the spray-splashed rocks, “I can hardly believe last night was anything but a dream.” “Let us pretend that it was,” she answered. She pointed down into the translucent water. “Life is like that,” she said. “We dive down into those wonderful depths when the glare of actuality is too great, and we see all the pretty shells down there; and then we have to come up to the surface again, or we should drown.” “I see,” he replied; “I was just a passing fancy of yours.”
  • 34. She answered him gravely. “Women in that respect are not so different to men. Judge me by yourself.” “Oh, but there’s a world of difference,” he said, chilled by her words. “I am simply a vagabond, a wandering Bedouin, here to-day and over the hills and far away to-morrow.” “I am also a wanderer,” she smiled. “We are both free beings who have broken away from the beaten path. We both earn our living, and claim our independence.” “Yet the difference is this,” he reminded her, “that the world will shrug its shoulders at my actions, but will condemn yours.” She made an impatient gesture. “Oh, that threadbare truism!” she said. “I have turned my back on the world, and I don’t care what it thinks. I act according to my principles, and in this sort of thing the first principle is very simple. If a woman is a thoughtful, responsible being, earning her own living, and able to lead her own life without being in the slightest degree dependent on the man of her choice, or on any other living soul, she is entitled to respond to the call of nature at that precious and rare moment when her heart tells her to do so. There should be no such thing as a different law for the man and for the woman: there should only be a different law for the self- supporting and the dependent. The sin is when a woman is a parasite.” With that she took a header into the water, and he watched her gliding amidst the swaying tendrils of the sea-plants, like a sinuous mermaiden. When she rose to the surface once more he dived in, and swam over to her, his face emerging but a few inches from hers. “Do you love me?” he asked, smiling amongst the bubbles. “No, I hate you,” she replied, striking out towards the shore. “Why?” he called after her. “Because you haven’t the sense to leave well alone,” she said, and thereat she dived once more, nor came to the surface again until
  • 35. she had reached shallow water. At luncheon she met him with an ambiguous smile upon her lips; but finding that he was not eating his food with much appetite, she at once became motherly and solicitous, refused to allow him to eat the salad, offered to cut up the meat for him, and directed the waiter to bring some toast in place of the over-fresh roll which he was about to break. At the conclusion of the meal she ordered him to take a siesta in his room, and in this he was glad enough to obey her, for he was certainly tired. When he woke up, an hour or so later, and presently went out on to the balcony, he saw her standing in her room, contemplating her painting materials. “May I come in?” he asked. She nodded. “Have you had a good sleep?” she inquired. “Sit down and talk to me. I have a feeling of loneliness this afternoon. I’m not in a mood to paint; yet I suppose I must, or I shall run short of money.” He went to her side and put his hands upon her shoulders, drawing her to him; but she pushed him away from her, with averted face. “I said ‘sit down,’” she repeated. Jim was abashed. “You’re very difficult,” he told her. “I think that under the circumstances I’d better go. I don’t know where I am with you.” “You haven’t tried to find out,” she answered. “You’re quite capable of understanding me: I should never have let you come into my life at all if I had not been certain that you had it in you to understand.” “Tact is not my strong point,” he said. “I’m just a man.” “Nonsense!” she replied. “Don’t belittle yourself.” He was puzzled. “Why, what’s wrong with men?”
  • 36. “Their refusal to study women,” she answered. She was not in a communicative mood, and would not be drawn into argument. He was left, thus, with a disconcerting sense of frustration, bordering on annoyance. It seemed evident to him that yesterday, by some secret conjunction of the planets, so to speak, their destinies had met together in one sentient hour of sympathy; but that now they had sprung apart once more, and he knew not what stars in their courses would bring back to him the ripe and mystic moment. An appalling loneliness descended like a cloud upon him, and he was conscious that she too, was experiencing the same feeling. It was the lot, he supposed, of all persons who were born with the Bedouin temperament; and he accepted it with resignation. At length she conducted him—or did he lead her?—down to the verandah of the hotel; and now she had her paints with her, and occupied herself in making some colour-notes of the brilliant sea which stretched before them, and of the golden rocks and vivid green palms. Jim, meanwhile, read an English newspaper, some weeks old, which he had chanced upon in the salon; but from time to time he sat back in his chair and watched her as she worked, his admiration manifesting itself in his eyes. “What are you staring at?” she asked him, presently. “I was admiring the way you handle your paints,” he replied. “You’re a real artist.” “The fact that a woman paints,” she remarked, “does not mean that she is an artist, any more than the fact that she talks means that she is a thinker. To be an artist requires two things, firstly, that you have something to express, and, only secondly, that you know technically how to express it. It is the point of view, the angle of vision, that counts; and in fact one can say that primarily one must live an art.” He nodded. He wondered whether the events of the previous night were but the living of her art; and the thought engendered a
  • 37. kind of mild bitterness which led him to give her measure for measure. “I know what you mean so well,” he said, “because I happen to have the talent to put things into nice metre and rhyme; but it is the subject matter that really counts, and that’s where I feel my stuff is so flat. Sometimes I am obliged to seek experience to help me.” “You must let me see some of these poems,” she said, pursuing the theme no further. He shook his head. “They are only doggerel, like the one I sang last night,” he laughed. “They are as shallow as my heart.” She resumed her painting and he his reading; but his mind was not following the movement of his eyes. He was thinking how little he understood his companion. She was clearly a woman of strong views, one who had taken her life into her own hands and was facing the world with reliant courage. In fact, it might be said of her that she was the sort of woman who would not be turned from what she knew to be right by any qualms of guilty conscience. He smiled to himself at the epigram, and again allowed his thoughts to speculate upon her alluring personality. He found at length, however, that the matter was beyond him; and presently he turned to his reading once more. It was while he was so engaged that suddenly he sat up in his chair, gazing with amazement at the printed page before him. “Great Scott!” he whispered, pronouncing the words slowly and capaciously. There was a crazy look of astonishment upon his face. “What’s the matter?” she asked, glancing at him, but unable to tell from the whimsical expression of his mouth and eyes what manner of news had taken his attention. He looked at her as though he did not see her. Then he read once more the words, which seemed to dance before him, and again stared through her into the distance of his breathless thoughts.
