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Liquids and Solids 216

9-1 Comparing Solids, Liquids, and Gases 216

9-2 Liquid-Vapor Equilibrium 217

9-3 Phase Diagrams 223

9-4 Molecular Substances; Intermolecular Forces 226

9-5 Network Covalent, Ionic, and Metallic Solids 232

9-6 Crystal Structures 238

The Human Side: Dorothy Crowfoot Hodgkin 241

Beyond the Classroom: Supercritical Carbon Dioxide 243 Summary Problem 245

Questions and Problems 245

Solutions 246

10-1 Concentration Units 246

10-2 Principles of Solubility 255

10-3 Colligative Properties of Nonelectrolytes 260

10-4 Colligative Properties of Electrolytes 269

Beyond the Classroom: Maple Syrup 272

Summary Problem 273

Questions and Problems 273

Rate of Reaction 274

11-1 Meaning of Reaction Rate 274

11-2 Reaction Rate and Concentration 277

11-3 Reactant Concentration and Time 283

11-4 Models for Reaction Rate 289

The Human Side: Henry Eyring 292

11-5 Reaction Rate and Temperature 293

11-6 Catalysis 296

11-7 Reaction Mechanisms 298

Beyond the Classroom: The Ozone Story 302 Summary Problem 304

Questions and Problems 305

Gaseous Chemical Equilibrium

306

12-1 The N2O4–NO2 Equilibrium System 307

12-2 The Equilibrium Constant Expression 310

12-3 Determination of K 315

12-4 Applications of the Equilibrium Constant 318

12-5 Effect of Changes in Conditions on an Equilibrium System 323

Beyond the Classroom: An Industrial Application of Gaseous Equilibrium 328

Summary Problem 330

Questions and Problems 330a

13 14 15 16

Acids and Bases 331

13-1 Brønsted-Lowry Acid-Base Model 331

13-2 The Ion Product of Water 333

13-3 pH and pOH 333

13-4 Weak Acids and Their Equilibrium Constants 339

13-5 Weak Bases and Their Equilibrium Constants 348

13-6 Acid-Base Properties of Salt Solutions 352

13-7 Extending the Concept of Acids and Bases: The Lewis Model 355

Beyond the Classroom: Organic Acids and Bases 356

Summary Problem 359

Questions and Problems 359a

Equilibria

in Acid-Base Solutions 360

14-1 Buffers 360

14-2 Acid-Base Indicators 371

14-3 Acid-Base Titrations 374

Beyond the Classroom: Acid Rain 382

Summary Problem 384

Questions and Problems 384

Complex Ion and Precipitation

Equilibria 385

15-1 Complex Ion Equilibria; Formation Constant (Kf) 385

15-2 Solubility; Solubility Product Constant (Ksp) 388

15-3 Precipitate Formation 394

15-4 Dissolving Precipitates 399

Beyond the Classroom: Qualitative Analysis 403

Summary Problem 405

Questions and Problems 405

Spontaneity of Reaction 406

16-1 Spontaneous Processes 407

16-2 Entropy, S 409

16-3 Free Energy, G 413

The Human Side: J. Willard Gibbs 415

16-4 Standard Free Energy Change, ΔG° 415

16-5 Effect of Temperature, Pressure, and Concentration on Reaction Spontaneity 419

16-6 The Free Energy Change and the Equilibrium Constant 424

16-7 Additivity of Free Energy Changes; Coupled Reactions 425

Beyond the Classroom: Rubber Elasticity: An Entropic Phenomenon 427

Summary Problem 429

Questions and Problems 429

Electrochemistry 430

17-1 Oxidation-Reduction Reactions Revisited 431

17-2 Voltaic Cells 435

17-3 Standard Voltages 439

17-4 Relations Between E°, ΔG°, and K 446

17-5 Effect of Concentration on Voltage 448

17-6 Electrolytic Cells 452

17-7 Commercial Cells 456

The Human Side: Michael Faraday 458

Beyond the Classroom: Fuel Cells: The Next Step in Chemical-to-Electrical-Energy Conversion? 461

Summary Problem 464

Questions and Problems 464

Nuclear Reactions 465

18-1 Nuclear Stability 465

18-2 Radioactivity 467

The Human Side: Marie and Pierre Curie 473

18-3 Rate of Radioactive Decay 473

18-4 Mass-Energy Relations 476

18-5 Nuclear Fission 480

18-6 Nuclear Fusion 483

Beyond the Classroom: Biological Effects of Radiation 485

Summary Problem 486

Questions and Problems 486

Complex

Ions 487

19-1 Composition of Complex Ions 488

19-2 Naming Complex Ions and Coordination Compounds 492

19-3 Geometry of Complex Ions 494

19-4 Electronic Structure of Complex Ions 498

The Human Side: Alfred Werner 498

Beyond the Classroom: Chelates: Natural and Synthetic 503

Summary Problem 505

Questions and Problems 505

Chemistry of the Metals 506

20-1 Metallurgy 506

20-2 Reactions of the Alkali and Alkaline Earth Metals 513

20-3 Redox Chemistry of the Transition Metals 516

Beyond the Classroom: Essential Metals in Nutrition 522

Summary Problem 524

Questions and Problems 524

Chemistry of the Nonmetals 525

21-1 The Elements and Their Preparation 526

21-2 Hydrogen Compounds of Nonmetals 530 21-3 Oxygen Compounds of Nonmetals 534

21-4 Oxoacids and Oxoanions 537

Beyond the Classroom: Arsenic and Selenium 545

Summary Problem 546

Questions and Problems 546a

Organic Chemistry 547

22-1 Saturated Hydrocarbons: Alkanes 548

22-2 Unsaturated Hydrocarbons: Alkenes and Alkynes 553

22-3 Aromatic Hydrocarbons and Their Derivatives 556

22-4 Functional Groups 558

22-5 Isomerism in Organic Compounds 566

22-6 Organic Reactions 571

Beyond the Classroom: Cholesterol 573

Summary Problem 575

Questions and Problems 575a

Organic Polymers, Natural and Synthetic 576

23-1 Synthetic Addition Polymers 577

23-2 Synthetic Condensation Polymers 580

23-3 Carbohydrates 583

23-4 Proteins 587

Beyond the Classroom: DNA Fingerprinting 595

Summary Problem 597

Questions and Problems 597

Appendices

1 Units, Constants, and Reference Data 599

2 Properties of the Elements 605

3 Exponents and Logarithms 607

4 Molecular Orbitals 613

5 Answers to Even-Numbered and Challenge Questions and Problems 619

Index/Glossary 641

Preface

It is always difficult for an author to praise the virtues of one’s own book. I could tell the instructors that the book is so inspiring that students will be turned on to chemistry with little or no effort on the instructor’s part. I doubt you would believe that. I could also tell you that the text is so clearly written, so attuned to the students in the twenty-first century that your students will learn chemistry with little or no effort on their part. You certainly would not believe that. I can tell you that the two goals in writing this edition have been to make it as clear and as interesting as possible. I hope you believe that, because it is true.

Today’s freshmen are quite different from those of a few years ago. Text messaging and TwitterTM have strongly influenced sentence length and structure. In current writing and conversation, short sentences or sentence fragments convey straight-to-the-point information. Multimedia presentations are a way of life. This edition, like the seventh, is written to be fully in tune with today’s technology and speech.

Why Write a Short Book?

Rising tuition costs, depleted forests, and students’ aching backs have kept me steadfast in my belief that it should be possible to cover a text completely (or at least almost completely) in a two-semester course. The students (and their parents) justifiably do not want to pay for 1000-page books with material that is never discussed in the courses taught with those texts.

The common perception is that a short book is a low-level book. I believe, however, that treating general concepts in a concise way can be done without sacrificing depth, rigor, or clarity. The criterion for including material continues to be its importance and relevance to the student, not its difficulty. To achieve this, the following guidelines are used.

1. Eliminate repetition and duplication wherever possible. Like its earlier editions, this text uses

Only one method for balancing redox reactions, the half-equation method introduced in Chapter 17.

Only one way of working gas-law problems, using the ideal gas law in all cases (Chapter 5).

Only one way of calculating ΔH (Chapter 8), using enthalpies of formation. Only one equilibrium constant for gas-phase reactions (Chapter 12), the thermodynamic constant K, often referred to as Kp. This simplifies not only the treatment of gaseous equilibrium but also the discussion of reaction spontaneity (Chapter 16) and electrochemistry (Chapter 17).

2. Relegate to the Appendices or Beyond the Classroom essays topics ordinarily covered in longer texts. Items in this category include

MO (molecular orbital) theory (Appendix 4). Experience has shown (and continues to show) that although this approach is important to chemical bonding, most general chemistry students do not understand it but only memorize the principles discussed in the classroom.

Nomenclature of organic compounds. This material is of little value in a beginning course and is better left to a course in organic chemistry.

Qualitative analysis. This is summarized in a few pages in an essay in Chapter 15 in the Beyond the Classroom section. An extended discussion of the qualitative scheme and the chemistry behind it belongs in a laboratory manual, not a textbook.

