![978-1-491-90577-7
[LSI]
Getting Started with Impala
by John Russell
Copyright © 2016 Cloudera, Inc. All rights reserved.
Printed in the United States of America.
Published by O’Reilly Media, Inc., 1005 Gravenstein Highway North, Sebastopol, CA 95472.
O’Reilly books may be purchased for educational, business, or sales promotional use. Online editions are
also available for most titles (http://safaribooksonline.com). For more information, contact our corporate/
institutional sales department: 800-998-9938 or corporate@oreilly.com.
Editor: Marie Beaugureau
Production Editor: Kristen Brown
Copyeditor: Gillian McGarvey
Proofreader: Linley Dolby
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Illustrator: Rebecca Demarest
October 2014: First Edition
Revision History for the First Edition
2014-09-19: First Release
2016-04-25: Second Release
See http://oreilly.com/catalog/errata.csp?isbn=9781491905777 for release details.
The O’Reilly logo is a registered trademark of O’Reilly Media, Inc. Getting Started with Impala, the cover
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While the publisher and the author have used good faith efforts to ensure that the information and
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or reliance on this work. Use of the information and instructions contained in this work is at your own
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licenses or the intellectual property rights of others, it is your responsibility to ensure that your use
thereof complies with such licenses and/or rights.](https://image.slidesharecdn.com/27645337-250518004132-ff8b9ec6/85/Getting-Started-With-Impala-Interactive-Sql-For-Apache-Hadoop-1st-Edition-John-Russell-8-320.jpg)
Getting Started With Impala Interactive Sql For Apache Hadoop 1st Edition John Russell
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- 8. 978-1-491-90577-7 [LSI] Getting Started with Impala by John Russell Copyright © 2016 Cloudera, Inc. All rights reserved. Printed in the United States of America. Published by O’Reilly Media, Inc., 1005 Gravenstein Highway North, Sebastopol, CA 95472. O’Reilly books may be purchased for educational, business, or sales promotional use. Online editions are also available for most titles (http://safaribooksonline.com). For more information, contact our corporate/ institutional sales department: 800-998-9938 or corporate@oreilly.com. Editor: Marie Beaugureau Production Editor: Kristen Brown Copyeditor: Gillian McGarvey Proofreader: Linley Dolby Interior Designer: David Futato Cover Designer: Ellie Volkhausen Illustrator: Rebecca Demarest October 2014: First Edition Revision History for the First Edition 2014-09-19: First Release 2016-04-25: Second Release See http://oreilly.com/catalog/errata.csp?isbn=9781491905777 for release details. The O’Reilly logo is a registered trademark of O’Reilly Media, Inc. Getting Started with Impala, the cover image, and related trade dress are trademarks of O’Reilly Media, Inc. While the publisher and the author have used good faith efforts to ensure that the information and instructions contained in this work are accurate, the publisher and the author disclaim all responsibility for errors or omissions, including without limitation responsibility for damages resulting from the use of or reliance on this work. Use of the information and instructions contained in this work is at your own risk. If any code samples or other technology this work contains or describes is subject to open source licenses or the intellectual property rights of others, it is your responsibility to ensure that your use thereof complies with such licenses and/or rights.
- 9. Table of Contents Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii 1. Why Impala?. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 Impala’s Place in the Big Data Ecosystem 1 Flexibility for Your Big Data Workflow 2 High-Performance Analytics 3 Exploratory Business Intelligence 3 2. Getting Up and Running with Impala. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 Installation 5 Connecting to Impala 6 Your First Impala Queries 7 3. Impala for the Database Developer. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 The SQL Language 11 Standard SQL for Queries 12 Limited DML 12 No Transactions 13 Numbers 13 Recent Additions 14 Big Data Considerations 15 Billions and Billions of Rows 15 HDFS Block Size 17 Parquet Files: The Biggest Blocks of All 17 How Impala Is Like a Data Warehouse 18 Physical and Logical Data Layouts 19 The HDFS Storage Model 19 Distributed Queries 20 iii
- 10. Normalized and Denormalized Data 22 File Formats 23 Text File Format 23 Parquet File Format 25 Getting File Format Information 26 Switching File Formats 27 Aggregation 27 4. Common Developer Tasks for Impala. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 Getting Data into an Impala Table 29 INSERT Statement 30 LOAD DATA Statement 30 External Tables 31 Figuring Out Where Impala Data Resides 31 Manually Loading Data Files into HDFS 32 Hive 32 Sqoop 33 Kite 33 Porting SQL Code to Impala 34 Using Impala from a JDBC or ODBC Application 35 JDBC 35 ODBC 36 Using Impala with a Scripting Language 36 Running Impala SQL Statements from Scripts 36 Variable Substitution 36 Saving Query Results 37 The impyla Package for Python Scripting 37 Optimizing Impala Performance 38 Optimizing Query Performance 39 Optimizing Memory Usage 40 Working with Partitioned Tables 42 Finding the Ideal Granularity 42 Inserting into Partitioned Tables 43 Adding and Loading New Partitions 44 Keeping Statistics Up to Date for Partitioned Tables 45 Writing User-Defined Functions 47 Collaborating with Your Administrators 47 Designing for Security 48 Anticipate Memory Usage 48 Understanding Resource Management 48 Helping to Plan for Performance (Stats, HDFS Caching) 49 Understanding Cluster Topology 50 iv | Table of Contents
- 11. Always Close Your Queries 51 5. Tutorials and Deep Dives. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 Tutorial: From Unix Data File to Impala Table 53 Tutorial: Queries Without a Table 55 Tutorial: The Journey of a Billion Rows 57 Generating a Billion Rows of CSV Data 57 Normalizing the Original Data 63 Converting to Parquet Format 67 Making a Partitioned Table 71 Next Steps 75 Deep Dive: Joins and the Role of Statistics 76 Creating a Million-Row Table to Join With 76 Loading Data and Computing Stats 77 Reviewing the EXPLAIN Plan 78 Trying a Real Query 81 The Story So Far 85 Final Join Query with 1B x 1M Rows 86 Anti-Pattern: A Million Little Pieces 86 Tutorial: Across the Fourth Dimension 88 TIMESTAMP Data Type 88 Format Strings for Dates and Times 88 Working with Individual Date and Time Fields 89 Date and Time Arithmetic 90 Let’s Solve the Y2K Problem 91 More Fun with Dates 94 Tutorial: Verbose and Quiet impala-shell Output 95 Tutorial: When Schemas Evolve 96 Numbers Versus Strings 98 Dealing with Out-of-Range Integers 99 Tutorial: Levels of Abstraction 102 String Formatting 102 Temperature Conversion 103 Tutorial: Subqueries 103 Subqueries in the FROM Clause 104 Subqueries in the FROM Clause for Join Queries 104 Subqueries in the WHERE Clause 105 Uncorrelated and Correlated Subqueries 108 Common Table Expressions in the WITH Clause 109 Tutorial: Analytic Functions 111 Analyzing the Numbers 1 Through 10 112 Running Totals and Moving Averages 120 Table of Contents | v
- 12. Breaking Ties 121 Tutorial: Complex Types 123 ARRAY: A List of Items with Identical Types 125 MAP: A Hash Table or Dictionary with Key-Value Pairs 127 STRUCT: A Row-Like Object for Flexible Typing and Naming 128 Nesting Complex Types to Represent Arbitrary Data Structures 130 Querying Tables with Nested Complex Types 132 Constructing Data for Complex Types 132 vi | Table of Contents
- 13. Introduction Cloudera Impala is an open source project that opens up the Apache Hadoop soft‐ ware stack to a wide audience of database analysts, users, and developers. The Impala massively parallel processing (MPP) engine makes SQL queries of Hadoop data sim‐ ple enough to be accessible to analysts familiar with SQL and to users of business intelligence tools, and it’s fast enough to be used for interactive exploration and experimentation. From the ground up, the Impala software is written for high performance of SQL queries distributed across clusters of connected machines. Who Is This Book For? This book is intended for a broad audience of users from a variety of database, data warehousing, or Big Data backgrounds. It assumes that you’re experienced enough with SQL not to need explanations for familiar statements such as CREATE TABLE, SELECT, INSERT, and their major clauses. Linux experience is a plus. Experience with the Apache Hadoop software stack is useful but not required. This book points out instances where some aspect of Impala architecture or usage might be new to people who are experienced with databases but not the Apache Hadoop software stack. The SQL examples in this book start from a simple base for easy comprehension, then build toward best practices that demonstrate high performance and scalability. Conventions Used in This Book The following typographical conventions are used in this book: Italic Indicates new terms, URLs, email addresses, filenames, and file extensions. vii