  • 38. “News that concerns you?” she asked. He nodded, holding his hand to his forehead. “Bad news?” “Yes,” he answered, as though speaking in a dream. “Very bad ... wonderful!” She could not help smiling, and her intuition quickly jumped to the truth. “Somebody has died and left you some money?” she suggested. He uttered an almost hysterical laugh. “I’m free!” he cried. “Free! I shall never have to go back to the mines.” He sprang to his feet, folding the newspaper, and crushing it in his hand. “Don’t go and faint again,” she said, quietly. He laughed loudly, and a moment later was hastening into the hotel. He snatched his hat from a peg in the hall, and hurried out through the dusty little garden at the front of the building, and so into the afternoon glare of the main road. Here he hailed a carriage, and, telling the driver to take him to the Eastern Exchange Telegraph office, sat back on the jolting seat, and directed his eyes once more to the Agony Column of the newspaper. The incredible message read thus: James Champernowne Tundering-West, heir to the late Stephen Tundering-West, of the Manor, Eversfield, Oxon, is requested to communicate with Messrs. Browne Beadle, 135a, Lincoln’s Inn Fields, London. His uncle was dead, then, and the two sons, his unknown cousins, must have predeceased him or died with him! He had never for one moment thought of himself as a possible heir to the little property; and heaven knows how long it might have been before he would
  • 39. have had knowledge of his good fortune had he not chanced upon this old newspaper. Arrived at his destination, he despatched a cablegram to the solicitors, notifying them that he would come to England by the first possible boat. Then he drove on to Cook’s office in the heart of the city, which he reached not long before it closed; and here, after some anxious delay, he was told that a berth, just returned by its prospective occupant, was available on a French liner sailing for Marseilles that night at eleven o’clock. This he secured without hesitation, and so went galloping back towards the hotel as the sun went down. In the open road, between the city and the hotel another carriage passed him in which Monimé was sitting, on her way to dine with some friends, of whom she had spoken to him. He waved to her, and both she and he called their drivers to a halt. Then, hastening across to her, he told her excitedly that he was sailing for England that night. “You see, I’ve inherited some property,” be explained. “I must go and claim it at once.” Her face was inscrutable, but there was no light of happiness in it. “I’m sorry it has come to an end so soon,” she cried. “What?” he cried, and it was evident that he was not listening to her. “You’ve been wonderful to me. We mustn’t lose sight of each other. This thing has got to go on and on for ever.” He hardly knew what he was saying. An hour ago she had been almost the main factor in his existence. Now she was but a fragment of a life he was setting behind him. It was almost as though she were fading into a memory before his very eyes. He was, as it were, looking through her at an amazing picture which was unfolding itself beyond. The yellow walls of the houses, the sea, the palms, the sunset, were dissolving; and in their stead he was staring at the green fields of England, at the timbered walls of an old manor-house
  • 40. last seen when he was a boy, at the grey stone church amongst the ilex-trees and the moss-covered tombstones. “I must go on and pack at once,” he said, standing first on one leg and then on the other. “You’re sure to be back before I leave. You can get away by ten, can’t you?” He wrung her hand effusively, and hurried to his carriage, from which, standing up, he waved his hat wildly to her as they drove off in opposite directions. But when the clock struck ten there was no sign of Monimé and a few minutes later the hotel porter, who was to accompany him to the harbour, began to urge him to delay his departure no longer. Being somewhat flurried, he thought to himself that he would write her a farewell letter from the steamer, and give it to the porter to carry back with him. But by the time he had found his cabin and seen to his baggage, the siren was blowing, and the porter in alarm was hurrying down the gangway. “I’ll write or cable from Marseilles,” he said to himself. “I don’t suppose she cares a rap about me: the whole thing was due to our romantic surroundings. But still one would be a fool to lose sight of a real woman like that.... I wish I knew her name.”
