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Numerical Methods in
Environmental Data
Analysis
This page intentionally left blank
Numerical Methods in
Environmental Data
Analysis

Moses Eterigho Emetere

Department of Mechanical Engineering Science,
University of Johannesburg, South Africa
Department of Physics, Covenant University, Ota, Ogun, Nigeria
Elsevier
Radarweg 29, PO Box 211, 1000 AE Amsterdam, Netherlands
The Boulevard, Langford Lane, Kidlington, Oxford OX5 1GB, United Kingdom
50 Hampshire Street, 5th Floor, Cambridge, MA 02139, United States

Copyright © 2022 Elsevier Inc. All rights reserved.

No part of this publication may be reproduced or transmitted in any form or by any
means, electronic or mechanical, including photocopying, recording, or any information
storage and retrieval system, without permission in writing from the publisher. Details on
how to seek permission, further information about the Publisher’s permissions policies
and our arrangements with organizations such as the Copyright Clearance Center and the
Copyright Licensing Agency, can be found at our website: www.elsevier.com/permissions.
This book and the individual contributions contained in it are protected under copyright
by the Publisher (other than as may be noted herein).

Notices
Knowledge and best practice in this field are constantly changing. As new research and
experience broaden our understanding, changes in research methods, professional
practices, or medical treatment may become necessary.

Practitioners and researchers must always rely on their own experience and knowledge in
evaluating and using any information, methods, compounds, or experiments described
herein. In using such information or methods they should be mindful of their own safety
and the safety of others, including parties for whom they have a professional responsibility.
To the fullest extent of the law, neither the Publisher nor the authors, contributors, or
editors, assume any liability for any injury and/or damage to persons or property as a
matter of products liability, negligence or otherwise, or from any use or operation of any
methods, products, instructions, or ideas contained in the material herein.

ISBN: 978-0-12-818971-9

For information on all Elsevier publications visit our website at

https://www.elsevier.com/books-and-journals

Publisher: Candice G. Janco

Acquisitions Editor: Peter Llewellyn
Editorial Project Manager: Aleksandra Packowska
Production Project Manager: Sreejith Viswanathan
Cover Designer: Mark Rogers
Typeset by TNQ Technologies
Contents
Preface .................................................................................................. ix

CHAPTER 1 Overview on data treatment ..................................... 1

1 Introduction ........................................................................ 1
1.1 Mathematical technique ...................................................6
1.2 Computational technique..................................................7
1.3 Statistical data treatment ..................................................7
References.............................................................................11
CHAPTER 2 Case study in environmental pollution research ......13
1 Introduction .......................................................................13
1.1 Air pollution ................................................................ 14
1.2 Land pollution.............................................................. 21
1.3 Water pollution............................................................. 24
1.4 Noise pollution............................................................. 32
1.5 Radioactive pollution..................................................... 33
1.6 Electronic waste pollution .............................................. 35
References.............................................................................38
Further reading.......................................................................39
CHAPTER 3 Typical environmental challenges...........................41
1 Introduction .......................................................................41
1.1 Thermal comfort as a source of environmental concern ....... 41
1.2 Rainfall as a source of environmental concern ................... 44
1.3 Recent environmental crisis and the problem of climate
change ........................................................................ 47
References.............................................................................51
CHAPTER 4 Generating environmental data: Progress and
shortcoming...........................................................53
1 Method of generating environmental data: common
challenges, safety, and errors.................................................53
1.1 Data quality and errors .................................................. 55
1.2 Satellite measurement.................................................... 60
1.3 Modeling procedure ...................................................... 63
1.4 Experimental procedure ................................................. 69
2 Common errors in laboratory practice.....................................74
3 Maintaining laboratory apparatus ...........................................75
References.............................................................................76

v
vi Contents

CHAPTER 5 Root finding technique in environmental research ...79

1 Application of root finding technique to environmental
data ..................................................................................79
1.1 The root finding method................................................. 79
1.2 Modification of the root finding method to data
application................................................................... 82
1.3 Computational application of root finding method to
data application .......................................................... 103
Reference............................................................................ 117
CHAPTER 6 Numerical differential analysis in environmental
research .............................................................. 119
1 Introduction ..................................................................... 119
1.1 Euler method ............................................................. 121
1.2 Improved Euler method ............................................... 122
1.3 RungeeKutta method.................................................. 123
1.4 Predictor Corrector method........................................... 126
1.5 Midpoint method ........................................................ 128
1.6 Application of numerical methods of solving
differentiation in environmental research......................... 128
1.7 Computational processing of numerical methods
for solving differential equation..................................... 136
1.8 Computational application of derivatives to
environmental data...................................................... 142
1.9 Case 1: derivative of experimental data........................... 142
References........................................................................... 147
Further reading..................................................................... 148
CHAPTER 7 Numerical integration application to
environmental data .............................................. 149
1 Introduction ..................................................................... 149
1.1 Midpoint ................................................................... 149
1.2 Trapezoidal rule.......................................................... 151
1.3 Simpson’s rule............................................................ 154
1.4 Computational application of numerical integration .......... 158
References........................................................................... 168
CHAPTER 8 Numerical interpolation in environmental
research .............................................................. 169
1 Introduction ..................................................................... 169
2 Application of interpolation to environmental data.................. 170
3 Lagrange interpolation ....................................................... 172
 Contents vii

4 Newton interpolation ......................................................... 176

5 Spline interpolation ........................................................... 179
6 Computational application of interpolation ............................ 181
References........................................................................... 189
CHAPTER 9 Environmental/atmospheric numerical models
formulations: model review .................................. 191
1 Introduction ..................................................................... 191
1.1 Global forecast system ............................................... 191
1.2 NOGAPS-ALPHA model ........................................... 192
1.3 Global Environmental Multiscale Model (GEM)............. 195
1.4 European Center for Medium Range Weather Forecasts... 196
1.5 Unified Model (UKMO)............................................. 197
1.6 French global atmospheric forecast model (ARPEGE)..... 199
1.7 Weather Research and Forecasting (WRF)..................... 200
1.8 Japan Meteorological Agency Nonhydrostatic Model
(JMA-NHM) ............................................................ 203
1.9 The fifth generation mesoscale model........................... 205
1.10 Advanced Region Prediction System (ARPS)................. 206
1.11 High Resolution Limited Area Model (HIRLAM)........... 207
1.12 Global Environmental Multiscale limited area model ...... 208
1.13 ALADIN model........................................................ 210
1.14 Eta model ................................................................ 213
1.15 Microscale model (MIMO) ......................................... 215
1.16 Regional atmospheric modeling system (RAMS) ............ 216
References........................................................................... 217
Further reading..................................................................... 221

Index...................................................................................................223
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Preface

Environmental data may be described in terms of quantitative, qualitative, or

geographically referenced facts that represent the state of the environment and its
changes. Quantitative environmental data consist of data, statistics and indicators
of databases, spreadsheets, compendia, and yearbook type products. Qualitative
environment data are descriptions (e.g., textual, pictorial) of the environment or
its constituent parts that cannot be adequately represented by accurate quantitative
or geographically referenced descriptors. Geographically referenced environmental
data are described in digital maps, satellite imagery, and other sources linked to a
location or map feature. Summarily, it can be postulated that dataset in environ-
mental studies is like blood to the human body. All decisions in environmental
studies are based on observables that are measurable, reliable, realistic, and consis-
tent with theories. Environmental theories are formulated from observables. Hence,
a faulty observable can lead to a colossal failure in processes, prediction, model
formulation, and decision.
The inevitable outcomes of climate change have redefined observables such that
new theories and models are necessary due to data inconsistency, noise, and spikes.
Aside from just getting dataset and simulating, it is now expedient that the integrity
of a dataset be the first line of operation in data analytics. This feat can be achieved
through the guidance of proven theories. The knowledge of this theory, when to
apply it on a dataset, how to apply it, and ways to validate emerging results are
salient in any field of environmental sciences. Hence, the focus of this book is to
educate beginners and professionals on the above.
Environmental indicators are usually the environment statistics that are in need
of further processing and interpretation. Based on this, there is the need of the appli-
cation of numerical methods to validate, expatiate, predict, back-trace, and create
new possibilities. Validation technique through numerical methods enables the
researcher to ascertain the pattern trend of series of observables and tie them to
certain established theories. Expatiation technique through numerical methods
enables the researcher to take an informed numerical guess to replace missing
data, noise, and data anomalies. Missing data is common in atmospheric research.
Missing data makes the genuity of the data to be questionable especially when
the user is a beginner or novice. Assume if the satellite measurement of a parameter
shows missing values for 7 months in a yearly dataset. Ignoring the missing data for
the remaining 5 months would certainly be erroneous to analyze monthly or season-
ally. The same scenario applies to noise in data and data anomalies. This book seeks
to train beginners and professionals on the aforementioned expertise.