- 14. Constant width Used for program listings, as well as within paragraphs to refer to program ele‐ ments such as variable or function names, databases, data types, environment variables, statements, and keywords. Constant width bold Shows commands or other text that should be typed literally by the user. This style is also used to emphasize the names of SQL statements within paragraphs. Constant width italic Shows text that should be replaced with user-supplied values or by values deter‐ mined by context. This element signifies a tip or suggestion. This element signifies a general note. This element indicates a warning or caution. Using Code Examples Supplemental material (code examples, exercises, etc.) is available for download at https://github.com/oreillymedia/get-started-impala. This book is here to help you get your job done. In general, if example code is offered with this book, you may use it in your programs and documentation. You do not need to contact us for permission unless you’re reproducing a significant portion of the code. For example, writing a program that uses several chunks of code from this book does not require permission. Selling or distributing a CD-ROM of examples from O’Reilly books does require permission. Answering a question by citing this book and quoting example code does not require permission. Incorporating a signifi‐ cant amount of example code from this book into your product’s documentation does require permission. viii | Introduction
- 15. We appreciate, but do not require, attribution. An attribution usually includes the title, author, publisher, and ISBN. For example: “Getting Started with Impala by John Russell (O’Reilly). Copyright 2016 Cloudera, Inc., 978-1-491-90577-7.” If you feel your use of code examples falls outside fair use or the permission given above, feel free to contact us at permissions@oreilly.com. Safari® Books Online Safari Books Online is an on-demand digital library that deliv‐ ers expert content in both book and video form from the world’s leading authors in technology and business. Technology professionals, software developers, web designers, and business and crea‐ tive professionals use Safari Books Online as their primary resource for research, problem solving, learning, and certification training. Safari Books Online offers a range of plans and pricing for enterprise, government, education, and individuals. Members have access to thousands of books, training videos, and prepublication manuscripts in one fully searchable database from publishers like O’Reilly Media, Prentice Hall Professional, Addison-Wesley Professional, Microsoft Press, Sams, Que, Peachpit Press, Focal Press, Cisco Press, John Wiley & Sons, Syngress, Morgan Kauf‐ mann, IBM Redbooks, Packt, Adobe Press, FT Press, Apress, Manning, New Riders, McGraw-Hill, Jones & Bartlett, Course Technology, and hundreds more. For more information about Safari Books Online, please visit us online. How to Contact Us Please address comments and questions concerning this book to the publisher: O’Reilly Media, Inc. 1005 Gravenstein Highway North Sebastopol, CA 95472 800-998-9938 (in the United States or Canada) 707-829-0515 (international or local) 707-829-0104 (fax) We have a web page for this book, where we list errata, examples, and any additional information. You can access this page at http://bit.ly/get-started-impala. To comment or ask technical questions about this book, send email to bookques‐ tions@oreilly.com. Introduction | ix
- 16. For more information about our books, courses, conferences, and news, see our web‐ site at http://www.oreilly.com. Find us on Facebook: http://facebook.com/oreilly Follow us on Twitter: http://twitter.com/oreillymedia Watch us on YouTube: http://www.youtube.com/oreillymedia Content Updates March 30, 2016 This update to the first edition includes details and examples for the following new features, added during the Impala 2.0 through 2.4 releases: • Subqueries in the WHERE clause. See “Tutorial: Subqueries” on page 103. • Analytic functions. See “Tutorial: Analytic Functions” on page 111. • Incremental statistics. See “Keeping Statistics Up to Date for Partitioned Tables” on page 45. • Complex types. See “Tutorial: Complex Types” on page 123. • Submission of Impala to the Apache Incubator. The official name is no longer Cloudera Impala; now it is Apache Impala (incubating). Although Impala was always Apache-licensed, now it has been submitted as an Apache project and is beginning to use Apache Software Foundation (ASF) infrastructure and pro‐ cesses. See the incubator website, where you can find the wiki, mailing lists, JIRA issue tracker, and git repository. • Some notes about Impala integration with Kudu (currently, still in a pre-release phase). The Kudu integration will add UPDATE and DELETE statements to the Impala repertoire, for Kudu tables only. At the moment, you run Kudu alongside a fork of Impala that has the extra statements and other Kudu support. x | Introduction
- 17. Time Marches On, and So Do Release Numbers Traditionally, this book has referred to Impala releases by their original numbering scheme in the 1.x and 2.x series. Since Impala 2.0, tight Impala integration with the Cloudera CDH 5 distribution has made the Impala release number synonymous with specific CDH release numbers. Under the governance of the Apache Soft‐ ware Foundation, the Impala release numbers will likely become prominent again, as the reference point for contributors and pack‐ agers. For your convenience, here is a quick reference for the corre‐ sponding levels: • Impala 2.0 = CDH 5.2 (subquery enhancements, analytic func‐ tions, VARCHAR and CHAR types, smaller Parquet block size, GRANT and REVOKE) • Impala 2.1 = CDH 5.3 (COMPUTE INCREMENTAL STATS for par‐ titioned tables, small-query optimization, stream decompres‐ sion for gzipped text) • Impala 2.2 = CDH 5.4 (automatic log rotation, beta support for Amazon S3, lots of TIMESTAMP improvements) • Impala 2.3 = CDH 5.5 (complex data types STRUCT, ARRAY, and MAP, TRUNCATE TABLE, optimizations for non-Impala Parquet files, lots of new built-in functions) • Impala 2.4 = CDH 5.6 (support for the EMC DSSD storage appliance; otherwise, the same as Impala 2.3 / CDH 5.5) Acknowledgments I have to start by acknowledging the vision and execution of the Impala development team, led by Marcel Kornacker. I have learned a lot from them—especially Justin Erickson, Alex Behm, Lenni Kuff, Alan Choi, and Nong Li—that has made it into this book. Thanks to all the Impala team members and to Gwen Shapira, Mark Grover, Kate Ting, and Uri Laserson for their feedback and insights on my drafts. Going a little further back, I’ve been lucky to be able to consult and collaborate with really good individuals and teams at each stage and transition in my career. Thanks to James Hamilton who convinced me to switch from programming languages to the database track all those years ago at IBM. Thanks to the late Mark Townsend at Ora‐ cle for many insights about the database industry. Thanks to Ken Jacobs who helped me switch into the open source group at Oracle, and the InnoDB team under Calvin Sun and later Sunny Bains for being great to work with and teaching me database internals. Thanks to Mike Olson and Justin Kestelyn at Cloudera for showing me the right way for a small company to tackle the enterprise software market, and to do Introduction | xi
- 18. developer and community outreach. Thanks to Paul Battaglia, Jolly Chen, and Frank Liva for building and supporting the Cloudera technical publications department. Last but not least, this book would not be possible if not for my wonderful and sup‐ portive wife, Lotus Goldstein. xii | Introduction
- 19. CHAPTER 1 Why Impala? The Apache Hadoop ecosystem is very data-centric, making it a natural fit for data‐ base developers with SQL experience. Much application development work for Hadoop consists of writing programs to copy, convert or reorganize, and analyze data files. A lot of effort goes into finding ways to do these things reliably, on a large scale, and in parallel across clusters of networked machines. Impala focuses on making these activities fast and easy, without requiring you to have a PhD in distributed com‐ puting, learn a lot of new APIs, or write a complete program when your intent can be conveyed with a single SQL statement. Impala’s Place in the Big Data Ecosystem The Cloudera Impala project arrives in the Big Data world at just the right moment. Data volume is growing fast, outstripping what can be realistically stored or pro‐ cessed on a single server. The Hadoop software stack is opening that field up to a larger audience of users and developers. Impala brings a high degree of flexibility to the familiar database ETL process. You can query data that you already have in various standard Hadoop file formats (see “File Formats” on page 23). You can access the same data with a combination of Impala and other Hadoop components such as Apache Hive, Apache Pig, and Clou‐ dera Search without duplicating or converting the data. When query speed is critical, the Parquet columnar file format makes it simple to reorganize data for maximum performance of data warehouse-style queries. Traditionally, Big Data processing has resembled batch jobs from the mainframe era where unexpected or tough questions required running jobs overnight or all week‐ end. The goal of Impala is to express even complicated queries directly with familiar SQL syntax, running fast enough that you can get an answer to an unexpected ques‐ 1