  • 41. Chapter V: THE SQUIRE OF EVERSFIELD The art of life is very largely the art of burying bones. That is the science of mental economy. When a man is confronted with a problem which he cannot solve; when, so to speak, Fate presents him with a bone which he cannot crack, sometimes, without intent, he slinks away with it and, like a dog, buries it, in the undefined hope that at a later date he may unearth it and find it then more manageable. Even so, during the sea voyage, Jim unconsciously buried the bewildering thought of Monimé. He was a careless fellow, very reprehensible, having no actual harm in him, yet bearing a record pock-marked, so to speak, with the sins of omission. He was one of the world’s tramps by nature; and now once more he was out upon the high road, and the lights of the city wherein he had slept had faded behind him as he wandered onwards into another sunrise. It is true that he wrote her a long and intense letter upon the day after his departure, and that he posted this upon his arrival at Marseilles; but his brain, by then full of other things, conjured up no clear vision of her, and his heart sent forth no impassioned message with the written word. He had been deeply stirred by her, but also he had been baffled; and, as in the case of a dream, he made no effort to retain the sweetness of the memory. On the morning of his arrival he called at the office of the solicitors who had inserted the advertisement, and was not a little startled to find himself greeted with that kind of obsequiousness which he had supposed to have vanished from Lincoln’s Inn fifty years ago.
  • 42. The little pink-and-white man who was the senior partner, and whose name was Beadle, rubbed his hands together as though he were washing them, and actually walked backwards for some paces in front of his visitor, bowing him into a shabby leather chair which stood beside the large, imposing desk. “I hope,” he crooned, when Jim had established his identity, “that we may still have the duty, and pleasure, of serving you, sir, as we have served your uncle and your grandfather.” “I hope so,” replied Jim. “I suppose you know all the ins and outs of the family affairs.” Mr. Beadle smilingly directed the young man’s attention to a number of black tin boxes stacked in the corner of the room. “The Tundering-West documents for the last two hundred years,” he declared, blowing his breath through his teeth, an action which served him for laughter. Jim had a vision of legal formalities and lawyers’ rigmaroles— things which he had always detested; and the passing thought contributed to the growing dislike he felt for the harmless, but sycophantic, Mr. Beadle. “Well, first of all,” he said, “tell me what my inheritance consists of, and what sort of income I’ve got.” Mr. Beadle explained that the little property comprised some two hundred acres, most of which were rented; the score of houses and cottages which constituted the tiny little village; the small but comfortable manor-house; and twenty thousand pounds of invested capital. This was better than Jim had expected, and his pleasure was manifest by the broad smile upon his tanned face. “You see, you will have quite a comfortable income in a small way,” the solicitor told him. “I do not think that your duties will embarrass you. You will find your tenants very respectful and deferential country-people, who will give you little bother; and your obligations as landlord will be very easily discharged.”
  • 43. “They’re a bit behind the times, eh?” suggested Jim. “Ah, my dear sir,” said Mr. Beadle, “I am thankful to say that there are still some parts of the English countryside where a gentleman may live in comfort, and where the people keep their place.” Jim was astonished by the remark, for he had believed such sentiments to be entombed in the novels of long ago. “Poor old England!” he murmured. “We’re a comic race, aren’t we, Mr. Beetle?” “‘Beadle,’” the little old man corrected him; and “Sorry!” said Jim. They spoke later of the tragedies which had thus brought the inheritance out of the direct line, and hereat came the conventional sighs from Mr. Beadle, as forced as his laughter. Jim was told how his cousin, Mark, had died in India of pneumonia, and how his uncle and the remaining son, James, having gone to the Lakes that the old gentleman might recover his equanimity, were both drowned in a sudden squall while sailing at a considerable distance from the shore. The bodies were recovered and brought to Eversfield for burial; and very solemnly the solicitor produced a photograph of the memorial tablet which had been set up in the church. “Some day, I trust a very long time hence, your own mural tablet will be set up there,” he said, after Jim had handed back the photograph in silence. “‘Nihil enim semper floret; ætas succedit ætati,’ as the good Cicero says.” “Quite so,” said Jim. “It has all been a terrible blow to me,” sighed Mr. Beadle. “The late Mr. Tundering-West treated me quite as a personal friend.” “Did he really?” Jim was going to be rude, but checked himself. He felt an extraordinary hostility to this well-meaning but servile little personage. “I shall go down there to-morrow,” he remarked, as he rose to take his departure, “and I’ll probably have the house thoroughly renovated before I go into it.” “I don’t think you will find much that requires alteration,” Mr. Beadle assured him, his hand raised in a gesture of deprecation.