Biochemistry. This material is traditionally covered in the last chapter of general chemistry texts. Although there are several biochemical topics included in the text (among them a discussion of heme in Chapter 19 and

carotenoids in Chapter 6), an entire chapter is not devoted to biochemistry. Interesting as this material is, it requires a background in organic chemistry that first-year students lack.

3. Avoid superfluous asides, applications to the real world, or stories about scientists in the exposition of principles. There are many applications incorporated in the context of problems and some of the exposition of general principles. In general, however, a bare-bones approach is used. Students can easily be distracted by interesting but peripheral tidbits while they are striving hard to understand the core concepts. Favorite real-world applications and personal stories about scientists are in separate sections, Beyond the Classroom and Chemistry: The Human Side. Students say that they read these two sections first and that these are the parts of the book that “we really enjoy the most.” (Talk about faint praise!) They do admit to enjoying the marginal notes too.

What Changes Have Been Made?

The eighth edition has not been as radically changed as the seventh. I talked to students, instructors, and TAs and listened to suggestions and complaints. While all the changes made to the seventh edition were enthusiastically received, there were areas where making small changes would make them better. For the eighth edition, the following changes were made:

The Example format has been revised, so that the strategy, analysis, and solution follow each part of the example. The most common comment was: “Show me first how to do part (a) before asking me about part (b).”

More flowcharts have been added. There was unanimous support and requests for more of them. We revised some of the existing ones and added a few more. The discussion of balancing redox equations has been moved from Chapter 4 to Chapter 17. Instructors comment that they have had to reintroduce redox equations in Chapter 17 and treat it like new material. Students and TAs both agree that Chapter 4 is a dense and heavy chapter. Thus, redox reactions are treated in Chapter 4 only as far as stoichiometric calculations are involved. Balanced equations are provided for these reactions.

Global Changes

Changes in about 25% of the topical end-of-chapter problems

Almost all of the summary problems have either been revised or are completely new to this edition

Revised artwork with enhanced labeling and several new photos

Almost all of the chapter opening art is new

Chapter 1

Redrawn flowchart for matter classification

New Examples 1.3 and 1.6

Chapter 2

Redrawn Figure 2.5 (Rutherford Experiment)

New Examples 2.1 and 2.5

New Beyond the Classroom essay on the origin of some elements’ names

Redrawn flowchart for naming molecular compounds

Chapter 3

New Examples 3.1 (b), 3.5, 3.7, and 3.11

Chapter 4

Redrawn Figure 4.1

New Example 4.5

Revised discussion of redox reactions excluding balancing of half and complete reactions

New flowchart for determining oxidation number

New figure summarizing differences between oxidation and reduction

New Beyond the Classroom essay on antacids

Chapter 5

New Figure 5.6

New Examples 5.2 and 5.4 (a) and (b)

Discussion of the relation of time and molar mass to the rate of effusion

Detailed List of Changes by Chapter

Chapter 6

New Example 6.1

New discussion on electron capacities for principal levels and subshells

New table summarizing electron capacities in principal levels and subshells

Chapter 7

New Figure 7.5

Chapter 8

Replaced Figure 8.10 with a new table

Chapter 9

Figure 9.3 redrawn

Chapter 10

New Examples 10.9 and 10.10

Figure 10.14 redrawn

Chapter 11

New Figure 11.4

Example 11.3 redone

Chapter 12

Examples 12.1 and 12.6 rewritten

Chapter 13

New Example 13.3

Examples 13.2 and 13.9 rewritten

Revised Figure 13.14

Chapter 14

Example 14.3 rewritten

Chapter 15

Example 15.3 rewritten

Example 15.1 reclassified as nongraded

Examples 15.8 and 15.9 reclassified as graded

Chapter 16

Example 16.2 rewritten

Chapter 17

New Section 17.1 on balancing redox half and complete reactions

Review of oxidation, reduction, oxidizing agents, and reducing agents

New schematic on balancing half-reactions

New Examples 17.1 and 17.2

Chapter 18

New Table 18.1—summary of different modes of radioactive decay

New paragraph about SPECT (single proton emission computer tomography) scans

Chapters 19–23

No changes

Alternate Editions

Chemistry: Principles and Reactions, Eighth Edition Hybrid Version with Access (24 months) to OWLv2 with MindTap Reader

ISBN: 978-1-305-08215-1

This briefer, paperbound version of Chemistry: Principles and Reactions, Eighth Edition does not contain the end-of-chapter problems, which can be assigned in OWLv2, the online homework and learning system for this book. Access to OWLv2 and the MindTap Reader eBook is included with the Hybrid version. The MindTap Reader is the full version of the text, with all end-of-chapter questions and problem sets.

Supporting Materials

Please visit http://www.cengage.com/chemistry/masterton/CPAR8e for information about student and instructor resources for this text, including custom versions and laboratory manuals.

Acknowledgments

Many people who have used this book—instructors, teaching assistants, students, and former students now teaching general chemistry—have e-mailed, written, and called with suggestions on how to improve the exposition. I am grateful to them all.

Reviewers who have helped in the preparation of this edition include the following:

Mamoun Bader (Penn State University)

Nancy Bryson (Berry College)

Andrea Gorczyca (Brookhaven College)

Arlin Gyberg (Augsburg College)

James Harris (Monadnock Regional High School)

Isaac Hon (Albertus Magnus College)

James Mack (University of Cincinnati)

Lawrence Mavis (St. Clair County Community College)

Alexander Nazarenko (SUNY Buffalo State)

Lorna Pehl (Eastern Wyoming College)

Richard Roberts (Des Moines Area Community College)

Joseph Sinski (Bellarmine University)

Jessica Thomas (Purdue University North Central)

John Wilterding (Olivet College)

Special thanks to Professor Fatma Selampinar (University of Connecticut) for her accuracy reviews. Her thoroughness and absolute attention to detail are incredible. She not only solved every new problem but was a sounding board and uncomplaining listener to a harried author.

This edition would not have been possible without the superb guidance of my content developer, Ed Dodd. He was a real gift. He smoothed rough patches and demanded perfection from everyone on the team. It was a real pleasure working with him.

Many people worked on the editorial and production team for this text. They took pages of manuscript, rough ideas, crude sketches, and long wish lists and put them together to create this edition. They prodded, cajoled, and set impossible deadlines. They are:

Mary Finch, Product Director

Maureen Rosener, Product Manager

Lisa Lockwood, Product Manager

Peter McGahey, Managing Developer

Elizabeth Woods, Associate Content Developer

Karolina Kiwak, Product Assistant

Lisa Weber, Media Developer

Brendan Killion, Media Developer

Nicole Hamm, Marketing Director

Janet del Mundo, Marketing Manager

Jennifer Risden, Senior Content Project Manager

Maria Epes, Art Director

Judy Inouye, Manufacturing Planner

John Sarantakis, Project Manager, Intellectual Property Acquisition

Jill Traut, Project Manager at MPS Limited

Dhanalakshmi Singaravelu, and Padmapriya Soundararajan, Image Researchers at Lumina Datamatics

Pinky Subi, Text Researcher at Lumina Datamatics

One person who does not belong to any team deserves special recognition. Jim Hurley picked up the slack when time was short, deadlines were imminent, and the list of tasks was long. He listened to endless complaints and commiserated. Thank you once again for continuing on this journey with me.

University of Connecticut Storrs, CT

November 2014

To the Student

You’ve probably already heard a lot about your general chemistry course. Many think it is more difficult than other courses. There may be some justification for that opinion. Besides having its very own specialized vocabulary, chemistry is a quantitative science—which means that you need mathematics as a tool to help you understand the concepts. As a result, you will probably receive a lot of advice from your instructor, teaching assistant, and fellow students about how to study chemistry. We would, however, like to acquaint you with some of the learning tools in this text. They are described in the pages that follow.

Learning Tools in Chemistry: Principles and Reactions, Eighth Edition

Examples

In a typical chapter, you will find ten or more examples each designed to illustrate a particular principle. These examples are either general (green bars), graded (purple bars), or conceptual (blue bars). These have answers, screened in color. They are presented in a two-column format. Most of them contain three parts:

Analysis, which lists

1. The information given.

2. The information implied—information not directly stated in the problem but data that you can find elsewhere.

3. What is asked for.

Strategy

This part gives you a plan to follow in solving the problem. It may lead you through a schematic pathway or remind you of conversion factors you have to consider or suggest equations that are useful.

Solution

This portion shows in a stepwise manner how the strategy given is implemented. Many of the examples end with a section called End Points. These are either checks on the reasonableness of your answer or relevant information obtained from the problem.

You should find it helpful to get into the habit of working all problems this way.

E x AMPLE

Calculate the wavelength in nanometers of the line in the Balmer series that results from the transition n 5 4 to n 5 2.