- 20. tion in seconds or at most a few minutes. We refer to this human-scale type of responsiveness as “interactive.” For users and business intelligence tools that speak SQL, Impala brings a more effec‐ tive development model than writing a new Java program to handle each new kind of analysis. Although the SQL language has a long history in the computer industry, with the combination of Big Data and Impala, it is once again cool. Now you can write sophisticated analysis queries using natural expressive notation, the same way Perl mongers do with text-processing scripts. You can interactively tra‐ verse large data sets and data structures, like a Pythonista inside the Python shell. You can avoid memorizing verbose specialized APIs; SQL is like a RISC instruction set that focuses on a standard set of powerful commands. When you do need access to API libraries for capabilities such as visualization and graphing, you can access Impala data from programs written in languages such as C++, Java, and Python through the standard JDBC and ODBC protocols. You can also take advantage of business tools that use SQL behind the scenes but don’t require you to code SQL directly. For example, you can use traditional business intelligence tools such as IBM Cognos, SAP Business Objects, and MicroStrategy, as well as the new generation of data discovery tools such as Tableau. Flexibility for Your Big Data Workflow Impala integrates with existing Hadoop components, security, metadata, storage management, and file formats. You keep the flexibility you already have with these Hadoop strong points and add capabilities that make SQL queries much easier and faster than before. With SQL, you can turn complicated analysis programs into simple, straightforward queries. To help answer questions and solve problems, you can enlist a wide audience of analysts who already know SQL or the standard business intelligence tools built on top of SQL. They know how to use SQL or BI tools to analyze large data sets and how to quickly get accurate answers for many kinds of business questions and “what if” scenarios. They know how to design data structures and abstractions that let you per‐ form this kind of analysis both for common use cases and unique, unplanned scenar‐ ios. The filtering, calculating, sorting, and formatting capabilities of SQL let you delegate those operations to the Impala query engine, rather than generating a large volume of raw results and coding client-side logic to organize the final results for presentation. Impala embodies the Big Data philosophy that large data sets should be just as easy and economical to work with as small ones. Large volumes of data can be imported instantaneously, without any changes to the underlying data files. You have the flexi‐ 2 | Chapter 1: Why Impala?
- 21. Random documents with unrelated content Scribd suggests to you:
- 22. "No! I hate books!" replied Felix: "they're awful stupid things. I never read if I can help it. I have more than all the reading I want at school; and I don't go to school when I don't want to, either." Mrs. Le Bras smiled to herself. "How often do you go to school, Felix?" she inquired. "Two or three times a week. I go when I can't think of any thing else to do." "Then, as you can't think of any thing else to do this evening, why not read a little while? that will help to pass away the time." "No! I don't want to read! what do I care about folks in Iceland? It's summer now, and I want to know what folks are doing in summer." "I've got a book that tells how some boys had a garden in summer, and sold vegetables enough to buy all the sleds and skates and caps and mittens they needed for the next winter," said Johnny. "Oh, ho! I can have all such things without having a garden." "But they couldn't, and it's real interesting to read how they managed their little farm." "Farm? I thought you said it was a garden." "It was such a large garden that they called it their farm: it was an acre of ground." "How much is an acre?" "You know how many acres there are in the park?" "How should I know?" "You know it is a quarter of a mile on each side, don't you?" "What of that?" "That makes a quarter of a mile square, don't it?" "I don't know."
- 23. "And it makes a quarter of a square mile." "Well, what of that?" "You know how many acres there are in a square mile, don't you?" "Of course I don't! Why should I?" "Haven't you learned square measure at school?" "Oh! I went past that long ago. I'm over in percentage." "Then, you know that six hundred and forty acres make a square mile." "No, I don't remember any thing about it. I don't expect to remember a thing after I've been past it a little while, and I never do: so I don't see what's the use of learning books at all." "And if there are six hundred and forty acres in one square mile," continued Johnny, "in a quarter of a square mile there would be one-fourth of that, which is one hundred and sixty acres." "Why, if there are that many acres in the park, one acre wouldn't be any thing," replied Felix. "It isn't a large park at all." Johnny laughed as he replied, "Isn't our yard of pretty good size?" "Yes." "Well, our yard hasn't a quarter of an acre in it, I am sure. Let's measure it to-morrow, and see just what part of an acre there is in it." "How can you tell?" replied Felix. "Why, don't you know?" replied Johnny. "No. How did you learn how?" "Why, by studying square measure at school."
- 24. "I guess your schools are different from ours, then: I didn't learn any thing but the table, and how to do a few sums; and just as soon as I had learned that, I forgot all about it!—I say, I can't stand this! I'll go and call Clyde in, and have a good time with him." Clyde had been in so many times, putting his muddy paws upon the furniture and her delicate dress, that Mrs. Le Bras was dismayed at this announcement. "I think you will enjoy yourself better with Clyde out on the platform," she suggested. "Come, Johnny, let's go out, then," said Felix. "I'll show you some of Clyde's tricks. He's a trained dog." "Can't I go?" said Sue. "Yes, come along if you want to; but I ain't used to having girls tagging me around." At first Sue was a little provoked, and thought she would not go; but she was so fond of romping, that she soon followed the boys, saying to her mother,— "Johnny will have to romp now, whether he wants to or not." "Poor Johnny!" sighed Mrs. Le Bras. Presently Mr. Le Bras came in; and his wife told him how restless and out of humor Felix had been, and said she could not imagine what they were to do with him, especially evenings, if they tried to be at all particular where he was, and what company he kept. "We must manage it somehow," replied Mr. Le Bras thoughtfully; "and I cannot have you and Johnny fretted either." "I don't know but I had better go to the cottage, whether you can go or not," continued Mrs. Le Bras; "for then he and Clyde will
- 25. wear out and soil Louis' furniture instead of ours. Clyde has nearly ruined my dress already, by jumping up upon me in his good- natured way; and I have been around trying to get stains off of the upholstering of the chairs. As for Sue, I cannot pretend to dress her up at all nicely while the dog is around; and I know it frets Johnny very much to have the mud-stains on his new drab suit. If we were at the seaside, the children could dress in common clothes, and there would be more harmless outdoor amusements." "It will never do for you to take the whole charge of that boy: it would make you ill. He must be under the eye of a man; I will see to him: and as for Clyde, I will soon settle him. I hope to be able to leave my business a while by the first of August, and then we will go to the cottage: by coming back for a few days at a time, now and then, I think I can stay some weeks; and whenever I come back, I shall bring Felix with me, unless he has greatly improved." Just then Johnny came in, and asked his father if he would let him take his large tape-measure. "What do you want it for?" replied Mr. Le Bras. "I want to show Felix how to find out what part of an acre there is in our yard." "Hasn't he learned enough arithmetic to do that himself?" "No, sir: he's been over as far as I have, but he says he don't know any thing about square measure." "I'll warrant!" replied Mr. Le Bras, taking the measure from one of the drawers under the library-shelves, and handing it to Johnny. When Johnny reached the garden again, he found Felix on the roof of the shed. "Come down, and help me measure, Felix," he said.