ix
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 CHAPTER

Overview on data
treatment
1
1. Introduction
Data is usually defined as raw or unprocessed facts or statistics that will need to be
processed or interpreted in order to get information. Technically, there are three
types of data based on their source and availability: primary, secondary, and mosaic.
Primary data is data that is collected through firsthand experiences, studies, or
research. Secondary data is data or information that has been collected from other
sources. Mosaic data refers to data and information that is collected by putting
together bits and pieces of information that are already publicly available. Environ-
mental data are large amounts of unprocessed observations and measurements about
the environment (or its components) and related processes. Data used for the produc-
tion of environment output, report, or statistics are compiled by many different
collection techniques and institutions whose data sources are hosted privately or
publicly at known sites. Understanding and knowing the pros and cons of each
source is key in environment reportage. Data sources are the initial locations where
the collected data originates from and runs public object for the establishment and
can be a flat file, database, scraped web data, social media, and database access
which profuse across the internet. Data source is considered to help users and appli-
cations to secure and move data to where it needs to be. The purpose of the data
source is to bundle connection information that is easier to comprehend. In environ-
mental science, data source can be classified into two: the primary and secondary
data. The primary data is original and accurate and is collected with the aim of get-
ting the solution to a problem at hand, and it includes surveys, observations, web-
sites, questionnaires, etc. It is reliable, objective, and authentic. The secondary
data are data that are readily available and are more accesible to the public than
the primary data (e.g., industry surveys, compilation).
The type of data that could be obtained from research could either be qualitative
or quantitative. Qualitative data research centers around getting information con-
cerning the attribute, characteristics, or qualities of sample. It does not involve
numbers. While quantitative data research are research studies whose data are quan-
tifiable with the use of numbers, where data are computed through discrete whole
number integers or continuous floating point values. There are a lot of examples
of numerical data; however, they are all categorized into two types: discrete and

Numerical Methods in Environmental Data Analysis. https://doi.org/10.1016/B978-0-12-818971-9.00001-6 1

Copyright © 2022 Elsevier Inc. All rights reserved.
2 CHAPTER 1 Overview on data treatment

continuous data. Discrete data are data that take numerical symbols as they are
countable list of items. They take values that can be grouped into categories or
list, where the list may either be finite or infinite. Discrete data takes number count-
ing from 1 to 10, or 1 to infinity, but it always occurs in a range. Continuous data is a
type of numerical data which represents measurements. These data are described as
values that take interval such as averages, largest or smallest number (among
ranges), and cumulative grade point.
There are different types of data source. Flat file is a database that stores data in a
plain text format and teaches how to upload, prepare, and update your csv files to
data-pines. This consists of a single table of data types table and cannot contain mul-
tiple tables of data types, and it has no folders or paths related to them and is used to
import data and store table information. Examples of flat file include plain text, bi-
nary file, delimited file, and flat file database. Another type of data source is data-
base. Database is one of the oldest data sources and the relational database is one
of the common databases that can easily be connected to the data-pines. Then
each database will then be represented as an individual data connection. They sup-
port the manipulation of data and electronic storage. The types of database are
network database, hierarchical database, and object-oriented database. A typical
example of environmental organizations that make use of the flat files is the
NASA-associated satellites extension such as MERRA and GIOVANNI. Fig. 1.1
shows the Global Precipitation Measurement (GPM) constellations that have
some of their dataset as flat file.
Web Services is a type of data source. It is a system of communication between
two electronic devices over a network and is also an assembly of the segment that the
software makes available over the internet. And it is formulated to communicate
with different programs rather than the users. In a web service the web technology
known as the “Http” this data source is used for transmitting machine-readable file
format (e.g., the XML). The types of web services include web template, web ser-
vice flow language, web service conversation language, web service metadata lan-
guage, and web service description language. Australian department of
agriculture, water, and the environment have several web services where a list of
environmental data can be downloaded.
The most popular form of data source is databases. Popular environment data-
bases include Proquest Natural Sciences Database, Engineering Village, Green-
FILE, Environmental Impact Statement (EIS) Database (EPA), Health &
Environmental Research Online, etc. There are several different types of databases,
and various companies sell databases with various plans and features. MS Access,
Oracle, DB2, Informix, SQL, MySQL, Amazon Simple DB, and a variety of other
databases are widely used today. In general, contingent databasesdthat is, databases
that document a company’s consistent transactions, such as CRM, HRM, and ERPd
are not considered to be suitable for business records. This is attributable to a num-
ber of reasons, including the fact that data is not enhanced for itemizing and inspect-
ing, and specifically querying these databases may block the layout and prevent the
databases from correctly tracking trades. Organizations can use an ETL tool to
 1. Introduction 3

FIGURE 1.1
Flat file user: Global Precipitation Measurement (GPM) constellations (Laviola et al.,
2020).

obtain information from their constrained servers, transform it into BI-ready format,
and weigh it into a data storage room and perhaps another data store. The one flaw in
this theory is that a data circulation focus is a perplexing and expensive plan, which
is why many organizations want to report explicitly against their stringent databases.
Online media information is a source of data. It is gathered from long range inter-
personal communication administrations like Facebook, microblogging stages like
twitter, media sharing destinations like YouTube and Instagram, sites, conversation
discussions, client audit locales, and new locales. This information can be gathered
from things had been posted, as, acknowledge or search about through your gadgets.
The method of generating primary data in disciplines related to environmental
science may be through survey, experiment, and observation. Survey is carried
out by questioning individuals based on different topics and reporting their re-
sponses, and are used to test the different concepts, reflect the attitude of different
people, reporting certain personalities of people, testing hypotheses of people’s na-
ture of relationships and personalities. Experiment is an organized study where the
analyzer gets to understand the effects, causes, and processes involved in a particular
process and involves manipulating one variable to determine if there are changes in
the other. The types of experimental design include completely random design,
4 CHAPTER 1 Overview on data treatment

randomized block design, Latin square design, and factorial design etc. Observation
is a method that engages vision as it main means of data collection, and is also study-
ing others’ behaviors without taking control of it. There are a few things to keep in
mind when carrying-out experiment in environmental science:
a. Measurement technique: This technique is relevant because it has an impact on
the success of your data. The configuration of the equipment as well as the use
of updated standards are essential parameters before taking measurement. Also,
the procedures for obtaining live samples are salient in experimental technique.
b. Multiple trials: This includes going through the investigation again and again.
The more preliminary work you do, the higher your average value would be and
the more accurate and reliable the results would look like.
The method of generating secondary dataset includes internet sources, external
sources, satellite measurement etc. Internal sources are dataset that are within the
organization and can be obtained within a short effort, a period of time than the
external sources and they include internal experts, data mining, sales-force report,
miscellaneous report, accounting sources etc. External sources are dataset that are
outside the organization and are quite difficult because they have many collections
and the sources are much more frequent, and they include syndicate service, govern-
mental publications, nongovernmental publications, etc.
Data treatment is a very essential part of any experimental work or analysis of a
secondary dataset. It is essential in all experiments, spanning from scientific to social
to business to medicine etc. Data treatment helps researchers identify errors, spot
trends, observe correlation and relationships, make inferences, and draw meaning
and conclusions from collected data. It involves all the actions and processes in
the investigation and collection of data and the additional processes performed on
data in order to arrive at useful information, so as to make deductions and inferences.
Every environmental researcher, regardless of their field, must have the basic
concept of data treatment for their research or their study to be reliable. Data treat-
ment is essential and equally important, as well as data organization, to draw appro-
priate conclusions in a given data set. Data treatment is a process to ensure its
reliability and uniqueness in experiments and data collection designs. This process
is vital to efficiently make use of a given data in the right way. It is essential to
correctly treat data to maintain the research’s authenticity, accuracy, and reliability.
A well-defined understanding is needed to perform suitable experiments with the
correct information obtained from any given data set. Data treatment can be descrip-
tive, that is, describing the relationship between variables in a population set so as to
distinguish between a noise, spike, and trend. It can also be inferential, that is, testing
a given hypothesis by making inferences from a collected data set or an establish law
or theory. To obtain the desired result, data must be processed using a variety of
methods. All experiments randomly produce errors or noise. Data noise can either
be systematic or random errors. It is advisable that errors and noise be taken into
consideration in the course of the experiment for the result of the experiment to
make sense.
 1. Introduction 5

Regardless of how cautious a researcher can be while measuring or extracting

samples in an environment, all experiments are vulnerable to inaccuracies caused
by three forms of errors: systematic, random, and spontaneous errors. These errors
are most times spotted during the treatment of data, and the correction can then be
reintegrated in the process. Spontaneous errors are widely reported in genetic code
(Griffiths et al., 2000). Systematic errors are errors that are caused by either the data
collection equipment or the method used to collect the data. Internal error can
emerge from measuring or characterizing instruments which most of the time
possess random errors that occur accidentally or unpredictably in the experimental
configuration. This type of error will continue to occur in all instances of the exper-
iment until the source of the error is addressed. Some examples of this kind of error
are an incorrectly calibrated measuring device, a worn out instrument, and a miscon-
ception on the observer’s end. Systematic errors are usually consistent in the amount
of error in the measured value. These experimental errors can lead to two different
kinds of conclusion errors: type 1 and type 2 errors. A type 1 error occurs when a
researcher rejects a true null hypothesis, resulting in a false positive. A type 2 error,
on the other hand, is a false negative caused by a researcher’s inability to reject a
false null hypothesis. In other words, the method of data treatment employed in
research depends on the field of research or kind of experiment being conducted,
as this would affect the kind of data being collected, and the desired form of the
data required to arrive at a conclusion. Random errors are errors that are caused
by irregular and unpredictable variations in the experiments. This variation could
be as a result of external environmental conditions surrounding the experiment; it
could also be caused by a fault in the measuring instrument. These types of errors
do not usually have the same errors in the same direction for all instances of the
experiment. Random errors occur unknowingly or unpredictably in the experimental
configuration. They arise unknowingly or unpredictably in the experimental setup.
Data treatment is one of the last operations in data analytics. There is preceding
operation i.e., data collection, data preparation, data processing, data cleaning, etc.,
that must be done before data treatment. Data collection is one of the initial stages of
every research endeavor that involves the collecting of data from all available plat-
forms. This could be through surveys and experiments in the laboratory or sites. It is
required that the data source be relevant, reliable, and authentic. Data preparation is
the process that often follows after the data collection stage. The data preparation
stage is often referred to as pre-processing stage. This is the stage at which data
is organized before it is processed into the required form. Data processing is the
stage at which data is translated into the readable, relatable, and required format.
It might involve placing data into rows and columns, and it might require the use
of a computer to process the input data. It may require complex programming, algo-
rithms, etc. The method of processing of data depends on the type of data to be pro-
cessed, processing tool/software, and size of dataset. For example, for a small ASCII
dataset and Microsoft excel are commonly used. For big ASCII data, structured pro-
gramming language is used to save time and reduce errors. Data cleaning is the pro-
cess where noise in data are removed. It is synonymous to data treatment but it is the
6 CHAPTER 1 Overview on data treatment

