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padding-left: 1em; vertical-align: bottom; white-space: nowrap;} - table.toc td.subject - {text-align: left; padding-left: 1em; text-indent: -1em; vertical-align: top; padding-right: 2em;} - th - {font-weight: normal;} - .tnbot - {border: dashed thin; margin: 1em 10%; padding: .5em;} - .tnbot h2 - {font-size: 1em;} - .tnbot p - {text-indent: -1em; margin-left: 1em;} - .tnbox - {border: dashed thin; margin: 1em 20%; padding: 1em;} - .top - {vertical-align: top;} - ul.index - {list-style: none; margin: 1.5em 0; text-align: left; max-width: 25em;} - ul.index li - {text-align: justify; margin-left: 1em; text-indent: -1em; clear: both;} - ul.index li.level1 - {margin-left: 2.5em;} - ul.index li.level2 - {margin-left: 5em;} - ul.index li.startletter - {margin-top: 1.25em;} - .ws05 - {word-spacing: .5em;} - - </style> - </head> -<body> -<p style='text-align:center; font-size:1.2em; font-weight:bold'>The Project Gutenberg eBook of Self-Help Mechanical Drawing, by Nehemiah Hawkins</p> -<div style='display:block; margin:1em 0'> -This eBook is for the use of anyone anywhere in the United States and -most other parts of the world at no cost and with almost no restrictions -whatsoever. You may copy it, give it away or re-use it under the terms -of the Project Gutenberg License included with this eBook or online -at <a href="https://www.gutenberg.org">www.gutenberg.org</a>. If you -are not located in the United States, you will have to check the laws of the -country where you are located before using this eBook. -</div> - -<p style='display:block; margin-top:1em; margin-bottom:0; margin-left:2em; text-indent:-2em'>Title: Self-Help Mechanical Drawing</p> -<p style='display:block; margin-left:2em; text-indent:0; margin-top:0; margin-bottom:1em;'>An Educational Treatise</p> -<p style='display:block; margin-top:1em; margin-bottom:0; margin-left:2em; text-indent:-2em'>Author: Nehemiah Hawkins</p> -<p style='display:block; text-indent:0; margin:1em 0'>Release Date: January 15, 2022 [eBook #67166]</p> -<p style='display:block; text-indent:0; margin:1em 0'>Language: English</p> - <p style='display:block; margin-top:1em; margin-bottom:0; margin-left:2em; text-indent:-2em; text-align:left'>Produced by: deaurider, Harry Lamé and the Online Distributed Proofreading Team at https://www.pgdp.net (This file was produced from images generously made available by The Internet Archive)</p> -<div style='margin-top:2em; margin-bottom:4em'>*** START OF THE PROJECT GUTENBERG EBOOK SELF-HELP MECHANICAL DRAWING ***</div> - -<div class="tnbox"> -<p class="center">Please see the <a href="#TN">Transcriber’s Notes</a> at the end of this text.</p> -</div> - -<hr class="chap" id="Page1" /> - -<div class="x-ebookmaker-drop"> - -<div class="container"> -<img src="images/cover.jpg" alt="Cover image" /> -</div> - -<hr class="chap" /> - -</div><!--ebookmaker-drop--> - -<div class="container w30em" id="Pageiii"> -<img src="images/illo003.jpg" alt="Minerva" /> -</div> - -<hr class="chap x-ebookmaker-drop" /> - -<div class="container w15em"> -<img src="images/illo004.jpg" alt="Lamp" /> -</div> - -<hr class="chap x-ebookmaker-drop" /> - -<h1>SELF-HELP<br /> -<span class="fsize150 gesp1">MECHANICAL DRAWING</span><br /> -<span class="fsize80">AN EDUCATIONAL TREATISE</span></h1> - -<hr class="chap x-ebookmaker-drop" /> - -<p><span class="pagenum" id="Pagevi"> </span></p> - -<div class="container w30em"> -<img src="images/illo006.png" alt="Hands with calipers" /> -</div> - -<hr class="chap x-ebookmaker-drop" /> - -<p><span class="pagenum" id="Pagevii"> </span></p> - -<p class="center highline2 fsize90">“<i>LEARN TO DO A THING BY DOING IT.</i>”—<span class="fsize70"><i>OLD -PROVERB</i></span></p> - -<p class="center highline2 fsize175">SELF-HELP<br /> -<span class="fsize125 gesp1">MECHANICAL DRAWING</span><br /> -<span class="fsize80"><i>AN EDUCATIONAL TREATISE</i></span></p> - -<div class="container w10em"> -<img src="images/illo007.png" alt="Logo" /> -</div> - -<p class="center highline15"><span class="fsize80">BY</span><br /> -<span class="fsize175"><b>N. HAWKINS, M. E.</b></span><br /> -<span class="fsize90"><i>Author of Handbook of Calculations, etc.</i></span></p> - -<p class="center highline2 blankbefore75"><span class="fsize125 gesp2"><i>New York</i>: THEO. AUDEL & CO., -Publishers</span><br /> -1902</p> - -<hr class="chap x-ebookmaker-drop" /> - -<p><span class="pagenum" id="Pageviii"> </span></p> - -<p class="center fsize150 highline2 blankbefore2 blankafter2"><i>Copyrighted<br /> -by<br /> -Theo. Audel & Co.<br /> -New York<br /> -1902</i><br /> -</p> - -<hr class="chap x-ebookmaker-drop" /> - -<p><span class="pagenum" id="Pageix"> </span></p> - -<p class="center highline15"><b><i>This work<br /> -is<br /> -most kindly and<br /> -respectfully dedicated to<br /> -<span class="fsize125 gesp2">THE COMING MAN</span><br /> -who at the present time<br /> -is undoubtedly devoting<br /> -a goodly share of<br /> -his spare time to<br /> -the study of<br /> -drawing.</i></b></p> - -<hr class="chap x-ebookmaker-drop" /> - -<div class="container w20em"> -<img src="images/illo010.jpg" alt="Drawing hand" /> -</div> - -<hr class="chap x-ebookmaker-drop" /> - -<p><span class="pagenum" id="Page11">[11-<br />12]</span><a id="Page12"></a></p> - -<div class="container w30em"> -<img src="images/illo011.png" alt="Introduction" /> -</div> - -<hr class="chap x-ebookmaker-drop" /> - -<div class="chapter"> - -<p><span class="pagenum" id="Page13">[13]</span></p> - -<h2 class="nobreak">Preface.</h2> - -</div><!--chapter--> - -<p><i>It is because of a personal and practical experience of the advantage to be gained by the -possession of a knowledge of drawing, that the author is prompted to undertake the rather pleasant -task of producing a self-help book relating to the subject.</i></p> - -<p><i>Since the days of youthful endeavor, the author has passed through an extended experience -of mechanical life, and scarcely ever without chalk, pencil or instrument in hand, to illustrate by -sketch or drawing, the tools to be employed, or to picture the finished product; accordingly, -throughout this work, words of explanation and the drawings will go together to aid the diligent -student.</i></p> - -<p><i>It has been said by an eminent writer, that “one workman is superior to another—other -circumstances being the same—directly in proportion to his knowledge in drawing, and those who -are ignorant of it must in many respects be subservient to others who have obtained that knowledge.”</i></p> - -<p><i>It has been also said that no man is fitted to be foreman of a shop who cannot draw, and -it is generally true that no one will be appointed to that position, except temporarily, who does -not possess some knowledge of the art, either “freehand” or instrumental.</i></p> - -<p><span class="pagenum" id="Page14">[14]</span></p> - -<p><i>It is a question how far a good working knowledge of drawing can be attained without a -teacher; it is true that but few have become proficient without such aid, but it is equally true -that “self-help” has been the key note to all advancement.</i></p> - -<p><i>The author received personal instruction in several ways and times, at home, in school, in -an architect’s office, and under an experienced mechanical engineer, but it was in the early morning -hours of a bright summer time—lang syne—that he made his first serious attempt to master the -art of mechanical drawing. It was a struggle and a battle to hold himself down to “the board” -to the finish, but it was a victory—one, won over slothfulness and impatience, and of such a -nature as to warrant the use of the term “self-help” to the encouragement of others.</i></p> - -<p><i>In conclusion two sentiments may be added; if a good working knowledge of drawing is -“worth the while” then, 1, the student should be thoroughly in earnest in acquiring it; 2, he -should be willing to take sufficient time and give much hard study to gain the skill necessary for -success.</i></p> - -<p><i>This persistence is not irksome. It carries its own reward, and the results are definite -and sure.</i></p> - -<div class="poetry-container"> - -<div class="poetry"> - -<div class="stanza"> -<span class="verse indent0">“<i>One step and then another, and the longest walk is ended;</i><br /></span> -<span class="verse indent4"><i>One stitch and then another, and the largest rent is mended.</i><br /></span> -<span class="verse indent0"><i>One brick upon another, and the highest wall is made;</i><br /></span> -<span class="verse indent4"><i>One flake upon another, and the deepest snow is laid.</i>”<br /></span> -</div> - -</div><!--poetry--> - -</div><!--poetry-container--> - -<hr class="chap x-ebookmaker-drop" /> - -<div class="chapter"> - -<p><span class="pagenum" id="Page15">[15]</span></p> - -<h2 class="nobreak">Introduction.</h2> - -</div><!--chapter--> - -<p>Drawing is one of the arts; art relates to something to be done, and art in the industrial and mechanical -sense aims chiefly at utility, and is governed by exact rules; hence mechanical drawing—so-called—tends first to -be useful and helpful, and second to accuracy in execution, including most minute details; it aspires to the -perfection of nature in adaptability of the means to the end.</p> - -<p>Drawing constitutes a universal language, to acquire which is a matter of importance, for by its use one is -able to illustrate the form and dimensions of an object, device, or utility, in very much less time, and far more -clearly, than by a verbal description.</p> - -<p>To a person who may not be able perfectly to understand the language of a country, to be able to draw is -an aid and a safeguard; to use the words of Sir Joshua Reynolds, “the pencil speaks the language of every land.”</p> - -<p>In extensive iron works and metal-working establishments the designer and draughtsman is always in -demand. His services are indispensable and his position is a highly responsible one. It becomes his -pecial<span class="pagenum" id="Page16">[16]</span> -province to design improvements, to furnish sketches and to make finished drawings; to calculate strains, strength, -power, motion, weight, friction and durability. All this and much more is the professional draughtsman’s work.</p> - -<p>In “directory” classification, he who accomplishes such comprehensive results as above described is termed -a “Draughtsman,” but the word has as wide a meaning as “Engineer,” which takes in civil, mechanical, naval, -sanitary, steam and other engineering specialists. So, in drafting, it includes the office boy employed in making -blue prints, it embraces the copyists, tracers and assistants, as well as the head draughtsman and chief engineer.</p> - -<p>Consequently the range is wide, and the line hard to draw between draughtsmen who work with their -hands, and those who work with their brains. It may be added that the best men are too frequently undervalued, -owing to the unavoidable difficulty in distinguishing the difference in true worth, between the two widely separated -classes.</p> - -<p>It may be remarked that they only draw well who draw intelligently; aptness in this, as in many other -virtues, is a matter of slow growth, “here a line and there a line”—it’s the proper direction, not the rate of -progress, that counts in the end.</p> - -<p>There are several methods of drawing—1, Free-hand; 2, Instrumental; 3, Geometrical; 4. Perspective. -In the first the work, also termed sketching, is executed by pencil, pen, crayon, or even paint-brush; in the second -the result is attained by the use of rule, tee-square, drawing pen, etc.; this method is also denominated -mechanical drawing, and suggests the title of this volume.</p> - -<p>The great usefulness, not to say necessity, of readiness in executing accurately, drawings “to scale,” -is<span class="pagenum" id="Page17">[17]</span> -emphasized by the fact that now, more than ever, is all machinery designed, and it may almost be said, is “built,” -in the draughting room—this is a valuable hint relating to “reading” drawings.</p> - -<p>It is wise, as well as easy, to begin at the beginning of things; thus, it is altogether the good part to mount -a ladder by the first and second rounds rather than to attempt it by taking the third, sixth, ninth, etc.—especially -are first and second rounds the very best to start upon; “Chalk-work,” is the first subject introduced, -next, that of “Free-hand.” These are the first steps leading upward in this most agreeable attainment—skill -in illustrating and designing of objects, tools, and utilities.</p> - -<p>A single word of advice before introducing the elementary work connected with mechanical drawing: if -the student should experience difficulty in mastering the diagrams and curves abounding in this book, let him -consult an experienced draughtsman or teacher, who, by a few strokes of a lead pencil, can easily make them plain; -that knowledge—which cannot be printed or self-taught—termed <i>the Craftsman’s Art</i>, is communicated largely by -personal telling and showing, from man to man; in drawing, this help should be thankfully availed of, when -necessity arises.</p> - -<div class="note"> - -<p><span class="smcap">Note.</span>—Sketching is often in demand because there is no time for finished or careful drawings, and the one who can draw a few -lines in a moment to let a sudden necessity be known, is the man of the hour. All candidates for First Class Engineer’s Certificates in -marine service in the navy have to undergo an examination in rough drawing; this is intended not so much as a proof of the applicant -possessing the capability of a draughtsman, but in the event of any injury to the engines in his charge, so that he may be able to send to -his Superintendent a rough drawing of the particular part, properly dimensioned, so that it could be worked from, and time saved on the -arrival of the ship at the port where the repairs are to be done.</p> - -</div><!--note--> - -<hr class="chap x-ebookmaker-drop" /> - -<p><span class="pagenum" id="Page18">[18]</span></p> - -<div class="container w20em"> -<img src="images/illo018.jpg" alt="Artist" /> -</div> - -<hr class="chap x-ebookmaker-drop" /> - -<p><span class="pagenum" id="Page19">[19]</span></p> - -<div class="container w30em"> -<img src="images/illo019.png" alt="PLAN OF THE WORK" /> -</div> - -<hr class="chap x-ebookmaker-drop" /> - -<p><span class="pagenum" id="Page20">[20]</span></p> - -<div class="ballard"> - -<p><span class="padl4">“<i>No matter how thorough our education may have been</i></span><br /> -<span class="padl3 ws05"><i>at the first, rules and formulas will slip from the</i></span><br /> -<span class="padl2"><i>memory, and every day’s experience gives additional</i></span><br /> -<span class="padl1"><i>evidence of the truth of the old adage that</i> ‘<span class="smcapall">THE</span><br /> -KEY THAT RESTS, RUSTS</span>.’”—<span class="smcap fsize90">Simpson Ballard.</span></p> - -</div><!--ballard--> - -<hr class="chap x-ebookmaker-drop" /> - -<div class="chapter"> - -<p><span class="pagenum" id="Page21">[21]</span></p> - -<h2 class="nobreak">The Plan of the Work.</h2> - -</div><!--chapter--> - -<p>The purpose or scope of this work may be briefly stated: It is to aid the aspiring student in making the first -advance towards a thorough and useful knowledge of drawing in its several divisions, as elsewhere defined.</p> - -<p>The method to be followed in presenting the subject will be the natural order clearly and simply defined, -as “from the less to the greater.”</p> - -<p>The first subject to be discussed comes under the heading of chalk-work, <i>i. e.</i>, such drawings as can be -executed on a blackboard, a floor, or even on more primitive surfaces, such as a smooth stone or board.</p> - -<p>This is indeed a lowly beginning, but the author is quite confident it will awaken as much interest as any part -of the book—even in the most experienced in the art of drawing, as to them it will revive the ambitions and first -crude attempts made in the golden days of their youth.</p> - -<p>Let it be clearly understood by all, and especially by those who wish to learn drawing, that the study of this -delightful art does not require any special qualification. We need only ask one question: Have you learned to -write? If so, be assured you may learn to draw, but to all the same rule applies, first the elements of the art, and -afterwards the more advanced study.</p> - -<p>It is not expected that all should exhibit a decided taste for drawing, for the possession of this is rather a gift -of nature than the result of education; but a knowledge of principles and a certain amount of executive ability<span class="pagenum" id="Page22">[22]</span> -may be obtained by every one of average capacity, and whatever the natural power may be, it will be increased -and developed by exercise; if the progress is steady and continuous and in the right direction, success is sure to -crown the work.</p> - -<p>The second division of the book will be free-hand drawing, <i>i. e.</i>, that which is executed without instruments. -Nothing to instruct has been spared in this important step in the path of advancement.</p> - -<p>The illustrations accompanying the two opening sections have been made designedly elementary, for there -are many who have a taste for drawing and who have a desire to learn, who from place of residence or other -circumstances have not the opportunity of receiving the assistance of a master. To such this book presents itself -as a friend directing to the right road, talking, reasoning, and explaining by the way.</p> - -<p>The “chalk-work” and “free-hand” sections of the book relate to the foundations upon which all must rest -who seek the aid to be derived from the art; hence, the following pages are written with a view to encourage all, -and those who are prepared to follow the directions given in them may look forward to the possession of sufficient -drawing power to add to their usefulness in after life.</p> - -<p>At this point of attainment there arises a need to know the meaning of many words and phrases used by -draughtsmen; these are grouped alphabetically from A to Z under the heading <span class="nowrap">of,——</span></p> - -<p>Useful Terms and Definitions: Memorizing these few pages will be of benefit, as an intimate knowledge -of the language of the drawing office stamps a man as worthy of a hearing, and assures attention to anything -which he may write or say pertaining to the art.</p> - -<p><span class="pagenum" id="Page23">[23]</span></p> - -<p>After the Definitions the subject explained will be the Instruments and Materials used in mechanical -drawings; following in due course appear Geometrical and Mechanical Drawing, Gearing, Linear Perspective, Projection, -Shading, Tracing, Lettering, Drawing Office Rules, Reading Drawings, Useful Tables and a General Index, -to which the student is referred. A careful reading is requested to the following helpful note.</p> - -<p>Grateful acknowledgment is made to George Perrott, Esq., M. E., for practical and technical assistance -throughout the work, and to Theo. Lucas, Engineer, for text and illustrations in the portions of the book relating -to Linear Perspective and Projection.</p> - -<div class="note"> - -<p><span class="smcap">Note.</span>—In <span class="smcap">Machinery</span> Prof. Chas. H. Benjamin says, referring to drawing, under heading “How and what to study,” “... I have -so far said nothing about drawing, for I do not think it of much use to learn that, until you know what you want of it. All this time that -you have been studying mechanism you should have had a sketch book or pad of note paper, and made free hand sketches of mechanical -movements which interested you and of various machine details. You should accustom yourself to use drawing as a means of expressing -ideas, just as you use written words, so that it becomes a second nature to you to sketch anything you wish to remember or describe. If -you work from blue-prints in the shop, or if you can borrow some to study, this will help you to understand how a drawing is made. You -can get some drawing instruments at any time and begin to practice on drawing straight lines and circles, so as to become familiar with -the instruments. And here it will be of great benefit to you if you can attend an evening drawing school for one night in the week -at least.</p> - -<p>“When you have become sufficiently familiar with the principles of drawing, a book on mechanism will tell you how to draw gear -teeth and cams, and how to design various link motions. Make up your own problems from what you see in the shop and make your drawing -a means to an end and not the principal thing; it is of little use to be able to make a nice drawing unless you know what to draw and why.</p> - -<p>“Drawing is a convenient tool as an aid in expressing to others the ideas which you wish to convey; in all cases take the problems -and the ideas from your every-day work and that which is around you; your success will depend upon the close connection which you -keep at all times between your acquired knowledge and your practical work.”</p> - -</div><!--note--> - -<hr class="chap x-ebookmaker-drop" /> - -<div class="chapter"> - -<p><span class="pagenum" id="Page24">[24]</span></p> - -<h2 class="nobreak">General List of Contents.</h2> - -</div><!--chapter--> - -<table class="toc" summary="Contents"> - -<tr> -<td class="subject"><span class="smcap">Introduction</span>,</td> -<td class="pages"><a href="#Page1">1</a>-<a href="#Page24">24</a></td> -</tr> - -<tr> -<td class="subject"><span class="smcap">Chalk Work</span>,</td> -<td class="pages"><a href="#Page25">25</a>-<a href="#Page38">38</a></td> -</tr> - -<tr> -<td class="subject"><span class="smcap">Preliminary Terms and Definitions</span>,</td> -<td class="pages"><a href="#Page39">39</a>-<a href="#Page52">52</a></td> -</tr> - -<tr> -<td class="subject"><span class="smcap">Freehand Drawing</span>,</td> -<td class="pages"><a href="#Page53">53</a>-<a href="#Page78">78</a></td> -</tr> - -<tr> -<td class="subject"><span class="smcap">Geometrical Drawing</span>,</td> -<td class="pages"><a href="#Page79">79</a>-<a href="#Page100">100</a></td> -</tr> - -<tr> -<td class="subject"><span class="smcap">Drawing Materials and Instruments</span>,</td> -<td class="pages"><a href="#Page101">101</a>-<a href="#Page134">134</a></td> -</tr> - -<tr> -<td class="subject"><span class="smcap">Mechanical Drawing</span>,</td> -<td class="pages"><a href="#Page135">135</a>-<a href="#Page188">188</a></td> -</tr> - -<tr> -<td class="subject"><span class="smcap">Penciling</span>,</td> -<td class="pages"><a href="#Page139">139</a>-<a href="#Page147">147</a></td> -</tr> - -<tr> -<td class="subject"><span class="smcap">Projection</span>,</td> -<td class="pages"><a href="#Page148">148</a>-<a href="#Page164">164</a></td> -</tr> - -<tr> -<td class="subject"><span class="smcap">Inking in Drawings</span>,</td> -<td class="pages"><a href="#Page167">167</a>-<a href="#Page170">170</a></td> -</tr> - -<tr> -<td class="subject"><span class="smcap">Lettering Drawings</span>,</td> -<td class="pages"><a href="#Page171">171</a>-<a href="#Page175">175</a></td> -</tr> - -<tr> -<td class="subject"><span class="smcap">Dimensioning Drawings</span>,</td> -<td class="pages"><a href="#Page176">176</a>-<a href="#Page179">179</a></td> -</tr> - -<tr> -<td class="subject"><span class="smcap">Shading Drawings</span>,</td> -<td class="pages"><a href="#Page180">180</a>-<a href="#Page181">181</a></td> -</tr> - -<tr> -<td class="subject"><span class="smcap">Section Lining and Colors</span>,</td> -<td class="pages"><a href="#Page182">182</a>-<a href="#Page185">185</a></td> -</tr> - -<tr> -<td class="subject"><span class="smcap">Reproducing Drawings</span>,</td> -<td class="pages"><a href="#Page186">186</a>-<a href="#Page188">188</a></td> -</tr> - -<tr> -<td class="subject"><span class="smcap">Drawing Office Rules</span>,</td> -<td class="pages"><a href="#Page189">189</a>-<a href="#Page195">195</a></td> -</tr> - -<tr> -<td class="subject"><span class="smcap">Gearing</span>,</td> -<td class="pages"><a href="#Page197">197</a>-<a href="#Page208">208</a></td> -</tr> - -<tr> -<td class="subject"><span class="smcap">Designing Gears</span>,</td> -<td class="pages"><a href="#Page209">209</a>-<a href="#Page216">216</a></td> -</tr> - -<tr> -<td class="subject"><span class="smcap">Working Drawings</span>,</td> -<td class="pages"><a href="#Page219">219</a>-<a href="#Page227">227</a></td> -</tr> - -<tr> -<td class="subject"><span class="smcap">Reading Working Drawings</span>,</td> -<td class="pages"><a href="#Page228">228</a>-<a href="#Page230">230</a></td> -</tr> - -<tr> -<td class="subject"><span class="smcap">Patent Office Rules for Drawings</span>,</td> -<td class="pages"><a href="#Page231">231</a>-<a href="#Page236">236</a></td> -</tr> - -<tr> -<td class="subject"><span class="smcap">Useful Hints and “Points,”</span></td> -<td class="pages"><a href="#Page237">237</a>-<a href="#Page244">244</a></td> -</tr> - -<tr> -<td class="subject"><span class="smcap">Linear Perspective</span>,</td> -<td class="pages"><a href="#Page245">245</a>-<a href="#Page265">265</a></td> -</tr> - -<tr> -<td class="subject"><span class="smcap">Personal, by the Editor</span>,</td> -<td class="pages"><a href="#Page281">281</a></td> -</tr> - -<tr> -<td class="subject"><span class="smcap">Useful Tables</span>,</td> -<td class="pages"><a href="#Page269">269</a>-<a href="#Page280">280</a></td> -</tr> - -<tr> -<td class="subject"><span class="smcap">Reference Index</span>,</td> -<td class="pages"><a href="#Page283">283</a></td> -</tr> - -</table> - -<hr class="chap x-ebookmaker-drop" /> - -<p><span class="pagenum" id="Page25">[25]</span></p> - -<div class="container w30em"> -<img src="images/illo025.png" alt="CHALK-WORK" /> -</div> - -<hr class="chap x-ebookmaker-drop" /> - -<p><span class="pagenum" id="Page26">[26]</span></p> - -<table class="allart" summary="Faux table"> - -<tr> -<td colspan="5" class="topbot"> </td> -</tr> - -<tr> -<td rowspan="5" class="leftright"> </td> -<td class="blank btd bbd bld"> </td> -<td class="text btd"><span class="padl2">The</span> peculiarity of all art is that it cannot</td> -<td class="blank btd brd bbd"> </td> -<td rowspan="5" class="leftright"> </td> -</tr> - -<tr> -<td class="blank brd"> </td> -<td class="text">be communicated in writing alone, craft is a</td> -<td class="blank bld"> </td> -</tr> - -<tr> -<td class="blank brd"> </td> -<td class="text">term which is synonymous with art; a craft</td> -<td class="blank bld"> </td> -</tr> - -<tr> -<td class="blank brd"> </td> -<td class="text">requires manual dexterity which cannot be</td> -<td class="blank bld"> </td> -</tr> - -<tr> -<td class="blank btd bbd bld"> </td> -<td class="text bbd">taught in books.</td> -<td class="blank btd brd bbd"> </td> -</tr> - -<tr> -<td colspan="5" class="topbot"> </td> -</tr> - -</table> - -<hr class="chap x-ebookmaker-drop" /> - -<div class="chapter"> - -<p><span class="pagenum" id="Page27">[27]</span></p> - -<h2 class="nobreak">Chalk Work.</h2> - -</div><!--chapter--> - -<p>The blackboard has been well called the great -weapon of the modern educator; this is especially true -in reference to instruction in an art dealing with lines, -curves and figures.</p> - -<div class="container leftfloat w20em" id="Fig6"> -<img src="images/illo027a.jpg" alt="Chalk-crayon" /> -<p class="caption">Fig. 6.</p> -</div> - -<p>Many a man can chalk out on a blackboard, or on -a piece of sheet-iron, or on the floor, just what he wants -to show, and make his meaning very plain; hence, in -every workshop, and many other places, a blackboard -is more than useful, and it has been said that no -draughting office is complete without one.</p> - -<p><a href="#Fig6">Fig. 6</a> represents a chalk-crayon.</p> - -<div class="container" id="Fig7"> - -<img src="images/illo027b028.jpg" alt="Blackboards" /> - -<div class="split5050"> - -<div class="left5050"> -<p class="caption">Fig. 7.</p> -</div> - -<div class="right5050"> -<p class="caption">Fig. 8.</p> -</div> - -<p class="thinline allclear"> </p> - -</div><!--split5050--> - -</div><!--container--> - -<p><span class="pagenum" id="Page28">[28]</span></p> - -<p><a href="#Fig7">Figs. 7 and 8</a> need no explanation, as they represent -two forms of the well-known blackboard.</p> - -<p>Chalk lines have this advantage—they are easily -altered or rubbed out when not needed any longer. -The work executed upon a blackboard is mostly -done by hand, without aid from instruments; a few -tools, however, are useful—such as, 1, large wooden -blackboard compasses holding a crayon, which are made -and sold by the trade in size twelve inches to thirty -inches in length; 2, a straight-edge; and 3, some crayons. -With the compasses circles and part of the circle -can be made, and with the straight-edge the larger -lines can be drawn.</p> - -<p>These instruments are shown on <a href="#Page29">page 29</a>, and are, -1, compasses, for holding chalk for making circles; 2, a -tee-square; 3, a straight-edge; 4, a protractor for measuring -angles; 5, a triangle 60° and 30°; 6, a brass -holder for crayons.</p> - -<p>Blackboard Drawing.—The use of a blackboard -comes principally and properly under the head of<span class="pagenum" id="Page29">[29]</span> -free-hand drawing, but its importance is such that a -separate division of the volume is assigned to it.</p> - -<div class="container w50em"> -<img src="images/illo029.jpg" alt="Instruments" /> -</div> - -<p><span class="pagenum" id="Page30">[30]</span></p> - -<p>Thus, chalk-work may be considered the first lesson -in “free-hand,” as all the examples can also be most -profitably practiced with pencil and paper.</p> - -<p>Very rapid drawing upon the board should not be -encouraged, as it is likely not to be accurate enough; -again, the board should be entirely free from grease. -Cloths, sponges or chamois skin rubbers may be used -to erase or change the chalk marks. Vertical lines -should be drawn from above downward; short lines -should be drawn with the fingers alone, those somewhat -longer with the hand, using the wrist-joint; the still -longer lines with the forearm, using the elbow-joint; -those longer yet with the whole arm, using the -shoulder-joint; lines should always be drawn with a -uniform motion, slow enough for the eye to follow.</p> - -<p>Practice in chalk-work should alternate with -sketching in a sketchbook and with geometrical drawing—to -be hereafter described. The student should -practice a short time on the board, at least once a week; -large sizes are the most profitable for the representations -to be made; when drawing in different directions the -hand should be turned, not the paper or board; the -hand should never be allowed to obstruct the sight, -hence the hand and fingers should be held in a position -of freedom—with fingers not nearer than 1<sup>1</sup>⁄<sub>2</sub> or 2 -inches from the board.</p> - -<div class="note"> - -<p><span class="smcap">Note.</span>—The first lesson of any kind the author received in -drawing was to make a straight line; this was effected by holding -the pencil nearly erect and guiding it along by the aid of the little -finger held pressed against the edge of a board; this was a useful -item of knowledge, as proved by passing years.</p> - -<p>A well-known artist, in telling his early experience, said: -“The first thing I was taught was to draw a line, divide it, erect -a perpendicular from its center, and afterwards to divide the angle -made by the perpendicular.” In answer to a question asking how -long he was kept at the lines, he replied, “about two months—or -a month or two,” indicating that even the longer time would have -been well spent in learning to draw a straight line.</p> - -</div><!--note--> - -<h3>PREPARATORY PRACTICE IN DRAWING.</h3> - -<p>Every visible object is bounded by lines which -enable the observer to determine its shape. If these<span class="pagenum" id="Page31">[31]</span> -lines are straight or curved, the shape of the object is -regular; if broken, the shape of the object is irregular.</p> - -<p>The elements, then, of form are lines, straight, -curved, or broken, and these, therefore, furnish the -beginning of all instruction in free-hand or mechanical -drawing.</p> - -<h3>PERPENDICULAR LINES.</h3> - -<p><a href="#Fig1516">Fig. 15</a> shows six lines—upright and perpendicular, -with points or “dots” indicated at the top and bottom -of each line; to draw these, proceed thus:</p> - -<div class="container w30em" id="Fig1516"> - -<img src="images/illo031.png" alt="Straight lines" /> - -<div class="split4060"> - -<div class="left4060"> -<p class="caption padr6">Fig. 15.</p> -</div> - -<div class="right4060"> -<p class="caption padl6">Fig. 16.</p> -</div> - -<p class="thinline allclear"> </p> - -</div><!--split4060--> - -</div><!--container--> - -<p>The learner should stand with his right shoulder -opposite the board, and the weight of the hand and the -arm should be allowed to fall naturally; now, make on -the board two points, one being six inches above the -other, these being merely “dots,” shown at the ends of -the lines, <a href="#Fig1516">figs. 15</a>, etc., and made with two motions; -the line between the points should now be drawn -not too quickly from the upper to the lower point; -three movements of the hand and arm complete the -line; to draw the other five lines the movements have -simply to be repeated.</p> - -<p>If the student pronounces to himself “one,” -“two,” “three,” at each motion, it will be helpful; in -this exercise, <a href="#Fig1516">fig. 15</a>, the aim is to make six lines, each -line being parallel to the first. Again, in the example, -it is intended that the lower point should be made -first, next the upper, and lastly the line drawn from the -upper to the lower point, but the order may be reversed; -at <i>one</i> the upper point, at <i>two</i> the lower, at -<i>three</i> the stroke upwards to complete the line.</p> - -<p><span class="pagenum" id="Page32">[32]</span></p> - -<h3>HORIZONTAL LINES.</h3> - -<p>To make these as shown in <a href="#Fig1516">fig. 16</a>, proceed as -follows: With the word <i>one</i> make a point, with <i>two</i> -another point six inches at the left, with <i>three</i> draw a -straight line from the left point to the right. All added -lines should be parallel: for practice, reverse the process -thus, <i>one</i>, make a “point,” at <i>two</i> another point at the -right, at <i>three</i> draw line to the left.</p> - -<p>The student will note that the two motions—at -the words <i>one</i> and <i>two</i>—are to fix the positions of the -ends of the lines; this practice will be found useful in -the most advanced examples and an item of elementary -practice never to be forgotten—like the help to be -derived by the first round of a ladder.</p> - -<div class="container w30em" id="Fig1718"> - -<img src="images/illo032.png" alt="Oblique lines" /> - -<div class="split5050"> - -<div class="left5050"> -<p class="caption">Fig. 17.</p> -</div> - -<div class="right5050"> -<p class="caption">Fig. 18.</p> -</div> - -<p class="thinline allclear"> </p> - -</div><!--split5050--> - -</div><!--container--> - -<h3>OBLIQUE LINES.</h3> - -<p>In drawing oblique straight lines as shown in <a href="#Fig1718">fig. -17</a>, at the word <i>one</i> let the student make the lower -point; at the word <i>two</i> the upper, a little to the<span class="pagenum" id="Page33">[33]</span> -right of the lower; at the word <i>three</i> draw a line -quickly from the upper to the lower point. In pronouncing -the words <i>one</i>, <i>two</i>, <i>three</i>, let the student -make the additional parallel lines.</p> - -<p>As shown in <a href="#Fig1718">fig. 18</a>, at the word <i>one</i> make the lower -point; at the word <i>two</i> the upper point, a little <i>to the -left</i>; at the word <i>three</i> draw a line rapidly from the -upper to the lower point, and “timing” the process -by repeating <i>one</i>, <i>two</i>, <i>three</i>, make the additional parallel -lines.</p> - -<div class="container w15em" id="Fig19"> -<img src="images/illo033a.png" alt="Broken line" /> -<p class="caption">Fig. 19.</p> -</div> - -<h3>BROKEN LINES.</h3> - -<p>A broken line is composed of two or more straight -lines at angles to each other (see <a href="#Fig19">fig. 19</a>). To draw -them begin (saying) <i>one</i>, make a point; <i>two</i> a point -below at the left; <i>three</i>, a point above at the left; -<i>four</i>, draw a line from the left hand point to the lower -point; at the word <i>five</i>, from the lower point to the -upper right hand point. For practice draw numerous -lines in the same way, keeping them parallel to each -other, as shown in <a href="#Fig2021">fig. 20</a>.</p> - -<div class="container w30em" id="Fig2021"> - -<img src="images/illo033b.png" alt="" /> - -<div class="split5050"> - -<div class="left5050"> -<p class="caption">Fig. 20.</p> -</div> - -<div class="right5050"> -<p class="caption">Fig. 21.</p> -</div> - -<p class="thinline allclear"> </p> - -</div><!--split5050--> - -</div><!--container--> - -<p><span class="pagenum" id="Page34">[34]</span></p> - -<div class="container w30em" id="Fig2224"> - -<img src="images/illo034a.png" alt="Lines" /> - -<div class="split5050"> - -<div class="left5050"> -<p class="caption">Fig. 22.</p> -</div> - -<div class="right5050"> -<p class="caption">Fig. 24.</p> -</div> - -<p class="thinline allclear"> </p> - -</div><!--split--> - -</div><!--container--> - -<div class="container w30em" id="Fig2325"> - -<img src="images/illo034b.png" alt="Lines" /> - -<div class="split5050"> - -<div class="left5050"> -<p class="caption">Fig. 23.</p> -</div> - -<div class="right5050"> -<p class="caption">Fig. 25.</p> -</div> - -<p class="thinline allclear"> </p> - -</div><!--split5050--> - -</div><!--container--> - -<p><span class="pagenum" id="Page35">[35]</span></p> - -<p>In example, <a href="#Fig2021">fig. 21</a>, the arrangement of the points -is changed—let the student draw at the words, as -follows: <i>One</i>, a point; <i>two</i>, a point above at the left; -<i>three</i>, a point below at the left; <i>four</i>, draw from the -point at the left to the upper point; <i>five</i>, from the -upper point to the lower right hand point; continue -to add parallel lines to complete the figure as shown.</p> - -<p><a href="#Fig2224">Figs. 22</a> and <a href="#Fig2325">23</a> are given as examples to practice, -making first the points and then the connecting -lines and afterward the parallel lines to complete the -figures.</p> - -<h3>CURVED LINES.</h3> - -<p>To draw curved lines, as shown in <a href="#Fig2224">fig. 24</a>. At the -word <i>one</i>, point; at the word <i>two</i>, point three inches -directly above; <i>three</i>, at the same distance above again -make a point; now draw a curve as shown, joining the -middle point and the upper point; now draw the -curve as shown below it; finally complete figure -as shown.</p> - -<div class="container w30em" id="Fig2627"> - -<img src="images/illo035a.png" alt="Curved lines" /> - -<div class="split5050"> - -<div class="left5050"> -<p class="caption">Fig. 26.</p> -</div> - -<div class="right5050"> -<p class="caption">Fig. 27.</p> -</div> - -<p class="thinline allclear"> </p> - -</div><!--split--> - -</div><!--container--> - -<div class="container w30em" id="Fig28"> -<img src="images/illo035b.png" alt="Lines" /> -<p class="caption">Fig. 28.</p> -</div> - -<p><span class="pagenum" id="Page36">[36]</span></p> - -<div class="container w30em" id="Fig2930"> - -<img src="images/illo036.png" alt="Curves" /> - -<div class="split5050"> - -<div class="left5050"> -<p class="caption">Fig. 29.</p> -</div> - -<div class="right5050"> -<p class="caption">Fig. 30.</p> -</div> - -<p class="thinline allclear"> </p> - -</div><!--split5050--> - -</div><!--container--> - -<p><a href="#Fig2325">Figs. 25</a> to <a href="#Fig2930">30</a> are to be practiced, making first the -points and then connecting them by the curves to -complete the figures.</p> - -<p>When two or more students are working together, -with each having a blackboard, the counting may be -in concert—or a teacher could count for a class. In -these line examples care should be used in making -them of uniform length. There is a difference to be -noted between a crooked line and a broken line, the -latter being a straight line and the former deviating -from it.</p> - -<p>Square chalk crayons are the best for hand work, -as lines of an even or uniform width can be drawn with -them.</p> - -<p>A very fine effect is produced by using two thicknesses -of chalk, one being double the thickness of the -other; the heavy lines being used on the shade side of -objects will produce a good effect, giving thickness and -body to the object.</p> - -<p>Round chalk crayons are used in the compasses to -draw circles, but hand lines drawn with them are not so -neat as those produced with the square-shaped chalk.</p> - -<p>To obliterate or remove the construction, or false -lines made on the blackboard, a wooden handle two -inches in diameter with a cone end 3 or 4 inches long, -covered with chamois skin or soft cloth tightly wrapped -round the cone and fastened with a tack or drawing -pin, makes the best implement to erase lines not -required, the point of the cone will remove these without -destroying the lines or curves which meet them.</p> - -<p><span class="pagenum" id="Page37">[37]</span></p> - -<p>Sponges, chamois skin or cloth rubbers are used -to rub out the chalk drawings and clean the blackboard.</p> - -<p>The best height for a diagram on the blackboard -is not higher than the head, nor lower than the elbow.</p> - -<p>Horizontal lines should be made from the left to -the right; the body and arm being moved with the -hand, and kept in the same relative position with it, -will steady the hand.</p> - -<p>Curved lines to the left should be drawn first, -enabling the eye to take in not only the curve in process -of formation but that already made.</p> - -<p>Passing the crayon in the hand, over the intended -curve previous to marking it, will guide the eye and -give confidence to the hand in chalking the curve.</p> - -<p>A proper distance from the blackboard is essential, -the face being about two feet away from it.</p> - -<p>Draw with the whole arm extended from the -shoulder-joint, not from the elbow or wrist.</p> - -<div class="container w50em" id="Fig31"> -<img src="images/illo037.jpg" alt="Crayon holder" /> -<p class="caption">Fig. 31.</p> -</div> - -<p><span class="pagenum" id="Page38">[38]</span></p> - -<table class="allart" summary="Faux table"> - -<tr> -<td colspan="3" class="topbot"> </td> -</tr> - -<tr> -<td class="leftright blanktop"> </td> -<td class="text btd brd bbd bld blanktop blankbot">“There are more ways than one of telling<br /> -things: by speech, by writing, by printing,<br /> -also by pictures and drawings.” Knowles</td> -<td class="leftright blankbot"> </td> -</tr> - -<tr> -<td colspan="3" class="topbot"> </td> -</tr> - -</table> - -<hr class="chap x-ebookmaker-drop" /> - -<p><span class="pagenum" id="Page39">[39]</span></p> - -<div class="container w30em"> -<img src="images/illo039.png" alt="TERMS DEFINITIONS" /> -</div> - -<hr class="chap x-ebookmaker-drop" /> - -<p><span class="pagenum" id="Page40">[40]</span></p> - -<div class="container w30em"> -<img src="images/illo040.jpg" alt="" /> -<p class="caption">ELECTRA.</p> -</div> - -<hr class="chap x-ebookmaker-drop" /> - -<div class="chapter"> - -<p><span class="pagenum" id="Page41">[41]</span></p> - -<h2 class="nobreak">Preliminary Terms and Definitions.</h2> - -</div><!--chapter--> - -<p>Like all the arts, drawing has a nomenclature of its -own, and nothing can be more helpful to the beginner -than to know the name of things relating to the art -of drawing. This is a language almost peculiar to -itself, and used daily and hourly by many thousands -of superintendents, foremen and master mechanics, as -well as by owners, designers and draughtsmen, hence -its introduction at this early stage.</p> - -<div class="definitions"> - -<p class="level0"><b>ALTITUDE.</b>—This is the elevation of an object above -its base, or the perpendicular distance between -the top and bottom of a figure.</p> - -<div class="container rightfloat w10em"> - -<div class="container w07em" id="Fig33"> -<img src="images/illo041.png" alt="Angle" /> -<p class="caption">Fig. 33.</p> -</div> - -<div class="container w05em" id="Fig34"> -<img src="images/illo042a.png" alt="Right angle" /> -<p class="caption">Fig. 34.</p> -</div> - -<div class="container w05em" id="Fig35"> -<img src="images/illo042b.png" alt="Acute angle" /> -<p class="caption">Fig. 35.</p> -</div> - -<div class="container w07em" id="Fig36"> -<img src="images/illo042c.png" alt="Obtuse angle" /> -<p class="caption">Fig. 36.</p> -</div> - -<div class="container w10em" id="Fig37"> -<img src="images/illo042d.png" alt="Angles" /> -<p class="caption">Fig. 37.</p> -</div> - -</div><!--container right--> - -<p class="level0" id="Ref4"><b>ANGLE</b> is the difference in the direction of two lines -which meet or tend to meet. The lines are called -<i>the sides</i> and the point of meeting, the <i>vertex</i> of -the lines.</p> - -<p class="level1">To make an angle apparent, -the two lines must meet in a -point, as <i>A B</i> and <i>A C</i>, which -meet in the point <i>A</i>, as shown -in <a href="#Fig33">fig. 33</a>.</p> - -<p class="level1">Angles are measured by degrees.</p> - -<p class="level1">A <i>Degree</i> is one of the three hundred and -sixty equal parts of the space about a point in a -plane.</p> - -<p class="level1">Angles are distinguished in respect to magnitude -by the terms Right, Acute and Obtuse -Angles.</p> - -<p><span class="pagenum" id="Page42">[42]</span></p> - -<p class="level1">A <i>Right Angle</i> is that formed -by one line meeting another, so as -to make equal angles with that -other.</p> - -<p class="level1">The lines forming a right angle are <i>perpendicular -to each other</i>.</p> - -<p class="level1">An <i>Acute Angle</i> is less than -a right angle. See <a href="#Fig35">Fig. 35</a>.</p> - -<p class="level1">An <i>Obtuse Angle</i> is greater -than a right angle. See <a href="#Fig36">Fig. 36</a>.</p> - -<p class="level1">Obtuse and acute angles are also called <i>oblique -angles</i>; and lines which -are neither parallel nor -perpendicular to each other -are called <i>oblique lines</i>.</p> - -<p class="level1">The <i>Vertex</i> or <i>Apex</i> of an angle is the point -in which the including lines meet.</p> - -<p class="level1">An angle is commonly designated by a letter -at its vertex; but when two or more angles have -their vertices at the same point, they cannot be -thus distinguished.</p> - -<p class="level1">For example, -when the three lines -<i>A B</i>, <i>A C</i>, and <i>A D</i> in -<a href="#Fig37">fig. 37</a> meet in the -common point <i>A</i>, we -designate either of the -angles formed, by -three letters, placing -that at the vertex -between those at the opposite extremities of the -including lines. Thus, we say, the angle <i>B A C</i>, etc.</p> - -<p class="level0"><b>APEX.</b>—The summit or highest point of an object.</p> - -<p class="level0"><b>ARC.</b>—See <a href="#Ref1">circle</a>.</p> - -<p class="level0"><b>AXIS OF A SOLID.</b>—An imaginary straight line passing -through its center.</p> - -<p><span class="pagenum" id="Page43">[43]</span></p> - -<p class="level0"><b>AXIS OF A FIGURE.</b>—A straight line passing through -the center of a figure, and dividing it into two -equal parts.</p> - -<p class="level0"><b>BASE.</b>—The base of a solid figure is that on which it -stands—the lowest part.</p> - -<p class="level0"><b>BISECT.</b>—To divide into two equal parts.</p> - -<p class="level0"><b>BISECTOR.</b>—A line which bisects.</p> - -<div class="container rightfloat w10em" id="Fig38"> -<img src="images/illo043.png" alt="Circle" /> -<p class="caption">Fig. 38.</p> -</div> - -<p class="level0" id="Ref1"><b>CIRCLE.</b>—A <i>Circle</i> is a plane -figure bounded by one uniformly -curved line, all of the -points in which are at the -same distance from a certain -point within, called the -<i>Center</i>.</p> - -<p class="level1">The <i>Circumference</i> of a circle is the curved -line that bounds it.</p> - -<p class="level1">The <i>Diameter</i> of a circle is a line passing -through its center, and terminating at both ends -in the circumference, as <i>A C B</i>.</p> - -<p class="level1">The <i>Radius</i> of a circle is a line extending -from its center to any point in the circumference. -It is one-half of the diameter. All the diameters -of a circle are equal, as are also all the radii <i>C D</i>, -<i>C B</i> and <i>C A</i>.</p> - -<p class="level1">An <i>Arc</i> of a circle is any portion of the circumference, -as <i>B D</i> and <i>A D</i>.</p> - -<p class="level1"><i>Semi-Circle.</i>—Half a circle formed by bisecting -it with a diameter, as <i>A C B</i>. <a href="#Fig38">Fig. 38</a>.</p> - -<p class="level1">An angle having its vertex at the center of a -circle is measured by the arc intercepted by its -sides. Thus, the arc <i>A D</i> measures the angle -<i>A C D</i>, and in general, to compare different angles, -we have but to compare the arcs, included by their -sides, of the equal circles having their centers at -the vertices of the angles.</p> - -<p class="level0" id="Ref3"><b>CIRCUMSCRIBE.</b>—To draw a line of figures about or -outside, such as a circle drawn around a square -touching its corners or angles.</p> - -<p><span class="pagenum" id="Page44">[44]</span></p> - -<p class="level1"><i>Inscribe.</i>—To draw a line or figure inside or -on the interior, such as a circle drawn within a -square touching its sides.</p> - -<p class="level0"><b>CONCAVE.</b>—Curving inwardly.</p> - -<p class="level0"><b>CONE.</b>—A solid body or figure having a circle for its -base, and its top terminated in a point or vertex.</p> - -<p class="level0"><b>CONSTRUCTION.</b>—The making of any object.</p> - -<p class="level0"><b>CONTOUR.</b>—The outline of the general appearance of -an object.</p> - -<p class="level0"><b>CONVERGENCE.</b>—Lines extending towards a common -point.</p> - -<p class="level0"><b>CONVEX.</b>—Rising or swelling into a round form—the -opposite to concave.</p> - -<p class="level0"><b>CORNER.</b>—The point of meeting of the edges of a -solid, or the two sides of a plane figure.</p> - -<p class="level0"><b>CROSS-HATCHES.</b>—In free-hand drawing the use of -lines crossing each other to produce light and -shade effects.</p> - -<p class="level0"><b>CURVE.</b>—A line of which no part is straight.</p> - -<p class="level1"><i>Reversed Curve.</i>—One whose curvature is first -in one direction and then in the opposite direction.</p> - -<p class="level1"><i>Spiral Curve.</i>—A plain curve which winds -about and recedes, according to some law, from its -point of beginning, which is called its center.</p> - -<p class="level0"><b>CYLINDER.</b>—A solid bounded by a curved surface and -by two opposite faces called bases; the bases may -be any curved figures and give the name to the -cylinder; thus a circular cylinder is one whose -bases are circles.</p> - -<p class="level0"><b>CYLINDRICAL.</b>—Having the general form of a cylinder.</p> - -<p class="level0"><b>DEGREE.</b>—The 360th part of a circle.</p> - -<p class="level0"><b>DESCRIBE.</b>—To make or draw a curved line; to draw -a plan.</p> - -<p class="level0"><b>DESIGN.</b>—Any arrangement or combination to produce -desired results in industry or art. To -delineate a form or figure by drawing the outline—a -sketch.</p> - -<p><span class="pagenum" id="Page45">[45]</span></p> - -<p class="level0"><b>DEVELOP.</b>—To unroll or lay out.</p> - -<p class="level0"><b>DIAGONAL.</b>—A right line drawn from angle to angle -of a quadrilateral or many angled figure and -dividing it into two parts.</p> - -<p class="level0"><b>DIAMETER.</b>—A right line passing through the center -of a circle or other round figure terminated by the -curve and dividing the figure symmetrically into -two equal parts.</p> - -<p class="level0"><b>EDGE.</b>—The intersection of any two surfaces.</p> - -<p class="level0" id="Ref7"><b>ELEVATION.</b>—The term elevation, vertical projection -and <i>front view</i>—applied to drawings—all have the -same meaning.</p> - -<p class="level0"><b>FACE.</b>—One of the plane surfaces of a solid; it may -be bounded by straight or curved edges.</p> - -<p class="level0"><b>FINISHING.</b>—Completing a drawing whose lines have -been determined by erasing unnecessary lines and -strengthening and accentuating where this is -needed.</p> - -<p class="level0"><b>FORESHORTENING.</b>—Apparent decrease in length, -owing to objects being viewed obliquely; thus a -wheel, when seen obliquely, instead of appearing -round, presents the appearance of an ellipse.</p> - -<p class="level0"><b>FREE-HAND.</b>—Executed by the hand unaided by -instruments.</p> - -<p class="level0"><b>GENERATED.</b>—Produced by.</p> - -<p class="level0"><b>GEOMETRIC.</b>—According to geometry.</p> - -<p class="level0"><b>HALF-TINT.</b>—The shading produced by means of -parallel equidistant lines.</p> - -<p class="level0"><b>HEMISPHERE.</b>—Half a sphere obtained by bisecting -a sphere by a plane.</p> - -<p class="level0"><b>HORIZONTAL.</b>—Parallel to the surface of smooth -water. In drawing, a line drawn parallel to the -top and bottom of the sheet is called horizontal.</p> - -<p class="level0"><b>INSCRIBE.</b>—See <a href="#Ref3">circumscribe</a>—its opposite.</p> - -<p class="level0"><b>INSTRUMENTAL.</b>—By the use of instruments.</p> - -<p><span class="pagenum" id="Page46">[46]</span></p> - -<p class="level0"><b>LINE.</b>—A line has length, only, as A C; a right line is -a straight line, the shortest line that can be drawn -between two points, A——C.</p> - -<p class="level1"><i>Straight.</i> One which has the same direction -throughout its entire length.</p> - -<p class="level1"><i>Curved.</i> One no part of which is straight.</p> - -<p class="level1"><i>Broken.</i> One composed of different successive -straight lines.</p> - -<p class="level1"><i>Mixed.</i> One of straight and curved lines.</p> - -<p class="level1"><i>Center.</i> A line used to indicate the center of -an object.</p> - -<p class="level1"><i>Construction.</i> A working line used to obtain -required lines.</p> - -<p class="level1"><i>Dotted.</i> A line composed of short dashes. <span class="nowrap">- - - - - -</span></p> - -<p class="level1"><i>Dash.</i> A line composed of long dashes. <span class="nowrap">— — —</span></p> - -<p class="level1"><i>Dot</i> and <i>Dash</i>. A line composed of dots and -dashes alternating. <span class="nowrap">— · — · —</span></p> - -<p class="level1"><i>Dimension.</i> A line upon which a dimension -is placed.</p> - -<p class="level1"><i>Full.</i> An unbroken line, usually representing -a visible edge. <span class="nowrap">———</span></p> - -<p class="level1"><i>Shadow.</i> A line about twice as wide as the -ordinary full line.</p> - -<p class="level1">A straight line is often called simply a line, -and a curved line a curve.</p> - -<p class="level0"><b>LONGITUDINAL.</b>—In the direction of the length of an -object.</p> - -<p class="level0"><b>MODEL.</b>—A form used for study.</p> - -<p class="level0"><b>OBLIQUE.</b>—Neither horizontal nor vertical.</p> - -<p class="level0"><b>OBLONG.</b>—A rectangle with unequal sides.</p> - -<p class="level0"><b>OVAL.</b>—A plane figure resembling the longitudinal -section of an egg; or elliptical in shape.</p> - -<p class="level0"><b>OVERALL.</b>—The entire length.</p> - -<p class="level0"><b>PARALLEL.</b>—Having the same direction and everywhere -equally distant.</p> - -<p class="level0"><b>PATTERN.</b>—That which is used as a guide or copy in -making things.</p> - -<p class="level1"><i>Flat.</i> One made of paper or other thin material.</p> - -<p><span class="pagenum" id="Page47">[47]</span></p> - -<p class="level1"><i>Solid.</i> One which reproduces the form -and size of the object to be made.</p> - -<p class="level0"><b>PERIMETER.</b>—The boundary of a closed plane figure.</p> - -<p class="level0"><b>PERPENDICULAR.</b>—At an angle of 90°.</p> - -<p class="level0"><b>PERSPECTIVE.</b>—View; drawing objects as they appear -to the eye from any given distance and situation, -real or imaginary.</p> - -<p class="level0"><b>PLAN.</b>—Plan, horizontal projection and <i>top view</i> have -the same meaning.</p> - -<p class="level0"><b>PLANE FIGURE.</b>—A part of a plane surface bounded -by straight or curved lines, or by both combined.</p> - -<div class="container rightfloat w10em" id="Fig39"> -<img src="images/illo047a.png" alt="Polygon" /> -<p class="caption">Fig. 39.</p> -</div> - -<p class="level0"><b>POLYGON.</b>—A plane figure bounded by straight lines -called the sides of the polygon. -The least number of -sides that can bound a -polygon is three. Polygons -bounded by a greater number -of sides than four are -denominated only by the number of sides.</p> - -<p class="level1">A polygon of five sides is called a <i>Pentagon</i>; -of six, a <i>Hexagon</i>; of seven, a <i>Heptagon</i>; -of eight, an <i>Octagon</i>; of nine, a <i>Nonagon</i>, etc.</p> - -<p class="level1"><i>Diagonals</i> of a polygon are lines joining the -vertices of angles not adjacent.</p> - -<p class="level1">The <i>Perimeter</i> of a polygon is its boundary -considered as a whole.</p> - -<p class="level1">The <i>Base</i> of a polygon is the side upon which -the polygon is supposed to stand.</p> - -<p class="level1">The <i>Altitude</i> of a polygon is the perpendicular -distance between the base and a side or angle -opposite the base.</p> - -<div class="container rightfloat w10em" id="Fig40"> -<img src="images/illo047b.png" alt="Parallelogram" /> -<p class="caption">Fig. 40.