  • 44. “Hasty changes are always undesirable; and, when you have grown into the spirit of the place I think you will find that you have a duty to the past.” He checked himself, and bowed. “I trust you will not mind an old man giving you that advice,” he murmured, as they shook hands. He bowed so low that it appeared to be a complete physical collapse. On the following day Jim motored to Eversfield in a hired open car. He could with greater ease have gone by train to Oxford, and could have driven over in a fly; but he wanted to have the pleasure of spending some of his new money, and, moreover, a fifty-mile drive through the fair lands of Berkshire and Oxfordshire in the radiance of a summer’s day appealed to his imagination. Nor was he disappointed. He acknowledged the beauties of the land of his birth with whole-hearted pleasure; and his eyes, weary with long gazing upon leaden skies and burning sands, were soothed in a manner beyond scope of words by the green fields, the soft foliage of the trees, and grey skies of a hot, hazy morning. It is true that the roads were extremely dusty, and that his face and clothes were soon thickly powdered; but, as the chauffeur had provided him with a pair of motoring glasses, he was not troubled in this respect. The little hamlet of Eversfield lay seemingly asleep in its hollow amidst the richly timbered hills, as, at midday, he drove up to the grey stone gates of his future home. Here was the narrow village green just as he had last seen it when he was a boy: on one side of the lane which opened on to it were these imposing gates; on the other side were the little church and moss-covered gravestones leaning at all angles, as though the dead were whispering together deferentially at the entrance of the manor. Upon the green were the old stocks, and the stump and worn steps of the ancient cross; and behind them stood the thatched cottages backed by the stately elms. “I suppose in years to come,” he thought, “I shall be walking through these gates to the church on Sundays, followed by the lady of my choice and half-a-dozen children; and the villagers will nudge
  • 45. one another and say ‘Here comes Squire and all his little squirrels.’ ... Good Lord!” The exclamation was due to the sudden feeling that he had walked into a trap, that he had been caught by immemorial society, and would soon be forced to conform to its ways; and, as the car passed in at the gates of the manor, he had, for a moment, a desire to jump out and run for his life. A short, straight drive, flanked by clipped box-trees, led to the main door of the timbered Tudor house; and here the new owner, dusty, and somewhat untidily dressed, was received by the gardener and his buxom wife, who had both grown grey in his uncle’s service. The man held his cap in his hand, and touched his wrinkled forehead with his finger a number of times, painfully anxious to find favour; while his wife curtseyed to him at least thrice. “Are you the gardener?—what is your name?” Jim asked briskly, feeling almost as awkward as the man he addressed, but determined to go through the ordeal with honour. “Peter, sir,” said the gardener. “Peter Longarm, sir. I rec’lect you, sir, when you was no more’n so ’igh, I do.” “Why, of course,” Jim replied. “I remember you now. You’re the fellow who told my uncle when I broke the glass of the forcing frame.” The old man looked sheepish. “I ’ad to do my dooty, sir,” he said. “I ask your pardon.” “Duty,” Jim thought to himself. “I’m beginning to know that word. I wonder what it really means.” He turned to the woman. “Now, please go and open the doors of all the rooms, and then leave me to walk through the house by myself.” He wanted to be alone to realize his new possession and to dream his dream of future ease. Mrs. Longarm eyed him nervously for a moment before obeying his instructions; she told her husband afterwards, with tears in her eyes, that she felt as though she were surrendering the house to a cut- throat foreigner.
  • 46. As he wandered, presently, from room to room he was at first overpowered by the feeling that he was intruding upon the privacy of some sort of family life which he did not understand. His uncle’s wife had been dead for three or four years, but there were still many traces of her influence: the drawing-room, for example, was furnished in a style which called to his mind faded pictures of feminine tea-parties. Here was the old piano upon which the good lady must have tinkled the songs of which the music still lay in the cabinet near by—songs such as My Mother Bids Me Bind My Hair, and Ah, Welladay my Poor Heart. And here was the little sewing- table where had doubtless rested the silks and needles for her embroidery. Perhaps it was she who had chosen the gilt-framed engravings upon the walls—the depressed picture of “Hagar and Ishmael in the Wilderness;” a youthful portrait of Alexandra, Princess of Wales; “Jacob weeping over Joseph’s coat;” the sprightly “Hawking Party,” and so forth. Looking around, he experienced a sensation of mingled mirth and awe, and he hoped that the ghost of his aunt would not haunt him when he laid sacrilegious and violent hands upon these things, as at first he intended to do. The chintzes appeared to be of more recent date; but these, too, would have to go, for, as a pattern, he detested sprays of red roses tied with blue ribbons. The dining-room, hall and staircase, being panelled and hung with family portraits, were impressive in their conveyance of a sense of many generations; and the hereditary library, if sombre, was interesting. Jim was very fond of old books, and he stood there for some time taking the calf-bound volumes from the shelves, and turning over the ancient pages. But, the morning-room, with its red- covered chairs, its mahogany sideboard, and its sham Chinese vases, was distressing. Yet here, as in the drawing-room, there was a chaste and awful solemnity, from which he shrank, as a conscientious Don Juan might shrink at a lady’s prie-Dieu. The larger bedrooms upstairs, with their mahogany wardrobes and heavy chests of drawers full of clothes, and cupboards full of boots
  • 47. and hats, were startling in their association with their late tenants. On a table beside his uncle’s bed there lay a recent novel, which Jim himself had also just read: it constituted a gruesome link between the living and the dead. He glanced about him and through the window, down the drive, almost expecting to see the apparitions of his relatives stalking up from the family vault in the churchyard to see what he was about. His uncle would probably think him a dreadful scallawag, for the old gentleman had been an accredited pillar of Church and State, with, so the cupboards testified, a mania for collecting the top hats he had worn on Sundays or when in town. He had been a model of propriety, and the monumental stone, the photograph of which he had seen at the solicitors, stated that he had “nobly upheld the traditions of his race.” Jim felt depressed, and presently went out into the garden which was ablaze with flowers; and here, after a late meal of sandwiches, eaten upon an ornamental stone bench, his spirits revived, for the manor and its setting formed a very beautiful picture. If only he could get rid of all those hats and clothes and old photographs! A sudden idea occurred to him: he would go and find the padre, and tell him to take these things for the poor of the parish. They must be got rid of at once, even though every man in the village be obliged to wear a top hat. They must all be gone before he came here again, or he would never bring himself to live in the house at all! He hurried down the drive, asked Peter Longarm at the lodge to point out the vicarage to him, and thereafter hastened on his errand. Near the church, however, and at a point where a gap in the trees revealed a distant view of the dreaming, huddled spires of Oxford, flanked by the lonely tower of Magdalen College, he met with a white-bearded clergyman whom he presumed to be the vicar, and at once accosted him. “Excuse me,” he said, ingratiatingly, barring his way. “Would you care to have some old hats?—I mean of course, would your flock like to wear them?—Top hats, you know, and old boots, too, if you want them.”