preliminary stage before data treatment. For example, when datasets are downloaded
from a satellite station in ASCII format, there could be missing data, which most of
the time appear as “9.9999,” “***,” and “9999” or blank. The removal of this anom-
alies is data cleaning not data treatment. Also, in the data cleaning stage, unneces-
sary data can be removed such as duplicates and errors. The data cleaning process
involves deduplication, matching records, identifying data inconsistencies, checking
the overall data quality, etc. The emerging dataset after data cleaning is expected to
be in the required, readable format. This readable format could be in the form of an
equation, image, video, graph, theory etc. The information obtained from this stage
is what will be used for data treatment.
There are three ways of data treatment in literature. They are:
(a) Mathematical technique (statistical data treatment)
(b) Computational technique (algorithm data analysis)
(c) Statistical technique

1.1 Mathematical technique

This is a technique that involves the use of mathematical theories, formulae, and
mathematical manipulation. Some of these mathematical processes include:
I. Regression analysis: This is an analysis used to evaluate the relationship be-
tween two or more set of numerical data. When using this technique, we look
for a correlation between the dependent numerical data and any number of
independent variables that might have an effect on these numerical data. The
aim of regression analysis is to estimate how one or more variables might
impact the dependent numerical data, in order to identify trends and patterns.
This was used specifically for prediction and forecasting future trends. It is also
important to note that regression analysis only helps to determine whether or
not there is a relationship between a set of numerical set of data, and it does not
say anything about the cause or effect.
II. Factor analysis: This is a technique used to reduce a large set of variables to a
smaller number of variables. It works on the idea of multiple separate,
observable variables correlate with each other because they are all associated
with an underlying set. This is useful not only because it reduces variable in a
particular set of numerical data into smaller understandable variables, but it
also helps to uncover hidden patterns.
III. Time series analysis: This is a statistical technique used to identify numerical
data using time interval. It records and separate data into groups based on the
data that have similar time interval or the time created.
Numerical analysis is mostly needed to solve engineering problems that result
into equations that cannot be solved analytically with simple formulas. Some appli-
cations are listed here:
a. Modern applications and computer software: Most sophisticated numerical
analysis software is embedded in popular software packages, e.g., spreadsheet
programs.
 1. Introduction 7

b. Business applications: Modern businesses these days make much use of opti-
mization methods in deciding what or how to allocate a resource most effi-
ciently, such as inventory control, scheduling, budgeting, and investment
strategies.

1.2 Computational technique

This is a technique that involves the use of AI systems such as the computer system.
This involves using programmed codes, encoded scripts formulas to arrange and pre-
sent numerical data in an organized manner meaningful to interpret and use. There
are a lot of programming software created to solve this problem. Some of the best
ones include these:
I. Analytica: This is a software created and developed by Lumina Decision Sys-
tems for receiving/retrieving, analyzing, and communicating numerical data. It
uses hierarchical influence diagrams for visual creation and view of models,
intelligent arrays for working on multidimensional data.
II. MATLAB: Matrix Laboratory is a proprietary multi-paradigm programming
language and numeric computing working environment developed by Math-
Works. MATLAB makes it possible for matrix manipulations, plotting of
functions and data, implementation of algorithms, creation of user interfaces,
and interfacing with programs written in other languages. MATLAB is made
for the source purpose of numerical data treatment.
III. FlexPro: This is a software designed for the analysis and presentation of sci-
entific and technical data. This software was created by the Weisang GmbH
team. It was designed to run Microsoft windows. FlexPro can analyze large
amount of data with high sampling rates. All data to be analyzed are stored in
an object database. FlexPro has a built-in programming language, FPScript,
which is optimized to carry out data analysis and support direct operations on
non-scalar objects such as vectors and matrices as well as composed data
structures like signal series.
IV. FreeMat: A free open-source numerical data treatment environment and pro-
gramming language, similar to MATLAB.
V. jLab: This is a numerical computational environment created with a Java
software and interface.

1.3 Statistical data treatment

There are various methods involved in the treatment of data, and one of the most
common methods is the statistical method of treatment of data. When you apply a
statistical approach to a data set in order to turn it from a list of meaningless numbers
into useful output, this is known as the statistical treatment of data. Statistical
method includes but not limited to; mean, median mode, range, standard deviation,
conditional probability, range, distribution range, sampling, correlation, regression,
8 CHAPTER 1 Overview on data treatment

and probability. There are some notable errors in data treatment, and using statistical
techniques to classify potential outliers and errors is an important aspect of data pro-
cessing. Statistical data treatment is one of the essential aspects of any experiment
conducted today. It can be seen using any known statistical method to draw meaning
from a set of given meaningless data sets. Statistical distribution can be classified
into two groups. To begin with, one of them is considered to have discrete random
variables, which means that each word includes a single numerical value. The sec-
ond form of statistical distribution, which includes continuous random variables, is
called a continuous random variable distribution (the data is known to take infinitely
many values). Statistical data treatment often entails defining the data collection, and
one of the most effective ways to do so is to use the measure of core tendencies such
as the mean, mode, and median.
The core tendencies described above make it simple for any researcher to
perform any research experiment and understand how the data set is concentrated.
Central tendencies such as the standard deviation, range, and uncertainty help the
researcher understand the data set’s distribution. Nevertheless, care should consis-
tently be taken to assume that all data sets are the same and evenly distributed.
Any of the above-mentioned central tendencies can be used to ensure that.
This method involves using some statistical methods to transform a given mean-
ingless data into meaningful data sets. It involves the use of some statistical
methods:
➢ MEAN: In statistics, this is a key idea. It describes the characteristics of a sta-
tistical distribution. In a set of numbers, it is the most common value.
To measure it, take into account the figures of the relative multitude of terms and
then divide by the number of terms. The mean of a collection of data can be deter-
mined in several ways. It can be determined using the arithmetic mean process,
which involves dividing the total number of data sets by the sum of the total number
of data sets. To find the mean, add all of the numbers in a set together, then divide the
total by the total number of numbers. A dataset’s mean can also be calculated by a
method known as the geometric mean, which is the nth root of the product of all
numbers in the data set. It includes the volatility and compounding effects of returns.
The arithmetic mean, also known as the mean or standard, is the sum of a set of
values divided by the number of values in the group.
Sum of all data points
Mean ¼
Number of data points

➢ MODE: The estimate of the word that occurs often in the form of dissemination
with a discrete arbitrary variable. The mode is the number that happens
frequently inside a bunch of numbers. It is feasible to have two modes
(bimodal), three modes (trimodal), or more modes inside bigger arrangements
of numbers. Bimodal appropriation refers to the appropriation that has two
modes. Trimodal appropriation is a three-mode appropriation. The most severe
 1. Introduction 9

estimate of capability is the form of dispersion with a constant irregular vari-

able. Similarly, discrete appropriations can have more than one mode. In this
case, it takes special expertise to identify errors or noise in a given dataset. The
advantages of the mode is its simplicity to identify and determine a value. Its
disadvantage of mode is the possibility that a set of values might have only one
mode, or no mode at all. Also, mode is not stable when the statistics has small
numbers.
➢ RANGE: The range of your data in statistics is the range from the lowest to the
highest value of the distribution. By subtracting the lowest from the highest
value, the spectrum is determined. A wide variance in a distribution implies
high variability, while a small range indicates low variability.
➢ MEDIAN: The middle value in distribution is referred to as the arithmetic
median, which is a positional average. It divides the sequence into two halves
by grouping the elements in ascending or descending order of magnitude before
finding the middle value and is denoted by the symbol X or M. It can also be
referred to as the middle position or the middle class, or median class. For
example, in a set of numbers 1, 2, 3, 4, 5, the median of the set of numbers
would be 3. In the case where two number are in the middle class (e.g., 1, 2, 3, 4,
5, 6) the median of the set of numbers is the average of 3 and 4 which is 3.5.
➢ STANDARD DEVIATION: The standard deviation is a calculation of a group of
values’ variance or dispersion. A low standard deviation means that the values
are similar to the set’s mean (also known as the predicted value), while a high
standard deviation indicates that the values are distributed out across a greater
spectrum. This can be calculated with the formula