- 26. "No," replied Felix: "I'll sit up here, and see you do it." "Oh! that's the kind of a surveyor you'll be," replied Johnny; "you'll survey from a distance: but this is ever so much more interesting. Come, Sue, you hold the measure for me, and I'll measure the width of the yard first. Stand back there, and keep the measure close to the fence; and when I say 'Come,' bring it to me." As it was getting pretty dark, Felix could not see much except Johnny's and Sue's forms as they moved about. Having measured the width of the yard, Johnny measured the length. "It is three times as long as it is broad," he announced. "I could have told that without measuring," returned Felix scornfully. "Arithmetic isn't of any use at all." "You had better come down before it gets any darker," said Johnny, "or you may fall." "Fall! Oh, ho! I guess not! I ain't a baby." "I'm going in now, to reckon this out," said Johnny. "Seventy- five feet wide, and two hundred and twenty-five feet long, or twenty-five yards wide, and seventy-five yards long. It will be easiest to find the square yards." "How do you find the square yards," demanded Felix. "Oh! I know that," remarked Sue; "just multiply the yards long by the yards wide: don't you, Prof.?" "Of course," replied Johnny. "'Of course!'" mimicked Felix. "Well, I guess I'll come down now, since the prospect isn't as good as it might be." Johnny went in to get a pencil and a piece of paper: Felix began to come down from the roof by swinging himself off, and letting his feet rest upon the slender railing that passed along the outer edge
- 27. of the platform. Just as he was putting his feet down, Clyde jumped upon him; and in trying to extricate himself from the dog, and touch the railing at the same time, he missed the railing in the darkness, and fell down, giving an impatient exclamation of pain as he reached the ground. Sue was frightened, and ran in with the announcement that Felix had fallen off of the roof. Mr. Le Bras went out immediately, followed by Johnny and Mrs. Le Bras. Felix had arisen, but was limping up the steps, and half crying with pain. "Oh, dear!" said he, "I've sprained my ankle awfully; so I'm about sure I can't ride my bicycle for a week; and then I'd like to know what I'm going to do, staying around in the house all the time!" Johnny's heart sank: he had counted on Felix's being off on his bicycle a good part of the next day, and what should he do if he were to be at home all the time expecting him to keep him company. Would he be able to enjoy his beautiful sky-room after all? "Perhaps it is not as bad as you imagine, Felix," said his aunt encouragingly, while his uncle helped him up the steps and into the house; but the boy limped badly, and there was an expression of genuine pain upon his face. Mr. Le Bras seated him in an easy-chair, and placed another chair for him to rest his foot upon, while Mrs. Le Bras got the arnica to bathe the ankle. After the ankle had been bathed and bandaged, and the slippers which Sue had found in Felix's trunk substituted in place of shoes, to accommodate the swollen foot, Felix began to exclaim desolately at his forlorn condition. "I can't even do any thing to amuse myself this evening," he said; "and it's no use to go to bed, because my foot pains me so that I couldn't sleep, even if it were not early in the evening."
- 28. "Sit up here by the table," replied Johnny, "and let's figure out what part of an acre there is in the yard. Here's an extra pencil and sheet of paper. It will be real fun: let's see who gets it right first." "It won't be any fun at all," replied Felix; "just as if there is any fun in figuring! you might as well say there is fun in going to school and studying old dry books." Johnny made no reply. He had begun to cipher. "What are you going to do first?" asked Felix languidly. "Why, multiply the length by the breadth in yards, to get the square yards in the garden." "What next?" "Why, then reduce an acre to square yards, so as to know how many square yards there are in an acre." "I can do that," said Felix, looking slightly interested; "but I never could see what use there was in it, and I don't see now." "Come and do it, then," said Johnny coaxingly. Felix hopped to the table slowly, on one foot, and sat down in the chair Sue placed for him; while Johnny brought the other chair for his foot. "How many square yards were there?" said Felix, taking the paper and pencil, and resting the paper on a book he took from the table. "You do it all yourself," replied Johnny; "seventy yards long, you know, and twenty-five yards wide." Presently Johnny stopped figuring. "Have you got through?" asked Felix. "No: I'm waiting for you to catch up." "1,875 square yards," said Felix.
- 29. "Yes; and now reduce an acre to square yards." After figuring a few minutes, Felix announced 4,840 square yards in an acre. "What do you do next?" he said. "One yard, then, would be what part of an acre?" asked Johnny. After a moment's hesitation, Felix said, "1/4840 of an acre." "Then, 1,875 square yards would be how many 4,84Oths of an acre?" "Why," replied Felix, after a little further consideration, "1875/4840 of an acre." "Now let's reduce that fraction as low as we can, by dividing both terms by five, and what does it give us?" "375/968 of an acre." "Now, is that about a fourth of an acre, or about a third of an acre?" Felix looked at the figures a moment, and then said, "It's a good deal more than a quarter of an acre, and—it's more than a third of an acre too." "Yes, it's a little more than a third of an acre: there's more ground in our house-lot than I thought there was. You know now about how large those boys' farm was,—nearly three times as large as our yard. Now let's see exactly how many roods and rods and yards and feet and inches there are." "How do you do that?" asked Felix, looking very blank. "Why, reduce your 1,875 square yards in the garden, to higher denominations." "Oh, yes!" replied Felix, brightening: "I've done those sums lots of times, and those denominate fractions like 1875/4840, but I never
- 30. could see any sense to it before. Let's see,—what do you divide by first? Oh! I remember, 30¼." Felix figured away bravely; but when he gave his result, it differed considerably from Johnny's. After some expressions of impatience, he looked it over, and, with some assistance from Johnny, found his mistake; their answers then agreed; and he read the result aloud, with something of an air of pride in his achievement,— "1 rood, 21 square rods, 29 square yards, 6 square feet, 108 square inches. And that's the first time I ever saw any sense in square measure, and all those things. I thought arithmetic was just to keep boys busy in school, and I could always find enough to do without it. I tell you, I've played more pranks on the teachers! and I didn't get found out very often neither; and when I did, they didn't dare punish me, for fear my folks would make a fuss; and they would too." "It is eight o'clock now; and I always read to our children for an hour or so before they go to bed," said Mrs. Le Bras, "or have them read aloud to me." "Let us all take turns to-night," said Johnny. "You or father begin." "Very well," said Mrs. Le Bras, taking a book from one of the library-shelves. "We are to begin our new book to-night, which is fortunate on Felix's account." "It'll be awful stupid, I know," said Felix: "all books are. I wish books had never been invented, and then a fellow would not have to go to school at all." "You begin, Frank," said Mrs. Le Bras.