Information given: n 5 2; n 5 4

ANALYSIS

Information implied:speed of light (2.998 3 108 m/s)

Rydberg constant (2.180 3 10 18 J)

Planck constant (6.626 3 10 34 J s)

Asked for: wavelength in nm

continued

STRATE g Y

1. Substitute into Equation 6.4 to find the frequency due to the transition.

Use the lower value for n as nlo and the higher value for nhi

2. Use Equation 6.1 to find the wavelength in meters and then convert to nanometers.

1. Frequency

2. Wavelength

END P o INT

Compare this value with that listed in Table 6.2 for the second line of the Balmer series.

Graded Examples

Throughout the text, you will encounter special graded examples. Note that they are the problems with the purple bars. A typical graded example looks like the following:

E x AMPLE 1.8 G RADED

For the reaction

determine

(a) the number of moles of A required to react with 5.0 mol of B.

(b) the number of grams of A required to react with 5.0 g of B.

(c) the volume of a 0.50 M solution of A required to react with 5.0 g of B.

(d) the volume of a 0.50 M solution of A required to react with 25 mL of a solution that has a density of 1.2 g/mL and contains 32% by mass of B.

There are two advantages to working a graded example:

1. By working parts (a) through (d) in succession, you can see how many different ways there are to ask a question about mass relations in a reaction. That should cushion the shock should you see only part (d) in an exam.

2. The parts of the graded example do not just progress from an easy mass relations question to a more difficult one. The value of the graded example is that the last question assumes the ability to answer the earlier ones. You may be able to answer parts (a) and (b) with a limited understanding of the material, but to answer part (d) you need to have mastered the material.

Use the graded example as you review for exams. Try to skip the earlier parts [in this case (a), (b) and (c)] and go directly to the last part (d). If you can solve (d), you do not need to try (a), (b), and (c); you know how to do them. If you can’t, then try (c) to see where you may have a problem. If you can’t do (c), then try (b).

As a last resort, start at (a) and work your way back through (d).

A 1 2B →: C

Marginal Notes

Sprinkled throughout the text are a number of short notes in the margin. Many of these are of the “now, hear this” variety, others are mnemonics, and still others make points that we forgot to put in the text. (These were contributed by your fellow students.) Some—probably fewer than we think—are supposed to be humorous.

Chemistry: The Human Side

Throughout the text, short biographies of some of the pioneers of chemistry appear in sections with this heading. They emphasize not only the accomplishments of these individuals but also their personalities.

Chemistry: Beyond the Classroom

Each chapter contains a Beyond the Classroom feature. It is a self-contained essay that illustrates a current example either of chemistry in use in the world or an area of chemical research. It does not intrude into the explanation of the concepts, so it won’t distract you. But we promise that those essays—if you read them—will make you more scientifically literate.

Chapter Highlights

At the end of each chapter, you will find a brief review of its concepts. A review is always helpful not only to refresh yourself about past material but also to organize your time and notes when preparing for an examination. The chapter highlights include

The Key Terms in the chapter. If a particular term is unfamiliar, refer to the index at the back of the book. You will find the term in the glossary that is incorporated in the index and also the pages in the text where it appears (if you need more explanation).

The Key Concepts and Key Equations introduced in the chapter. These are indexed to the corresponding examples and end-of-chapter problems. End-ofchapter problems available on OWLv2 are also cross-referenced. If you have trouble working a particular problem here, it may help to go back and reread the example that covers the same concept.

Summary Problem

Each chapter is summarized by a multistep problem that covers all or nearly all of the key concepts in the chapter. You can test your understanding of the chapter by working this problem. A major advantage of the summary problems is that they tie together many different ideas, showing how they correlate with one another. An experienced general chemistry professor always tells his class, “If you can answer the summary problem without help, you are ready for a test on its chapter.”

Questions and Answers

At the end of each chapter is a set of questions and problems that your instructor may assign for homework. They are also helpful in testing the depth of your knowledge about the chapter. These sets include

Conceptual problems that test your understanding of principles. A calculator is not (or should not be) necessary to answer these questions.

Questions that test your knowledge of the specialized vocabulary that chemists use (e.g., write the names of formulas, write the chemical equation for a reaction that is described).

Quantitative problems that require a calculator and some algebraic manipulations.

Classified problems start the set and are grouped by type under a particular heading that indicates the section and/or topic from the chapter that they address. The classified problems occur in matched pairs, so the second member illustrates the same principle as the first. This allows you more than one opportunity to test yourself. The second problem (whose number is even) is answered in Appendix 5. If your instructor assigns the odd problems without answers for homework, wait until the problem solution is discussed and solve the even problem to satisfy yourself that you understand how to solve the problem of that type.

Each chapter also contains a smaller number of Unclassified problems, which may involve more than one concept, including, perhaps, topics from a preceding chapter.

The section of Challenge problems presents problems that may require extra skill and/or insight and effort. They are all answered in Appendix 5.

Even-numbered questions and Challenge Problems answered in Appendix 5 have fully worked solutions available in the Student Solutions Manual. Please visit http://www.cengage.com/chemistry/masterton/CPAR8e for information about the Student Solutions Manual

Appendices

The appendices at the end of the book provide not only the answers to the evennumbered problems but also additional materials you may find useful. Among them are

Appendix 1, which includes a review of SI base units as well as tables of thermodynamic data and equilibrium constants.

Appendix 3, which contains a mathematical review touching on just about all the mathematics you need for general chemistry. Exponential notation and logarithms (natural and base 10) are emphasized.

Other Resources to Help You Pass Your General Chemistry Course

Besides the textbook, several other resources are available to help you study and master general chemistry concepts. Please visit http://www.cengage.com /chemistry/masterton/CPAR8e for information about student resources for this text, including custom versions and laboratory manuals.

Matter and Measurements

almost certainly, this is your first college course in chemistry; perhaps it is your first exposure to chemistry at any level. Unless you are a chemistry major, you may wonder why you are taking this course and what you can expect to gain from it. To address that question, it is helpful to look at some of the ways in which chemistry contributes to other disciplines.

If you’re planning to be an engineer, you can be sure that many of the materials you will work with have been synthesized by chemists. Some of these materials are organic (carbon-containing). They could be familiar plastics like polyethylene (Chapter 23) or the more esoteric plastics used in unbreakable windows and nonflammable clothing. Other materials, including metals (Chapter 20) and semiconductors, are inorganic in nature.

Perhaps you are a health science major, looking forward to a career in medicine or pharmacy. If so, you will want to become familiar with the properties of aqueous solutions (Chapters 4, 10, 14, and 16), which include blood and other body fluids. Chemists today are involved in the synthesis of a variety of life-saving products. These range from drugs used in chemotherapy (Chapter 19) to new antibiotics used against resistant microorganisms.

Beyond career preparation, an objective of a college education is to make you a better-informed citizen. In this text, we’ll look at some of the chemistry-related topics that make the news:

depletion of the ozone layer (Chapter 11).

alternative sources of fuel (Chapter 17).

the pros and cons of nuclear power (Chapter 18).

Another goal of this text is to pique your intellectual curiosity by trying to explain the chemical principles behind such recent advances as

“self-cleaning” windows (Chapter 1).

“the ice that burns” (Chapter 3).

“maintenance-free” storage batteries (Chapter 17).

“chiral” drugs (Chapter 22).

We hope that when you complete this course you too will be convinced of the importance of chemistry in today’s world. We should, however, caution you on one point.

1

The painting shows measuring instruments used in the Middle Ages. We still use many of them today.

There is measure in everything.

Chapter Outline

1-1 Matter and Its Classifications

1-2 Measurements

1-3 Properties of Substances

Museum of the History of Science in Oxford, England

Chemistry deals with the properties and reactions of substances.

Although we will talk about many of the applications of chemistry, our main concern will be with the principles that govern chemical reactions ▼ Only by mastering those principles will you understand the basis of the applications mentioned above.

This chapter begins the study of chemistry by considering the different types of matter: pure substances versus mixtures, elements versus compounds (Section 1-1). looking at the kinds of measurements fundamental to chemistry, the uncertainties associated with those measurements, and a method to convert measured quantities from one unit to another (Section 1-2). focusing on certain physical properties, including density and water solubility, which can be used to identify substances (Section 1-3).

1-1 Matter and Its classifications

Matter is anything that has mass and occupies space. It can be classified either with respect to its physical phases or with respect to its composition (Figure 1.1).

The three phases of matter are solid, liquid, and gas. A solid has a fixed shape and volume. A liquid has a fixed volume but is not rigid in shape; it takes the shape of its container. A gas has neither a fixed volume nor a shape. It takes on both the shape and the volume of its container.

Matter can also be classified with respect to its composition:

pure substances, each of which has a fixed composition and a unique set of properties. mixtures, composed of two or more substances.

Pure substances are either elements or compounds (Figure 1.1), whereas mixtures can be either homogeneous or heterogeneous.

Elements

An element is a type of matter that cannot be broken down into two or more pure substances. There are 118 known elements, of which 91 occur naturally. Many elements are familiar to all of us. The charcoal used in outdoor grills is nearly pure carbon. Electrical wiring, jewelry, and water pipes are often made from copper, a metallic element. Another such element, aluminum, is used in many household utensils.