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
P
ðxi  mÞ2
s¼
N
where
s ¼ standard deviation
N ¼ size of the population
xi ¼ each value from the population
m ¼ population mean
➢ SAMPLING: Data sampling is a predictive research methodology that involves
selecting, manipulating, and analyzing a representative subset of data points in
order to uncover correlations and trends in a broader data collection. There are
various methods used to sample data:
• Simple random sampling
• Systematic sampling
• Stratified sampling
• Cluster sampling
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Exploring the Variety of Random
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that they were at the corner of Willowtree Road, and that the
address written on the paper must be close by. So Uncle Luke
alighted with Madeline, paid their fare, and stood hesitating, while
the omnibus rolled away.
Willowtree Road consisted, from end to end, of detached and
semi-detached villas, only variegated at two of the corners by public-
houses. It was very quiet and suburban, and as all the trees in the
gardens were already green, and many of them in flower, it looked
quite rural and bright.
Paper in hand Uncle Luke trotted up and down for some time, in a
vain search for the house he sought. The road was quite deserted,
and there was no one whom he could consult. At last he came
against a telegraph boy, sauntering along and whistling in the
leisurely manner of those swift Mercuries of the period.
‘I’ve just come from there,’ said Mercury, after inspecting the
paper. ‘You see that house with the verander? Well, you don’t go up
the front steps, but walk round to the side, and you’ll see a bell
marked “Stoodio”; ring that, and ask for Mr. White.’
Thus directed, Uncle Luke approached the house, a small, semi-
detached villa, and passing round, as directed, to the side,
discovered with some little difficulty the bell in question. Without any
hesitation, he rang. Scarcely had he done so, when the door opened
as it were of its own accord, and he found himself in a dilapidated
garden, face to face with a small building which looked like a
diminutive Methodist chapel. Approaching the door of this edifice, he
was about to knock, when his eyes fell upon a paper pasted upon it.
On this paper was printed rather than written these words—
Mr. White out of town. Back this day week.
With Madeline’s aid Uncle Luke spelt out the inscription, and it
filled him with complete consternation. There being no date to the
announcement, ‘this day week’ was curiously indefinite, particularly
as the paper showed signs of having been there for a considerable
time already. While he stood gaping and scratching his head the
studio door suddenly opened, and a very small boy with a very old
face, clad in a very dirty page’s uniform, made his appearance.
‘Well, what is it’ cried this worthy, snappishly.
‘Who do you want?’
Uncle Luke took off his hat respectfully, and handed over the
paper. Strange to say, the boy would not deign to inspect it.
‘If it’s the milk bill, you’re to call again next week. If it’s a
summons, nobody ain’t at home. Which of the gents is it for?’
‘I’m a-looking for Master White,’ said Uncle Luke, timidly, ‘and if
you please——’
‘But he don’t please,’ answered the boy, with a fierce sense of
grievance. ‘He ain’t at home. Didn’t you see the paper on that there
door?’
At this juncture another head appeared in the background, and a
pair of human eyes seemed rapidly to inspect the intruders. Then a
voice said—
‘It’s all right, Judas. Let ’em come in.’
Thus instructed, the page threw open the door, and Uncle Luke
entered, with Madeline clinging to him. Their astonishment was
considerable when they found themselves in a large apartment,
lighted by glass windows from above, and full of all the
paraphernalia of an artist’s workshop—several easels, two or three
lay figures, paintings in various states of completion. In one corner
stood a stove, on the top of which was a loaf of brown bread and a
tin coffee pot, and close to the stove was a perfect hecatomb of
egg-shells. Indeed, what with general dust and debris of all kinds,
the entire ‘studio’ seemed sadly in need of cleaning out.
 Fronting them as they entered was the only tenant of the
apartment—a young man with a very light moustache, a watery blue
eye, and a large amount of unkempt flaxen hair. He grasped a
palette in one hand, a paint brush in the other, and in his mouth he
held a black meerschaum pipe.
‘Is it anything I can do for you?’ he said, with a rather vacant
smile. ‘I’m Mr. Cheveley.’
‘I want to see Master White,’ said Uncle Luke in a faltering voice.
‘I’ve come all the way from the country, all along o’ Madlin, here.
Haven’t I, Madlin? If so be he’s away, can’t some one fetch him, and
tell him Luke Peartree wants him, and that Uncle Mark’s dead, and
that poor Aunt Jane’s a widder, and that things has all gone contrary,
and all our hearts is broke?’
Tears rose in Uncle Luke’s eyes, and he stood choking, while
Madeline clung to him and began crying too. The young man looked
at them in astonishment for some minutes; then, struck by an idea,
he walked rapidly to an inner door and cried loudly—
‘Here, White.’
A sleepy voice answered from within—
‘What’s the matter?’
‘Some one to see you—come, get up!’
The answer seemed a combination of strong expressions,
combined with inarticulate groans. After listening for a moment,
Cheveley turned to Uncle Luke—
‘Here, I say!’ he said, with the vacant helpless manner peculiar to
him. ‘He’s writing in bed, and he won’t rise. You’d better go in and
explain your own business. The little girl can wait here.’
Not without some little fear and trembling, Uncle Luke released
Madeline’s hand, and moved with timid steps into the inner room. It
was a very small chamber, furnished as a bedroom; that is to say, it
contained an iron bedstead, a washstand, a table, and other
conveniences. A chest of drawers gaping open was covered with
articles of attire in most admired disorder, and other articles were
hung on the walls or scattered about the room.
Perched up on the bed, with an embroidered smoking-cap on his
head, was a gentleman in gold spectacles. He was writing rapidly
with a pencil in a large manuscript book, and he scarcely looked up
as Uncle Luke entered. But when Uncle Luke, whose heart was full
and overflowed at the sight of one whom he believed to be a friend
of the family, trotted over to the bedside and took his hand, crying
like a child, he dropped his notebook and seemed aghast. Then,
recognising his visitor, he questioned him, and soon knew the whole
sad story—of Uncle Mark’s accidental death, of the break-up of the
little home, of the despair of the family, and their conviction that
they could no longer do their duty by Madeline.
‘And Madlin’s here,’ cried Uncle Luke. ‘I brung her, but, Lord, she
don’t guess why I brung her; she thinks she’s a-going back. Oh, Mr.
White, be a father to her! She ain’t got ne’er another, now her Uncle
Mark’s dead.’ Mr. White wiped his spectacles, and seemed utterly
stupefied; at last he nodded, as if he had made up his mind.
‘Give me those trousers,’ he said, ‘I’ll get up.’
In another minute he had slipped into an old pair of tweed
trousers, a pair of very dirty fancy slippers, and an old dressing-
gown. Thus attired he even looked less engaging than when
composing in bed. His hands were greatly in need of soap, his
whiskers were ragged and ornamented with fragments of yolk of
egg, and his face, which was otherwise kindly and good-humoured,
looked parboiled. Seizing a brush, he went through the formality of
brushing the very minute bunches of hair which ornamented his bald
head, and then, after a momentary struggle with his whiskers, led
the way into the ‘studio.’ Here they found Madeline in high delight,
for Cheveley, seizing a piece of charcoal, had dashed off a rough
likeness of her on a canvas which stood vacant. The wild locks, the
great wistful eyes, the delicate mouth, were happily caught, and for
the moment the child forgot all her troubles.
‘Look, Uncle Luke,’ she cried, running to him and pointing out the
likeness. ‘It’s me.’
Uncle Luke, still pale and trembling with his great grief, grinned
from ear to ear, and gazed upon the artist in pathetic admiration.
Meantime White stood blinking benignly through his spectacles; at
last Madeline caught his look, and returned it with no little
astonishment.
‘This is Madlin,’ said Uncle Luke, gently.
Thus introduced, Madeline dropped her eyes timidly, and gave a
country curtsey, as she had been accustomed to do to the magnates
of the village.
 CHAPTER VIII.—UNCLE LUKE IS
BROKEN-HEARTED.