</p> -</div> - -<p class="level1" id="Ref5">A <i>Quadrilateral</i> is a polygon having four sides -and four angles.</p> - -<p class="level1">A <i>Parallelogram</i> is a -quadrilateral which has its -opposite sides parallel.</p> - -<p class="level1">The side upon which a -parallelogram stands and the opposite side are -called respectively its lower and upper bases.</p> - -<p><span class="pagenum" id="Page48">[48]</span></p> - -<p class="level1">A <i>Rectangle</i> is a parallelogram -having its angles right -angles.</p> - -<p class="level1">A <i>Square</i> is an equilateral -rectangle, <a href="#Fig41">fig. 41</a>.</p> - -<div class="container leftfloat w07em allclear"> - -<div class="container w05em" id="Fig41"> -<img src="images/illo048a.png" alt="Square" /> -<p class="caption">Fig. 41.</p> -</div> - -<div class="container w05em" id="Fig42"> -<img src="images/illo048b.png" alt="Rhombus" /> -<p class="caption">Fig. 42.</p> -</div> - -<div class="container w05em" id="Fig43"> -<img src="images/illo048c.png" alt="Trapezium" /> -<p class="caption">Fig. 43.</p> -</div> - -<div class="container" id="Fig44"> -<img src="images/illo048d.png" alt="Trapezoid" /> -<p class="caption">Fig. 44.</p> -</div> - -</div><!--container--> - -<div class="container rightfloat w07em" id="Fig4549"> - -<img src="images/illo048e.jpg" alt="Polyhedrons" /> -<p class="caption">Figs. 45-49.</p> - -</div><!--container--> - -<p class="level1">A <i>Rhomboid</i> is an oblique-angled -parallelogram.</p> - -<p class="level1">A <i>Rhombus</i> is an equilateral -rhomboid, <a href="#Fig42">fig. 42</a>.</p> - -<p class="level1">A <i>Trapezium</i> is a quadrilateral -having no two sides parallel, -<a href="#Fig43">fig. 43</a>.</p> - -<p class="level1">A <i>Trapezoid</i> is a quadrilateral -in which two opposite sides -are parallel, and the other two -oblique, <a href="#Fig44">fig. 44</a>.</p> - -<p class="level0"><b>A POLYHEDRON</b> is a solid bounded -by planes. There are five regular -solids which are shown in -<a href="#Fig4549">figs. 45, 46, 47, 48 and 49</a>. A -regular solid is bounded by -similar and regular plane figures.</p> - -<p class="level1"><a href="#Fig4549">Fig. 45</a>.—The <i>tetrahedron</i>, -bounded by four equilateral -triangles.</p> - -<p class="level1"><a href="#Fig4549">Fig. 46</a>.—The <i>hexahedron</i>, -or cube, bounded by six squares.</p> - -<p class="level1"><a href="#Fig4549">Fig. 47</a>.—The <i>octahedron</i>, -bounded by eight equilateral -triangles.</p> - -<p class="level1"><a href="#Fig4549">Fig. 48</a>.—The <i>dodecahedron</i>, -bounded by twelve pentagons.</p> - -<p class="level1"><a href="#Fig4549">Fig. 49</a>.—The <i>icosahedron</i>, -bounded by twenty equilateral -triangles.</p> - -<p><span class="pagenum" id="Page49">[49]</span></p> - -<p class="level0"><b>PRISM.</b>—A solid whose bases or ends are very similar -plane figures, and whose sides are parallelograms; -prisms are called triangular, square, etc., according -as the bases are triangles, squares, etc.</p> - -<p class="level0"><b>PRODUCE.</b>—To continue or extend.</p> - -<p class="level0"><b>PROFILE.</b>—An outline or contour.</p> - -<p class="level0"><b>PROJECTION.</b>—The view of an object obtained upon -a plane by projecting lines perpendicular to the -plane.</p> - -<p class="level0"><b>QUADRANT.</b>—The fourth part; a quarter; the quarter -of a circle.</p> - -<p class="level0"><b>QUADRISECT.</b>—To divide into four equal parts.</p> - -<p class="level0"><b>SECTION.</b>—A projection upon a plane parallel to a -cutting plane which intersects any object. The -section generally represents the part behind the -cutting plane, and represents the cut surfaces by -diagonal lines.</p> - -<p class="level0"><b>SECTIONAL.</b>—Showing the section made by a plane.</p> - -<p class="level0"><b>SHADOW.</b>—Shade and shadow have about the same -meaning.</p> - -<p class="level0"><b>SOLID.</b>—A solid has three dimensions—length, breadth -and thickness.</p> - -<p class="level0"><b>SPHERE.</b>—A solid bounded by a curved surface every -point of which is equally distant from a point -within called the center.</p> - -<p class="level0"><b>SURFACE.</b>—The boundary of a solid. It has but two -dimensions—length and breadth. Surfaces are -plane or curved.</p> - -<p class="level1">A <i>Plane Surface</i> is one upon which a straight -line can be drawn in any direction.</p> - -<p class="level1">A <i>Curved Surface</i> is one no part of which is -plane.</p> - -<p class="level1">The surface of the sphere is curved in every -direction, while the curved surfaces of the cylinder -and cone are straight in one direction.</p> - -<p class="level1">The surface of a solid is no part of the solid, -but is simply the boundary of the solid. It has -two dimensions only, and any number of surfaces -put together will give no thickness.</p> - -<p><span class="pagenum" id="Page50">[50]</span></p> - -<div class="container leftfloat w07em"> - -<div class="container w07em" id="Fig50"> -<img src="images/illo050a.png" alt="Triangle" /> -<p class="caption">Fig. 50.</p> -</div> - -<div class="container w05em" id="Fig51"> -<img src="images/illo050b.png" alt="Triangle" /> -<p class="caption">Fig. 51.</p> -</div> - -<div class="container w05em" id="Fig52"> -<img src="images/illo050c.png" alt="Triangle" /> -<p class="caption">Fig. 52.</p> -</div> - -</div><!--container--> - -<div class="container rightfloat w10em"> - -<div class="container w10em" id="Fig53"> -<img src="images/illo050d.png" alt="Triangle" /> -<p class="caption">Fig. 53.</p> -</div> - -<div class="container w10em" id="Fig54"> -<img src="images/illo050e.png" alt="Triangle" /> -<p class="caption">Fig. 54.</p> -</div> - -</div><!--container--> - -<p class="level0"><b>SYMMETRY.</b>—<i>Design.</i> A proper adjustment or adaptation -of parts to one another and to the whole.</p> - -<p class="level0"><b>TRISECT.</b>—To divide into three equal parts.</p> - -<p class="level0" id="Ref6"><b>TRIANGLE.</b>—A triangle is a polygon having three -sides and three angles. <i>Tri</i> is a Latin prefix signifying -three; hence a Triangle is literally a figure -containing three angles.</p> - -<p class="level1">A <i>Scalene Triangle</i> is one -in which no two sides are equal. -See <a href="#Fig50">fig. 50</a>.</p> - -<p class="level1">An <i>Isosceles Triangle</i> is one -in which two of the sides are -equal. See <a href="#Fig51">fig. 51</a>.</p> - -<p class="level1">An <i>Equilateral Triangle</i> is -one in which the three sides are -equal. An <i>Equiangular Triangle</i> -is one having its three angles -equal. An <i>Acute-Angled Triangle</i> -is one in which each angle is acute.</p> - -<p class="level1">A <i>Right-Angled Triangle</i> is -one which has one of the angles a -right angle. See <a href="#Fig53">fig. 53</a>.</p> - -<p class="level1">An <i>Obtuse-Angled Triangle</i> -is one having an -obtuse angle. <a href="#Fig54">Fig. 54</a>.</p> - -<p class="level1">Equiangular triangles are also equal sided, -and vice versa.</p> - -<p><span class="pagenum" id="Page51">[51]</span></p> - -<p class="level0"><b>VERTICAL.</b>—Upright or perpendicular. Vertical and -perpendicular are not synonymous terms.</p> - -<p class="level0"><b>VERTEX.</b>—See <a href="#Ref4">Angle</a>, -<a href="#Ref5">Quadrilateral</a>, <a href="#Ref6">Triangle</a>. The -vertex of a solid is the point in which its axis intersects -the lateral surface.</p> - -<p class="level0"><b>VIEW.</b>—See <a href="#Ref7">Elevation</a>. Views are called front, top, -right or left side, back, or bottom, according as -they are made on the different planes of projection. -They are also sometimes named according to the -part of the object shown, as edge view, end view, -or face view.</p> - -<p class="level0"><b>WORKING DRAWING.</b>—One which gives all the information -necessary to enable the workman to -construct the object.</p> - -</div><!--definitions--> - -<p><span class="pagenum" id="Page52">[52]</span></p> - -<div class="container w30em"> -<img src="images/illo052.jpg" alt="Knife" /> -</div> - -<hr class="chap x-ebookmaker-drop" /> - -<p><span class="pagenum" id="Page53">[53]</span></p> - -<div class="container w30em"> -<img src="images/illo053.png" alt="FREEHAND DRAWING" /> -</div> - -<hr class="chap x-ebookmaker-drop" /> - -<p><span class="pagenum" id="Page54">[54]</span></p> - -<div class="container w40em" id="Fig55"> -<img src="images/illo054.png" alt="Free(-)hand Drawing" /> -<p class="caption">Fig. 55.</p> -</div> - -<hr class="chap x-ebookmaker-drop" /> - -<div class="chapter"> - -<p><span class="pagenum" id="Page55">[55]</span></p> - -<h2 class="nobreak">Free-Hand Drawing.</h2> - -</div><!--chapter--> - -<p>A free-hand drawing is executed with the unaided -hand and eye, without guiding instruments or other -artificial help. It is necessary to be known that all -drawing required cannot possibly be done by rule and -compass, but that some portions must be drawn “free-hand,” -trusting to the eye alone.</p> - -<p>Hence, it is important that the student should be -able to sketch at sight from objects he may see, or to -draw roughly, with a piece of chalk or a pencil, pieces -of mechanism required to be represented.</p> - -<p>Practice in free-hand should go along with mechanical -drawing as progress is made, and thus cultivating -both branches equally.</p> - -<p>“A simple sketch will often,” as has been rather -roughly said, “express more than yards of talk.”</p> - -<p>Even a slight sketch refreshes the memory, and in -the case of the preparation of a complete set of drawings, -with a view to the making of a thoroughly finished -mechanical drawing, the proper course to pursue is, to -make a general sketch, letter the various parts for -reference, and then prepare a series of detailed sketches, -similarly lettered, and diffuse with dimensions.</p> - -<p>Everyone, whatever his specialty, feels to-day that -the ability to sketch rapidly and clearly is among the -absolute necessities for correct and prompt transactions -of business, in giving and executing orders and doing -business with persons outside his profession.</p> - -<p><span class="pagenum" id="Page56">[56]</span></p> - -<p>Mistakes and misunderstandings may be averted -by means of rough sketches taken at the time and -shown for confirmation; this also saves assistants from -getting into trouble, especially if they pin the sketch -to the order, for reference, in case of the arising of -any dispute. These are a few of the advantages of -knowing how to sketch quickly and correctly.</p> - -<p>In “free-hand” any sort of pencil is better than -none, but there is a considerable advantage in having a -good serviceable article—a pencil not too soft nor too -hard, and one which will retain its point for some little -time.</p> - -<p><a href="#Fig55">Fig. 55</a> shows the approved position in which the -pencil should be held while sketching. The pencil -should be held firmly between the thumb and first -finger of the right hand; press the second finger against -the pencil at the opposite side to the thumb pressure, -so that the pencil is firmly held by the contact of the -thumb and two fingers—the third and fourth fingers -just coming into easy reach of the paper surface—the -wrist or ball of the hand resting lightly on the surface -of the work—the arm resting on the desk or drawing-board -for steadiness.</p> - -<p>The motion of the pencil is produced from the -movement of the fingers and thumb, principally in the -vertical strokes, and the horizontal strokes are produced -by fingers and thumb, combined with a wrist or -elbow motion; the oblique lines and curves are produced -with a free movement, with nothing cramped or -confined about the finger joints.</p> - -<h3>POSITION.</h3> - -<p>It should be observed that nothing is more prejudicial -to good execution than the habit of leaning over -the paper, which ought to be placed on a surface sufficiently -inclined to bring every portion equally under -the eye, thus obviating the necessity of leaning forward. -All support to the figure should be obtained by resting -on the left arm, the right being left free for work. By -attention to these rules that awkwardness of position,<span class="pagenum" id="Page57">[57]</span> -so detrimental to a good figure, will be avoided. It is -better to have the light on the left hand, as in this direction -the shadow of the pencil does not interfere with -the view of the drawing.</p> - -<div class="container leftfloat w15em" id="Fig56"> -<img src="images/illo057.jpg" alt="Pencil sharpening" /> -<p class="caption">Fig. 56.</p> -</div> - -<h3>HOW TO CUT A PENCIL.</h3> - -<p>Hold the pencil firmly in the -left hand, as in the drawing, -allowing about an inch to project -beyond the fingers, and -turn it gradually as the knife -removes the wood. The knife -should be held so that the blade -alone projects beyond the -fingers, and the part of it -nearest the handle used for cutting. -The pencil should be -placed against the inside of the -thumb of the right hand, as in -the drawing (<a href="#Fig56">fig. 56</a>), and the wood removed by slight -shaving. The lead should not be cut at the same time -as the wood, but rested on the thumb and pared -gently afterwards; by attention to these directions the -pencil will be economized.</p> - -<h3>HOW TO DRAW STRAIGHT LINES.</h3> - -<p>Before a line is drawn, the point at which it is to -commence and the point where it is to end, should be -known; and let it be distinctly understood that <i>this -judgment of the eye</i>, and placing of points, should invariably -precede the drawing of every line.</p> - -<p>The first effort should, therefore, be to produce a -line of points exactly parallel with the upper edge of -the paper, and at equal distances from each other. -Commence with point <i>A</i> and place the point <i>B</i> carefully -level with it, now place a slip of paper against -these points in the original, mark their distance apart, -and see if the same proportion has been given in your -copy; if not, make the necessary correction. Proceed -with the next point, examine it, and so on to the end of<span class="pagenum" id="Page58">[58]</span> -the line. When this is complete, examine each point -in succession, to try if it is at the same distance from -the top of the paper; when this is correct, proceed to -draw the first level line. Hold the pencil as in the -drawing, <a href="#Fig57">fig. 57</a>, keeping the elbow near the side; -join <i>A</i> to <i>B</i> by one light, steady stroke, produced by a -movement of the wrist, and add stroke upon stroke -until the line is of the required depth. Continue this -process to the end of the line of points. Now place -the point <i>D</i> at the right distance below the <i>A</i>, proceed -with the points for another line as before, and continue -the lines until the paper is covered. In producing the -stroke the pencil should not be jerked, or any stop be -made between the points, but the movement should be -even throughout, and it is much better to produce each -line by several soft strokes, as <i>the repetition of delicate -lines induces lightness of touch and freedom of hand</i>; -and it is also no small advantage that lines thus produced -are more easily removed by the India rubber, -should they require correction.</p> - -<h3>TO DRAW THE FIRST OBLIQUE LINE.</h3> - -<p>Prepare three rows of points down the side of the -paper, on the left hand; examine them to see that they -are at equal distances from the side and from each -other; hold the pencil as in the drawing, <a href="#Fig58">fig. 58</a>, move -the elbow a little from the side, and join the points <i>A</i> -and <i>B</i> with one light line, produced by a movement of -the fingers and thumb, repeating the strokes until the -line is of the requisite depth; proceed to join <i>B</i> to <i>C</i>, -taking care previously to bring the hand a little down -the paper, as the line from <i>A</i> to <i>C</i> is too long to be -produced from one position. When the three rows of -points are filled, make another set, examine them and -proceed as before. By these means the paper will be -covered with oblique lines, and if the points have been -placed exactly, the sheet will have a neat and regular -appearance.</p> - -<div class="note"> - -<p><span class="smcap">Note.</span>—The drawings of hands are introduced to show the -positions for holding the pencil, and are not intended for copying.</p> - -</div><!--note--> - -<p><span class="pagenum" id="Page59">[59]</span></p> - -<div class="container w40em" id="Fig57"> -<img src="images/illo059.png" alt="Drawing lines" /> -<p class="caption">Fig. 57.</p> -</div> - -<p><span class="pagenum" id="Page60">[60]</span></p> - -<div class="container w40em" id="Fig58"> -<img src="images/illo060.png" alt="Drawing lines" /> -<p class="caption">Fig. 58.</p> -</div> - -<p><span class="pagenum" id="Page61">[61]</span></p> - -<p>It is a common, and at the same time highly injurious -habit, to draw this line by a movement of the -wrist, the fingers remaining rigid. This may be detected -by watching the action of the thumb; if it bends -as the line is produced, all is right; but if it does not -the wrist is at work.</p> - -<h3>TO DRAW THE UPRIGHT OR PERPENDICULAR LINE.</h3> - -<p>This line demands the greatest attention, and any -care bestowed upon it will be amply repaid in the after -studies.</p> - -<p>Commence by placing a line of points down the -side of the paper, examine them very carefully to see -that they are all the same distance from its edge, hold -the pencil as in the drawing, <a href="#Fig59">fig. 59</a>, move the elbow -well out from the side, and join the points by a movement -of the fingers and thumb. When one line is -complete, place the points for the next, and examine -them from the edge of the paper, not from the line just -drawn. Proceed in this manner until the paper is covered.</p> - -<p>There is in most cases a tendency to place the -points for this line in a slightly inclined direction, as in -writing, though in some instances the tendency is the -opposite, a thoroughly correct eye in this respect being -a rare gift: and it may be useful to suggest that the -paper be so placed that the line of points to be produced -may be exactly in front of the eye.</p> - -<h3>TO DRAW THE SECOND OBLIQUE LINE.</h3> - -<p>Prepare three rows of points down the side of the -paper, examine them for correctness of position, hold -the pencil as in the drawing, <a href="#Fig60">fig. 60</a>, remove the elbow -as far as possible from the side, and join the points by -a movement of the fingers and thumb, and continue the -exercise until the paper is covered.</p> - -<p><span class="pagenum" id="Page62">[62]</span></p> - -<div class="container w40em" id="Fig59"> -<img src="images/illo062.png" alt="Drawing lines" /> -<p class="caption">Fig. 59.</p> -</div> - -<p><span class="pagenum" id="Page63">[63]</span></p> - -<div class="container w40em" id="Fig60"> -<img src="images/illo063.png" alt="Drawing lines" /> -<p class="caption">Fig. 60.</p> -</div> - -<p>It will be noticed that each change in direction -of the line to be drawn, has been accompanied with a<span class="pagenum" id="Page64">[64]</span> -corresponding change in the position of the elbow and -wrist. The following simple rule will assist the memory -when placing the hand for any given line; the -pencil should be held so that it may form a T with the -line to be drawn:</p> - -<div class="trule image"> -<img src="images/illo064a.png" alt="T-rule" /> -</div> - -<div class="trule text"> -<p>For the horizontal line, elbow near -the side.</p> -</div> - -<p class="thinline allclear"> </p> - -<div class="trule image"> -<img src="images/illo064b.png" alt="T-rule" /> -</div> - -<div class="trule text"> -<p>For the first oblique, elbow a little -removed.</p> -</div> - -<p class="thinline allclear"> </p> - -<div class="trule image"> -<img src="images/illo064c.png" alt="T-rule" /> -</div> - -<div class="trule text"> -<p>For the perpendicular, elbow more -removed.</p> -</div> - -<p class="thinline allclear"> </p> - -<div class="trule image"> -<img src="images/illo064d.png" alt="T-rule" /> -</div> - -<div class="trule text"> -<p>For the second oblique, elbow most -removed.</p> -</div> - -<p class="thinline allclear"> </p> - -<div class="container rightfloat w15em x-ebookmaker-drop"> - -<p class="fingerlines">Finger and thumb lines.</p> - -<div class="split1090"> - -<div class="left1090"> -<p class="wristlines">W<br />r<br />i<br />s<br />t<br /> <br />l<br />i<br />n<br />e<br />s<br />.</p> -</div> - -<div class="right1090"> - -<div class="split9208"> - -<div class="left9208"> - -<div class="container nomargin w12em"> -<img src="images/illo064e.png" alt="Lines" /> -</div> - -</div><!--left9208--> - -<div class="right9208"> -<p class="wristlines">W<br />r<br />i<br />s<br />t<br /> <br />l<br />i<br />n<br />e<br />s<br />.</p> -</div> - -</div><!--split9208--> - -</div><!--right1090--> - -<p class="thinline allclear"> </p> - -</div><!--split1090--> - -<p class="fingerlines">Finger and thumb lines.</p> - -</div><!--container--> - -<div class="noscr"> - -<div class="container w12em"> -<img src="images/illo064e1.png" alt="Lines" /> -</div> - -</div><!--noscr--> - -<p>It may also be interesting to notice, with regard to -the movements by which lines are produced, that they -are divided into two systems; the first is that of the -wrist, which includes the horizontal, and lines in nearly -the same direction; -the second is that of -the fingers and -thumb, by which all -other lines are -formed. The following -diagram exhibits -the two systems and -their various lines -grouped, and it will -be observed that -there is a space marked (a) between the two sets, which -may be considered neutral ground. Lines in this -direction may be produced by either movement, as -may be most convenient, but it will always be found -that these lines are the most trying to the hand.</p> - -<p><span class="pagenum" id="Page65">[65]</span></p> - -<h3>ON FIGURES FORMED OF STRAIGHT LINES.</h3> - -<p>Before commencing this subject, let it be clearly -understood that future success will, in a great measure, -depend upon the amount of care bestowed upon it. -The aim should be to obtain absolute accuracy, and for -this end the copies should be tested by the most careful -measurements, and corrected until they are true -with the originals, but it should be distinctly understood -that these measurements are only to be made -after the eye and hand have done their best.</p> - -<div class="note"> - -<p><span class="smcap">Note.</span>—To some it may appear that too much time and care -has been bestowed on mere lines, but let it be understood that a -good system of line drawing is the basis of all education—the -slightest outline by a hand thus trained has a bold, free and -masterly character; and with regard to shading, which is simply -an aggregation of good lines, it is only by such a practiced hand -its most charming effects can be produced.</p> - -</div><!--note--> - -<p><a href="#Fig6667">Fig. 66</a>: Place the points <i>A</i>, <i>B</i>. Examine them -to see that they are the same distance apart as in the -original, and that they are level; place the point <i>C</i> exactly -under <i>A</i>, and make <i>A C</i> equal in distance to <i>A B</i>; -now place the point <i>D</i> opposite <i>C</i> and under <i>B</i>; try -the distances between each point to see that they are -the same; divide each side by a point half way, and -then draw the lines.</p> - -<p><a href="#Fig6667">Fig. 67</a>: Repeat the last figure and add the -lines <i>A</i> and <i>B</i>, taking great care that the points for -them are correctly placed.</p> - -<p><a href="#Fig6869">Fig. 68</a>: Commence with the square as before; -then join the half-way points.</p> - -<p><a href="#Fig6869">Fig. 69</a>: After the square is drawn, place the -points <i>A</i> and <i>B</i> at the right height above the half-way -points, and <i>C</i>, <i>D</i> at the proper distance from the corners, -then draw the figure.</p> - -<p><a href="#Fig7071">Fig. 70</a>: The greatest care should be taken with -the squares for this and the following figure, as the -slightest error in them will destroy the symmetry of -the drawing within; when the square is completed, join -the opposite corners, and place on the crossed lines the -points <i>B</i>, <i>C</i>, <i>D</i>, <i>E</i>; examine these to see that they are -each at the same distance from the centre <i>A</i>, and that -this distance is equal to the space from <i>A</i> to the sides -of the square; when all are proved to be correct, complete -the figure.</p> - -<p><span class="pagenum" id="Page66">[66]</span></p> - -<div class="container w40em" id="Fig6667"> -<img src="images/illo066.png" alt="Figures" /> - -<div class="split5050"> - -<div class="left5050"> -<p class="caption">Fig. 66.</p> -</div> - -<div class="right5050"> -<p class="caption">Fig. 67.</p> -</div> - -<p class="thinline allclear"> </p> - -</div><!--split5050--> - -</div><!--container--> - -<p><span class="pagenum" id="Page67">[67]</span></p> - -<div class="container w40em" id="Fig6869"> -<img src="images/illo067.png" alt="Figures" /> - -<div class="split5050"> - -<div class="left5050"> -<p class="caption">Fig. 68.</p> -</div> - -<div class="right5050"> -<p class="caption">Fig. 69.</p> -</div> - -<p class="thinline allclear"> </p> - -</div><!--split5050--> - -</div><!--container--> - -<p><span class="pagenum" id="Page68">[68]</span></p> - -<div class="container w40em" id="Fig7071"> -<img src="images/illo068.png" alt="Figures" /> - -<div class="split5050"> - -<div class="left5050"> -<p class="caption">Fig. 70.</p> -</div> - -<div class="right5050"> -<p class="caption">Fig. 71.</p> -</div> - -<p class="thinline allclear"> </p> - -</div><!--split5050--> - -</div><!--container--> - -<p><span class="pagenum" id="Page69">[69]</span></p> - -<p><a href="#Fig7071">Fig. 71</a>: Repeat the last drawing with, if possible, -greater exactness, and outside the octagon place -the points <i>A</i>, <i>B</i>, <i>C</i>, <i>D</i>, etc.; examine each of these -points to see that they are all at the same distance -from the centre, and then complete the figure.</p> - -<h3>ON CURVED LINES.</h3> - -<div class="container rightfloat w15em"> -<img src="images/illo069a.png" alt="Curves" /> -</div> - -<p>The right position of the hand for drawing any -curved line is that required for a straight line which -would touch the extremities of -the curve. The straight lines -given in the exercises are valuable, -not only as a guide to the -position of the hand, but as an assistance to the eye -when forming the curves or examining them after they -are produced.</p> - -<p>The direction given for drawing a straight line was -to form it by one steady movement from point to point, -without any jerk or stop by the way. This instruction -requires to be changed for the curve, <i>which is better -produced by several short strokes</i>, thus:</p> - -<div class="container w20em"> -<img src="images/illo069b.png" alt="Curves" /> -</div> - -<p class="noindent">or by overlapping -lines, any outside bits -being cleared away -with India rubber.</p> - -<p>These exercises will test the drawing power and -try the patience of the pupil, but they are worthy of all -the care which can be bestowed, which in future efforts -will meet with its full reward.</p> - -<p><a href="#Fig7677">Fig. 76</a>: Draw first the square as directed in the -previous lesson, join the points <i>A</i>, <i>B</i>, <i>C</i> and add the -short lines at <i>E</i> and <i>F</i>, proceed with the curve <i>A B</i>, -drawing it with faint lines at first, and adding stroke -upon stroke until the required depth is obtained; the -curve <i>A C</i> is more difficult to produce, in consequence -of the formation of the hand; it should, therefore, be -drawn in shorter pieces, joining them together afterwards -by over strokes.</p> - -<p><span class="pagenum" id="Page70">[70]</span></p> - -<div class="container w40em" id="Fig7677"> - -<img src="images/illo070.png" alt="Drawings" /> - -<div class="split5050"> - -<div class="left5050"> -<p class="caption">Fig. 76.</p> -</div> - -<div class="right5050"> -<p class="caption">Fig. 77.</p> -</div> - -<p class="thinline allclear"> </p> - -</div><!--split5050--> - -</div><!--container--> - -<p><span class="pagenum" id="Page71">[71]</span></p> - -<div class="container rightfloat w05em"> -<img src="images/illo071.png" alt="Oval" /> -</div> - -<p><a href="#Fig7677">Fig. 77</a>: Draw the square and straight -lines first, then add the curves, taking -care to give the greatest fullness at the -right place.</p> - -<p><a href="#Fig7879">Fig. 78</a>: Draw the square and straight -lines, proceed with the curves, taking care -to make each of the same proportion.</p> - -<p><a href="#Fig7879">Figs. 79</a> and <a href="#Fig8081">80</a>: The ovals contained -in these figures are simply foreshortened -circles, and as such forms are of frequent -occurrence in sketching from objects, in bridges, -wheels, ends of timber, etc., they should be carefully -studied; the greatest difficulty is to turn the narrow -ends, and prevent their looking like corners. For this -purpose it is better to draw the short curves first, thus:</p> - -<p class="noindent">and then join the longer sides to them.</p> - -<p><a href="#Fig8081">Fig. 81</a>: If this figure can be drawn correctly, a -great success has been achieved; the circle is a most -difficult form to delineate, and without system could -not be accomplished. Draw the square and straight -lines within it with great care, examine each point of -the octagon to see that it is at the same distance from -the centre, and then draw the circle.</p> - -<h3>EXAMPLES FOR PRACTICE.</h3> - -<p>Several figures, <a href="#Fig83">83</a> to <a href="#Fig96">96</a>, representing more or less -familiar parts of machines, utilities, etc., are introduced -for practice in free-hand, <span class="nowrap">but—</span></p> - -<p>It must be noted that even in free-hand the wise -student will occasionally use the straight edge and -compasses, so as to make his first attempts fairly creditable. -Many good draughtsmen have begun by simply -copying such figures and illustrations as are used -throughout this volume and other similar sources; -perhaps there is nothing better for practice or training -than the copying and reproducing of samples of good -mechanical drawings, yet it must always be remembered -that advancement in free-hand must be made in -the line of less to greater efforts, and that the why and -wherefore will be constantly asked by the aspiring student; -that good and correct drawings are to be aimed -for at all times in every line and dimension—never -forgetting the law of proportion in the smallest outlines -of objects to be represented.</p> - -<p><span class="pagenum" id="Page72">[72]</span></p> - -<div class="container w40em" id="Fig7879"> - -<img src="images/illo072.png" alt="Figures" /> - -<div class="split5050"> - -<div class="left5050"> -<p class="caption">Fig. 78.</p> -</div> - -<div class="right5050"> -<p class="caption">Fig. 79.</p> -</div> - -<p class="thinline allclear"> </p> - -</div><!--split--> - -</div><!--container--> - -<p><span class="pagenum" id="Page73">[73]</span></p> - -<div class="container w40em" id="Fig8081"> - -<img src="images/illo073.png" alt="Figures" /> - -<div class="split5050"> - -<div class="left5050"> -<p class="caption">Fig. 80.</p> -</div> - -<div class="right5050"> -<p class="caption">Fig. 81.</p> -</div> - -<p class="thinline allclear"> </p> - -</div><!--split--> - -</div><!--container--> - -<p><span class="pagenum" id="Page74">[74]</span></p> - -<p><a href="#Fig83">Fig. 83</a> is a section, or end view of a bar of angle -iron; the student will find helpful practice in attempting -this figure; he may be allowed to use a straight-edge -in drawing the lines, but no measurements; the -work should be tested on completion by a rule, or -better by penciling from the original on tracing paper, -and comparing the free-hand with the copy, when the -defective proportions, if any, will be clearly exhibited.</p> - -<p><a href="#Fig84">Fig. 84</a> is a section of tee iron, and <a href="#Fig85">fig. 85</a> is a -section of channel iron. These three figures on <a href="#Page75">page -75</a> should be practiced alternately, although seeming -similar in shape.</p> - -<p><a href="#Fig86">Fig. 86</a> is a side and end view of an angle plate -shaded. <a href="#Fig87">Fig. 87</a> is a wrench shaded.</p> - -<p>Examples of bolt ends are shown in the two next -numbers; <a href="#Fig8891">fig. 88</a> exhibits the common square-head -bolt, and <a href="#Fig8891">fig. 89</a> the hexagon or six-sided bolt-head; -these are also examples of <i>straight-line shading</i>. <a href="#Fig8891">Fig. -90</a> is a lathe-dog, and shows an example of <i>curved -shading</i>; <a href="#Fig9293">fig. 92</a> is an engine crank, and an example of -<i>straight and curved shading</i>; <a href="#Fig8891">fig. 91</a> is a screw clamp.</p> - -<p><a href="#Fig9293">Fig. 93</a> is a section of boiler plates riveted together; -a caulking tool is also shown.</p> - -<p>In the example, <a href="#Fig9495">fig. 94</a>—a hand-wheel—the principal -difficulty, even for the most advanced student -in free-hand, will be in drawing the circles; a coin, if -convenient, can be used to scribe about, in drawing -these; the other parts can afterwards be filled in around -the circle. <a href="#Fig96">Fig. 96</a> is introduced for practice in penciling -and shading; the figure represents a water-wheel -on a stone pier.</p> - -<p>The familiar oil can is shown in <a href="#Fig9495">fig. 95</a>. These all -are excellent objects for practice.</p> - -<p><span class="pagenum" id="Page75">[75]</span></p> - -<div class="split2575"> - -<div class="left2575"> - -<div class="container" id="Fig83"> -<img src="images/illo075a.png" alt="" /> -</div> - -</div><!--left2575--> - -<div class="right2575"> - -<div class="split5050"> - -<div class="left5050"> - -<div class="container" id="Fig84"> -<img src="images/illo075b.png" alt="" /> -</div> - -</div><!--left5050--> - -<div class="right5050"> - -<div class="container" id="Fig85"> -<img src="images/illo075c.png" alt="" /> -</div> - -</div><!--right5050--> - -</div><!--split5050--> - -</div><!--right2575--> - -<p class="thinline allclear"> </p> - -<p class="caption">Fig. 83.—Fig. 84.—Fig. 85.</p> - -</div><!--split2575--> - -<div class="split5050"> - -<div class="left5050"> - -<div class="container" id="Fig86"> -<img src="images/illo075d.png" alt="" /> -</div> - -</div><!--left5050--> - -<div class="right5050"> - -<div class="container" id="Fig87"> -<img src="images/illo075e.png" alt="" /> -</div> - -</div><!--right5050--> - -<p class="thinline allclear"> </p> - -</div><!--split5050--> - -<div class="split5050"> - -<div class="left5050"> -<p class="caption">Fig. 86.</p> -</div><!--left5050--> - -<div class="right5050"> -<p class="caption">Fig. 87.</p> -</div><!--right5050--> - -<p class="thinline allclear"> </p> - -</div><!--split5050--> - -<p><span class="pagenum" id="Page76">[76]</span></p> - -<div class="container" id="Fig8891"> - -<img src="images/illo076a.jpg" alt="Drawings" /> - -<p class="caption">Fig. 88.—Fig. 89.—Fig. 90.—Fig. 91.</p> - -</div><!--container--> - -<div class="container" id="Fig9293"> - -<img src="images/illo076b.jpg" alt="Drawings" /> - -<div class="split5050"> - -<div class="left5050"> -<p class="caption">Fig. 92.</p> -</div> - -<div class="right5050"> -<p class="caption">Fig. 93.</p> -</div> - -<p class="thinline allclear"> </p> - -</div><!--split5050--> - -</div><!--container--> - -<p><span class="pagenum" id="Page77">[77]</span></p> - -<div class="container" id="Fig9495"> - -<img src="images/illo077.jpg" alt="" /> - -<div class="split6040"> - -<div class="left6040"> -<p class="caption">Fig. 94.</p> -</div> - -<div class="right6040"> -<p class="caption">Fig. 95.</p> -</div> - -<p class="thinline allclear"> </p> - -</div><!--split6040--> - -</div><!--container--> - -<p><span class="pagenum" id="Page78">[78]</span></p> - -<div class="container w25em" id="Fig96"> -<img src="images/illo078.jpg" alt="Water wheel" /> -<p class="caption">Fig. 96.</p> -</div> - -<hr class="chap x-ebookmaker-drop" /> - -<p><span class="pagenum" id="Page79">[79]</span></p> - -<div class="container w30em"> -<img src="images/illo079.png" alt="GEOMETRICAL DRAWING" /> -</div> - -<hr class="chap x-ebookmaker-drop" /> - -<p><span class="pagenum" id="Page80">[80]</span></p> - -<div class="container w40em"> -<img src="images/illo080.png" alt="Drawing tools" /> -</div> - -<hr class="chap x-ebookmaker-drop" /> - -<div class="chapter"> - -<p><span class="pagenum" id="Page81">[81]</span></p> - -<h2 class="nobreak">Geometrical Drawing.</h2> - -</div><!--chapter--> - -<p>Geometry is the science of measurement; it has -been known for more than three thousand years; -many lives have been devoted to its development, and -it exists to-day as the foundation of all mathematics.</p> - -<p>Geometrical drawing is the art of representing, to -the eye, the problems “worked out” by geometricians, -and the importance of a knowledge of geometrical -drawing is paramount. The student will find that the -figures delineated and explained in the next few pages -constantly occur in mechanical drawing. Says Walter -Smith, State Director of Art Education in Massachusetts, -“I have never known a case where a student did -not progress more satisfactorily in his studies after a -course of practical geometry.”</p> - -<p>The elementary conceptions of geometry are few:</p> - -<div class="diagonalp"> - -<p>1.—A point.<br /> -<span class="padl4">2.—A line.</span><br /> -<span class="padl8">3.—A surface.</span><br /> -<span class="padl12">4.—A solid, and</span><br /> -<span class="padl16">5.—An angle.</span></p> - -</div><!--diagonalp--> - -<p>All of which elements are used in mechanical drawings.</p> - -<p>From these, as data, a vast number of mathematical -problems have been deduced; of which a few of -the most elementary will be illustrated in this work; -but these few will repay the attention of the student.</p> - -<p>In “freehand” drawing the crayon and pencil -are used; in geometrical drawings the dividers, as<span class="pagenum" id="Page82">[82]</span> -shown in illustration, <a href="#Fig97">fig. 97</a>, together with a rule, are -all that is necessary to accomplish the work.</p> - -<p>A problem is something to be done, and geometry -has been defined as the science of measurement; the -relation between geometry and mechanical drawing -is very close, hence the term “geometrical problem.”</p> - -<div class="container w40em" id="Fig97"> -<img src="images/illo082a.jpg" alt="Compasses" /> -<p class="caption">Fig. 97.</p> -</div> - -<div class="container w40em" id="Fig98"> -<img src="images/illo082b.jpg" alt="Ruler" /> -<p class="caption">Fig. 98.</p> -</div> - -<p>Before proceeding with the examples, a few -elementary statements belonging to the science of -geometry are presented; these will be useful to the -student, not only while “doing” the problems, but in -many cases of every-day—future—experience.</p> - -<p>Geometry is one of the oldest and simplest of -sciences; it may be defined as <i>the science of measurement</i>; -geometry is <i>the root</i> from which all regular -mathematical calculations issue. It has claimed the -best thought of practical men from the times of the -Greeks and Romans two thousand years ago; they -derived their knowledge of the science from the Egyptians, -who in turn were indebted to the Chaldeans and -Hindoos in times beyond any authentic history; -hence it was under the operations of -the laws explained in geometry, that the pyramids -of Egypt and the temples of Greece were -constructed, as well as the engines of war and -appliances of peace of ancient times.</p> - -<p><i>A point</i> is mere position, and has no magnitude.</p> - -<p><i>A line</i> is that which has extension in length only. -The extremities of lines are points.</p> - -<p><i>A surface</i> is that which has extension in length -and breadth only.</p> - -<p><span class="pagenum" id="Page83">[83]</span></p> - -<div class="container leftfloat w03em"> -<img src="images/illo083a.png" alt="Angle" /> -</div> - -<p><i>A solid</i> is that which has extension in length, -breadth and thickness.</p> - -<p><i>An angle</i> is the difference in the direction -of two lines proceeding from the same -point.</p> - -<p>Lines, Surfaces, Angles and Solids constitute the -different kinds of quantity called <i>geometrical</i> magnitudes.</p> - -<div class="container allclear leftfloat w03em"> -<img src="images/illo083b.png" alt="Lines" /> -</div> - -<p><i>Parallel lines</i> are lines which have the -same direction; hence parallel lines can -never meet, however far they may be produced; for -two lines taking the same direction cannot approach or -recede from each other.</p> - -<p>An <i>Axiom</i> is a self-evident truth, not only too -simple to require, <i>but too simple to admit of demonstration</i>.</p> - -<p>A <i>Proposition</i> is something which is either proposed -to be done, or to be demonstrated, and is either a -problem or a theorem.</p> - -<p>A <i>Problem</i> is something proposed to be done.</p> - -<p>A <i>Theorem</i> is something proposed to be demonstrated.</p> - -<p>A <i>Hypothesis</i> is a supposition made with a view to -draw from it some consequence which establishes the -truth or falsehood of a proposition, or solves a problem.</p> - -<p>A <i>Lemma</i> is something which is premised, or -demonstrated, in order to render what follows more -easy.</p> - -<p>A <i>Corollary</i> is a consequent truth derived immediately -from some preceding truth or demonstration.</p> - -<p>A <i>Scholium</i> is a remark or observation made upon -something going before it.</p> - -<p>A <i>Postulate</i> is a problem, the solution of which is -self-evident.</p> - -<p>Let it be <span class="nowrap">granted—</span></p> - -<p><span class="dontshow">II</span>I. That a straight line can be drawn from any -one point to any other point;</p> - -<p><span class="pagenum" id="Page84">[84]</span></p> - -<p><span class="dontshow">I</span>II. That a straight line can be produced to any -distance, or terminated at any point;</p> - -<p>III. That the circumference of a circle can be -described about any center, at any distance from that -center.</p> - -<p>The common algebraic signs are used in Geometry, -and it is necessary that the student in geometry should -understand some of the more simple operations of -algebra. As the terms circle, angle, triangle, hypothesis, -axiom, theorem, corollary and definition are constantly -occurring in a course of geometry, they are -abbreviated as shown in the following list:</p> - -<table class="symbols" summary="Symbols"> - -<tr> -<td class="descr">Addition is expressed by</td> -<td class="symbol">+</td> -</tr> - -<tr> -<td class="descr">Subtraction is expressed by</td> -<td class="symbol">-</td> -</tr> - -<tr> -<td class="descr">Multiplication is expressed by</td> -<td class="symbol">×</td> -</tr> - -<tr> -<td class="descr">Equality and Equivalency are expressed by</td> -<td class="symbol">=</td> -</tr> - -<tr> -<td class="descr">Greater than, is expressed by</td> -<td class="symbol">></td> -</tr> - -<tr> -<td class="descr">Less than, is expressed by</td> -<td class="symbol"><</td> -</tr> - -<tr> -<td class="descr"><span class="padl2">Thus <i>B</i> is greater than <i>A</i>, is written</span></td> -<td class="symbol"><i>B</i> > <i>A</i></td> -</tr> - -<tr> -<td class="descr"><span class="padl2"><span class="dontshow">Thus </span><i>B</i> is less than <i>A</i>, is written</span></td> -<td class="symbol"><i>B</i> < <i>A</i></td> -</tr> - -<tr> -<td class="descr">A circle is expressed by</td> -<td class="symbol">O</td> -</tr> - -<tr> -<td class="descr">An angle is expressed by</td> -<td class="symbol">L</td> -</tr> - -<tr> -<td class="descr">A right angle is expressed by</td> -<td class="symbol">R. L</td> -</tr> - -<tr> -<td class="descr">Degrees, minutes and seconds are expressed by</td> -<td class="symbol">° ′ ″</td> -</tr> - -<tr> -<td class="descr">A triangle is expressed by</td> -<td class="symbol">△</td> -</tr> - -<tr> -<td class="descr">The term Hypothesis is expressed by</td> -<td class="symbol">(Hy.)</td> -</tr> - -<tr> -<td class="descr">The term Axiom is expressed by</td> -<td class="symbol">(Ax.)</td> -</tr> - -<tr> -<td class="descr">The term Theorem is expressed by</td> -<td class="symbol">(Th.)</td> -</tr> - -<tr> -<td class="descr">The term Corollary is expressed by</td> -<td class="symbol">(Cor.)</td> -</tr> - -<tr> -<td class="descr">The term Definition is expressed by</td> -<td class="symbol">(Def.)</td> -</tr> - -<tr> -<td class="descr">The term Perpendicular is expressed by</td> -<td class="symbol">⊥</td> -</tr> - -<tr> -<td class="descr">The difference of two quantities, when it is not known which is the greater, is expressed by the symbol</td> -<td class="symbol">~</td> -</tr> - -<tr> -<td class="descr">Thus, the difference between <i>A</i> and <i>B</i> is written</td> -<td class="symbol"><i>A</i> ~ <i>B</i></td> -</tr> - -</table> - -<h3>GEOMETRICAL AXIOMS.</h3> - -<p> 1. <i>Things which are equal to the same thing are -equal to each other.</i></p> - -<p> 2. <i>When equals are added to equals the wholes are -equal.</i></p> - -<p><span class="pagenum" id="Page85">[85]</span></p> - -<p> 3. <i>When equals are taken from equals the remainders -are equal.</i></p> - -<p> 4. <i>When equals are added to unequals the wholes -are unequal.</i></p> - -<p> 5. <i>When equals are taken from unequals the -remainders are unequal.</i></p> - -<p> 6. <i>Things which are double of the same thing, or -equal things, are equal to each other.</i></p> - -<p> 7. <i>Things which are halves of the same thing, or -of equal things, are equal to each other.</i></p> - -<p> 8. <i>The whole is greater than any of its parts.</i></p> - -<p> 9. <i>Every whole is equal to all its parts taken -together.</i></p> - -<p>10. <i>Things which coincide, or fill the same space, -are identical, or mutually equal in all their parts.</i></p> - -<p>11. <i>All right angles are equal to one another.</i></p> - -<p>12. <i>A straight line is the shortest distance between -two points.</i></p> - -<p>13. <i>Two straight lines cannot enclose a space.</i></p> - -<div class="chapter"> - -<p><span class="pagenum" id="Page86">[86]</span></p> - -<h2 class="nobreak">Problems in Geometrical Drawing.</h2> - -</div><!--chapter--> - -<div class="container leftfloat nomargin w12em" id="Fig99"> -<img src="images/illo086a.png" alt="Lines" /> -<p class="caption">Fig. 99.</p> -</div> - -<p><span class="smcap">Example</span> 1.—<i>To bisect</i> -(cut in two) <i>a straight line or -an arc of a circle</i>, <a href="#Fig99">Fig. 99</a>. -From the ends of <i>A B</i> as -centers, describe arcs cutting -each other at <i>C</i> and <i>D</i>, and -draw <i>C D</i>, which cuts the -line at <i>E</i> or the arc at <i>F</i>.</p> - -<p><span class="smcap">Ex.</span> 2.—<i>To draw a perpendicular to a straight line, -or a radial line to a circular arc</i>, <a href="#Fig99">Fig. 99</a>. Operate as -in the foregoing problem. The line <i>C D</i> is perpendicular -to <i>A B</i>; the line <i>C D</i> is also radial to the arc -<i>A B</i>.</p> - -<p class="allclear"> </p> - -<div class="container leftfloat nomargin w15em" id="Fig100"> -<img src="images/illo086b.png" alt="Perpendiculars" /> -<p class="caption">Fig. 100.</p> -</div> - -<div class="container rightfloat nomargin w12em" id="Fig101"> -<img src="images/illo087a.png" alt="Example" /> -<p class="caption">Fig. 101.</p> -</div> - -<p><span class="smcap">Ex.</span> 3.—<i>To draw a -perpendicular to a straight -line, from a given point in -that line</i>, <a href="#Fig100">Fig. 100</a>. With -any radius from any given -point <i>A</i> in the line <i>B C</i>, -cut the line at <i>B</i> and <i>C</i>. -Next, with a longer radius, -describe arcs from <i>B</i> and <i>C</i>, cutting each other at <i>D</i>, -and draw the perpendicular <i>D A</i>.</p> - -<p><span class="pagenum" id="Page87">[87]</span></p> - -<p><i>Second Method</i>, <a href="#Fig101">Fig. -101</a>. From any center <i>F</i> -above <i>B C</i>, describe a circle -passing through the -given point <i>A</i>, and cutting -the given line at <i>D</i>; draw -<i>D F</i>, and produce it to cut -the circle at <i>E</i>; and draw -the perpendicular <i>A E</i>.</p> - -<p class="allclear"> </p> - -<div class="container leftfloat nomargin w10em" id="Fig102"> -<img src="images/illo087b.png" alt="Example" /> -<p class="caption">Fig. 102.</p> -</div> - -<p><i>Third Method</i>, <a href="#Fig102">Fig. 102</a>. From -<i>A</i> describe an arc <i>E C</i>, and from <i>E</i>, -with the same radius, the arc <i>A C</i> -cutting the other at <i>C</i>; through <i>C</i> -draw a line <i>E C D</i> and set off <i>C D</i> -equal to <i>C E</i>, and through <i>D</i> draw -the perpendicular <i>A D</i>.</p> - -<p class="allclear"> </p> - -<div class="container leftfloat nomargin w10em" id="Fig103"> -<img src="images/illo087c.png" alt="Example" /> -<p class="caption">Fig. 103.</p> -</div> - -<div class="container rightfloat nomargin w15em" id="Fig104"> -<img src="images/illo088a.png" alt="Example" /> -<p class="caption">Fig. 104.</p> -</div> - -<p><span class="smcap">Ex.</span> 4.—<i>To draw a perpendicular -to a straight line from -any point without it</i>, <a href="#Fig103">Fig. 103</a>. -From the point <i>A</i> with a sufficient -radius cut the given line at -<i>F</i> and <i>G</i>; and from these points -describe arcs cutting at <i>E</i>. Draw -the perpendicular <i>A E</i>.</p> - -<p>If there be no room below the line, the intersection -may be taken above the line; that is to say, between -the line and the given point.</p> - -<p><span class="pagenum" id="Page88">[88]</span></p> - -<p><i>Second Method</i>, -<a href="#Fig104">Fig. 104</a>. From any two -points <i>B C</i> at some distance -apart, in the given -line, and with the radii -<i>B A</i>, <i>C A</i>, respectively, -describe arcs cutting at -<i>A D</i>. Draw the perpendicular -<i>A D</i>.</p> - -<p class="allclear"> </p> - -<div class="container leftfloat nomargin w12em" id="Fig105"> -<img src="images/illo088b.png" alt="Example" /> -<p class="caption">Fig. 105.</p> -</div> - -<div class="container rightfloat nomargin w12em" id="Fig106"> -<img src="images/illo088c.png" alt="Example" /> -<p class="caption">Fig. 106.</p> -</div> - -<p><span class="smcap">Ex.</span> 5.—<i>To draw a parallel -line through a given -point</i>, <a href="#Fig105">Fig. 105</a>. With a radius -equal to the given point <i>C</i> -from the given line <i>A B</i>, -describe the arc <i>D</i> from <i>B</i>, taken considerably distant -from <i>C</i>. Draw the parallel through <i>C</i> to touch the -arc <i>D</i>.</p> - -<p><i>Second Method</i>, <a href="#Fig106">Fig. 106</a>. -From <i>A</i>, the given point, -describe the arc <i>F D</i>, cutting -the given line at <i>F</i>; from <i>F</i>, -with the same radius, describe -the arc <i>E A</i>, and set off <i>F D</i>, -equal to <i>E A</i>. Draw the parallel through the points <i>A D</i>.</p> - -<p class="allclear"> </p> - -<div class="container leftfloat nomargin w15em" id="Fig107"> -<img src="images/illo088d.png" alt="Example" /> -<p class="caption">Fig. 107.</p> -</div> - -<p>When a series of parallels are required perpendicular -to a base line <i>A B</i>, they may be drawn as in <a href="#Fig107">fig. -107</a> through points in -the base line set off at -the required distances -apart. This method is -convenient also where -a succession of parallels -are required to a -given line <i>C D</i>, for the -perpendicular may be -drawn to it, and any number of parallels may be drawn -on the perpendicular.</p> - -<p class="allclear"> </p> - -<p><span class="pagenum" id="Page89">[89]</span></p> - -<div class="container leftfloat nomargin w15em" id="Fig108"> -<img src="images/illo089a.png" alt="Example" /> -<p class="caption">Fig. 108.</p> -</div> - -<div class="container rightfloat nomargin w12em" id="Fig109"> -<img src="images/illo089b.png" alt="Example" /> -<p class="caption">Fig. 109.</p> -</div> - -<p><span class="smcap">Ex.</span> 6.—<i>To divide a line into a number of equal -parts</i>, <a href="#Fig108">Fig. 108</a>.</p> - -<p>To divide the -line <i>A B</i> into, say, -five parts. From <i>A</i> -and <i>B</i> draw parallels -<i>A C</i>, <i>B D</i> on opposite -sides; set off any -convenient distance four times (one less than the given -number), from <i>A</i> on <i>A C</i>, and on <i>B</i> on <i>B D</i>; join the -first on <i>A C</i> to the fourth on <i>B D</i>, and so on. The -lines so drawn divide <i>A B</i> as required.</p> - -<p><i>Second Method</i>, <a href="#Fig109">Fig. 109</a>. -Draw the line at <i>A C</i>, at an -angle from <i>A</i>, set off, say, five -equal parts; draw <i>B</i> 5, and -draw parallels to it from the -other points of division in <i>A -C</i>. These parallels divide <i>A -B</i> as required.</p> - -<p class="allclear"> </p> - -<div class="container leftfloat nomargin w20em" id="Fig110"> -<img src="images/illo089c.png" alt="Example" /> -<p class="caption">Fig. 110.</p> -</div> - -<p><span class="smcap">Ex.</span> 7.—<i>Upon a straight line to draw an angle -equal to a given angle</i>, <a href="#Fig110">Fig. 110</a>. Let <i>A</i> be the given -angle and <i>F G</i> the line. With any radius from the -points <i>A</i> and <i>F</i>, describe arcs <i>D E</i>, <i>I H</i>, cutting the -sides of the angle <i>A</i> and the line <i>F G</i>.</p> - -<p>Set off the arc <i>I H</i>, equal to <i>D E</i> and draw <i>F H</i>. -The angle <i>F</i> is equal to <i>A</i> -as required.</p> - -<p class="allclear"> </p> - -<div class="container rightfloat nomargin w12em" id="Fig111"> -<img src="images/illo089d.png" alt="Example" /> -<p class="caption">Fig. 111.</p> -</div> - -<p><span class="smcap">Ex.</span> 8.—<i>To bisect an angle</i>, -<a href="#Fig111">Fig. 111</a>. Let <i>A C B</i> be -the angle; on the center <i>C</i> -cut the sides at <i>A B</i>. On <i>A</i> -and <i>B</i> as centers describe arcs -cutting at <i>D</i> dividing the -angle into two equal parts.</p> - -<p class="allclear"> </p> - -<p class="allclear"><span class="pagenum" id="Page90">[90]</span></p> - -<div class="container leftfloat nomargin w15em" id="Fig112"> -<img src="images/illo090a.png" alt="Example" /> -<p class="caption">Fig. 112.</p> -</div> - -<p><span class="smcap">Ex.</span> 9.—<i>To find -the center of a circle -or of an arc of a circle.</i> -<a href="#Fig112">Fig. 112</a>. Draw -the chord <i>A B</i>, bisect -it by the perpendicular -<i>C D</i>, bounded -both ways by the circle; -and bisect <i>C D</i> -for the center <i>G</i>.</p> - -<p class="allclear"> </p> - -<div class="container leftfloat nomargin w12em" id="Fig113"> -<img src="images/illo090b.png" alt="Example" /> -<p class="caption">Fig. 113.</p> -</div> - -<div class="container rightfloat nomargin w12em" id="Fig114"> -<img src="images/illo090c.png" alt="Example" /> -<p class="caption">Fig. 114.</p> -</div> - -<p><span class="smcap">Ex.</span> 10.—<i>Through two -given points to describe an -arc of a circle with a given -radius</i>, <a href="#Fig113">Fig. 113</a>. On the -points <i>A</i> and <i>B</i> as centers, -with the given radius, describe -arcs cutting at <i>C</i>; and -from <i>C</i>, with the same radius, -describe an arc <i>A B</i> as required.</p> - -<p>Second, for a circle or -an arc, <a href="#Fig114">Fig. 114</a>. Select three -points <i>A</i>, <i>B</i>, <i>C</i> in the circumference, -well apart; with -the same radius describe -arcs from these three points -cutting each other, and draw -two lines <i>D E</i>, <i>F G</i>, through -their intersections according -to <a href="#Fig107">Fig. 107</a>. The point where -they cut is the center of the circle or arc.</p> - -<p><span class="smcap">Ex.</span> 11.—<i>To describe a circle passing through three -given points</i>, <a href="#Fig114">Fig. 114</a>. Let <i>A</i>, <i>B</i>, <i>C</i> be the given points -and proceed as in last problem to find the center <i>O</i>, -from which the circle may be described.</p> - -<p>This problem is variously useful; in finding the -diameter of a large fly-wheel, or any other object of -large diameter when only a part of the circumference -is accessible; in striking out arches when the span and -rise are given, etc.</p> - -<p class="allclear"> </p> - -<p><span class="pagenum" id="Page91">[91]</span></p> - -<div class="container rightfloat nomargin w20em" id="Fig115"> -<img src="images/illo091a.png" alt="Example" /> -<p class="caption">Fig. 115.</p> -</div> - -<p><span class="smcap">Ex.</span> 12.—<i>To draw a tangent to a circle from a given -point in the circumference</i>, <a href="#Fig115">Fig. 115</a>. From <i>A</i> set off -equal segments <i>A B</i>, -<i>A D</i>, join <i>B D</i> and -draw <i>A E</i>, parallel to -it, for the tangent.</p> - -<p class="allclear"> </p> - -<div class="container leftfloat nomargin w20em" id="Fig116"> -<img src="images/illo091b.png" alt="" /> -<p class="caption">Fig. 116.</p> -</div> - -<p><span class="smcap">Ex.</span> 13.—<i>To -draw tangents to a -circle from points -without it</i>, <a href="#Fig116">Fig. 116</a>. -From <i>A</i> with the -radius <i>A C</i> describe -an arc <i>B C D</i>, and -from <i>C</i> with a radius -equal to the diameter -of the circle, -cut the arc at <i>B D</i>, -join <i>B C</i>, <i>C D</i>, cutting -the circle at <i>E F</i>, and draw <i>A E</i>, <i>A F</i>, the tangents.</p> - -<p class="allclear"> </p> - -<div class="container rightfloat nomargin w20em" id="Fig117"> -<img src="images/illo091c.png" alt="Example" /> -<p class="caption">Fig. 117.</p> -</div> - -<p><span class="smcap">Ex.</span> 14.