- 31. Mr. Le Bras put down his paper, and began to read in the book. It was an account of a pedestrian excursion made by two boys in the Alps: they were German boys, and this was the way they spent their summer vacation. Felix did not intend to listen to the reading: he had begun to draw comic pictures on his sheet of paper; he was trying to represent himself and Clyde, as he was falling from the roof; his attempt, however, was not very artistic. But soon he became very much interested in the story, and sat quite still, listening. Mr. Le Bras, after reading about fifteen minutes, passed the book to Mrs. Le Bras. She read about the same length of time, and then passed the book to Felix. Felix said at first that he did not like to read aloud, and would have passed the book to Johnny. But his uncle said, "No, Felix, I want to hear you read;" and Felix, who stood rather in awe of his uncle Frank, did not like to disobey him. He made so many mistakes, and mixed his words up so badly by reading too fast, that Sue was about to say she could not understand his reading, when her mother shook her head at her. When Johnny's turn came, he read remarkably well,—so much so, that Felix felt quite ashamed of his own reading, which he knew was not good, although he did not know exactly what was the matter with it, except that he could not pronounce all the words. Sue read exceedingly well for a little girl,—very much better than Felix. "It is nine o'clock now," said Mrs. Le Bras at length, "and we must put the book aside until to-morrow night." "Oh, no!" exclaimed Felix: "we are at the most interesting part now."
- 32. But Mrs. Le Bras explained that they never read more than an hour in this way; and, as she said this, she replaced the book on the shelf, remarking that it was time for the children to go to bed. "I never go to bed till I get ready," replied Felix, "and generally I sit up until ten." "What time do you rise in the morning?" inquired his uncle. "Most any time,—about eight generally." "We breakfast at half-past seven," replied his aunt: "so you see you will need to go to bed earlier than you do at home." Mrs. Le Bras then bathed Felix's ankle again with the arnica, and Mr. Le Bras said he would help him up to his room. So ended the first day of Felix's visit. The next morning Felix's ankle was so badly swollen that it was evident bicycle-riding was out of the question for the present. "I wish now," said he, "that I had brought my pony and dog- cart; but I was tired of them at home." "Where are they?" asked Johnny. "They're at our summer place, with the other horses and carriages. Oliver has gone down there to take care of the horses and things while father is gone." "If we go to the cottage, can I ride in your dog-cart?" asked Sue. "Yes, if you want to; it's just fit for girls: but give me a bicycle or a boat. We've got a sail-boat; but father won't trust me without Oliver goes, and Oliver hates to go sailing with boys. I've got a row- boat of my own." After breakfast, it was discovered that Clyde was missing. He had been put in the summer kitchen for the night, and the door had
- 33. been left open. The whole household called him, and searched for him, except Mr. Le Bras; but nothing could be heard or seen of him. A sudden suspicion flashed upon the mind of Mrs. Le Bras; and she said, in a low tone, to her husband, "Do you know where Clyde is?" "The fewer questions you ask me, the better," he replied; and she said no more. "If he is not found by to-night," said Felix, "I shall have an advertisement put in the paper." "That would be of no use," replied Mrs. Le Bras; "since his name, you say, was on his collar, with the words, 'Owned by F. Le Bras.' As your uncle is the only man by the name of Le Bras in town, and F. is his first initial, any one who found him accidentally would bring him here." "While, if he was taken intentionally from the shed during the night, as I have no doubt he was, the person who took him does not mean to return him," added Mr. Le Bras. "Then, I must have another dog," replied Felix. "Very well," said his uncle: "if you do not find Clyde by the time we go to the seaside, you shall have another; but I think, while you are in town, you can get on very well without a dog, provided Clyde does not find his way back." "He would have woke us all up if the thief had not muzzled him," said Felix. "I presume he was muzzled," replied Mr. Le Bras. "This is a bad neighborhood for dogs; I have no idea that you could keep a dog safe here a week; there is a great prejudice in this neighborhood against dogs."
- 34. Mr. Le Bras then turned the conversation by saying to his wife, "You remember Pierre was to stay here while his folks are away?" "Yes," replied Mrs. Le Bras: "I am quite willing he should come at any time; he makes scarcely any trouble at all." "Trouble!" exclaimed Sue: "I think he makes a great deal of pleasure." "So do I," said Johnny. "When is he coming?" "Week after next, I believe," replied Mr. Le Bras, taking his hat, and going toward the door. "His father and mother have decided to spend the rest of the summer at the White Mountains, on account of his father's health: he is suffering seriously from malaria." The next thing was, what was to be done with Felix that day, since he was contented with nothing but lively outdoor amusements. Johnny was too polite and kind-hearted to leave him to his own slender devices, while he was in such a helpless condition; but he thought sadly of the quiet and beauty of the sky-room, which he had not been able to visit since Felix arrived. CHAPTER V. COMPROMISES. "How will you amuse yourself to-day, Felix?" asked Johnny, as they walked aimlessly into the sitting-room. Johnny was thinking to himself, "I wish school was not out, and then there would not be so much time in which I should have to think of being polite to Felix,
- 35. instead of going about the things I like to do myself, and which he don't care any thing at all about." "Oh! I don't know, I'm sure," replied Felix, yawning: "can't you think up something? I know it's going to be as stupid as can be. I wish I had insisted on going to Europe." "I know what I would do, if I was only tall enough," said Sue: "I'd try to ride Felix's bicycle myself. I think it must be great fun." This made Felix laugh. "It would be good as a play to see you try," he said; "I just wish you could; it would give us some fun to see you wobble about on it, and scream every time you thought it was going to fall over." "Why don't you have Johnny try?" suggested Sue; "it would be pretty near as much fun; only Johnny wouldn't scream, if he did fall over; he never screams at any thing." "That's an idea," said Felix. "Yes, Johnny, you try the bicycle: it's great fun to see a beginner." Now, the truth was, Johnny had for some time been wishing he had a bicycle, although he had not as much as hinted this desire to his father or mother; since he belonged to a society of boys and girls who called themselves "Independents," because they had pledged themselves not to spend any money for amusement, etc., which they had not earned themselves. Johnny wore the badge of the society, and had taken great pleasure in earning the not very large amount of money he needed for his chemicals and other trifling expenses, by carrying papers, and doing various other little odd jobs which came in his way. Indeed, he had got to be the great errand-boy of the neighborhood, because it had come to be understood that he was willing to make himself useful for a very reasonable remuneration.
- 36. His father and mother had not discouraged this endeavor, because Johnny was inclined to read and study too much, and any thing which would divert his mind out of doors in healthful exercise was beneficial to him. But as for earning enough to buy a bicycle, of course that was beyond Johnny's present abilities as an Independent. "Would you be willing that I should try it?" replied Johnny. "Why, of course! You may hurt yourself, but you can't hurt the bicycle; and if you did, I could have it mended or get another before my ankle gets well." "You must ask mother, Johnny," said Sue, who began to look rather sober over the possibility of Johnny's getting hurt. Mrs. Le Bras was just entering the room. "May I try Felix's bicycle, mother?" asked Johnny, with a wistful look. "Why, yes," she said, "if you can try it in a safe way: you will have to have some one hold it for you." "I'll hold it, ma'am," said Kate, who was clearing off the table in the dining-room: "I'm very strong in my arms." "The platform will be a grand good place to mount," said Felix. "You can step up on the railing, and get right on: you can't get on as I do, very well, until you get used to it." "Come right out now, before I wash my dishes," said Kate. "But you must promise, Johnny, that if think there is any danger, and ask you to get down, you will obey me at once," said Mrs. Le Bras: "I am almost sorry I said you could try, before your father came home."