I
t appeared on explanation that the notice on the outside door of
the ‘studio’ was a common ruse of Mr. Marmaduke White
whenever he desired perfect solitude, and when the visits of
even friends and acquaintances, not to speak of ambassadors from
certain adamantine creditors, would be considered irksome.
Although White dwelt in a studio, he was not an artist—not, that is
to say, an artist by profession, though he could paint a little, and had
a very pretty feeling for colour. By profession he was a man of
letters; by special taste and habit, a writer for the theatre. Some of
his less ambitious plays had been acted with no little éclat, and
everybody had thriven through them except the author. Others had
failed, and these failures constituted his glory. They were really
productions of considerable literary merit. In literary circles White
was spoken of as a man of genius whose mission it was to revive
‘the poetical drama,’ but who had fallen on dark days, when the
Muses, having discarded classic drapery altogether, had taken to
fleshings and the can-can.
He was a gentle creature, with as soft a heart as ever throbbed in
human bosom, and as little power of managing his worldly affairs as
of creating a profitable taste for dramas in ‘five acts and in blank
verse.’ He lived in a studio, with one artist or another for a
companion, not because the place was necessary for his vocation,
but because he was naturally a Bohemian, and a studio was a
thoroughly Bohemian sort of abode. He was forty years of age,
unmarried, and unlikely to marry. The number of his follies could
only have been measured by the number of his good deeds, and
those were legion. To see him was to like him; to know him was to
love him well.
For years past he had paid a small stipend—not much, but a sharp
pinch sometimes to him—for the maintenance of Madeline. The way
in which he had contracted this responsibility was characteristic, and
may at once be explained. A friend of his who was a ‘genius’—that is
to say, an individual who promised prodigies, and on the strength of
his promises, which were never fulfilled, discarded all conventional
morality and lived the life of a shabby Don Juan—had become
entangled with a country girl. Dying penitent, as well as penniless,
he confided to White, who watched by his sick bed like a woman,
that he had betrayed the girl, and that she had given birth to a child,
then about one year old. White promised that he would seek both
mother and child, and help them if possible. So after putting his poor
friend into the ground, and moving heaven and earth to get a few
tender things about him inserted in the newspapers, White betook
himself to the lonely seaside village where the widow dwelt. He
found a comely but ignorant girl in a state of comparative
destitution, and, to make matters worse, in the last stage of
consumption, brought on by exposure and neglect, In the course of
the interviews which ensued, he learned such things of his dead
friend’s treacherous and selfish conduct as would have shaken his
faith in genius altogether had he been less simple-hearted. A little
later the girl died in his arms, giving him her last blessing and
consigning her little daughter to his care.
After considerable reflection, he decided that the best course he
could adopt with the little one was to find some good motherly soul,
in the mother’s sphere of life, who would rear her kindly. During an
artistic excursion to Grayfleet he discovered Mrs. Peartree, and, after
certain pecuniary preliminaries were arranged, committed the child
to her care. What had been originally only a temporary arrangement
presently became fixed and habitual. Years passed away. Madeline
remained with the Peartrees, who were childless. White, in a very
irregular manner, sent them small sums from time to time; but it had
never occurred to him to take any more serious responsibility in the
matter. He meant the girl to grow up happy in the sphere to which
her mother belonged. Though he had beheld her once or twice in
infancy, he had for years afterwards seen nothing of her, only
hearing of her existence through correspondence from time to time.
When, therefore, Uncle Luke turned up in St. John’s Wood, with
Madeline under his charge, and explained that sad events had
broken up the little home and left Madeline helpless on their hands,
White was staggered. It was clear that the Peartrees thought him
her natural guardian, and could not comprehend that he stood in no
closer relationship to her than they did themselves.
He looked at Madeline, and was astonished to see her so fair and
elf-like, with a touch in her eyes of his poor dead friend, the literary
Bohemian. Somehow or other he had always pictured her as a fat
little country cherub, with very hard cheeks, a pug nose, and ugly
feet. As she gazed at him with her great blue eyes, he felt troubled
more and more.
‘You don’t remember poor Fred Hazelmere?’ he said to Cheveley.
‘No, he was gone before your time. But you’ve read his “Ballads of
Bohemia”—by Jove, sir, some of them are worthy of the “Buch der
Lieder.”’ And he added in a whisper, ‘That’s his child.’
He had led Cheveley aside, and was conversing with him apart,
while Madeline and Uncle Luke sat waiting in the centre of the
studio. ‘Look at her face,’ he proceeded. ‘Never saw such a likeness
in my life—it quite turns me over. She looks a wild little thing, don’t
she? The man with her is a sort of natural. It was absurd to think of
sending her to me, for what on earth can I do with her? I’m not her
father, after all. Upon my soul, I’m in a dilemma. I must persuade
him to take her back.’
But when White took Uncle Luke aside and tried to explain
matters to him, the little man only began to cry. The home was
broken up, he said; Aunt Jane’s only means of subsistence was to go
out as a monthly nurse; and he himself was going to join a distant
relation on the coast of Kent.
‘It ain’t that we want to lose her,’ he asseverated; ‘but oh, Master
White, there be no home for Madlin now. Our hearts be broke, sir, to
part wi’ her; but we know you’re next door to her father, and a
gentleman born.
She’ll be a heap better off here than ever she was along of us.’
‘Here?’ gasped the dramatist.
‘She’s your’n, sir, more than our’n, bless her heart. We couldn’t
feed her no more, let alone clothe her, now Mark’s gone to glory; but
you’re a gentleman born, and can bring her up well-nigh like a lady.
I brung her, Master White,’ he continued, reverting to his first fear;
‘but I dustn’t let her know I’m a-going to leave her—I dustn’t,
indeed. She thinks she’s a-going back with me.’
‘But I can’t take her!’ exclaimed White. ‘This is no place for a child,
and even if it were she needs a woman’s care. I really can’t think of
it; the very idea’s absurd.’
Uncle Luke looked astonished. In his simple judgment, the power
of a ‘gentleman born,’ like Mr. White, was unlimited, and he could
not fathom the significance of his refusal.
‘She’s that good,’ he explained gently, ‘that she’d be no manner o’
trouble to any, ’cept when she’s in her tantrums, and they’re gone as
soon as come. And she’s clever, Master White. I’ve heerd
schoolmaster say that she can spell like a good ’un, and her writin’s
as clear as print. I see her write out the Lord’s Prayer on a piece of
paper, and she guv it to her Uncle Mark, and if he’d ha’ lived, he was
a-going to get it framed like a pictur’ and hung up on the cabin of
the barge.’
This special pleading had little or no effect on White. He was
puzzling his brain what to do. Once or twice he thought of
repudiating the responsibility altogether, but he was far too good-
natured for that. Then he suggested that Luke should take the child
back and leave him to think it over, but he soon discovered that such
a delay was impracticable.
‘Mother said,’ explained Uncle Luke, firmly (his sister-in-law, it will
be remembered, had always been addressed as ‘mother’ by her
husband, and by all the house)—‘mother said I was to leave her
along o’ you, cause you was her best friend; and mother said you’d
never grudge her the wittles what she eat, for you were a gentleman
born. Them were her own words. You’d never grudge her the wittles
what she eat, for you was a gentleman born.’
‘How old is she?’ asked White, desperately, not that he had any
special reason for asking, but because, in his perplexity, he hardly
knew what to say.
Uncle Luke cocked his eye, calculating, and after due deliberation
replied—
‘Mother says it be just eight year come Whit-Monday since you
brung her to us. She remembers the year well, mother does, ’cause
’twas the year when her cousin Jim he was drowned off Woolwich
Pier, after he had deserted and was running away for his precious
life; and they held a ’quest upon him, and said he was drownded
accidental, and had hisself to blame.’
‘Between eight and nine years old,’ muttered White, pursuing his
own feeble reflections. ‘Is there no place where she could be put?
No person who, for a small consideration, would take her in?’
Uncle Luke shook his head dolefully. He had never questioned for
a moment but that White would give the child a welcome, and he
was quite incapable of conceiving the manifold objections there
might be to her immediate adoption.
Things were at this juncture when Madame de Bemy, who
occupied the adjoining house, and from whom White rented the
studio, came in smiling. She was a stout little old lady, with a very
profound respect for her tenant, who had been useful to her in many
ways, as indeed he was almost invariably to everybody with whom
he came in close contact. To his surprise she cut the Gordian knot by
offering to take care of the child on White’s behalf.
All this time Madeline had been listening with growing suspicion.
At last the whole truth dawned upon her, and she burst into
lamentation. Clinging to Uncle Luke, she cried that she would never
leave him, and that she would return to Grayfleet in his company.
It was an exciting scene, over which we have no intention to
linger.
Uncle Luke did not depart that night. They made him up a bed in
the corner of the studio, where he lay awake till morning, weeping
and wondering, but still firm in his desire to see Madeline made into
a little lady. The child herself was taken care of by Madame de
Berny. But she would not depart from the studio until Uncle Luke
had avowed positively that he would be there, waiting for her, in the
morning. His simple promise satisfied her, for never in all her life had
she known him to break his word.
 CHAPTER IX.—MADELINE FINDS
NEW FRIENDS.