—<i>Between two inclined lines to draw a series -of circles touching these lines and touching each other</i>, -<a href="#Fig117">Fig. 117</a>. Bisect the inclination of the given lines <i>A B</i>, -<i>C D</i> by the line <i>N O</i>. From a point <i>P</i> in this line draw -the perpendicular <i>P B</i> to the line <i>A B</i>, and on <i>P</i> describe -the circle <i>B D</i>, touching the lines and cutting the -center lines at <i>E</i>. From <i>E</i> draw <i>E F</i> perpendicular to -the center line, cutting <i>A B</i> at <i>F</i>, and from <i>F</i> describe -an arc <i>E G</i>, cutting <i>A B</i> at <i>G</i>. Draw <i>G H</i> parallel to -<i>B P</i>, giving <i>H</i>, the center of the next circle, to be described -with the radius <i>H E</i>, and so on for the next -circle, <i>I N</i>.</p> - -<p class="allclear"> </p> - -<p><span class="pagenum" id="Page92">[92]</span></p> - -<div class="container leftfloat nomargin w10em" id="Fig118"> -<img src="images/illo092a.png" alt="Example" /> -<p class="caption">Fig. 118.</p> -</div> - -<div class="container rightfloat nomargin w12em" id="Fig119"> -<img src="images/illo092b.png" alt="Example" /> -<p class="caption">Fig. 119.</p> -</div> - -<p><span class="smcap">Ex.</span> 15.—<i>To construct a triangle -on a given base, the sides -being given.</i></p> - -<p>First. An equilateral triangle, -<a href="#Fig118">Fig. 118</a>. On the ends of a given -base <i>A B</i>, with <i>A B</i> as a radius -describe arcs cutting at <i>C</i>, and -draw <i>A C</i>, <i>C B</i>.</p> - -<p>Second. Triangle of unequal sides, <a href="#Fig119">Fig. 119</a>. On -either end of the base <i>A D</i>, with the side <i>B</i> as a radius -describe an arc; and with the side <i>C</i> as a radius, on -the other end of the base as a center, describe arcs cutting -the arc at <i>E</i>; join <i>A E</i>, -<i>D E</i>.</p> - -<p>This construction may be -used for finding the position -of a point <i>C</i> or <i>E</i> at given -distances from the ends of a -base, not necessarily to form -a triangle.</p> - -<p class="allclear"> </p> - -<div class="container leftfloat nomargin w12em" id="Fig120"> -<img src="images/illo092c.png" alt="Example" /> -<p class="caption">Fig. 120.</p> -</div> - -<div class="container rightfloat nomargin w10em" id="Fig121"> -<img src="images/illo092d.png" alt="Example" /> -<p class="caption">Fig. 121.</p> -</div> - -<p><span class="smcap">Ex.</span> 16.—<i>To construct a -square rectangle on a given -straight line.</i></p> - -<p>First. A square, <a href="#Fig120">Fig. -120</a>. On the ends <i>B A</i> as -centers, with the line <i>A B</i> -as radius, describe arcs cutting -at <i>C</i>; on <i>C</i> describe -arcs cutting the others at -<i>D E</i>; and on <i>D</i> and <i>E</i> cut these at <i>F G</i>. Draw -<i>A F</i>, <i>B G</i> and join the intersections <i>H I</i>.</p> - -<p>Second. A rectangle, <a href="#Fig121">Fig. -121</a>. On the base <i>E F</i> draw the -perpendiculars <i>E H</i>, <i>F G</i>, equal -to the height of the rectangle, -and join <i>G H</i>.</p> - -<p class="allclear"> </p> - -<p><span class="pagenum" id="Page93">[93]</span></p> - -<div class="container leftfloat nomargin w12em" id="Fig122"> -<img src="images/illo093a.png" alt="Example" /> -<p class="caption">Fig. 122.</p> -</div> - -<p><span class="smcap">Ex.</span> 17.—<i>To construct a -parallelogram of which the -sides and one of the angles -are given</i>, <a href="#Fig122">Fig. 122</a>. Draw -the side <i>D E</i> equal to the -given length <i>A</i>, and set off -the other side <i>D F</i> equal to -the other length <i>B</i>, forming -the given angle <i>C</i>. From <i>E</i> with <i>D F</i> as radius, -describe an arc, and from <i>F</i>, with the radius <i>D E</i> cut -the arc at <i>G</i>. Draw <i>F G</i>, <i>E G</i>. Or, the remaining -sides may be drawn as parallels to <i>D E</i>, <i>D F</i>.</p> - -<p class="allclear"> </p> - -<div class="container rightfloat nomargin w12em" id="Fig123"> -<img src="images/illo093b.png" alt="Example" /> -<p class="caption">Fig. 123.</p> -</div> - -<p><span class="smcap">Ex.</span> 18.—<i>To describe a -circle about a triangle</i>, <a href="#Fig123">Fig. -123</a>. Bisect two sides <i>A B</i>, -<i>A C</i> of the triangle at <i>E F</i>, -and from these points draw -perpendiculars cutting at <i>K</i>. -On the center <i>K</i>, with the -radius <i>K A</i> draw the circle -<i>A B C</i>.</p> - -<p class="allclear"> </p> - -<div class="container leftfloat nomargin w10em" id="Fig124"> -<img src="images/illo093c.png" alt="Example" /> -<p class="caption">Fig. 124.</p> -</div> - -<p><span class="smcap">Ex.</span> 19.—<i>To describe a circle about a square, and -to inscribe a square in a circle</i>, <a href="#Fig124">Fig. 124</a>.</p> - -<p>First. To describe the circle. -Draw the diagonals <i>A B</i>, <i>C D</i> of -the square, cutting at <i>E</i>; on the -center <i>E</i> with the radius <i>E A</i> -describe the circle.</p> - -<p>Second. To inscribe the square. Draw the two -diameters <i>A B</i>, <i>C D</i> at right angles and join the points -<i>A B</i>, <i>C D</i> to form the square.</p> - -<p><i>In the same way a circle may be described about a -triangle.</i></p> - -<p class="allclear"> </p> - -<p><span class="pagenum" id="Page94">[94]</span></p> - -<div class="container rightfloat nomargin w10em" id="Fig125"> -<img src="images/illo094a.png" alt="Example" /> -<p class="caption">Fig. 125.</p> -</div> - -<p><span class="smcap">Ex.</span> 20.—<i>To inscribe a circle on a square, and to -describe a square about a circle</i>, <a href="#Fig125">Fig. 125</a>.</p> - -<p>First. To inscribe the circle. Draw the diagonals -<i>A B</i>, <i>C D</i> of the square, cutting at <i>E</i>; draw the perpendicular -<i>E F</i> to one side, and with the radius <i>E F</i> -describe the circle.</p> - -<p>Second. To describe the square. Draw two diameters -<i>A B</i>, <i>C D</i> at right angles, and produce them; -bisect the angle <i>D E B</i> at the center by the diameter -<i>F G</i>, and through <i>F</i> and <i>G</i> draw perpendiculars <i>A C</i>, -<i>B D</i>, and join the points <i>A D</i> and <i>B C</i> where they -cut the diagonals to complete the square.</p> - -<p class="allclear"> </p> - -<div class="container leftfloat nomargin w15em" id="Fig126"> -<img src="images/illo094b.png" alt="Example" /> -<p class="caption">Fig. 126.</p> -</div> - -<p><span class="smcap">Ex.</span> 21.—<i>To inscribe -a circle in a -triangle</i>, <a href="#Fig126">Fig. 126</a>. -Bisect two of the -angles <i>A C</i> of the -triangle by lines -cutting at <i>D</i>; from -<i>D</i> draw a perpendicular <i>D E</i> to any side, and with -<i>D E</i> as radius describe a circle.</p> - -<p class="allclear"> </p> - -<div class="container rightfloat nomargin w12em" id="Fig127"> -<img src="images/illo094c.png" alt="Example" /> -<p class="caption">Fig. 127.</p> -</div> - -<p><span class="smcap">Ex.</span> 22.—<i>To inscribe a pentagon in a circle</i>, <a href="#Fig127">Fig. 127</a>. -Draw two diameters <i>A C</i>, -<i>B D</i> at right angles cutting -at <i>O</i>; bisect <i>A O</i> at -<i>E</i>, and from <i>B</i> with radius -<i>B E</i> cut the circumference -at <i>G H</i> and with the same -radius step round the circle -to <i>I</i> and <i>K</i>; join the points -to form the pentagon.</p> - -<p class="allclear"> </p> - -<p><span class="pagenum" id="Page95">[95]</span></p> - -<div class="container leftfloat nomargin w15em" id="Fig128"> -<img src="images/illo095a.png" alt="Example" /> -<p class="caption">Fig. 128.</p> -</div> - -<p><span class="smcap">Ex.</span> 23.—<i>To construct -a hexagon upon a given -straight line</i>, <a href="#Fig128">Fig. 128</a>. -From <i>A</i> and <i>B</i>, the ends -of the given line, describe -arcs cutting at <i>G</i>; from <i>G</i> -with the radius <i>G A</i> describe -a circle. With the -same radius set off the -arcs <i>A C</i>, <i>C F</i> and <i>B D</i>, -<i>D E</i>; join the points so found to form the hexagon.</p> - -<p class="allclear"> </p> - -<div class="container rightfloat nomargin w15em" id="Fig129"> -<img src="images/illo095b.png" alt="Example" /> -<p class="caption">Fig. 129.</p> -</div> - -<p><span class="smcap">Ex.</span> 24.—<i>To inscribe a hexagon in a circle</i>, <a href="#Fig129">Fig. 129</a>. -Draw a diameter <i>A C B</i>; -from <i>A</i> and <i>B</i> as centers, -with the radius of the circle -<i>A C</i> cut the circumference -at <i>D</i>, <i>E</i>, <i>F</i>, <i>G</i>, and -draw <i>A D</i>, <i>D E</i>, etc., to -form the hexagon. The -points <i>D E</i>, etc., may be -found by stepping the -radius (with the dividers) -six times round the circle.</p> - -<p class="allclear"> </p> - -<div class="container leftfloat nomargin w15em" id="Fig130"> -<img src="images/illo095c.png" alt="Example" /> -<p class="caption">Fig. 130.</p> -</div> - -<p><span class="smcap">Ex.</span> 25.—<i>To describe an -octagon on a given straight -line</i>, <a href="#Fig130">Fig. 130</a>. Produce the -given line <i>A B</i> both ways -and draw perpendiculars -<i>A E</i>, <i>B F</i>; bisect the external -angles <i>A</i> and <i>B</i> by -the lines <i>A H</i>, <i>B C</i>, which -make equal to <i>A B</i>. Draw -<i>C D</i> and <i>H G</i> parallel to -<i>A E</i> and equal to <i>A B</i>; -from the center <i>G D</i>, with the radius <i>A B</i>, cut the perpendiculars -at <i>E F</i>, and draw <i>E F</i> to complete the hexagon.</p> - -<p class="allclear"> </p> - -<div class="container rightfloat nomargin w15em" id="Fig131"> -<img src="images/illo095d.png" alt="Example" /> -<p class="caption">Fig. 131.</p> -</div> - -<p><span class="smcap">Ex.</span> 26.—<i>To convert a -square into an octagon</i>, <a href="#Fig131">Fig. -131</a>.—Draw the diagonals -of the square cutting at <i>E</i>; -from the corners <i>A</i>, <i>B</i>, <i>C</i>, <i>D</i>, -with <i>A E</i> as radius, describe -arcs cutting the -sides at <i>G</i>, <i>H</i>, etc., and -join the points so found -to complete the octagon.</p> - -<p class="allclear"> </p> - -<p><span class="pagenum" id="Page96">[96]</span></p> - -<div class="container rightfloat nomargin w12em" id="Fig132"> -<img src="images/illo096a.png" alt="Example" /> -<p class="caption">Fig. 132.</p> -</div> - -<p><span class="smcap">Ex.</span> 27.—<i>To inscribe -an octagon in a circle</i>, <a href="#Fig132">Fig. -132</a>. Draw two diameters -<i>A C</i>, <i>B D</i>, at right angles; -bisect the arcs <i>A B</i>, <i>B C</i>, -at <i>E</i>, <i>F</i>, etc., to form the -octagon.</p> - -<p class="allclear"> </p> - -<div class="container leftfloat nomargin w12em" id="Fig133"> -<img src="images/illo096b.png" alt="Example" /> -<p class="caption">Fig. 133.</p> -</div> - -<p><span class="smcap">Ex.</span> 28.—<i>To describe -an octagon about a circle</i>, <a href="#Fig133">Fig. 133</a>. Describe a square -about the given circle <i>A B</i>, -draw perpendiculars <i>H</i> -and <i>K</i>, to the diagonals, -touching the circle to form -the octagon. Or, the points -<i>H</i>, <i>K</i>, etc., may be found -by cutting the sides from -the corners, by lines parallel -to the diagonals.</p> - -<p class="allclear"> </p> - -<div class="container rightfloat nomargin w20em" id="Fig134"> -<img src="images/illo096c.png" alt="Example" /> -<p class="caption">Fig. 134.</p> -</div> - -<p id="Ref2"><span class="smcap">Ex.</span> 29.—<i>To describe an ellipse when the length and -breadth are given</i>, <a href="#Fig134">Fig. 134</a>. On the center <i>C</i>, with <i>A E</i> -as radius, cut the axis <i>A B</i> at <i>F</i> and <i>G</i>, the foci, fix -a couple of pins into the axis at <i>F</i> and <i>G</i>, and loop on a -thread or cord -upon them -equal in length -to the axis <i>A B</i>, -so as when -stretched to -reach the extremity -<i>C</i> of -the conjugate -axis, as shown -in dot-lining. -Place a pencil -or drawpoint -inside the cord, as at <i>H</i>, and guiding the pencil in this -way, keeping the cord equally in tension, carry the -pencil round the pins <i>F</i>, <i>G</i>, and so describe the ellipse.</p> - -<div class="note"> - -<p><span class="smcap">Note.</span>—The ellipse is an oval figure, like a circle in perspective. -The line that divides it equally in the direction of its -great length is the <i>transverse axis</i>, and the line which divides the -opposite way is the <i>conjugate axis</i>.</p> - -</div> - -<p><span class="pagenum" id="Page97">[97]</span></p> - -<p><i>Second Method.</i> Along the straight edge of a -piece of stiff paper mark off a distance <i>a c</i> equal to -<i>A C</i>, half the transverse axis; and from the same point -a distance <i>a b</i> equal to <i>C D</i>, half the conjugate axis. -Place the slip so as to bring the point <i>b</i> on the line <i>A B</i> -of the transverse axis, and the point <i>c</i> on the line -<i>D E</i>; and set off on the drawing the position of -the point <i>a</i>. Shifting the slip, so that the point -travels on the transverse axis, and the point <i>c</i> on -the conjugate axis, any number of points in the curve -may be found, through which the curve may be traced. -See <a href="#Fig135">fig. 135</a>.</p> - -<p class="allclear"> </p> - -<div class="container w25em" id="Fig135"> -<img src="images/illo097.png" alt="Example" /> -<p class="caption">Fig. 135.</p> -</div> - -<hr class="chap x-ebookmaker-drop" /> - -<div class="chapter"> - -<p><span class="pagenum" id="Page98">[98]</span></p> - -<h2 class="nobreak">Trigonometry.</h2> - -</div><!--chapter--> - -<p>Trigonometry is that portion of geometry which -has for its object the measurement of triangles. When -it treats of plane triangles, it is called <i>Plane Trigonometry</i>; -and as the engineer will continually meet -in his studies of higher mathematics <i>the terms</i> used -in plane trigonometry, it is advantageous for him -to become familiar with some of the principles and -definitions relating to this branch of mathematics.</p> - -<p>The circumferences of all circles contain the same -number of degrees, but the greater the radius the -greater is the absolute measures of a degree. The -circumference of a fly wheel or the circumference of -the earth have the same number of degrees; yet the -same number of degrees in each and every circumference -is the measure of precisely the same angle.</p> - -<p>The circumference of a circle is supposed to be -divided into 360 degrees or divisions, and as the total -angularity about the center is equal to four right -angles, each right angle contains 90 degrees, or 90°, -and half a right angle contains 45°. Each degree is -divided into 60 minutes, or 60′; and for the sake of still -further minuteness of measurement, each minute is -divided into 60″. In a whole circle there are, therefore, -360 × 60 × 60 = 1,296,000 seconds. The annexed diagram, -<a href="#Fig136">fig. 136</a>, exemplifies the relative positions of the</p> - -<div class="diagonalp"> - -<p>Sine,<br /> -<span class="padl2">Co-sine,</span><br /> -<span class="padl4">Versed Sine,</span></p> - -</div><!--diagonalp--> - -<div class="diagonalp"> - -<p>Tangent,<br /> -<span class="padl2">Co-Tangent,</span><br /> -<span class="padl4">Secant and</span><br /> -<span class="padl6">Co-secant</span></p> - -</div><!--diagonalp--> - -<p class="noindent">of an angle.</p> - -<div class="container w30em" id="Fig136"> -<img src="images/illo099.png" alt="" /> -<p class="caption">Fig. 136.</p> -</div> - -<p>These may be defined thus:</p> - -<p><span class="pagenum" id="Page99">[99]</span></p> - -<h3>DEFINITIONS.</h3> - -<p>1. The <i>Complement</i> of an arc is 90° minus the arc.</p> - -<p>2. The <i>Supplement</i> of an arc is 180° minus the arc.</p> - -<p>3. The <i>Sine</i> of an angle, or of an arc, is a line -drawn from one end of an arc, perpendicular to a diameter -drawn through the other end.</p> - -<p>4. The <i>Cosine</i> of an arc is the perpendicular distance -from the center of the circle to the sine of the -arc; or, it is the same in magnitude as the sine of the -complement of the arc.</p> - -<p>5. The <i>Tangent</i> of an arc is a line touching the -circle in one extremity of the arc, and continued from -thence, to meet a line drawn through the center and -the other extremity.</p> - -<p>6. The <i>Cotangent</i> of an arc is the tangent of the -complement of the arc. The <i>Co</i> is but a contraction of -the word complement.</p> - -<p>7. The <i>Secant</i> of an arc is a line drawn from the -center of the circle to the extremity of the tangent.</p> - -<p>8. The <i>Cosecant</i> of an arc is the secant of the -complement.</p> - -<p>9. The <i>Versed Sine</i> of an arc is the distance from -the extremity of the arc to the foot of the sine.</p> - -<p>For the sake of brevity, these technical terms are -contracted thus: for sine <i>A B</i>, we write <i>sin. A B</i>; for -cosine <i>A B</i>, we write <i>cos. A B</i>; for tangent <i>A B</i>, we -write <i>tan. A B</i>, etc.</p> - -<hr class="chap x-ebookmaker-drop" /> - -<p><span class="pagenum" id="Page100">[100-<br />101]</span><a id="Page101"></a></p> - -<div class="container w30em"> -<img src="images/illo101.png" alt="INSTRUMENTS AND MATERIALS" /> -</div> - -<hr class="chap x-ebookmaker-drop" /> - -<p><span class="pagenum" id="Page102">[102]</span></p> - -<div class="container w40em" id="Fig137"> -<img src="images/illo102.png" alt="Drawing board" /> -<p class="caption">Fig. 137.</p> -</div> - -<hr class="chap x-ebookmaker-drop" /> - -<div class="chapter"> - -<p><span class="pagenum" id="Page103">[103]</span></p> - -<h2 class="nobreak">Drawing Materials and Instruments.</h2> - -</div><!--chapter--> - -<p>Drawing tools or instruments are contrived solely -for mechanical drawing; aside from this use they are -perfectly worthless, hence the quality of these special -utensils is a matter of the first consideration to the earnest -student.</p> - -<p>There are several degrees of excellence to be found -in the make-up of drawing instruments and materials; -it may be remarked with truth that “any kind are good -enough, and the best none too good,” i. e., a learner in -this delightful art should not stop at the lack of goodness -or the low grade existing in his “tools,” but -rather do the best work possible with the means at -hand.</p> - -<p>However, in order that acceptable work may be -accomplished, fairly good instruments should be procured. -The advice of some one experienced in the use -and care of draughting tools should be sought before -purchasing. A drawing board, a single sheet of paper -and a pencil is the simplest “outfit” to be thought of; -to this small beginning may be added, soon afterwards, -an inexpensive pair of compasses, a T-square and a -couple of triangles; a vast range of work can be executed -with these few tools.</p> - -<p>Nothing else will be needed to do fine work -except, perhaps, one or two pairs of better compasses -and a few sweeps or means of drawing irregular -curves; all these had best be purchased separately; for -in buying a “box of instruments,” it may contain some -articles which are not desired, or that are of a wrong -size, or even duplicates of those already possessed.</p> - -<div class="container leftfloat w20em" id="Fig138"> -<img src="images/illo104.jpg" alt="Drawing table" /> -<p class="caption">Fig. 138.</p> -</div> - -<p><span class="pagenum" id="Page104">[104]</span></p> - -<p>An outfit recommended by the author of “Reed’s -Hand Book” is as follows.</p> - -<p>Large compasses with -movable leg.</p> - -<p>A pair of dividers.</p> - -<p>Bow pencil.</p> - -<p>Bow pen.</p> - -<p>Pencil leg for large compasses.</p> - -<p>Pen leg for large compasses.</p> - -<p>Drawing pen.</p> - -<p>Louis Rouillon, B. S., Instructor of Drawing in -Pratt Institute, New York, recommends the following:</p> - -<p>Compasses, 5<sup>1</sup>⁄<sub>2</sub> inches, with needle point; pen -pencil and lengthening bar.</p> - -<p>Drawing pen, 4<sup>1</sup>⁄<sub>2</sub> inches.</p> - -<p>T-square, 24-inch blade.</p> - -<p>45-degree triangle, 9 inches.</p> - -<p>30 and 60 degree triangle, 9 inches.</p> - -<p>1 Scroll.</p> - -<p>Dixon’s V. H. pencil.</p> - -<p>12-inch boxwood scale, flat, graduated <sup>1</sup>⁄<sub>16</sub> inch -the entire length.</p> - -<p>Bottle of liquid India ink, four thumb-tacks, pen -and ink eraser.</p> - -<p>20 sheets drawing paper, 11 × 15 inches, and a -drawing-board about 16 × 23 inches will also be necessary; -students can usually make the board themselves -for less money than it can be bought.</p> - -<div class="note"> - -<p><span class="smcap">Note.</span>—The purchasing of drawing tools is one of the most -difficult points to settle that can present itself to a person about to -buy a drawing outfit for the first time. Nothing can be so productive -of distress to a person drawing as to have his tools getting out -of order, joints one day too tight, next day too slack, points getting -blunt or perhaps turning up altogether; if needle points, then -the needles slip up, and drawing spoiled; in fact, the purchaser -can be annoyed in numberless different ways.—<span class="smcap">W. H. Thorn.</span></p> - -</div><!--note--> - -<p><span class="pagenum" id="Page105">[105]</span></p> - -<div class="container" id="Fig139"> -<img src="images/illo105.jpg" alt="Drawing set" /> -<p class="caption">Fig. 139.</p> -</div> - -<p><span class="pagenum" id="Page106">[106]</span></p> - -<div class="container" id="Fig140"> -<img src="images/illo106.png" alt="Drawing board" /> -<p class="caption">Fig. 140.</p> -</div> - -<p><span class="pagenum" id="Page107">[107]</span></p> - -<h3>THE DRAWING BOARD.</h3> - -<p>A drawing-board should be made of well seasoned -pine of a convenient size, say 23 × 16, which will take -half a sheet of imperial paper, leaving <sup>1</sup>⁄<sub>2</sub>-inch margin -all around.</p> - -<p>The working surface of the board—or its front -side—should be perfectly smooth, but instead of being -flat it should have a very slight camber, or rounding, -breadthways, this latter feature in its construction -being to prevent the possibility of a sheet of paper -when stretched on its surface having any vacuity -beneath it.</p> - -<p>The <i>four edges</i> of the board need not form an -exact rectangle, as much valuable time is often wasted -in the attempts to produce such a board; but it will -answer every purpose of the draughtsman so long as -the adjacent edges at the lower left-hand corner of it -are at right angles, or square to each other.</p> - -<p>An English authority recommends the use of two -drawing-boards, 42 inches long and 30 inches wide, -made of plain stuff, without cleets, 1<sup>1</sup>⁄<sub>4</sub> inches thick—seasoned—with -edges perfectly straight and at right -angles to each other. <i>With two boards, one may be -used for sketching and drawing details and the other for -the finished drawing.</i></p> - -<p>The board should be <sup>3</sup>⁄<sub>4</sub> inch in thickness, and -fitted at the back, at right angles to its longest side, -with a couple of hardwood battens, about 2 inches wide -and <sup>3</sup>⁄<sub>4</sub> inch thick; the use of these battens being to -keep the board from casting or winding and to allow -of its expansion or contraction through changes of -temperature. This latter purpose, however, is only -effected by attaching the battens to the back of the -board in the following manner: ... At the middle -of the length of each batten—which should be one -inch less than the width of the board—a stout, well-fitted -wood screw is firmly inserted into it, and made to -penetrate the board for about <sup>1</sup>⁄<sub>2</sub> inch, the head of the -screw being made flush with the surface of the batten; -on either side of the central screw, two others, about -3<sup>1</sup>⁄<sub>2</sub> inches apart, are passed through oblong holes in -the battens, and screwed into the body of the board -until their heads are flush with the central one; fitted -in this way the board itself can expand or contract -lengthwise or crosswise, while its surface is prevented -from warping or bending.</p> - -<p><span class="pagenum" id="Page108">[108]</span></p> - -<div class="container" id="Fig141"> -<img src="images/illo108.png" alt="Drawing board" /> -<p class="caption">Fig. 141.</p> -</div> - -<p><span class="pagenum" id="Page109">[109]</span></p> - -<p>A further improvement in such a drawing board -as above shown is made by cutting lengthwise along its -ends a narrow groove and inserting an ebony or hardwood -strip; this is cut or sawn apart at about every -inch to admit of contraction; this strip serves as a guide -to the stock of the drawing square, allowing an easy -sliding movement.</p> - -<p>To produce really good work in the shape of a -mechanical drawing, one perfect straight edge only is -required on a drawing board, and that the left one, -which is always known as the <i>working-edge</i>; but for -the convenience of being able to draw a long line across -the board at right angles to its lower edge, this edge is -made truly square with that on the left side of the -board.</p> - -<p>The details for building these drawing boards are -given, because they are easy to be made by one who -understands the use of a few wood-working tools; while -the boards themselves are difficult of transportation—in -case of the change of residence of their owners—quite -unlike the instruments which are to accompany -them.</p> - -<p><a href="#Fig141">Fig. 141</a> represents the board which has been described -in the text, with provisions for the contraction -and expansion; the very dark lines are intended to -represent the ebony insertions—as described. <a href="#Fig140">Fig. 140</a> -represents a plain pine board with dovetailed battens.</p> - -<p><span class="pagenum" id="Page110">[110]</span></p> - -<div class="container w30em" id="Fig142"> -<img src="images/illo109.jpg" alt="Thumb-tacks" /> -<p class="caption">Fig. 142.</p> -</div> - -<p><a href="#Fig142">Fig. 142</a> represents the common means used to attach -or secure slightly or temporarily the drawing paper -to the drawing board; these are called thumb-tacks, -and are usually forced through the paper into the wood -by the hand, whence they are easily detached. These -are made to have as slight a projection as may be, so as -not to interfere with the free movement of the tee-square.</p> - -<p>For mechanical drawing the invariable practice is -to secure the paper on which the drawing is to be made -to the drawing board by pinning it; this is effected by -various kinds of <i>drawing pins</i> or <i>thumb-tacks</i>.</p> - -<p>The best kind for this purpose have a head as -thin as possible without cutting at its edges, slightly -concave on the under side next the paper, and only so -much convex on its upper side as will give it sufficient -thickness to enable the pin to be secured to it; better -use four or more small pins along the edge of a sheet -of paper, than use one clumsy, badly made pin at each -end.</p> - -<div class="container" id="Fig143144"> - -<img src="images/illo110.jpg" alt="Trestles" /> - -<div class="split5050"> - -<div class="left5050"> -<p class="caption">Fig. 143.</p> -</div> - -<div class="right5050"> -<p class="caption">Fig. 144.</p> -</div> - -<p class="thinline allclear"> </p> - -</div><!--split--> - -</div><!--container--> - -<p><a href="#Fig143144">Fig. 143 and fig. 144</a> represent a pair of plain -trestles or horses in common use for supporting large -size drawing boards. This pattern is found frequently -in the laying-out shop. <a href="#Fig145146">Fig. 145 and fig. 146</a> represent<span class="pagenum" id="Page111">[111]</span> -<i>adjustable</i> horses or trestles—these are designed, -primarily, for office use. As will be seen by viewing the -illustration, the upper part is supported by two hard-wood -sliding pieces; these are provided with strong -pins and numerous holes, and pass through the frame -of the trestle, as shown, so that the upper portions can -be arranged at any angle convenient to the draughtsman, -as he lies over his work or stands by it.</p> - -<div class="container" id="Fig145146"> - -<img src="images/illo111a.jpg" alt="Trestles" /> - -<div class="split5050"> - -<div class="left5050"> -<p class="caption">Fig. 145.</p> -</div> - -<div class="right5050"> -<p class="caption">Fig. 146.</p> -</div> - -<p class="thinline allclear"> </p> - -</div><!--split--> - -</div><!--container--> - -<p><a href="#Fig137">Fig. 137</a> is introduced to exhibit the paper attached -to the drawing board with the thumb-tacks, and with -the T-square and set-squares arranged to commence -work; the paper should not extend to the edges of the -board; three, four or more tacks may be used on -each edge of the sheet of paper, instead of two, as shown -in illustration.</p> - -<div class="container w30em" id="Fig147"> -<img src="images/illo111b.jpg" alt="Drawing" /> -<p class="caption">Fig. 147.</p> -</div> - -<p>A most convenient—and except for its extreme -lightness, which is not good in a drawing stand—a -most admirable device is shown in <a href="#Fig138">fig. 138</a>. The drawing -table is simply a drawing board with folding legs; -these are made from hard-wood, while the top is made<span class="pagenum" id="Page112">[112]</span> -of soft, seasoned pine, with square corners; while the -device is strong and well braced, it can be folded and -easily carried about—all as shown in the illustration.</p> - -<div class="container" id="Fig148"> -<img src="images/illo112a.jpg" alt="T-square" /> -<p class="caption">Fig. 148.</p> -</div> - -<h3>THE TEE-SQUARE.</h3> - -<p>This is an instrument in the form of a letter T, as -shown in the <a href="#Fig149150">figures 149 and 150</a>; the two parts are -known as <i>stock</i> and <i>blade</i>; the horizontal part of the -letter (T) is the stock, and the vertical part the blade—hence -the name, T-square; to form the square, -the two parts are joined together in such a way as to -make them exactly at right angles to each other; the -stock, which is applied to the working edge of the -drawing board, being about one-third the length of the -blade, and about three times its thickness.</p> - -<div class="container" id="Fig149150"> -<img src="images/illo112b.jpg" alt="T-squares" /> -<p class="caption">Figs. 149 and 150.</p> -</div> - -<p>To be perfect in construction, a tee-square should -be as light as is consistent with its necessary strength -and stiffness of parts; it should be made of suitable -material easily manufactured, put together, and repaired, -and withal as truly correct as is possible to be -made. Such a square is represented in <a href="#Fig148">fig. 148</a>; it -has a taper blade, which is generally about double -the width where secured to the stock as it is at the -end.</p> - -<p><span class="pagenum" id="Page113">[113]</span></p> - -<div class="container leftfloat w20em" id="Fig151152"> -<img src="images/illo113.png" alt="T-square" /> -<p class="caption">Figs. 151 and 152.</p> -</div> - -<p>The manner in which the stock is united to the -blade determines its adaptability or otherwise to the -use made of it; in some the stock is rectangular in section, -and the blade mortised into it; in others the -blade is dovetailed and let into the stock for the whole -of its thickness.</p> - -<h3>ADJUSTABLE BLADED SQUARE.</h3> - -<p>In cases where many parallel lines have to be -drawn, of lengths beyond the capabilities of ordinary -set-squares, and in directions other than square with or -parallel to the working edge of the drawing board it is -convenient to have for use an <i>adjustable</i> bladed tee-square, -or one whose blade can be set at any desired -angle. The blade of such a square should be tapered -as in illustration, but shaped at its wide end as shown, -and having a stock wide enough to allow for the surface -required in the washers of the fittings necessary to -make the blade adjustable. These fittings, though requiring -to be well made and neatly finished, are not -expensive or difficult to make, as they consist merely -of two washers, a square-necked bolt, and a fly nut.</p> - -<p>The tee-square, as -shown, has four parts: 1, -blade; 2, fixed head; 3, -shifting head; 4, swivel. -The head is held firmly -by the left hand to the left -edge of the drawing board, -and the blade serves as a -straight-edge for horizontal -lines that may extend -the whole length of the -paper. It can be used for -either horizontal, or, by -reversing to the bottom of -the board, for vertical -lines; and, by turning it -over, so that the shifting -head is against the edge of the drawing board instead<span class="pagenum" id="Page114">[114]</span> -of the fixed head, lines at different angles may -be drawn. The length of the blade should be the length -of the drawing board; if it is shorter, inconvenience will -be experienced when lines the whole length of the -board are wanted.</p> - -<h3>TRIANGLES, OR SET-SQUARES.</h3> - -<p>Set-squares are invariably used in connection with -the tee-square, as shown in <a href="#Fig148">fig. 148</a>. The illustrations -below show several patterns of the device; by these, -vertical lines, triangles, squares and hexagonal, octagonal -and twelve-sided figures, diagonal section lines, -etc., can be easily drawn. For ordinary purposes, a -triangle or set-square with angles of 45° may be 4 -inches long and the other 8 inches in length, but a -six-inch set-square having angles 90°, 45° and 45°, -and an eight-inch one having angles of 90°, 60° and -30°, will be found sufficient for all purposes; there are -other triangles used specially for making letters.</p> - -<div class="container" id="Fig153156"> - -<img src="images/illo114a.jpg" alt="Triangles" /> - -<p class="caption">Fig. 153.—Fig. 154.—Fig. 155.—Fig. 156.</p> - -</div><!--container--> - -<p>In practice the triangles or set-squares are slid -along the edge of the blade, and need not be any -thicker than it.</p> - -<h3>PARALLEL RULE.</h3> - -<div class="container w40em" id="Fig157"> -<img src="images/illo114b.jpg" alt="Parallel rule" /> -<p class="caption">Fig. 157.</p> -</div> - -<p>This instrument is used to mark lines which are -neither horizontal nor vertical (usually these are drawn -by the square and set-square), and which are parallel -to one another; by adjusting the edge of the parallel -ruler to a line, it can be extended or opened out (or<span class="pagenum" id="Page115">[115]</span> -vice-versa closed), and the line or lines drawn will be -parallel or equally distant from the base or first line it -was set by. See <a href="#Fig157">fig. 157</a>.</p> - -<p><a href="#Fig158">Fig. 158</a> is a parallel ruler, constructed with two -rollers fixed on a rod so that they move the same -distance, carrying the ruler parallel to the starting line.</p> - -<div class="container" id="Fig158"> -<img src="images/illo115.jpg" alt="Rule" /> -<p class="caption">Fig. 158.</p> -</div> - -<div class="note"> - -<p><span class="smcap">Note.</span>—It has been said that “a workman may be known by his tools,” but the statement must be taken with a good deal of allowance. -Some workmen may possess a very fine set of tools and never use them, because they have not the ability or inclination to learn -how; especially is this the case with drawing instruments.</p> - -<p>If all the fine sets of drawing instruments that are owned by workmen were put to frequent use the owners would find a marked improvement -in their abilities in other lines as well as drawing; for it is a noticeable fact that when a person’s mind has been trained in a -business that requires close calculation and a knowledge of materials, he is capable of showing good qualifications in other lines, and the -more skilled he is in one the easier can he acquire skillfulness in another, if he applies the same amount of energy, thought and interest -as he did to acquire skill in the first.</p> - -</div><!--note--> - -<p><span class="pagenum" id="Page116">[116]</span></p> - -<h3>SECTION LINER.</h3> - -<p><a href="#Fig159">Fig. 159</a> shows an improved section liner which can -be adjusted to any angle, and will space the parallel -lines at any desired regular distance.</p> - -<div class="container" id="Fig159"> -<img src="images/illo116.png" alt="Section liner" /> -<p class="caption">Fig. 159.</p> -</div> - -<p><span class="pagenum" id="Page117">[117]</span></p> - -<h3>IRREGULAR CURVE OR SCROLL.</h3> - -<p>Irregular curves, or, as they are sometimes termed, -sweeps, represented by <a href="#Fig160166">figs. 160-166</a>, are used for curves -that cannot be put in by the other instruments. They -are very useful when elliptical or parabolic curves are -desired, in preference to circles or arcs of a circle. -They are much used in design and architectural drawing. -They are made of thin hardwood or rubber, and -sometimes of horn.</p> - -<div class="container" id="Fig160166"> -<img src="images/illo117.png" alt="Curves" /> -<p class="caption">Figs. 160-166.</p> -</div> - -<p><span class="pagenum" id="Page118">[118]</span></p> - -<div class="container rightfloat w10em" id="Fig167168"> - -<img src="images/illo118.jpg" alt="Pencils" /> - -<div class="split5050"> - -<div class="left5050"> -<p class="caption">Fig. 167.</p> -</div> - -<div class="right5050"> -<p class="caption">Fig. 168.</p> -</div> - -<p class="thinline allclear"> </p> - -</div><!--split--> - -</div><!--container--> - -<p>Curves are irregular lines; a circle is a regular line. -If a curve is to be passed through a number of predetermined -points it should be first sketched in lightly, -free-hand; a section of the scroll is then applied to the -curve so as to embrace as many points as possible; -only the central points of those thus embraced should -be inked in; this process is continued until the desired -curve is completed.</p> - -<p>Curves are made of various material, pearwood, -cardboard, xylonite, hard rubber, and a strip of soft -lead is sometimes used, which may be easily adjusted -to the curve required.</p> - -<p>The curves generally used in mechanical drawing -are shown on <a href="#Page117">previous page</a>.</p> - -<p><a href="#Fig208">Fig. 208</a>, <a href="#Page134">page 134</a>, is a logarithmic <i>spiral</i> curve. -It is mathematically constructed and contains every -curve within the limit of its size.</p> - -<h3>ELLIPSES.</h3> - -<p>An ellipse is a geometrical figure, and can be -drawn as described in <a href="#Ref2">geometrical problem 29</a>, <a href="#Page96">page -96</a>; many drawing offices keep sets of hard rubber -ellipses, to economize time constructing them.</p> - -<div class="container leftfloat w10em" id="Fig169170"> - -<img src="images/illo119.jpg" alt="Compasses" /> - -<div class="split5050"> - -<div class="left5050"> -<p class="caption">Fig. 169.</p> -</div> - -<div class="right5050"> -<p class="caption">Fig. 170.</p> -</div> - -<p class="thinline allclear"> </p> - -</div><!--split5050--> - -</div><!--container--> - -<h3>DRAWING PENCILS.</h3> - -<p>These are instruments for marking, drawing or -writing, formed of graphite, colored chalk or materials -of similar properties, and having a tapering end, -inclosed, generally, in a cylinder of -softwood. <a href="#Fig167168">Fig. 167</a> represents a -ruling pencil; its point is a parallelogram -or of a wedge shape. In -ruling, the length view rests against -the square; its shape gives considerable -strength to the lead and -allows the making of a very fine -line. <a href="#Fig167168">Fig. 168</a> differs in the point -of the pencil shown, as may be -observed in the illustration.</p> - -<p>A pencil that is hard is best -for mechanical drawing; one that -will retain a good point for some<span class="pagenum" id="Page119">[119]</span> -considerable time. Pencil lines -should be made as light as possible; -the presence of lead on the surface -of the paper tends to prevent -the ink passing to the paper, and -in rubbing out pencil lines the ink -is reduced in blackness, and the -surface of paper is roughened, -which is a disadvantage. As little -erasing or rubbing out as possible -should be done.</p> - -<h3>DIVIDERS AND COMPASSES.</h3> - -<p>These instruments, while they -appear alike, have a separate use: -the dividers are used to space off -distances and dimensions; especially -are they necessary in reading -drawings made to scale. <i>Compasses</i> -are used for describing circles, curves, etc., <i>dividers</i> -are used for marking out spaces.</p> - -<p>Two forms of the dividers are shown in <a href="#Fig169170">figs. 169 -and 170</a>; the simplest, plainest form is shown in <a href="#Fig169170">fig. -169</a>; these are used for rough spacings; <a href="#Fig169170">fig. 170</a> represents -a pair of dividers fitted with an adjustable screw -controlled by a steel spring in one leg; by this a very -exact measurement can be made. <a href="#Fig169170">Fig. 170</a> is intended -to exhibit what is called a “hair-spring divider.”</p> - -<h3>PROPORTIONAL DIVIDERS.</h3> - -<p>These dividers differ from the ordinary ones -shown in <a href="#Fig169170">figs. 169 and 170</a> in that they are provided -with four steel points, one pair of which being set to -the full dimension will be reproduced by the other -pair, but in a smaller, or reduced size.</p> - -<p><a href="#Fig171174">Fig. 171</a> are “bisecting” dividers, being proportional -dividers, which, when open, one end measures -double the distance of the other.</p> - -<p><a href="#Fig171174">Fig. 172</a> are proportional dividers; the points at -one end are capable of being changed, -to measure practically any desired -proportion at the other end, by -altering the position of the pivot -where the legs cross one another. -The lower connecting link is a -micrometer adjustment, for minute -measurements.</p> - -<p><a href="#Fig171174">Fig. 173</a> are proportional dividers -which are marked for the proportions -of lines and radii of circles, being -provided with a rack movement for -adjustment.</p> - -<p><a href="#Fig171174">Fig. 174</a> represents three-leg dividers, -used for taking the position of -three points; this instrument is very -useful in finding the position of a point in a -figure.</p> - -<p><span class="pagenum" id="Page120">[120]</span></p> - -<div class="container" id="Fig171174"> - -<img src="images/illo120.jpg" alt="Dividers" /> - -<p class="caption">Fig. 171.—Fig. 172.—Fig. 173.—Fig. 174.</p> - -</div><!--container--> - -<p><span class="pagenum" id="Page121">[121]</span></p> - -<div class="container w20em" id="Fig175179"> - -<img src="images/illo121.jpg" alt="Compasses" /> - -<p class="caption">Fig. 175.—Fig. 176.—Fig. 177.—Fig. 178.—Fig. 179.</p> - -</div><!--container--> - -<h3>COMPASSES.</h3> - -<p>Compasses consist of two -pointed legs; they are instruments -for describing circles or for—sometimes—measuring -figures, in -absence of dividers. <a href="#Fig175179">Fig. 175</a> -represents compasses fitted as -dividers.</p> - -<p>Compasses should have jointed -legs, which will allow the points -to be placed at right angles to the -paper, whatever the size of the -circle to be drawn. Compasses -should not be used for circles -which are too large to allow the points to be thus -placed; a lengthening bar is generally provided, which -greatly increases the diameters of circles which may be -drawn by this attachment; it is shown in <a href="#Fig175179">fig. 176</a>.</p> - -<p>One leg of the compasses is usually provided with -a socket to which are fitted three points: a divider -point, <a href="#Fig175179">fig. 179</a>; a pencil point, <a href="#Fig175179">fig. 177</a>; -and a point,<span class="pagenum" id="Page122">[122]</span> -<a href="#Fig175179">fig. 178</a>, carrying a special pen for the inking of circles. -Each of these points is generally provided with a joint, -so that it may be placed at right angles to the paper.</p> - -<p>The other leg should be jointed; it is often provided -with a socket which receives -two points, one a divider point, and -the other carrying a needle point. -Such an instrument may be used as -dividers for spacing, or as compasses -for penciling or inking circles.</p> - -<p>The joint at the head of the -compasses (see <a href="#Fig175179">fig. 175</a>) is the most -important feature. It should hold the -legs firmly in any position, so that in -going over a circle several times only -one line will result. It should allow -the legs to move smoothly and evenly, -and should be capable of adjustment.</p> - -<div class="container w40em" id="Fig180184"> - -<img src="images/illo122.jpg" alt="Compasses" /> - -<p class="caption">Fig. 180.—Fig. 181.—Fig. 182.—Fig. 183.—Fig. 184.</p> - -</div><!--container--> - -<p>As shown in <a href="#Fig171174">fig. 174</a>, one leg has -a hinge or joint, and a needle point,<span class="pagenum" id="Page123">[123]</span> -which can be regulated by a thumb screw; the other -leg has a socket or recess into which interchangeable -parts can be inserted. The four figures to the right of -the compasses show the parts which are provided with -shanks or insertion pieces. <a href="#Fig180184">Fig. 180</a> and <a href="#Fig180184">fig. 181</a> represent -compasses specially used for making small circles, -and work too minute for the larger instruments described -above.</p> - -<p>To do work of this nature easily a pair of spring -dividers are frequently used. This instrument has one -point attached to a spring, which is regulated by a -screw, so that very slight changes in the space may be -made with ease.</p> - -<p>Compasses specially used for putting in fine circles -and dimensions are called “bows.” When a pen point -it is a “bow pen,” with a pencil point a “bow pencil,” -and if with needle point a “bow dividers.” <a href="#Fig180184">Fig. 180</a> -is a “bow dividers”, this fitted with screw for fine adjustment -in one leg, <a href="#Fig180184">fig. 181</a>, is called a “hair-spring -bow dividers”; for small details, bows with steel spring -legs without any joint are used; these are called “steel-spring -bows.”</p> - -<div class="container w30em" id="Fig185187"> - -<img src="images/illo123.jpg" alt="Compasses" /> - -<p class="caption">Fig. 185.—Fig. 186.—Fig. 187.</p> - -</div><!--container--> - -<p><span class="pagenum" id="Page124">[124]</span></p> - -<h3>SPRING BOWS.</h3> - -<p>These were originally developed from the common -form of compasses, with a single spring leg; later, the -demand for smaller sizes made changes necessary, and -spring bows are now made symmetrical, both sides of -the bow being made to “spring.”</p> - -<p><a href="#Fig180184">Fig. 182</a> are spring dividers.</p> - -<p><a href="#Fig180184">Fig. 183</a> is a spring pencil.</p> - -<p><a href="#Fig180184">Fig. 184</a> is a spring pen.</p> - -<p>In these figures it will be seen that the two -threads, a right and a left, are moved with one central -thumbscrew; in the <a href="#Fig185187">figs. 185 to 187</a> a single screw is -used.</p> - -<p>In choosing spring bows, care must be exercised -to select a sufficiently strong, stiff spring, as the relation -between spring pressure and thumbscrew is important.</p> - -<h3>BEAM COMPASSES AND TRAMMELS.</h3> - -<p>In <a href="#Fig188">fig. 188</a> is shown a set of beam compasses, -together with a portion of the wooden rod or beam -on which they are used.</p> - -<div class="container" id="Fig188"> -<img src="images/illo124.jpg" alt="Bem compasses" /> -<p class="caption">Fig. 188.</p> -</div> - -<p>The latter, as will be seen by the section drawn -to one side, <i>A</i>, is in the shape of a T. This form has -considerable strength and rigidity. Beam compasses -are provided with extra points for pencil or ink work, -as shown.</p> - -<p>While the general adjustment is effected by means -of the clamp against the wood, minute variations are -made by the screw, <i>B</i>, shifting one of the points, as -shown in the <a href="#Fig188">figure</a>.</p> - -<p><span class="pagenum" id="Page125">[125]</span></p> - -<p>This instrument is quite delicate, and, when in -good order, is very accurate. It should be used only -for fine work on paper, and never for scribing on -metal.</p> - -<div class="container leftfloat w20em" id="Fig189"> -<img src="images/illo125.jpg" alt="Trammel" /> -<p class="caption">Fig. 189.</p> -</div> - -<p>A coarser instrument, and one especially designed -for use upon metal, is shown in <a href="#Fig189">fig. 189</a>, and is called a -trammel. There are various forms of this instrument, -all being the same in principle. The engraving shows -a form in common use. A heavier stick is used with -it than with the beam compasses, and no other adjustment -is provided than that which is afforded by clamping -against the stick.</p> - -<p>In the <a href="#Fig189">illustration</a>, a carrier at the side is shown, -in which a pencil may be placed. Some trammels are -arranged in such a manner, that either of the points -may be detached and a pencil substituted.</p> - -<p>A trammel, by careful arrangement, can be made -to describe very accurate curves, and hence can be -used in place of the beam compasses in many instances. -For all coarse work it is to be preferred to beam compasses.<span class="pagenum" id="Page126">[126]</span> -It is useful for all short sweeps upon sheets of -metal, but for curves of a very long radius a strip of -sheet iron or a piece of wire will be found of a more -practical service than even this tool.</p> - -<p>The length of rods for both beam compasses and -tramels, up to certain limits, is determined by the -nature of the work to be done. The extreme length -is determined by the strength and rigidity of the rod -itself. It is usually convenient to have two rods for -each instrument, one about 1<sup>1</sup>⁄<sub>2</sub> or 2 feet in length and -the other considerably longer—as long as the strength -of the material will admit.</p> - -<h3>DRAWING SCALES.</h3> - -<p>Scales are proportioned rules or mathematical instruments -of wood, metal, etc., on which are marked -lines and figures for the purpose of measuring sizes and -distances. It is usual to make scales in the proportion -of parts of an inch equalling a foot; the most generally -adopted scale for machine drawing is one and a half -inches, equalling one foot; that is, twelve-eighths of an -inch (each eighth of an inch representing one inch); -there is no fixed rule in the choice of a scale, as they -are varied according to the coarseness or fineness of the -parts of the machine to be drawn and the space or surface -of paper to be utilized.</p> - -<p>When objects are of moderate proportions they -may be represented full size; but when large, the -drawings must be smaller. Standard scales for mechanical -drawings are <sup>1</sup>⁄<sub>2</sub>, <sup>1</sup>⁄<sub>4</sub>, -<sup>1</sup>⁄<sub>8</sub> and <sup>1</sup>⁄<sub>16</sub> full size. These -scales are often written 6″ = 1 ft.; 3″ = 1 ft.; 1<sup>1</sup>⁄<sub>2</sub>″ = 1 ft., -and <sup>3</sup>⁄<sub>4</sub>″ = 1 ft.</p> - -<div class="container leftfloat w07em" id="Fig190"> -<img src="images/illo127a.jpg" alt="Scale" /> -<p class="caption">Fig. 190.</p> -</div> - -<div class="container rightfloat w07em" id="Fig191"> -<img src="images/illo127b.jpg" alt="Scale" /> -<p class="caption">Fig. 191.</p> -</div> - -<p>Instead of selecting one of the scales named or one -found upon the ordinary scales used by draughtsmen, -drawings may be made to any scale whatever. Thus, -if any object is to be represented in a certain space, a -scale should be constructed which will cause the whole -of the object to be shown.</p> - -<p>Drawing to Scale.—The meaning of this is, that -the drawing when done bears a definite proportion to<span class="pagenum" id="Page127">[127]</span> -the full size of the particular part, or, in other words, -is precisely the same as it would appear if viewed -through a diminishing glass.</p> - -<p>The two-foot rule shown in <a href="#Fig192">fig. 192</a> is the most -useful instrument for the comparison of linear dimensions—it -can be used as a scale of one-twelfth, or 1 -inch equal to a foot, 12 inches = 12 feet, it being divided -into portions or spaces, each of which is subdivided -into halves, quarters, eighths and sixteenths; -frequently in the latter class of two-foot rules there are -graduations of scales, and it is then also called a -draughting scale.</p> - -<p><a href="#Fig190">Fig. 190</a> represents a flat scale, graded so that one -inch represents a foot—<sup>1</sup>⁄<sub>12</sub>th size—etc., as shown.</p> - -<p><a href="#Fig191">Fig. 191</a> represents a triangular scale (broken). -The triangular scale should read on its different edges -as follows: Three inches and 1<sup>1</sup>⁄<sub>2</sub>″ to one foot, 1″ and -<sup>1</sup>⁄<sub>2</sub>″ to one foot, <sup>3</sup>⁄<sub>4</sub>″ -and <sup>3</sup>⁄<sub>8</sub>″ to one foot, <sup>1</sup>⁄<sub>4</sub>″ and <sup>1</sup>⁄<sub>8</sub>″ to one -foot, <sup>3</sup>⁄<sub>16</sub>″ and <sup>3</sup>⁄<sub>32</sub>″ to one foot, and one edge read sixteenths -the whole 12″ of its length.</p> - -<p><span class="pagenum" id="Page128">[128]</span></p> - -<p><a href="#Fig190">Fig. 190</a> shows such a scale broken. An explanation -of the 1″ and <sup>1</sup>⁄<sub>2</sub>″ side will suffice for all. Where -it is used as a scale of 1″ to one foot, each large space, -as from 0 to 12 or 0 to 1, represents a foot, and is a -foot at that scale. There being 12″ in one foot, the -twelve long divisions at the left represent inches; each -inch is divided into two equal parts, so from 0 to one -division at the left of 9 is 9<sup>1</sup>⁄<sub>2</sub>″ and so on. The 1″ and -<sup>1</sup>⁄<sub>2</sub>″ scales being at opposite ends of the same edge, it -is obvious that one foot on the 1″ scale is equal to two -feet on the <sup>1</sup>⁄<sub>2</sub>″ scale, and conversely, one foot on the <sup>1</sup>⁄<sub>2</sub>″ -scale is equal to six inches on the 1″ scale; and 1″ -being equal to one foot, the total feet in length of scale -will be 12; at <sup>1</sup>⁄<sub>2</sub>″ to 1 foot the total feet will be 24.</p> - -<p>In working to regular scales, such as <sup>1</sup>⁄<sub>2</sub>, -<sup>1</sup>⁄<sub>8</sub>, or <sup>1</sup>⁄<sub>16</sub> -size, a good plan is to use a common rule, instead of a -graduated scale. There is nothing more convenient for -a mechanical draughtsman than to be able to readily -resolve dimensions into various scales, and the use of a -common rule for fractional scales trains the mind, so -that computations come naturally, and after a time -almost without effort.</p> - -<p>The protractor shown in <a href="#Fig193">fig. 193</a> is an instrument -for laying down and measuring angles on paper; it is<span class="pagenum" id="Page129">[129]</span> -used in connecting with a scale to define the inclination -of one line to another.</p> - -<p>Protractors have the degrees of a half circle -marked upon them; as the whole circle contains 360 -degrees, half of it will contain 180, one-quarter 90, etc. -Hence, protractors showing 180° exhibit all that is -needed. To protract means to extend, so this instrument -is also useful in “extending” the lines of inclination -at the circle.</p> - -<div class="container w30em" id="Fig192"> -<img src="images/illo128a.jpg" alt="Scale" /> -<p class="caption">Fig. 192.</p> -</div> - -<div class="container w30em" id="Fig193"> -<img src="images/illo128b.jpg" alt="Protractor" /> -<p class="caption">Fig. 193.</p> -</div> - -<h3>DRAWING-PENS.</h3> - -<p>A special pen called a drawing-pen, and also special -ink, are required to ink a drawing; <a href="#Fig194">figs. 194</a> and <a href="#Fig195">195</a> represent -two sizes of drawing-pens—one being best adapted -for fine work, and the other for coarse or heavy line -work. The points, as will be observed in the illustration, -are made of two steel blades which open and close -as required for thickness of lines by a regulating screw.</p> - -<div class="container" id="Fig194"> -<img src="images/illo129a.jpg" alt="Pen" /> -<p class="caption">Fig. 194.</p> -</div> - -<div class="container" id="Fig195"> -<img src="images/illo129b.jpg" alt="Pen" /> -<p class="caption">Fig. 195.</p> -</div> - -<p>A good drawing pen should be made of properly -tempered steel, neither too soft nor hardened to brittleness. -The nibs should be accurately set, both of -the same length, and both equally firm when in contact -with the drawing paper. The points should be so -shaped that they are fine enough to admit of absolute -control of the contact of the pen in starting and ending -lines, but otherwise as broad and rounded as possible, -in order to hold a convenient quantity of ink without -dropping it. The lower (under) blade should be sufficiently -firm to prevent the closing of the blades of the -pen, when using the pen against a straightedge.</p> - -<div class="container w30em" id="Fig196"> -<img src="images/illo130a.jpg" alt="Pen" /> -<p class="caption">Fig. 196.</p> -</div> - -<div class="container w15em" id="Fig197"> -<img src="images/illo130b.jpg" alt="Ink bottle" /> -<p class="caption">Fig. 197.</p> -</div> - -<p>The spring of the pen, which separates the two -blades, should be strong enough to hold the upper<span class="pagenum" id="Page130">[130]</span> -blade in its position, but not so strong that it would -interfere with easy adjustment by the thumbscrew. -The thread of the thumbscrew must be deeply and -evenly cut so as not to strip.</p> - -<p>An important requisite after the pencil lines have -been put in is ink, with which to line the drawing. -This should be of the best that can be procured. The -pen is filled by dropping the ink between the blades, or -nibs, while held in a nearly vertical position, as shown -in <a href="#Fig196">fig. 196</a>.</p> - -<p>Liquid India ink can be procured in bottles with -glass tube feeders, which are very good, and keep the -hands and fingers free of -the ink. <a href="#Fig197">Fig. 197</a> is a sectional -view of such a bottle -and “filler,” or feeder. This -generally answers all requirements, -but the dry ink -of good quality, in sticks or -bars, cannot be surpassed, -although it requires skill for -its preparation. <a href="#Fig198">Fig. 198</a> -represents a sloping dish or -“tile” for mixing, which -should be done with little -pressure, in clean, filtered or -distilled water, care being taken to keep the liquid free -of dust, which obstructs the free flow of the ink in -the pens.