- 37. They all went out on the platform; and Johnny brought the bicycle out of the shed, and leaned it up against the railing of the platform, near the steps on which Kate was standing. Kate came out, and held the wheel with a firm grip, while Johnny stepped on the railing, and got upon the seat. "Now, Katie," said Johnny, "just help me wheel it out, where I can balance it." Kate cautiously pulled the machine away from the platform; while Johnny placed his feet firmly on the pedals, and turned the wheel slowly at first, while Kate was holding it. "Let go now, Katie," he said. "Shall I?" asked Kate doubtfully, looking at Mrs. Le Bras. "No, no!" cried Sue: "he'll fall if you do, I know he will!" "I am afraid so too," said Mrs. Le Bras. "We don't want two boys with sprained ankles, Johnny." "But I think I can keep my balance," replied Johnny; "and of course I can't learn to ride while Katie is holding the wheel still." "Oh, let go of it!" said Felix. "I don't believe he would fall; anyway, he can jump off: he'll only waver around a little, but he's got to do that before he learns." "Move it over gently, Katie," said Mrs. Le Bras. Kate tried to do this; but in moving her hands to turn the wheel, Johnny, who was working the pedals, eluded her, and sailed off into the garden. After he had gone a little way, the bicycle wavered to the left. Sue shrieked; Kate rushed forward with outstretched arms; and Mrs. Le Bras called out, "Jump off, Johnny!" But Johnny quickly recovered his balance, and went bravely on down the garden-walk.
- 38. "I knew he wasn't going to fall off," said Felix. "He's getting on all right." Johnny experienced a slight difficulty in turning around the walk at the foot of the garden, but performed that feat without falling, and arrived safely at the platform amid hearty congratulations, and loud clapping of hands. "I knew that boy could do any thing he undertook," said Kate admiringly; for she was very fond of Johnny. "All that is necessary," said Johnny, "is to preserve the centre of gravity." Johnny then took a more extensive tour, going around the house, and making another circuit of the yard. "I guess I can try the street now," he said: "I might as well get really used to it while I am about it. I don't go very straight yet: but there are ever so many beginners who go on the street; I see them almost every day." "Yes," replied Sue: "you go better than Walter Cross now, and he's been trying ever so long." So they all went out to the front-door, to see how the novice would succeed there. The sequel was, that Johnny rode out of sight, and left them gazing into vacancy. "If that boy don't beat all!" said Kate. "Law, ma'am, he'll be on the race-course before we know it." "That is a good joke!" said Mrs. Le Bras, laughing: "our professor on the race-course! Aren't you afraid you have lost your bicycle, Felix?" "No," replied Felix: "this is prime! for uncle will have to get Johnny a bicycle now, and then we can ride everywhere together,
- 39. when my ankle gets well; for by that time he can ride capitally, I'll bet." Johnny came back in about half an hour, quite flushed with success and exercise, and looking very animated. "I surprised the boys I met," said he. "I met Alec and Fred walking together, and they said, 'Oh, you've got a bicycle too! Now you must go to ride with us.' They were a good deal disappointed when I said it wasn't my own." "You've got to have one," said Felix: "I'm going to tell uncle Frank so this noon!" "No," replied Johnny. "I can't buy one,—they cost too much: but perhaps I can hire one while you are here, sometimes; I know a boy who rents his for so much an hour, when he don't want to use it himself." The bicycle was put away; and then Johnny, who had enjoyed his success and the ride very much, began to feel grateful to Felix for letting him take it, and for saying he could use it every day until his ankle got well. It no longer seemed such a heavy task to think up some amusement for his cousin. Mrs. Le Bras had sat down at the sitting-room window with her sewing. Johnny stole up to her, while Felix was whittling into the waste-basket, with his back turned that way, and whistling rather drearily. "Mother," said he, "I have a mind to ask Felix to come up and see the sky-room." "Then," said his mother, in a whisper too low for Felix to notice it, "you must not blame any one if you are not able afterwards to have it to yourself." "No; but I'll make a bargain with him about it."
- 40. "Do as you please, only don't get fretted over the consequences." Felix was trying to cut out the deck of a boat. "Where is your boat?" asked Johnny. "I thought I'd make the deck first: I haven't got the right piece of wood for the boat. Have you any thick blocks of wood?" "No, but I can get some. Richard Scott is a great friend of the man who has charge of the wood-working room at the brass-works, and the man gives him any odd pieces of wood he wants, and lets him use the machinery too: he could cut out your boat in a very short time, with a circular saw and other machines." "I wish I could get him to do it, then: I'll pay him for it. What I like to do, is to rig a ship: I can't make the hull very well." "If you will let me take your bicycle again, this afternoon, I will go down and see Dick about it." "Of course you can have the bicycle whenever you want it, till my ankle gets well." "You didn't know I had a room all to myself. I have a room where no one can come in unless I tell them they may: my father gave it to me to read and study in." "What a dismal place it must be!—I guess I'll keep on with this deck, and then you can take it down and tell Dick I want the hull made of about that size." "No, it isn't a dismal room at all: it is the pleasantest room in the house, I think." "Oh! you'd think a room was pleasant if it just had some books and bottles in it, and an old mortar and pestle, and a lot of such trash."
- 41. "I was going to say that if you want to come in and see it some time, you can ask me, and I will unlock it for you. I shall be in there a good deal of the time, probably; so, if you miss me, you will know where I am, and can come up if you want to. Of course I will let you in, if I am not very busy indeed." "So it's up-stairs, is it? Is it what you call 'the spare room'?" "No: it's an unfinished part of the French roof." "Ho! It's up in the attic, is it?" "Yes." "Well, I guess you won't find me troubling you much up in the attic this hot weather: you must like to read, to go up there to do it! When you get a room down-cellar, let me know, and perhaps I'll pay you a visit once in a while." So it did not seem very likely that Johnny's generous disclosure would cost him very dear, at present at least. But how to get away from Felix was still a question; although sitting around, and seeing him whittle, and hearing him fret about his ankle, was not very delightful employment. He had proposed, too, that, as soon as he finished the deck, Johnny should assist him in writing an advertisement to have put in the paper, in case Clyde did not appear by the next day. Johnny finally took a book from the bookcase, and sat down to read. "Bother your book!" said Felix. "Why don't you talk?" "I don't see as there is any thing in particular to say." "Who wants you to say any thing in particular? There! I've got that old deck done, I hope! What's your old book about?" "It's about those boys and their one-acre farm." "Haven't you read that about a thousand times before?"
- 42. "I have read it twice." "And I don't believe it's fit to read half a time." "If you want me to, I'll read a little of the first chapter aloud, so that you can see how you like it." "Fire away, then! Only stop when I tell you to, for I know I can't stand much of it." Johnny began to read, in a clear, expressive tone, while Felix picked up one of the pine sticks he had laid on the floor, and began to whittle a mast. Pretty soon the shavings began to fall almost anywhere except into the basket; and Sue, who was playing with her dolls in the corner, said, "Look out, Felix! your shavings are falling over everywhere." "Bother the shavings!" replied Felix, seeming to notice them for the first time, and getting down to pick them up. "I don't believe they ever spaded over a whole acre of ground in any such time as that. Just read that over.—Oh! I thought you said in one hour. I mean to have father let me have an acre of ground by the cottage next season, and go down early, and see what I can do with it." "But you have all the money you want without earning it," said Sue. "That's so,—I forgot that; but I just wish my father was a poor man. I'll bet I could do as well as either of those boys. Go on now: let's see what they did next." The morning had advanced considerably, and yet Felix had not asked Johnny to stop; although the masts were finished, and the shipbuilder was lying on the floor with his head on a hassock, for lack of any further employment. Johnny's throat ached with reading so long, and at last he felt obliged to say,—
- 43. "My throat is getting tired: let's put the book up now, until some other time." "No: go on a little farther; just finish up that chapter, so you'll know where you left off." "Stop a few moments, and rest, Johnny, and then, if Felix wants you to, you can finish the chapter," suggested Mrs. Le Bras, giving a significant glance towards Felix, which was intended for Johnny's benefit. Johnny looked, and saw that Felix's eyes were closed. Johnny put down the book, and in a few moments it was evident his audience was sound asleep. Johnny immediately rose softly, and left the room: he went into the back entry, and then ran up-stairs with light bounds to the sky-room. He opened all the windows; and the breeze, which was scarcely perceptible below, began to blow in very freshly. Johnny got one of his philosophies, and sat down by one of the front windows to read. He did not lock the door, since Felix had expressed himself as disinclined to pay him any calls. There was no danger of visits from any other source, for Sue understood that Johnny was not to be disturbed without permission. After reading in that book a while, he took down another, still leaving the first open upon the table. After consulting the second book, he took down the dictionary, and consulted that. While he was still in the midst of his researches, he was startled by a loud voice behind him. "Well! I say! This isn't so bad, is it? Let's call this aboard ship, with the sky for sea; 'cause you can't see any land up here, except off at a distance as you do on the water. But I'd like to know if this is how you lock yourself in?" "I didn't think of any one's coming up," replied Johnny, looking blankly at the open door. "But that's all right," he added, smiling.