T
he next day Uncle Luke went away.
Words would fail us to describe the parting. The little man
wept like a child, and Madeline threw herself, again and again,
into his arms, in a perfect frenzy of passion. It was terrible to see so
fierce a storm shaking the fragile form of so young a child. Madame
de Berny led her, sobbing, into the house, and tried in vain to give
her consolation; but for hours upon hours she wept wildly, and her
little heart seemed broken.
Poor Marmaduke White was utterly at a loss how to act; but he
had resolved, come what might, to accept his burthen and bear it as
well as he could. Every look, every gesture of the child, especially
during her fierce access of sorrow, reminded him more and more of
his dead friend. Her weird and elf-like beauty, moreover, appealed to
his strong artistic sense. Yes, he would do what he could for her, and
trust to that Providence which feeds the literary raven to find him
ways and means.
During his perplexity he found an excellent adviser in Madame de
Berny. The good woman, who had a large heart for children, entered
cordially into his wishes, and at the end of a long consultation
readily undertook the charge of Madeline for the time being. She
had plenty of leisure on her hands, the Chevalier de Berny, her
husband, a professor of music, being from home, teaching, all day,
while her only daughter, an actress at the Pall Mall Theatre, was
engaged every evening, and nearly every day, in the pursuit of the
business and the pleasures of her profession.
 So it was speedily settled, and Madeline was soon installed, as an
informal boarder, in the De Berny household, having a little room
upstairs next to the gorgeous chamber occupied by Mademoiselle
Mathilde.
The grief of childhood heals quickly, and with childhood’s
inquisitiveness Madeline was soon busy observing the manners and
customs of her new friends. Though her heart was still wild and
weary, and though every night she sobbed as she thought of her
happy home at Grayfleet, hers was too quick and keen a nature to
be quite deadened by its sorrow.
And Madame de Berny was very kind; even Aunt Jane could not
have been kinder. As to the Chevalier, who came in late at night and
departed very early in the morning, she found him a fat, fretful,
overworked, but naturally good-hearted little Frenchman, who spent
the whole of his one leisure day, Sunday, in smoking a big pipe and
reading the French journals. But the queen of the dwelling was
Mathilde, a tall, thin blonde, with golden hair, very fine eyes, and a
very hard mouth. She dressed very loudly and used a great deal of
paint and powder; her whole style, indeed, was ‘fast,’ and, though
she was a Frenchman’s daughter, her conversation and all her ideas
were vulgarly suggestive of Cockaigne.
Her character, however, was unimpeachable; she was far too
calculating and worldly wise to commit herself in any way. Her
parents adored her. She had the best room in the house, a little
study also where she conned her parts, and these were as the
sanctuary of a saint. The Chevalier was firmly convinced that she
was only prevented by the malice and wickedness of the world from
becoming recognised as a great actress.
‘My daughter is too good,’ he would say to his friends; ‘it is her
virtue which keeps her back. If she vere like de rest of de vomen on
your stage, it would be different—ah ciel, yes I De managers are in a
conspiracy to give her bad parts and to break her leetel heart.’
 And Mathilde herself was of the same opinion. Her face was quite
worn and haggard with brooding over her professional wrongs, her
heart torn daily by the success of her rivals and the real or fancied
neglect of the public. Once or twice a week she had violent fits of
hysteria, during which she would think and talk of suicide.
Recovering from these, she would eat a hearty dinner and drink
large quantities of bottled stout—to which she was very partial,
chiefly because it was said to be fattening, and her enemies in the
stalls considered her too lean.
In the eyes of Madeline, who had hitherto only known the coarse
beauties of Grayfleet, Mathilde was a vision of loveliness. The child
loved colour and splendour and beauty, and Mathilde seemed to
represent all these. The actress’s bedroom, too, was like a palace of
enchantment, with its delicate rose-coloured curtains, its white
French bed and bedding, its bright carpet, and its delicious
perfumes.
Mathilde was not particularly fond of children, but homage from
any one pleased her, and thus it happened that Madeline became a
constant visitor in the sanctuary. When, one day, Mathilde opened
her wardrobe and showed all her magnificent costumes, both those
she used in private life and those she reserved for the theatre, the
bliss of the sight was almost too much to bear. It was like a glimpse
of heaven itself!
So the weeks passed away, and the new strange life was growing
gradually familiar. The thought of the little Grayfleet home was still
bright in the child’s mind, and every night she said a prayer that
Uncle Luke had taught her, and every night she cried when she went
over the beloved names, but her spirit was kindled into a new kind
of feverish activity, such as she had never been conscious of before.
In the course of her daily visits to the studio, where even the
misanthropic Judas, as he had been profanely christened on account
of his forbidding aspect, now gave her a welcome, she saw many
things which awakened her wonder. Her previous ideas of Art had
been chiefly connected with house-decoration and sign-painting, and
she marvelled much at the creations on canvas of young Mr.
Cheveley. For White she soon contracted a passionate affection,
which deepened into idolatry when the good-natured Bohemian
began, in his idle moments, to teach her to draw.
The quickness with which she learned the rudiments of this
accomplishment reminded White that her general education was
being neglected altogether.
‘My dear,’ he said to her one afternoon, 41 think I shall have to
send you to school.’
She was standing at his side, looking over his shoulder, as he
‘touched up’ for her a picture of a house which reeled to one side
like the leaning tower at Pisa, a tree or two like inverted mops, and
a very shabby-looking bridge.
She looked at him right in the eyes, which was her custom.
‘I hate school,’ she said emphatically.
‘So did I at your age, and the child who doesn’t always comes to
be hung. But I really think you’d pay for a little schooling. You write
a shocking hand, to begin with.’
‘Uncle Luke said it was beautiful writing, and as clear as print.’
‘Humph! well, you see, he looked at it from a different point of
view. I don’t question its legibility, which after all is the first thing to
be aimed at, but it wants style. Then, your grammar is more shady
than befits the protégée of a master-stylist, like myself.’
‘What’s grammar?’ asked Madeline, swinging her right foot
irritably. ‘Nouns, verbs, “I am,” “thou art,” and all that? I hate ’em
all.’
White laid down the drawing on which he had been busy, and took
her by the two hands.
 ‘You hate a good many things,’ he said mildly. ‘Pray, what do you
particularly like?’
‘I like drawing. I like to hear Mamzelle singing the pretty songs,
and trying on her new dresses. I like dancing, too, and music, and
all that. And I like to be here with you. I like you better than Mr.
Cheveley. If I was big enough I’d marry you, and then you could
take me to the theayter, where Mamzelle goes.’
‘Pronounce it theatre,’ said White, while his eyes opened in
amused wonder. ‘So you are beginning to think of marrying already,
are you? Precocious child! And you’d marry me, would you? Why,
I’m old enough to be your father, and by the time you are a young
woman I shall be quite on the shelf.’
Madeline surveyed him for some moments critically; then she
threw her arms round his neck and kissed him impulsively.
‘When I marry you, Mr. White,’ she said, ‘I’ll buy you a nice wig,
and then, you see, no one will know!’
‘A wig—the gods forbid!’
‘A beautiful black, like the Chevalier wears. I know it’s a wig,
because he takes it off and puts on a nightcap when he goes to bed.’
White threw back his head and laughed heartily; then forcing a
serious look into his face, he said—
‘Don’t let us wander from the subject; I began by saying that you
must go to school.’
Madeline’s face darkened, and her lips pouted.
‘I shan’t,’ she said.
‘Come, come, Madeline! Don’t you care to learn?’
‘No.’
 ‘Nevertheless, learning is a physic which you will be compelled to
take. You mustn’t grow up a little ignoramus. English grammar,
geography, and—yes, by Jove—you shall learn French and music.’
‘French!’ she cried, with a sudden sparkle in her eyes. ‘Like
Mamzelle talks sometimes to her pa?’
‘Exactly.’
‘And music! I love music! And then I shall understand every word
they say, and play like Mamzelle on the piano. Oh, Mr. White, do let
me go to school and learn French and music!’
All. opposition being thus speedily withdrawn, White determined
that Madeline should go to school forthwith. In his customary
fashion, therefore, he dismissed the subject from his mind; and it is
a question how soon he would have practically carried out the
scheme if Madeline herself had not worried him every day with the
question, ‘Oh, Mr. White, when am I to go to school and learn
French and music?’ But after a consultation with the Chevalier, a
school was found in the neighbourhood—which he himself attended
two or three times a week—and after a slight discussion over terms,
which were specially reduced in her case, Madeline was sent there
as a day scholar.
Once or twice since her translation to London, Madeline had heard
from her foster-mother, who was then going from house to house as
a monthly nurse. Mrs. Peartree could not write herself, but she sent
by deputy many fond and loving messages, which Madeline
answered with letters a thousand times more passionate. Since the
day of their parting, however, she had heard nothing from Uncle
Luke.
But some few weeks after she went to school there arrived a letter
for her bearing the post-mark of a small town in Essex. Opening it
eagerly, she read as follows:—
 Mi dere Madlin,—This comes from uncle Luke, hopping you are
quite wel and a good gel which it leaves me at present. I be ni art-
broke far away from you and mother working on the river down
alonger mi cussin Joss don’t kry cos I brung you to London but be a
good gel and give my umble respecs to Mister wite mi dere Madlin
mi dere Madlin there be no bargis in thes parts and neer a brethren
but aples be pourful big and I wish you see the aple-tree in cussin
Joss his garding with luv & kisses & hopping you are a good gel &
my humble respecks to mister wito good bi at present I am ever
fecksonit uncle luke peartree.
P.S. Be a good gel & don’t kri cos I brung you.
Many and many a burning kiss did Madeline press on this simple
epistle. She wetted it with her most tender tears, and placed it
beneath her pillow at night, and carried it about all day in her
bosom, to be kissed and kissed yet again. With a certain intuitive
shame, she did not show it to any member of the De Berny family,
whose fault was a snobbishness characteristic of shabby gentility,
but she fearlessly confided in Mr. White and let him read it through.
He was touched by its simple affection, penetrating through the rude
orthography to the staunch and loving soul of the writer; and he
encouraged the girl to talk to him of Uncle Luke and all her lowly
friends.
‘Those who did not know him,’ he thought, as he listened to her
eager words and watched her flushed face, ‘called poor Fred callous.
It’s a lie! He had a noble heart, and so, thank God, has his little
child!’
 CHAPTER X.—A TELEGRAPHIC
THUNDERBOLT.