  • 48. The elderly gentleman was annoyed, and, with a curt “No thank you, not to-day,” proceeded on his way. Jim, however, called after him, coaxingly: “They are quite good hats really; they only want brushing.” At this the man of God stopped and turned, looking at Jim’s somewhat dusty figure with wonderment. “Do I understand that you are selling old hats?” he asked, endeavouring to speak politely. Jim rushed feverishly into explanation. “No, I want to get rid of them,” he gabbled; “I want to get rid of all sorts of things—hats, coats, trousers, dressing-gowns, shirts, vests, boots, slippers, old photographs, umbrellas ...” He paused for breath, inwardly laughing. Very slowly and deliberately the clergyman adjusted his eyeglasses low down upon his nose, and stared at Jim. “Young man,” he said, “is this a jest at my expense?” “Good Lord, no!” Jim answered. “I’m in deadly earnest. I can’t possibly live in the house with all these things. You will help me, won’t you? How would it be if you came over to-morrow and cleared them all out, and then had a meeting or something, and gave them as prizes to the regular church-goers?” “I don’t know what you are talking about,” the clergyman responded, gently but firmly pushing him aside. “Good-day!” Jim stared at him as he walked. “You are the vicar, aren’t you?” he asked. “No, I’m not,” the other replied somewhat sharply, over his shoulder; “I’m the President of Magdalen.” Jim uttered an exclamation of impatience, and hastened on to the Vicarage. The servant who appeared in response to his knock, was about to ask him his name, when the vicar, an old man with a clean-shaven, kindly face, and grey hair, happened to cross the hall.
  • 49. “Yes, what is it, what is it?” he asked, coming to the door, while the maid retired. “Are you the vicar?” Jim asked, beginning more cautiously. “I am,” the other responded. “You really are? Well I want to ask you about some old clothes. I....” The vicar held up his hand. “No, I have none to sell you,” he said smiling sadly. “I wear mine out.” Jim laughed aloud. “First I’m thought to be selling them, and now you think I’m buying them,” he exclaimed. “We certainly are a nation of shop-keepers.” The vicar was puzzled. “I don’t understand. What is it you want?” “I have a lot of hats and old clothes I want to get rid of. I thought you might like them.” The clergyman bowed stiffly. “It is very kind of you,” he said frigidly. “My stipend, I admit, is small, but I am not yet reduced to the necessity of wearing a stranger’s cast-off clothing.” “Oh, I didn’t mean that,” Jim hastily explained. “And they’re not mine: they belonged to my late relatives. I am just coming to live at the manor, and I thought the poor of the parish would....” The vicar interrupted him. “I beg your pardon. Are you ...?” He hesitated, incredulous. “Yes, I’m the new Tundering-West,” Jim told him. The other held out his hands. “Well, well!” he cried. “And I thought you were....” He hesitated. “The old clothes man,” laughed Jim. “Oh, very droll!” the vicar smiled, shaking him warmly by the hand. “How ridiculous of me! Do come in, my dear sir!”
  • 50. Jim followed him into the drawing-room, and here he found a little old lady, who was introduced to him as Miss Proudfoote, and a florid, middle-aged man with a waxed moustache, who looked like a sergeant-major, and proved to be Dr. Spooner, the local medical man. They had evidently been lunching at the Vicarage, and were now drinking the post-prandial concoction which the English believe to be coffee. They both greeted him with a sort of deference, which however, did not conceal their curiosity. During the next ten minutes Jim heard a great deal of his “poor dear uncle” and his unfortunate cousins. The tragedy of their deaths, it seemed, had cast the profoundest gloom over the village; but it was a case of “the King is dead; long live the King!” and all three of his new acquaintances appeared to be anxious to pay him every respect. Dr. Spooner asked him from what part of England he had just come, and the news that he had been living abroad and had not visited the land of his birth for many years caused a sensation. The thought occurred to him that he ought not to mention Egypt, or any other land which had recently known him as Jim Easton; for any such revelations might bring discredit upon him, and he wished to start his life at Eversfield without any handicap. He therefore spoke only of California, referring to it casually as a country where he had resided. Miss Proudfoote turned to the vicar. “Is it not extraordinary,” she said, “how many of our young men shoulder what Mr. Kipling calls ‘the white man’s burden’ and go forth to live amongst the heathen?” Her geography was evidently at fault, but out of consideration for her years and her sex, no correction was forthcoming. “I suppose,” she proceeded, “you met with our missionaries out there? It is wonderful what a great work the Church Missionary Society is doing all over the world.” The Doctor here had the hardihood to interpose. “Oh, but California is a part of the United States of America ...” he ventured.