- 44. "I'm not very busy now: I've got about through with my studying." "What are you studying?" "I am studying about heat and light." "What can you learn about those things, I'd like to know? When it's light, it's light; and when it's hot, it's hot; and when it isn't either of them, it's dark and cold." "If folks didn't know any more about heat and light than that, you would have to go without a good many things you have now; for instance, there wouldn't be any machine-shops and railroads, and you couldn't have your picture taken." "Why not?" said Felix. "I can't tell you very well to begin with, any more than you could learn the back part of the arithmetic before you had studied fractions. But here is a magnifying-glass: we'll use it for a sun-glass." As Johnny spoke, he placed a piece of white paper on the window-sill where there was a patch of sunshine, and, taking a magnifying-glass from the stand, held it above the paper in such a manner as to bring the rays to a focus. "That is a regular sun-glass," said Felix: "I have had one many a time. It will burn the paper in a minute." "It is something like a sun-glass," replied Johnny, "because it is a double convex lens." "What do you mean by a double convex lens?" "I'll show you in a moment." Just then the paper began to burn, and Johnny removed the glass. "Why didn't you let it go on burning?" said Felix.
- 45. "Because, you see, it was blackening the paint on the sill, and might have burned into the wood if I had kept the glass there. Now, what made the paper burn?" "Why, you held the glass so that it made a focus, and that made the paper burn." "But why was there what you call a focus? and why did that make the paper burn?" "I never thought any thing about that," replied Felix, looking a little confused. "Do you know the reason?" "Oh, yes! I knew that the first time I ever saw a sun-glass: my father told me. Just look at the shape of the glass on both sides; it's convex, you see; that is, it rounds out toward the centre. The rounding of the glass causes the rays of light to strike it obliquely everywhere except in the very centre; and when a ray enters a transparent surface obliquely, or comes out of it obliquely, it is bent out of its course in a particular manner,—it would take too long to tell you exactly in what manner, although I can lend you a book that will show you exactly,—and in passing through this convex lens, the rays are all bent towards a point at a little distance from the glass, and exactly opposite the centre of it; so that, if you hold any thing that will burn easily exactly at that point where the rays all join together, their united heat is sufficient to burn the article. I know exactly why each side is made convex, and why the glass is so much thicker in the middle; but it would take a long time to explain it to you, although you could read about it all in fifteen minutes in one of those volumes of 'Science for the Young,' there on the shelf. Any time you want to look it up, I will show you the place."
- 46. "No: I don't want to be bothered with reading it. I guess what you've told me will do." Johnny then held the glass over the paper again. "The focus is the gathering together, or concentration, of the rays of light; and as every ray of the sun has heat in it, the concentration of the heat of all the rays at that point makes the paper burn." "Then, the larger the glass,"— "The convex lens, you mean," said Johnny. "Yes: the larger the lens, the more rays of the sun would be brought together at the focus, and the more heat there would be?" "Of course." "Then, if I had a real big convex lens in my room, in front of the window, I could sit in the focus of it, in the winter, and keep warm without any fire." "You could keep too warm, perhaps; for you know a sun-glass will burn your hand: but even if the focus would be just right on a winter day, the light would be too bright for your eyes; and sometimes the sun wouldn't shine in at your window, and you would get very tired of sitting in one place. Besides, a convex lens of that size would cost a great deal more than a very nice stove and ever so much coal. So I guess convex lenses will never take the place of wood and coal, which are the best provisions the sun has made for warming people, that we know of yet, when it is not nearly enough over their heads to warm them itself, or when its rays are shut out by bad weather." "I don't see what the sun has to do with wood and coal," replied Felix, sitting down by the table, and holding the magnifying-glass
- 47. over Johnny's books and various other objects on the table. "Why, the sun has stored up a lot of its heat in wood and coal, and all those things which we call combustibles." "Come, now! none of your fooling," said Felix, staring at Johnny incredibly: "there isn't one bit of heat in wood or coal till you burn them." Johnny began to laugh. "Why, of course they are not hot until they begin to burn; if they were, you couldn't say that the heat was stored up; it would be escaping all the time: and then, wouldn't it be dreadful to have the trees hot instead of making a nice cool shade? and how could the miners get the coal if it were hot? and how could we carry fuel about from place to place? and we should have to be made like salamanders, if every thing around us that the sun had put heat into was hot: we couldn't sit at this table, or in these chairs, or handle these books; and the floor would burn our feet, and our clothes would feel hot." "My clothes do feel hot," said Felix, beginning to laugh, also, at Johnny's vivid picture of what would be if the sun had not locked its stored heat up so coolly and comfortably for our use. "It isn't your clothes that are hot, though, unless your body has heated them, or you have been sitting or standing in the sun; it is you who are warm, and your clothes keep the heat that comes from your body from passing freely into the air: your clothes themselves are not any hotter than they would be if they were in an ice-chest; that is, I mean the heat that the sun has stored in your clothes would be every particle there if your clothes were kept next to ice." "I'd like to know, now, how you make all that nonsense out?"