</p> - -<div class="container" id="Fig198"> -<img src="images/illo131a.jpg" alt="Dish" /> -<p class="caption">Fig. 198.</p> -</div> - -<p>The bars of India ink are shown, as they are imported, -in <a href="#Fig199202">figs. 199 to 202</a>.</p> - -<p>Pure India or China ink is only made in those<span class="pagenum" id="Page131">[131]</span> -countries, because the special wood from which it is -prepared is found only in those regions. So-called -India inks, made of lampblack and animal glue, are -only imitations; therefore India ink should be purchased -from a reliable importing house—shape is little -guarantee of quality.</p> - -<div class="container w40em" id="Fig199202"> - -<img src="images/illo131b.jpg" alt="Ink" /> - -<p class="caption">Fig. 199.—Fig. 200.—Fig. 201.—Fig. 202.</p> - -</div><!--container--> - -<p><span class="pagenum" id="Page132">[132]</span></p> - -<div class="container w30em" id="Fig203"> -<img src="images/illo132a.jpg" alt="Eraser" /> -<p class="caption">Fig. 203.</p> -</div> - -<p>Soft gray vulcanized rubber (<a href="#Fig203">fig. 203</a>) should be -used for cleaning drawing paper; for erasing any portion -of a line in pencil, a piece of prepared white vulcanized -rubber is the best, small in size and of rectangular -shape (see <a href="#Fig204205">fig. 205</a>).</p> - -<div class="container w30em" id="Fig204205"> - -<img src="images/illo132b.jpg" alt="Erasers" /> - -<div class="split4060"> - -<div class="left4060"> -<p class="caption">Fig. 204.</p> -</div> - -<div class="right4060"> -<p class="caption">Fig. 205.</p> -</div> - -<p class="thinline allclear"> </p> - -</div><!--split--> - -</div><!--container--> - -<div class="container leftfloat w07em" id="Fig206207"> - -<img src="images/illo132c.jpg" alt="Erasers" /> - -<div class="split5050"> - -<div class="left5050"> -<p class="caption">Fig. 206.</p> -</div> - -<div class="right5050"> -<p class="caption">Fig. 207.</p> -</div> - -<p class="thinline allclear"> </p> - -</div><!--split5050--> - -</div><!--container--> - -<p>An ink eraser is made of a composition of rubber -and ground glass, and it should be used as sparingly as -possible on drawings, as it roughens the paper and removes -the gloss from its surface (see <a href="#Fig204205">fig. 204</a>). Steel -ink erasers are useful in removing defects, overrun -lines, joint of lines if swollen, etc.; they have a fine -point and can be used to advantage with a little practice; -they are used with a scratching, not a cutting, -motion (see <a href="#Fig206207">figs. 206, 207</a>).</p> - -<h3>DRAWING PAPER.</h3> - -<p>The first thing to be considered in selecting drawing -paper is the kind most suitable for the proposed -plan. Paper may be purchased in sheets 22 × 30 -inches, that make four exercise sheets 11 × 15 inches; -this may be of several grades and tints.</p> - -<p><span class="pagenum" id="Page133">[133]</span></p> - -<p>The qualities that constitute good paper are -strength, uniformity of thickness and surface, neither -repelling nor absorbing liquids, admitting of considerable -erasing without destroying the surface, not becoming -brittle nor discolored by reasonable exposure or age, -and not buckling when stretched, or when ink or color -is applied.</p> - -<p>The sizes and names of paper made in sheets is -as follows:</p> - -<table class="paper" summary="Paper sizes"> - -<tr> -<td class="size">Cap</td> -<td class="inches">13×17</td> -<td class="ditto">ins.</td> -</tr> - -<tr> -<td class="size">Demy</td> -<td class="inches">15×20</td> -<td class="ditto">„</td> -</tr> - -<tr> -<td class="size">Medium</td> -<td class="inches">17×22</td> -<td class="ditto">„</td> -</tr> - -<tr> -<td class="size">Royal</td> -<td class="inches">19×24</td> -<td class="ditto">„</td> -</tr> - -<tr> -<td class="size">Super Royal</td> -<td class="inches">19×27</td> -<td class="ditto">„</td> -</tr> - -<tr> -<td class="size">Imperial</td> -<td class="inches">22×30</td> -<td class="ditto">„</td> -</tr> - -<tr> -<td class="size">Atlas</td> -<td class="inches">26×34</td> -<td class="ditto">„</td> -</tr> - -<tr> -<td class="size">Double Elephant</td> -<td class="inches">27×40</td> -<td class="ditto">„</td> -</tr> - -<tr> -<td class="size">Antiquarian</td> -<td class="inches">30×53</td> -<td class="ditto">„</td> -</tr> - -</table> - -<p>For large drawings paper is made in rolls. “Detail -paper” is especially made for marking out new -designs; it is made in rolls 36, 42 and 54 inches wide; -it has excellent erasing qualities and takes ink and -color with facility.</p> - -<p>When working by artificial light it is desirable that -the paper be of a light-brown color, which is less trying -to the eyes than a pure white.</p> - -<p>If it is a shop drawing or sketch not to be preserved, -use detail paper, which is the most economical -and will stand a great deal of handling without becoming -soiled. If it is a detailed plan, finished drawing -or a picture, use the best white drawing paper to be -obtained, so that your drawings can be preserved -indefinitely without danger of fading, which is due -either to the paper being poorly made and discoloring -with age, or being of poor fiber and absorbing the ink -or color, and the drawing consequently losing its -brightness.</p> - -<p>After deciding on the size of paper most suitable -for the work, then carefully select the paper -embracing the most qualities of value for the proposed -drawing.</p> - -<hr class="chap x-ebookmaker-drop" /> - -<p><span class="pagenum" id="Page134">[134]</span></p> - -<div class="container w40em" id="Fig208"> -<img src="images/illo134.png" alt="Spiral" /> -<p class="caption">Fig. 208.</p> -</div> - -<hr class="chap x-ebookmaker-drop" /> - -<p><span class="pagenum" id="Page135">[135]</span></p> - -<div class="container w30em"> -<img src="images/illo135.png" alt="MECHANICAL DRAWING" /> -</div> - -<hr class="chap x-ebookmaker-drop" /> - -<p><span class="pagenum" id="Page136">[136]</span></p> - -<div class="container w40em" id="Fig209"> -<img src="images/illo136.png" alt="Hand and compasses" /> -<p class="caption">Fig. 209.</p> -</div> - -<hr class="chap x-ebookmaker-drop" /> - -<div class="chapter"> - -<p><span class="pagenum" id="Page137">[137]</span></p> - -<h2 class="nobreak">Mechanical Drawing.</h2> - -</div><!--chapter--> - -<p>In distinction to “free-hand,” mechanical drawing -is executed almost entirely by the use of the instruments -previously described; hence its other term, -instrumental drawing. To define it particularly it may -be said <span class="nowrap">that,—</span></p> - -<p>Mechanical drawing is the correct reproduction of -any figure or part of a machine, whether of full size or -reduced in the proportion of one part to another; it -also comprises the art of delineating the interior parts -which are hidden from view in solid bodies.</p> - -<p>A mechanical drawing is the vehicle for conveying -the ideas of the designer to those who are to embody -them in wood and metal, and the considerations which -should govern its production are those which affect its -clearness and legibility or those which facilitate reference -to it.</p> - -<p>Drawings consist of plans, elevations and sections; -plans being views on the top of the object in a -horizontal plane; elevations, views on the sides of the -object in vertical planes; and sections, views taken on -bisecting planes, at any angle through an object.</p> - -<p>Drawings in true elevation or in section are based -upon flat planes, and given dimensions parallel to the -planes in which the views are taken.</p> - -<p>Two elevations taken at right angles to each other -fix all points, and give all dimensions of parts that have -their axis parallel to the planes on which the views are -taken; but when a machine is complex, or when several -parts lie in the same plane, three and sometimes four -views are required to display all the parts in a comprehensive -manner.</p> - -<p>A man must have either a natural talent for hand-drawing<span class="pagenum" id="Page138">[138]</span> -or years of experience, before he can produce -a sketch and “dimension” it, fit to work from; hence -the elementary character of the examples given for -practice. A “pretty” drawing is not expected from -a beginner; it should always be borne in mind, that -correctness of dimensions and general clearness, rather -than elaborate finish, are what will save the battle in -the days of competition.</p> - -<p>Mechanical drawings should be made with reference -to all the processes that are required in the construction -of the work, and the drawings should be -responsible, not only for dimensions, but for adaptation -to fitting, forging, pattern-making, moulding, and so on.</p> - -<p>Every part laid down should have something to -govern it that may be termed a “base”—some position -which, if understood, will suggest size, shape and relation -to other parts. Searching after a base for each -and every part and detail, the draughtsman should proceed -upon a regular system, continually maintaining a -test of what is done.</p> - -<p>A mechanical drawing consists chiefly of three -views:</p> - -<div class="diagonalp"> -<p>1. The plan or top view.<br /> -<span class="padl4">2. The side elevation.</span><br /> -<span class="padl8">3. The end elevation.</span></p> -</div> - -<p>In addition to the above, drawings are used to -show interior portions of the figure; these are termed -“sections,” and they may be taken where any plane -crosses another.</p> - -<div class="note"> - -<p><span class="smcap">Note.</span>—The word <i>elevation</i>, as applied to mechanical drawings, -means simply a view; hence a side elevation is a side view, -or an end elevation is an end view.</p> - -<p>The word <i>plan</i> is employed in place of the word top; hence -a plan view is a top view or a view looking down upon the top of -the piece.</p> - -<p>A <i>general</i> view means a view showing the machine put together -or assembled, while a detail drawing is one containing a -detail, as a part of the machine or a single piece disconnected -from the other parts of the whole machine.</p> - -</div><!--note--> - -<hr class="chap x-ebookmaker-drop" /> - -<div class="chapter"> - -<p><span class="pagenum" id="Page139">[139]</span></p> - -<h2 class="nobreak">Penciling.</h2> - -</div><!--chapter--> - -<div class="container rightfloat w05em" id="Fig211"> -<img src="images/illo139.jpg" alt="Pencil" /> -<p class="caption">Fig. 211.</p> -</div> - -<p>It is very nearly true, as has been said, that every mechanical drawing is, in the first instance, -penciled; if this is so, then more work is done with the pencil than with the pen; therefore the -first attention of the student of mechanical drawing should be directed to the following instructions -for penciling a drawing.</p> - -<p>With all necessary materials in hand, and in good order for the beginning of a drawing, the -first thing to do is to pin the paper on the board quite square.</p> - -<p>To do this effectively, lay the paper flat and put on the T-square with its head at the left -side of the board; slide the square up nearly to the top, and arrange the paper level with the -blade; with the right hand hold the paper still and move the square down a little; now, pin the -top of the paper with thumb-tacks.</p> - -<p><span class="pagenum" id="Page140">[140]</span></p> - -<p>Next, pressing the square lightly to the paper, -slide it down to the bottom and pin that part of the -paper to the board. The paper must not project outside -or over the edges of the board, and the pins or -tack-heads should be forced down flush with the paper, -so as not to interfere with the free movement of the -tee-square up and down the board as occasion may -require.</p> - -<p>The accuracy of the work depending upon their -condition, it is first needful to see that the pencil and -pencil compasses are properly sharpened. Reference -is made to valuable directions contained on pages beginning -with 55, under the heading of “Free-hand -Drawing,” to which may be added <span class="nowrap">that—</span></p> - -<p>All lines should be drawn with the pencil slightly -inclined in the direction in which it is moved.</p> - -<p>Any and all lines not needed in the finished drawing -should be erased at one time after the final lines -have been determined, for the surface of the paper is -soiled very quickly when worked upon after erasures -have been made.</p> - -<p>The working lines and other lines that are to be -removed should be erased when the drawing is ready -to finish and before its outlines have been strengthened, -in order that the final lines may be left in perfect -condition.</p> - -<p>To show where the lines meet or terminate it is -needful that all pencil lines pass the actual ending -place, making a distinct intersection. This does not -apply to “inking in” the lines, but rather to prevent -the over-drawing of the ink lines, because the edge of -the rule and the pen itself obstruct or partly cover the -view of the line, it is very liable to pass over or beyond -the required point in inking the lines, which must -not occur.</p> - -<p><span class="pagenum" id="Page141">[141]</span></p> - -<p>In the preliminary operation of producing a regular -mechanical or instrumental drawing, it is necessary -to make a “sketch,” in pencil, of the object to be -represented. The <span class="smcap">American Machinist</span> has given in -a few words the order to be followed, in effecting the -best results; we quote, as follows:</p> - -<p>“In making a free-hand sketch of an object from -the model it is well to observe the following order: -Look the model over carefully and determine the -number of views necessary to illustrate it fully, drawing -the same, free-hand, in their proper relation to each -other, on sketching paper. Look the sketch over -carefully to see that nothing has been omitted, and put -on dimension lines, after which scale the model carefully -and put on dimensions. Do not put in the -dimensions at the same time the dimension lines are -drawn; have all the dimension lines in place before -attempting to insert dimensions.</p> - -<p>“Follow the same order in making the drawing -with instruments as was used in making the sketch; -that is, draw the views in their proper relation to each -other, put in dimension lines, then dimensions, and -lastly notes and title. If section drawing is made, do -not draw section lines in pencil.”</p> - -<h3>POINTS TO BE OBSERVED IN SKETCHING.</h3> - -<p>1. Especial attention is to be paid to outlines—edges -of plane surfaces are lines; when a line is made -it represents the edge or outside of something.</p> - -<p>2. Learn to be accurate before being rapid.</p> - -<p>3. A sketch should be intelligible to any one, -even if they are unacquainted with drawing.</p> - -<p>4. Horizontal and vertical lines and a few curves -will enable one to make almost any simple sketch.</p> - -<p>5. It must be also remembered in making drawings -from actual measurement that the instruments are -not in the first place employed; the rough sketch is -first made and then it is converted into a drawing. -The draughtsman makes a rough sketch entirely by -the hand and eye, measures the various parts, and jots<span class="pagenum" id="Page142">[142]</span> -down the measurements in his sketch; after this he -reduces the whole to the desired scale, and proceeds to -make his mechanical drawing.</p> - -<p>6. Let the sketch book be the constant companion -of the student; it may be advantageously -filled with outlines of machine or other work suitable -for preservation, to be made into finished drawings, or -for reference. Sketches are often valuable for reference -as aids in originating new designs.</p> - -<p>7. A sketch, when possible, should have all the -dimensions written upon it, <span class="nowrap">but—</span></p> - -<p>8. Sketches in shop practice should not take the -place of working-drawings; the latter have a check -upon them in being drawn to a scale—hence the -figures written upon them and dimensions by scale -must agree.</p> - -<p>9. Place title and date on each sketch—no matter -how seemingly unimportant—for future reference.</p> - -<p>10. Practice sketching at every favorable opportunity. -There is no necessity for detail at first—simply -the outlines of the article and its parts.</p> - -<p>11. Sketch-books, with paper bound in cloth -covers, are utilized for bold, off-hand sketches by -experienced draughtsmen, but a single sheet of paper, -used on both sides, is not unworthy of service in an -emergency—or even the blank side of a letter may be -available. Sketching-blocks, or paper “pads,” 4 × 6, or -more, in size, and containing 48 sheets, are sold by -stationers, and are found to be most convenient to -have in hand and for practical use. Portfolio-envelopes, -made of extra length paper (manila) are -useful in filing away sketches and drawings. The size -10<sup>1</sup>⁄<sub>2</sub> × 15 is used for United States Patent Office -drawings.</p> - -<p>The function of the pencil—in mechanical drawing—is -to make a path for the pen to follow. If it were -possible to make a drawing with all its lines ending at -the proper place, at the first time, there would be no -necessity for using the pencil. One is obliged, however, -so to use the pencil that all lines pass beyond the -actual ending place, thus making a distinct point for -the drawing pen to stop at.</p> - -<p><span class="pagenum" id="Page143">[143]</span></p> - -<p>The pencil should be pressed to the paper just -enough to make a clean, fine line, and no more; once -over the path is sufficient, if the line is visible and true.</p> - -<p>To sharpen drawing pencils, 1, use a fine file, after -taking off enough of the wood with a knife; 2, make a -conical point for the free-hand drawing pencils and a -chisel point for ruling and marking distances.</p> - -<p>Pencil compasses are instruments where one leg is -provided with a pencil point. <a href="#Fig209">Fig. 209</a> shows the mode -of manipulation of those shown in <a href="#Fig180184">fig. 180</a> and <a href="#Fig180184">fig. 181</a>.</p> - -<p>The pencil compass is held by the projection -above the joint between the thumb and first finger, -which enables it to be rotated by a movement of the -finger without causing any undue pressure on the points. -Should much pressure be applied, there is a tendency -to force the point or center through the paper, making -an ugly center mark; at the same time the pressure -tends to break off the pencil point.</p> - -<p>These few illustrations from <a href="#Fig212">fig. 212</a> to <a href="#Fig216219">fig. 219</a> are -made designedly simple, so that they may be utilized -in “free-hand” work, for which they are good practice, -as well as serving for examples in mechanical -drawing.</p> - -<div class="container w40em" id="Fig212"> -<img src="images/illo143.png" alt="Bobbin" /> -<p class="caption">Figs. 212.</p> -</div> - -<p><a href="#Fig212">Figs. 212</a>, showing a spool or bobbin, exhibit three -views, viz.: front elevation or plan, and section; both -are drawn with simple lines, the end elevation by -circles.</p> - -<p><span class="pagenum" id="Page144">[144]</span></p> - -<div class="container w30em" id="Fig213214"> - -<img src="images/illo144a.png" alt="Bolts" /> - -<p class="caption">Fig. 213.—Fig. 214.</p> - -</div><!--container--> - -<p><a href="#Fig213214">Figs. 213 and 214</a> are two side views of a hexagon -head bolt. <a href="#Fig216219">Figs. 216 and 217</a> are a square head bolt—two -side views and end view. <a href="#Fig216219">Figs. 218 and 219</a> are -a front and edge view of a forked or double joint.</p> - -<div class="container w40em" id="Fig215"> -<img src="images/illo144b.png" alt="Handle" /> -<p class="caption">Figs. 215.</p> -</div> - -<p><a href="#Fig215">Figs. 215</a> show three views of a file handle; -the front view and section are practice for compound -curves and curved lines meeting straight ones; all -these are capable of being produced by instruments.</p> - -<p>Moreover, many of the views and illustrations used -to instruct and explain machine tools and other devices -in other parts of the volume, are drawn so that they -may be used also as examples in advanced instrumental -practice. This is a “hint” to the diligent and painstaking -student worthy of remembering.</p> - -<p><span class="pagenum" id="Page145">[145]</span></p> - -<div class="container" id="Fig216219"> - -<img src="images/illo145.png" alt="Drawings" /> - -<p class="caption">Fig. 216.—Fig. 217.—Fig. 218.—Fig. 219.</p> - -</div><!--container--> - -<p><span class="pagenum" id="Page146">[146]</span></p> - -<p>The designing and drawing of arcs and whole circles -occupy a large proportion of space in nearly all -mechanical drawings. The making of a complete circle -is a matter of no great difficulty, but the beginning -and termination of parts of circles require both judgment -and considerable practice.</p> - -<p>To aid the student these two illustrations of circles -are introduced. To draw <a href="#Fig220">fig. 220</a> with a pencil, -using the upper edge of the blade of the T-square -as a guide, draw a center line, <i>A B</i>, mark on it a distance -of 4 inches, space this into half inches, using the -dividers and making the points with it; then with the -pencil compasses or bow pencil, which must be held as -shown on page 209, and rotated from left to right, or -clockwise, draw a series of circles through these points, -tangent to one another or all touching at <i>A</i>, care being -taken that the pencil lines exactly meet at <i>A</i>, and -also cut the divided points as shown in the illustration. -For <a href="#Fig221">fig. 221</a> divide the center line as before, and draw -the semi-circles on it <i>A B</i>, <i>B C</i>, meeting at <i>B</i>, and -<i>C D</i>, <i>D E</i>, etc.</p> - -<div class="container w30em" id="Fig220"> -<img src="images/illo146a.png" alt="Circles" /> -<p class="caption">Fig. 220.</p> -</div> - -<div class="container w30em" id="Fig221"> -<img src="images/illo146b.png" alt="Circles" /> -<p class="caption">Fig. 221.</p> -</div> - -<p><span class="pagenum" id="Page147">[147]</span></p> - -<p>Now from center <i>B</i> draw circles <i>A C</i>, <i>C E</i>, meeting -in <i>C</i>, and so on with the circles, arcs or segments; -success in drawing this figure depends on the correct -spacing of the center line in the first instance into -equal parts.</p> - -<p>The T-square should be used for drawing horizontal -lines only. Its head should always be placed upon -the left edge of the board. Vertical lines should be -drawn by the use of a triangle placed upon the T-square -and not by means of the T-square only; because -the edges of a board are seldom at right angles to each -other, and the blade of the T-square is often not at -right angles to the head, so that lines at right angles to -each other will not result from the use of the T-square -upon all edges of the board. Only the upper edge of -the T-square should be used, as the edges are often not -quite straight or parallel.</p> - -<p>The 45° triangle has two angles of 45° and one of -90°. The 30° and 60° triangle has an angle of 30°, one -of 60°, and one of 90°. By placing these triangles upon -the T-square, lines at any of these angles with a vertical -or horizontal line may be drawn.</p> - -<p>Drawings finished in ink are much more effective -and desirable than pencil drawings; but as a good inked -drawing cannot be made except upon an accurate pencil -drawing, students should begin with the pencil, and -should not use ink until they are able to produce satisfactory -results in pencil.</p> - -<hr class="chap x-ebookmaker-drop" /> - -<div class="chapter"> - -<p><span class="pagenum" id="Page148">[148]</span></p> - -<h2 class="nobreak">Projection.</h2> - -</div><!--chapter--> - -<p>The word projection means to throw forward, and in ordinary machine drawing it is the projecting or -throwing forward of one view from another view.</p> - -<p>In drawings the lines in one view or plan may be availed of to find those of others of the same object, -and also to find their shape or curvature as they would appear in the other representations; this is called -projection-drawing.</p> - -<p><a href="#Fig222">Fig. 222</a> is the illustration as shown in <a href="#Fig212">fig. 212</a> on -page 143, with the addition of dotted projection line, -which illustrates the method of throwing forward the -section and the end view of the object; these two -views are procured from the plan or first figure, as -shown in <a href="#Fig222">fig. 222</a>.</p> - -<p><a href="#Fig224">Fig. 224</a> represents the square bolt and nut shown -in <a href="#Fig216219">fig. 216</a>, and the mode of projecting is similarly -shown by dotted lines.</p> - -<p><a href="#Fig223">Fig. 223</a> shows file handle shown in <a href="#Fig215">fig. 215</a> and -the mode of projecting.</p> - -<div class="container w40em" id="Fig222"> -<img src="images/illo149a.png" alt="" /> -<p class="caption">Fig. 222.</p> -</div> - -<div class="container w40em" id="Fig223"> -<img src="images/illo149b.png" alt="" /> -<p class="caption">Fig. 223.</p> -</div> - -<div class="container w40em" id="Fig224"> -<img src="images/illo149c.png" alt="" /> -<p class="caption">Fig. 224.</p> -</div> - -<p>The principles upon which “projection” in drawing -is based, are illustrated in the following examples<span class="pagenum" id="Page149">[149]</span> -and text: As a real object can be scaled with a foot -rule, so a drawing must permit of scaling and measuring. -This measuring may take place as with the real -object in full size or the drawing may, for the sake of -convenience, be reproduced and measured in a reduced -scale, as half, or in still smaller sizes. Sometimes it<span class="pagenum" id="Page150">[150]</span> -may prove convenient to enlarge the drawing to twice -the natural size of the object, as a means of making it -stand out more clearly than the real size would -accomplish.</p> - -<p>For practical purposes, it is productive of economy -of time to mark the dimensions of height and width -or depth on the drawing in figures, to avoid the scaling. -This marking of the dimensions is best done at the -time of making the drawing, while the conception of -the object is clear.</p> - -<p>To convey a correct impression of the object, all -lines that are marked to be of equal length should appear -equally long on the drawing and be capable of being -scaled to such equal length; for this, it must be assumed -that the eye of the observer is equally distant -from all points of a plane through the nearest point, or -one of the axes of the object, and that the lines -of sight are all parallel to each other and square to -this plane.</p> - -<p>In <a href="#Fig225">fig. 225</a> these lines of sight are seen as directed -toward one side of a cube or block; it will be readily -understood, however, that in this way nothing is visible -and accessible for scaling and dimensioning except -this front face of the block, thus, a determination of -the dimensions of only height and width would be possible, -while the dimension of depth is entirely undetermined.</p> - -<div class="container w30em" id="Fig225"> -<img src="images/illo151.png" alt="Sight lines" /> -<p class="caption">Fig. 225.</p> -</div> - -<p>It is thus necessary to get a view of the block from -another side; the direction in which it will be most -instructive to obtain additional views is in the direction -of the breadth and of the length and square to the -lines of sight of the first view.</p> - -<p><a href="#Fig226">Fig. 226</a> shows how the lines of sight would strike -the object in the three directions. If these lines should -be rays of light, some of them would pass by the body<span class="pagenum" id="Page151">[151]</span> -until they squarely strike the large plane surfaces, -<i>I</i>, <i>II</i>, <i>III</i>; naturally the rays of light on the faces of -the object will be retained, and cannot strike the plane -surfaces, thus leaving dark shadows of exactly the same -outlines as the block; these would be exact drawings -of the faces, and if by some means they can be fixed -and retained on the plane they can be completely -measured and dimensioned.</p> - -<p>This throwing forward of the outline of the object -in different views on the planes is called projection of -the object, and furnishes a highly important means of -fixing the outlines and dimensions in the three main -directions of height, width and depth; evidently, the -light rays passing by the front face may not all reach -the plane of projection, but they may be retained by -protruding parts of the object behind the front face. -These protruding parts naturally would also be projected -on the plane in the same manner as the main -body of the block.</p> - -<p><span class="pagenum" id="Page152">[152]</span></p> - -<p>These projections of the protruding part are plainly -visible in plane <i>II</i> and plane <i>III</i>, while the part would -not be drawn in outline in plane <i>I</i>. It may be imagined, -however, that the greater thickness of the body -in the direction of the protruding part would intensify -also the shadow, thus outlining the face of the protruding -part in plane <i>I</i>.</p> - -<p>It is apparent that these three projections are all -needed, but as drawing is all done in one single plane, -the three projections will for the sake of convenience -have to be brought into a single plane. This can be -realized if plane <i>II</i> is swung around axis <i>O Z</i> and -plane <i>III</i> around axis <i>O Y</i>, until all three surfaces are -in one single plane, which would then appear as shown -in <a href="#Fig227">fig. 227</a>.</p> - -<p>It is also possible to assume transparent planes in -front of the body and extend the parallel lines of sight -forward instead of backward. Thus an outline picture -will be created on each of the three planes <i>I</i>, <i>II</i>, <i>III</i> in -<a href="#Fig228">fig. 228</a>, in a manner similar to <a href="#Fig226">fig. 226</a>. For drawing -purposes, all three views again have to be brought into -a single plane, which is done by swinging <i>II</i> around -<i>O Z</i>, and <i>III</i> around <i>O Y</i> in the same manner as <a href="#Fig227">fig. 227</a> -was evolved from <a href="#Fig226">fig. 226</a>.</p> - -<p>It will be noted that in <a href="#Fig229">fig. 229</a> plane <i>III</i> is now -above <i>I</i> and plane <i>II</i> on the left-hand side of <i>I</i>, while -in <a href="#Fig227">fig. 227</a> they were below and at the right-hand side -of plane <i>I</i>. As the swinging of the top and side planes -takes place around the edges of the front plane <i>I</i> two -systems may thus be distinguished, according to the -position of plane <i>I</i> in regard to the object. <a href="#Fig226">Fig. 226</a> -thus represents the system of backward projection, -while <a href="#Fig228">fig. 228</a> represents the system of forward projection.</p> - -<p>Either system can have, however, the plane <i>II</i> at -the right- or left-hand side edge, while plane <i>III</i> may -be attached to the top or bottom edge of plane <i>I</i>; it -is readily understood that a number of combinations -are possible for each system, as it is not necessary to -adhere absolutely to one rule. The system of forward -projection is the one generally practiced and further -examples are all executed by this system, meaning that -the planes are always between the observer and the object.</p> - -<p><span class="pagenum" id="Page153">[153]</span></p> - -<div class="container w40em" id="Fig226"> -<img src="images/illo153.png" alt="Projections" /> -<p class="caption">Fig. 226.</p> -</div> - -<p><span class="pagenum" id="Page154">[154]</span></p> - -<div class="container w40em" id="Fig227"> -<img src="images/illo154.png" alt="Projections" /> -<p class="caption">Fig. 227.</p> -</div> - -<p><span class="pagenum" id="Page155">[155]</span></p> - -<div class="container w40em" id="Fig228"> -<img src="images/illo155.png" alt="Projections" /> -<p class="caption">Fig. 228.</p> -</div> - -<p><span class="pagenum" id="Page156">[156]</span></p> - -<p>For the clearness of the drawing, it is desirable to -have all corners, edges and outlines appear in such -solid lines as they appear to the eye. If, therefore, -certain sharply defined outlines occur on one side more -than on the opposite one, it is most desirable to take the -view against the side that has the most definitely -marked outlines.</p> - -<p>If the opposite side should show a number of -wholly different features, it may prove even desirable -to show this side also, thus gaining four views instead -of the usual three, and so obtain a more complete -understanding of the shape of the object, besides -giving increased facilities for dimensioning each part of -the body.</p> - -<p>This additional view may be taken from the sides, -as well as up or down, thus making a maximum of five -views possible by which the outside of the object may -be delineated.</p> - -<p><a href="#Fig230">Fig. 230</a> shows why it may be desirable to take -five views of a block that has a receding space of different -outlines in each of the side and top and bottom -faces.</p> - -<p>It is not necessary, however, to resort to five -views in such a case as is represented in <a href="#Fig230">fig. 230</a>, as the -only differing feature, the circular space in <i>III</i> bottom, -might be shown in <i>III</i> top by dotted lines, and the -difference of <i>II</i> right might be shown in <i>II</i> left, also by -dotted lines. It is desirable to show four or five views -only where great complication and consequent lack of -clearness through numerous dotted lines would result -from having a less number of views.</p> - -<div class="container w40em" id="Fig229"> -<img src="images/illo157.png" alt="Projections" /> -<p class="caption">Fig. 229.</p> -</div> - -<p>So far the projections and views have only represented -the outlines of the object; it may often be -desirable, however, to show central holes or other perforations<span class="pagenum" id="Page157">[157]</span> -or variations of sections; in this case it is -possible to imagine the object cut in slices, by planes, -through certain well defined axes, or other lines of -distinctive importance, and then take a view of this -sectional plane with its newly created intersections or -sharply marked outlines; thus, a section may often -take the place of the third, fourth or fifth view to great -advantage.</p> - -<p><span class="pagenum" id="Page158">[158]</span></p> - -<div class="container w35em" id="Fig230"> -<img src="images/illo158.png" alt="Projections" /> -<p class="caption">Fig. 230.</p> -</div> - -<p><span class="pagenum" id="Page159">[159]</span></p> - -<p>It is not always possible to get a view against a -face or side of the object, but, with irregularly shaped -bodies or under special conditions, it may be necessary -to take a view of corners, sloping planes, curved -or irregularly shaped surfaces.</p> - -<p><a href="#Fig231">Fig. 231</a> shows a hexagonal nut in the three normal -projections; from the top view it is readily seen -that the front view shows the side of the hexagon in a -contracted scale, and that therefore the scaling and -dimensioning for the horizontal direction have all to be -done in the top or plan view; the front and side views -convey, however, the dimension of height correctly, -and these are therefore the right places for scaling and -dimensioning in the vertical direction.</p> - -<p><a href="#Fig231">Fig. 231</a> shows how a cylindrical outline appears -in the three views; the hole in the nut presents itself -as circular in the top view, while it appears in the front -and side views as a rectangle. For simple objects, it -is unnecessary to show the edges of the planes, and the -three views are grouped, as regards distances and positions, -as most convenient for the execution of the -drawing.</p> - -<p>Where sloping surfaces are of irregular form, it -may be necessary to employ help lines for their full determination -in the three views. <a href="#Fig232">Fig. 232</a> shows how -the surface that is produced by a slanting cut through -a cylinder would appear in the three views. The help -lines are placed in the top view in eight equal divisions -around the circumference of the cylinder. These division -lines are shown by dotted lines on the cylinder in<span class="pagenum" id="Page160">[160]</span> -the front and side views. Their intersections, with the -sloping cut in the front view, furnish also the height -of the corresponding points for the side view.</p> - -<div class="container w40em" id="Fig231"> -<img src="images/illo160.png" alt="Projections" /> -<p class="caption">Fig. 231.</p> -</div> - -<p>By progressive determination of points, lines and -surfaces, even the most complicated bodies can be -completely represented for their reproduction in any -application to mechanical or industrial purposes.</p> - -<p><span class="pagenum" id="Page161">[161]</span></p> - -<div class="container w40em" id="Fig232"> -<img src="images/illo161.png" alt="Projections" /> -<p class="caption">Fig. 232.</p> -</div> - -<p><span class="pagenum" id="Page162">[162]</span></p> - -<p>The spur wheel shown on <a href="#Page163">page 163</a> is an example -of projection drawing.</p> - -<p>The wheel is illustrated in three views: <a href="#Fig233235">fig. 235</a> is -a side view, or elevation; <a href="#Fig233235">fig. 234</a> is a front elevation; -<a href="#Fig233235">fig. 233</a> is a section view on <i>C D</i>. The section is projected -from the front elevation by drawing parallel -lines from the points in front elevation where the lines -are intersected by the center line <i>C D</i>, cutting the -plane of view and showing the interior shape at <i>C D</i>.</p> - -<p>The side elevation, <a href="#Fig233235">fig. 235</a>, is projected from the -front elevation, <a href="#Fig233235">fig. 234</a>, by drawing parallel lines -from the edges in the front view across its face.</p> - -<p>In actual drawing practice the figures should be -made about three times larger than the example, and -as follows:</p> - -<p>For the front elevation draw the center lines <i>A B</i>, -<i>C D</i>, and from their point of intersection as a center, -with the compasses draw the inner circle or hole, also -the pitch line <i>E E</i>. With the dividers space this line -into nineteen equal divisions; each point on this line -will be the center of a tooth, and the distance from one -point to the next one is the pitch of the tooth.</p> - -<p>Now, with the dividers mark off the thickness of -tooth at each side of these points on pitch line; with -the compasses draw the outer circle for points of teeth, -the inner circle for the root of teeth, and circles for -thickness of rim and hub; also circles representing the -fillets at rim and hub. For clearness and to prevent -confusion these lines are shown on one-half the wheel -only, terminating in center line <i>C D</i>; all the lines of -the front elevation are now complete excepting the -teeth.</p> - -<p>In the drawing office it is unusual to delineate all -the teeth in a gear wheel, the lines without the teeth -as now completed being deemed sufficient, giving all -particulars; however, to prevent the error of mistaking -the circles it is well to represent one or two teeth on -the drawing.</p> - -<p><span class="pagenum" id="Page163">[163]</span></p> - -<div class="container" id="Fig233235"> - -<img src="images/illo163.png" alt="Gear" class="bl br" /> - -<p class="caption">Fig. 233.—Fig. 234.—Fig. 235.</p> - -</div><!--container--> - -<p>In the example, proceed and complete the entire<span class="pagenum" id="Page164">[164]</span> -wheel, taking on the compasses a radius equal to the -pitch of the tooth; set them on the pitch line at the -point <i>G</i>, already spaced for thickness of tooth, draw -line <i>H</i> from pitch line to root of tooth; proceed similarly -all around the circle, completing one side. Next, -reverse the operation and draw the corresponding side -of the root of tooth. Now take a radius equal to half -the space between teeth and the thickness of tooth on -pitch line, and, with center in pitch line, as shown at -<i>I</i>, draw the outside or addendum of tooth, <i>J</i>; it will be -apparent that the reverse addendum of the tooth next -adjoining can be formed at the same time, with one -setting of the compasses; finish all the teeth similarly; -the front elevation will thus be completed.</p> - -<p><a href="#Fig233235">Fig. 233</a> is an excellent example of sectional drawing, -to be executed as follows:</p> - -<p>First draw the center line <i>L M</i> of <a href="#Fig233235">fig. 233</a>, lay off -at each side of it half the breadth of face and of the -hub; now project, from center line <i>C D</i>, in the front -elevation, <a href="#Fig233235">fig. 234</a>, with the T-square the upper and -lower teeth, the fillets, the chamfers, the hub and center -hole, also dot in the pitch line <i>F F</i>, take the radii -and draw the fillets and chamfers; draw section lines -and the view will appear as shown in <a href="#Fig233235">fig. 233</a>.</p> - -<p><a href="#Fig233235">Fig. 235</a> is a side elevation of <a href="#Fig233235">fig. 234</a>, and is a fine -sample of projection, to be executed as follows:</p> - -<p>Proceed similarly as for <a href="#Fig233235">fig. 233</a>, projecting the -lines from the outside edges of the front elevation, instead -of from the center line <i>C D</i> as in last figure, and -the end elevation will be as shown in <a href="#Fig233235">fig. 235</a>.</p> - -<p>The student will be assisted in understanding this -working drawing by consulting the <a href="#Page196">pages</a> under the -heading of “Gearing.”</p> - -<hr class="chap x-ebookmaker-drop" /> - -<p><span class="pagenum" id="Page165">[165]</span></p> - -<div class="container w30em"> -<img src="images/illo165.png" alt="LETTERING, INKING, SECTION LINING" /> -</div> - -<hr class="chap x-ebookmaker-drop" /> - -<p><span class="pagenum" id="Page166">[166]</span></p> - -<div class="container w40em" id="Fig236"> -<img src="images/illo166.png" alt="Drawing" /> -<p class="caption">Fig. 236.</p> -</div> - -<hr class="chap x-ebookmaker-drop" /> - -<div class="chapter"> - -<p><span class="pagenum" id="Page167">[167]</span></p> - -<h2 class="nobreak">“Inking In” Drawings.</h2> - -</div><!--chapter--> - -<p>When a drawing is completely finished in penciling, -it should next be “inked in” for preservation.</p> - -<p>Care should be used that the pen may be perfectly -clean; the pen should be held nearly vertical, leaning -just enough to prevent it from catching on the paper; -the pen should be held between the thumb and first -and second fingers, the knuckles being bent, so that it -may be at right angles with the length of the hand.</p> - -<p>The ink should be rubbed up fresh whenever it is -about to be used, for it is better to waste a little time -in preparing ink slowly than to be at a continual -trouble with pens, which will occur if the ink is ground -too rapidly or on a rough surface.</p> - -<p>To test ink, a few lines can be drawn on the -margin of a sheet, noting the shade, how the ink flows -from the pen, and whether the lines are sharp. After -the lines have dried, cross them with a wet brush; if -they wash readily, the ink is too soft; if they resist the -water for a time and then wash tardily, the ink is -good.</p> - -<p>Care must be exercised not to overload the pen -with ink, and, like the pencil, the pen should always -be moved from left to right and from the bottom to -the top of the board. When inking, both “nibs” of -the pen point must rest evenly on the paper and the -pen be pressed only lightly against the T-square. -Never ink any portion of a drawing until the penciling -is complete.</p> - -<p><span class="pagenum" id="Page168">[168]</span></p> - -<p>In inking long, fine lines it is well to go over each -line twice, without moving the T-square, trying not to -widen the line on the second passage; also see that -the pen contains ink enough to finish a line, as it is -difficult to continue with the same width of line after -re-filling.</p> - -<p>To produce finished drawings, it is necessary that -no portion should be erased, otherwise the color applied -will be unequal in tone; thus, when highly finished -mechanical drawings are required, it is usual to draw -an original and to copy it. Where sufficient time cannot -be given to draw and copy, a very good way is to -take the surface off the paper with fine sand-paper -before commencing the drawing; if this be done, the -color will flow equally over any erasure it may be -necessary to make afterwards.</p> - -<p>The rules of procedure in drawing the lines in -“inking” are, 1, ink in the small circles and curves; -2, ink in the larger circles and curves; 3, then all -the horizontal lines, beginning at the top of the -drawing and working downward; 4, next ink in all the -vertical lines, commencing at the left and moving back -to the right; 5, draw in the oblique lines; 6, all the -center lines and dimension and reference lines. The figuring -and lettering should be always done with India -ink, thoroughly black; the last lines to be drawn are -the section lines. The reason why irregular curves -and arcs of circles are inked in first is, that it is easier -to draw a straight line up to a curve than to take a -curve up to a straight line.</p> - -<p>In practice, the flat side of the drawing-pen is laid -against the tee-square or ruler; the taper of the blade -of the pen is sufficient to throw the point enough away -from the edge to prevent blotting; the pen is drawn -from left to right and from the bottom to the top of -the board.</p> - -<p>This is shown in <a href="#Fig237">fig. 237</a>, intended to represent -“short work” with the drawing-pen. The wrist is -shown resting upon the blade of the square.</p> - -<div class="container w30em" id="Fig237"> -<img src="images/illo169.png" alt="" /> -<p class="caption">Fig. 237.</p> -</div> - -<p><span class="pagenum" id="Page169">[169]</span></p> - -<div class="container w25em" id="Fig238"> -<img src="images/illo170.png" alt="Drawing" /> -<p class="caption">Fig. 238.</p> -</div> - -<p>In a similar figure, <a href="#Fig238">238</a>, the position of the hand -holding the pen indicates the best relative posture for -inking long lines. In one of these illustrations the -work is executed principally by the wrist—in the other -by the arms and fingers working together.</p> - -<p>The pen should be held with even pressure against -the straight-edge or curve. If the pressure varies, the -blades will spring and the width of the line will change. -The blades should be of such length that both will -bear equally upon the paper when the pen is inclined -slightly, so as to bring the inner blade near the straight-edge; -the angle of the pen should not be changed -while drawing any line.</p> - -<p>When the inking is finished, the whole drawing -may be cleaned by rubbing it with bread which is not -greasy or so fresh as to stick to the paper. If the -paper is much soiled it may be necessary to use an -eraser. A soft pencil eraser should be used and great -care taken that the ink lines are not lightened and -broken by it.</p> - -<p><span class="pagenum" id="Page170">[170]</span></p> - -<p>To avoid the necessity of using an eraser upon a -finished drawing, instruments and paper must be kept -free from dust and dirt. The triangles and T-square -should be cleaned often, by rubbing them vigorously -upon rough, clean paper.</p> - -<p>Pounce is a powder used to prevent blotting in -rewriting over erasures; it is held in a bag or small -box with a perforated lid for convenience in sprinkling -on paper; when used it should be distributed evenly -with a piece of chamois, and the surplus or loose particles -removed before applying the ink.</p> - -<p>A drawing is made to be read, and the skill in inking, -as in “free-hand” and in penciling, does not consist -so much in the fineness of the lines as in their -clearness.</p> - -<hr class="chap x-ebookmaker-drop" /> - -<div class="chapter"> - -<p><span class="pagenum" id="Page171">[171]</span></p> - -<h2 class="nobreak">Lettering Drawings.</h2> - -</div><!--chapter--> - -<p>Lettering is an important part of making drawings, -the object aimed at being to identify any portion -by reference letter or letters; thus in <a href="#Fig239">fig. 239</a> the line -<i>A C</i> describes the -line extending from -<span class="fig239" id="Fig239"><span class="top"><img src="images/illo171.png" alt="Line" /></span> -<span class="bot">Fig. 239.</span></span></p> - -<p>Any information which cannot be expressed in the -drawing is always expressed by lettering, and it is desirable -to confine the lettering of drawings to one or -two standard alphabets that are plain and distinct, and -the principles of which are easily acquired. These conditions -are fulfilled in the Gothic fonts shown on <a href="#Page173">page 173</a>.</p> - -<p>Both letters and figures must be carefully made -and of uniform proportion; it is well to “lay out” -these by regular measurement before permanently -inking them. Letters should not be less than one-eighth -of an inch in height and penciled carefully -before inking.</p> - -<p>On <a href="#Page173">page 173</a> are printed two forms of numerals and -letters of the alphabet; it is recommended that these -be used both for practice in free-hand and for regular -office work.</p> - -<p>For easy reference, letters should not be crowded -nor allowed to interfere with one another; they should -be drawn neatly, avoiding all lines of the drawing; -plain letters are always used on mechanical drawings, -whether for title, scale, reference, etc.</p> - -<p><span class="pagenum" id="Page172">[172]</span></p> - -<p>Arrow-heads, figures and letters should be in black, -and made with a writing pen. A pen with a ball point -is preferable, giving an equal thickness of line, no matter -in which direction the stroke is made.</p> - -<div class="container" id="Fig240"> -<img src="images/illo172.png" alt="Nibs" /> -<p class="caption">Fig. 240.</p> -</div> - -<p>Neat, well-lettered drawings go far towards establishing -a high standing for the aspiring draughtsman. -All lettering should be done free-hand, first with the -pencil, sharpened to a fine round point, and afterwards -written in ink. For this purpose common writing pens -are best to be used; <a href="#Fig240">fig. 240</a> represents the several -numbers of the approved Gillott’s pens adapted to this -purpose.</p> - -<p>In lettering, it is well, for a guide for size and -location, to draw, with a round-pointed pencil, two -horizontal lines just the height the letters are to be; -the letters are also best made with careful use of the -instruments, rather than free-hand.</p> - -<p>In order to letter systematically, it is a good plan -to start with the middle letter of the inscription and -work in both directions; making too prominent letters -should be avoided, plain and distinct letters being most -desirable.</p> - -<p>Finally, with an ordinary writing pen, trace over -the penciling in ink; the pencil guide lines being -erased after the letters are inked in completes the -operation.</p> - -<p><span class="pagenum" id="Page173">[173]</span></p> - -<div class="container"> -<img src="images/illo173.png" alt="Letters and numbers" /> -</div> - -<p><span class="pagenum" id="Page174">[174]</span></p> - -<p>An important matter in connection with lettering -a drawing is the location of the letters; these should -be so placed as not to interfere with the lines of the -drawing and should clearly point out the part intended -to be described. When single letters are used, they -should be inked in before the shade or section lines are -drawn.</p> - -<p><a href="#Fig241">Fig. 241</a> is an example introduced to show the -method of lettering a descriptive mechanical drawing.</p> - -<p>The figure shows a “blow-off valve” of approved -design drawn in section; the letters designate the -several parts; the reading to accompany the lettering -is as follows:</p> - -<p class="hind05"><b>A</b>—Inlet communicating with annular passage (<i>C</i>) to -admit steam, which blows off scale and sediment -from seat (<i>E</i>) before disc (<i>L</i>) comes in contact -with same.</p> - -<p class="hind05"><b>B</b>—Plug to permit passage of rod to clean out blow-off -pipe.</p> - -<p class="hind05"><b>C</b>—Annular steam passage around casing (<i>D</i>) and communicating -with inlet (<i>A</i>).</p> - -<p class="hind05"><b>D</b>—Removable bronze casing, in which plug (<i>L</i>) fits -snugly.</p> - -<p class="hind05"><b>E</b>—Removable bronze seat ring, which also holds casing -(<i>D</i>) in place.</p> - -<p class="hind05"><b>J</b>—Slot in casing (<i>D</i>) arranged to discharge sheet of -steam from <i>C</i>, which, blowing across seat (<i>E</i>), -cleans off scale and sediment before contact with -disc (<i>L</i>).</p> - -<p class="hind05"><b>K</b>—Non-rotating washer to prevent loosening of locknut -(<i>H</i>) when opening valve.</p> - -<p class="hind05"><b>L</b>—Reversible disc, having two Babbitt-metal seating -faces (<i>F</i>) (<i>F</i>).</p> - -<p><span class="pagenum" id="Page175">[175]</span></p> - -<div class="container w30em" id="Fig241"> -<img src="images/illo175.jpg" alt="Valve" /> -<p class="caption">Fig. 241.</p> -</div> - -<hr class="chap x-ebookmaker-drop" /> - -<div class="chapter"> - -<p><span class="pagenum" id="Page176">[176]</span></p> - -<h2 class="nobreak">Dimensioning Drawings.</h2> - -</div><!--chapter--> - -<p>To “dimension” working drawings is to place -measurements upon the parts represented, to enable -the workman to proceed without measuring the drawing -itself.</p> - -<p>These dimensions should be placed so as not to interfere -with nor crowd the lines of the drawing, nor yet -interfere with one another.</p> - -<p>Arrow-heads are used at the extreme points of -measurement, the figures are generally inserted midway -between the arrows; a dot and dash line reaches -from the figure to the arrow-heads, as shown below.</p> - -<div class="container w20em"> -<img src="images/illo176a.png" alt="Dimension" /> -</div> - -<p>When the dimension is short these lines are -omitted and the dimension is -placed outside the drawing, thus -<img src="images/illo176b.png" class="inline h2em" alt="Dimension" /> -and connected by a curved line; at other times it is -found needful to place arrow-heads outside -the drawing and the measurement inside. -<img src="images/illo176c.png" class="inline h3em" alt="Dimension" /> -</p> - -<p>When the dimension is long and narrow it is -usual to carry the dimensions under the drawing by -dotted and dash lines, as shown below.</p> - -<div class="container w20em"> -<img src="images/illo176d.png" alt="Dimension" /> -</div> - -<p><span class="pagenum" id="Page177">[177]</span></p> - -<p>Arrow-heads and figures should be drawn free-hand -with a common writing pen.</p> - -<p>Usually dimensions are given in inches, up to 24 -inches, as it is found less confusing; for instance, if -written 1′ 1″ it may be mistaken for 11″; if written 13″ -no mistake could be made.</p> - -<div class="container rightfloat w03em"> -<img src="images/illo177a.png" alt="Dimension" /> -</div> - -<p>Again, 1′ 0″ may be mistaken for 10″; if written -12″ it would not; in addition to being more -distinct, it occupies less space on the drawing. In -large measurements there is more room for the -figures, and, therefore, they can be spaced -further apart—in feet and inches.</p> - -<p>All figures should be made of a fairly -large size. Vertical dimensions should read -from the right hand, thus, as shown:</p> - -<p>Measurements of importance, such as -the diameter of a circle, the pitch or distance -apart of rivets and bolts, etc., should -be marked in figures on the drawing. When -rough or unfinished work is mixed with -machined or finished portions, it is usual to mark F, -or “fin.,” after the latter dimension.</p> - -<p>In practice, at times, instead of dimensions reference -letters are used, thus:</p> - -<div class="container w30em"> - -<img src="images/illo177b.png" alt="Machine part" /> - -<div class="centerblock"> - -<p>D = diam. of shaft, 2<sup>1</sup>⁄<sub>2</sub> inches.<br /> -L = length of bearing, 3<sup>3</sup>⁄<sub>4</sub> inches.<br /> -T = thickness of collar, <sup>7</sup>⁄<sub>8</sub> inch.<br /> -d = diam. of collar, 3<sup>1</sup>⁄<sub>2</sub> inches.</p> - -</div><!--centerblock--> - -</div><!--container--> - -<p>Generally it is preferable to give the diameters of -turned and bored work on a section, instead of an end -drawn separately; confusion is sometimes caused by a -number of radial dimensions.</p> - -<p><span class="pagenum" id="Page178">[178]</span></p> - -<p><a href="#Fig243244">Fig. 242 and fig. 243</a> are introduced to show the -principal measurements required in practical work, and -the usual way in which such dimensions are marked -when ordering parts of machinery.</p> - -<p><a href="#Fig243244">Fig. 242</a> is a pedestal, or metal frame; three views -are shown, the center figure being an elevation, the -lower figure is the plan of the base, the upper figure is -a view of the top, on which is bolted the bearing block, -it being on the outside of the center figure. The -essential measurements are marked by letters. <i>H</i> is -the vertical height from base to the seat of bearing -block: <i>L</i> being the length, and <i>W</i> the width of the -base; <i>P</i> is the length between checks, and <i>B</i> the width -of seat for bearing block; <i>C</i> is the distance from center -to center of the holding down bolt holes, and <i>T</i> is the -depth of the holes in the base; <i>K</i> is the distance from -center to center of the bolt holes in the top for bearing -block.