  • 51. “How foolish of me!—of course,” smiled the old lady. “The Americans are quite an educated people. I met an American traveller once in Oxford: a pleasant spoken young man he seemed, so far as I could understand what he said.” “Yes,” remarked the vicar, “America can no longer be called ‘the common sewer of England,’ as it was when I was a boy.” Jim stared from one to the other in amazement. “But America is the largest and most progressive part of the Anglo-Saxon race,” he protested. “They are already ahead of us in many ways.” Miss Proudfoote was shocked, and she showed it. “It is evident that you do not know England,” she replied, coldly. “I mean,” he emphasized, “it always seems to me a fine thought that England can never die, because she will live again over there; and then she’ll have another lease of life in Australia; and so on. This England here may die, but the English will go on for ever and ever, it seems to me. And wherever their home may be,” he added, laughing, “they’ll always think it ‘God’s own country,’ and think themselves the chosen people.” Miss Proudfoote looked anxiously at him, hoping that there was some good in him. “I trust,” she said, “that it is now your intention to settle down?” “Yes,” he replied. “I fancy my wanderings are over.” “Heaven has placed you in a very responsible position,” she said, gazing earnestly at him. “I am sure our best wishes will be with you in your duties.” “Yes, indeed,” sighed the vicar, whose name, as Jim had just ascertained, was Glenning. “Are you a married man, may I ask?” “Oh no,” Jim replied. Miss Proudfoote patted his arm. “We shall have to find you a wife,” she smiled.
  • 52. Jim was aghast, and hastily changed the subject. “Now about the old clothes,” he began. Mr. Glenning coloured, slightly. “What an absurd error for me to have made,” he said. “Now, tell me, what is it you wish me to do?” “I’m going back to London to-day,” Jim explained, “and I want you, while I am away, to go through all my uncle’s things, and give away to the poor everything you think I shall not want. Just use your own judgment.” “It will be a melancholy duty,” he replied. “I’m sure it will,” the new Squire answered, “but, I tell you frankly, anything useless I find here when I return I shall burn.” The vicar raised his hands; the doctor sniffed; and Miss Proudfoote looked at the stranger indignantly. “That is rather hasty, is it not?” she asked, tremulously. Jim felt awkward. He had made a bad impression, and he knew it. “You see,” he tried to explain, “my uncle died so suddenly and the place is littered with his things. All I want to keep is the furniture, and the silver, and the books, and that sort of thing, but I will see to that myself.” Miss Proudfoote turned away suddenly and Jim, to his horror, saw her raise a handkerchief to her eyes. He could have kicked himself. He wished the floor would open and engulf him. He looked in despair at the two men. “You know I haven’t seen my uncle since I was a boy,” he stammered. “I am a complete stranger.” “He was our very dear friend,” said Mr. Glenning.
  • 53. Chapter VI: SETTLING DOWN While the congregation in the little church at Eversfield was singing the last hymn of the morning service the October sun passed from behind an extensive bank of cloud, and its rays shot down through the plain glass window upon the figure of a young woman, whose sudden and surprising illumination instantly attracted many pairs of eyes to her. She looked, and knew it, like a little angel as she stood in this shaft of brilliance, hymn-book in hand, singing the well-known words in a voice which enhanced their ancient sweetness; and the vicar, from his place at the side of the small chancel, fixed his gaze upon her with an expression of such saintly beatitude upon his face as to be almost idiotic. Her name was Dorothy Darling; but her mother, who here stood beside her in the shadow under the wall, called her Dolly, and rightly congratulated herself upon having chosen for her only baby, twenty- three years ago, a name of which the diminutive was so appropriate to the now grown woman. In the sunshine the girl’s soft, fair hair looked like a puff of gold, and her skin like coral; and the play of light and shade accentuated the pretty lines of her figure, so that they were by no means lost under the folds of her smart little frock. Her large, soft eyes were as innocent as they were blue, and never a glance betrayed the fact that she was singing for the direct benefit of the new Squire, whose head and shoulders appeared above the carved wooden walls of the sort of loose-box which was his family pew. The miniature church, though dating from the twelfth century, still retained the features by which it had been transformed and modernized in the obsequious days of Walpole and the first of the Georges. The pews for the “gentry” were boxed in, and each was fitted with its door; but the walls of Jim’s pew were higher than the