- 48. "Heat is force: in one sense, the heat of the sun is the force of the sun. Now, when things are growing, the force of the sun goes into them in some way, and makes them take carbon out of the air, and hydrogen out of the water in the ground, and from the rain and dew: and just exactly as much heat or force as the sun has put into a tree or plant, or any thing else, can be got out of it by causing it to burn; that is, making the carbon and hydrogen contained in it, unite with the oxygen in the air. "I don't wonder the boys call you professor," said Felix: "I'd like to know how you ever got to know so much about every thing. What you say is a great deal harder to believe than fairy-stories: I guess I'll go to believing fairy-stories." Johnny laughed again. "Because some very strange things are true, that is no reason every thing strange should be true, or why some things should be true that wouldn't be so very strange. Do you like fairy-stories?" "Yes, I like them as well as any thing: I've never read many stories but fairy-tales. Story-books are all lies; and if I'm going to read lies, I'd rather read some good big ones." "I don't think story-books are all lies. I don't think that story about the boys and their farm is all a lie." "Do you suppose there were two just such boys, and that they had just such a farm, and did just as those boys did?" "No: I think very likely that was not all true, and I don't much care whether it was or not: but I know there might be two such boys, and that they might do just as is described; and that makes the story interesting, and a good deal more so than a story might be about two other boys with every thing told exactly as it was and
- 49. happened. But I don't like fairy-stories, because they couldn't be true, and so are not like any thing I am interested in. If there ever was a fairy, I should like very much to hear one described, even although this particular fairy was only a made-up one. I should say, 'I have learned how a fairy might look and act, which is a good deal as real fairies do look and act.'" "I like a good fairy-story, anyhow: only I don't see why the fairies can't be men instead of women; men-fairies could do a great deal more wonderful things than women-fairies." Johnny thought to himself that Felix was much too large a boy to care for fairy-stories, and to know nothing about books of a more mature description; for Felix was nearly fourteen,—a year older than Johnny, and also taller and broader. "Suppose you tell us how it is that this glass magnifies these letters so much," said Felix, after a little pause. At that instant Sue entered the room, saying,— "Why! you let Felix in the very first time he came up, didn't you? That's funny enough! But dinner is ready, and papa has come, and Katie is going to ring the bell before we come down, if we don't hurry; and you know papa don't like to have us late." "I'll explain about the magnifying some other time, then, Felix," said Johnny; and they all went down-stairs. Johnny forgot to lock his door when he went out. And when they reached the next floor, Sue reminded him of it. "Never mind," replied Johnny: "I guess there won't any one go up before I do." As soon as they entered the dining-room, Felix said to his uncle, who was just sitting down at his place,—
- 50. "Uncle Frank, Johnny's got to have a bicycle right off: he's been riding mine around finely this morning, and he likes it ever so much." "Ah!" replied Mr. Le Bras. "Is that so, Johnny?" "Part of it is so; it's so that I rode on Felix's bicycle, and that I like it: but I haven't got to have one right off, because, in the first place, I don't suppose you would feel rich enough to buy me one; and in the next place, I couldn't have one if you did; because I am an Independent, and it would be spending money for amusement which I did not earn." "But it would not be your spending it, if I made you a present of a bicycle; it would be my spending money for my amusement or pleasure or some other reason: I am not an Independent, and even if I were, I have earned my own money." This was such an entirely different aspect of the case, that Johnny was quite surprised. "Why, I didn't think of that," he said. "You see, lawyers can look at matters from a good many aspects," remarked Mrs. Le Bras, who had been inclined to think, as Johnny did, that so expensive and unnecessary an article as a bicycle would interfere with his being an Independent. "But then," said Johnny, "of course you are not able to buy me a bicycle; and, if you are, you probably won't think it best for me to have one." "You are wrong in both instances. To be sure, I am not able to buy you a bicycle as a mere amusement; but if a bicycle will save me doctors' bills on your account, or have a tendency to aid in your becoming a strong, able-bodied man, it would be money in my
- 51. pocket, now and for years to come, to get you one. It would save me considerable worry, too, if you could be diverted from your books, and engaged in open-air exercise, far more than you have heretofore been inclined. Yes, Johnny, if you want a bicycle, go down street with me after dinner, while you are in that mind, and I'll fit you out. But remember, after I have spent so much for the sake of your health, you must not let it become an unnecessary expense to me instead of a great saving of money, by not using the bicycle more or less, every day, when it is reasonably pleasant." At first, Johnny was so astonished and grateful and happy, that he could not reply; but Felix said,— "There! I knew he'd do it right straight off, Johnny! That's just the way my father does." Mr. Le Bras laughed at this. "Johnny is not so used to having what he wants at the first hint," he said; "but, in this case, he happens to want just what I have been wishing he would ask for, and so it comes easy." Johnny went down street with his father after dinner, and came back on his own bicycle, almost too happy to express his delight at the acquisition. After Felix had examined the new bicycle, he remarked,— "It isn't quite as fancy as mine, but it's exactly as good for riding: yes, it's a real good bicycle, Johnny. How I wish my ankle was well! We'd go right off to ride together." "I'll go right down now, and see Dick about your boat," said Johnny; "and then you can amuse yourself this afternoon, rigging it. I saw him, and asked him if he should be at the shop this afternoon; and he said, 'Yes, come down,' and I said I would."
- 52. CHAPTER VI. TWO LESSONS FROM NATURE. After his first terror over the prospect of having Felix with him for three months, Johnny got on very well with his cousin. Although it was evident Felix had been accustomed to be very wilful and disobedient towards his seniors, and overbearing, with his companions, the respect with which his uncle's decided yet friendly manner inspired him, and Mrs. Le Bras' firm though mild manners, held his forwardness and self-will well in check. He soon began to appreciate the advantage, also, of having a boy like Johnny for a companion; he had never before had the benefit of a constant companion; and the boys with whom he had been accustomed to associate were more or less undisciplined, like himself, ready to be offended and quarrel at the first provocation. It would have been very difficult to quarrel with Johnny, because he never gave any ground for offence himself, and was not disposed to find any such ground in the manners of others; the most that he asked was not to be disturbed in his quiet and studious ways; and there was something in his gentle and thoughtful manner which impressed even such a reckless boy as Felix with something like deference and consideration. About two weeks after Johnny had been presented with his bicycle, and when he had learned to ride it so well that none but an experienced wheelman would have noticed that he was a novice, Mr.
- 53. Le Bras met the grammar-school teacher who had been Johnny's instructor the past year, preparatory to his entrance to the high school. "I see Johnny has become a bicyclist," said Mr. Farnsworth. "Yes," replied Mr. Le Bras: "what do you think of the amusement?" "A very good thing for Johnny, and a very bad thing for some other boys." "Ah!" replied Mr. Le Bras. "How is that?" "Why, there is Harrison Brown, for instance: it would be the best thing for him if he could be wholly deprived of his bicycle for a time, and then allowed to ride it only Saturdays. That boy's education is all going into his legs, and all his vigor is going the same way. He rides his bicycle before school in the morning, at noon, after school at night, and every Saturday. Now, he is a backward scholar, to begin with, and this wheeling has just used him up, so far as learning any thing is concerned: he comes to school all tired out, without enough life and energy left to even give attention to what the teacher says; and as to studying, he hardly knows what lesson he is expected to get from day to day; he sits half asleep and dreaming,—probably dreaming of his bicycle-rides,—and knows almost nothing of what is going on around him: he has been a mere figure-head all this year, and is no nearer to entering the high school than he was a year ago." "I can see the disadvantage in such a case as that," replied Mr. Le Bras: "in fact, I have a nephew at my house who is wholly given up to outdoor sports, fun, etc.; although he is such a vigorous, wide- awake fellow, that he is not often caught dreaming or asleep: he and
- 54. Johnny are having very good counter-influences upon each other, I find; he is getting Johnny into outdoor exercise more, and Johnny is beginning to put the idea into Felix's head, that there is some use and interest in books. I think riding a bicycle is a very good thing for Johnny: he is so much inclined to sit down and read and study, that we have apprehended serious danger from it; indeed, the doctor is constantly warning us to put some stop to it. The teachers have been very kind about heeding my request to hold him back as much as possible at school, but we have found it no easy matter at home to keep him from his books. I hope much from his taking to bicycle- riding." "A very good thing! a very good thing indeed!" replied Mr. Farnsworth. "The quickness with which Johnny learns, and his fondness for books, are extraordinary; considering that, I think we have kept him back pretty well: a good many quite ordinary scholars get into the high school at thirteen, provided they have been to school pretty steadily." "Oh, yes!" returned Mr. Le Bras. "I began to prepare for college at twelve; but I was very strong and healthy, and exceedingly fond of outdoor sports. I was fully as well balanced physically as I was mentally, and that is what I believe in." "Just so! just so! you've got the right of it: but I can tell you, there are very few boys who are well balanced nowadays; they are chiefly one thing or the other,—brains or brawn. But I hope you'll bring Johnny out all right." "You know Pierre Stein?" said Mr. Le Bras. "Pierre? Oh, yes! he's just right, isn't he?"
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