</p> - -<p><a href="#Fig243244">Fig. 243</a> is a hanger, or metal bracket, and shows -the center figure or elevation, the plan of the top and -the plan of the seat for bearing block, which is bolted -on the interior of the center figure. <i>H</i> is the vertical -distance from the top to the seat for bearing block; -the other measurements required are marked by letters -similar to <a href="#Fig243244">figure 242</a>.</p> - -<p>Now, one of the important matters in connection -with dimensioning a drawing is the location of the figures. -One rule, whose utility cannot be gainsaid, is -that they should be so located that they can be altered -or erased without damage to the lines of the drawing, -as changes may be necessitated either by original errors -in writing down the figures or by changes in the design -being found desirable during the construction of -the machine.</p> - -<p><span class="pagenum" id="Page179">[179]</span></p> - -<div class="container" id="Fig243244"> - -<img src="images/illo179.png" alt="Pedestal and hanger" /> - -<p class="caption">Fig. 243.—Fig. 244.</p> - -</div><!--container--> - -<hr class="chap x-ebookmaker-drop" /> - -<div class="chapter"> - -<p><span class="pagenum" id="Page180">[180]</span></p> - -<h2 class="nobreak">Shading Drawings.</h2> - -</div><!--chapter--> - -<p>To produce an effect, drawings are shaded; that -is, shadow lines about twice the width of the regular -line are drawn according to a recognized rule, which -always represents the same peculiarity of form in the -same way.</p> - -<p>In working drawings light lines only are permitted; -shade lines are wider than the working lines, and in -reading scale measurements the extra thickness of line -would make a difference.</p> - -<p>Instead of representing the shadow as it is really -cast by the object, the edges which cast the shadow -are determined, and all the views are treated as if the -light came from behind and from the left, downwards, -at an angle of 45° to the horizontal line, as shown by -the arrows in <a href="#Fig245248">figs. 245 to 248</a>.</p> - -<div class="container" id="Fig245248"> - -<img src="images/illo180.png" alt="Shading" /> - -<p class="caption">Fig. 245.—Fig. 246.—Fig. 247.—Fig. 248.</p> - -</div> - -<p>The lower and right-hand outlines of projecting -parts will cast shadows, and the student should make -them of extra width.</p> - -<p><span class="pagenum" id="Page181">[181]</span></p> - -<p><a href="#Fig249">Fig. 249</a>: In shading curves, divide the center line as -before (see <a href="#Page146">page 146</a>) and describe circles from center, <i>D</i>; -these lines are not to be shaded in penciling, but when -inking. The figures represent two rings, <i>A</i> and <i>C</i>, and -spaces, <i>B</i> and <i>D</i>. The outside of a surface is shaded -according to circle 1, and the inside surface according -to circle 2. This will give the desired shading, but it -makes a drawing incorrect, and therefore shading is not -used in working drawings.</p> - -<p>This shading is accomplished by inking the circle -first with regular width of line; then with the same radius -remove the point of compasses from the <i>true center</i>, -placing it outside, according to the desired position -of the shaded line, and describe an arc of a circle.</p> - -<p>In <a href="#Fig250">fig. 250</a> divide center line as before; with the -45° triangle or set square, draw through the center the -diagonals shown by dotted lines; and through the -points <i>A</i>, <i>B</i>, <i>C</i>, etc., draw the perpendiculars, cutting -the diagonals; from the points of intersection draw the -horizontal lines, completing the squares.</p> - -<div class="container w25em" id="Fig249"> -<img src="images/illo181a.png" alt="Shading" /> -<p class="caption">Fig. 249.</p> -</div> - -<div class="container w25em" id="Fig250"> -<img src="images/illo181b.png" alt="Shading" /> -<p class="caption">Fig. 250.</p> -</div> - -<p>Now, take a radius -of half an inch, -and in the corner of -each square draw -with the bow-pencil -a circular arc meeting -the pencil lines -exactly; with the -bow-pen <i>ink in the -arcs</i> first, then ink -carefully the lines -joining with the -arcs; all lines must -be of the same -width; put in the -shade on arcs and -lines as in <a href="#Fig249">fig. 249</a>; -and, finally, erase -the pencil lines at -corners, etc.</p> - -<hr class="chap x-ebookmaker-drop" /> - -<div class="chapter"> - -<p><span class="pagenum" id="Page182">[182]</span></p> - -<h2 class="nobreak">Section-Lining.</h2> - -</div><!--chapter--> - -<p>Cross-hatching has been defined in the “preliminary -definitions” to drawing; this term represents the -practice of drawing diagonal lines representing the interior -of an object, shown as a piece cut in half or -when a piece is broken away. This is done to make -more of the parts show, or to exhibit more clearly the -nature of the materials; hence section lining and cross-hatching -tell the same thing, <i>i. e.</i>, the drawing of diagonal -lines, usually at an angle of 45°, to show that the -object is broken away and the interior designed to be -represented.</p> - -<div class="container" id="Fig251258"> - -<div class="x-ebookmaker-drop"> - -<div class="split5050"> - -<div class="left5050"> - -<div class="split5050"> - -<div class="left5050"> -<img src="images/illo182a.png" alt="Section" /> -<p class="caption"><span class="material">Cast iron.</span><br /> -Fig. 251.</p> -</div> - -<div class="right5050"> -<img src="images/illo182b.png" alt="Section" /> -<p class="caption"><span class="material">Wrought iron.</span><br /> -Fig. 252.</p> -</div> - -</div><!--split5050--> - -</div><!--left5050--> - -<div class="right5050"> - -<div class="split5050"> - -<div class="left5050"> -<img src="images/illo182c.png" alt="Section" /> -<p class="caption"><span class="material">Steel.</span><br /> -Fig. 253.</p> -</div> - -<div class="right5050"> -<img src="images/illo182d.png" alt="Section" /> -<p class="caption"><span class="material">Composition.</span><br /> -Fig. 254.</p> -</div> - -</div><!--split5050--> - -</div><!--right5050--> - -<p class="thinline allclear"> </p> - -</div><!--split5050--> - -<div class="split5050"> - -<div class="left5050"> - -<div class="split5050"> - -<div class="left5050"> -<img src="images/illo182e.png" alt="Section" /> -<p class="caption"><span class="material">Vulcanite.</span><br /> -Fig. 255.</p> -</div> - -<div class="right5050"> -<img src="images/illo182f.png" alt="Section" /> -<p class="caption"><span class="material">Wood.</span><br /> -Fig. 256.</p> -</div> - -</div><!--split5050--> - -</div><!--left5050--> - -<div class="right5050"> - -<div class="split5050"> - -<div class="left5050"> -<img src="images/illo182g.png" alt="Section" /> -<p class="caption"><span class="material">Leather.</span><br /> -Fig. 257.</p> -</div> - -<div class="right5050"> -<img src="images/illo182h.png" alt="Section" /> -<p class="caption"><span class="material">Brick.</span><br /> -Fig. 258.</p> -</div> - -</div><!--split5050--> - -</div><!--right5050--> - -<p class="thinline allclear"> </p> - -</div><!--split5050--> - -</div><!--ebookmaker drop--> - -<div class="noscr"> - -<img src="images/illo182a.png" alt="Section" /> -<p class="caption"><span class="material">Cast iron.</span><br /> -Fig. 251.</p> - -<img src="images/illo182b.png" alt="Section" /> -<p class="caption"><span class="material">Wrought iron.</span><br /> -Fig. 252.</p> - -<img src="images/illo182c.png" alt="Section" /> -<p class="caption"><span class="material">Steel.</span><br /> -Fig. 253.</p> - -<img src="images/illo182d.png" alt="Section" /> -<p class="caption"><span class="material">Composition.</span><br /> -Fig. 254.</p> - -<img src="images/illo182e.png" alt="Section" /> -<p class="caption"><span class="material">Vulcanite.</span><br /> -Fig. 255.</p> - -<img src="images/illo182f.png" alt="Section" /> -<p class="caption"><span class="material">Wood.</span><br /> -Fig. 256.</p> - -<img src="images/illo182g.png" alt="Section" /> -<p class="caption"><span class="material">Leather.</span><br /> -Fig. 257.</p> - -<img src="images/illo182h.png" alt="Section" /> -<p class="caption"><span class="material">Brick.</span><br /> -Fig. 258.</p> - -</div><!--noscr--> - -</div><!--container--> - -<div class="container leftfloat w20em" id="Fig259"> -<img src="images/illo183a.png" alt="Cog wheel" /> -<p class="caption">Fig. 259.</p> -</div> - -<p><a href="#Fig251258">Figs. 251 to 258</a>, inclusive, show the section lining -and cross-hatching by which it is customary to represent -the various materials entering into a construction.</p> - -<p><span class="pagenum" id="Page183">[183]</span></p> - -<p>In <a href="#Fig259">fig. 259</a> is outlined a -representation of a section of -a cog-wheel; section 1 being -the wood cogs; 2, the iron -wheel, and 3 the wedges at -the root of the gear. It would -be impossible to convey the -same ideas by ordinary plan -or elevation drawing; all the objects on the same page -are more clearly represented by the use of section -lines or cross-hatching.</p> - -<p>Sectioning is executed by drawing a series of parallel -lines about <sup>3</sup>⁄<sub>32</sub> inches apart. Lay the 45° triangle -on the upper edge of the T-square and draw the top-most -line of the sectioning. Then slide the triangle -along the T-square for each successive line. The sectioning -should be inked in without previous penciling -and the lines should be finer than the lines of the general -drawing.</p> - -<p>Various devices are in use for mechanically equalizing -the distances in section lining, but the trained -eye is the most practical method. When two abutting -pieces are sectioned, the section lining on one piece -slants in an opposite direction to that on the other.</p> - -<p>To draw an object to be sectioned on both sides -of its center line, only one side is sectioned, while the -other side is drawn in full.</p> - -<p>Sections are necessary in nearly all machine drawings; -they are usually taken horizontally or vertically, -but they may be taken in any direction; the position -of a section should be shown by a line upon the object; -this line is called the cutting plane.</p> - -<p>In <a href="#Fig261">fig. 261</a> is shown the hub of a wheel, it is also a -sample of work for practice.</p> - -<p><span class="pagenum" id="Page184">[184]</span></p> - -<div class="container w30em" id="Fig260"> -<img src="images/illo183b.jpg" alt="Wheel hub" /> -<p class="caption">Fig. 260.</p> -</div> - -<div class="container w30em" id="Fig261"> -<img src="images/illo184.png" alt="Hatching" /> -<p class="caption">Fig. 261.</p> -</div> - -<p><a href="#Fig260">Fig. 260</a> shows the mode of representing two -different materials in one plane, or a section may be -represented by the darker portion, and the lighter -shaded portion being a surface resting on the section.</p> - -<p><a href="#Fig261">Fig. 261</a> shows the section of a shaft surrounded -by the surface of a wheel.</p> - -<h3>TINTS AND COLORS.</h3> - -<p>For special purposes of illustration drawings are -made which must be tinted. In such cases the paper -must be expanded and stretched evenly all over its -surface; otherwise when the moist tint is applied the -paper will wrinkle and get out of shape; to do this -cut the paper at least half an inch less in size than the -drawing board; lay the paper face down, turn up a -margin or edge of about three-fourths of an inch all -round, then dampen the paper with a sponge and clean -water; allow it to soak for a few minutes until it is -evenly dampened or moistened all over, turn the paper -upside down (face up).</p> - -<p>Apply strong paste to the under side of the margin -all round; rub down, on the drawing-board, working -from the center of the board outwards so as to exclude -the air and prevent creases or furrows. The board is -then inclined and left to dry slowly; make sure that the -paper is all well pasted and every part of the edges -attached to the board.</p> - -<p>If tracings are required to be tinted or shaded, -the color may be applied before the tracing is cut off, -or what is more usual, the color may be applied on the -back of the tracing; then there is no liability to wash -out the lines.</p> - -<p><span class="pagenum" id="Page185">[185]</span></p> - -<p>Mechanical drawings are seldom tinted, but are -mainly produced in India ink. Where, however, a fine -effect is desired, working drawings are colored, so as to -show at a glance the material of which the different -parts are to be made.</p> - -<p>The colors required are few but should be of the -best quality. Besides India ink the following water-colors -are generally used:</p> - -<p>1, Neutral-tint. 2, Prussian Blue. 3, Chrome -Yellow. 4, Gamboge. 5, Raw Sienna. 6, Carmine. -7, Vermillion. 8, Venetian Red. 9, Sepia. 10, Indigo. -These come in hard cakes.</p> - -<p>Certain colors and tints represent different metals -and materials as follows:</p> - -<p>Wrought Iron—Prussian Blue.</p> - -<p>Steel—Carmine and Prussian Blue, mixed to give -a purple shade.</p> - -<p>Steel Casting—Same as the above darkened by -Venetian Red.</p> - -<p>Cast-Iron—Neutral Tint made of India Ink, indigo, -mixed with a little carmine.</p> - -<p>Brass—Gamboge or Chrome Yellow.</p> - -<p>Babbitt—Emerald Green; sometimes light mixture -of India Ink.</p> - -<p>Copper—Purple Lake.</p> - -<p>It is sometimes found necessary to prepare a highly -finished and shaded drawing of the work in hand. -Such elaborations, in fact, are much admired by the -uninitiated, although the complete shading of the -drawing is no criterion as to the scientific value of the -machine. An illustration of this is told in the note.</p> - -<div class="note"> - -<p><span class="smcap">Note.</span>—A consulting engineer had to lay before a board of -directors plans of horizontal engines for their consideration. One -of these drawings was of a very superior machine, but being only -depicted lineally was at once rejected by them, for a highly -finished representation of a very inferior apparatus. The engineer, -wishing to induce the board to decide for the best, suggested that -the matter should be postponed to a future day, and in the meantime -had the drawing of the superior machine highly colored and -finished. At the next meeting the directors unanimously decided -that this was the very one which they preferred and had chosen.</p> - -</div><!--note--> - -<hr class="chap x-ebookmaker-drop" /> - -<div class="chapter"> - -<p><span class="pagenum" id="Page186">[186]</span></p> - -<h2 class="nobreak">Reproducing Drawings.</h2> - -</div><!--chapter--> - -<p>When once finished, one or more copies of drawings -are frequently required; these are produced, 1, by -blue printing, as described before; 2, by tracing. A -tracing is a mechanical copy of a design or drawing, -made by reproducing its lines as seen through a transparent -medium—as tracing-cloth or tracing-paper.</p> - -<p>Tracing-cloth is a thin linen fabric, coated with -size; this is called <i>tracing-lines</i>; <i>tracing-paper</i> is so -prepared as to be transparent, so that it will receive -marks either in pencil or with pen and ink.</p> - -<p>Tracing-cloth must be fastened to the board, over -the drawing, by pins or other tacks; moisture or dampness -should be carefully avoided and the drawing done -on the smooth side of the cloth.</p> - -<p>When tracing cloth will not take ink readily a -small quantity of pounce may be applied to the surface -of the cloth and distributed evenly with a piece -of cotton waste, chamois, or similar material, but the -pounce should be thoroughly removed—by washing—before -applying the ink.</p> - -<p>In making tracings the same order is followed as -described under the section “Inking”—to repeat: -1, ink in the small circles and curves; 2, ink in the -larger circles and curves; 3, then all the horizontal -lines, beginning at the top of the drawing and working -downward; 4, next ink in all the vertical lines, commencing -at the left and moving back to the right; -5, draw in the oblique lines; 6, all the center lines red -(carmine), and dimension and reference lines in blue -(Prussian blue) or <i>vice versa</i>. The figuring and lettering -should always be done with India ink, thoroughly -black.</p> - -<p><span class="pagenum" id="Page187">[187]</span></p> - -<h3>BLUE PRINTING.</h3> - -<p>Copies of drawings or parts representing details -and measurements are frequently needed for the office, -pattern shop, machine and blacksmith shop, etc. These -copies are best made by printing on sensitized or -specially prepared paper, from tracings drawn on transparent -cloth or paper, as hereabove described. The -original design may be guarded with the utmost care -for long preservation, but the blue prints, so called, are -for ready reference and use without much regard to -the length of time they are to be in existence.</p> - -<p>The usual practice is to carefully trace from the -drawing on transparent cloth or paper an exact reproduction -of it, filling in all detail lettering and sizes or -figured dimensions.</p> - -<p>This tracing is fixed in a frame similar to a picture -frame, with the side on which the drawing is made -next to the glass: 1, place the sensitized side of the -paper (which has been prepared previously) against the -back of the tracing; 2, fix soft padding against the -back of the paper and fasten it up so that both paper -and tracing are compressed firmly against the glass, -permitting no creases or air spaces between them.</p> - -<div class="container w40em" id="Fig262"> -<img src="images/illo187.jpg" alt="Blue print" /> -<p class="caption">Fig. 262.</p> -</div> - -<p>This should be done in a darkened room; 3, expose -for three to six minutes, according to the intensity -of the sun; 4, take the sensitized paper out of the<span class="pagenum" id="Page188">[188]</span> -frame and quickly wash well in clean running cool -water, and the drawing will appear in white lines on -blue ground; 5, hang the print up by one edge so that -the water will run off and the print will soon dry and -be ready for use.</p> - -<h3>TEST-PIECES.</h3> - -<p>To make good blueprints, being guided only by -the appearance of the exposed edge of sensitized -paper, requires considerable experience. Very often, -especially on a cloudy day, the edge looks just about -right, but when taken out of the frame and given a -rinsing, it is only to find that the print looks pale -because it should have been allowed to remain exposed -for a longer period.</p> - -<p>Now simply take a small test-piece of the same -paper (say about 4 inches square) and a piece of -tracing cloth with several lines on its surface and -lay these small pieces out at the same time the real -print is being exposed, and cover these samples -with a piece of glass about 4 inches square. As a -general rule, we can find a place on top of the frame -for the testing-piece, and by having a small dish of -water at hand for testing the print by tearing off a -small bit and washing same to note its appearance, -the novice can get just as good results as the experienced -hand without danger of failure.</p> - -<h3>BLACK PROCESS COPYING.</h3> - -<p>This is accomplished by specially sensitized paper -by which a fac-simile of the original drawing can be -made; that is, black lines upon white ground. It also -avoids the objection to the blue print paper of shaded -drawings which show light and shade reversed.</p> - -<p>The prints made by the process are said to be -absolutely permanent and can be altered, added to or -colored the same as original drawings.</p> - -<p>The sensitized paper is sold ready for use, but it -can be prepared by dissolving two ounces of citrate of -iron and ammonium in eight ounces of soft water; -keep in a dark bottle, also, one and one-third ounces of -red prussiate of potash in eight ounces of water; keep -in another dark bottle; when about to use mix an -equal quantity of each in a cup and apply in a dark -room with a soft brush or sponge to one side of white -rag paper, similar to envelope paper, let it dry and put -away in a dark place until required for use.</p> - -<hr class="chap x-ebookmaker-drop" /> - -<p><span class="pagenum" id="Page189">[189]</span></p> - -<div class="container w30em"> -<img src="images/illo189.png" alt="DRAWING OFFICE RULES" /> -</div> - -<hr class="chap x-ebookmaker-drop" /> - -<div class="chapter"> - -<p><span class="pagenum" id="Page190">[190-<br />191]</span><a id="Page191"></a></p> - -<h2 class="nobreak" id="FNanchor1">Drawing Office Rules.<a href="#Footnote1" class="fnanchor">[1]</a></h2> - -</div><!--chapter--> - -<div class="footnote"> - -<p><a id="Footnote1"></a><a href="#FNanchor1"><span class="label">[1]</span></a> -<span class="smcap">Note.</span>—A. W. Robinson, M.E., Montreal, must have all -credit for these admirable rules and regulations. They bring into -a single focus the whole science and art of mechanical drawing.</p> - -</div><!--footnote--> - -<p>There are drawing offices where from ten to nearly one hundred people are busily employed in making -new plans and sketches by the hundreds, and where thousands of completed drawings are filed for reference -or for changes, as these are needed in the shop management.</p> - -<p>To be introduced for the first time into such a company is a trial for the “new man” both of nerve and -manners, and a test as well of skill; nothing helps more at such a time than an acquaintance with the rules -and routine of the office, for the old saying holds good in a drawing office, of “doing in Rome as the Romans -do.” The author of this book has felt this strangeness in a new position and so adds the following model-rules -for the guidance of the student when first entering a regular position in an office where many are employed -and where success depends upon a systematic ordering of the work in hand.</p> - -<h3>SIZE OF DRAWINGS.</h3> - -<p>1. The standard size shall be 23 inches by 36 -inches, subdivided into half, quarter and eighth sheets.</p> - -<p>2. Full-size drawings shall be reserved, as far as -possible, for general views and parts not capable of -being shown on smaller sheets.</p> - -<p>3. All shop detail shall, as far as possible, be -shown on quarter and eighth sheets.</p> - -<h3>CHARACTER OF DRAWINGS.</h3> - -<p>4. Detail drawings shall, as far as possible, classify -the different kinds of works, such as castings, forgings, -shafts, levers, piping, etc. Different kinds of work -shall not be shown on the same detail drawing.</p> - -<p><span class="pagenum" id="Page192">[192]</span></p> - -<p>5. All shop drawings liable to repetition shall be -traced and blue-printed. All temporary details, requiring -only one copy, may be made on sketch sheets -and press copied.</p> - -<p>6. A shop drawing is to be considered as an order -or instruction to the shop, and not merely as a statement -or illustration. For this purpose it must convey -clearly and distinctly all the information necessary -to make the article.</p> - -<p>7. Every dimension necessary to the execution -of the work is to be clearly stated by figures on the -drawing, so that no measurements need to be taken in -the shop by scale. All measurements to be given with -reference to the base or starting point from which the -work should be laid out, and also with reference to -center lines.</p> - -<p>8. All figured dimensions on drawings to be -plain, round vertical figures, not less than one-eighth -inch high, and formed by a line of uniform width and -sufficiently heavy to insure printing well. No thin, -sloping, or doubtful figures, or diagonal-barred fractions -will be tolerated. All figured dimensions below two -feet to be expressed in inches.</p> - -<p>9. All center lines to be alternate dot and dash -in fine black line. All dimension lines to be double -dot and dash, with a central space for the figure, and of -such strength as to show on blue-print more faintly than -lines of drawing. Lines of drawing to be bold and -clearly defined in proportion to the scale, and may be -shade-lined by making the right-hand and bottom lines -heavier. No ornamental shading or other “frills” -allowed on shop drawings.</p> - -<p>10. Every drawing, whether whole or half-sheet, -shall have the title, date, scale and number of the sheet -stamped in lower right-hand corner, and the quarter -and eighth sheets printed on top.</p> - -<p>11. The name of the drawing, as given in the -title, is invariably to consist of two divisions in one -line separated by a hyphen. The first division is to -state the general name of the thing or machine, and<span class="pagenum" id="Page193">[193]</span> -the second name is to clearly designate the part or -parts represented (or if a general view should so state). -The wording of titles should be submitted to the chief -engineer or head draughtsman for approval.</p> - -<p>12. Each drawing shall bear the name of the -draughtsman and examiner, the surname being used -without initials.</p> - -<p>13. Drawings of piping details shall be made in -diagram form, using standard symbols.</p> - -<p>14. All detail parts for standard or repetition -work shall be shown unassembled as far as possible.</p> - -<h3>DRAWING SYMBOLS.</h3> - -<p>15. Detail shop drawings should state:</p> - -<p>(a) The pattern number of every casting in plain -figures of larger size than the dimension figures.</p> - -<p>(b) The material of which the parts are made, -using symbols as follows: C.I.—Cast iron. W.I.—Wrought -iron. M.S.—Machinery steel. H.S.—Hammered -steel. Bs.—Brass. Bbt.—Babbitt. Bz.—Bronze. -C.R.S.—Cold rolled steel.</p> - -<p>Other materials write full name.</p> - -<p>(c) Finished surfaces will be indicated by “f” -written on the line or surface to be finished. When -not so marked it is understood that the part is to be -left black or rough. In cases where finish might be -presumed but not required, follow the figured dimensions -by the word “cast,” if a casting, and “rough,” if -a forging.</p> - -<h3>STANDARDS.</h3> - -<p>16. The following standards shall be strictly -adhered to as given in the tables noted:</p> - -<p>(1.) Table of standard diameters of shafting and -key seats.</p> - -<p>(2.) Table of standard stock sizes of rounds.</p> - -<p>(3.) Table of standard stock sizes of flat steel.</p> - -<p>(4.) Table of standard clearance fits.</p> - -<p>(5.) Table of standard symbols for notation of -riveting.</p> - -<p>(6.) Table of standard symbols for pipe fittings.</p> - -<p>Also such other standards as may be adopted from -time to time.</p> - -<p><span class="pagenum" id="Page194">[194]</span></p> - -<h3>NUMBERING OF DRAWINGS.</h3> - -<p>17. Drawers and filing cases shall be numbered -consecutively. Drawers shall contain 100 sheets each, -and filing cases 200 sheets each, and to be fully indexed. -Drawings shall be numbered by a number indicating -both drawer number and serial number in the -drawer—thus, 7,604 is the fourth sheet in drawer 76, etc.</p> - -<p>18. Drawing numbers shall be checked off the -index as required, and the index posted up in uniform -handwriting by the clerk.</p> - -<p>19. Standard size drawings shall be kept in -drawers and quarter and eighth sheets in filing cases. -All drawings shall be indexed by an index sheet kept -in each drawer or case.</p> - -<h3>CHECKING.</h3> - -<p>20. All drawings must be approved before being -traced. When tracing is completed it will be given -immediately to the chief draughtsman, who will have -a preliminary print made and carefully checked, before -being used.</p> - -<h3>PATTERNS.</h3> - -<p>21. All patterns shall bear the number of the -drawing on which they are first detailed, followed by a -serial letter, according to the number of patterns on -the drawing.</p> - -<p>22. Standard patterns used repeatedly and liable -to be ordered from in repairs must not be changed. -Other patterns may only be changed when absolutely -necessary and by order. When so changed they will -bear the original number and letter, followed by A for -the first change, B for the second change, and so on -thus: 4860 AB is the second change in pattern 4860 A.</p> - -<h3>SKETCH BOOKS.</h3> - -<p>23. Each draughtsman will be supplied with a -sketch book by the company, in which he shall make -all his notes, calculations and data referring to his -work, and under no circumstances shall notes of value -be made on loose sheets. Each entry should invariably -be commenced with the subject and date, and full<span class="pagenum" id="Page195">[195]</span> -notes made of data on which the calculations were -based, and the results obtained clearly stated. These -books are to remain the property of the company.</p> - -<h3>IN GENERAL.</h3> - -<p>24. Changes in drawings, sketches or order lists -issued to the shop shall only be made when authorized -by the chief engineer, or, in his absence, by the chief -draughtsman, and when so authorized shall be made by -the order clerk.</p> - -<p>25. The names of all similar parts in order lists -and drawings are to be uniform.</p> - -<p>26. Tracings must be kept in safe, for blue-printing -purposes only. Office copies of blue-prints must -be used for references.</p> - -<p>27. No drawing, print or photograph shall be -taken from office without permission.</p> - -<h3>NUMBERING WORKING DRAWINGS.</h3> - -<p>There are a great many different systems used in -indexing drawings, most of which have some good -points, but very few are sufficiently elastic to cover a -wide field. A plan based upon the decimal system of -notation is very simple, and, as there is no practical -limit to the number of subdivisions, it can be expanded -indefinitely. Following are the main outline -features of the system as adapted to the needs of -drawing offices belonging to large works.</p> - -<p>The main division numbers, 000, 100, 200, 300, etc., -are used respectively for all plans and general sheets -referring to the division concerned. 100 includes -general plans covering more than one department, -and all small-scale plans with cross references to departments -covered.</p> - -<p>The class or tens divisions contain general -drawings of the subdivisions, the subclasses or units -divisions being limited to details only. Further subdivisions -would probably be necessary in some cases. -A card index with cross references and written by -someone who knew what to do is an essential part -of the system.</p> - -<hr class="chap x-ebookmaker-drop" /> - -<p><span class="pagenum" id="Page196">[196-<br />197]</span><a id="Page197"></a></p> - -<div class="container w30em"> -<img src="images/illo197.png" alt="GEARING AND DESIGN" /> -</div> - -<hr class="chap x-ebookmaker-drop" /> - -<p><span class="pagenum" id="Page198">[198]</span></p> - -<div class="container" id="Fig263"> -<img src="images/illo198.png" alt="Gears" /> -<p class="caption">Fig. 263.</p> -</div> - -<hr class="chap x-ebookmaker-drop" /> - -<div class="chapter"> - -<p><span class="pagenum" id="Page199">[199]</span></p> - -<h2 class="nobreak">Gearing.</h2> - -</div><!--chapter--> - -<p>Under this heading the author has grouped some information relating to a subject of wide interest and one -sure to interest a student of mechanical drawing.</p> - -<p>The diagrams are intended for exercises in drawing, <i>i. e.</i>, to be redrawn as parts of practice; the text is to be -studied not only for the good to be gained from the study of gearing, but as an example of the way in which -written or printed descriptions are necessary to explain a subject illustrated by drawings.</p> - -<p><i>A gear</i> is primarily a toothed wheel; gearing is a -train of toothed wheels for transmitting motions; there -are two chief sorts of toothed gearing, viz., spur gearing -and bevel gearing.</p> - -<p><i>A spur wheel</i> has teeth around the edge pointing -to the center; commencing at the center, a spur wheel -may be said to consist of a hole, square, octagonal or -round, for its axle or shaft; a hub; the web, body or -arms; a rim, and the teeth; see <a href="#Fig263">fig. 263</a>.</p> - -<p><i>A spur wheel</i> has teeth on its circumference which -run parallel to its shaft; wheels as shown in <a href="#Fig271">fig. 271</a> are -termed <i>helical wheels</i>; these are similar to spur wheels -except their teeth are arranged upon different angles -to the shaft.</p> - -<p><i>A bevel</i> is a slant or inclination of a surface from a -right line, hence a bevel wheel is one whose teeth stand -beveling or at an oblique angle to the shaft, or towards -the center; see <a href="#Fig267">fig. 267</a>.</p> - -<p><i>Miter wheels</i> are bevel wheels of the same size, -working at right angles with one another; see <a href="#Fig268">fig. 268</a>.</p> - -<p><i>The diameter of both spur and bevel wheels</i> is -measured and calculated neither from the outside nor -from the bottom of the teeth, but on the pitch circle. -When we speak of the diameter of a spur or bevel<span class="pagenum" id="Page200">[200]</span> -wheel, we mean the diameter of the pitch circle, without -any reference to the form of tooth.</p> - -<p><i>The addendum circle</i> of a toothed wheel is as -shown in illustration, <a href="#Fig264">fig. 264</a>; <i>addendum</i> means “something -added,” and, as shown in the figure, it is the part -added beyond the pitch “line” or circle.</p> - -<div class="container w40em" id="Fig264"> -<img src="images/illo200.png" alt="Definitions" /> -<p class="caption">Fig. 264.</p> -</div> - -<p><i>The pitch line</i> is the most important one in gearing; -the “pitch line” or “pitch circle” is supposed to be -the working circle. This is shown in P—P in <a href="#Fig274">fig. 274</a>.</p> - -<p><i>The periphery</i> of a wheel is the extreme circumference, -as N in <a href="#Fig274">fig. 274</a>.</p> - -<p>All parts of gear-wheels consist of portions, to -which have been given generally accepted names. -<a href="#Fig264">Fig. 264</a> shows the “addendum circle” and the “pitch -line” as marked. The teeth and rim are shown in -white, and the other portions are indicated by the names.</p> - -<p><i>The circular pitch line</i>, as opposed to the diametral -pitch, is the same as the pitch circle. It is a line which -bisects all the teeth of a toothed wheel.</p> - -<p><i>The rolling circle</i> is the same as the circular -pitch line.</p> - -<p><i>Diametral</i> means pertaining to a diameter or the -length of a diameter; hence a diametral pitch is a -system of measures or enumeration based upon the -diameter instead of the circular pitch line; it is used -very generally in spacing for fine tooth gear. Wheels -of this description usually have their teeth cut in a -gear-cutting machine, <i>i. e.</i>, medium and fine tooth -gears.</p> - -<p><span class="pagenum" id="Page201">[201]</span></p> - -<div class="container rightfloat w15em" id="Fig265"> -<img src="images/illo201.png" alt="Cog wheel" /> -<p class="caption">Fig. 265.</p> -</div> - -<p><i>A cog wheel</i> is the general name for any wheel -which has a number of cogs placed around its circumference.</p> - -<p>When the teeth of a wheel are -made of the same material and -formed of the same piece as the -body of the wheel, they are called -<i>teeth</i>; when they are made of wood -or some other material and fixed to -the circumference of the wheel, they -are called <i>cogs</i>; see <a href="#Fig265">fig. 265</a>.</p> - -<p><i>A pinion</i> is a small wheel. When two toothed -wheels act upon one another, the smaller is generally -called the pinion. The terms <i>trundle</i> and <i>lantern</i> are -applied to small wheels having cylindrical bars instead -of teeth. The teeth in pinions are sometimes termed -<i>leaves</i>; in a trundle, <i>staves</i>. See <a href="#Fig273">fig. 273</a>.</p> - -<p>The wheel which acts is called a <i>leader</i> or <i>driver</i>; -and the wheel which is acted upon by the former is -called a <i>follower</i> or the <i>driven</i>. When a screw or <i>worm</i> -revolves in the teeth of a wheel, the latter is termed a -<i>worm wheel</i> or <i>worm gear</i>; see <a href="#Fig270">fig. 270</a>. When a -pinion acts with a rack having teeth, we speak of <i>rack</i> -and pinion. When the teeth are on the inside of the -rim, and not on the periphery, the wheel is termed an -<i>internal gear</i>; see <a href="#Fig272">fig. 272</a>.</p> - -<p>Two wheels acting upon one another in the same -plane are called <i>spur gear</i>; the teeth are parallel with -the axis. When wheels act at an angle, they are -called <i>bevel gear</i>.</p> - -<p><i>Friction gear-wheels</i> are those which communicate -motion one to the other by the simple contact of -their surfaces.</p> - -<p>In frictional gearing the wheels are toothless and -one wheel drives the other by means of the friction -between the two surfaces which are pressed together.</p> - -<p>Grooved friction wheels are used to give greater -cohesion than can be obtained by the plain surface.</p> - -<p><span class="pagenum" id="Page202">[202]</span></p> - -<p><a href="#Fig263">Fig. 263</a> shows a pair of spur-wheels in -gear. The dotted circles which meet are -the rolling circles, called the “pitch line” -or “pitch circle.”</p> - -<div class="container w30em" id="Fig266"> -<img src="images/illo202.png" alt="Spur mortise wheel" /> -<p class="caption">Fig. 266.</p> -</div> - -<p>A spur mortise wheel is similarly -shown in <a href="#Fig266">fig. 266</a>; it is very like in appearance -to a spur wheel; it differs essentially -in that the teeth are separate cogs, -fixed in singly to the rim; see also <a href="#Fig265">fig. 265</a>, -<a href="#Page201">page 201</a>.</p> - -<div class="note"> - -<p><span class="smcap">Note.</span>—The teeth of spur wheels cast from a -pattern must of necessity be larger at one side than -at the other, because the teeth must have taper to -permit the extraction of the pattern from the -mould; therefore, in fixing wheels to gear, the -large side of one should meet the smaller side of -the other; should the two large sides come together -the teeth will meet only at the large side, -and the teeth will probably break away from the -excessive strain on that point.</p> - -</div><!--note--> - -<p><span class="pagenum" id="Page203">[203]</span></p> - -<p><i>Skew gearing</i> are bevel wheels working out of -center; the teeth do not form radial lines from the -wheel center.</p> - -<p><a href="#Fig267">Fig. 267</a> shows a pair of bevel wheels in gear as -described on <a href="#Page199">page 199</a>. A bevel mortise wheel, <i>i. e.</i>, -one having cogs inserted in its rim instead of teeth.</p> - -<div class="container" id="Fig267"> -<img src="images/illo203.png" alt="Bevel wheels" /> -<p class="caption">Fig. 267.</p> -</div> - -<p><span class="pagenum" id="Page204">[204]</span></p> - -<p>A bevel wheel and pinion must be made to suit -one another by both having teeth forming together an -angle of 90°, therefore they are pairs, or proportioned -in the number of teeth one to the other. Any other -proportion used would not exactly gear and would be -termed a “bastard” gear.</p> - -<div class="container w30em" id="Fig268"> -<img src="images/illo204.png" alt="Miter wheels" /> -<p class="caption">Fig. 268.</p> -</div> - -<p><a href="#Fig268">Fig. 268</a> represents a pair of miter wheels in gear; -it will be noted that the shafts, when connected, will -be at right angles to each other, the wheels being in -all particulars of the same dimensions; the figure -answers the purpose of a much longer description, if -given in words.</p> - -<p>A miter-wheel can easily be known by putting -a square upon the face of the teeth, which are always -at an angle of 45° with one another, irrespective -of size.</p> - -<p><i>A miter-wheel</i> is a particular kind of bevel-wheel, -the bevel being limited to an angle of 45° in each -wheel.</p> - -<p>The curve of the teeth in bevel-gears, when correctly -formed, changes constantly from one end of the -tooth to the other, therefore bevel-gears whose teeth -are produced with a forced cutter are not theoretically -correct.</p> - -<p><span class="pagenum" id="Page205">[205]</span></p> - -<p><a href="#Fig269">Fig. 269</a> -represents a -rack and pinion: -the teeth -in this form of -gear are shaped -similarly to -those in the spur -wheel, shown on -<a href="#Page198">page 198</a>, with -the difference -that the teeth -of one are on a circle and -on the rack are made on -a straight line.</p> - -<div class="container" id="Fig269"> -<img src="images/illo205.png" alt="Rack and pinion" /> -<p class="caption">Fig. 269.</p> -</div> - -<p>A flange or addition -to the end of a tooth and -the rim connecting them -together is used to -strengthen the teeth. This -extends from the root to -pitch line when the wheel -and pinion are both -flanged: if only one is -flanged it extends from -the root to the addendum.</p> - -<p><span class="pagenum" id="Page206">[206]</span></p> - -<div class="container w40em" id="Fig270"> -<img src="images/illo206.png" alt="Worm and worm wheel" /> -<p class="caption">Fig. 270.</p> -</div> - -<p><a href="#Fig270">Fig. 270</a> illustrates a worm and -a worm wheel, sometimes called -screw gears. This is a slow but -powerful method of transmitting -power, one revolution of the worm -only moving the wheel the distance -of one tooth and space.</p> - -<p><i>A worm gear</i> is a spur wheel -with teeth at an angle to the axis, -so as to work with a worm which -is a <i>screw</i>, or has teeth shaped in -the form of a spiral wound round -its circumference; the screw or -worm is called an endless screw, -because it never comes to a stopping -place in the circumference of -the wheel.</p> - -<p><span class="pagenum" id="Page207">[207]</span></p> - -<div class="container" id="Fig271"> -<img src="images/illo207a.jpg" alt="Helical gear" /> -<p class="caption">Fig. 271.</p> -</div> - -<p><a href="#Fig271">Fig. 271</a> represents a gear with helical teeth. It is similar to a spur wheel, and is used -in place of same in heavy and slow moving machinery, the formation of teeth preventing—in -large measure—the jar or concussion noticeable in common spur gears.</p> - -<p>In recent years the speed at which gearing is run has been greatly increased. A -striking instance is that of a pair of <i>cast-iron</i> helical wheels, 6 ft. 3 in. diameter, 12 in. -wide, making 220 revolutions -per minute, the speed of the -pitch line being 4,319 feet per -minute; these wheels are running -continuously and with -little noise. There is also a <i>cut</i> -gear in a mill in Massachusetts, -30 feet in diameter, and the -speed of pitch line is 4,670 feet -per minute.</p> - -<div class="container w30em" id="Fig272"> -<img src="images/illo207b.png" alt="Annular gear" /> -<p class="caption">Fig. 272.</p> -</div> - -<p><i>An internal or annular gear wheel</i> is one in which the faces of the teeth are within -and the flank without the pitch circle, hence the pinion operates within the wheel. -See <a href="#Fig272">fig. 272</a>.</p> - -<p>In internal geared wheels there is almost an entire absence of friction and consequent -wear of the teeth, as compared to ordinary spur gearing.</p> - -<p><span class="pagenum" id="Page208">[208]</span></p> - -<p><a href="#Fig273">Fig. 273</a> shows a <i>crown-wheel</i> which has pin teeth -which are fixed by one end only, on its side face and -gear into a trundle wheel.</p> - -<div class="container w40em" id="Fig273"> -<img src="images/illo208.png" alt="Trundle wheel" /> -<p class="caption">Fig. 273.</p> -</div> - -<p><i>A trundle wheel</i> has no teeth, properly speaking. -Instead of teeth, it has pins as shown on illustration, -<a href="#Fig273">fig. 273</a>, arranged like the rungs of a ladder between -two walls. See <a href="#Page201">page 201</a>.</p> - -<p><i>Trains of Gears.</i>—When two wheels mesh—that -is, engage with each other—as in <a href="#Fig263">fig. 263</a>, one axle -revolves in the opposite direction to the other; but -when internal gears mesh as shown in <a href="#Fig272">fig. 272</a>, the shafts -revolve in the same direction; three or more gears running -together are often called <i>a train of gears</i>.</p> - -<p>Maximum speed of gears under favorable conditions -for safety is <span class="nowrap">comparatively—</span></p> - -<table class="gears" summary="Gear speed"> - -<tr> -<td class="wheel">Ordinary cast-iron wheels,</td> -<td class="speed">1,800</td> -<td class="unit">feet per minute.</td> -</tr> - -<tr> -<td class="wheel">Helical cast-iron wheels,</td> -<td class="speed">2,400</td> -<td class="unit">feet per minute.</td> -</tr> - -<tr> -<td class="wheel">Mortise wood cog wheels,</td> -<td class="speed">2,400</td> -<td class="unit">feet per minute.</td> -</tr> - -<tr> -<td class="wheel">Ordinary cast-steel wheels,</td> -<td class="speed">2,600</td> -<td class="unit">feet per minute.</td> -</tr> - -<tr> -<td class="wheel">Helical cast-steel wheels,</td> -<td class="speed">3,000</td> -<td class="unit">feet per minute.</td> -</tr> - -<tr> -<td class="wheel">Cast-iron machine cut wheels,</td> -<td class="speed">3,000</td> -<td class="unit">feet per minute.</td> -</tr> - -</table> - -<p>It is not, however, advisable to run gears at their -maximum speeds, as great noise and vibration are -caused.</p> - -<hr class="chap x-ebookmaker-drop" /> - -<div class="chapter"> - -<p><span class="pagenum" id="Page209">[209]</span></p> - -<h2 class="nobreak">Designing Gears.</h2> - -</div><!--chapter--> - -<p>This section is introduced into the work for a double purpose; 1, as an exercise in drawing; 2, as a study in -accurate measurements. It is a sample of the work that the advanced student in mechanical drawing will be -confronted with as he puts in practice the theory of the art of drawing.</p> - -<p>Some sample rules are given in the following pages to aid in calculations relating to gears, and still others are -given under the <a href="#Page269">section</a> “Useful Rules and Tables” at the end of the volume; these are to be carefully studied.</p> - -<p>To accurately divide the pitch circle of a gear -wheel by hand requires both patience and skill. On -the accuracy of spacing lies the essential requisite of a -good gear wheel.</p> - -<p>The drawing in plate, <a href="#Fig274">fig. 274</a>, illustrates a pair -of spur wheels, shown in gear, the office instructions -for which being:</p> - -<p>“Required, <i>a detail plan</i> of a pair of spur wheels; -dimensions: wheel, 76 teeth, 3<sup>1</sup>⁄<sub>2</sub> inches pitch, 7-inch -eye, 6 arms; pinion, 19 teeth; scale, 1<sup>1</sup>⁄<sub>2</sub> inches = 1 -foot.”</p> - -<p>The drawing, as illustrated, is the result of the -above instructions, all pencil lines being removed, and -this result is worked out as follows:</p> - -<p>76 teeth × 3<sup>1</sup>⁄<sub>2</sub> inches, pitch = 266 inches in circum. -= 7 ft. 0<sup>11</sup>⁄<sub>16</sub> in. diam. = 3 ft. 6<sup>11</sup>⁄<sub>32</sub> in. radius; with this -measurement as represented on scale, draw line <i>P P</i> on -drawing. This is called the pitch line.</p> - -<p>Draw next diameter line, produce or extend this -diameter line for pinion, and with radius of 10<sup>19</sup>⁄<sub>32</sub> (19 -teeth × 3<sup>1</sup>⁄<sub>2</sub>) from pitch line of wheel, draw pitch line of -pinion.</p> - -<p><span class="pagenum" id="Page210">[210]</span></p> - -<p>Take any point in this pitch line of wheel, mark -off 3<sup>1</sup>⁄<sub>2</sub> inches as represented on scale, mark this around -the pitch line, it will be the center of each of the 76 -teeth; then the breadth of thickness of each tooth -(= pitch × 0.475) must be marked from these centers, -then mark from <i>P L</i>, length of tooth to point (= pitch -× 0.35) and <i>P L</i> to root (= pitch × 0.4), draw circles for -outside of teeth <i>N</i> and root of tooth <i>O</i>; now with -compass set to the pitch (3<sup>1</sup>⁄<sub>2</sub>) of the wheel, draw the -outer portion from pitch line of tooth.</p> - -<p>The radius will center in the pitch line of next -tooth where thickness of tooth has been marked; after -finishing outer portion of both sides of teeth, set the -compass from <i>center</i> of tooth with radius to the thickness -marked on pitch line and draw the portion of tooth -from pitch line to root.</p> - -<p>Now mark off with dividers and draw thickness of -rim (= pitch × 0.5), divide this line into six parts, draw -radii for centers of arms; draw the bore hole 7″ and -the thickness of metal for hub same as pitch.</p> - -<p>On radii lines of arms, draw the breadth of arm at -rim (= pitch and thickness of tooth), increase in breadth -approaching the center (1″ per foot), draw the thickness -of feather of arm (= pitch × 0.35); draw web on -inside of rim (= pitch × 0.375); fill in arcs for the joining -of arms in rim and hub (radii = pitch × 0.8) and -feather to rim and hub (radii = pitch × 0.37).</p> - -<p>Proceed in similar manner, completing the teeth -of pinion, and when pencil lines are all in, ink the drawing, -erasing all needless lines.</p> - -<p><i>P P</i> shows the pitch line; <i>B</i>, thickness of tooth; -<i>c</i>, breadth of space; <i>A</i>, the pitch; <i>E</i>, clearance at root; -<i>N</i>, the addendum of tooth; <i>O</i>, the root of tooth; <i>H</i>, -length of tooth from pitch line to point; <i>I</i>, length of -tooth pitch line to root; <i>G</i>, whole length of tooth; <i>F</i>, -thickness of rim; <i>J</i>, web or feather on rim; <i>K</i>, breadth -of arm; <i>L</i>, thickness of feather; <i>M</i>, hub, or thickness -round the eye.</p> - -<div class="note"> - -<p><span class="smcap">Note.</span>—It must be remembered that no fixed standard has -ever been agreed upon for these proportions, and workshops differ -considerably in practice.</p> - -</div><!--note--> - -<p><span class="pagenum" id="Page211">[211]</span></p> - -<div class="container" id="Fig274"> -<img src="images/illo211.png" alt="Spur wheels" /> -<p class="caption">Fig. 274.</p> -</div> - -<p><span class="pagenum" id="Page212">[212]</span></p> - -<p>The number of teeth, their -proportions, pitch and diameter of -pitch circle are frequently determined -on the “Manchester” principle. -This system originated in -Manchester (Eng.), and is now -generally used in the United States -for determining diameters and -number of teeth, which, of course, -regulate speeds. The principle is -not applicable to large wheels, but -is limited in its application to small -wheels, or wheels having “fine -pitch,” as will be seen in the following -explanation, which is introduced -as very useful and indispensable -knowledge for the acquisition -of the student in mechanical -drawing.</p> - -<div class="container w45em" id="Fig275"> -<img src="images/illo212.png" alt="Gear" /> -<p class="caption">Fig. 275.</p> -</div> - -<p>The “pitch” of teeth has -already been stated to be the distance -from center of one tooth to -the center of another on the “pitch -line,” measured on the chord of<span class="pagenum" id="Page213">[213]</span> -the arc. In determining the number of teeth or pitch -of wheels on this principle, the pitch is reckoned -on the <i>diameter</i> of the wheel, <i>in place of the circumference</i>, -and distinguished as wheels of “4 pitch,” “6 -pitch,” “8 pitch,” etc. In other words, this means -that there are four, six, or eight teeth in the circumference -of the wheel for every inch of diameter.</p> - -<p>In designing gears to transmit power the stress on -a tooth is calculated; it determines the breadth or -width and also the thickness of the tooth on pitch line; -the space between the teeth is in proportion to the -thickness of tooth, and the thickness of both combined -(one tooth and one space), measured on the pitch line -or circle, is the pitch of the wheel.</p> - -<p>From the pitch all the proportions and measurements -for the sizes and strength of the parts of the wheel -are taken <i>by rule</i>, and a symmetrical form is produced.</p> - -<p>In machine drawing the practice is to represent -wheels by circles only; the teeth are never shown -except on enlarged details and then only in very rare -instances; the circles drawn are always the <i>pitch lines</i> -or the rolling points of contact of the wheels.</p> - -<p>The addendum circle is seldom if ever used in -practical drawing. Should it be necessary to show it -in an exceptional case, the circle would be represented -by “dotted” line.</p> - -<p>The shape of tooth and mode of constructing it, -as practiced in drawing offices, differs from the true -theoretical curve of the tooth, although very minutely.</p> - -<p>In all calculations for the speed of toothed gears the -estimates are based upon the pitch line, the latter standing -in the same place as the circumference of a pulley.</p> - -<p>To find the <i>diameter of a gear-wheel</i> multiply the -number of teeth by the pitch, divide by 3.1416.</p> - -<p>To find the <i>pitch of a gear-wheel</i> multiply the diameter -by 3.1416 and divide by the number of teeth.</p> - -<p>To find the <i>number of teeth in a gear-wheel</i> multiply -the diameter by 3.1416 and divide by the pitch.</p> - -<p>The <i>breadth of wheels</i>, where practicable, should be -at least three times the pitch.</p> - -<p><span class="pagenum" id="Page214">[214]</span></p> - -<div class="container w20em" id="Fig276"> -<img src="images/illo214.png" alt="Proportions" /> -<p class="caption">Fig. 276.</p> -</div> - -<p><a href="#Fig276">Fig. 276</a> shows a scale for proportions of teeth; it -is divided into tenths and used thus:</p> - -<p>Say wheel is 2″ pitch, then from pitch circle to -addendum will be 3<sup>1</sup>⁄<sub>2</sub> tenths, and from pitch circle to -root of tooth will be 4 tenths measured at the 2″ line -on scale, and so on.</p> - -<p>The decimal proportions already given in example, -page 210, are adopted in many workshops. Many -others use the proportions approved of by Sir William -Fairbairn, which are:</p> - -<p>Table of proportion of gears:</p> - -<table class="gears" summary="Proportions"> - -<tr> -<td class="wheel">Depth of tooth above pitch line</td> -<td class="speed">.35</td> -<td class="unit">of the pitch.</td> -</tr> - -<tr> -<td class="wheel">Depth of tooth below pitch line</td> -<td class="speed">.40</td> -<td class="unit">of the pitch.</td> -</tr> - -<tr> -<td class="wheel">Working depth of tooth</td> -<td class="speed">.70</td> -<td class="unit">of the pitch.</td> -</tr> - -<tr> -<td class="wheel">Total depth of tooth</td> -<td class="speed">.75</td> -<td class="unit">of the pitch.</td> -</tr> - -<tr> -<td class="wheel">Clearance at root</td> -<td class="speed">.05</td> -<td class="unit">of the pitch.</td> -</tr> - -<tr> -<td class="wheel">Thickness of tooth</td> -<td class="speed">.45</td> -<td class="unit">of the pitch.</td> -</tr> - -<tr> -<td class="wheel">Width of space</td> -<td class="speed">.55</td> -<td class="unit">of the pitch.</td> -</tr> - -</table> - -<p><span class="pagenum" id="Page215">[215]</span></p> - -<p>The diameter of a wheel or pinion is invariably the -diameter measured on pitch circle, except it is specially -described otherwise, thus the diameter “over all,” etc.</p> - -<p>The shape of the curved face of the teeth of gears -extending from the root to the addendum is the curve -conforming to the passage of the teeth described on -its fellow entering and leaving, as they rotate or roll -together on their pitch circles.</p> - -<p>The curve of teeth outside the pitch circle is called -“the face,” and the curve from pitch circle to root is -called “the flank.”</p> - -<p>The difference between the width of a space and -the thickness of a tooth is called clearance or side -clearance.</p> - -<p>The play or movement permitted by clearance is -called the backlash; clearance is necessary to prevent -the teeth of one wheel becoming locked in the spaces -of the other.</p> - -<p>Wheels are in gear or geared together when their -pitch lines engage, <i>i. e.</i>, when the pitch circles meet.</p> - -<p>Wheels to be geared together must have their -teeth spaced the same distance apart, or in other -words, of the same pitch.</p> - -<p>The teeth of spur wheels are arranged on its -periphery parallel to the wheel axis, or shaft on which -it is hung.</p> - -<p>The teeth of a bevel wheel or bevel gears are -always arranged at an angle to the shaft.</p> - -<p>When the <i>teeth</i> of bevel gears form an angle of -45° they are called miter wheels.</p> - -<p>Miter wheels to gear must be of equal sizes.</p> - -<p>A crown wheel is a disc that has teeth which are -on its side face; that is, teeth on a flat circular -surface all parallel to the axis of the wheel.</p> - -<p>A rack has teeth on a flat surface or plane all -parallel to one another.</p> - -<p>A gear cut by machine is called a <i>cut gear</i>. It has -teeth with less clearance than cast wheels, which are -not so true or perfect, and therefore require more -clearance.</p> - -<p><span class="pagenum" id="Page216">[216]</span></p> - -<p>A worm with even a light load is liable to heat -and cut if run at over 300 feet of rubbing surface -travel. The wheel teeth will keep cool, as they form -part of a large radiating surface; the worm itself is so -small that its heat is dissipated slowly.</p> - -<p>A worm throws a severe end thrust or strain on -its shaft.</p> - -<p><i>Steel Gears.</i>—There is great economy in the use -of cast-steel over cast-iron in gears; the average life of -the former is nearly twice as great as of cast-iron gears. -And, apart from their longer life and efficiency, there -is less danger of breaking.</p> - -<p>The most accurate teeth, strongest and most -uniform in wearing, are to be found in steel gears cut -from solid stock, or made by cutters of proper shape.</p> - -<p><a href="#Fig275">Fig. 275</a> shows an elevation and a vertical section -of a spur wheel. From these views the various parts -in spur gears can be better understood, as they are -represented here in combination, and the wheel in its -entirety.