  • 54. others and its area bigger. At the back of the church there were the open seats for the villagers and persons of vulgar birth; but the woodwork here was not carved, save with the occasional initials of lads long since passed out of memory. At the sides of the chancel were set the mural tablets which recorded the genealogical lustres of dead Tundering-Wests, back to the day when a certain Captain of Horse had obtained a grant of the manor from the Commonwealth, in lieu of his devastated estate in Devon, and, with admirable tact, had married the daughter of the exiled Royalist owner. Around the whitewashed walls of the small nave large wooden boards were hung, upon which were painted the arms and quarterings of the successive Squires and their spouses; and above the chancel arch the royal Georgian escutcheon was displayed in still vivid colours. The church, indeed, was a tiny monument to all that glory of caste which its Divine Founder abhorred, and which the aforesaid Roundhead, misapprehending the unalterable character of his fellow- countrymen, had apparently fought in his own day to suppress. When the hymn was finished, the blessing spoken, and Mr. Glenning gone into the vestry behind the organ, this traditional distinction between the classes was emphasized by the behaviour of the little congregation. Nobody of the meaner sort moved towards the sunlit doorway until Jim, looking extraordinarily embarrassed, had marched down the aisle and had passed out into the autumnal scurry of falling leaves, followed closely by Mrs. and Miss Darling, Mr. Merrivall of Rose Cottage, Dr. and Mrs. Spooner, and old Miss Proudfoote of the Grange; and, when these were gone, way had still to be made for young Farmer Hopkins and his wife, Farmer Cartwright and his idiot son, and the other families of local standing. Outside, in the keen October air, Jim paused under the ancient ilex-tree, and turned to bid good-morning to the Darlings. Dolly had interested and attracted him during these three months since he took up his residence at the manor; but he had been so much occupied in settling himself into his new home that he had not given
  • 55. her all the attention he felt was her due, now that the shaft of sunlight in the church had revealed her to him in the palpable charm of her maidenhood. He greeted her, therefore, with cheery ardour, as though she were a new discovery, and walked beside her and her mother down the path which wound between the moss-covered gravestones, and out into the lane under the rustling elms. A great change had come over him since he had returned to England: he had become in some ways more normal, and the quiet, simple life of an English village had, as it were, taken much of the exotic colour out of his thoughts. In the romantic East he had looked for romance, but here in the domestic West his mind had turned towards domesticity. His poetic imagination was temporarily blunted; and whereas in Alexandria he had responded eagerly to the enchantments of hour and place, in Eversfield he was readily satisfied with a more rational aspect of life. He turned to the mother. “What a little picture your daughter looked, singing that hymn in the sunlight,” he remarked, with enthusiasm. Mrs. Darling sighed. Twenty years ago she, too, had been a little picture; but, so she thought to herself, she had had more character in her face than Dolly, and less softness. Outwardly her little girl took after that scamp of a father of hers, whose innocent blue eyes and boyish face had won him more frequent successes than his continence could handle. “Yes,” she replied, evasively, “that is Dolly’s favourite hymn.... She has a nice little voice.” “Delightful!” said Jim. “I didn’t know hymns could sound so beautiful!” Dolly looked at him as our great-grandmothers must have looked when they said, “Fie!” “Aren’t you a regular church-goer?” she asked, gazing up at him with childlike eyes.
  • 56. “Can’t say I am,” he answered, with a quick laugh. “I’m new to all this, you know. I’ve knocked about all over the world since I left school. But, I say!—that family pew, and the respectful villagers!— they give me the hump!” “Oh, I think it is charming, perfectly charming,” said Mrs. Darling. “Well,” he replied, “I expect I’ll get used to it. I suppose this sort of life grows on one: in some ways I’m beginning to have a sort of settled feeling already.” They were walking away from the gates of the Manor, which rose opposite the ivy-covered church, and were approaching the picturesque little cottage where the Darlings lived. Jim paused, and as he did so Dolly experienced a sudden sense of disappointment. She had hoped that he would accompany them to their door, and she had intended then to entice him through it, and to show him over their pretty rooms and round the flower-garden and the orchard. Until now they had only occasionally met, and their exchanges of conversational trivialities had been carried on in the lane, or at the door of the church, or outside the cottage which served as the post-office. He seemed to be a difficult man to take hold of; and during the last few weeks, since her mind had begun to be so disastrously full of the thought of him, she had felt ridiculously frustrated in her attempts to develop their friendship. Frustration, of course, is woman’s destiny, which meets her at every turn; but in youth it sometimes serves as her incentive. “Won’t you come in and see our little home?” she asked. “It’s rather a treasure.” He shook his head. “I’m afraid I can’t,” he replied. “I promised to go round my place with the gardener this morning. He’ll be waiting for me now. But, I say, what about dinner to-night? Won’t you both dine with me?” He was feeling reckless. Dolly’s heart leapt, and, in a flash, she had selected the dress she would put on, and had considered whether she should wear the little diamond pendant or the sham pearls.