Some elements come in and out of fashion, so to speak. Sixty years ago, elemental silicon was a chemical curiosity. Today, ultrapure silicon has become the basis for the multibillion-dollar semiconductor industry. Lead, on the other hand, is an element moving in the other direction. A generation ago it was widely used to make paint pigments, plumbing connections, and gasoline additives. Today, because of the toxicity of lead compounds, all of these applications have been banned in the United States.

In chemistry, an element is identified by its symbol. This consists of one or two letters, usually derived from the name of the element. Thus the symbol for carbon is C; that for aluminum is Al. Sometimes the symbol comes from the Latin name of the element or one of its compounds. The two elements copper and mercury, which were known in ancient times, have the symbols Cu (cuprum) and Hg (hydrargyrum).

Table 1.1 (p. 4) lists the names and symbols of several elements that are probably familiar to you. In either free or combined form, they are commonly found in the laboratory or in commercial products. The abundances listed measure the relative amount of each element in the earth’s crust, the atmosphere, and the oceans. Curiously, several of the most familiar elements are really quite rare. An example is mercury, which has been known since at least 500 b.c., even though its abundance is only 0.00005%. It can easily be prepared by heating the red mineral cinnabar (Figure 1.2, p. 4).

Same composition throughout?

Made up of one atom?

Mercury is the only metal that is a liquid at room temperature. It is also one of the densest elements. Because of its high density, mercury was the liquid extensively used in thermometers and barometers. In the 1990s all instruments using mercury were banned because of environmental concerns. ▼ Another useful quality of mercury is its ability to dissolve many metals, forming solutions (amalgams). A silver-mercury-tin amalgam is still used to fill tooth cavities, but many dentists now use tooth-colored composites because they adhere better and are aesthetically more pleasing.

In contrast, aluminum (abundance 5 7.5%), despite its usefulness, was little more than a chemical curiosity until about a century ago. It occurs in combined form in clays and rocks, from which it cannot be extracted. In 1886 two young chemists, Charles Hall in the United States and Paul Héroult in France, independently worked out a process for extracting aluminum from a relatively rare ore,

Figure 1.1 classification of matter into solid, liquid, and gas.

Mercury thermometers, both for laboratory and clinical use, have been replaced by digital ones.

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to one master? The dog who loses one master, to be kindly adopted by another, suffers from the change only until he has grown accustomed to the new touch upon his head. His heart beats as happily in a little while to the new tread along the garden walk. He is still faithful in his allegiance—to the hand that feeds him. When the old master returns he will remember, till then he will philosophize.

The Burmese woman who is sold to the white man has this advantage over his dog. The Unexpected does not occur. She knows that she will, possibly, change masters more than once in her life. She may prefer one to another, but, in most cases, the change is accepted philosophically and is followed by few heart-burnings and useless regrets. So that the man be just to her and kind, so that he clothe her and approve of her housekeeping, she is content. Her lighthearted affection goes to the children, who are bone of her bone, and of whom she need not stand in awe.

If the man has any notion of fair play, when the time comes for him to leave her, he will provide for the children; if he deny all responsibility, there are still the missions, who look upon such things with solemn and sentimental eyes, and are, consequently, helpful.

Cyprian learnt during the next two years to understand this enduring passivity of the Buddha's children. Not that they followed blindly the precepts of the Great Teacher: they had simply adapted them to the changing times and needs of the Race.

Little Hla Byu was a regular attendant on festival occasions at the Aracan Pagoda in Mandalay. She knelt before the big gold Buddha, solid from many coatings of precious metal, when the flickering candles dripped grease, and the scent of the incense-sticks penetrated through the scent of perspiring humanity.

There, she prayed for her son. She did not consciously connect him with the foreign father who might, any day, desert her for a woman of his own race, and legitimately deny all that linked him to his former life. She prayed quaintly, mechanically, regarding the proceeding in the light of a charm, and with no very clear idea as to who should hear the prayer. The priests should know. But the priests, indeed, if they knew anything up at their bare stone

monastery, should have taught that the Master could not hear the cry of human suffering or desire, even if he would, since he had obtained the final Silence, "where beyond these voices there is peace." But, to Hla Byu, spirits there must be—Someone, Anyone. Prayer could do no harm, anyway, and might certainly do good. Contemplation was not for the Burman-in-thestreet, but any follower of the Buddha can hold a wooden rosary and repeat two thousand times in a dull monotone, some such golden truth as that "Honesty is the best policy," before leaving the lighted Pagoda and going back to the bazaar to cheat his brother.

At least, her creed gave some outlet to those emotions which the practical things of life cannot satisfy.

She was richer than Cyprian, who had none. The simple honesty of her beautified their relationship. Nature, surely, must have meant just this simplicity between the sexes in ministering to each other's needs. He knew that Ferlie would have been struck with the hypocrisy of Society-life in the big towns of Burma.

There the white women-folk knew of such as little Hla Byu but pretended ignorance. No aspiring mother would encourage her daughter to join hands with an ex-public-school boy at the beginning of his career and flit away into the jungles to share the making of his future. That was Hla Byu's part. But, later, when the same future was assured, when the publicschool boy had become submerged in the fever-eaten official with a bankbook and, possibly, a passion-ravaged past, then it was the turn of some clear-eyed débutante to receive with thankfulness God's gift of a good man's love—and his motor-car.

Cyprian's face, bent over the official note-paper upon which he had been idly sketching while listening to the klop-klop of the postman's mule mounting the hill, was less lean now and far less strained. The great bitterness curving the corners of his mouth was contradicted by the level calm with which his eyes looked out across to the horizon despite their awareness that the Lot had fallen unto him in a rugged ground.

A slight stir in the vicinity of the waste-paper basket caused him to turn his head, and, with an oddly detached air, he surveyed for some moments the explorations therein of a naked baby.

Its creamy amber skin shone like satin in the sunlight, relieved by its stiff cap of black hair. And the eyes riveted suddenly upon Cyprian's were widely set apart and, most incongruously, most tellingly, blue.

The man, unexpectedly, with a brusque movement of his head, shook down the eye-glasses he used to correct his astigmatic vision when concentrating for long upon close writing, and the small inquiring face receded, mercifully blurred.

But its marked and precocious intelligence remained branded upon his mentality as if somebody had pasted an imperfectly-developed photograph there.

"One is responsible," and he turned the word over in his mind, stupidly probing its meaning.

Hla Byu picked up the restless bundle as she flitted into the shaded gloom of the sitting-room, out of the white glare blocked by the verandah chicks.

Cyprian absently received his letters from her hands.

"The school is in Maymyo," he said inconsequently. "It will be best for him to go where there will be others like him."

The puzzled wonderment of her expression merged into amusement. She had learnt something of this man during the last two years. Something, also, of latent powers in herself which he would have paid much, in after life, to have left unstirred. She gave a tiny exclamatory chirp of laughter.

"At fourteen months, Thakin? That would, indeed, be somewhat early, even for him."

With relief he recalled that the time for such decisions was not yet. One might drift a little longer....

But Fate disproved that. Among the official letters lay one in a strange handwriting. He turned it over incuriously, but there was a seal on the back which quickened his interest. He could not recollect where he had seen it before. The first words of the letter startled him.

"Dear Ferlie's Cyprian,"—Stiffening, he turned the sheet over to read the signature, "B. Trefusis." Then he remembered. A tea-shop.... Ferlie buried in ice-cream and, to the right of her, a vivacious shingled head ... the same seal on a thin white wrinkled finger, curved over a plate of honeycoloured scones. He spread the letter out upon the blotting-paper and, resting his drawn forehead on sheltering palms, read it slowly through.

"If you were ever a friend of Ferlie's, try and come to her. Once, I should have said, if you were ever a friend of Ferlie's try and leave her. I never considered you a successful substitute for the uncle she did not possess, but the very difference in age between you, which I deplored, I now rejoice in. Perhaps, she will confide in you; perhaps, you will be able to help where the few that are near and dear to her are excluded from helping.

"For all I know, you may have forgotten that there ever was a Ferlie. This may find you with another woman at your side. You may have ties— children; then, for their sakes, come and hold out your hand in friendship to a child you once knew. I am not satisfied with the little I gleaned about her marriage. I am not satisfied with the accounts I heard of you then. The only thing I am satisfied about is that Ferlie needs you and would tell you what she will not tell me. Perhaps, you may have the key to the whole situation; perhaps, you know nothing. At any rate, if you were ever a friend of Ferlie's come and learn."

After all, the ties which held him were slenderer than cobwebs; surprising the ease with which he snapped them.

Hla Byu did not question. She merely accepted. But her slanting brows creased painfully.

"Will the Thakin let me come back to him?"

Through the rising tumult of his mind he detected the note of alarm.

"There is nothing to fear," he told her. "I will arrange for regular money to be supplied to you. The child shall be provided for all during his life."

The momentary relief in her face struck a feeling of shame to Cyprian's soul. There were men, he knew, who would consider him quixotic. He blinked away the thought. Custom could not lessen the dominion of the Daimon in this matter. Responsible. For all that he had made of life. For the weakness which had originally driven him from his acknowledged sphere. For the narrowness which had spurned Ferlie's confidence in its rightful setting; for the indecision which had kept him from following his truest instincts to love and to declare his love; for the apathetic purposelessness through which he had accepted Burma's bribe of Hla Byu, and the child with the questioning blue eyes.