</p> - -<p><i>AA</i> is the horizontal center line, <i>BB</i>, <i>BB</i> the vertical -center lines, <i>II</i> and <i>II</i> the pitch lines, <i>N</i> thickness -of tooth, <i>O</i> space of tooth, <i>D</i> total depth of tooth, -<i>C</i> breadth of face, <i>F</i> diameter on pitch line, <i>P</i> diameter -over all, <i>G</i> diameter of hub, <i>E</i> diameter of hole, <i>H</i> depth -of hole, <i>L</i> thickness of rim, <i>M</i> thickness of web.</p> - -<p>Much has been and still is being written on gearing. -No general rule is followed by the writers; the elementary -principles given will enable the student to master -spur gearing, and bevel and combinations of many -kinds of wheels will afterwards be found easier to -delineate than the numerous lines seem to indicate.</p> - -<hr class="chap x-ebookmaker-drop" /> - -<p><span class="pagenum" id="Page217">[217]</span></p> - -<div class="container w30em"> -<img src="images/illo217.png" alt="WORKING DRAWINGS" /> -</div> - -<hr class="chap x-ebookmaker-drop" /> - -<p><span class="pagenum" id="Page218">[218]</span></p> - -<div class="container w40em" id="Fig277"> -<img src="images/illo218.png" alt="Crane" /> -<p class="caption">Fig. 277.</p> -</div> - -<hr class="chap x-ebookmaker-drop" /> - -<div class="chapter"> - -<p><span class="pagenum" id="Page219">[219]</span></p> - -<h2 class="nobreak">Working Drawings.</h2> - -</div><!--chapter--> - -<p>From the “plans” made in the office are produced “working drawings”—which represent in detail the work -to be done to exact measurement and of material, as indicated, by the pattern-maker, the foundry, the forge, the -shop, and finally, by the erector of the completed mechanism.</p> - -<p>How to satisfactorily fulfill the directions contained in these drawings, representing only a part of the work, so -that it will fit, with needed accuracy, to all other parts of the design, is the task before each separate worker.</p> - -<p>It is by means of this division of the process of -manufacture through these drawings, that scores and -hundreds of men can be employed at the same time -upon a single engine or machine; thus, while handwork -has been superseded by machines in many quarters, -the art of drawing has not been narrowed nor -diminished, for no drawings or designs have yet been -made by machinery, nor are they likely to be.</p> - -<p>It is thus that a good designer and draughtsman -“projects” or extends himself, to the advantage of -many fellow workers.</p> - -<p>The drawing, <a href="#Fig277">fig. 277</a>, shows a simple form of pillar -crane: it consists of an upright cast-iron pillar, which is -bolted on a cap stone, under which is the foundation plate -not shown in the drawing; the boom is of rolled steel, -supported by steel tie rods, and provided with rollers -at the base; the hoisting gear is shown in broken -lines and circles; all as seen in the drawing.</p> - -<p><span class="pagenum" id="Page220">[220]</span></p> - -<div class="container" id="Fig278279"> -<img src="images/illo220.png" alt="Beam bender" /> -<p class="caption">Fig. 278.—Fig. 279.</p> -</div> - -<p><span class="pagenum" id="Page221">[221]</span></p> - -<div class="container w40em" id="Fig280"> -<img src="images/illo221.png" alt="Beam bender" /> -<p class="caption">Fig. 280.</p> -</div> - -<p><a href="#Fig278279">Figs. 278, 279</a> and <a href="#Fig280">280</a> show a drawing -of a “hydraulic beam bending machine” in -three views; <a href="#Fig280">fig. 280</a> is a plan, <a href="#Fig278279">fig. 278</a> is an -end elevation, and <a href="#Fig278279">fig. 279</a> a side elevation, -and a portion of the latter in section shows -the interior construction.</p> - -<div class="note"> - -<p><span class="smcap">Note.</span>—These three views are a practical illustration -of drawings for a machine of the following -dimensions: this machine has a bed 3 × 5 feet in area, -with 27 holes in each side for the bending pins. The -frame and cylinders are made of cast iron, the rams of -machinery steel, and the slides for holding the bending -blocks, of steel casting. The distance between -the bending blocks is 17 inches. The cylinders are -copper lined, 8 inches diameter, and the rams have -a 6-inch stroke. The rams, which are independent -and single acting, are returned by counterweights -placed as shown under the table. The cylinders can -be operated independently from either side of the -machine by an arrangement of valves and levers. -The machine complete weighs about 7,500 lbs.</p> - -</div><!--note--> - -<p><span class="pagenum" id="Page222">[222]</span></p> - -<div class="container" id="Fig281283"> -<img src="images/illo222.png" alt="Press" /> -<p class="caption">Fig. 281.—Fig. 282.—Fig. 283.</p> -</div> - -<p><span class="pagenum" id="Page223">[223]</span></p> - -<p>The drawing, <a href="#Page222">page 222</a>, shows three views of a -power punching press.</p> - -<p><a href="#Fig281283">Fig. 282</a> is a side elevation.</p> - -<p><a href="#Fig281283">Fig. 283</a> a front elevation.</p> - -<p><a href="#Fig281283">Fig. 281</a> a vertical sectional view; from these views -the proportion, general arrangement and disposition of -the automatic devices can be easily understood; it may -be well to call particular attention to the automatic -clutch on the top shaft and the tripping device.</p> - -<div class="container w40em" id="Fig284"> -<img src="images/illo223.png" alt="Packing" /> -<p class="caption">Fig. 284.</p> -</div> - -<p>This drawing, <a href="#Fig284">fig. 284</a>, shows a side elevation in -section of a self-adjusting piston-rod packing.</p> - -<p><i>A</i> is the gland, <i>B</i> is the piston rod, <i>C</i> is a brass -sleeve which contains the packing <i>D</i>, <i>E</i> is the cylinder -cover, <i>F</i> is a coil spring. It will be seen that the spring -<i>F</i> abuts on a bushing in the bottom of the stuffing box -and is prevented from scoring the piston rod by stepping -over the ends of the bushing and follower. All -as shown in the drawing.</p> - -<p><span class="pagenum" id="Page224">[224]</span></p> - -<p>The drawing, <a href="#Fig285">fig. 285</a>, shows a sectional view of a -large pulley fixed on a “quill,” or hollow shaft: the -driving shaft passes through the hollow shaft and is -attached to the friction clutch shown at the right-hand -end; this friction clutch drives the hollow shaft and -pulley.</p> - -<div class="container" id="Fig285"> -<img src="images/illo224.png" alt="Drive train" /> -<p class="caption">Fig. 285.</p> -</div> - -<p><span class="pagenum" id="Page225">[225]</span></p> - -<p><a href="#Fig286">Fig. 286</a> shows the mechanism, called the link-motion, employed to reverse an engine, or to enable it to be -run in either direction. Many forms of link-motion have been devised, but the Stephenson form, as shown in the -figure, is, however, the one in almost universal use.</p> - -<div class="container" id="Fig286"> - -<img src="images/illo225.png" alt="Link-motion" /> - -<p class="caption">Fig. 286.</p> - -<p class="center highline15">This drawing shows shading and the mode of figuring the parts for identification.</p> - -</div><!--container--> - -<p><span class="pagenum" id="Page226">[226]</span></p> - -<div class="container" id="Fig287289"> -<img src="images/illo226.png" alt="Bumping post" /> -<p class="caption">Fig. 287.—Fig. 288.—Fig. 289.</p> -</div> - -<p><span class="pagenum" id="Page227">[227]</span></p> - -<p><a href="#Fig287289">Figs. 287 to 289</a> represent a bumping-post for -the end of railway tracks, reproduced on an enlarged -scale from the columns of the <i>Engineering News</i>.</p> - -<p>In addition to the lettering and dimensions, admirably -shown in the drawings, the following description -is appended to show how printed text and mechanical -drawings mutually aid in practical—or commercial—usage.</p> - -<p>The unique feature of the arrangement shown, -is that the center line of the post does not coincide -with the track, thus adapting itself to the nature of -the blows of a car-bumper, as received in the single-post -style of the mechanism.</p> - -<h3>BUMPING POST FOR RAILWAY TRACKS.</h3> - -<p>The post is a 15-in. steel I-beam, resting on a base -plate <sup>3</sup>⁄<sub>4</sub>-in. thick, and supported by anchor rods 1<sup>3</sup>⁄<sub>4</sub> ins. -diameter, with upset ends held by nuts on a heavy -forging bolted to the top of the post. These rods -extend forward and outward to clear the rails, and then -pass vertically through a 4 × 6-in. angle iron crosstie, -and an ordinary wooden tie, extending down to an -anchor block or deadman buried in the ground 6<sup>1</sup>⁄<sub>2</sub> ft. -below the top of the rail.</p> - -<p>Vertical braces or spreaders are fitted between the -anchor timber and a longitudinal timber under the ties, -so as to prevent the loosening of the anchor rods when -the post is struck. The rods are held in position -against the rails by steel forgings bolted to the rail -with 1-in. turned bolts. An oak striking block, 12 × 12 -ins., 3 ft. long, is bolted between angle iron brackets -on the face of the post.</p> - -<p><span class="pagenum" id="Page228">[228]</span></p> - -<div class="container w40em" id="Fig290291"> - -<img src="images/illo228.png" alt="Steady rest" /> - -<div class="split6733"> - -<div class="left6733"> -<p class="caption">Fig. 290.<br /> -Front View.</p> -</div> - -<div class="right6733"> -<p class="caption">Fig. 291.<br /> -Side View.</p> -</div> - -<p class="thinline allclear"> </p> - -</div><!--split6733--> - -<p class="caption">Scale, 3 in. = 1 ft.</p> - -</div><!--container--> - -<hr class="chap x-ebookmaker-drop" /> - -<div class="chapter"> - -<p><span class="pagenum" id="Page229">[229]</span></p> - -<h2 class="nobreak">To Read Working Drawings.</h2> - -</div><!--chapter--> - -<p>One of the advantages resulting from a knowledge of practical draughting is, that it enables a mechanic to -<i>read</i> a drawing when given him as a guide for his work. It is getting every day more general among draughtsmen -to figure exactly and minutely every part of their drawings which are made to a scale.</p> - -<p>Drawings are almost always made “finished size,” -that is, the dimensions are for the work when it is -completed. Consequently all the figures written on -the different parts indicate the exact size of the work -when finished, without any regard to the size of the -drawing itself, which may be made to any reduced and -convenient scale.</p> - -<p>Even in full size drawings this system of figuring -is not objectionable. It is a system which should be -followed whenever a drawing is made “to work to,” -for it allows the workman to comprehend at a glance -the size of his work and the pieces he has to get made. -Figuring makes a drawing comprehensible even to -those who cannot make drawings.</p> - -<p><span class="pagenum" id="Page230">[230]</span></p> - -<p>A working drawing should be made, primarily, as -plain as possible by the draughtsman; second, the -workman should patiently and carefully study it, so -that it is thoroughly understood.</p> - -<p>In studying a drawing, the object it is intended to -represent should be made as familiar as possible to the -mind of the student, so that he may fill out in imagination -the parts designedly left incomplete—as in a -gear wheel where only two or three teeth are drawn in, -that he may see, mentally, the whole.</p> - -<p>The following is a description of reading drawings -when dimensions are not figured. Here we have a -piece of machinery represented by <a href="#Fig290291">fig. 290</a>, and the -information we have is that it is to scale, three inches -= one foot. Now, with scale and dividers, we can -arrive at its actual dimensions.</p> - -<p>Measurements should be first taken <i>with the -dividers from the drawing</i>, and then the dividers -applied to the scale to which the drawing is made; -this scale is always marked on the working drawing; if -the dividers are set to the length of the base of the -example, <a href="#Fig290291">fig. 290</a>, they will measure, on an ordinary -two-foot rule, three and three-fourths inches, <i>but if -applied to the three-inch scale they will read</i> one foot -three inches, the actual length of the part; the “reading” -is from the scale; thus, in both figures the drawings -are “three-inch scale.”</p> - -<p>Now, 3 inches is one-fourth of a foot, hence -3<sup>3</sup>⁄<sub>4</sub> × 4 = 1 ft. 3 in., the full size, and so on for all -parts of the drawing.</p> - -<p><a href="#Fig290291">Fig. 291</a> shows <i>a side view</i> of the “steady rest,” -illustrated in front elevation, <a href="#Fig290291">fig. 290</a>; from the scale -as before we get the sizes; the two views combined -give length, breadth and thickness of the parts.</p> - -<p>In some figures it is necessary to show end views, -also section views, to enable all measurements to be -read from the drawing.</p> - -<hr class="chap x-ebookmaker-drop" /> - -<p><span class="pagenum" id="Page231">[231-<br />232]</span><a id="Page232"></a></p> - -<div class="container w30em"> -<img src="images/illo231.png" alt="PATENT OFFICE DRAWINGS" /> -</div> - -<hr class="chap x-ebookmaker-drop" /> - -<div class="chapter"> - -<p><span class="pagenum" id="Page233">[233]</span></p> - -<h2 class="nobreak">Patent Office Drawing Rules.</h2> - -</div><!--chapter--> - -<h3 class="center">U. S. PATENT OFFICE RULES.</h3> - -<h4>AS APPLIED TO PREPARATION OF DRAWINGS.</h4> - -<p>Each applicant for a patent is required by law to -furnish a drawing of his invention whenever the nature -of the case admits of it. The drawing must be signed -by the inventor or the name of the inventor may be -signed on the drawing by his attorney-in-fact, and in -either case must be attested by two witnesses. The -drawing must show every feature of the invention -covered by the claims.</p> - -<p>When the invention consists of an improvement -on an old machine, the drawing must exhibit, in one or -more views, the invention proper, disconnected from -the old structure, and also, in another view, so much -only of the old structure as will clearly show the connection -of the invention with the old machine.</p> - -<p>Several editions of the patent-drawings are printed, -the smallest of which is about 3 × 4<sup>3</sup>⁄<sub>4</sub> inches, so that the -drawing must be so made that it will stand a reduction -of about one-fourth. This work is done by the photo-lithographic -process, and therefore the character of the<span class="pagenum" id="Page234">[234]</span> -original drawing must be brought as nearly as possible -to a uniform standard of excellence suited to the -requirements of the process.</p> - -<div class="note"> - -<p><span class="smcap">Note.</span>—These rules will be found most useful to many -readers of this work—hence their introduction at this point. -Nearly 50,000 patents are “applied for” in the United States -every year.</p> - -</div><!--note--> - -<p>The following rules are given by the Patent Office -for guidance:</p> - -<p>1. Drawings must be made upon pure white -paper of a thickness corresponding to three-sheet -Bristol board. The surface of the paper must be -calendered and smooth. India ink alone must be used, -so as to secure perfectly black and solid lines.</p> - -<p>2. The size of a sheet on which a drawing is -made must be exactly 10 × 15 inches. One inch from -its edges a single marginal line is to be drawn, leaving -the “sight” precisely 8 × 13 inches. Within this margin -all work and signatures must be included. One of the -shorter sides of the sheet is regarded as its top, and -measuring downwardly from the marginal line, a space -of not less than 1<sup>1</sup>⁄<sub>4</sub> inches is to be left blank for the -heading of title, name, number and date.</p> - -<p>3. All drawings must be made with the pen only. -Every line and letter, signature included, must be -absolutely black. This direction applies to all lines, -however fine, to shading, and to lines representing cut -surfaces in sectional views. All lines must be clean, -sharp, and solid, and they must not be too fine or -crowded. Surface shading, when used, should be open. -Sectional shading should be made by oblique parallel -lines about <sup>1</sup>⁄<sub>20</sub> of an inch apart. Solid black should not -be used for sectional or surface shading.</p> - -<p>4. Drawing must be made of the fewest lines -possible, consistent with cleanness. The plane upon -which a sectional view is taken should be indicated by -a broken or dotted line. Heavy lines on the shade -side of objects should be used, except where they tend -to thicken the work and obscure letters of reference. -The light is always supposed to come from the upper -left hand corner at an angle of 45 degrees.</p> - -<p>5. The scale to which a drawing is made should -be large enough to show the mechanism without -crowding. The number of sheets used must never be -more than is absolutely necessary.</p> - -<p><span class="pagenum" id="Page235">[235]</span></p> - -<div class="container w30em" id="Fig292"> -<img src="images/illo235.png" alt="Invention" /> -<p class="caption">Fig. 292.</p> -</div> - -<p><span class="pagenum" id="Page236">[236]</span></p> - -<p>6. The different views should be consecutively -numbered. Letters and figures of reference must be -carefully formed. They should, if possible, measure -at least one-eighth of an inch in height.</p> - -<p>If the same part of an invention appears in more -than one view of the drawing it must always be represented -by the same character.</p> - -<p>7. The signature of the inventor is to be placed -in the lower right-hand corner of each sheet, and those -of the witnesses at the lower left-hand corner.</p> - -<p>The title should be written with pencil on the back -of the sheet.</p> - -<p>Drawings should be rolled for transmission, never -folded.</p> - -<p>On <a href="#Page235">page 235</a>, <a href="#Fig292">fig. 292</a> exhibits a reproduction of a -patent office drawing, used in connection with specification -papers in an application for a United States -patent.</p> - -<h4>ENGLISH PRACTICE.</h4> - -<p>The rules for patent drawings in England are -practically the same as in the United States; the -paper sizes are, however, different. They must be on -sheets of one of the two following sizes (the smaller -being preferable), 13 inches at the sides by 8 inches -at the top and bottom, or 13 inches at the sides by 16 -inches at the top and bottom, including margin, which -must be one-half an inch wide.</p> - -<p>If there are more figures than can be shown on -one of the smaller-sized sheets, two or more of these -sheets should be used in preference to employing the -large size. When an exceptionally large drawing is -required, it should be “<i>continued</i>” on subsequent -sheets. There is no limit to the number of sheets that -may be sent in.</p> - -<hr class="chap x-ebookmaker-drop" /> - -<p><span class="pagenum" id="Page237">[237]</span></p> - -<div class="container w30em"> -<img src="images/illo237.png" alt="PRACTICAL POINTS" /> -</div> - -<hr class="chap x-ebookmaker-drop" /> - -<p><span class="pagenum" id="Page238">[238]</span></p> - -<div class="container w40em" id="Fig293"> -<img src="images/illo238.png" alt="Practice figure" /> -<p class="caption">Fig. 293. See <a href="#Page244">page 244</a>.</p> -</div> - -<hr class="chap x-ebookmaker-drop" /> - -<div class="chapter"> - -<p><span class="pagenum" id="Page239">[239]</span></p> - -<h2 class="nobreak">Useful Hints and “Points.”</h2> - -</div><!--chapter--> - -<p>Many of these “points” are repetitions, with but little variation from the way they have been previously -stated; they are thus repeated to emphasize their practical worth.</p> - -<p>A good draughtsman leaves his work in such a -state that any competent person can without difficulty -ink in what he has drawn.</p> - -<p>The criterion of a good set of drawings is that -with a properly prepared specification they are complete -in themselves and require no explanation.</p> - -<p>A “break” in a figure or object in a drawing is -shown in rough irregular lines, as in <a href="#Fig134">fig. 134</a>, on <a href="#Page131">page -131</a>; this is useful when the paper is not large enough -to show the whole.</p> - -<p>Never use a sloping line in writing fractions on a -drawing. The objection arises from the fact that such -a dimension as 1<sup>3</sup>⁄<sub>16</sub>, if written with the inclined line, -unless very distinctly executed, may be read as <sup>13</sup>⁄<sub>16</sub>.</p> - -<p>In inking do not draw the lines further than you -wish them to go, but in penciling it is well to extend -the lines, free up.</p> - -<p>Never use a scale for a ruler.</p> - -<p>Do not overload the pen with ink.</p> - -<p><span class="pagenum" id="Page240">[240]</span></p> - -<p>Having filled the pen, nearly close the nibs and -try the width of the line on a piece of paper or the -margin of the drawing.</p> - -<p>Never refill or lay the pen aside without first cleaning -it.</p> - -<p>The application of the science of geometry to the -drawing-board is absolutely necessary to success, for -the reason that the whole fabric of mechanical drawing -rests on the principles of geometry, which is well -termed the science of measurements.</p> - -<p>Section lines should be the last inked and always -without previous penciling.</p> - -<p>Center lines are necessary in working drawings.</p> - -<p>In choosing T-squares, care should be exercised to -see that the head slides up and down the <i>left</i>-hand side -of the board easily, and that when pressed against the -board with the left hand there is no “slogging” of the -blade up or down, or in other words, that the head is -bearing firmly for its whole length against the board.</p> - -<p>The best place for the title of a drawing is said to -be the upper left-hand corner; this facilitates the filing -of the sheet.</p> - -<p>Never use a soft pencil except for finishing in -shadow lines.</p> - -<p>The rubber should always be kept clean.</p> - -<p>Great care should be taken to keep drawing boards -out of the way of heat or damp, as these cause the -wood to warp.</p> - -<p>Circles and curves are to be “inked in” before -straight lines. First ink the smallest and afterwards -the larger curves.</p> - -<p>Do not press heavily on the pencil so as to cut the -paper, but draw lightly, so that the mark can be erased -and leave no trace, especially if the drawing is to be -inked.</p> - -<p>The draughtsman should commence his work at -the top of the paper, keeping the lower part covered -over until he needs to use it.</p> - -<p><span class="pagenum" id="Page241">[241]</span></p> - -<p>Shade lines should be avoided in all working -drawings, as their use interferes with accurate measurements.</p> - -<p>To make ink stick to the tracing cloth, with a -woolen cloth rub some powdered chalk or pounce over -the surface on which the ink lines are to be drawn, then -wipe the surface clean and use a good quality of ink.</p> - -<p>For striking small circles a small bow pen should -be used.</p> - -<p>To fix lead pencil marks on sketches so that they -cannot be readily erased, sponge them with milk carefully -skimmed, then lay blotting paper over them and -iron with a hot flat-iron.</p> - -<p>To have the ink preserve its fluidity and to keep -out all dirt and dust, keep the cover on the ink slab; -the mistake is often made of putting too liberal a supply -of water in ink well, which causes a waste of both -time and ink; no more should be prepared than to -meet immediate requirements.</p> - -<p>Always draw on the right side of the sheet, which -can be found by holding the sheet up to the light and -looking across its surface with the eye nearly in the -same plane as the paper; note which side is the smoothest -and has the least number of blemishes on it; this is -the right side to draw on.</p> - -<p>As to sharpening pencils, it is always best to cut a -chisel point on the pencil used for drawing, and put a -circular point on the pencils in the bow pencil and -pencil leg. The chisel point makes a finer line and -lasts much longer than a round point.</p> - -<p>The varnish used in many large drawing-rooms is -simply white shellac dissolved in alcohol; it requires a -little experience to mix these to a proper consistency, -but this is soon acquired.</p> - -<p>Never sharpen your pencil over the drawing.</p> - -<p>A center line of a drawing is the line upon which -the figure is to be constructed; the center line is the -first line to be drawn.</p> - -<p><span class="pagenum" id="Page242">[242]</span></p> - -<p>The T-square belongs to the left side of the drawing-board, -and is operated by the left hand. The right -hand should be kept free for the purpose of picking up -pencil, pen and bows, adjusting and marking off. The -left hand controls the T-square and the triangle that -slides along the upper edge of the square; the right -hand is for the instruments.</p> - -<p>The advantage of a paper rule or scale is that the -paper will expand and contract under varying degrees -of atmospheric moisture the same as the drawing does.</p> - -<p>Avoid rubbing out and constantly cleaning the -drawing with India rubber; if wrong lines are made or -it is desired to make alterations, the part to be changed -should be rubbed out and completely re-drawn.</p> - -<p>When using the bows see to it that the steel-pointed -leg that is put down first on the paper, to -secure a center for a curve or a circle, is a trifle longer -than the pencil or pen leg.</p> - -<p>To clearly indicate the position of a center which -is to be used again, lightly pencil a small circle about -it; never put the point of a pencil in the center hole -to enlarge or blacken it; the prick point made by the -dividers and needle points should be no more than can -be just seen, hence the circle to be made as advised -above.</p> - -<div class="container rightfloat w07em" id="Fig294"> -<img src="images/illo244.jpg" alt="Drawing case" /> -<p class="caption">Fig. 294.</p> -</div> - -<p>Be particular in having the legs of the dividers -exactly the same length, and sharp, so that in pricking -off distances, and dimensions, and centers, the indent -or hole made in the paper is as small as possible.</p> - -<p>The term “plane” means a perfectly flat surface; -that is, something which has length and breadth but -no thickness.</p> - -<p>The best way to indicate on the drawing the surfaces -which are to be finished is to write on the lines -which represent the finished surfaces “finished,” tool-finish, -or “faced,” according to the degree of finish required. -The single letter <i>f</i> is frequently used.</p> - -<p>Avoid fingering the drawing sheet as much as possible; -in pointing to any part of the drawing use a -pencil and not the finger.</p> - -<p>Remember that a drawing is made to be read.</p> - -<p><span class="pagenum" id="Page243">[243]</span></p> - -<p>The skill in inking does not depend on the fineness -of the line, but on its clearness.</p> - -<p>A soft pencil should never be used on a mechanical -drawing unless in rare cases when it is used for pencil -shading; the hardness or softness of pencils is denoted -by letters.</p> - -<p>Never ink any portion of a drawing until the -penciling is entirely finished.</p> - -<p>Stretching or pasting the paper to the board is -very seldom resorted to, for the reason that the -mechanical drawings are <i>to scale</i> and the paper is -natural when pinned to the board and more correct -than if under a strain. Mechanical drawings are -always required in practice <i>right away</i>, and time would -be wasted and lost in damping and pasting and drying -again.</p> - -<p>A working drawing, whether made to a scale or -not, must have all the dimensions plainly written upon -it, for a workman should never be compelled to measure -a drawing.</p> - -<p>In marking off distances, centers, etc., a fine needle -point is useful; the hole should not be punctured -through the paper, merely a prick point, so that it -will leave an impression, which will not be obliterated -by the use of rubber; drawing-pens are often equipped -with such a needle point in the end of the handle, -that is visible only when the pen is unscrewed from -the handle; but in the absence of one of this kind the -point of the divider leg will be of use.</p> - -<p>Mechanical construction drawings represent a large -amount of mental and manual work, as well as a considerable -cost in money; hence, they are of value quite -as much as property which has been acquired by the -expenditure of either labor or capital. It is wise to -keep copies of original designs and sketches, as well as -data and formulæ, for record and comparison.</p> - -<p>The best system for keeping drawings is to make -them of certain standard sizes, and to keep them flat, -unrolled, in drawers, numbered, lettered and labeled.</p> - -<p><span class="pagenum" id="Page244">[244]</span></p> - -<p>In an office where space is limited and drawings -have to be rolled it is well to use a number of pasteboard -cases about three feet long and three inches in -diameter. These are shown in <a href="#Fig294">fig. 294</a>.</p> - -<p>A puncture can be made near the top and, when a -new drawing or blue-print is inserted in this cylindrical -case, a cardboard tag can be looped through the puncture. -This label will give the title and number of -drawings in that case.</p> - -<p>A manuscript book methodically and neatly kept -should tell immediately the number of the drawing -and the case.</p> - -<p><a href="#Fig293">Fig. 293</a> is good for practice in line drawing and -also as an optical illusion. “You look and are deceived. -At first glance you say, ‘Of course, those two -lines are curved.’ You are mistaken. They are exactly -parallel. In order to prove this hold them up edgewise -to the eye. It is, of course, the subsidiary lines which -lead the vision astray. It is a case of first impressions -being quite wrong.”</p> - -<hr class="chap x-ebookmaker-drop" /> - -<p><span class="pagenum" id="Page245">[245]</span></p> - -<div class="container w30em"> -<img src="images/illo245.png" alt="LINEAR PERSPECTIVE" /> -</div> - -<hr class="chap x-ebookmaker-drop" /> - -<p><span class="pagenum" id="Page246">[246]</span></p> - -<div class="container" id="Fig295"> -<img src="images/illo246.jpg" alt="Fishing boy" /> -<p class="caption">Fig. 295.</p> -</div> - -<hr class="chap x-ebookmaker-drop" /> - -<div class="chapter"> - -<p><span class="pagenum" id="Page247">[247]</span></p> - -<h2 class="nobreak">Linear Perspective.</h2> - -</div><!--chapter--> - -<p>It should be mentioned that this subject is outside -the limits of mechanical drawing, which only deals -with objects that can be measured, projected or -dimensioned to an accurate scale.</p> - -<p>But, in rounding out the more formal subjects it -is well to look a little outside the rigid lines of mechanics -into the methods of nature, for no system of -teaching drawing is complete that does not include -some explanations for sketching from nature—the -objects being always around the student, the eye -always clear to see and the hand only needing -the training to make permanent the impressions received.</p> - -<p>The word perspective means to <i>see through</i>; the -word perspective being derived from the Latin word -<i>perspicere</i>, to look through, hence, perspective is a -science which teaches us to <i>see</i> correctly and enables -us to represent the <i>appearance</i> of anything we may -wish to draw; care should be taken in perspective -drawing, to select objects interesting in themselves, and -the best specimens of their class, so as to cultivate -taste, while they at the same time afford useful and -instructive drawing lessons.</p> - -<p>The meaning of the term linear perspective is a -line view; the previous examples have been composed -of surfaces placed fronting the eye; perspective is the -science which treats of the changes of form produced -by viewing them in various oblique positions.</p> - -<p><span class="pagenum" id="Page248">[248]</span></p> - -<p>The slightest alteration of <i>position</i> -will change the <i>appearance</i> -of an object; this can be easily -shown—for illustration take a coin, -the actual shape of which is a -perfect round; or, strictly speaking, -a circle. If we take the coin -between the thumb and the first -finger, holding it in an upright -position, and exactly facing the -eyes, as in <a href="#Fig296298">Fig. 296</a>, it appears of its true form, viz., a -circle. If we alter its position, balancing it upon the -thumb, in a level position, with its edge directly opposite -the eye, as in <a href="#Fig296298">Fig. 297</a>, its appearance is changed, -and what we know to be really a circle, appears to us -as a straight line.</p> - -<div class="container w40em" id="Fig296298"> -<img src="images/illo248.jpg" alt="Perspective" /> -<p class="caption">Fig. 296.—Fig. 297.—Fig. 298.</p> -</div> - -<p>Now, still balancing the coin upon the thumb, but -changing its position with regard to the eye, by holding -it a little lower than in the last position, that is slightly -beneath the level of the eye, as in <a href="#Fig296298">fig. 298</a>, we see both -the edge and the surface, the coin now appearing -neither a circle nor a straight line, but a curved figure -of an elliptical form. Thus the same coin held in three -different positions has assumed three different shapes.</p> - -<p>Let us take two coins of the same size, holding (in -the position shown at <a href="#Fig296298">fig. 296</a>) one in each hand. Now, -closing one eye, (which will make the experiment more -clear), hold one coin out -at arm’s length, and the -other at about the distance -of a foot from the eye. -On comparing them, we -find that the coin which -is further from the eye -appears less than the -nearer one. We know that -the coins are really equal -in size, yet one appears -smaller than the other.</p> - -<p><span class="pagenum" id="Page249">[249]</span></p> - -<p>We thus see that when we change the position of -an object, we have as a consequence a change of -appearance; also that the change of appearance may -affect both the shape and the size of the object.</p> - -<p>These diversities of appearance may be remarked -in everything around us. We can observe them in the -street by looking at a building from different points of -view, or by comparing the apparent sizes of the street -lamps; in the railway station, by watching the arriving -or departing train; and at sea, by noticing the vessels -as they approach, or as they retire, ultimately vanishing -from our sight in that line where the sea and sky -appear to meet.</p> - -<p>All these interesting variations of appearance are -in strict accordance with the laws of <b>GEOMETRY</b> and -<b>OPTICS</b>. The former subject has been enlarged upon -beginning with <a href="#Page81">page 81</a> of this work, where a line, a -point, an angle, etc., are defined; other terms are -explained at <a href="#Page41">page 41</a> and the following pages; to these -we add a few definitions essential to the subject.</p> - -<p><b>A PLANE</b> is a surface which is perfectly even and -flat; to use a familiar illustration, a plane is like the -surface of a sheet of plate glass; recollect particularly, -that a surface which is at all curved, is not a plane.</p> - -<p>The <b>GROUND-PLANE</b> is the plane on which we -stand; the <i>base-line</i> is an imaginary line passing -through the middle of the feet as we stand square and -erect; and the <i>vertical plane</i> is supposed to stand -on the base-line and perpendicular to it.</p> - -<div class="container" id="Fig299"> -<img src="images/illo249.png" alt="Perspective" /> -<p class="caption">Fig. 299.—See <a href="#Page255">page 255</a>.</p> -</div> - -<p><span class="pagenum" id="Page250">[250]</span></p> - -<p>Planes are parallel to each other when they are -throughout their entire surfaces the same distance -apart.</p> - -<div class="container w30em" id="Fig300"> -<img src="images/illo250a.png" alt="View plane" /> -<p class="caption">Fig. 300.</p> -</div> - -<p><b>THE PERSPECTIVE PLANE</b> is an upright square -of glass, usually framed like a picture, with a base, so that -it can stand up alone. This is placed between the eye -of the spectator and the subject to be drawn, and as -the drawing is sometimes made directly upon it, it is -sometimes called the <i>Picture</i> or the <i>Plane of the -Picture</i>.</p> - -<div class="container w30em" id="Fig301"> -<img src="images/illo250b.png" alt="House" /> -<p class="caption">Fig. 301.</p> -</div> - -<p><b>HORIZONTAL</b> means perfectly level, like the surface -of still water. We must be careful to understand -perfectly the difference between the terms “level” and -“even” or “flat.” A surface may be even or flat, -without being level. Thus the wall is even and flat, -but it is upright, not level; level means a fixed, constant -position.</p> - -<p><span class="pagenum" id="Page251">[251]</span></p> - -<p>In <a href="#Fig301">fig. 301</a> a house is shown in perspective in -which the line <i>H L</i> is the line of the horizon and <i>V P</i> -is <span class="nowrap">the,—</span></p> - -<p><b>VANISHING POINT.</b>—The vanishing point is familiarly -represented by the rails on a trolley track on a -straight road, which seem to approach each other in the -distance, as shown in <a href="#Fig302">fig. 302</a> at <i>V P</i>.</p> - -<div class="container w40em" id="Fig302"> -<img src="images/illo251a.jpg" alt="Perspective" /> -<p class="caption">Fig. 302.</p> -</div> - -<p><i>All parallel lines seen in perspective appear to meet -in the same vanishing point.</i></p> - -<p>The value of the vanishing point may be seen in -the view of a wooden house, <a href="#Fig303">fig. 303</a>, where it (<i>V P</i>) -gives direction to the retiring lines of the roof, side -planks and door.</p> - -<div class="container w40em" id="Fig303"> -<img src="images/illo251b.png" alt="Perspective" /> -<p class="caption">Fig. 303.</p> -</div> - -<p><b>POINT OF SIGHT.</b>—This is that point in the eye -where the lines or rays from the object cross each -other, as shown at <i>P</i> in <a href="#Fig305">fig. 305</a>, also in <a href="#Fig299">fig. 299</a> at <i>S</i>.</p> - -<p><b>VERTICAL</b> means perfectly upright. If we attach -a piece of thread to a weight, a small piece of lead for<span class="pagenum" id="Page252">[252]</span> -example, and hold the thread with the lead hanging -downwards, the thread will fall in an upright or vertical -position.</p> - -<p><b>PARALLEL</b> lines are said to be parallel to each -other when they are throughout their whole lengths -the same distance apart.</p> - -<p><b>PERPENDICULAR.</b> When one straight line, meeting -another, makes the angles at the point of contact -equal, each of the angles is called a right angle, and -the lines are said to be perpendicular to each other. -Remember especially that perpendicular and vertical -have not the same meaning. Vertical means an unvarying -upright position. Perpendicular means that -one line or plane meets another line or plane at right -angles.</p> - -<p>The <a href="#Fig295">fig. 295</a> on <a href="#Page246">page 246</a> is a study in perspective, -showing a water reflection. As rays from every visible -part of the object are reflected, all following the same -law, the reflection will appear to the eye <i>inverted</i>, and -of the <i>same size as the object</i>. The arch itself forms -the upper half of a hollow cylinder, and the reflection -forms the lower half. The reflection shows much -more of the interior of the arch than can be seen -directly. The leaning tree, the boy fishing, and the -receding banks, all are seen in accordance with the laws -of reflection and perspective.</p> - -<p><b>THE HORIZONTAL LINE, THE POINT OF -SIGHT AND THE VANISHING POINTS</b> are the principal -items. These should be studied in every room -and during every walk, and the more pleasing accidents -of form stored in the mind or committed to paper for -future use.</p> - -<div class="container leftfloat w15em" id="Fig304"> -<img src="images/illo253a.jpg" alt="Eye" /> -<p class="caption">Fig. 304.</p> -</div> - -<p><b>OPTICS</b>, the science of sight, gives us the following -laws:</p> - -<p>1. That we see by the agency of light.</p> - -<p>2. That light passes from objects to our eyes.</p> - -<p>3. That light travels in straight lines, which are -called Visual Rays.</p> - -<p><span class="pagenum" id="Page253">[253]</span></p> - -<p>The human eye may be briefly described as a -chamber of a spherical or globular form, with a circular -opening in front. This circular -opening is called the pupil, and -through it the visual rays pass to -the interior of the eye. The visual -rays, passing from space in all directions -through the small pupil, are -received upon what may be called the interior wall of -the globular chamber forming the eye (see <a href="#Fig305">fig. 305</a>). -This interior wall is called the retina, and upon it the -impressions of external objects are received, just as -they are received upon a screen in a dark chamber. -These impressions are conveyed by the optic nerve -from the retina to the brain.</p> - -<p>In front of the pupil is a segment of a small -sphere, composed of the cornea and the aqueous -humor, both of which are transparent, and from their -shape and density have a convergent effect upon the -rays passing through them.</p> - -<p>Behind the pupil is the transparent crystalline lens, -which, from its shape and its elasticity, is a powerful -agent in aiding the convergence of the rays, and in -bringing objects at various distances to a clear focus -upon the retina.</p> - -<div class="container w40em" id="Fig305"> -<img src="images/illo253b.png" alt="Eye" /> -<p class="caption">Fig. 305.</p> -</div> - -<p>The pupil has the power of contraction and dilation, -which is influenced by the quantity of light entering -the eye, but when it is dilated to the utmost its<span class="pagenum" id="Page254">[254]</span> -size is very small in comparison with the great chamber -forming the body of the eye.</p> - -<p>In <a href="#Fig305">fig. 305</a> we have a rough sectional diagram of -the eye and an object in front of it. This object, an -arrow, is seen by means of the visual rays proceeding -from it, the principal two of which are shown. The -visual ray from <i>A</i> passes through the pupil and is -received upon the retina at <i>a</i>. In the same way the -visual ray from <i>B</i> passes through the pupil and is -received upon the retina at <i>b</i>. It will thus be seen -that the impressions or images received upon the -retina are inverted; but, by long reason and experience, -the mind has acquired the habit of determining -the real positions of objects, and does not, though -the image is so received, imagine them to be upside -down.</p> - -<p>It will also be observed, in the same way, that that -portion of an object which is upon the right will be -pictured upon the retina upon the left, and <i>vice versa</i>, -but the mind, for the reasons before stated, never -imagines the object to be reversed. This fact is -another proof that, as mentioned at the commencement -of our study, to see accurately is a matter of education -and practice.</p> - -<p>And first of Optics; it was asserted, <a href="#Page252">page 252</a>, that -we see by the agency of light which passes from objects -to our eyes in straight lines which are called Visual -Rays.</p> - -<p>We see by the agency of light, as all objects, -except such as may be styled self-luminous, when -placed in a dark chamber are not perceivable by us, -except by touch, smell or hearing; we cannot <i>see</i> -them; they are invisible. But when, by removing a -shutter or igniting a flame, we introduce something to -the chamber which was not present when the chamber -was dark, we become at once conscious of the appearance -of the object, we perceive it by the sense of sight.</p> - -<p>This something which must always be present to -enable us to see, is called Light; all objects are made -visible to the sense of seeing by its agency.</p> - -<p><span class="pagenum" id="Page255">[255]</span></p> - -<p>Without light, natural or artificial, it would be -impossible to distinguish one object from another.</p> - -<div class="container w30em" id="Fig306"> -<img src="images/illo255.jpg" alt="Experiment" /> -<p class="caption">Fig. 306.</p> -</div> - -<p>That the Visual Rays pass from objects in straight -lines to the eye may be proved by the following -experiment (see <a href="#Fig306">fig. 306</a>):—Pierce two screens with a -large pin, and place them so that the holes are in a -straight line with a flame, as the light of a candle or -lamp. On fixing the eye to one of these holes we are -able to see the flame; but if we slightly move the -flame, one of the screens, or the eye, the flame is no -longer visible. To be visible, the flame, the holes in -the screens, and the eye must all be in the same straight -line. See <a href="#Fig306">fig. 306</a>.</p> - -<p>In <a href="#Fig299">fig. 299</a> the picture plane is represented by -the rectangle <i>W X Y Z</i>. Although the picture plane -is here shown as a rectangle, it may be of any shape -or of any size.</p> - -<p>The observer is at <i>S</i>, looking through the picture -plane at the cross <i>R C O H</i>. The observer is standing -upon a horizontal surface, which is called the ground -plane. If we are in a room, the window may be called -a picture plane and the floor a ground plane.</p> - -<p>The picture plane rests, as it were, upon the -ground plane, in a line which passes from <i>Y</i> to <i>Z</i>. The<span class="pagenum" id="Page256">[256]</span> -two planes meet or intersect in this line, which is called -the ground line. The ground line is sometimes called -the picture line, or the measuring line.</p> - -<p>The visual rays, by means of which the observer -sees the cross, will, in their course from it to the eye, -pass through the picture plane. These visual rays will -intersect the picture plane in a number of points, and -if we mark the true positions of these points the result -will be a perspective image of the cross.</p> - -<p>The rays are shown passing from the cross to the -eye of the observer, and meeting the picture plane in -points <i>r</i>, <i>c</i>, <i>o</i>, <i>h</i>; <i>r</i> being joined to <i>o</i>, and <i>c</i> to <i>h</i>, we -have the perspective image of the cross as it would -appear to the observer at <i>S</i>. Of course an infinite -number of rays proceed from the cross to the eye -of the observer; but it is quite evident that we need -only consider those proceeding from the extremities of -the object.</p> - -<hr class="chap x-ebookmaker-drop" /> - -<div class="chapter"> - -<p><span class="pagenum" id="Page257">[257]</span></p> - -<h2 class="nobreak">Scale or Approximate Perspective.</h2> - -</div><!--chapter--> - -<p>Real, or true perspective, represents the object exactly as it is seen in nature, where the parts that are -far away from the eye of the observer appear smaller than those nearby. Occasions arise, however, in practical -life, with its numerous phases of industrial requirements, where the convenience of showing the complete form -of the object in a single view might preferably be coupled with the convenience of scale dimensions.</p> - -<p>This has led to a modified perspective, that sacrifices -some of the accuracy in the appearance of the -object to gain the advantage of scale dimensions; this -form of perspective may be distinguished by the -name—<i>approximate or scale perspective</i>—which does not -represent the object exactly as seen in nature, but -where those parts that are afar off are shown of the -same size as those that are near by, and where the -lines that run out into space are parallel to each other -and do not converge into a vanishing point.</p> - -<p>To represent an object in perspective, the horizon -and the point of vision will have to appear in the -drawing as the fundamental starting points.</p> - -<p>Three dimensions are distinguished for the fixing -of an object in space from a certain reference point. -They are height, breadth and thickness, and are in -their direction square to each other. The height is the -fundamental direction, being derived from the direction -of gravity, that invariably extends to the center of -the earth.</p> - -<p>All directions in the perspective determination of -an object are parallel to these.</p> - -<p>Vertical lines and planes point toward the center -of the earth, while horizontal planes, including the -directions of breadth and thickness, are square to the -vertical direction. In this, the principal visual ray -extends in the direction of thickness.</p> - -<p><span class="pagenum" id="Page258">[258]</span></p> - -<p>For a clear understanding of perspective, it must be firmly fixed in mind, that for each prominent point of -the object behind the picture plane, a corresponding point lies in the picture plane, in that position where a -straight line or ray of sight that is going -from the eye to the point of the object, -cuts through the picture plane.</p> - -<p>Suppose we could replace these rays -of sight by thin, visible threads of wire -that would go through little holes in -the picture plane, we could then walk -around this bundle of rays, and by looking -at it from three different directions, -we would get three different views of -it. We may look upon it from the top, -from the side or from the end, where the -bundle of rays all concentrate in the eye -of the observer.</p> - -<div class="container" id="Fig307"> -<img src="images/illo258.png" alt="Viewpoints" /> -<p class="caption">Fig. 307.</p> -</div> - -<p><a href="#Fig307">Figs. 307</a> and <a href="#Fig308">308</a> show, in two cases, how these three -views would appear. The end views are those where -the perspective picture appears on the plane, while the top and side views only show where the rays intersect -the picture plane. The top view shows how far, for example, point <i>A</i> is distant from -a vertical line <i>O Z</i>, while<span class="pagenum" id="Page259">[259]</span> -the side view shows how far point <i>A</i> is below horizontal line <i>O X</i>, which is at the same height above the -ground as the eye of the observer, <i>O</i>. Thus, all points of the cube can be located on the picture plane, and the -outlines of the cube reproduced in perspective.</p> - -<div class="container" id="Fig308"> -<img src="images/illo259.png" alt="Viewpoints" /> -<p class="caption">Fig. 308.</p> -</div> - -<p>Modified arrangements are shown in <a href="#Fig309">figs. 309</a> and -<a href="#Fig310">310</a> for parallel and angular perspective.</p> - -<p><span class="pagenum" id="Page260">[260]</span></p> - -<div class="container w30em" id="Fig309"> -<img src="images/illo260a.png" alt="Perspective" /> -<p class="caption">Fig. 309.</p> -</div> - -<p>The views are so arranged in relation to each other -that the picture plane in the top view is parallel to the -horizon and the ground-line, which latter is the intersection -of the picture plane with the level ground of -the end or perspective view. At the same time the -eye of the observer is in one and the same vertical line -for both views, two vanishing points may be found in -the horizon outside of the principal visual ray. To -find the position of these two vanishing points in -the picture plane, the modified top view, <a href="#Fig310">fig. 310</a>, is -used.</p> - -<div class="container w40em" id="Fig310"> -<img src="images/illo260b.png" alt="Perspective" /> -<p class="caption">Fig. 310.</p> -</div> - -<p><span class="pagenum" id="Page261">[261]</span></p> - -<p>As all lines that end in a vanishing point must be -parallel in reality, this parallelism may be seen in the -top view and lines through the eye of the observer, -parallel to the directions of the main lines of the object, -will cut the picture plane at the vanishing points.</p> - -<p>Through these two vanishing points the directions -of two sets of lines are found, the starting points of -which are determined from the plane of measurement. -The third set of lines, being vertical, also appears vertical -and parallel in the picture.</p> - -<p>The position of each vertical line is found in the -top view, where the light rays from the observing eye -to the ends of the vertical lines intersect with the -picture plane. Projecting these points down upon the -rays to the vanishing points produces the vertical lines -in the picture.</p> - -<p>For example, in <a href="#Fig311">fig. 311</a>, the purpose of perspective -is entirely defeated by placing the eye of the observer -directly in front of the object and arriving at the view -taken in mechanical drawing which needs supplementary -views for complete comprehension of the form of -the object.</p> - -<div class="container w40em" id="Fig311"> -<img src="images/illo261.png" alt="Defeated perspective" /> -<p class="caption">Fig. 311.</p> -</div> - -<p>In <a href="#Fig312">fig. 312</a> the eye of the observer is first placed directly -opposite the object, then it sees the object to the -left but a short distance away, while in the third figure -the observer is farther away from -the object. In each case the -picture plane and plane of measurement -is at the front face of -the cube.</p> - -<p><span class="pagenum" id="Page262">[262]</span></p> - -<div class="container" id="Fig312"> -<img src="images/illo262.png" alt="Perspective" /> -<p class="caption">Fig. 312.</p> -</div> - -<p><span class="pagenum" id="Page263">[263]</span></p> - -<div class="container w40em"> -<img src="images/illo263.png" alt="Perspective" /> -<p class="caption">Fig. 312 (second part).</p> -</div> - -<p>For such simple objects, it is -not necessary to draw the top view -at all. The only reminder of the -top view is the eye or point of -vision, the picture plane that falls -together for the sake of convenience -with the horizon of the end -view and the ray that determines -the measurement point <i>M</i>, which -is, in this suppressed reproduction, -absolutely necessary, in order to -find the apparent position of the -real corners behind the picture -plane.</p> - -<p><span class="pagenum" id="Page264">[264]</span></p> - -<p>So far, only square or sharp-cornered objects have -been represented in perspective.</p> - -<p>It is evident, however, that round objects can also -be shown in linear perspective, placing reference lines -on the object and representing these as if they were real -lines. A cylinder is thus shown in <a href="#Fig313">fig. 313</a> of which the -end planes will appear very distinctly in sharp outlines.</p> - -<div class="container w30em" id="Fig313"> -<img src="images/illo264.png" alt="Cylinder" /> -<p class="caption">Fig. 313.</p> -</div> - -<p>Vertically, only the outlines of the cylinder, as contrasted -against space, will appear as distinct outlines, -while the reference lines will not appear and are therefore -shown only as dotted lines.</p> - -<p><a href="#Fig314">Fig. 314</a> shows the approximate or scale perspective -with all the axes drawn and the corresponding angles -and scales marked. The outlines of the object running -in these directions appear all parallel to the axes.</p> - -<p>The approximate or scale perspective completely -avoids all the difficulties of choosing a point of sight, -of having several views, vanishing points and measurement -points, and thus offers a representative view, with -a great saving of time and labor. Particularly for -mechanical purposes, where an artistic impression is -not called for, it presents a distinct advantage over the -true or real perspective.</p> - -<p><span class="pagenum" id="Page265">[265]</span></p> - -<div class="container" id="Fig314"> -<img src="images/illo265.png" alt="Perspective" /> -<p class="caption">Fig. 314.</p> -</div> - -<hr class="chap x-ebookmaker-drop" /> - -<p><span class="pagenum" id="Page266">[266-<br />267]</span><a id="Page267"></a></p> - -<div class="container w30em"> -<img src="images/illo267.png" alt="TABLES AND INDEX" /> -</div> - -<hr class="chap x-ebookmaker-drop" /> - -<p><span class="pagenum" id="Page268">[268]</span></p> - -<div class="container w20em"> -<img src="images/illo268.png" alt="" /> -<p class="caption">MARINERS’ COMPASS.</p> -</div> - -<hr class="chap x-ebookmaker-drop" /> - -<div class="chapter"> - -<p><span class="pagenum" id="Page269">[269]</span></p> - -<h2 class="nobreak">Useful Tables for Draughtsmen.</h2> - -</div><!--chapter--> - -<h3 class="center">TABLE OF DECIMAL EQUIVALENTS.<br /> -8ths, 16ths, 32ds and 64ths of an Inch.</h3> - -<table class="fracdec" summary="Decimal fractions"> - -<tr> -<td colspan="3" class="denom">8ths.</td> -</tr> - -<tr> -<td class="fraction"><sup>1</sup>⁄<sub>8</sub></td> -<td class="equals">=</td> -<td class="decimal">.125</td> -</tr> - -<tr> -<td class="fraction"><sup>1</sup>⁄<sub>4</sub></td> -<td class="equals">=</td> -<td class="decimal">.250</td> -</tr> - -<tr> -<td class="fraction"><sup>3</sup>⁄<sub>8</sub></td> -<td class="equals">=</td> -<td class="decimal">.375</td> -</tr> - -<tr> -<td class="fraction"><sup>1</sup>⁄<sub>2</sub></td> -<td class="equals">=</td> -<td class="decimal">.500</td> -</tr> - -<tr> -<td class="fraction"><sup>5</sup>⁄<sub>8</sub></td> -<td class="equals">=</td> -<td class="decimal">.625</td> -</tr> - -<tr> -<td class="fraction"><sup>3</sup>⁄<sub>4</sub></td> -<td class="equals">=</td> -<td class="decimal">.750</td> -</tr> - -<tr> -<td class="fraction"><sup>7</sup>⁄<sub>8</sub></td> -<td class="equals">=</td> -<td class="decimal">.875</td> -</tr> - -<tr> -<td colspan="3" class="denom">16ths.