  • 57. “We shall be delighted,” murmured Mrs. Darling. “Eh, Dolly?” The girl looked doubtful. “I don’t know that we ought to to-night,” she answered. “We had half promised to drive over to a sort of sacred concert affair in Oxford.” “Oh, don’t disappoint me,” said Jim. “I’ve got the house almost shipshape now; I’d like you to see it.” Dolly did not require really to be pressed; and soon the young man was striding homewards down the lane, wondering why it had taken him three months to realize that this girl was perfectly adorable; while she, on her part, was pinching Mrs. Darling’s arm and saying: “Oh, mother dear, doesn’t he look delightfully wicked!” “Yes, he seems a nice, sardonic fellow,” her mother remarked grimly, as they entered their house. “Why did you begin by saying we were engaged to-night? It’s the first I’ve heard of it.” Dolly smiled. “Oh, I made that up, because I thought you were too prompt in accepting. He’ll want us all the more if we are stand- offish. Men are like that.” Mrs. Darling sniffed. She was a lazy, plump, and rather languid little woman; and sometimes she grew impatient at her daughter’s ingenious method of dealing with these sorts of situations. She herself had grown more direct in her Yea and Nay: perhaps at the age of forty-five she was a little tired of dissimulation. The world had treated her scurvily; and, having a settled grievance, she was inclined now to take whatever pleasant things were to be had for the asking, without any subtle manœuvering for position. Her husband had left her when Dolly was five years old, and, so far as she knew, he was now dead. For several years she had bravely maintained herself in a tiny Kensington flat by writing social and theatrical articles for pretentious papers. She had been a purveyor of gossip, a tattle-monger, a dealer in bibble-babble; and she had carried on her trade with an increasing inclination to yawn over it, and a growing consciousness of her daughter’s contempt,
  • 58. until the editors who had supported her became aware that her heart was not in her work, and five years ago gave her her congé. Then, with a temporary display of energy, she had followed Dolly’s cultured advice, and had established a little business off Sloane Square, which she called “The Purple Shop.” Here she sold purple cushions and lamp-shades, poppy-heads dipped in purple paint, poetry-books in purple covers, sketches by Bakst in purple frames, lengths of purple damask, and so forth. But purple went out of fashion, and her once very considerable profits sank to the vanishing point. She introduced other colours, and softer shades of mauve and lilac. She sold a doll which had mauve hair and naughty black eyes; she took in a stock of bottled new potatoes tinged with a harmless purple liquid, and presented them to the jaded world of fashion as Pommes de terre pourpres de Tyr; she even sold brilliant bath-robes for bored bachelors, with coloured soap to match. A financial crash followed, and, after a few months spent in dodging her creditors, she heard of this little cottage at Eversfield, and fled to it with her daughter, leaving no address. She was in receipt of a small annual allowance from the estate of a deceased brother, and this she supplemented by writing the monthly fashion article in one of the journals devoted to the world, the flesh and the devil. She wrote under the nom-de-plume of “Countess X”; and her material was obtained by a monthly visit to London and a tour of the leading modistes. For eighteen months now she had lain low in this nook of the Midlands where Time stood still, and gradually she had ceased to dread the visit of the postman, and had begun to take a languid interest in the cottage. The colour purple no longer set her fat knees knocking together, and lately she had been able even to look up some of her old friends in London and to greet them with the sad, brave smile of a wronged woman. To Dolly, however, the enforced seclusion had been a sore trial, and there were times when her pretty eyes were red with weeping. She had been utterly bored by the purposeless existence she was
  • 59. called upon to lead; but now the arrival of the new Squire at the manor, which had hardly seen its previous owner during the last year of his life, had aroused her from her sorrows and had set her heart in a flutter. She liked his strange, swarthy face and his moody eyes, and thought he looked artistic and even intellectual; and she liked his obvious embarrassment at the deference paid to him in this little kingdom which he had inherited. She spent the afternoon, therefore, in a condition of pleasurable excitement, stitching at the dress she was going to wear and making certain alterations to the shape of the neck. While she plied her needle, Mrs. Darling sat at the low window overlooking the orchard, and scribbled her monthly article upon a writing-pad resting on her knee. “Here is a charming little conceit I chanced upon in Bond Street t’other day,” she wrote. “It is really a tub-time frock; but its success in the drawing-room is likely to be immediate. Organdy ruchings of moonlight blue, and a soupçon of jet cabochons on the corsage. It is named ‘Hopes in turmoil.’” And again, “I noticed, too, a crisp little trotteur frock, with a nipped-in waist-line hesitating behind a moyenage girdle of beige velours delaine. They have called it ‘Cupid’s Teeth.’ Oh, very snappy, I assure you, my dears!” She smiled lazily as she wrote, but once she sighed so heavily that her daughter asked her if anything were amiss. “No,” she replied. “I was only just wondering whether anybody in their senses could understand the nonsense I am writing. The editor’s orders are to make the thing sound French: I should lose my job if I wrote in plain English.” “Oh dear,” sighed Dolly, “how tedious all that sort of thing seems! I wonder that you can bother with it.” “I’ve got to,” her mother answered, with irritation. “I shan’t be able to give it up till you are married and off my hands.” “Yes, so you are always telling me,” said Dolly; and therewith their silence was renewed.
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