B
ut only a few days later, as White sat alone in the studio
working at the scenario of a new play, the door was thrown
open and in rushed Madeline. Her hair was dishevelled, her
dress disordered, her whole face distorted with passion. Before he
had time to speak she threw herself on a sofa and burst into an
agony of tears.
‘Madeline!’ he cried, bending over her, ‘what is the matter? Why
are you not at school?’
For a time there was no answer, but at last, between the sobs, the
girl spoke—
‘Oh! take me home; let me go back to Grayfleet!’
White took her hand softly, and spoke to her soothingly, but his
gentleness only made her worse. At last he yielded to his irritation
and insisted on an explanation.
Drying her eyes she sat up and looked at him, and he was startled
by the white determination in her delicate face.
‘Why are you not at school?’ he repeated.
‘Because I’ve left, and I’ll never go back to school again.’
‘Madeline!’
‘It’s true, and I want to go home, I won’t stay here, and I won’t
go back to school.’
‘But what has happened?7
 Madeline gave a wild hysterical laugh, and her face assumed an
expression of exultation.
‘I struck her in the face, Mr. White, and I pulled down her hair, and
when she saw I was angry she was frightened and screamed. If I
had been stronger, I would have killed her—I would! I would!’
Completely perplexed by this enigmatical tirade, White quietly took
his hat and walked off to the young ladies’ seminary, which was only
a few streets away. Arrived there, he found everything in commotion
and the lady superintendent highly indignant.
It appeared, on explanation, that Madeline, for some reason
unexplained, had, during the midday play hour, made a savage
attack upon a young lady of sixteen, a parlour boarder excellently
connected; had sprung upon her with fury, scratched her face, and
had clung to her until torn away by force. The superintendent’s mind
was made up: Madeline must not return to the school.
‘She is a very violent child. I have again and again had to rebuke
her for fits of passion. I have now discovered, moreover, that her
connections are not what I should wish in members of my seminary.
Miss de Castro, whom she assaulted, is a sweet girl, incapable of
provocation. Her papa is in the India Office. She is niece of Sir
Michael de Castro, late Governor of Chickerabad, and I cannot have
her assaulted by a common child.’
White stared silently at the lady, and without a word strode back
to the studio. There, with a severity unusual to him, he demanded a
full explanation. He thus learned that the fons et origo of all the
mischief was Uncle Luke’s letter. By some accident it had fallen from
Madeline’s bosom and been picked up by Miss de Castro. That ‘sweet
girl’ had read it through to a group of the elder pupils, doing full
justice to the orthography, and mimicking, as far as she could
imagine them, the living manners of the writer. In the midst of her
amusement, Madeline had appeared and demanded her property,
which Miss de Castro immediately thrust behind her back, while she
indulged in a series of witticisms at the expense of Madeline and all
her relations, especially the country correspondent. This was
enough. Almost before she herself knew it Madeline was at her
throat, and in a white heat of passion. The sweet girl screamed.
Madeline was torn away and thrust violently out of the school-yard
gate, but not before she had recovered her uncle’s letter and thrust
it into her bosom. Then she had flown home.
White was greatly perplexed how to act. In his secret heart he
sided with the child, and cursed the cruelty of ignorance and caste;
but he nevertheless perceived that fits of passion and violence were
not to be encouraged. So he frowned terribly, and read Madeline a
long and stern lecture on the wickedness of giving up to wrath.
She heard him out with great attention, and with her great eyes
fixed pathetically on his. At the conclusion of the harangue, she took
out Uncle Luke’s letter and quietly kissed it—then smiled faintly
through her tears at the thought of her wrongs. It was clear that she
was quite impenitent.
Madeline did not go back to school. For some months she
remained at home with the De Bernys; White, in his indolent way,
postponing the question of where she was to go next.
He was a good deal occupied at this time with the adaptation of a
new play which was being acted with great success at the Porte St.
Martin, and, as it was necessary to see the play represented by the
French actors, he spent some weeks in Paris. He discovered that by
carefully lopping the leading idea, making the chief female virtuous
instead of vicious, altering the scenes, and turning the moral upside
down, he could make the great drama pure enough for the sight of
the British playgoer. His English manager approved, sent him a small
cheque on account, and begged him ‘to do the trick’ as quickly as
possible.
At this period, therefore, Madeline was thrown more and more
into the society of Mademoiselle Mathilde. That vision of loveliness
found the child useful, sent her on endless errands, made of her a
sort of companion in miniature, and extempore lady’s maid.
Madeline was only too delighted to serve and worship, and great
was her joy when any of the cast-off splendour fell to her share. One
evening Madame de Berny took her to the theatre, on the occasion
of her daughter’s ‘benefit.’ There was a serio-comedy in which
Mathilde played the leading part, and a burlesque to follow, in which
(for that occasion only, for she generally despised burlesque) she
enacted a fairy prince. Madeline was entranced; the spell of the
footlights came upon her once and for ever.
That night, after they had returned home, and the Vision had
supped well on oysters and bottled stout, Madeline proffered a
request which had lately become a very common one with her,
‘Oh, Mamzelle, let me brush your hair!’
Mathilde took a sleepy sensuous pleasure in that part of her
toilette, and would sit by the hour together under the soothing
manipulation of the brush. So she let down her golden locks, and
placed herself, with her eyes half closed, before the mirror, while
Madeline began her task, prattling between whiles of the theatre, of
all the wonders she had seen, and of the longing that would possess
her until she saw them again.
‘I used to feel like you once,’ yawned Mathilde, ‘when I was a dear
little thing, with my hair growing down to my waist, and little satin
shoes on my feet, and Pa used to take me to the pantomimes. Ah,
dear, that’s over and done. I hate the theatre.’
‘You hate it, Mamzelle?’
‘Yes, and sometimes I hate Pa for ever letting me go nigh to it. I
suppose it all comes of Ma marrying a Frenchman; for Pa used to
teach me to say those long speeches in rhyme out of the French
plays, and then I got a taste for recitation. But I hate French now,
and I hate the theatre. It’s nothing but worry and vexation. There
was only five pounds ten in the stalls to-night besides the tickets Pa
and Ma sold, and the dress circle was not half full. Did you notice a
dark fat man in a private box, who threw a bouquet to Miss
Harlington?’
‘Do you mean a gentleman with a hook nose, Mamzelle, and his
fingers all over big rings?’
‘Yes. Well, that was Isaacs, proprietor of the “Evening Scrutator.” A
nasty beast, always smelling of cigars and rum-and-water. He hates
me because I keep myself respectable, and he never suffers any one
of his critics to say a good word about me.’
‘Who are they, Mamzelle?’
‘The critics? Tomfools who write in the papers, and don’t know
good acting from bad, and if they did daren’t say so. Why, they
praise Miss Harlington—who played “Princess Pretty pet” in the
burlesque!’
‘Oh, yes,’ cried Madeline, in rapture. ‘Her in the pink dress with the
spangles and the flowers in her hair. Oh, wasn’t she lovely,
Mamzelle?’
Mathilde tossed her head under the brush, and flushed With
virtuous contempt.
‘A bandy-legged thing with a voice like a goat. Did you hear the
creature sing? I wonder they don’t hiss her off the stage. But the
men run after her, and she’s kept by an earl; and there she is every
day in her victoria, driving in the Row among real ladies, while I
must go down to rehearsal in the bus. It’s disgusting—that’s what it
is. Do take care. Madeline—you’re brushing it all the wrong way.’
She added as an afterthought, less in real consideration for her
hearer than as a parade of her own wrongs—
‘Never you be an actress, child. Sweep a crossing first, or serve
behind a counter, or do anything dreadful. The stage isn’t fit for any
decent person, and so I’ve told Pa and Ma a thousand times.’
 From this and from many other similar conversations, and from
several subsequent visits to the theatre, both before and behind the
scenes, Madeline began to acquire a precocious insight into some of
the mysteries of life in London. She was clever and quick, and soon
understood as much as was comprehensible to so pure a child.
Mathilde de Berny, like many of her class, talked freely about things
which might well have been nameless, and never seemed to reflect
that the listener was so young. Fortunately, Madeline’s perfect
innocence and simplicity, combined with her real strength of
character, kept her pure from taint; but by slow degrees the glory
was beginning to depart from the great world of which she knew so
little.
Not at all too soon White saw that Madeline was in danger of
degeneration. He was a shrewd fellow, and understood that Mathilde
de Berny, though a perfectly virtuous young woman, was not really
the best companion she could have found. It irritated him too, at
last, to see the child sinking into a mere appendage of the actress
and general drudge of the house.
‘I must get her away,’ he said to himself, ‘before they spoil her
altogether. They neglect her and impose upon her, and teach her
things she ought not to know. I don’t want Fred’s child to grow into
a little slattern, with the education, and perhaps the moral instinct,
of a ballet-girl. They make a small parasite of her, and she goes
errands; they’ve even got in the habit of sending her for the beer. I’ll
put a stop to it at once.’
The only way of putting a stop to it was to send Madeline to a
boarding-school; and this he ultimately determined to do. He had
begun to feel quite a paternal interest in her, and he was more and
more struck by her physical beauty and strong natural affection.
After seeking about for some time, and studying the advertising
columns of the daily newspapers, he discovered a quiet school at
Merton, in Surrey, under the superintendence of a very superior
French lady. Hither it was arranged that Madeline should go.
 So, after a fond parting with White, Madeline repaired to the
seminary at Merton.
For a long time after her departure White was melancholy.
He missed her bright face and her loving ways; and so, in a less
degree, did his companion of the studio. But White was a busy man,
part of a busy world, and he had no time to be heartbroken about a
little girl. Every month or so he received a formal account of her
doings, signed by the superintendent, and still oftener a very
effusive and loving letter from Madeline herself. She appeared to
have become resigned very rapidly to the new conditions of her life;
to be sanguine and full of promise; and the official notes of her
educational progress were flattering in the extreme.

At this point, our business with Madeline’s childhood ceases. We

take the dramatist’s licence, and at one leap pass over a period of
several years.
The school was in connection with a similar one in Normandy, and
the pupils had the advantage of being transferred, at a certain stage
of their progress, and at little additional expense, to the French
establishment. The superintendent was a sensible woman, and so
White told her the whole story.
It was presently decided that it would be for Madeline’s advantage
to go to France for a year, without seeing anything of White or any
of her new friends. She was still only a very rough diamond, and
needed very considerable polishing to make her approach perfection.
A long period spent in pleasant discipline, and with only the most
refined surroundings, was absolutely essential to her moral
development. So at least thought the lady superintendent; and
White agreed.
On receiving the information that she was to be again
transplanted, Madeline was in high grief and dudgeon, for she had
been thoroughly happy with the De Bernys, and desired no better
than to become again a kind of Cinderella to the fair Mathilde.
During her residence at Merton Marmaduke White has been fairly
well satisfied with his ward. Beyond complaints of certain erratic
habits, and of her general disposition to act from passionate
impulse, he had heard little to her detriment, much to her credit.
He had seen her from time to time, and she had spent many of
her holidays at Willowtree Road.
From the tone of her letters, and from her words when they met,
he gathered that she was happy. She had gained the wish of her
heart; had learnt ‘French and music,’ as well as the other elegances
which constitute a good education.
So Madeline was sent to Normandy, with a contingent of young
girls from the school at Merton.
One day, when nearly eighteen months had elapsed since their
last meeting, White received a photograph from France. It
represented a fair maiden, with great wistful eyes, and a face of
singular beauty.
At first he scarcely knew it; then he turned it over, and read in a
bold handwriting:—
Madeline Hasleere, taken at Rouen on her 17th birthday.
‘Little Madeline!’ he exclaimed. ‘Why, she looks quite a woman!’
About a week after this event, Judas (now grown into a disjointed
being of seventeen or eighteen) entered with a telegram. White
opened it, and saw with astonishment that it was from Madame
Brock, the lady superintendent of the school at Merton.
Then he read as follows:—
Please come down at once. I have had terrible news from
Millefleurs.
Your ward, Madeline Haslemere, has run away. I fear it is an
elopement.
 CHAPTER XI.—THE HAWK AND THE
DOVE.