</td> -</tr> - -<tr> -<td class="fraction"><sup>1</sup>⁄<sub>16</sub></td> -<td class="equals">=</td> -<td class="decimal">.0625</td> -</tr> - -<tr> -<td class="fraction"><sup>3</sup>⁄<sub>16</sub></td> -<td class="equals">=</td> -<td class="decimal">.1875</td> -</tr> - -<tr> -<td class="fraction"><sup>5</sup>⁄<sub>16</sub></td> -<td class="equals">=</td> -<td class="decimal">.3125</td> -</tr> - -<tr> -<td class="fraction"><sup>7</sup>⁄<sub>16</sub></td> -<td class="equals">=</td> -<td class="decimal">.4375</td> -</tr> - -<tr> -<td class="fraction"><sup>9</sup>⁄<sub>16</sub></td> -<td class="equals">=</td> -<td class="decimal">.5625</td> -</tr> - -<tr> -<td class="fraction"><sup>11</sup>⁄<sub>16</sub></td> -<td class="equals">=</td> -<td class="decimal">.6875</td> -</tr> - -<tr> -<td class="fraction"><sup>13</sup>⁄<sub>16</sub></td> -<td class="equals">=</td> -<td class="decimal">.8125</td> -</tr> - -<tr> -<td class="fraction"><sup>15</sup>⁄<sub>16</sub></td> -<td class="equals">=</td> -<td class="decimal">.9375</td> -</tr> - -<tr> -<td colspan="3" class="denom">32nds.</td> -</tr> - -<tr> -<td class="fraction"><sup>1</sup>⁄<sub>32</sub></td> -<td class="equals">=</td> -<td class="decimal">.03125</td> -</tr> - -<tr> -<td class="fraction"><sup>3</sup>⁄<sub>32</sub></td> -<td class="equals">=</td> -<td class="decimal">.09375</td> -</tr> - -<tr> -<td class="fraction"><sup>5</sup>⁄<sub>32</sub></td> -<td class="equals">=</td> -<td class="decimal">.15625</td> -</tr> - -<tr> -<td class="fraction"><sup>7</sup>⁄<sub>32</sub></td> -<td class="equals">=</td> -<td class="decimal">.21875</td> -</tr> - -<tr> -<td class="fraction"><sup>9</sup>⁄<sub>32</sub></td> -<td class="equals">=</td> -<td class="decimal">.28125</td> -</tr> - -<tr> -<td class="fraction"><sup>11</sup>⁄<sub>32</sub></td> -<td class="equals">=</td> -<td class="decimal">.34375</td> -</tr> - -<tr> -<td class="fraction"><sup>13</sup>⁄<sub>32</sub></td> -<td class="equals">=</td> -<td class="decimal">.40625</td> -</tr> - -<tr> -<td class="fraction"><sup>15</sup>⁄<sub>32</sub></td> -<td class="equals">=</td> -<td class="decimal">.46875</td> -</tr> - -<tr> -<td class="fraction"><sup>17</sup>⁄<sub>32</sub></td> -<td class="equals">=</td> -<td class="decimal">.53125</td> -</tr> - -<tr> -<td class="fraction"><sup>19</sup>⁄<sub>32</sub></td> -<td class="equals">=</td> -<td class="decimal">.59375</td> -</tr> - -<tr> -<td class="fraction"><sup>21</sup>⁄<sub>32</sub></td> -<td class="equals">=</td> -<td class="decimal">.65625</td> -</tr> - -<tr> -<td class="fraction"><sup>23</sup>⁄<sub>32</sub></td> -<td class="equals">=</td> -<td class="decimal">.71875</td> -</tr> - -<tr> -<td class="fraction"><sup>25</sup>⁄<sub>32</sub></td> -<td class="equals">=</td> -<td class="decimal">.78125</td> -</tr> - -<tr> -<td class="fraction"><sup>27</sup>⁄<sub>32</sub></td> -<td class="equals">=</td> -<td class="decimal">.84375</td> -</tr> - -<tr> -<td class="fraction"><sup>29</sup>⁄<sub>32</sub></td> -<td class="equals">=</td> -<td class="decimal">.90625</td> -</tr> - -<tr> -<td class="fraction"><sup>31</sup>⁄<sub>32</sub></td> -<td class="equals">=</td> -<td class="decimal">.96875</td> -</tr> - -<tr> -<td colspan="3" class="denom">64ths.</td> -</tr> - -<tr> -<td class="fraction"><sup>1</sup>⁄<sub>64</sub></td> -<td class="equals">=</td> -<td class="decimal">.015625</td> -</tr> - -<tr> -<td class="fraction"><sup>3</sup>⁄<sub>64</sub></td> -<td class="equals">=</td> -<td class="decimal">.046875</td> -</tr> - -<tr> -<td class="fraction"><sup>5</sup>⁄<sub>64</sub></td> -<td class="equals">=</td> -<td class="decimal">.078125</td> -</tr> - -<tr> -<td class="fraction"><sup>7</sup>⁄<sub>64</sub></td> -<td class="equals">=</td> -<td class="decimal">.109375</td> -</tr> - -<tr> -<td class="fraction"><sup>9</sup>⁄<sub>64</sub></td> -<td class="equals">=</td> -<td class="decimal">.140625</td> -</tr> - -<tr> -<td class="fraction"><sup>11</sup>⁄<sub>64</sub></td> -<td class="equals">=</td> -<td class="decimal">.171875</td> -</tr> - -<tr> -<td class="fraction"><sup>13</sup>⁄<sub>64</sub></td> -<td class="equals">=</td> -<td class="decimal">.203125</td> -</tr> - -<tr> -<td class="fraction"><sup>15</sup>⁄<sub>64</sub></td> -<td class="equals">=</td> -<td class="decimal">.234375</td> -</tr> - -<tr> -<td class="fraction"><sup>17</sup>⁄<sub>64</sub></td> -<td class="equals">=</td> -<td class="decimal">.265625</td> -</tr> - -<tr> -<td class="fraction"><sup>19</sup>⁄<sub>64</sub></td> -<td class="equals">=</td> -<td class="decimal">.296875</td> -</tr> - -<tr> -<td class="fraction"><sup>21</sup>⁄<sub>64</sub></td> -<td class="equals">=</td> -<td class="decimal">.328125</td> -</tr> - -<tr> -<td class="fraction"><sup>23</sup>⁄<sub>64</sub></td> -<td class="equals">=</td> -<td class="decimal">.359375</td> -</tr> - -<tr> -<td class="fraction"><sup>25</sup>⁄<sub>64</sub></td> -<td class="equals">=</td> -<td class="decimal">.390625</td> -</tr> - -<tr> -<td class="fraction"><sup>27</sup>⁄<sub>64</sub></td> -<td class="equals">=</td> -<td class="decimal">.421875</td> -</tr> - -<tr> -<td class="fraction"><sup>29</sup>⁄<sub>64</sub></td> -<td class="equals">=</td> -<td class="decimal">.453125</td> -</tr> - -<tr> -<td class="fraction"><sup>31</sup>⁄<sub>64</sub></td> -<td class="equals">=</td> -<td class="decimal">.484375</td> -</tr> - -<tr> -<td class="fraction"><sup>33</sup>⁄<sub>64</sub></td> -<td class="equals">=</td> -<td class="decimal">.515625</td> -</tr> - -<tr> -<td class="fraction"><sup>35</sup>⁄<sub>64</sub></td> -<td class="equals">=</td> -<td class="decimal">.546875</td> -</tr> - -<tr> -<td class="fraction"><sup>37</sup>⁄<sub>64</sub></td> -<td class="equals">=</td> -<td class="decimal">.578125</td> -</tr> - -<tr> -<td class="fraction"><sup>39</sup>⁄<sub>64</sub></td> -<td class="equals">=</td> -<td class="decimal">.609375</td> -</tr> - -<tr> -<td class="fraction"><sup>41</sup>⁄<sub>64</sub></td> -<td class="equals">=</td> -<td class="decimal">.640625</td> -</tr> - -<tr> -<td class="fraction"><sup>43</sup>⁄<sub>64</sub></td> -<td class="equals">=</td> -<td class="decimal">.671875</td> -</tr> - -<tr> -<td class="fraction"><sup>45</sup>⁄<sub>64</sub></td> -<td class="equals">=</td> -<td class="decimal">.703125</td> -</tr> - -<tr> -<td class="fraction"><sup>47</sup>⁄<sub>64</sub></td> -<td class="equals">=</td> -<td class="decimal">.734375</td> -</tr> - -<tr> -<td class="fraction"><sup>49</sup>⁄<sub>64</sub></td> -<td class="equals">=</td> -<td class="decimal">.765625</td> -</tr> - -<tr> -<td class="fraction"><sup>51</sup>⁄<sub>64</sub></td> -<td class="equals">=</td> -<td class="decimal">.796875</td> -</tr> - -<tr> -<td class="fraction"><sup>53</sup>⁄<sub>64</sub></td> -<td class="equals">=</td> -<td class="decimal">.828125</td> -</tr> - -<tr> -<td class="fraction"><sup>55</sup>⁄<sub>64</sub></td> -<td class="equals">=</td> -<td class="decimal">.859375</td> -</tr> - -<tr> -<td class="fraction"><sup>57</sup>⁄<sub>64</sub></td> -<td class="equals">=</td> -<td class="decimal">.890625</td> -</tr> - -<tr> -<td class="fraction"><sup>59</sup>⁄<sub>64</sub></td> -<td class="equals">=</td> -<td class="decimal">.921875</td> -</tr> - -<tr> -<td class="fraction"><sup>61</sup>⁄<sub>64</sub></td> -<td class="equals">=</td> -<td class="decimal">.953125</td> -</tr> - -<tr> -<td class="fraction"><sup>63</sup>⁄<sub>64</sub></td> -<td class="equals">=</td> -<td class="decimal">.984375</td> -</tr> - -</table> - -<p><span class="pagenum" id="Page270">[270]</span></p> - -<h3 class="center">TABLE OF DECIMAL EQUIVALENTS<br /> -Of Millimeters and Fractions of Millimeters.</h3> - -<table class="fracdec" summary="Millimeters"> - -<tr> -<th><i>mm.</i></th> -<th> </th> -<th><i>Inches.</i></th> -</tr> - -<tr> -<td class="mm"><sup>1</sup>⁄<sub>50</sub></td> -<td class="equals">=</td> -<td class="inch">.00079</td> -</tr> - -<tr> -<td class="mm"><sup>2</sup>⁄<sub>50</sub></td> -<td class="equals">=</td> -<td class="inch">.00157</td> -</tr> - -<tr> -<td class="mm"><sup>3</sup>⁄<sub>50</sub></td> -<td class="equals">=</td> -<td class="inch">.00236</td> -</tr> - -<tr> -<td class="mm"><sup>4</sup>⁄<sub>50</sub></td> -<td class="equals">=</td> -<td class="inch">.00315</td> -</tr> - -<tr> -<td class="mm"><sup>5</sup>⁄<sub>50</sub></td> -<td class="equals">=</td> -<td class="inch">.00394</td> -</tr> - -<tr> -<td class="mm"><sup>6</sup>⁄<sub>50</sub></td> -<td class="equals">=</td> -<td class="inch">.00472</td> -</tr> - -<tr> -<td class="mm"><sup>7</sup>⁄<sub>50</sub></td> -<td class="equals">=</td> -<td class="inch">.00551</td> -</tr> - -<tr> -<td class="mm"><sup>8</sup>⁄<sub>50</sub></td> -<td class="equals">=</td> -<td class="inch">.00630</td> -</tr> - -<tr> -<td class="mm"><sup>9</sup>⁄<sub>50</sub></td> -<td class="equals">=</td> -<td class="inch">.00709</td> -</tr> - -<tr> -<td class="mm"><sup>10</sup>⁄<sub>50</sub></td> -<td class="equals">=</td> -<td class="inch">.00787</td> -</tr> - -<tr> -<td class="mm"><sup>11</sup>⁄<sub>50</sub></td> -<td class="equals">=</td> -<td class="inch">.00866</td> -</tr> - -<tr> -<td class="mm"><sup>12</sup>⁄<sub>50</sub></td> -<td class="equals">=</td> -<td class="inch">.00945</td> -</tr> - -<tr> -<td class="mm"><sup>13</sup>⁄<sub>50</sub></td> -<td class="equals">=</td> -<td class="inch">.01024</td> -</tr> - -<tr> -<td class="mm"><sup>14</sup>⁄<sub>50</sub></td> -<td class="equals">=</td> -<td class="inch">.01102</td> -</tr> - -<tr> -<td class="mm"><sup>15</sup>⁄<sub>50</sub></td> -<td class="equals">=</td> -<td class="inch">.01181</td> -</tr> - -<tr> -<td class="mm"><sup>16</sup>⁄<sub>50</sub></td> -<td class="equals">=</td> -<td class="inch">.01260</td> -</tr> - -<tr> -<td class="mm"><sup>17</sup>⁄<sub>50</sub></td> -<td class="equals">=</td> -<td class="inch">.01339</td> -</tr> - -<tr> -<td class="mm"><sup>18</sup>⁄<sub>50</sub></td> -<td class="equals">=</td> -<td class="inch">.01417</td> -</tr> - -<tr> -<td class="mm"><sup>19</sup>⁄<sub>50</sub></td> -<td class="equals">=</td> -<td class="inch">.01496</td> -</tr> - -<tr> -<td class="mm"><sup>20</sup>⁄<sub>50</sub></td> -<td class="equals">=</td> -<td class="inch">.01575</td> -</tr> - -<tr> -<td class="mm"><sup>21</sup>⁄<sub>50</sub></td> -<td class="equals">=</td> -<td class="inch">.01654</td> -</tr> - -<tr> -<td class="mm"><sup>22</sup>⁄<sub>50</sub></td> -<td class="equals">=</td> -<td class="inch">.01732</td> -</tr> - -<tr> -<td class="mm"><sup>23</sup>⁄<sub>50</sub></td> -<td class="equals">=</td> -<td class="inch">.01811</td> -</tr> - -<tr> -<td class="mm"><sup>24</sup>⁄<sub>50</sub></td> -<td class="equals">=</td> -<td class="inch">.01890</td> -</tr> - -<tr> -<td class="mm"><sup>25</sup>⁄<sub>50</sub></td> -<td class="equals">=</td> -<td class="inch">.01969</td> -</tr> - -<tr> -<td class="mm"><sup>26</sup>⁄<sub>50</sub></td> -<td class="equals">=</td> -<td class="inch">.02047</td> -</tr> - -<tr> -<td class="mm"><sup>27</sup>⁄<sub>50</sub></td> -<td class="equals">=</td> -<td class="inch">.02126</td> -</tr> - -<tr> -<td class="mm"><sup>28</sup>⁄<sub>50</sub></td> -<td class="equals">=</td> -<td class="inch">.02205</td> -</tr> - -<tr> -<td class="mm"><sup>29</sup>⁄<sub>50</sub></td> -<td class="equals">=</td> -<td class="inch">.02283</td> -</tr> - -<tr> -<td class="mm"><sup>30</sup>⁄<sub>50</sub></td> -<td class="equals">=</td> -<td class="inch">.02362</td> -</tr> - -<tr> -<td class="mm"><sup>31</sup>⁄<sub>50</sub></td> -<td class="equals">=</td> -<td class="inch">.02441</td> -</tr> - -<tr> -<td class="mm"><sup>32</sup>⁄<sub>50</sub></td> -<td class="equals">=</td> -<td class="inch">.02520</td> -</tr> - -<tr> -<td class="mm"><sup>33</sup>⁄<sub>50</sub></td> -<td class="equals">=</td> -<td class="inch">.02598</td> -</tr> - -<tr> -<td class="mm"><sup>34</sup>⁄<sub>50</sub></td> -<td class="equals">=</td> -<td class="inch">.02677</td> -</tr> - -<tr> -<td class="mm"><sup>35</sup>⁄<sub>50</sub></td> -<td class="equals">=</td> -<td class="inch">.02756</td> -</tr> - -<tr> -<td class="mm"><sup>36</sup>⁄<sub>50</sub></td> -<td class="equals">=</td> -<td class="inch">.02835</td> -</tr> - -<tr> -<td class="mm"><sup>37</sup>⁄<sub>50</sub></td> -<td class="equals">=</td> -<td class="inch">.02913</td> -</tr> - -<tr> -<td class="mm"><sup>38</sup>⁄<sub>50</sub></td> -<td class="equals">=</td> -<td class="inch">.02992</td> -</tr> - -<tr> -<td class="mm"><sup>39</sup>⁄<sub>50</sub></td> -<td class="equals">=</td> -<td class="inch">.03071</td> -</tr> - -<tr> -<td class="mm"><sup>40</sup>⁄<sub>50</sub></td> -<td class="equals">=</td> -<td class="inch">.03150</td> -</tr> - -<tr> -<td class="mm"><sup>41</sup>⁄<sub>50</sub></td> -<td class="equals">=</td> -<td class="inch">.03228</td> -</tr> - -<tr> -<td class="mm"><sup>42</sup>⁄<sub>50</sub></td> -<td class="equals">=</td> -<td class="inch">.03307</td> -</tr> - -<tr> -<td class="mm"><sup>43</sup>⁄<sub>50</sub></td> -<td class="equals">=</td> -<td class="inch">.03386</td> -</tr> - -<tr> -<td class="mm"><sup>44</sup>⁄<sub>50</sub></td> -<td class="equals">=</td> -<td class="inch">.03465</td> -</tr> - -<tr> -<td class="mm"><sup>45</sup>⁄<sub>50</sub></td> -<td class="equals">=</td> -<td class="inch">.03543</td> -</tr> - -<tr> -<td class="mm"><sup>46</sup>⁄<sub>50</sub></td> -<td class="equals">=</td> -<td class="inch">.03622</td> -</tr> - -<tr> -<td class="mm"><sup>47</sup>⁄<sub>50</sub></td> -<td class="equals">=</td> -<td class="inch">.03701</td> -</tr> - -<tr> -<td class="mm"><sup>48</sup>⁄<sub>50</sub></td> -<td class="equals">=</td> -<td class="inch">.03780</td> -</tr> - -<tr> -<td class="mm"><sup>49</sup>⁄<sub>50</sub></td> -<td class="equals">=</td> -<td class="inch">.03858</td> -</tr> - -<tr> -<td class="mm">1</td> -<td class="equals">=</td> -<td class="inch">.03937</td> -</tr> - -<tr> -<td class="mm">2</td> -<td class="equals">=</td> -<td class="inch">.07874</td> -</tr> - -<tr> -<td class="mm">3</td> -<td class="equals">=</td> -<td class="inch">.11811</td> -</tr> - -<tr> -<td class="mm">4</td> -<td class="equals">=</td> -<td class="inch">.15748</td> -</tr> - -<tr> -<td class="mm">5</td> -<td class="equals">=</td> -<td class="inch">.19685</td> -</tr> - -<tr> -<td class="mm">6</td> -<td class="equals">=</td> -<td class="inch">.23622</td> -</tr> - -<tr> -<td class="mm">7</td> -<td class="equals">=</td> -<td class="inch">.27559</td> -</tr> - -<tr> -<td class="mm">8</td> -<td class="equals">=</td> -<td class="inch">.31496</td> -</tr> - -<tr> -<td class="mm">9</td> -<td class="equals">=</td> -<td class="inch">.35433</td> -</tr> - -<tr> -<td class="mm">10</td> -<td class="equals">=</td> -<td class="inch">.39370</td> -</tr> - -<tr> -<td class="mm">11</td> -<td class="equals">=</td> -<td class="inch">.43307</td> -</tr> - -<tr> -<td class="mm">12</td> -<td class="equals">=</td> -<td class="inch">.47244</td> -</tr> - -<tr> -<td class="mm">13</td> -<td class="equals">=</td> -<td class="inch">.51181</td> -</tr> - -<tr> -<td class="mm">14</td> -<td class="equals">=</td> -<td class="inch">.55118</td> -</tr> - -<tr> -<td class="mm">15</td> -<td class="equals">=</td> -<td class="inch">.59055</td> -</tr> - -<tr> -<td class="mm">16</td> -<td class="equals">=</td> -<td class="inch">.62992</td> -</tr> - -<tr> -<td class="mm">17</td> -<td class="equals">=</td> -<td class="inch">.66929</td> -</tr> - -<tr> -<td class="mm">18</td> -<td class="equals">=</td> -<td class="inch">.70866</td> -</tr> - -<tr> -<td class="mm">19</td> -<td class="equals">=</td> -<td class="inch">.74803</td> -</tr> - -<tr> -<td class="mm">20</td> -<td class="equals">=</td> -<td class="inch">.78740</td> -</tr> - -<tr> -<td class="mm">21</td> -<td class="equals">=</td> -<td class="inch">.82677</td> -</tr> - -<tr> -<td class="mm">22</td> -<td class="equals">=</td> -<td class="inch">.86614</td> -</tr> - -<tr> -<td class="mm">23</td> -<td class="equals">=</td> -<td class="inch">.90551</td> -</tr> - -<tr> -<td class="mm">24</td> -<td class="equals">=</td> -<td class="inch">.94488</td> -</tr> - -<tr> -<td class="mm">25</td> -<td class="equals">=</td> -<td class="inch">.98425</td> -</tr> - -<tr> -<td class="mm">26</td> -<td class="equals">=</td> -<td class="inch">1.02362</td> -</tr> - -</table> - -<table class="fracdec" summary="Units"> - -<tr> -<td class="inch">10 mm.</td> -<td class="equals">=</td> -<td class="center">1</td> -<td class="inch">Centimeter</td> -<td class="equals">=</td> -<td class="center">0.3937</td> -<td class="inch">inches.</td> -</tr> - -<tr> -<td class="inch">10 cm.</td> -<td class="equals">=</td> -<td class="center">1</td> -<td class="inch">Decimeter</td> -<td class="equals">=</td> -<td class="center">3.937</td> -<td class="center">„</td> -</tr> - -<tr> -<td class="inch">10 dm.</td> -<td class="equals">=</td> -<td class="center">1</td> -<td class="inch">Meter</td> -<td class="equals">=</td> -<td class="center">39.37</td> -<td class="center">„</td> -</tr> - -<tr> -<td class="inch">25.4 mm.</td> -<td class="equals">=</td> -<td colspan="5" class="inch">1 English Inch.</td> -</tr> - -</table> - -<p><span class="pagenum" id="Page271">[271]</span></p> - -<h3 class="center">RULES RELATIVE TO THE CIRCLE.</h3> - -<p class="center highline4">The circle contains a greater area than any other plane figure bounded by -an equal perimeter or outline.</p> - -<p class="findwhat">TO FIND <span class="nowrap">CIRCUMFERENCE—</span></p> - -<table class="circle" summary="Properties"> - -<tr> -<td class="text">Multiply diameter by</td> -<td class="number">3.1416.</td> -</tr> - -<tr> -<td class="text">Or divide diameter by</td> -<td class="number">0.3183.</td> -</tr> - -</table> - -<p class="findwhat">TO FIND <span class="nowrap">DIAMETER—</span></p> - -<table class="circle" summary="Properties"> - -<tr> -<td class="text">Multiply circumference by</td> -<td class="number">0.3183.</td> -</tr> - -<tr> -<td class="text">Or divide circumference by</td> -<td class="number">3.1416.</td> -</tr> - -</table> - -<p class="findwhat">TO FIND <span class="nowrap">RADIUS—</span></p> - -<table class="circle" summary="Properties"> - -<tr> -<td class="text">Multiply circumference by</td> -<td class="number">0.15915.</td> -</tr> - -<tr> -<td class="text">Or divide circumference by</td> -<td class="number">6.28318.</td> -</tr> - -</table> - -<p class="findwhat">TO FIND SIDE OF AN INSCRIBED <span class="nowrap">SQUARE—</span></p> - -<table class="circle" summary="Properties"> - -<tr> -<td class="text">Multiply diameter by</td> -<td class="number">0.7071.</td> -</tr> - -<tr> -<td class="text">Or multiply circumference by</td> -<td class="number">0.2251.</td> -</tr> - -<tr> -<td class="text">Or divide circumference by</td> -<td class="number">4.4428.</td> -</tr> - -</table> - -<p class="findwhat">TO FIND SIDE OF AN EQUAL <span class="nowrap">SQUARE—</span></p> - -<table class="circle" summary="Properties"> - -<tr> -<td class="text">Multiply diameter by</td> -<td class="number">0.8862.</td> -</tr> - -<tr> -<td class="text">Or divide diameter by</td> -<td class="number">1.1284.</td> -</tr> - -<tr> -<td class="text">Or multiply circumference by</td> -<td class="number">0.2821.</td> -</tr> - -<tr> -<td class="text">Or divide circumference by</td> -<td class="number">3.545.</td> -</tr> - -</table> - -<p class="findwhat">SQUARE—</p> - -<table class="circle" summary="Properties"> - -<tr> -<td class="text">A side multiplied by</td> -<td colspan="3" class="number">1.4142 equals diameter of its circumscribing circle.</td> -</tr> - -<tr> -<td class="text">A side multiplied by</td> -<td colspan="3" class="number">4.443 equals circumference of its circumscribing circle.</td> -</tr> - -<tr> -<td class="text">A side multiplied by</td> -<td class="number">1.128 equals diameter</td> -<td rowspan="3" class="text"><span class="fsize300">}</span></td> -<td rowspan="3" class="text">of an<br />equal<br />circle.</td> -</tr> - -<tr> -<td class="text">A side multiplied by</td> -<td class="number">3.545 equals circumference</td> -</tr> - -<tr> -<td class="text">A side multiplied by</td> -<td class="number">1.273 equals circle inches</td> -</tr> - -</table> - -<p class="findwhat">TO FIND THE AREA OF A <span class="nowrap">CIRCLE—</span></p> - -<table class="circle" summary="Properties"> - -<tr> -<td colspan="2" class="text">Multiply circumference by one-quarter of the diameter.</td> -</tr> - -<tr> -<td class="text">Or multiply the square of diameter by</td> -<td class="number">0.7854.</td> -</tr> - -<tr> -<td class="text">Or multiply the square of circumference by</td> -<td class="number"> .07958.</td> -</tr> - -<tr> -<td class="text">Or multiply the square of <sup>1</sup>⁄<sub>2</sub> diameter by</td> -<td class="number">3.1416.</td> -</tr> - -</table> - -<p>Contents of cylinder = area of end × length. Contents of wedge = area of base × -<sup>1</sup>⁄<sub>2</sub> altitude. Surface of cylinder = area of -both ends × length × circumference. Surface of sphere = diameter squared × 3.1416, -or = diameter × circumference. Contents of -sphere = diameter cubed × .5236. Contents of pyramid or cone, right or oblique, -regular or irregular = area of base × <sup>1</sup>⁄<sub>3</sub> altitude. Area -of triangle = base × <sup>1</sup>⁄<sub>2</sub> altitude. Area of parallelogram -= base × altitude. Area of trapezoid = altitude × <sup>1</sup>⁄<sub>2</sub> the sum of parallel sides.</p> - -<p><span class="pagenum" id="Page272">[272]</span></p> - -<h3>ROMAN TABLE.</h3> - -<table class="roman" summary="numbers"> - -<tr> -<td class="number">I.</td> -<td class="equals">denotes</td> -<td class="text">One.</td> -</tr> - -<tr> -<td class="number">II.</td> -<td class="equals">„</td> -<td class="text">Two.</td> -</tr> - -<tr> -<td class="number">III.</td> -<td class="equals">„</td> -<td class="text">Three.</td> -</tr> - -<tr> -<td class="number">IV.</td> -<td class="equals">„</td> -<td class="text">Four.</td> -</tr> - -<tr> -<td class="number">V.</td> -<td class="equals">„</td> -<td class="text">Five.</td> -</tr> - -<tr> -<td class="number">VI.</td> -<td class="equals">„</td> -<td class="text">Six.</td> -</tr> - -<tr> -<td class="number">VII.</td> -<td class="equals">„</td> -<td class="text">Seven.</td> -</tr> - -<tr> -<td class="number">VIII.</td> -<td class="equals">„</td> -<td class="text">Eight.</td> -</tr> - -<tr> -<td class="number">IX.</td> -<td class="equals">„</td> -<td class="text">Nine.</td> -</tr> - -<tr> -<td class="number">X.</td> -<td class="equals">„</td> -<td class="text">Ten.</td> -</tr> - -<tr> -<td class="number">XI.</td> -<td class="equals">„</td> -<td class="text">Eleven.</td> -</tr> - -<tr> -<td class="number">XII.</td> -<td class="equals">„</td> -<td class="text">Twelve.</td> -</tr> - -<tr> -<td class="number">XIII.</td> -<td class="equals">„</td> -<td class="text">Thirteen.</td> -</tr> - -<tr> -<td class="number">XIV.</td> -<td class="equals">„</td> -<td class="text">Fourteen.</td> -</tr> - -<tr> -<td class="number">XV.</td> -<td class="equals">„</td> -<td class="text">Fifteen.</td> -</tr> - -<tr> -<td class="number">XVI.</td> -<td class="equals">„</td> -<td class="text">Sixteen.</td> -</tr> - -<tr> -<td class="number">XVII.</td> -<td class="equals">„</td> -<td class="text">Seventeen.</td> -</tr> - -<tr> -<td class="number">XVIII.</td> -<td class="equals">„</td> -<td class="text">Eighteen.</td> -</tr> - -<tr> -<td class="number">XIX.</td> -<td class="equals">„</td> -<td class="text">Nineteen.</td> -</tr> - -<tr> -<td class="number">XX.</td> -<td class="equals">„</td> -<td class="text">Twenty.</td> -</tr> - -<tr> -<td class="number">XXX.</td> -<td class="equals">„</td> -<td class="text">Thirty.</td> -</tr> - -<tr> -<td class="number">XL.</td> -<td class="equals">„</td> -<td class="text">Forty.</td> -</tr> - -<tr> -<td class="number">L.</td> -<td class="equals">„</td> -<td class="text">Fifty.</td> -</tr> - -<tr> -<td class="number">LX.</td> -<td class="equals">„</td> -<td class="text">Sixty.</td> -</tr> - -<tr> -<td class="number">LXX.</td> -<td class="equals">„</td> -<td class="text">Seventy.</td> -</tr> - -<tr> -<td class="number">LXXX.</td> -<td class="equals">„</td> -<td class="text">Eighty.</td> -</tr> - -<tr> -<td class="number">XC.</td> -<td class="equals">„</td> -<td class="text">Ninety.</td> -</tr> - -<tr> -<td class="number">C.</td> -<td class="equals">„</td> -<td class="text">One hundred.</td> -</tr> - -<tr> -<td class="number">D.</td> -<td class="equals">„</td> -<td class="text">Five hundred.</td> -</tr> - -<tr> -<td class="number">M.</td> -<td class="equals">„</td> -<td class="text">One thousand.</td> -</tr> - -<tr> -<td class="number">X̅.</td> -<td class="equals">„</td> -<td class="text">Ten thousand.</td> -</tr> - -<tr> -<td class="number">M̅.</td> -<td class="equals">„</td> -<td class="text">One million.</td> -</tr> - -</table> - -<h3>SOLID MEASURE, OR CUBIC MEASURE.</h3> - -<p>This is used in measuring bodies, or things having -length, breadth and height or depth.</p> - -<p class="tabhead">TABLE.</p> - -<table class="measures" summary="Measures"> - -<tr> -<td class="number">1728</td> -<td class="text">cubic inches (cu. in.)</td> -<td class="equals">make</td> -<td class="text">1 cubic foot (cu. ft.).</td> -</tr> - -<tr> -<td class="number">27</td> -<td class="text">cubic feet,</td> -<td class="equals">„</td> -<td class="text">1 cubic yard (cu. yd.).</td> -</tr> - -<tr> -<td class="number">128</td> -<td class="text">cubic feet,</td> -<td class="equals">„</td> -<td class="text">1 cord (C.).</td> -</tr> - -</table> - -<h3>CIRCULAR MEASURE.</h3> - -<table class="measures" summary="Measures"> - -<tr> -<td class="number">60</td> -<td class="text">seconds (″)</td> -<td class="equals">make</td> -<td class="text">1 minute (′).</td> -</tr> - -<tr> -<td class="number">60</td> -<td class="text">minutes</td> -<td class="equals">„</td> -<td class="text">1 degree (°).</td> -</tr> - -<tr> -<td class="number">360</td> -<td class="text">degrees</td> -<td class="equals">„</td> -<td class="text">1 circum. (C.).</td> -</tr> - -</table> - -<p>The circumference of every circle whatever, is -supposed to be divided into 360 equal parts, called -<i>degrees</i>.</p> - -<p>A degree is <sup>1</sup>⁄<sub>360</sub> of the circumference of any circle, -small or large.</p> - -<p>A quadrant is a fourth of a circumference, or an -arc of 90 degrees.</p> - -<p>A degree is divided into 60 parts called minutes, -expressed by the sign (′), and each minute is divided -into 60 seconds, expressed by (″); so that the circumference -of any circle contains 21,600 minutes, or -1,296,000 seconds.</p> - -<h3>LONG MEASURE—MEASURES OF LENGTH.</h3> - -<table class="measures" summary="Measures"> - -<tr> -<td class="number nomargin">12</td> -<td rowspan="2"> </td> -<td class="text">inches</td> -<td class="equals">=</td> -<td class="text">1 foot.</td> -</tr> - -<tr> -<td class="number nomargin">3</td> -<td class="text">feet</td> -<td class="equals">=</td> -<td class="text">1 yard.</td> -</tr> - -<tr> -<td class="number nomargin">5</td> -<td class="text"><sup>1</sup>⁄<sub>2</sub> </td> -<td class="text">yards</td> -<td class="equals">=</td> -<td class="text">1 rod.</td> -</tr> - -<tr> -<td class="number nomargin">40</td> -<td rowspan="3"> </td> -<td class="text">rods</td> -<td class="equals">=</td> -<td class="text">1 furlong.</td> -</tr> - -<tr> -<td class="number nomargin">8</td> -<td class="text">furlongs </td> -<td class="equals">=</td> -<td class="text">1 common mile.</td> -</tr> - -<tr> -<td class="number nomargin">3</td> -<td class="text">miles</td> -<td class="equals">=</td> -<td class="text">1 league.</td> -</tr> - -</table> - -<p>The mile (5,280 feet) of the above table is the -legal mile of the United States and England, and is -called the statute mile.</p> - -<p><span class="pagenum" id="Page273">[273]</span></p> - -<h2>Tables of Diameters, -Circumferences and Areas of Circles.</h2> - -<table class="diamarea" summary="Circles"> - -<tr class="btd bb"> -<th class="br">Diam.</th> -<th colspan="2" class="br">Area.</th> -<th colspan="2">Circum.</th> -</tr> - -<tr> -<td class="diam"> 0.0</td> -<td colspan="2" class="area br"> </td> -<td colspan="2" class="circumf"> </td> -</tr> - -<tr> -<td class="diam">  .1</td> -<td class="area int"> </td> -<td class="area dec">.007854</td> -<td class="circumf int"> </td> -<td class="circumf dec">.31416</td> -</tr> - -<tr> -<td class="diam">  .2</td> -<td class="area int"> </td> -<td class="area dec">.031416</td> -<td class="circumf int"> </td> -<td class="circumf dec">.62832</td> -</tr> - -<tr> -<td class="diam">  .3</td> -<td class="area int"> </td> -<td class="area dec">.070686</td> -<td class="circumf int"> </td> -<td class="circumf dec">.94248</td> -</tr> - -<tr> -<td class="diam">  .4</td> -<td class="area int"> </td> -<td class="area dec">.12566</td> -<td class="circumf int">1</td> -<td class="circumf dec">.2566</td> -</tr> - -<tr> -<td class="diam">  .5</td> -<td class="area int"> </td> -<td class="area dec">.19735</td> -<td class="circumf int">1</td> -<td class="circumf dec">.5708</td> -</tr> - -<tr> -<td class="diam">  .6</td> -<td class="area int"> </td> -<td class="area dec">.28274</td> -<td class="circumf int">1</td> -<td class="circumf dec">.8850</td> -</tr> - -<tr> -<td class="diam">  .7</td> -<td class="area int"> </td> -<td class="area dec">.38485</td> -<td class="circumf int">2</td> -<td class="circumf dec">.1991</td> -</tr> - -<tr> -<td class="diam">  .8</td> -<td class="area int"> </td> -<td class="area dec">.50266</td> -<td class="circumf int">2</td> -<td class="circumf dec">.5133</td> -</tr> - -<tr> -<td class="diam">  .9</td> -<td class="area int"> </td> -<td class="area dec">.63617</td> -<td class="circumf int">2</td> -<td class="circumf dec">.8274</td> -</tr> - -<tr> -<td class="diam"> 1.0</td> -<td class="area int"> </td> -<td class="area dec">.7854</td> -<td class="circumf int">3</td> -<td class="circumf dec">.1416</td> -</tr> - -<tr> -<td class="diam">  .1</td> -<td class="area int"> </td> -<td class="area dec">.9503</td> -<td class="circumf int">3</td> -<td class="circumf dec">.4558</td> -</tr> - -<tr> -<td class="diam">  .2</td> -<td class="area int">1</td> -<td class="area dec">.1310</td> -<td class="circumf int">3</td> -<td class="circumf dec">.7699</td> -</tr> - -<tr> -<td class="diam">  .3</td> -<td class="area int">1</td> -<td class="area dec">.3273</td> -<td class="circumf int">4</td> -<td class="circumf dec">.0841</td> -</tr> - -<tr> -<td class="diam">  .4</td> -<td class="area int">1</td> -<td class="area dec">.5394</td> -<td class="circumf int">4</td> -<td class="circumf dec">.3982</td> -</tr> - -<tr> -<td class="diam">  .5</td> -<td class="area int">1</td> -<td class="area dec">.7671</td> -<td class="circumf int">4</td> -<td class="circumf dec">.7124</td> -</tr> - -<tr> -<td class="diam">  .6</td> -<td class="area int">2</td> -<td class="area dec">.0106</td> -<td class="circumf int">5</td> -<td class="circumf dec">.0265</td> -</tr> - -<tr> -<td class="diam">  .7</td> -<td class="area int">2</td> -<td class="area dec">.2698</td> -<td class="circumf int">5</td> -<td class="circumf dec">.3407</td> -</tr> - -<tr> -<td class="diam">  .8</td> -<td class="area int">2</td> -<td class="area dec">.5447</td> -<td class="circumf int">5</td> -<td class="circumf dec">.6549</td> -</tr> - -<tr> -<td class="diam">  .9</td> -<td class="area int">2</td> -<td class="area dec">.8353</td> -<td class="circumf int">5</td> -<td class="circumf dec">.9690</td> -</tr> - -<tr> -<td class="diam"> 2.0</td> -<td class="area int">3</td> -<td class="area dec">.1416</td> -<td class="circumf int">6</td> -<td class="circumf dec">.2832</td> -</tr> - -<tr> -<td class="diam">  .1</td> -<td class="area int">3</td> -<td class="area dec">.4636</td> -<td class="circumf int">6</td> -<td class="circumf dec">.5973</td> -</tr> - -<tr> -<td class="diam">  .2</td> -<td class="area int">3</td> -<td class="area dec">.8013</td> -<td class="circumf int">6</td> -<td class="circumf dec">.9115</td> -</tr> - -<tr> -<td class="diam">  .3</td> -<td class="area int">4</td> -<td class="area dec">.1548</td> -<td class="circumf int">7</td> -<td class="circumf dec">.2257</td> -</tr> - -<tr> -<td class="diam">  .4</td> -<td class="area int">4</td> -<td class="area dec">.5239</td> -<td class="circumf int">7</td> -<td class="circumf dec">.5398</td> -</tr> - -<tr> -<td class="diam">  .5</td> -<td class="area int">4</td> -<td class="area dec">.9087</td> -<td class="circumf int">7</td> -<td class="circumf dec">.8540</td> -</tr> - -<tr> -<td class="diam">  .6</td> -<td class="area int">5</td> -<td class="area dec">.3093</td> -<td class="circumf int">8</td> -<td class="circumf dec">.1681</td> -</tr> - -<tr> -<td class="diam">  .7</td> -<td class="area int">5</td> -<td class="area dec">.7256</td> -<td class="circumf int">8</td> -<td class="circumf dec">.4823</td> -</tr> - -<tr> -<td class="diam">  .8</td> -<td class="area int">6</td> -<td class="area dec">.1575</td> -<td class="circumf int">8</td> -<td class="circumf dec">.7965</td> -</tr> - -<tr> -<td class="diam">  .9</td> -<td class="area int">6</td> -<td class="area dec">.6052</td> -<td class="circumf int">9</td> -<td class="circumf dec">.1106</td> -</tr> - -<tr> -<td class="diam"> 3.0</td> -<td class="area int">7</td> -<td class="area dec">.0686</td> -<td class="circumf int">9</td> -<td class="circumf dec">.4248</td> -</tr> - -<tr> -<td class="diam">  .1</td> -<td class="area int">7</td> -<td class="area dec">.5477</td> -<td class="circumf int">9</td> -<td class="circumf dec">.7389</td> -</tr> - -<tr> -<td class="diam">  .2</td> -<td class="area int">8</td> -<td class="area dec">.0425</td> -<td class="circumf int">10</td> -<td class="circumf dec">.0531</td> -</tr> - -<tr> -<td class="diam">  .3</td> -<td class="area int">8</td> -<td class="area dec">.5530</td> -<td class="circumf int">10</td> -<td class="circumf dec">.3673</td> -</tr> - -<tr> -<td class="diam">  .4</td> -<td class="area int">9</td> -<td class="area dec">.0792</td> -<td class="circumf int">10</td> -<td class="circumf dec">.6814</td> -</tr> - -<tr> -<td class="diam">  .5</td> -<td class="area int">9</td> -<td class="area dec">.6211</td> -<td class="circumf int">10</td> -<td class="circumf dec">.9956</td> -</tr> - -<tr> -<td class="diam">  .6</td> -<td class="area int">10</td> -<td class="area dec">.1788</td> -<td class="circumf int">11</td> -<td class="circumf dec">.3097</td> -</tr> - -<tr> -<td class="diam">  .7</td> -<td class="area int">10</td> -<td class="area dec">.7521</td> -<td class="circumf int">11</td> -<td class="circumf dec">.6239</td> -</tr> - -<tr> -<td class="diam">  .8</td> -<td class="area int">11</td> -<td class="area dec">.3411</td> -<td class="circumf int">11</td> -<td class="circumf dec">.9381</td> -</tr> - -<tr> -<td class="diam">  .9</td> -<td class="area int">11</td> -<td class="area dec">.9456</td> -<td class="circumf int">12</td> -<td class="circumf dec">.2522</td> -</tr> - -<tr> -<td class="diam"> 4.0</td> -<td class="area int">12</td> -<td class="area dec">.5664</td> -<td class="circumf int">12</td> -<td class="circumf dec">.5664</td> -</tr> - -<tr> -<td class="diam">  .1</td> -<td class="area int">13</td> -<td class="area dec">.2025</td> -<td class="circumf int">12</td> -<td class="circumf dec">.8805</td> -</tr> - -<tr> -<td class="diam">  .2</td> -<td class="area int">13</td> -<td class="area dec">.8544</td> -<td class="circumf int">13</td> -<td class="circumf dec">.1947</td> -</tr> - -<tr> -<td class="diam">  .3</td> -<td class="area int">14</td> -<td class="area dec">.5220</td> -<td class="circumf int">13</td> -<td class="circumf dec">.5088</td> -</tr> - -<tr> -<td class="diam">  .4</td> -<td class="area int">15</td> -<td class="area dec">.2053</td> -<td class="circumf int">13</td> -<td class="circumf dec">.8230</td> -</tr> - -<tr> -<td class="diam">  .5</td> -<td class="area int">15</td> -<td class="area dec">.9043</td> -<td class="circumf int">14</td> -<td class="circumf dec">.1372</td> -</tr> - -<tr> -<td class="diam">  .6</td> -<td class="area int">16</td> -<td class="area dec">.6190</td> -<td class="circumf int">14</td> -<td class="circumf dec">.4513</td> -</tr> - -<tr> -<td class="diam">  .7</td> -<td class="area int">17</td> -<td class="area dec">.3494</td> -<td class="circumf int">14</td> -<td class="circumf dec">.7655</td> -</tr> - -<tr> -<td class="diam">  .8</td> -<td class="area int">18</td> -<td class="area dec">.0956</td> -<td class="circumf int">15</td> -<td class="circumf dec">.0796</td> -</tr> - 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-<tr> -<td class="diam">  .5</td> -<td class="area int">2002</td> -<td class="area dec">.9617</td> -<td class="circumf int">158</td> -<td class="circumf dec">.6504</td> -</tr> - -<tr> -<td class="diam">  .6</td> -<td class="area int">2010</td> -<td class="area dec">.9020</td> -<td class="circumf int">158</td> -<td class="circumf dec">.9646</td> -</tr> - -<tr> -<td class="diam">  .7</td> -<td class="area int">2018</td> -<td class="area dec">.8581</td> -<td class="circumf int">159</td> -<td class="circumf dec">.2787</td> -</tr> - -<tr> -<td class="diam">  .8</td> -<td class="area int">2026</td> -<td class="area dec">.8299</td> -<td class="circumf int">159</td> -<td class="circumf dec">.5929</td> -</tr> - -<tr> -<td class="diam">  .9</td> -<td class="area int">2034</td> -<td class="area dec">.8174</td> -<td class="circumf int">159</td> -<td class="circumf dec">.9071</td> -</tr> - -<tr> -<td class="diam">51.0</td> -<td class="area int">2042</td> -<td class="area dec">.6206</td> -<td class="circumf int">160</td> -<td class="circumf dec">.2212</td> -</tr> - -<tr> -<td class="diam">  .1</td> -<td class="area int">2050</td> -<td class="area dec">.8895</td> -<td class="circumf int">160</td> -<td class="circumf dec">.5354</td> -</tr> - -<tr> -<td class="diam">  .2</td> -<td class="area int">2058</td> -<td class="area dec">.8742</td> -<td class="circumf int">160</td> -<td class="circumf dec">.8495</td> -</tr> - -<tr> -<td class="diam">  .3</td> -<td class="area int">2066</td> -<td class="area dec">.9245</td> -<td class="circumf int">161</td> -<td class="circumf dec">.1637</td> -</tr> - -<tr> -<td class="diam">  .4</td> -<td class="area int">2074</td> -<td class="area dec">.9905</td> -<td class="circumf int">161</td> -<td class="circumf dec">.4779</td> -</tr> - -<tr> -<td class="diam">  .5</td> -<td class="area int">2083</td> -<td class="area dec">.0723</td> -<td class="circumf int">161</td> -<td class="circumf dec">.7920</td> -</tr> - -<tr> -<td class="diam">  .6</td> -<td class="area int">2091</td> -<td class="area dec">.1697</td> -<td class="circumf int">162</td> -<td class="circumf dec">.1062</td> -</tr> - -<tr> -<td class="diam">  .7</td> -<td class="area int">2099</td> -<td class="area dec">.2829</td> -<td class="circumf int">162</td> -<td class="circumf dec">.4203</td> -</tr> - -<tr> -<td class="diam">  .8</td> -<td class="area int">2107</td> -<td class="area dec">.4118</td> -<td class="circumf int">162</td> -<td class="circumf dec">.7345</td> -</tr> - -<tr> -<td class="diam">  .9</td> -<td class="area int">2115</td> -<td class="area dec">.5563</td> -<td class="circumf int">163</td> -<td class="circumf dec">.0487</td> -</tr> - -<tr> -<td class="diam">52.0</td> -<td class="area int">2123</td> -<td class="area dec">.7166</td> -<td class="circumf int">163</td> -<td class="circumf dec">.3628</td> -</tr> - -<tr> -<td class="diam">  .1</td> -<td class="area int">2131</td> -<td class="area dec">.8926</td> -<td class="circumf int">163</td> -<td class="circumf dec">.6770</td> -</tr> - -<tr> -<td class="diam">  .2</td> -<td class="area int">2140</td> -<td class="area dec">.0843</td> -<td class="circumf int">163</td> -<td class="circumf dec">.9911</td> -</tr> - -<tr> -<td class="diam">  .3</td> -<td class="area int">2148</td> -<td class="area dec">.2917</td> -<td class="circumf int">164</td> -<td class="circumf dec">.3053</td> -</tr> - -<tr> -<td class="diam">  .4</td> -<td class="area int">2156</td> -<td class="area dec">.5149</td> -<td class="circumf int">164</td> -<td class="circumf dec">.6195</td> -</tr> - -<tr> -<td class="diam">  .5</td> -<td class="area int">2164</td> -<td class="area dec">.7537</td> -<td class="circumf int">164</td> -<td class="circumf dec">.9336</td> -</tr> - -<tr> -<td class="diam">  .6</td> -<td class="area int">2173</td> -<td class="area dec">.0082</td> -<td class="circumf int">165</td> -<td class="circumf dec">.2479</td> -</tr> - -<tr> -<td class="diam">  .7</td> -<td class="area int">2181</td> -<td class="area dec">.2785</td> -<td class="circumf int">165</td> -<td class="circumf dec">.5619</td> -</tr> - -<tr> -<td class="diam">  .8</td> -<td class="area int">2189</td> -<td class="area dec">.5644</td> -<td class="circumf int">165</td> -<td class="circumf dec">.8761</td> -</tr> - -<tr> -<td class="diam">  .9</td> -<td class="area int">2197</td> -<td class="area dec">.8661</td> -<td class="circumf int">166</td> -<td class="circumf dec">.1903</td> -</tr> - -<tr> -<td class="diam">53.0</td> -<td class="area int">2206</td> -<td class="area dec">.1834</td> -<td class="circumf int">166</td> -<td class="circumf dec">.5044</td> -</tr> - -<tr> -<td class="diam">  .1</td> -<td class="area int">2214</td> -<td class="area dec">.5165</td> -<td class="circumf int">166</td> -<td class="circumf dec">.8186</td> -</tr> - -<tr> -<td class="diam">  .2</td> -<td class="area int">2222</td> -<td class="area dec">.8653</td> -<td class="circumf int">167</td> -<td class="circumf dec">.1327</td> -</tr> - -<tr> -<td class="diam">  .3</td> -<td class="area int">2231</td> -<td class="area dec">.2298</td> -<td class="circumf int">167</td> -<td class="circumf dec">.4469</td> -</tr> - -<tr> -<td class="diam">  .4</td> -<td class="area int">2239</td> -<td class="area dec">.6100</td> -<td class="circumf int">167</td> -<td class="circumf dec">.7610</td> -</tr> - -<tr> -<td class="diam">  .5</td> -<td class="area int">2248</td> -<td class="area dec">.0059</td> -<td class="circumf int">168</td> -<td class="circumf dec">.0752</td> -</tr> - -<tr> -<td class="diam">  .6</td> -<td class="area int">2256</td> -<td class="area dec">.4175</td> -<td class="circumf int">168</td> -<td class="circumf dec">.3894</td> -</tr> - -<tr> -<td class="diam">  .7</td> -<td class="area int">2264</td> -<td class="area dec">.8448</td> -<td class="circumf int">168</td> -<td class="circumf dec">.7035</td> -</tr> - -<tr> -<td class="diam">  .8</td> -<td class="area int">2273</td> -<td class="area dec">.2879</td> -<td class="circumf int">169</td> -<td class="circumf dec">.0177</td> -</tr> - -<tr> -<td class="diam">  .9</td> -<td class="area int">2281</td> -<td class="area dec">.7466</td> -<td class="circumf int">169</td> -<td class="circumf dec">.3318</td> -</tr> - -<tr> -<td class="diam">54.0</td> -<td class="area int">2290</td> -<td class="area dec">.2210</td> -<td class="circumf int">169</td> -<td class="circumf dec">.6460</td> -</tr> - -<tr> -<td class="diam">  .1</td> -<td class="area int">2298</td> -<td class="area dec">.7112</td> -<td class="circumf int">169</td> -<td class="circumf dec">.9602</td> -</tr> - -<tr> -<td class="diam">  .2</td> -<td class="area int">2307</td> -<td class="area dec">.2171</td> -<td class="circumf int">170</td> -<td class="circumf dec">.2743</td> -</tr> - -<tr> -<td class="diam">  .3</td> -<td class="area int">2315</td> -<td class="area dec">.7386</td> -<td class="circumf int">170</td> -<td class="circumf dec">.5885</td> -</tr> - -<tr> -<td class="diam">  .4</td> -<td class="area int">2324</td> -<td class="area dec">.2759</td> -<td class="circumf int">170</td> -<td class="circumf dec">.9026</td> -</tr> - -<tr> -<td class="diam">  .5</td> -<td class="area int">2332</td> -<td class="area dec">.8289</td> -<td class="circumf int">171</td> -<td class="circumf dec">.2168</td> -</tr> - -<tr> -<td class="diam">  .6</td> -<td class="area int">2341</td> -<td class="area dec">.3976</td> -<td class="circumf int">171</td> -<td class="circumf dec">.5310</td> -</tr> - -<tr> -<td class="diam">  .7</td> -<td class="area int">2349</td> -<td class="area dec">.9820</td> -<td class="circumf int">171</td> -<td class="circumf dec">.8451</td> -</tr> - -<tr> -<td class="diam">  .8</td> -<td class="area int">2358</td> -<td class="area dec">.5821</td> -<td class="circumf int">172</td> -<td class="circumf dec">.1593</td> -</tr> - -<tr> -<td class="diam">  .9</td> -<td class="area int">2367</td> -<td class="area dec">.1979</td> -<td class="circumf int">172</td> -<td class="circumf dec">.4735</td> -</tr> - -<tr> -<td class="diam">55.0</td> -<td class="area int">2375</td> -<td class="area dec">.8294</td> -<td class="circumf int">172</td> -<td class="circumf dec">.7876</td> -</tr> - -<tr> -<td class="diam">  .1</td> -<td class="area int">2384</td> -<td class="area dec">.4767</td> -<td class="circumf int">173</td> -<td class="circumf dec">.1017</td> -</tr> - -<tr> -<td class="diam">  .2</td> -<td class="area int">2393</td> -<td class="area dec">.1396</td> -<td class="circumf int">173</td> -<td class="circumf dec">.4159</td> -</tr> - -<tr> -<td class="diam">  .3</td> -<td class="area int">2401</td> -<td class="area dec">.8183</td> -<td class="circumf int">173</td> -<td class="circumf dec">.7301</td> -</tr> - -<tr> -<td class="diam">  .4</td> -<td class="area int">2410</td> -<td class="area dec">.5126</td> -<td class="circumf int">174</td> -<td class="circumf dec">.0442</td> -</tr> - -<tr> -<td class="diam">  .5</td> -<td class="area int">2419</td> -<td class="area dec">.2227</td> -<td class="circumf int">174</td> -<td class="circumf dec">.3584</td> -</tr> - -<tr> -<td class="diam">  .6</td> -<td class="area int">2427</td> -<td class="area dec">.9485</td> -<td class="circumf int">174</td> -<td class="circumf dec">.6726</td> -</tr> - -<tr> -<td class="diam">  .7</td> -<td class="area int">2436</td> -<td class="area dec">.6899</td> -<td class="circumf int">174</td> -<td class="circumf dec">.9867</td> -</tr> - -<tr> -<td class="diam">  .8</td> -<td class="area int">2145</td> -<td class="area dec">.4471</td> -<td class="circumf int">175</td> -<td class="circumf dec">.3009</td> -</tr> - -<tr class="bb"> -<td class="diam">  .9</td> -<td class="area int">2454</td> -<td class="area dec">.2200</td> -<td class="circumf int">175</td> -<td class="circumf dec">.6150</td> -</tr> - -</table> - -<p><span class="pagenum" id="Page278">[278]</span></p> - -<h3 class="center">UNITED STATES STANDARD SIZES OF WROUGHT IRON WELDED PIPE.</h3> - -<table class="ironpipe" summary="Pipes"> - -<tr class="bt bb"> -<th colspan="2" class="br">Inside<br />diam-<br />eter<br />nom.</th> -<th colspan="2" class="br">Actual<br />outside<br />Diam-<br />eter.</th> -<th class="br">Thick-<br />ness.</th> -<th colspan="2" class="br">Actual<br />Inside<br />Diam-<br />eter.</th> -<th colspan="2" class="br">External<br />circum-<br />ference.</th> -<th colspan="2" class="br">Internal<br />circum-<br />ference.</th> -<th colspan="2" class="br">Length<br />of pipe<br />per<br />square<br />foot of<br />outside<br />surface.</th> -<th colspan="2" class="br">Length<br />of pipe<br />per<br />square<br />foot of<br />inside<br />surface.</th> -<th colspan="2" class="br">External<br />area.</th> -<th colspan="2" class="br">Actual<br />internal<br />area.</th> -<th colspan="2" class="br">Length<br />of pipe<br />con-<br />taining<br />one<br />cubic<br />foot.</th> -<th colspan="2" class="br">Weight<br />per<br />foot of<br />length.</th> -<th colspan="2" class="br">No. of<br />threads<br />per<br />Inch<br />of<br />screw.</th> -<th>Length<br />perfect<br />screw.</th> -</tr> - -<tr> -<td class="int"> </td> -<td class="frac br"><sup>1</sup>⁄<sub>8</sub></td> -<td> </td> -<td class="dec br">.405</td> -<td class="center br">.068</td> -<td class="int">0</td> -<td class="frac br">.269</td> -<td class="int">1</td> -<td class="frac br">.272</td> -<td class="int">0</td> -<td class="frac br">.848</td> -<td class="int">9</td> -<td class="frac br">.440</td> -<td class="int">14</td> -<td class="frac br">.15</td> -<td> </td> -<td class="dec br">.129</td> -<td> </td> -<td class="dec br">.0572</td> -<td class="int">2500</td> -<td class="dec br">.</td> -<td> </td> -<td class="dec br">.243</td> -<td class="int">27</td> -<td class="frac br"> </td> -<td class="center">0.19</td> -</tr> - -<tr> -<td class="int"> </td> -<td class="frac br"><sup>1</sup>⁄<sub>4</sub></td> -<td> </td> -<td class="dec br">.54</td> -<td class="center br">.088</td> -<td class="int">0</td> -<td class="frac br">.364</td> -<td class="int">1</td> -<td class="frac br">.696</td> -<td class="int">1</td> -<td class="frac br">.144</td> -<td class="int">7</td> -<td class="frac br">.075</td> -<td class="int">10</td> -<td class="frac br">.50</td> -<td> </td> -<td class="dec br">.229</td> -<td> </td> -<td class="dec br">.1041</td> -<td class="int">1385</td> -<td class="dec br">.</td> -<td> </td> -<td class="dec br">.422</td> -<td class="int">18</td> -<td class="frac br"> </td> -<td class="center">0.29</td> -</tr> - -<tr> -<td class="int"> </td> -<td class="frac br"><sup>3</sup>⁄<sub>8</sub></td> -<td> </td> -<td class="dec br">.675</td> -<td class="center br">.091</td> -<td class="int">0</td> -<td class="frac br">.493</td> -<td class="int">2</td> -<td class="frac br">.121</td> -<td class="int">1</td> -<td class="frac br">.552</td> -<td class="int">5</td> -<td class="frac br">.657</td> -<td class="int">7</td> -<td class="frac br">.67</td> -<td> </td> -<td class="dec br">.358</td> -<td> </td> -<td class="dec br">.1916</td> -<td class="int">751</td> -<td class="frac br">.5</td> -<td> </td> -<td class="dec br">.561</td> -<td class="int">18</td> -<td class="frac br"> </td> -<td class="center">0.30</td> -</tr> - -<tr> -<td class="int"> </td> -<td class="frac br"><sup>1</sup>⁄<sub>2</sub></td> -<td> </td> -<td class="dec br">.840</td> -<td class="center br">.109</td> -<td class="int">0</td> -<td class="frac br">.622</td> -<td class="int">2</td> -<td class="frac br">.652</td> -<td class="int">1</td> -<td class="frac br">.957</td> -<td class="int">4</td> -<td class="frac br">.502</td> -<td class="int">6</td> -<td class="frac br">.13</td> -<td> </td> -<td class="dec br">.554</td> -<td> </td> -<td class="dec br">.3048</td> -<td class="int">472</td> -<td class="frac br">.4</td> -<td> </td> -<td class="dec br">.845</td> -<td class="int">14</td> -<td class="frac br"> </td> -<td class="center">0.39</td> -</tr> - -<tr> -<td class="int"> </td> -<td class="frac br"><sup>3</sup>⁄<sub>4</sub></td> -<td class="int">1</td> -<td class="frac br">.050</td> -<td class="center br">.113</td> -<td class="int">0</td> -<td class="frac br">.824</td> -<td class="int">3</td> -<td class="frac br">.299</td> -<td class="int">2</td> -<td class="frac br">.589</td> -<td class="int">3</td> -<td class="frac br">.637</td> -<td class="int">4</td> -<td class="frac br">.635</td> -<td> </td> -<td class="dec br">.866</td> -<td> </td> -<td class="dec br">.5333</td> -<td class="int">270</td> -<td class="frac br">.0</td> -<td class="int">1</td> -<td class="frac br">.126</td> -<td class="int">14</td> -<td class="frac br"> </td> -<td class="center">0.40</td> -</tr> - -<tr> -<td class="int">1</td> -<td class="frac br"> </td> -<td class="int">1</td> -<td class="frac br">.315</td> -<td class="center br">.134</td> -<td class="int">1</td> -<td class="frac br">.047</td> -<td class="int">4</td> -<td class="frac br">.134</td> -<td class="int">3</td> -<td class="frac br">.292</td> -<td class="int">2</td> -<td class="frac br">.903</td> -<td class="int">3</td> -<td class="frac br">.679</td> -<td class="int">1</td> -<td class="frac br">.357</td> -<td> </td> -<td class="dec br">.8627</td> -<td class="int">166</td> -<td class="frac br">.9</td> -<td class="int">1</td> -<td class="frac br">.670</td> -<td class="int">11</td> -<td class="frac br"><sup>1</sup>⁄<sub>2</sub></td> -<td class="center">0.51</td> -</tr> - -<tr> -<td class="int">1</td> -<td class="frac br"><sup>1</sup>⁄<sub>4</sub></td> -<td class="int">1</td> -<td class="frac br">.660</td> -<td class="center br">.140</td> -<td class="int">1</td> -<td class="frac br">.38</td> -<td class="int">5</td> -<td class="frac br">.215</td> -<td class="int">4</td> -<td class="frac br">.335</td> -<td class="int">2</td> -<td class="frac br">.301</td> -<td class="int">2</td> -<td class="frac br">.768</td> -<td class="int">2</td> -<td class="frac br">.164</td> -<td class="int">1</td> -<td class="frac br">.496</td> -<td class="int">96</td> -<td class="frac br">.25</td> -<td class="int">2</td> -<td class="frac br">.258</td> -<td class="int">11</td> -<td class="frac br"><sup>1</sup>⁄<sub>2</sub></td> -<td class="center">0.54</td> -</tr> - -<tr> -<td class="int">1</td> -<td class="frac br"><sup>1</sup>⁄<sub>2</sub></td> -<td class="int">1</td> -<td class="frac br">.90</td> -<td class="center br">.145</td> -<td class="int">1</td> -<td class="frac br">.61</td> -<td class="int">5</td> -<td class="frac br">.969</td> -<td class="int">5</td> -<td class="frac br">.061</td> -<td class="int">2</td> -<td class="frac br">.010</td> -<td class="int">2</td> -<td class="frac br">.371</td> -<td class="int">2</td> -<td class="frac br">.835</td> -<td class="int">2</td> -<td class="frac br">.038</td> -<td class="int">70</td> -<td class="frac br">.65</td> -<td class="int">2</td> -<td class="frac br">.694</td> -<td class="int">11</td> -<td class="frac br"><sup>1</sup>⁄<sub>2</sub></td> -<td class="center">0.55</td> -</tr> - -<tr> -<td class="int">2</td> -<td class="frac br"> </td> -<td class="int">2</td> -<td class="frac br">.375</td> -<td class="center br">.154</td> -<td class="int">2</td> -<td class="frac br">.067</td> -<td class="int">7</td> -<td class="frac br">.461</td> -<td class="int">6</td> -<td class="frac br">.494</td> -<td class="int">1</td> -<td class="frac br">.611</td> -<td class="int">1</td> -<td class="frac br">.848</td> -<td class="int">4</td> -<td class="frac br">.430</td> -<td class="int">3</td> -<td class="frac br">.355</td> -<td class="int">42</td> -<td class="frac br">.36</td> -<td class="int">3</td> -<td class="frac br">.667</td> -<td class="int">11</td> -<td class="frac br"><sup>1</sup>⁄<sub>2</sub></td> -<td class="center">0.58</td> -</tr> - -<tr> -<td class="int">2</td> -<td class="frac br"><sup>1</sup>⁄<sub>2</sub></td> -<td class="int">2</td> -<td class="frac br">.875</td> -<td class="center br">.204</td> -<td class="int">2</td> -<td class="frac br">.467</td> -<td class="int">9</td> -<td class="frac br">.032</td> -<td class="int">7</td> -<td class="frac br">.754</td> -<td class="int">1</td> -<td class="frac br">.328</td> -<td class="int">1</td> -<td class="frac br">.547</td> -<td class="int">6</td> -<td class="frac br">.491</td> -<td class="int">4</td> -<td class="frac br">.783</td> -<td class="int">30</td> -<td class="frac br">.11</td> -<td class="int">5</td> -<td class="frac br">.773</td> -<td class="int">8</td> -<td class="frac br"> </td> -<td class="center">0.89</td> -</tr> - -<tr> -<td class="int">3</td> -<td class="frac br"> </td> -<td class="int">3</td> -<td class="frac br">.50</td> -<td class="center br">.217</td> -<td class="int">3</td> -<td class="frac br">.066</td> -<td class="int">10</td> -<td class="frac br">.996</td> -<td class="int">9</td> -<td class="frac br">.636</td> -<td class="int">1</td> -<td class="frac br">.091</td> -<td class="int">1</td> -<td class="frac br">.245</td> -<td class="int">9</td> -<td class="frac br">.621</td> -<td class="int">7</td> -<td class="frac br">.388</td> -<td class="int">19</td> -<td class="frac br">.40</td> -<td class="int">7</td> -<td class="frac br">.547</td> -<td class="int">8</td> -<td class="frac br"> </td> -<td class="center">0.95</td> -</tr> - -<tr> -<td class="int">3</td> -<td class="frac br"><sup>1</sup>⁄<sub>2</sub></td> -<td class="int">4</td> -<td class="frac br">.0</td> -<td class="center br">.226</td> -<td class="int">3</td> -<td class="frac br">.548</td> -<td class="int">12</td> -<td class="frac br">.566</td> -<td class="int">11</td> -<td class="frac br">.146</td> -<td> </td> -<td class="dec br">.955</td> -<td class="int">1</td> -<td class="frac br">.077</td> -<td class="int">12</td> -<td class="frac br">.566</td> -<td class="int">9</td> -<td class="frac br">.837</td> -<td class="int">14</td> -<td class="frac br">.56</td> -<td class="int">9</td> -<td class="frac br">.055</td> -<td class="int">8</td> -<td class="frac br"> </td> -<td class="center">1.00</td> -</tr> - -<tr> -<td class="int">4</td> -<td class="frac br"> </td> -<td class="int">4</td> -<td class="frac br">.50</td> -<td class="center br">.237</td> -<td class="int">4</td> -<td class="frac br">.026</td> -<td class="int">14</td> -<td class="frac br">.137</td> -<td class="int">12</td> -<td class="frac br">.648</td> -<td> </td> -<td class="dec br">.849</td> -<td class="int">0</td> -<td class="frac br">.949</td> -<td class="int">15</td> -<td class="frac br">.901</td> -<td class="int">12</td> -<td class="frac br">.730</td> -<td class="int">11</td> -<td class="frac br">.31</td> -<td class="int">10</td> -<td class="frac br">.728</td> -<td class="int">8</td> -<td class="frac br"> </td> -<td class="center">1.05</td> -</tr> - -<tr> -<td class="int">4</td> -<td class="frac br"><sup>1</sup>⁄<sub>2</sub></td> -<td class="int">5</td> -<td class="frac br">.0</td> -<td class="center br">.247</td> -<td class="int">4</td> -<td class="frac br">.506</td> -<td class="int">15</td> -<td class="frac br">.708</td> -<td class="int">14</td> -<td class="frac br">.153</td> -<td> </td> -<td class="dec br">.765</td> -<td class="int">0</td> -<td class="frac br">.848</td> -<td class="int">19</td> -<td class="frac br">.635</td> -<td class="int">15</td> -<td class="frac br">.939</td> -<td class="int">9</td> -<td class="frac br">.03</td> -<td class="int">12</td> -<td class="frac br">.492</td> -<td class="int">8</td> -<td class="frac br"> </td> -<td class="center">1.10</td> -</tr> - -<tr> -<td class="int">5</td> -<td class="frac br"> </td> -<td class="int">5</td> -<td class="frac br">.563</td> -<td class="center br">.259</td> -<td class="int">5</td> -<td class="frac br">.045</td> -<td class="int">17</td> -<td class="frac br">.475</td> -<td class="int">15</td> -<td class="frac br">.849</td> -<td> </td> -<td class="dec br">.629</td> -<td class="int">0</td> -<td class="frac br">.757</td> -<td class="int">24</td> -<td class="frac br">.299</td> -<td class="int">19</td> -<td class="frac br">.990</td> -<td class="int">7</td> -<td class="frac br">.20</td> -<td class="int">14</td> -<td class="frac br">.564</td> -<td class="int">8</td> -<td class="frac br"> </td> -<td class="center">1.16</td> -</tr> - -<tr> -<td class="int">6</td> -<td class="frac br"> </td> -<td class="int">6</td> -<td class="frac br">.625</td> -<td class="center br">.280</td> -<td class="int">5</td> -<td class="frac br">.065</td> -<td class="int">20</td> -<td class="frac br">.813</td> -<td class="int">19</td> -<td class="frac br">.054</td> -<td> </td> -<td class="dec br">.577</td> -<td class="int">0</td> -<td class="frac br">.630</td> -<td class="int">34</td> -<td class="frac br">.471</td> -<td class="int">28</td> -<td class="frac br">.889</td> -<td class="int">4</td> -<td class="frac br">.98</td> -<td class="int">18</td> -<td class="frac br">.767</td> -<td class="int">8</td> -<td class="frac br"> </td> -<td class="center">1.26</td> -</tr> - -<tr> -<td class="int">7</td> -<td class="frac br"> </td> -<td class="int">7</td> -<td class="frac br">.625</td> -<td class="center br">.301</td> -<td class="int">7</td> -<td class="frac br">.023</td> -<td class="int">23</td> -<td class="frac br">.954</td> -<td class="int">22</td> -<td class="frac br">.063</td> -<td> </td> -<td class="dec br">.505</td> -<td class="int">0</td> -<td class="frac br">.544</td> -<td class="int">45</td> -<td class="frac br">.663</td> -<td class="int">38</td> -<td class="frac br">.737</td> -<td class="int">3</td> -<td class="frac br">.72</td> -<td class="int">23</td> -<td class="frac br">.410</td> -<td class="int">8</td> -<td class="frac br"> </td> -<td class="center">1.36</td> -</tr> - -<tr> -<td class="int">8</td> -<td class="frac br"> </td> -<td class="int">8</td> -<td class="frac br">.625</td> -<td class="center br">.322</td> -<td class="int">7</td> -<td class="frac br">.981</td> -<td class="int">27</td> -<td class="frac br">.096</td> -<td class="int">25</td> -<td class="frac br">.076</td> -<td> </td> -<td class="dec br">.444</td> -<td class="int">0</td> -<td class="frac br">.478</td> -<td class="int">58</td> -<td class="frac br">.426</td> -<td class="int">50</td> -<td class="frac br">.039</td> -<td class="int">2</td> -<td class="frac br">.88</td> -<td class="int">28</td> -<td class="frac br">.348</td> -<td class="int">8</td> -<td class="frac br"> </td> -<td class="center">1.46</td> -</tr> - -<tr> -<td class="int">9</td> -<td class="frac br"> </td> -<td class="int">9</td> -<td class="frac br">.688</td> -<td class="center br">.344</td> -<td class="int">9</td> -<td class="frac br">.00</td> -<td class="int">30</td> -<td class="frac br">.433</td> -<td class="int">28</td> -<td class="frac br">.277</td> -<td> </td> -<td class="dec br">.394</td> -<td class="int">0</td> -<td class="frac br">.425</td> -<td class="int">73</td> -<td class="frac br">.715</td> -<td class="int">63</td> -<td class="frac br">.633</td> -<td class="int">2</td> -<td class="frac br">.26</td> -<td class="int">34</td> -<td class="frac br">.677</td> -<td class="int">8</td> -<td class="frac br"> </td> -<td class="center">1.57</td> -</tr> - -<tr class="bb"> -<td class="int">10</td> -<td class="frac br"> </td> -<td class="int">10</td> -<td class="frac br">.750</td> -<td class="center br">.366</td> -<td class="int">10</td> -<td class="frac br">.018</td> -<td class="int">33</td> -<td class="frac br">.772</td> -<td class="int">31</td> -<td class="frac br">.475</td> -<td> </td> -<td class="dec br">.355</td> -<td class="int">0</td> -<td class="frac br">.381</td> -<td class="int">90</td> -<td class="frac br">.762</td> -<td class="int">78</td> -<td class="frac br">.838</td> -<td class="int">1</td> -<td class="frac br">.80</td> -<td class="int">40</td> -<td class="frac br">.641</td> -<td class="int">8</td> -<td class="frac br"> </td> -<td class="center">1.68</td> -</tr> - -</table> - -<p class="fsize90">Thread taper three-fourths inch to one foot.