"What will happen no one can foretell," he said. "Serve another Thakin, or wait; in either case you can always appeal to me for your needs."

Seemingly satisfied, she nodded and then turned from him to hide something on her lashes which made rainbows of the sunshine. She had always been a little afraid of him, although he never got drunk, nor beat her, nor threw things about the house as she knew, from her friends, so many foreign masters did. He was always silent, work-absorbed, apart from her— it was like living with the marble Buddha on the river-bank, who eternally contemplated, in the regulation attitude, the water traffic slipping by on its very mortal affairs, from town to town. She clutched the baby to her in a spasm of passionate regret—although, of course, there remained nothing to regret since their future was assured.

"It has been peace here, Thakin?" she said, on a timid note of interrogation.

He laid a gentle hand upon the yielding shoulder; her tiny bones felt soft like a kitten's bones.

"It is never peace for long, child," he answered.

He had wired the date of his arrival to Miss Trefusis; the compromise of a reply to the letter he had not felt capable of answering. But he was not prepared to see the severely stately figure of that decisive lady waiting at the docks.

She greeted him as if they had parted yesterday.

"People remain vivid to me," she said in explanation, leading him to the closed limousine. "We are motoring to my place near town, and your heavy luggage can go by train. You are coming to stay with me until you've had time to choose your roost. On the way down in the car I can elucidate. Meanwhile, a brief catechism will clear the air. Married?"

Cyprian shook his head.

"I am glad," said the old lady. "Your having no responsibilities will simplify matters. Was leave due to you?"

"I took 'Urgent Private Affairs'."

"Good. They should more than occupy your attention. Get in."

Her hand directed him towards the car.

Cyprian obeyed, hypnotized. Once they were seated she swung sideways to look him full in the face.

"Do you know why I have risked this? For love of Ferlie. You might have consigned me to the devil, had you developed into an official of high standing, very much married, with a brace of inarticulate, spectacled children. Instinct told me that you were alone in spirit, even if among your fellow-men; overworking, and living at the bottom of a mine, not of rubies, but of buried hopes. Was I right?"

He nodded, blinking nervously at his hands. Her voice had lost its hardedged clarity.

"When I saw you two, one afternoon at the Zoo—you remember?—I thought that the link, strengthening between you as the years went on, was wholly unnatural. You were Ferlie's sun, though neither of you realized it. And she stood to you for refreshment and comfort and utter peace. Again— Was I right?"

He stirred uneasily.

"Can you not spare me this?"

"No," said Aunt Brillianna emphatically. "I can spare you nothing if Ferlie is to be spared a little. Listen."

She lowered her tone and, above the humming of the car, her voice ran on earnestly. Pain was again wrenching at his nerves and the sentences sounded blurred and disconnected....

"And no one knows the real truth. They are not, officially, separated, but she lives alone at Black Towers with John, her little boy...."

A companion of lesser perception might have faltered discouraged before his immobility. This one had the good sense to keep her eyes upon the shifting hedges.

"She tells us nothing, and lives like a nun, cloistered in her pathetic youth behind the walls of that crumbling old tomb. Mainwaring fills the town house with his friends, and there are queer stories afloat about him. He has never shown any interest in the child—looks upon its arrival as a duty mutually performed. There has been no public quarrel; no cruelty that we know of, and the rumours, however unsavoury, do not provide the evidence for divorce proceedings. In any case, Ferlie has joined the Church of Rome. Gave no explanation why; merely announced it as an accomplished fact. I saw a marble statue once, called 'Endurance.' It was in a private show, by an unknown man. A nude figure with hands extended to push back some invisible advancing foe. I bought it. There is terror in the face, lest the

unknown power should crush completely; but there is also cold resistance and the strength of despair. I will show you the thing. You, who remember Ferlie as so poignantly alive...."

The speaker broke off for a moment.

"... But I must come to the incident which prompted my letter to you. I had gone unexpectedly to Black Towers, and only John greeted me in that mausoleum of a hall. He is a Ferlie product all right, but only just four. And ... one never knows.... The servants told me that Lady Greville-Mainwaring was at home but could not be disturbed. I asked if she were ill. They denied that and, politely resistant to further inquiries, supplied me with papers, afternoon tea, and, being well acquainted with my erratic habits, asked if I would stay the night. I said 'yes,' and turned my whole attention to John in the hope of discovering what his mother was doing.

"'No one could ever go up between five and six,' he informed me. 'But go up where, John?' I asked. With some difficulty I extracted the fact that Ferlie was in the West Tower. I knew there were unused rooms in the towers. I asked him what his mother did there between five and six, and he said she shut the door and 'just was quiet,' adding proudly that he took her up messages if it was important.

"I hated the sound of these proceedings which he evidently regarded as normal. 'This is important, John,' I said. 'We won't tell anybody else, but you take me up to Mother.' He demurred at first—thought the occasion did not justify that weary journey—but, at last, I persuaded him. The steps were high and dark and narrow. We might have been perambulating in Dante's Purgatory as we circled round and round. We stopped outside the door of a circular room. So strict were her orders that she had ceased to expect intrusion, and only a curtain hid her from us. I stood for some while behind it, listening to the silence. John, queer intense little soul that he is, sat down on the top step nursing his legs, for he was never very strong and I suppose they ached from the climb. And suddenly perched up at that height in the dark, relieved only by the spears of ghost-coloured light shooting through the slit windows behind us on the stair, I lost my nerve and felt that, dishonourable or not, I must know what Ferlie was doing. If she had turned into a witch in that setting I was not prepared to be surprised."

Miss Trefusis stopped to wipe from her face the dampness which had gathered there. She gave a little gasp and moistened her lips.

"Cyprian. I stood and peeped through the curtain folds at a room soaked in gold light. I thought I was demented until I realized that the rays of the western sun must touch this turret last of any room in the house, and then they struck through a round aperture glazed with orange glass. When no longer dazzled by the discovery I found Ferlie. The place was unfurnished save for a cushioned oak chair in which she was sitting, motionless as if she had been dead for years. On the palm of one opened hand lay a spherical object which retained at one spot a pin-point of reflected light like a minute star. On this it seemed to me Ferlie's eyes were fixed, and, even when throwing discretion to the winds, I went in to her she neither spoke nor stirred.

"I stooped low to her face and realized that she could not be aware of my presence. She was in some sort of a trance. Terrified, my first idea was to rush for help. Mercifully, I thought better of it. I did not know what kind of help was needed. I could only guess that Ferlie was self-hypnotized. But with what object? And had the thing been accidental, or deliberate. Not daring to pick up what she held in her hand I saw it was a small golden apple.

"I went back to John and asked him where the nearest doctor lived. We were some while whispering while I dug for information, and during that delay I heard Ferlie give a long sigh. Back I sped to her side. The apple had rolled into her lap and her body relaxed as I hovered round like a distracted hen. Then, to my joy, I perceived that she was realizing me. She did not seem astonished, and lifting her head spoke as if hardly out of a dream.

"'Nearly,' she said. 'Very nearly. But there is always some Presence standing between him and myself—and it is not God.'

"I was tactful and apologetic, putting the blame of my intrusion on to John and pretending I saw nothing out of the way in finding her in the turret.

"But, later, by deduction and confidences half-won, I arrived at some sort of explanation. Ferlie had been dipping deep into the ultra-ancient and ultra-modern volumes of every species of literature which stock the Black Towers library.

"'Do you believe that mankind have lost the power of communicating with one another by thought-transference?' she asked me. 'If they ever had it,' I said, determined not to encourage her.

"But her face checked my inclination to snub.

"'Christ had it,' she said. 'He healed from a distance, and promised that all He did we might do. No one seems to have taken that promise seriously enough to test it—unless perhaps the Christian Scientists.'

"'I'd prefer to rely upon the twopenny post, myself,' I insisted. She shook her head and said, 'That would not be right in my case, Aunt B. I may only struggle to attain the fulfilment of the promise.'

"'With whom do you want to communicate by this unnatural method,' I asked. But she would not tell me. Only by accident I stumbled upon that item.

"Late that same night I heard through my open window a faint sound of somebody crying. It was one of those desperately still star-saturated nights. I was up in an instant and along the corridor without waiting for a candle. Ferlie's room was next to John's. Through his open door I watched her, but this time I did not rush in to put to flight any stray ministering angel who might be in the offing. Cyprian, it is a terrible thing to come, unawares, upon a soul in Gethsemane. What has lain between you two in the past I do not know; what may lie between you in the future I dare not think. But I at my eavesdropping post grew colder and colder. If Ferlie continued much longer to carry this secret burden I was certain she would go out of her mind. And I am convinced that whatever the stereotyped and doubtless to your mind worthy, principles to which you have succumbed in this matter, no man can count himself wholly irresponsible whose name is thus centred in a woman's prayers."