T
he scene of our story changes for a time from smoky London
to a lonely road close to the sea-coast of Normandy. It is the
sunset of a rainy day, a fierce red light beats down on the
yellow colza fields, sprinkled with great bells of crimson poppy; on
the deep, wind-swept patches of yellow wheat; on the little villages
embowered in foliage, each with its old-fashioned auberge and its
glittering spire.
An open post-chaise, drawn by a pair of heavy horses, is flying
seaward, towards the marine town of Fécamp. Side by side within it
sit two figures, a very young lady, wrapped in a fur-lined silk cloak,
and a tall, haggard-looking man of thirty, with very long hair and a
jet-black moustache.
Every now and again the man leans forward and urges on the
driver, then, after a quick glance on the road, which winds far away
behind them, he sinks back upon his seat.
They halt and change horses in a quaint little village, where old
women and maidens ply their antique spinning-wheels at the cottage
doors, and blue-bloused loungers puff their sous cigars on wooden
forms before the auberge. They do not alight, but the gentleman
brings the lady a tiny glass of the liqueur called ‘Bénédictin,’ and
some wine biscuits. She sips the liqueur and breaks a biscuit, while
the loungers in blue blouses look on in admiration.
The young lady is very pale, and looks so young that the loungers
whisper wonderingly at each other. Now and then her lip quivers,
and her eyes fill with tears. The gentleman with her watches her
anxiously, trying to anticipate every look and wish, but she scarcely
looks at him—her thoughts are far away.
‘How far to Fécamp?’ the gentleman asks of the ostler, as he slips
the pour-boire into his hand; and when he finds that it is still many
kilometres away, and that it is impossible to reach it in less than
three or four hours, he mutters an imprecation.
There is a quick, cat-like look in his eyes, as he converses with the
world at large; but when he turns to his companion the look is
exchanged for one of touching humility and sweetness.
They are ready to start again, the driver is in his place, when the
young lady springs up and cries in French, ‘Arrêtez!’ The gentleman,
who is again seated by her side, looks at her in astonishment,
‘Madeline! mon ange!’
She answers him in English.
‘It is not too late—let us turn and go back. I am sorry now I came
away. Monsieur Belleisle, I insist on turning back.’
‘Mais non!’
‘Madame Collemache will forgive me—I will go upon my knees and
ask her—Madame is a good woman. Oh, why did you ask me to do
anything so foolish? Look how these people are staring! Turn back at
once!’
But, at a sign from the gentleman, the driver has started off, and
they are soon leaving the village at full gallop. To comfort her,
Monsieur slips his hand round her waist. He is not prepared for the
result, which came in the shape of a sharp slap in the face from the
little gloved hand.
‘How dare you? I will not be pulled about, and I will go back to
Madame. If you are a gentleman you will take me back at once.’
 Monsieur rubs his cheek and tries to smile, but there is an angry
light in his eyes nevertheless.
‘You are cruel, and I—ah, how I love you! Have you not promised
to be my little wife? Mine own Madeline!’
He is about to embrace her again, but the look in her face deters
him.
‘I was angry with Madame because I thought her cruel and unjust.
She made me mad, and so I listened to you. Drive me back,
Monsieur, and I will like you very much. I will take all the blame
upon myself—only drive me back.’
‘Do not speak so,’ is the reply. ‘We love each other—we will be
happy—ah, so happy—-with one another. Madeline! my bride!’
‘I have changed my mind. I will not marry you, Monsieur Belleisle!’
‘Ah ciel, you do not mean what you say!’
‘I do mean it. Why should I marry you? I do not like you. I shall
hate you soon.’
‘It is too late to say that.’
‘But it is true.’
‘Ah, I will not beliefe it! You are triste—the journey make you triste
and fatiguée—to-morrow you will smile again upon your own
Auguste.’
‘Pray don’t talk nonsense,’ answered the young lady. ‘I liked you
very well when you gave me my lessons, and last night in my anger,
in my wickedness, I thought I would come with you, because I
wished to be revenged on Madame and Mademoiselle Blanche. But
now I have repented, Monsieur. I was a little fool, and I will beg
their pardon. They have been very kind to me. I was ungrateful. I
will return.’
 All this in an impetuous stream, half soliloquy, half entreaty. In her
passion and excitement the girl looks very lovely, and the Frenchman
gazes at her in growing admiration. Then a thought seems to strike
him, and he looks at her slyly and smiles.
‘Why are you laughing, Monsieur?’ she cries.
‘I was thinking, mignonne, how ridiculous you would look if you
returned. Ah, Dieu, how they would laugh!’ This is a move in the
right direction. The young lady cannot bear ridicule, and she frowns
at the very thought of it. For some minutes she seems plunged in
bitter reflection; then she speaks again.
‘No, I am not afraid,’ she cries; ‘I do not fear any but Madame,
and when I have apologised she will take my part. Oh, why did I
come with you? why did I think of running away?’
‘Because you love me, mon ange!’
‘Love you, Monsieur Belleisle? I like you better than Herr Bunsen,
because he is always cross and stupid and you are good-tempered.
And I thought you handsome. Well, I did not know my mind. I will
not marry you—the thought is ridiculous. You are thirty years old,
and I do not like Frenchmen.’
Despite her protestations, the post-chaise still continues its wild
career. It is dark at last, and the darkness is deepened by long
avenues of spectral fir-trees which line the road on either side. A
diligence passes swiftly by, with murmur of voices and jingling of
bells.
As night comes on the girl grows frightened, shrinks away from
her companion, and sobs bitterly. He tries to comfort her with
embraces and loving words, but she avoids his touch, and rejects all
his consolations.
If there were enough light to show his face, it would reveal an
aspect almost Mephistophelean in its cat-like expression. His long
fingers close and unclose nervously; he would like to use force, but
he lacks the courage.
At last he wins her to comparative quiescence by proving to her
that return is impossible before the morrow, and by promising that
when the morrow comes he will, if she still wishes it, see her safely
back to school. With this poor comfort she is obliged to be content;
for the house she left at daybreak lies thirty miles behind, and it
would be useless to turn thither now.
Presently the lights of a town gleam before them, and, after
rattling through some dark suburbs, they draw up before the
threshold of an inn—the Lion d’Or. It is a large dreary place, with
little or no custom. A ghostly waiter shows them to a great salle à
manger, which is totally deserted.
‘While dinner is preparing, perhaps Madame would like to make
her toilette?’
He lays emphasis on the ‘Madame’; and then demands,
respectfully, how many chambers will be required.
Madeline does not hear, but her companion explains that two
chambers will be wanted—one for the young lady, one for himself.
The waiter bows and withdraws. An elderly chambermaid soon
appears, and shows Madeline up to a great bedroom, grim and
lonely as an empty barn, with one little chilly bed in the corner.
There are no curtains to the window, and the moonlight is creeping
in with a ghastly gleam.
Left alone, Madeline resigns herself to remorse and despair, and
sobs as if her heart would break. An hour passes thus. Then the
chambermaid appears with the intimation that Monsieur is waiting
dinner, and is impatient. After a moment’s hesitation Madeline
descends.
They are alone in the salle à manger, and the first course is
served, when there enters a muscular young man in a shooting coat,
a shirt very loose about the collar, and a loose necktie. ‘Englishman’
is written in every lineament of his brown, sun-tanned countenance.
In the manner of many of his nation, he scowls at his fellow-guests,
and then, without a word, falls upon the soup.
Dish after dish goes from Madeline untasted. She breaks a little
bread, that is all, and drinks a little Bordeaux and water. Her face is
white as death, and all the tremendousness of the situation is full
upon her.
Monsieur Belleisle, for his part, feeds ravenously, and drinks more
than one bottle of light wine. He is agitated, but preserves his
composure. In his heart he curses the unwelcome third party
present; he burns for a tête-à-tête.
Third party proceeds leisurely with his dinner, only addressing the
waiter in monosyllables. He is a man of thirty, of splendid physique
and perfect health. He seems to see and hear nothing, but all the
time his eyes and ears are wide open. He starts when the young
lady—whom he has been watching quietly—speaks in the English
tongue.
‘The chambermaid says there is a train from this place to Rouen.
It leaves at daybreak, Monsieur Belleisle.’
‘We will talk of that to-morrow,’ murmurs the Frenchman, with his
mouth full.
‘That will be too late. I will leave by the first train, and get a cab
from Rouen to Millefleurs. I will explain all—they may punish me as
they please—I do not care.’
‘Diable, and what will then become of me?’
‘I don’t know—I suppose you will lose your situation, but you will
soon get another.’
Monsieur sinks his voice and whispers—
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