The great car swept forward, increasing speed along a clear stretch of road. Between the occupants for some moments there reigned an unbroken silence.

Then Cyprian spoke, still without moving; his rigidity outlined against the transparent pane.

"How far are we from Black Towers?"

"We pass within thirty miles of it."

"Then...." Their eyes met.

Aunt B.'s head jerked suddenly forward.

"I thought you'd understand." ...

CHAPTER XI

The Autumn twilight was thickening with milky opal reflections when they rolled through the heavy iron gates of the park. Gigantic trees shadowed the curving drive; every now and then sending a swirl of jewelcoloured leaves to join their brothers carpeting the soft turf.

They passed one copper beech, tinted like the understrands of Ferlie's hair. But, though the grounds were obviously well cared-for, nothing could relieve a brooding sense of desolation, due to the over-luxuriant vegetation which darkened the surroundings of an already dark, if beautiful, house.

Well-merited the name, Cyprian thought, as the solid old turret towers rose at last, picked out in inky silhouette against the flaming aftermath of sunset cloud.

Upon the flight of black marble steps a child was standing; a miniature bull's-eye lamp in his hands. He had evidently been trying to light it with the aid of a box of matches which would not strike.

A footman came down the stairs as the car drew up, and his expression of surprise gave way to placid recognition of its lady-occupant.

"Her ladyship said she was expecting you, Madam, but did not think that you would be arriving till Wednesday."

"I have brought a friend of hers with me," Miss Trefusis told him. "Where is she?"

The man did not answer; he had turned back to speak to his colleagues, now gathering about the limousine.

Jardine, the old butler, with the forceful impassive face, informed them that her ladyship should be told. He left them before the hall fire and glided away.

"I always regard him as a sort of Keeper of the Keys," whispered Miss Trefusis, hysterical with fatigue and achievement.

Cyprian took out his watch as if suddenly reminded of something, but he did not look at the time; only at the securing ring of a small gold key dangling from the watch-chain.

"He has been in the Family so many years," went on Aunt Brillianna, "that Ferlie says he believes himself a kind of Influence on the GrevilleMainwaring destinies."

The child, whose lamp one of the footmen had lighted now, passed through the hall, carrying it carefully. She called to him.

"Come here, John. Don't you know me to-day? Where is your mother?"

He was advancing towards her but checked himself at the inquiry.

"She said not to take no one up the stairs," he informed them with emphasis. "She are having a key made for the door."

He spoke clearly and with only a slight slurring of the S's which could not be described as a lisp but which gave a more human childishness to his unnatural gravity.

Scarcely concealing the effort it cost, Cyprian raised his head and looked at him. Yes. That hair, also, would have flaunted a rebellious crop of sunny waves had they been allowed to grow. He was too white and fraillooking for prettiness but it was with his mother's wide steady gaze that he returned Cyprian's survey which shifted first.

"Nonsense!" said Aunt B. on a low quaver of amusement, "you can't afford to be jealous of Ferlie's son."

Cyprian replied with a vexed laugh,

"Don't read me so clearly out loud. There are some things a man wishes to hide from himself."

She rose, holding out her hand to John.

"Take us to the foot of the stairs, laddie. I do not want you to go up. We may hear Mother coming down."

John hesitated, but, finally, led the way, vouchsafing one piece of news as he pushed back a nail-studded door.

"I have got a tricycle."

It gave Aunt B. her opening. At the foot of the stairs she turned and gestured to Cyprian, standing behind her.

"The key is not yet made to lock you out," she reminded him in an undertone. And aloud to John, "Show me the tricycle."

Was it not yet made? Cyprian asked himself; or, rather, would the lock be too rusty for it to turn, after such long disuse?

Up and always up. And Ferlie climbed thus, daily, the ascent of her lonely Purgatory for the little hour when she might unmask her suffering, and face the truth that her soul was exceeding heavy.

It was a long time to Cyprian before he stood outside that door. It had a heavy looped iron handle like that which turns the latch of a church.

He paused but heard no sound within.

His hand grasping the ring was steady; the oaken panels swung back easily under that strong pressure.

She was leaning against the Gothic window, and the lingering touch of long sun-fingers rested upon her head in comforting caress.

He spoke her name in a whisper. Her head turned slowly but she did not move. So often had he come to her at this time and, so often, faded back into the gloaming.

His shoulders relaxed as dawned the explanation for her dumb acceptance of his presence. He crossed the threshold with outstretched hands.

"My dear ... Oh, my dear..."

She crumpled up in his arms, not unconscious, but sick with shock.

The last red ray withdrew from the turret, leaving them in the gloom of a grave from which resurrection seemed very far away.

The presence of Aunt B. made all the difference to the situation. She effaced herself and entertained John, but lent a more commonplace air to his visit than would have seemed possible, in the circumstances.

The erratic arrivals and departures of Lady Greville-Mainwaring's elderly aunt had ceased to be a matter for comment in the servants' hall. Jardine palpably respected her uncompromising utterances; John met her as

an equal, and Cyprian and Ferlie, at peace in one another's companionship along the garden walks, passionately blessed her in their hearts. She had done wisely in warning Cyprian that Ferlie's appearance must startle him. She wore the look of some Inquisition victim whom the torturer's power had reduced to that exhaustion which ceases to feel. Instead of the limp body, incapable of further suffering, Ferlie betrayed a like condition of soul.

"Was this change of religion any use?" Cyprian asked her.

Her eyes might swiftly have become sightless as she replied, "There was no 'change.' It had to be that or Father's way of thinking. And I could not trust my small strength with Father's self-sufficient philosophy. This represented one more cage, but a necessary one, if I was to obtain enough self-discipline to enable me to live. You know I am not being dramatic. Sometimes I thought of that way out, only it did not seem quite fair to John, until he should be old enough to understand about heredity and choose for himself."

"You—you don't make yourself exactly clear."

"No. Well, never mind! ... Peter, by chance, knocked up against a clever Jesuit. I do admire that much-criticized sect, Cyprian. Their hard logic; their cold positivity of thought. This one thrilled one's sense of humour first by a speech made to a Church of England padre, which, beginning on a note of toleration crashed to conclusion on a chord of glorious bigotry. 'After all,' he assured his vacillating companion, 'We both serve the same Master; you in your way, I in His.'

"Later, this man was discussing the conversion of a well-known statesman with Peter. 'He was too intellectual,' said the Jesuit, 'to be satisfied longer with less than all the Truth his brain could assimilate.' That speech impressed Peter as, doubtless, it was meant to do, with his tendency to brain-worship. He, also, began to be sure that the World's Thinkers, among whom he would like to be numbered some time, must, universally, find the Whole Truth here.

"And you know, Cyprian, he is clever. They did not make the mistake of approaching him on the sentimental, or even the romantically beautiful side,

of the religion. He is certainly a more valuable ally to the Catholic Church than undoctrinal I."

"The thing has not yet interfered with Peter's instinctive love of liberty," Cyprian pointed out. "Whereas, you and I are, surely, threatened by its precepts."

He went no further. Not yet had he broached to her that which he understood to be passing in Aunt Brillianna's mind; more tentatively in his own. But Ferlie smiled with wistful understanding.

"There is no public cause for a divorce, that I know of," she said quietly, "And, apart from Catholicity, isn't divorce rather impossible as a solution for Us?"

She was placing her finger upon something which formed the basis of their mutual pride. They did not give to take back again, whatever the type of altar to which they had dedicated the gift.

The mockery of her marriage-service struck him afresh.... "That theirs may be the love which knows no ending, Whom Thou for evermore doth join in one...."

"Dear," and his voice was vibrant with pain, "How could you ever have imagined that any public vows could unite you to him, who were already part of..."

Habit of mind checked him; Ferlie was braver.

"Of you," she finished steadily.

They walked the whole length of the lawn before she added,

"You did not realize that, Cyprian, while there was time. If you had realized it I should not have been free. There was no time to give you time to weigh your love. When you held back my light seemed clear."

"And I had no light," he said shortly.

"You haven't told me whether you now share these modern views about divorce," she reminded him. "Even the Church you nominally belong to is divided in its opinions on the subject. Its members talk very fluently, and go on their way, self-convinced. Like Peter, who, at nineteen, could talk himself into that sort of convinced state about anything."

"There are exceptional circumstances..." Cyprian began, but she stopped him then.

"And now you are going to do it! No, Cyprian. You must be either 'for' or 'against,' with principle at the back of you. Don't you see that everybody's exceptional circumstances would always be his own? That is how the Individual now dethrones God in favour of himself."

"Ferlie, you forget you have not yet told me your circumstances. And I have a right to know."

He watched her clouded face and waited. Twice she seemed about to speak but the constrained reticence of the past two years still fettered her tongue.

"I have never told anyone," she said huskily. "I don't know how much I ought to tell. I only believe that it may be a divorcing matter, according to Law; if I had not put myself under Catholic discipline."

He placed his hands on her shoulders and pushed her down on to a moss-upholstered bench near which, perched on a pillar, mocked a laughing stone faun.

"You must tell me," he said. And took his place beside her, covering her hand with his own.

Presently, with an obvious effort, she asked,

"You will not have forgotten Muriel Vane?"

His fingers contracted and she paused to reflect that if Cyprian had not remained so true in the abstract to his First Vision he would hardly have

been Cyprian; and her god.

But she could not long mis-read the expression of raw disgust on his face as she lifted hers. It puzzled her.

"Nothing would hurt now, Cyprian—if you knew. She is—not quite normal now. Not since a long time has she——"

"I know all that." His tone was cruelly hard. "For a long while I would not allow myself to believe those rumours.... And once I thought to put her before you! It is that I shall never forget." Even so does a man resent his mistakes on their object instead of on himself.

"Cyprian, don't. Haven't the years taught you compassion?"

He shrugged that view away.

"What compassion is possible, or even right and decent?"

"You may feel inclined to shun a leper but, surely, you would desire to help him, too?"

She surprised him.

"What makes you think of it that way?"

"Experience," said Ferlie, so low that he hardly caught the word.

She braced herself for explanation.

"You once met a woman called Ruth Levine." She went on without heeding his start of acquiescence. "She has been very good to Muriel Vane. Muriel's people separated; then her mother died. Her father took to drugs, or something; they were a queer family, degenerating, like—like so many. And Muriel developed into—what people said. Ruth thought she had foreseen it and might have done something to prevent it happening. I should have imagined that impossible; often it is caused by heredity insanity. Anyhow, she saved Muriel from the usual kind of 'Home.' It is always the woman, Ruth says, who is judged; men so affected can often live undetected or

screened from public criticism.... Ruth knew Clifford before I married him and when I concluded that, for John's sake—if only for that—there must be a complete break between Clifford and myself, she came to ask me to get divorced, as she had cared for him first. She was quite matter-of-fact about it. I told her that I could not dream of using the evidence she offered to supply. I told her that Clifford and I had privately arranged to live apart but that I was a Catholic and it was not in my power to unsay vows once spoken. I told her that I did not think she understood why Clifford ought to be in other hands than those of women. She looked at me as if I were crazy and went away.... I—I don't know any more, Cyprian."

Ferlie's voice had almost vanished. Suddenly her head went down upon her knees and her body shook with dry sobbing.

Cyprian, with half-closed eyes which did not wish to see, was wondering whether he had understood.

She had conjured up dark visions the like of which had rarely crossed his horizon. He was inclined, like many self-sheltered individuals, to blink at the most sinister of Life's shadows, as if by so doing he could blink them out of existence as easily as out of his thoughts.

His inarticulate prayer: "Et ne nos indue as in tentationem!" A wise one with reference to the safety of his individual soul but hardly conducive of expansive sympathy to others.

The horror he experienced in hearing this child, a score of years younger than himself, approaching for commonplace—as indeed they might be elsewhere in the world, for all he cared—issues which, until now, he had always succeeded in pushing far from his own sphere of action, hindered him from pressing her further.

He might never have realized the immensities at stake for her, but that Chance interfered to drive his newly-acquired knowledge home.

At that moment Jardine was seen to be coming across the lawn, a silver salver in his hand.

Cyprian aroused Ferlie in time. When the old butler stood before them, with the telegram, she was presentably calm.

"Mrs. Minchin sent me out with it, your ladyship; it was addressed to her. His lordship wishes her to inform you that he is arriving to-night and would like one of the cars to meet the 8.15." Mrs. Minchin was the housekeeper.

Ferlie took the yellow envelope from the tray and, as she did so, Cyprian wondered whether it were only in his imagination that a look passed between mistress and man, electric with mutual warning.

Just the flash of an eyelid, and Jardine was pursuing his majestic course over the grass, his back-view impervious to criticism and comment. Not until the last glimpse of his black coat-tails had disappeared behind the yew-bushes did Ferlie rise to her feet and face Cyprian beside the laughing faun. Again that illusory sightlessness filmed her dilated pupils. She looked through him and beyond into a blank pall of darkness.

"Cyprian," the voice was dead like her face, "Take me away."

He fancied the half-human leering thing of stone stirred in evil exultation. The twisted weather-beaten features made an unholy contrast to those others of still soft flesh on a level with them.

"I have nothing more to say to you than that," she said, when he did not answer. "I will tell you nothing more. Whether you go with us or not, John and I leave here to-night—in time. You could not trust me five years ago; can you trust me now?"

"It was not you five years ago; it was my own creed that I could not trust."

"But now it is different, Cyprian. You have out-lived one stage of selfmistrust now."

Did man ever arrive beyond the reach of that urging Power in a world peopled with mortal flesh, he wondered.

Strange that, in forcing a decision upon himself concerning Ferlie's future, Cyprian forgot the very existence of Hla Byu and his son. It was not his intention to conceal from Ferlie the temporary loss of will-power which had changed the tenour of his life during the last two years. But the Burmese girl, received in a moment of sick physical weakness and retained in pure apathy of soul, had existed so mistily for the real Cyprian that, the practical arrangements for her safe-keeping concluded, she simply slipped out of the picture. When he did remember her she had become so superfluous among the host of living memories he and Ferlie were storing up that he could not bring himself to recall her, even by speech.

"I know too thoroughly by what means the latent forces of the body can accomplish the spirit's murder"—she was speaking again and he recollected himself—"But you and I have nothing to do with such perishable links. Nor do we require witnesses to ratify a spiritual marriage for which we should not have been prepared without these last enforced years of disciplined control."

She stopped, confronted with his unyielding silence, and, all at once, grew limp and human by that other inhuman watcher in stone. Her shoulders relaxed, bowed and aged beneath their invisible burden.

"I am not playing the part of Eve. It is all right. I promised that you should never need to ask me, a second time, to leave you. I understand. I am going now, alone."

He drew towards her then.

"You are going with me. I am giving you no choice. Do you understand? This decision is mine, not yours. You are going where I shall take you and under whatsoever conditions I lay down, now, and during your whole future. The responsibility is mine; you have got to put your trust in me."

Was it credible that the ripple of breeze through the swaying stalks of a bed of tall Madonna lilies drowned a satyr-laugh of derision?

Standing shoulder to shoulder they made no attempt to touch one another's hands.

So might the Little Saint of Assisi have mythically wedded Poverty, while Chastity and Obedience supported her on either hand.

Said Ferlie, "I have nothing to give you that you have not already. Everything of yours has been guarded safely behind a locked door. And, Cyprian, you have the key."

To Miss Trefusis he outlined his scheme and found her a little dubious.

"But, my dear man, this is the twentieth century. Why not meet this flyby-night lord and arrange matters with modern sanity over a whisky and soda?"

"You are the only modern one of us three," he reminded her, amusedly recognizing that her unusually broad views, contact with which he had once feared for Ferlie, were responsible for their present re-union. "Ferlie tells me that she has no evidence for a divorce, nor can she seek it, in consideration of the Church she has joined."

"Bless my soul!" exclaimed Aunt B., exasperated that any Church should continue to consider joined what she had been at such infinite pains to put asunder. "Surely you, Cyprian, are old enough to smile at sects and Churches! Ferlie would not be true to type if, at her age, a cardinal did not seem too picturesque to be a liar. And, believe me, the Pope was the only safe substitute for you."

"You, surely, are not advocating collusion?" asked Cyprian, tickled, in spite of himself, at this feminine Juggernaut, the wheels of whose commonsense responded to no brake till she had guided them triumphantly past her goal.

"I don't believe there is 'no cause,'" she snapped: "If he is a gentleman he will make one, since he has obviously admitted her right to leave him. It can't affect the child's inheritance. An atom of patience, and the whole affair might be straightened out with a minimum of scandal."

"There is no necessity for even a perfectly respectable scandal," Cyprian assured her. "Ferlie is coming out to Burma with me, to live there as my sister. After a time, the man can get his marriage annulled if he wishes, on the ground of desertion; but that is unlikely to affect us."

Miss Trefusis searched his face with an expression of mingled admiration and incredulity on her own.

"Yes, I am afraid you mean what I think you mean," she said. "You are more of a child than she is, and I'd like to shake you. I'd almost rather you eloped healthily—without a new wedding-ring."

"I am so sorry to disappoint you," Cyprian said.

She laid a hand on his arm which he immediately imprisoned in his.

"Excelsior, then! Go and freeze to death upon your mountain top, both of you. I have interfered enough in bringing your bodily forms together. I dare not dig inquisitive fingers into your souls."

It was arranged that her chauffeur should return with them to the coast so as to render negligible the chance of delay if any suspicion were aroused.

"But there is no earthly reason why Clifford should want to argue it out with me," said Ferlie.

At the last moment she gave way to a curious attack of nerves, and again Cyprian suspected that the incident was due to some secret reminder conveyed to her by Jardine.

From the step of the limousine, into which the sleeping John had been carried, she let go Cyprian's arm and darted back up the steps.

"Aunt B.! You will go home yourself to-night, won't you? Take the Daimler!"

"Hurry, child! It is twenty minutes to eight. Yes. I am all ready to start, and you can trust me to take care of myself."

"Come, Ferlie, don't waste any more time."

She ignored even that quiet voice, looking uncertainly at Jardine who dropped his eyes with an almost imperceptible movement of his head.

"You will see my aunt comfortably off, Jardine?"

"Ferlie, don't be foolish! Since when have I needed dry-nursing? Make her get in, Cyprian. There, darling! There. Shut the door. That's right, Cyprian. Write to me, both of you. What is she shaking about? I won't let Clifford eat me in any case. Good-bye. Look after her, Cyprian. Good-bye! Good-bye!"

They were whirled out of her sight.

Whereupon, the temptation of Eve descended upon Aunt B.

She had never met this husband of Ferlie's and, on reconsidering that fact, it seemed that Ferlie herself had always intervened in the past to prevent a meeting. There was really no need for her to hurry home to-night; she might even serve the fugitives best by staying to produce some plausible reason for Ferlie's sudden "journey to town."

Jardine, to her amazement, was respectfully inhospitable in his opposition to this proposed change of plan. He made it unmistakably clear that he wished to be rid of her. And the more insistently he conveyed that impression, the more obstinately did Miss Trefusis desire to see the owner of Black Towers.

To settle the matter out of hand she went to her room, unpacked a dinner dress of silver-grey velvet, and came downstairs wearing it and an assured

air which discouraged argument.

Said Jardine to her in the hall where he was hovering like a distressed bat among the chain-mailed ancestors.

"It is to be expected that his lordship will dine in his own apartments, Madam. I have not put off the dinner hour to suit his late arrival."

Therefore, at 8.15 precisely, Aunt B. found herself frustrated thus far, at the end of the long table.

Half-way through the meal came the sounds of arrival: the footman's hurrying steps and a man's voice in the hall.

She strained her ears, but silence soon followed the retreating feet and then Jardine came in to ask if she would have coffee on the terrace.

"Too chilly," was her cross verdict, and he agreed that the little drawingroom and a fire would be more comfortable.

Even after she had drunk the coffee and was immersed in the newspaper, she remained aware of the old servant's flitting presence. He appeared to be finding matters to occupy him in the small drawing-room and only after she had twice looked up inquiringly over the printed page did he make reluctantly for the door.

She sat on when the paper, restlessly devoured, had slipped from her knees to the floor. Soft radiance glowed about her through orange silk shades, etherealizing the dignified feminine figure with its close-fitting crown of silvery hair. The features, in repose not unlike Ferlie's, were attractively gentle. She leant back in the dark tapestried chair and thought of the lovers, of the long trail which lay before them, of the spiritual courage supporting their rare decision. Could a man and a woman live under such conditions, loving as these two loved?

And something told her that it was just because they so loved that the improbable became possible.

If they failed that Utopian ideal in the end— She broke off her reflections with a sigh.

"Who is to judge?" she asked aloud of the flames on the open hearth. "Who is to judge These, or Any?"

A man on the terrace, rolling a cigarette with uncertain fingers, heard the quiet question and paused in his occupation. His eyes glittered oddly over the flickering match, just struck, and the face, as he lifted it starwards, was not unlike the face of the deriding faun, aged by the battering years into a very surely alive satyr.

Cold, suffocating darkness in the hall, and the comforting impassive bulk of old Jardine.

Later, a square of corpse-coloured light, and the black marble steps making a row of ebony mirrors for the waning moon. Beyond them, the blurred lines of Ferlie's Daimler, heralding escape to the dainty simplicity of the lavender-scented garden and rooms sweet with the pot-pourri of clean sane memories.

Finding her voice, she turned fiercely upon the man supporting her trembling descent.

"And you knew—and remained silent, while she was facing That!"

His slow gesture was controlled but unyielding.

"For forty years, Madam, I have served the Greville-Mainwarings. As their like dies out so does my like die out which has learnt the lesson of silence."

He closed the door of the car upon her, adding with cold dignity,

"Her ladyship chose to become a Greville-Mainwaring."

CHAPTER XII

"Do you know what I think, Cyprian?" asked John, lost in admiration for the ingenuity which had lined the channel leading from his sand-castle with practically watertight slates and stones, "I think you've got a Brain."

"So that's what your mother tells Miss Trefusis of you," deduced Cyprian. "By the way, I have an uneasy suspicion that she intended you to address me as 'Uncle.'"

"What for?"

"As a mark of well-deserved respect, I fancy, and in token of my thinning locks."

"You don't look like 'uncle.'"

"Oh, I don't know. Considering I had reached a man's estate when your mother was not much higher than you——"

"Did Mother call you 'Uncle' then?"

"Just you ask her if not why not," advised Cyprian.

John mused awhile.

"Anyhow, I won't," he decided.

"Won't ask her?"

"Will call you by your real name."

"That's what she said," Cyprian admitted. "But, as man to man, John, I must warn you that she will probably have the last word in the matter, even

if it is an inconsistent one. I have known her longer than you have."

"But I have known her most," returned John in some agitation. "She was my mother first."

Cyprian took warning.

"God bless you, yes. She would be the first to admit it. Go your rebel way, then, and get the better of the woman. I shan't interfere. I have my own troubles."

The conversation took place on a sunny portion of the Brittany coast where Ferlie had, for some weeks, been trustfully waiting for John and Cyprian to decide that they liked one another. Neither of them possessing gaily expansive natures the discovery took time.

A neutrality pact had been sealed earlier on this particular afternoon when Cyprian, armed with an offering of peppermint rock, having fallen unawares into the well of sea-water outside John's castle, had aroused in himself a throng of dimly ecstatic recollections and intimations of the Immortality of Childhood, as the poet simply puts it, and so flung himself whole-heartedly into the business of constructing an aqueduct, a smouldering ambition of his childhood, ever frustrated by the inopportune interference of the old and wise....

"You," said John presently, touched by his conscientious absorption, "may have the 'nother stick of peppermint rock when you've done."

"If it's to save your life I will accept it but I feel it only honest to confess that I am not allowed to eat sweets between meals."

"Neither am I when Mother comes out with us.... I want Mother."

"So do I want her. But I am man enough to put the aqueduct before the yearnings of my softer nature."

"Well, but you don't want to be sick."

Cyprian dropped the spade to look at him.

"What on earth are we going to do about it?" he asked at length. John showed him.

"And now," said Cyprian bitterly, "as, prompted by a kind and noble heart, I bought you the beastly stuff, I suppose she'll blame me!"

"I won't tell," John assured him faintly. And didn't.

Almost immediately after this incident sealing his position in John's world, Cyprian received news of his Company's affiliation to a branch of mines in another district, and of his own transfer to a station more or less populated.

It meant a fresher beginning for himself and Ferlie in Burma than if he had remained under the eye of old acquaintances. He would be now, practically, in a managing position with much sedentary office-work in head-quarters and only a limited amount of inspecting.

But Ferlie and he would find it difficult to isolate themselves from their neighbours, even if Cyprian's reputation as a recluse preceded him and Ferlie's advertised one as a widow.

Fortunate for her now that the Burma Season had never materialized before her father's enforced retirement; for, though Burma is not the size of a London suburb, news there travels in more persistent circles.

As things were, the few remaining officials who had known her father well enough to remember he had a daughter would hardly connect the knowledge with the advent of "Mrs. Clifford" to keep house for a brother, up-country, who was not a Member of the Services. Cyprian felt that the change might result in a more normal and wholesome life for Ferlie, at her age, than he could originally have offered her, and she owned to rejoicing in the prospect of medical aid should John get ill.

The first time she saw their bungalow of dark crimson wood, with its shingled roof and white painted verandah, the porch trembled beneath the

red tubes of blossoming kuskwalis, the subtle velvet scent of which mingled with the thick creamy sweetness pouring from the waxen stars of two leafless frangipani trees in the garden.

"Cyprian, how beautiful!" as the loose crowns showered over her with every gust of breeze. "I wonder why there is something sorrowful in the message their scent holds for me."

But he remembered that the lilies sentinelling the church for Ferlie's wedding had been numerous enough to saturate the air with a similar sickly-sweet fragrance.

Since they were seeking forgetfulness in these surroundings he said nothing.

The radiance of their life together during the next few months was an amazement to his unintrospective soul.

He had sometimes wondered on what foundation rested Ferlie's invincible faith that, in this purely spiritual companionship, they would not be tempted beyond their strength to trample the Code.

He did not know that, since John's birth and her husband's development in a direction which made normal married life with him impossible, Ferlie, with her passion for complete understanding unclouded by merciful ignorance, had delved into strange formidably-backed volumes in her efforts to tear out by the roots the tragedy which had shattered her innocence. She had shrunk at first towards asceticism as an answer to the racking question "What shall we do to be saved?"—from Self; a mankind weak and bewildered but sub-conscious, nevertheless, of an attainable state of grace synonymous with Immortality.

But, with Cyprian dwelling still in her heart, and refusing to be ejected even during this complete reaction, she had been forced to seek a more modified code than that of the professed nun.

Quite by chance, she discovered it in Chrysostom's outcry against the anti-pagan, but, as he considered it, also the anti-Christian, custom, which

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