</p> - -<p class="fsize90">All pipe below 1<sup>1</sup>⁄<sub>2</sub> inches is butt-welded, and -proved to 300 pounds per square inch; 1<sup>1</sup>⁄<sub>2</sub> inch and above is lap-welded and proved -to 500 pounds per square inch.</p> - -<p><span class="pagenum" id="Page279">[279]</span></p> - -<h3 class="center">STANDARDS FOR WIRE GAUGES IN USE IN THE UNITED STATES.<br /> -Dimensions of Sizes in Decimal Parts of an Inch.</h3> - -<table class="gauges" summary="Gauges"> - -<tr class="bt bb"> -<th class="br">Number<br />of Wire<br />Gauge.</th> -<th class="br">American<br />or<br />Brown<br />&<br />Sharpe.</th> -<th class="br">Birming-<br />ham,<br />or<br />Stubs’<br />Wire.</th> -<th class="br">Washburn<br />& Moen<br />Mfg. Co.,<br />Worces-<br />ter, Ms.</th> -<th class="br">Impe-<br />rial<br />Wire<br />Gauge.</th> -<th class="br">Stubs’<br />Steel<br />Wire.</th> -<th class="br">U. S.<br />Stand.<br />for<br />Plate.</th> -<th>Number<br />of Wire<br />Gauge.</th> -</tr> - -<tr> -<td class="gauge br">000000</td> -<td class="center br">....</td> -<td class="center br">....</td> -<td class="center br">....</td> -<td class="numbers">.464</td> -<td class="center br">....</td> -<td class="numbers">.46875</td> -<td class="gauge">000000</td> -</tr> - -<tr> -<td class="gauge br">00000</td> -<td class="center br">....</td> -<td class="center br">....</td> -<td class="center br">....</td> -<td class="numbers">.432</td> -<td class="center br">....</td> -<td class="numbers">.4375</td> -<td class="gauge">00000</td> -</tr> - -<tr> -<td class="gauge br">0000</td> -<td class="numbers">.46</td> -<td class="numbers">.454</td> -<td class="numbers">.3938</td> -<td class="numbers">.400</td> -<td class="center br">....</td> -<td class="numbers">.40625</td> -<td class="gauge">0000</td> -</tr> - -<tr> -<td class="gauge br">000</td> -<td class="numbers">.40964</td> -<td class="numbers">.425</td> -<td class="numbers">.3625</td> -<td class="numbers">.372</td> -<td class="center br">....</td> -<td class="numbers">.375</td> -<td class="gauge">000</td> -</tr> - -<tr> -<td class="gauge br">00</td> -<td class="numbers">.3648</td> -<td class="numbers">.38</td> -<td class="numbers">.3310</td> -<td class="numbers">.348</td> -<td class="center br">....</td> -<td class="numbers">.34375</td> -<td class="gauge">00</td> -</tr> - -<tr> -<td class="gauge br">0</td> -<td class="numbers">.32486</td> -<td class="numbers">.34</td> -<td class="numbers">.3065</td> -<td class="numbers">.324</td> -<td class="center br">....</td> -<td class="numbers">.3125</td> -<td class="gauge">0</td> -</tr> - -<tr> -<td class="gauge br">1</td> -<td class="numbers">.2893</td> -<td class="numbers">.3</td> -<td class="numbers">.2830</td> -<td class="numbers">.300</td> -<td class="numbers">.227</td> -<td class="numbers">.28125</td> -<td class="gauge">1</td> -</tr> - -<tr> -<td class="gauge br">2</td> -<td class="numbers">.25763</td> -<td class="numbers">.284</td> -<td class="numbers">.2625</td> -<td class="numbers">.276</td> -<td class="numbers">.219</td> -<td class="numbers">.265625</td> -<td class="gauge">2</td> -</tr> - -<tr> -<td class="gauge br">3</td> -<td class="numbers">.22942</td> -<td class="numbers">.259</td> -<td class="numbers">.2437</td> -<td class="numbers">.252</td> -<td class="numbers">.212</td> -<td class="numbers">.25</td> -<td class="gauge">3</td> -</tr> - -<tr> -<td class="gauge br">4</td> -<td class="numbers">.20431</td> -<td class="numbers">.238</td> -<td class="numbers">.2253</td> -<td class="numbers">.232</td> -<td class="numbers">.207</td> -<td class="numbers">.234375</td> -<td class="gauge">4</td> -</tr> - -<tr> -<td class="gauge br">5</td> -<td class="numbers">.18194</td> -<td class="numbers">.22</td> -<td class="numbers">.2070</td> -<td class="numbers">.212</td> -<td class="numbers">.204</td> -<td class="numbers">.21875</td> -<td class="gauge">5</td> -</tr> - -<tr> -<td class="gauge br">6</td> -<td class="numbers">.16202</td> -<td class="numbers">.203</td> -<td class="numbers">.1920</td> -<td class="numbers">.192</td> -<td class="numbers">.201</td> -<td class="numbers">.203125</td> -<td class="gauge">6</td> -</tr> - -<tr> -<td class="gauge br">7</td> -<td class="numbers">.14428</td> -<td class="numbers">.18</td> -<td class="numbers">.1770</td> -<td class="numbers">.176</td> -<td class="numbers">.199</td> -<td class="numbers">.1875</td> -<td class="gauge">7</td> -</tr> - -<tr> -<td class="gauge br">8</td> -<td class="numbers">.12849</td> -<td class="numbers">.165</td> -<td class="numbers">.1620</td> -<td class="numbers">.160</td> -<td class="numbers">.197</td> -<td class="numbers">.171875</td> -<td class="gauge">8</td> -</tr> - -<tr> -<td class="gauge br">9</td> -<td class="numbers">.11443</td> -<td class="numbers">.148</td> -<td class="numbers">.1483</td> -<td class="numbers">.144</td> -<td class="numbers">.194</td> -<td class="numbers">.15625</td> -<td class="gauge">9</td> -</tr> - -<tr> -<td class="gauge br">10</td> -<td class="numbers">.10189</td> -<td class="numbers">.134</td> -<td class="numbers">.1350</td> -<td class="numbers">.128</td> -<td class="numbers">.191</td> -<td class="numbers">.140625</td> -<td class="gauge">10</td> -</tr> - -<tr> -<td class="gauge br">11</td> -<td class="numbers">.090742</td> -<td class="numbers">.12</td> -<td class="numbers">.1205</td> -<td class="numbers">.116</td> -<td class="numbers">.188</td> -<td class="numbers">.125</td> -<td class="gauge">11</td> -</tr> - -<tr> -<td class="gauge br">12</td> -<td class="numbers">.080808</td> -<td class="numbers">.109</td> -<td class="numbers">.1055</td> -<td class="numbers">.104</td> -<td class="numbers">.185</td> -<td class="numbers">.109375</td> -<td class="gauge">12</td> -</tr> - -<tr> -<td class="gauge br">13</td> -<td class="numbers">.071961</td> -<td class="numbers">.095</td> -<td class="numbers">.0915</td> -<td class="numbers">.092</td> -<td class="numbers">.182</td> -<td class="numbers">.09375</td> -<td class="gauge">13</td> -</tr> - -<tr> -<td class="gauge br">14</td> -<td class="numbers">.064084</td> -<td class="numbers">.083</td> -<td class="numbers">.0800</td> -<td class="numbers">.080</td> -<td class="numbers">.180</td> -<td class="numbers">.078125</td> -<td class="gauge">14</td> -</tr> - -<tr> -<td class="gauge br">15</td> -<td class="numbers">.057068</td> -<td class="numbers">.072</td> -<td class="numbers">.0720</td> -<td class="numbers">.072</td> -<td class="numbers">.178</td> -<td class="numbers">.0703125</td> -<td class="gauge">15</td> -</tr> - -<tr> -<td class="gauge br">16</td> -<td class="numbers">.05082</td> -<td class="numbers">.065</td> -<td class="numbers">.0625</td> -<td class="numbers">.064</td> -<td class="numbers">.175</td> -<td class="numbers">.0625</td> -<td class="gauge">16</td> -</tr> - -<tr> -<td class="gauge br">17</td> -<td class="numbers">.045257</td> -<td class="numbers">.058</td> -<td class="numbers">.0540</td> -<td class="numbers">.056</td> -<td class="numbers">.172</td> -<td class="numbers">.05625</td> -<td class="gauge">17</td> -</tr> - -<tr> -<td class="gauge br">18</td> -<td class="numbers">.040303</td> -<td class="numbers">.049</td> -<td class="numbers">.0475</td> -<td class="numbers">.048</td> -<td class="numbers">.168</td> -<td class="numbers">.05</td> -<td class="gauge">18</td> -</tr> - -<tr> -<td class="gauge br">19</td> -<td class="numbers">.03589</td> -<td class="numbers">.042</td> -<td class="numbers">.0410</td> -<td class="numbers">.040</td> -<td class="numbers">.164</td> -<td class="numbers">.04375</td> -<td class="gauge">19</td> -</tr> - -<tr> -<td class="gauge br">20</td> -<td class="numbers">.031961</td> -<td class="numbers">.035</td> -<td class="numbers">.0348</td> -<td class="numbers">.036</td> -<td class="numbers">.161</td> -<td class="numbers">.0375</td> -<td class="gauge">20</td> -</tr> - -<tr> -<td class="gauge br">21</td> -<td class="numbers">.028462</td> -<td class="numbers">.032</td> -<td class="numbers">.03175</td> -<td class="numbers">.032</td> -<td class="numbers">.157</td> -<td class="numbers">.034375</td> -<td class="gauge">21</td> -</tr> - -<tr> -<td class="gauge br">22</td> -<td class="numbers">.025347</td> -<td class="numbers">.028</td> -<td class="numbers">.0286</td> -<td class="numbers">.028</td> -<td class="numbers">.155</td> -<td class="numbers">.03125</td> -<td class="gauge">22</td> -</tr> - -<tr> -<td class="gauge br">23</td> -<td class="numbers">.022571</td> -<td class="numbers">.025</td> -<td class="numbers">.0258</td> -<td class="numbers">.024</td> -<td class="numbers">.153</td> -<td class="numbers">.028125</td> -<td class="gauge">23</td> -</tr> - -<tr> -<td class="gauge br">24</td> -<td class="numbers">.0201</td> -<td class="numbers">.022</td> -<td class="numbers">.0230</td> -<td class="numbers">.022</td> -<td class="numbers">.151</td> -<td class="numbers">.025</td> -<td class="gauge">24</td> -</tr> - -<tr> -<td class="gauge br">25</td> -<td class="numbers">.0179</td> -<td class="numbers">.02</td> -<td class="numbers">.0204</td> -<td class="numbers">.020</td> -<td class="numbers">.148</td> -<td class="numbers">.021875</td> -<td class="gauge">25</td> -</tr> - -<tr> -<td class="gauge br">26</td> -<td class="numbers">.01594</td> -<td class="numbers">.018</td> -<td class="numbers">.0181</td> -<td class="numbers">.018</td> -<td class="numbers">.146</td> -<td class="numbers">.01875</td> -<td class="gauge">26</td> -</tr> - -<tr> -<td class="gauge br">27</td> -<td class="numbers">.014195</td> -<td class="numbers">.016</td> -<td class="numbers">.0173</td> -<td class="numbers">.0164</td> -<td class="numbers">.143</td> -<td class="numbers">.0171875</td> -<td class="gauge">27</td> -</tr> - -<tr> -<td class="gauge br">28</td> -<td class="numbers">.012641</td> -<td class="numbers">.014</td> -<td class="numbers">.0162</td> -<td class="numbers">.0149</td> -<td class="numbers">.139</td> -<td class="numbers">.015625</td> -<td class="gauge">28</td> -</tr> - -<tr> -<td class="gauge br">29</td> -<td class="numbers">.011257</td> -<td class="numbers">.013</td> -<td class="numbers">.0150</td> -<td class="numbers">.0136</td> -<td class="numbers">.134</td> -<td class="numbers">.0140625</td> -<td class="gauge">29</td> -</tr> - -<tr> -<td class="gauge br">30</td> -<td class="numbers">.010025</td> -<td class="numbers">.012</td> -<td class="numbers">.0140</td> -<td class="numbers">.0124</td> -<td class="numbers">.127</td> -<td class="numbers">.0125</td> -<td class="gauge">30</td> -</tr> - -<tr> -<td class="gauge br">31</td> -<td class="numbers">.008928</td> -<td class="numbers">.01</td> -<td class="numbers">.0132</td> -<td class="numbers">.0116</td> -<td class="numbers">.120</td> -<td class="numbers">.0109375</td> -<td class="gauge">31</td> -</tr> - -<tr> -<td class="gauge br">32</td> -<td class="numbers">.00795</td> -<td class="numbers">.009</td> -<td class="numbers">.0128</td> -<td class="numbers">.0108</td> -<td class="numbers">.115</td> -<td class="numbers">.01015625</td> -<td class="gauge">32</td> -</tr> - -<tr> -<td class="gauge br">33</td> -<td class="numbers">.00708</td> -<td class="numbers">.008</td> -<td class="numbers">.0118</td> -<td class="numbers">.0100</td> -<td class="numbers">.112</td> -<td class="numbers">.009375</td> -<td class="gauge">33</td> -</tr> - -<tr> -<td class="gauge br">34</td> -<td class="numbers">.006304</td> -<td class="numbers">.007</td> -<td class="numbers">.0104</td> -<td class="numbers">.0092</td> -<td class="numbers">.110</td> -<td class="numbers">.00859375</td> -<td class="gauge">34</td> -</tr> - -<tr> -<td class="gauge br">35</td> -<td class="numbers">.005614</td> -<td class="numbers">.005</td> -<td class="numbers">.0095</td> -<td class="numbers">.0084</td> -<td class="numbers">.108</td> -<td class="numbers">.0078125</td> -<td class="gauge">35</td> -</tr> - -<tr> -<td class="gauge br">36</td> -<td class="numbers">.005</td> -<td class="numbers">.004</td> -<td class="numbers">.0090</td> -<td class="numbers">.0076</td> -<td class="numbers">.106</td> -<td class="numbers">.00703125</td> -<td class="gauge">36</td> -</tr> - -<tr> -<td class="gauge br">37</td> -<td class="numbers">.004453</td> -<td class="center br">....</td> -<td class="center br">....</td> -<td class="numbers">.0068</td> -<td class="numbers">.103</td> -<td class="numbers">.006640625</td> -<td class="gauge">37</td> -</tr> - -<tr> -<td class="gauge br">38</td> -<td class="numbers">.003965</td> -<td class="center br">....</td> -<td class="center br">....</td> -<td class="numbers">.0060</td> -<td class="numbers">.101</td> -<td class="numbers">.00625</td> -<td class="gauge">38</td> -</tr> - -<tr> -<td class="gauge br">39</td> -<td class="numbers">.003531</td> -<td class="center br">....</td> -<td class="center br">....</td> -<td class="numbers">.0052</td> -<td class="numbers">.099</td> -<td class="center br">....</td> -<td class="gauge">39</td> -</tr> - -<tr class="bb"> -<td class="gauge br">40</td> -<td class="numbers">.003144</td> -<td class="center br">....</td> -<td class="center br">....</td> -<td class="numbers">.0048</td> -<td class="numbers">.097</td> -<td class="center br">....</td> -<td class="gauge">40</td> -</tr> - -</table> - -<p><span class="pagenum" id="Page280">[280]</span></p> - -<h3 class="center">UNITED STATES STANDARD SIZES OF BOLTS.</h3> - -<table class="bolts" summary="Bolts"> - -<tr class="bt bb"> -<th colspan="2" class="bl br">DIAM-<br />ETER.</th> -<th colspan="2" class="br"><span class="smcap">Distance<br />Across<br />Flats,<br />Square<br />and<br />Hex.</span></th> -<th colspan="2" class="br"><span class="smcap">Distance<br />Across<br />Corners,<br />Hex.</span></th> -<th colspan="2" class="br"><span class="smcap">Thickness<br />of Head.</span></th> -</tr> - -<tr> -<td class="integer bl"> </td> -<td class="fraction"><sup>1</sup>⁄<sub>4</sub>″</td> -<td class="integer"> </td> -<td class="fraction"><sup>1</sup>⁄<sub>2</sub>″</td> -<td class="integer"> </td> -<td class="fraction"><sup>9</sup>⁄<sub>16</sub>″</td> -<td class="integer"> </td> -<td class="fraction"><sup>1</sup>⁄<sub>4</sub>″</td> -</tr> - -<tr> -<td class="integer bl"> </td> -<td class="fraction"><sup>3</sup>⁄<sub>8</sub></td> -<td class="integer"> </td> -<td class="fraction"><sup>11</sup>⁄<sub>16</sub></td> -<td class="integer"> </td> -<td class="fraction"><sup>25</sup>⁄<sub>32</sub></td> -<td class="integer"> </td> -<td class="fraction"><sup>11</sup>⁄<sub>32</sub></td> -</tr> - -<tr> -<td class="integer bl"> </td> -<td class="fraction"><sup>1</sup>⁄<sub>2</sub></td> -<td class="integer"> </td> -<td class="fraction"><sup>7</sup>⁄<sub>8</sub></td> -<td class="integer">1</td> -<td class="fraction"> </td> -<td class="integer"> </td> -<td class="fraction"><sup>7</sup>⁄<sub>16</sub></td> -</tr> - -<tr> -<td class="integer bl"> </td> -<td class="fraction"><sup>5</sup>⁄<sub>8</sub></td> -<td class="integer">1</td> -<td class="fraction"><sup>1</sup>⁄<sub>16</sub></td> -<td class="integer">1</td> -<td class="fraction"><sup>7</sup>⁄<sub>32</sub></td> -<td class="integer"> </td> -<td class="fraction"><sup>17</sup>⁄<sub>32</sub></td> -</tr> - -<tr> -<td class="integer bl"> </td> -<td class="fraction"><sup>3</sup>⁄<sub>4</sub></td> -<td class="integer">1</td> -<td class="fraction"><sup>1</sup>⁄<sub>4</sub></td> -<td class="integer">1</td> -<td class="fraction"><sup>7</sup>⁄<sub>16</sub></td> -<td class="integer"> </td> -<td class="fraction"><sup>5</sup>⁄<sub>8</sub></td> -</tr> - -<tr> -<td class="integer bl"> </td> -<td class="fraction"><sup>7</sup>⁄<sub>8</sub></td> -<td class="integer">1</td> -<td class="fraction"><sup>7</sup>⁄<sub>16</sub></td> -<td class="integer">1</td> -<td class="fraction"><sup>21</sup>⁄<sub>32</sub></td> -<td class="integer"> </td> -<td class="fraction"><sup>21</sup>⁄<sub>32</sub></td> -</tr> - -<tr> -<td class="integer bl">1</td> -<td class="fraction"> </td> -<td class="integer">1</td> -<td class="fraction"><sup>5</sup>⁄<sub>8</sub></td> -<td class="integer">1</td> -<td class="fraction"><sup>7</sup>⁄<sub>8</sub></td> -<td class="integer"> </td> -<td class="fraction"><sup>13</sup>⁄<sub>16</sub></td> -</tr> - -<tr> -<td class="integer bl">1</td> -<td class="fraction"><sup>1</sup>⁄<sub>8</sub></td> -<td class="integer">1</td> -<td class="fraction"><sup>13</sup>⁄<sub>16</sub></td> -<td class="integer">2</td> -<td class="fraction"><sup>3</sup>⁄<sub>32</sub></td> -<td class="integer"> </td> -<td class="fraction"><sup>29</sup>⁄<sub>32</sub></td> -</tr> - -<tr> -<td class="integer bl">1</td> -<td class="fraction"><sup>1</sup>⁄<sub>4</sub></td> -<td class="integer">2</td> -<td class="fraction"> </td> -<td class="integer">2</td> -<td class="fraction"><sup>5</sup>⁄<sub>16</sub></td> -<td class="integer">1</td> -<td class="fraction"> </td> -</tr> - -<tr> -<td class="integer bl">1</td> -<td class="fraction"><sup>3</sup>⁄<sub>8</sub></td> -<td class="integer">2</td> -<td class="fraction"><sup>3</sup>⁄<sub>16</sub></td> -<td class="integer">2</td> -<td class="fraction"><sup>1</sup>⁄<sub>2</sub></td> -<td class="integer">1</td> -<td class="fraction"><sup>3</sup>⁄<sub>32</sub></td> -</tr> - -<tr> -<td class="integer bl">1</td> -<td class="fraction"><sup>1</sup>⁄<sub>2</sub></td> -<td class="integer">2</td> -<td class="fraction"><sup>3</sup>⁄<sub>8</sub></td> -<td class="integer">2</td> -<td class="fraction"><sup>3</sup>⁄<sub>4</sub></td> -<td class="integer">1</td> -<td class="fraction"><sup>3</sup>⁄<sub>16</sub></td> -</tr> - -<tr> -<td class="integer bl">1</td> -<td class="fraction"><sup>5</sup>⁄<sub>8</sub></td> -<td class="integer">2</td> -<td class="fraction"><sup>9</sup>⁄<sub>16</sub></td> -<td class="integer">2</td> -<td class="fraction"><sup>15</sup>⁄<sub>16</sub></td> -<td class="integer">1</td> -<td class="fraction"><sup>9</sup>⁄<sub>32</sub></td> -</tr> - -<tr> -<td class="integer bl">1</td> -<td class="fraction"><sup>3</sup>⁄<sub>4</sub></td> -<td class="integer">2</td> -<td class="fraction"><sup>3</sup>⁄<sub>4</sub></td> -<td class="integer">3</td> -<td class="fraction"><sup>3</sup>⁄<sub>16</sub></td> -<td class="integer">1</td> -<td class="fraction"><sup>3</sup>⁄<sub>8</sub></td> -</tr> - -<tr> -<td class="integer bl">1</td> -<td class="fraction"><sup>7</sup>⁄<sub>8</sub></td> -<td class="integer">2</td> -<td class="fraction"><sup>15</sup>⁄<sub>16</sub></td> -<td class="integer">3</td> -<td class="fraction"><sup>13</sup>⁄<sub>32</sub></td> -<td class="integer">1</td> -<td class="fraction"><sup>15</sup>⁄<sub>32</sub></td> -</tr> - -<tr> -<td class="integer bl">2</td> -<td class="fraction"> </td> -<td class="integer">3</td> -<td class="fraction"><sup>1</sup>⁄<sub>8</sub></td> -<td class="integer">3</td> -<td class="fraction"><sup>5</sup>⁄<sub>8</sub></td> -<td class="integer">1</td> -<td class="fraction"><sup>9</sup>⁄<sub>16</sub></td> -</tr> - -<tr> -<td class="integer bl">2</td> -<td class="fraction"><sup>1</sup>⁄<sub>4</sub></td> -<td class="integer">3</td> -<td class="fraction"><sup>1</sup>⁄<sub>2</sub></td> -<td class="integer">4</td> -<td class="fraction"><sup>1</sup>⁄<sub>16</sub></td> -<td class="integer">1</td> -<td class="fraction"><sup>3</sup>⁄<sub>4</sub></td> -</tr> - -<tr> -<td class="integer bl">2</td> -<td class="fraction"><sup>1</sup>⁄<sub>2</sub></td> -<td class="integer">3</td> -<td class="fraction"><sup>7</sup>⁄<sub>8</sub></td> -<td class="integer">4</td> -<td class="fraction"><sup>1</sup>⁄<sub>2</sub></td> -<td class="integer">1</td> -<td class="fraction"><sup>15</sup>⁄<sub>16</sub></td> -</tr> - -<tr> -<td class="integer bl">2</td> -<td class="fraction"><sup>3</sup>⁄<sub>4</sub></td> -<td class="integer">4</td> -<td class="fraction"><sup>1</sup>⁄<sub>4</sub></td> -<td class="integer">4</td> -<td class="fraction"><sup>7</sup>⁄<sub>8</sub></td> -<td class="integer">2</td> -<td class="fraction"><sup>1</sup>⁄<sub>8</sub></td> -</tr> - -<tr class="bb"> -<td class="integer bl">3</td> -<td class="fraction"> </td> -<td class="integer">4</td> -<td class="fraction"><sup>5</sup>⁄<sub>8</sub></td> -<td class="integer">5</td> -<td class="fraction"><sup>11</sup>⁄<sub>32</sub></td> -<td class="integer">2</td> -<td class="fraction"><sup>5</sup>⁄<sub>16</sub></td> -</tr> - -</table> - - -<h3 class="center">UNITED STATES STANDARD SCREW -THREAD GAUGE.</h3> - -<div class="container w30em" id="Fig316"> -<img src="images/illo280.jpg" alt="Gauge" /> -<p class="caption">Fig. 316.</p> -</div> - -<hr class="chap x-ebookmaker-drop" /> - -<div class="chapter"> - -<p><span class="pagenum" id="Page281">[281]</span></p> - -<h2 class="nobreak">Some Things Personal.</h2> - -</div><!--chapter--> - -<p>In the preparation of this work the idea of self-help has never been forgotten; -nothing has been held back or omitted which would, in the author’s opinion, tend -to advance the student in the draughtsman’s art.</p> - -<p>The volume contains the experience in practical drawing, as related to engineering -and mechanics, of over one hundred years, i. e., the author’s, Mr. Perrott’s and Mr. Lucas’ -experiences added together exceed that period.</p> - -<p>Hence, the work should be really helpful; it has been aimed also to be entertaining -and with easy tasks; all the illustrations of the book are recommended as -models for practice—they have been selected with that view.</p> - -<p>Moreover, as between author and publishers, the latter have agreed to issue the -work in the most thorough style possible—as to paper, printing and binding—and to -sell it at a very generously low price, considering all things.</p> - -<p>With the closing words “hail and farewell,” the author bids adieu (God be with -you) to the reader and the student.</p> - -<hr class="chap x-ebookmaker-drop" /> - -<p><span class="pagenum" id="Page282">[282]</span></p> - -<div class="container w30em"> -<img src="images/illo282.jpg" alt="" /> -<p class="caption">BEACON LIGHT.</p> -</div> - -<hr class="chap x-ebookmaker-drop" /> - -<div class="chapter"> - -<p><span class="pagenum" id="Page283">[283]</span></p> - -<h2 class="nobreak">Hawkins’ <span class="horsplit"><span class="top noline">Self</span><span class="bot">Help</span></span> -Mechanical Drawing.<br /> -<span class="high">Index.</span></h2> - -</div><!--chapter--> - -<ul class="index"> - -<li><span class="righttext fsize70">PAGE</span></li> - -<li><b>Acute Angle</b>, def. <span class="righttext"><a href="#Page42">42</a></span></li> - -<li><b>Acute-Angled Triangle</b>, def. <span class="righttext"><a href="#Page50">50</a></span></li> - -<li><b>Addendum Circle</b>, illus. <span class="righttext"><a href="#Page200">200</a></span></li> - -<li><b>Alphabets</b>, Gothic, desc. <span class="righttext"><a href="#Page171">171</a></span></li> - -<li><b>Altitude</b>, def. <span class="righttext"><a href="#Page41">41</a></span></li> - -<li><b>Altitude of a Polygon</b>, def. <span class="righttext"><a href="#Page47">47</a></span></li> - -<li><b>American Machinist</b>, Quotation from <span class="righttext"><a href="#Page141">141</a></span></li> - -<li><b>Angle</b>, def. <span class="righttext"><a href="#Page41">41</a>, <a href="#Page83">83</a></span></li> -<li class="level1">To bisect an <span class="righttext"><a href="#Page89">89</a></span></li> -<li class="level1">To draw an <span class="righttext"><a href="#Page89">89</a></span></li> - -<li><b>Angle-Iron</b>, illus. <span class="righttext"><a href="#Page75">75</a></span></li> - -<li><b>Angle-Plate</b>, illus. <span class="righttext"><a href="#Page75">75</a></span></li> - -<li><b>Angular Perspective Drawing</b>, illus. <span class="righttext"><a href="#Page260">260</a>, -<a href="#Page265">265</a></span></li> - -<li><b>Apex</b>, def. <span class="righttext"><a href="#Page42">42</a></span></li> - -<li><b>Apex of an Angle</b>, def. <span class="righttext"><a href="#Page42">42</a></span></li> - -<li><b>Arc</b>, def. <span class="righttext"><a href="#Page42">42</a></span></li> -<li class="level1">Complement of an <span class="righttext"><a href="#Page99">99</a></span></li> -<li class="level1">Cosecant of an <span class="righttext"><a href="#Page99">99</a></span></li> -<li class="level1">Cotangent of an <span class="righttext"><a href="#Page99">99</a></span></li> -<li class="level1">Sine of an <span class="righttext"><a href="#Page99">99</a></span></li> -<li class="level1">Supplement of an <span class="righttext"><a href="#Page99">99</a></span></li> -<li class="level1">Tangent of an <span class="righttext"><a href="#Page99">99</a></span></li> -<li class="level1">Versed Sine of an <span class="righttext"><a href="#Page99">99</a></span></li> - -<li><b>Arc of Circle</b>, To find the center of an <span class="righttext"><a href="#Page90">90</a></span></li> - -<li><b>Arcs</b>, Drawing<span class="pagenum" id="Page284">[284]</span> -<span class="righttext"><a href="#Page146">146</a></span></li> -<li class="level1">Illus. <span class="righttext"><a href="#Page146">146</a></span></li> - -<li><b>Arrow-Heads</b>, how made <span class="righttext"><a href="#Page172">172</a>, <a href="#Page176">176</a></span></li> - -<li><b>Axiom</b>, def. <span class="righttext"><a href="#Page83">83</a></span></li> - -<li><b>Axis</b>, Conjugate, def. <span class="righttext"><a href="#Page96">96</a></span></li> -<li class="level1">Of a Figure, def. <span class="righttext"><a href="#Page43">43</a></span></li> -<li class="level1">Of a Solid, def. <span class="righttext"><a href="#Page42">42</a></span></li> -<li class="level1">Transverse, def. <span class="righttext"><a href="#Page96">96</a></span></li> - -<li class="startletter"><b>Backlash in Gearing</b> <span class="righttext"><a href="#Page215">215</a></span></li> - -<li><b>Backward Projection</b> <span class="righttext">desc. <a href="#Page152">152</a>, illus. -<a href="#Page152">152-3</a></span></li> - -<li><b>Base</b>, def. <span class="righttext"><a href="#Page43">43</a></span></li> -<li class="level1">Of a Polygon, def. <span class="righttext"><a href="#Page47">47</a></span></li> - -<li><b>Beacon Light</b>, illus. <span class="righttext"><a href="#Page282">282</a></span></li> - -<li><b>Beam Compasses</b> <span class="righttext">desc. <a href="#Page124">124</a>, illus. -<a href="#Page124">124</a></span></li> - -<li><b>Bending Machine</b>, Hydraulic <span class="righttext">desc. <a href="#Page221">221</a>, illus. -<a href="#Page220">220-1</a></span></li> - -<li><b>Benjamin, Prof. Chas.</b>, “How and What to Study” <span class="righttext"><a href="#Page23">23</a></span></li> - -<li><b>Bevel-Gear</b>, desc. <span class="righttext"><a href="#Page201">201</a></span></li> - -<li><b>Bevel Mortise Wheel</b>, desc. <span class="righttext"><a href="#Page203">203</a></span></li> - -<li><b>Bevel Wheel</b> <span class="righttext">desc. <a href="#Page199">199</a>, illus. -<a href="#Page203">203</a></span></li> - -<li><b>Bisect</b>, def. <span class="righttext"><a href="#Page43">43</a></span></li> - -<li><b>Bisector</b>, def. <span class="righttext"><a href="#Page43">43</a></span></li> - -<li><b>Blackboard</b>, illus. and desc. <span class="righttext"><a href="#Page27">27</a></span></li> - -<li><b>Blackboard Drawing</b> <span class="righttext"><a href="#Page28">28</a></span></li> - -<li><b>Blue Printing</b> <span class="righttext">desc. <a href="#Page186">186</a>, illus. -<a href="#Page187">187</a></span></li> -<li class="level1">Test pieces <span class="righttext"><a href="#Page188">188</a></span></li> - -<li><b>Blue Prints</b>, Office rules for <span class="righttext"><a href="#Page196">196</a></span></li> - -<li><b>Black Process Copying</b> <span class="righttext"><a href="#Page188">188</a></span></li> - -<li><b>Boiler-Plate</b>, Riveted, illus. <span class="righttext"><a href="#Page76">76</a></span></li> - -<li><b>Bolt</b>, Square-head, illus. <span class="righttext"><a href="#Page76">76</a></span></li> - -<li><b>Bolt and Nut</b>, Square-head <span class="righttext">desc. <a href="#Page144">144</a>, illus. -<a href="#Page145">145</a></span></li> -<li class="level1">Hexagon <span class="righttext">desc. <a href="#Page144">144</a>, illus. <a href="#Page76">76</a>, -<a href="#Page144">144</a></span></li> - -<li><b>Bow-Dividers</b> <span class="righttext">desc. <a href="#Page123">123</a>, illus. <a href="#Page122">122</a></span></li> - -<li><b>Bow-Pencil</b>, desc. <span class="righttext"><a href="#Page123">123</a></span></li> - -<li><b>Bows</b>, Use of <span class="righttext"><a href="#Page242">242</a></span></li> - -<li><b>Brick</b>, Section Lining, illus. <span class="righttext"><a href="#Page182">182</a></span></li> - -<li><b>Broken Lines</b>, How to Draw <span class="righttext"><a href="#Page33">33</a></span></li> -<li class="level1">Def. <span class="righttext"><a href="#Page46">46</a></span></li> - -<li><b>Bumping Post</b>, illus. <span class="righttext"><a href="#Page226">226</a></span></li> - -<li class="startletter"><b>Calipers</b>, illus. <span class="righttext"><a href="#Pagevi">vi</a></span></li> - -<li><b>Cast-Iron</b>, Section-Lining, illus. <span class="righttext"><a href="#Page182">182</a></span></li> - -<li><b>Caulking Tool</b>, illus.<span class="pagenum" id="Page285">[285]</span> -<span class="righttext"><a href="#Page76">76</a></span></li> - -<li><b>Center Line</b>, def. <span class="righttext"><a href="#Page46">46</a></span></li> - -<li><b>Center Lines</b>, In Drawings <span class="righttext"><a href="#Page240">240-1</a></span></li> -<li class="level1">In Shop Drawings <span class="righttext"><a href="#Page192">192</a></span></li> - -<li><b>Chalk-Crayon</b> <span class="righttext">desc. <a href="#Page27">27</a>, illus. <a href="#Page27">27</a>, -<a href="#Page37">37</a></span></li> - -<li><b>Chalk-Work</b> <span class="righttext"><a href="#Page27">27</a></span></li> -<li class="level1">Instruments for Drawing, illus. <span class="righttext"><a href="#Page29">29</a></span></li> - -<li><b>Channel-Iron</b>, illus. <span class="righttext"><a href="#Page75">75</a></span></li> - -<li><b>Checking Drawings</b> <span class="righttext"><a href="#Page194">194</a></span></li> - -<li><b>Circle</b>, def. <span class="righttext"><a href="#Page43">43</a></span></li> -<li class="level1">To describe about a square <span class="righttext"><a href="#Page93">93</a></span></li> -<li class="level2">about a triangle <span class="righttext"><a href="#Page93">93</a></span></li> -<li class="level2">through two points <span class="righttext"><a href="#Page90">90</a></span></li> -<li class="level2">through three points <span class="righttext"><a href="#Page90">90</a></span></li> -<li class="level1">To find the center <span class="righttext"><a href="#Page90">90</a></span></li> -<li class="level1">To inscribe in a square <span class="righttext"><a href="#Page94">94</a></span></li> -<li class="level2">in a triangle <span class="righttext"><a href="#Page94">94</a></span></li> - -<li><b>Circles</b>, Drawing <span class="righttext">desc. <a href="#Page146">146</a>, illus. -<a href="#Page146">146</a></span></li> - -<li><b>Circumference of a Circle</b> <span class="righttext"><a href="#Page43">43</a></span></li> - -<li><b>Circumscribe</b>, def. <span class="righttext"><a href="#Page43">43</a></span></li> - -<li><b>Circular Pitch Line</b>, illus. <span class="righttext"><a href="#Page200">200</a></span></li> - -<li><b>Classifying Drawings</b>, Office Rules for <span class="righttext"><a href="#Page191">191</a></span></li> - -<li><b>Clearance in Wheel Teeth</b> <span class="righttext"><a href="#Page215">215</a></span></li> - -<li><b>Cog-Wheel</b> <span class="righttext">def. <a href="#Page201">201</a>, illus. <a href="#Page201">201</a></span></li> -<li class="level1">Section Lining, illus. <span class="righttext"><a href="#Page183">183</a></span></li> - -<li><b>Coin</b>, Perspective View of a, illus. <span class="righttext"><a href="#Page248">248</a></span></li> - -<li><b>Color and Tints</b> <span class="righttext"><a href="#Page185">185</a></span></li> - -<li><b>Compass</b>, Mariners’, illus. <span class="righttext"><a href="#Page268">268</a></span></li> - -<li><b>Compasses</b>, Beam, desc. and illus. <span class="righttext"><a href="#Page124">124</a></span></li> -<li class="level1">Desc. and illus. <span class="righttext"><a href="#Page121">121</a></span></li> -<li class="level1">For holding chalk, illus. <span class="righttext"><a href="#Page29">29</a></span></li> -<li class="level1">How to hold, illus. <span class="righttext"><a href="#Page136">136</a></span></li> - -<li><b>Complement of an Arc</b> <span class="righttext"><a href="#Page99">99</a></span></li> - -<li><b>Composition</b>, Section-Lining, illus. <span class="righttext"><a href="#Page182">182</a></span></li> - -<li><b>Concave</b>, def. <span class="righttext"><a href="#Page44">44</a></span></li> - -<li><b>Cone</b>, def. <span class="righttext"><a href="#Page44">44</a></span></li> - -<li><b>Conjugate Axis</b>, def. <span class="righttext"><a href="#Page96">96</a></span></li> - -<li><b>Construction</b>, def. <span class="righttext"><a href="#Page44">44</a></span></li> -<li class="level1">Line, def. <span class="righttext"><a href="#Page46">46</a></span></li> - -<li><b>Contents</b>, Table of <span class="righttext"><a href="#Page24">24</a></span></li> - -<li><b>Contour</b>, def. <span class="righttext"><a href="#Page44">44</a></span></li> - -<li><b>Convergence</b>, def. <span class="righttext"><a href="#Page44">44</a></span></li> - -<li><b>Convex</b>, def.<span class="pagenum" id="Page286">[286]</span> -<span class="righttext"><a href="#Page44">44</a></span></li> - -<li><b>Copying Drawings</b>, Black Process <span class="righttext"><a href="#Page188">188</a></span></li> -<li class="level1">Blue Printing <span class="righttext"><a href="#Page186">186</a></span></li> -<li class="level1">Tracing <span class="righttext"><a href="#Page184">184</a></span></li> - -<li><b>Copyright</b> <span class="righttext"><a href="#Pageviii">viii</a></span></li> - -<li><b>Corner</b>, def. <span class="righttext"><a href="#Page44">44</a></span></li> - -<li><b>Corollary</b>, def. <span class="righttext"><a href="#Page83">83</a></span></li> - -<li><b>Co-secant of an Arc</b>, def. <span class="righttext"><a href="#Page99">99</a></span></li> - -<li><b>Co-sine of an Arc</b>, def. <span class="righttext"><a href="#Page99">99</a></span></li> - -<li><b>Co-tangent of an Arc</b>, def. <span class="righttext"><a href="#Page99">99</a></span></li> - -<li><b>Crane</b>, desc. <span class="righttext"><a href="#Page219">219</a></span></li> -<li class="level1">Working drawing of, illus. <span class="righttext"><a href="#Page218">218</a></span></li> - -<li><b>Cross-Hatches</b>, def. <span class="righttext"><a href="#Page44">44</a></span></li> - -<li><b>Cross-hatching Drawings</b> <span class="righttext"><a href="#Page182">182</a></span></li> - -<li><b>Crown Wheel</b>, illus. <span class="righttext"><a href="#Page208">208</a></span></li> - -<li><b>Curve</b>, def. <span class="righttext"><a href="#Page44">44</a></span></li> - -<li><b>Curved Line</b>, def. <span class="righttext"><a href="#Page46">46</a></span></li> - -<li><b>Curved Lines</b>, Drawing, desc. <span class="righttext"><a href="#Page69">69</a></span></li> -<li class="level1">Drawing Figures of <span class="righttext"><a href="#Page70">70</a>, <a href="#Page72">72</a>, -<a href="#Page73">73</a></span></li> -<li class="level1">How to Draw <span class="righttext"><a href="#Page35">35</a></span></li> -<li class="level1">Illus. <span class="righttext"><a href="#Page70">70</a></span></li> - -<li><b>Curved Surface</b>, def. <span class="righttext"><a href="#Page49">49</a></span></li> - -<li><b>Curve or Scroll</b>, illus. <span class="righttext"><a href="#Page117">117</a></span></li> - -<li><b>Cut Gears</b>, desc. <span class="righttext"><a href="#Page215">215</a></span></li> - -<li><b>Cylinder</b>, def. <span class="righttext"><a href="#Page44">44</a></span></li> - -<li><b>Cylindrical</b>, def. <span class="righttext"><a href="#Page44">44</a></span></li> - -<li><b>Cylindrical Projection</b>, illus. <span class="righttext"><a href="#Page161">161</a></span></li> - -<li class="startletter"><b>Dash Line</b>, def. <span class="righttext"><a href="#Page46">46</a></span></li> - -<li><b>Decimal Equivalents</b>, Table of <span class="righttext"><a href="#Page269">269</a></span></li> - -<li><b>Dedication</b> <span class="righttext"><a href="#Pageix">ix</a></span></li> - -<li><b>Definitions</b>, Preliminary <span class="righttext"><a href="#Page41">41</a></span></li> - -<li><b>Degree</b>, def. <span class="righttext"><a href="#Page41">41</a>, <a href="#Page44">44</a></span></li> - -<li><b>Describe</b>, def. <span class="righttext"><a href="#Page44">44</a></span></li> - -<li><b>Design</b>, def. <span class="righttext"><a href="#Page44">44</a></span></li> -<li class="level1">Symmetry in, def. <span class="righttext"><a href="#Page50">50</a></span></li> - -<li><b>Designing Gears</b> <span class="righttext"><a href="#Page209">209</a></span></li> - -<li><b>Detail Drawings</b>, Office Rules for <span class="righttext"><a href="#Page191">191</a></span></li> - -<li><b>Develop</b>, def. <span class="righttext"><a href="#Page45">45</a></span></li> - -<li><b>Diagonal</b>, def. <span class="righttext"><a href="#Page45">45</a></span></li> - -<li><b>Diagonals of a Polygon</b>, def. <span class="righttext"><a href="#Page47">47</a></span></li> - -<li><b>Diameter</b>, def. <span class="righttext"><a href="#Page45">45</a></span></li> - -<li><b>Diameter</b>, Of a Circle<span class="pagenum" id="Page287">[287]</span> -<span class="righttext"><a href="#Page43">43</a></span></li> - -<li><b>Diameters of Wheels</b>, How to Measure <span class="righttext"><a href="#Page199">199</a></span></li> - -<li><b>Diametral Pitch</b>, desc. <span class="righttext"><a href="#Page200">200</a></span></li> -<li class="level1">Of Gears <span class="righttext"><a href="#Page212">212</a></span></li> - -<li><b>Dimensioning Drawings</b> <span class="righttext">desc. <a href="#Page176">176</a>, illus. -<a href="#Page177">177</a>, <a href="#Page179">179</a></span></li> - -<li><b>Dimension Line</b>, def. <span class="righttext"><a href="#Page46">46</a></span></li> - -<li><b>Dimensions on Drawings</b>, Office Rules for <span class="righttext"><a href="#Page192">192</a></span></li> - -<li><b>Dividers and Compasses</b>, desc. <span class="righttext"><a href="#Page119">119</a></span></li> - -<li><b>Dividers</b>, illus. <span class="righttext"><a href="#Page82">82</a>, <a href="#Page119">119</a></span></li> -<li class="level1">Bisecting, desc. <span class="righttext"><a href="#Page119">119</a></span></li> -<li class="level1">Bow, illus. <span class="righttext"><a href="#Page122">122</a></span></li> -<li class="level1">“Point” <span class="righttext"><a href="#Page242">242</a></span></li> -<li class="level1">Proportional <span class="righttext">desc. <a href="#Page119">119</a>, illus. -<a href="#Page120">120</a></span></li> -<li class="level1">Spring Bow, desc. <span class="righttext"><a href="#Page124">124</a></span></li> - -<li><b>Dodecahedron</b>, def. <span class="righttext"><a href="#Page48">48</a></span></li> - -<li><b>Dot-and-Dash Line</b>, def. <span class="righttext"><a href="#Page46">46</a></span></li> - -<li><b>Dotted Line</b>, def. <span class="righttext"><a href="#Page46">46</a></span></li> - -<li><b>Draughtsmen</b>, Useful Tables for -<span class="righttext"><a href="#Page269">269</a>-<a href="#Page280">280</a></span></li> - -<li><b>Drawing</b>, Blackboard <span class="righttext"><a href="#Page28">28</a></span></li> -<li class="level1">Free hand <span class="righttext"><a href="#Page55">55</a></span></li> -<li class="level1">Linear Perspective <span class="righttext"><a href="#Page247">247</a></span></li> -<li class="level1">Parallel Perspective <span class="righttext"><a href="#Page260">260-1</a></span></li> -<li class="level1">Projection, desc. <span class="righttext"><a href="#Page148">148</a></span></li> -<li class="level1">Scale Perspective <span class="righttext"><a href="#Page257">257</a></span></li> -<li class="level1">Spur Gear, illus. <span class="righttext"><a href="#Page163">163</a>, -<a href="#Page211">211</a></span></li> -<li class="level1">Spur Wheel, desc. <span class="righttext"><a href="#Page162">162</a></span></li> -<li class="level1">Straight Line Figures <span class="righttext">desc. <a href="#Page65">65</a>, illus. -<a href="#Page66">66-7-8</a></span></li> -<li class="level1">Symbols <span class="righttext"><a href="#Page193">193</a></span></li> -<li class="level1">The Pitch Line <span class="righttext"><a href="#Page209">209</a></span></li> -<li class="level1">To Scale, desc. <span class="righttext"><a href="#Page126">126</a></span></li> -<li class="level1">Working, def. <span class="righttext"><a href="#Page51">51</a></span></li> - -<li><b>Drawing-Board</b> <span class="righttext">desc. <a href="#Page107">107</a>, illus. <a href="#Page102">102</a>, -<a href="#Page106">106</a>, <a href="#Page108">108</a></span></li> -<li class="level1">Expansion and Contraction of <span class="righttext"><a href="#Page108">108</a></span></li> -<li class="level1">How to Construct <span class="righttext"><a href="#Page107">107</a></span></li> -<li class="level1">Trestles, illus. <span class="righttext"><a href="#Page110">110</a>, -<a href="#Page111">111</a></span></li> - -<li><b>Drawing Instruments</b>, desc. <span class="righttext"><a href="#Page103">103</a></span></li> -<li class="level1">How to Select <span class="righttext"><a href="#Page104">104</a></span></li> -<li class="level1">Illus. <span class="righttext"><a href="#Page105">105</a></span></li> -<li class="level1">Outfit Recommended <span class="righttext"><a href="#Page104">104</a></span></li> - -<li><b>Drawing Materials</b>, desc. <span class="righttext"><a href="#Page103">103</a></span></li> - -<li><b>Drawing Office Rules</b> <span class="righttext"><a href="#Page191">191</a></span></li> - -<li><b>Drawing Paper</b>, desc. <span class="righttext"><a href="#Page132">132</a></span></li> -<li class="level1">Erasing lines<span class="pagenum" id="Page288">[288]</span> -<span class="righttext"><a href="#Page140">140</a></span></li> -<li class="level1">Fixing of, illus. <span class="righttext"><a href="#Page102">102</a></span></li> -<li class="level1">Fixing on the Board <span class="righttext"><a href="#Page139">139</a></span></li> -<li class="level1">Pasting <span class="righttext"><a href="#Page184">184</a></span></li> -<li class="level1">“Points” <span class="righttext"><a href="#Page243">243</a></span></li> -<li class="level1">Patent Office Sizes <span class="righttext"><a href="#Page234">234</a></span></li> -<li class="level1">Sizes of <span class="righttext"><a href="#Page133">133</a></span></li> - -<li><b>Drawing Pencils</b>, desc. and illus. <span class="righttext"><a href="#Page118">118</a></span></li> -<li class="level1">How to Use <span class="righttext"><a href="#Page56">56</a></span></li> - -<li><b>Drawing Pen</b>, Filling with ink, illus. <span class="righttext"><a href="#Page130">130</a></span></li> - -<li><b>Drawing Pens</b>, desc. and illus. <span class="righttext"><a href="#Page129">129</a></span></li> - -<li><b>Drawing-Pins</b>, desc. <span class="righttext"><a href="#Page110">110</a></span></li> - -<li><b>Drawing Scales</b>, desc. <span class="righttext"><a href="#Page126">126</a></span></li> - -<li><b>Drawings</b>, Cleaning, desc. <span class="righttext"><a href="#Page169">169</a></span></li> -<li class="level1">Color and Finish, note <span class="righttext"><a href="#Page185">185</a></span></li> -<li class="level1">Dimensioning, desc. <span class="righttext"><a href="#Page176">176</a></span></li> -<li class="level1">Inking in, desc. <span class="righttext"><a href="#Page167">167</a></span></li> -<li class="level1">Lettering, desc. <span class="righttext"><a href="#Page171">171</a></span></li> -<li class="level1">Patent Office Rules for <span class="righttext"><a href="#Page233">233</a></span></li> -<li class="level1">Reproducing <span class="righttext"><a href="#Page186">186</a></span></li> -<li class="level1">Section-Lining, desc. <span class="righttext"><a href="#Page182">182</a></span></li> -<li class="level1">Shading <span class="righttext">desc. <a href="#Page180">180</a>, illus. <a href="#Page180">180</a>, -<a href="#Page225">225</a></span></li> -<li class="level1">Size of, Office Rules <span class="righttext"><a href="#Page191">191</a></span></li> -<li class="level1">Tint and Color, desc. <span class="righttext"><a href="#Page184">184</a></span></li> - -<li><b>Drawing-Table</b>, desc. <span class="righttext"><a href="#Page111">111</a></span></li> -<li class="level1">Folding Legs, illus. <span class="righttext"><a href="#Page104">104</a></span></li> - -<li class="startletter"><b>Edge</b>, def. <span class="righttext"><a href="#Page45">45</a></span></li> - -<li><b>Elevation</b>, def. <span class="righttext"><a href="#Page45">45</a></span></li> - -<li><b>Elevation and Section</b>, Spur Wheel <span class="righttext">desc. <a href="#Page216">216</a>, illus. -<a href="#Page212">212</a></span></li> - -<li><b>Ellipse, An</b>, desc. <span class="righttext"><a href="#Page96">96</a>, <a href="#Page118">118</a></span></li> -<li class="level1">To describe when length and breadth are given <span class="righttext"><a href="#Page96">96</a></span></li> - -<li><b>Envelopes</b>, Portfolio, desc. <span class="righttext"><a href="#Page142">142</a></span></li> - -<li><b>Equiangular Triangle</b>, def. <span class="righttext"><a href="#Page45">45</a></span></li> - -<li><b>Equilateral Triangle</b>, def. <span class="righttext"><a href="#Page50">50</a></span></li> - -<li><b>Erasing</b>, “Points” on <span class="righttext"><a href="#Page242">242</a></span></li> - -<li><b>Eye</b>, illus. and desc. <span class="righttext"><a href="#Page253">253</a></span></li> -<li class="level1">Effect of Light on <span class="righttext"><a href="#Page253">253</a></span></li> - -<li class="startletter"><b>Face</b>, def. <span class="righttext"><a href="#Page45">45</a></span></li> - -<li><b>Faced Surfaces</b>, Points, etc. <span class="righttext"><a href="#Page242">242</a></span></li> - -<li><b>Figures</b>, Drawing Straight-line <span class="righttext"><a href="#Page65">65</a></span></li> -<li class="level1">Numerals, examples of<span class="pagenum" id="Page289">[289]</span> -<span class="righttext"><a href="#Page173">173</a></span></li> -<li class="level1">Straight-line, illus. <span class="righttext"><a href="#Page66">66</a></span></li> - -<li><b>File Handle</b>, desc. and illus. <span class="righttext"><a href="#Page144">144</a></span></li> - -<li><b>Finger and Thumb Lines</b>, illus. <span class="righttext"><a href="#Page64">64</a></span></li> - -<li><b>Finished Surfaces</b>, How to indicate <span class="righttext"><a href="#Page193">193</a></span></li> -<li class="level1">“Points” <span class="righttext"><a href="#Page242">242</a></span></li> - -<li><b>Finishing</b>, def. <span class="righttext"><a href="#Page45">45</a></span></li> - -<li><b>Flanged-tooth Wheel</b>, desc. <span class="righttext"><a href="#Page205">205</a></span></li> - -<li><b>Flat Pattern</b>, def. <span class="righttext"><a href="#Page47">47</a></span></li> - -<li><b>Foreshortening</b>, def. <span class="righttext"><a href="#Page45">45</a></span></li> - -<li><b>Forward Projection</b> <span class="righttext">desc. <a href="#Page151">151</a>, <a href="#Page152">152</a>, -illus. <a href="#Page155">155</a></span></li> - -<li><b>Free-hand</b>, def. <span class="righttext"><a href="#Page45">45</a></span></li> - -<li><b>Free-hand Drawing</b> <span class="righttext"><a href="#Page55">55</a>, <a href="#Page78">78</a></span></li> -<li class="level1">First Lesson in <span class="righttext"><a href="#Page30">30</a></span></li> -<li class="level1">Penciling, illus. <span class="righttext"><a href="#Page54">54</a></span></li> - -<li><b>Free-hand Illustration</b>, a Water Wheel <span class="righttext"><a href="#Page78">78</a></span></li> - -<li><b>Friction-Clutch and Pulley</b>, desc. <span class="righttext"><a href="#Page224">224</a></span></li> - -<li><b>Friction Gear-Wheels</b>, desc. <span class="righttext"><a href="#Page201">201</a></span></li> - -<li><b>Full Line</b>, def. <span class="righttext"><a href="#Page46">46</a></span></li> - -<li class="startletter"><b>Gear</b>, def. <span class="righttext"><a href="#Page199">199</a></span></li> - -<li><b>Gearing</b>, desc. <span class="righttext"><a href="#Page199">199</a></span></li> -<li class="level1">Drawing <span class="righttext">desc. <a href="#Page162">162</a>, illus. -<a href="#Page163">163</a></span></li> - -<li><b>Gearing and Design</b> <span class="righttext"><a href="#Page197">197</a></span></li> - -<li><b>Gears</b>, A Train of, desc. <span class="righttext"><a href="#Page208">208</a></span></li> -<li class="level1">Speed of <span class="righttext"><a href="#Page208">208</a></span></li> - -<li><b>Gear-Wheels</b>, Spur, illus. <span class="righttext"><a href="#Page198">198</a></span></li> - -<li><b>Generated</b>, def. <span class="righttext"><a href="#Page45">45</a></span></li> - -<li><b>Geometric</b>, def. <span class="righttext"><a href="#Page45">45</a></span></li> - -<li><b>Geometrical Axioms</b> <span class="righttext"><a href="#Page84">84</a></span></li> - -<li><b>Geometrical Drawing</b>, desc. <span class="righttext"><a href="#Page81">81</a></span></li> -<li class="level1">Problems in <span class="righttext"><a href="#Page86">86</a></span></li> - -<li><b>Geometrical Signs</b> <span class="righttext"><a href="#Page84">84</a></span></li> - -<li><b>Geometry</b>, defs. <span class="righttext"><a href="#Page249">249</a></span></li> -<li class="level1">Elements of <span class="righttext"><a href="#Page81">81</a></span></li> - -<li><b>Gothic Letters</b>, illus. <span class="righttext"><a href="#Page173">173</a></span></li> - -<li><b>Grooved Friction Wheels</b>, desc. <span class="righttext"><a href="#Page201">201</a></span></li> - -<li><b>Ground-Plane</b> <span class="righttext">def. <a href="#Page249">249</a>, <a href="#Page255">255</a>, illus. -<a href="#Page249">249</a></span></li> - -<li class="startletter"><b>Half-Tint</b>, def. <span class="righttext"><a href="#Page45">45</a></span></li> - -<li><b>Hand-Wheel</b>, illus. <span class="righttext"><a href="#Page77">77</a></span></li> - -<li><b>Hanger</b>, illus.<span class="pagenum" id="Page290">[290]</span> -<span class="righttext"><a href="#Page179">179</a></span></li> - -<li><b>Helical Wheel</b> <span class="righttext">desc. <a href="#Page199">199</a>, illus. -<a href="#Page207">207</a></span></li> - -<li><b>Hemisphere</b>, def. <span class="righttext"><a href="#Page45">45</a></span></li> - -<li><b>Heptagon</b>, def. <span class="righttext"><a href="#Page47">47</a></span></li> - -<li><b>Hexagon</b>, def. <span class="righttext"><a href="#Page47">47</a></span></li> -<li class="level1">To Construct a <span class="righttext"><a href="#Page95">95</a></span></li> - -<li><b>Hexagon-Head Bolt</b>, illus. <span class="righttext"><a href="#Page144">144</a></span></li> - -<li><b>Hexahedron</b>, def. <span class="righttext"><a href="#Page48">48</a></span></li> - -<li><b>Horizontal</b>, def. <span class="righttext"><a href="#Page45">45</a>, <a href="#Page250">250</a></span></li> - -<li><b>Horizontal Line</b>, in Drawing, illus. <span class="righttext"><a href="#Page250">250</a></span></li> -<li class="level1">How to Draw <span class="righttext"><a href="#Page32">32</a></span></li> -<li class="level1">In Perspective <span class="righttext"><a href="#Page252">252</a></span></li> - -<li><b>Hypothesis</b>, def. <span class="righttext"><a href="#Page83">83</a></span></li> - -<li class="startletter"><b>Icosahedron</b>, def. <span class="righttext"><a href="#Page48">48</a></span></li> - -<li><b>India Ink</b>, desc. and illus. <span class="righttext"><a href="#Page131">131</a></span></li> -<li class="level1">Dish or Tile, illus. <span class="righttext"><a href="#Page131">131</a></span></li> - -<li><b>India Rubber Eraser</b>, illus. <span class="righttext"><a href="#Page132">132</a></span></li> -<li class="level1">Use of <span class="righttext"><a href="#Page240">240</a></span></li> - -<li><b>Ink</b>, Preparing, for Drawings, desc. <span class="righttext"><a href="#Page167">167</a></span></li> -<li class="level1">Test for Good, desc. <span class="righttext"><a href="#Page167">167</a></span></li> - -<li><b>Ink Eraser</b>, Steel, desc. and illus. <span class="righttext"><a href="#Page132">132</a></span></li> - -<li><b>Inking</b>, illus. <span class="righttext"><a href="#Page166">166</a>, <a href="#Page169">169</a></span></li> -<li class="level1">Long Lines, illus. <span class="righttext"><a href="#Page170">170</a></span></li> -<li class="level1">Rules of Procedure <span class="righttext"><a href="#Page168">168</a></span></li> -<li class="level1">Short Work, illus. <span class="righttext"><a href="#Page169">169</a></span></li> - -<li>“<b>Inking in</b>” Drawings, desc. <span class="righttext"><a href="#Page167">167</a></span></li> -<li class="level1">“Points,” etc. <span class="righttext"><a href="#Page239">239</a>, <a href="#Page243">243</a></span></li> -<li class="level1">Patent Office Drawings <span class="righttext"><a href="#Page234">234</a></span></li> - -<li><b>Inscribe</b>, def. <span class="righttext"><a href="#Page45">45</a></span></li> - -<li><b>Instrumental</b>, def. <span class="righttext"><a href="#Page45">45</a></span></li> - -<li><b>Instruments</b> for Chalk-work, illus. <span class="righttext"><a href="#Page29">29</a></span></li> - -<li><b>Internal Gear</b>, desc. <span class="righttext"><a href="#Page201">201</a></span></li> - -<li><b>Internal-Gear Wheel</b>, illus. <span class="righttext"><a href="#Page207">207</a></span></li> - -<li><b>Introduction</b> <span class="righttext"><a href="#Page15">15</a></span></li> - -<li><b>Isosceles Triangle</b>, def. <span class="righttext"><a href="#Page50">50</a></span></li> - -<li class="startletter"><b>Lantern-Wheel</b>, desc. <span class="righttext"><a href="#Page201">201</a></span></li> - -<li><b>Lathe-Dog</b>, illus. <span class="righttext"><a href="#Page76">76</a></span></li> - -<li><b>Lemma</b>, def. <span class="righttext"><a href="#Page83">83</a></span></li> - -<li><b>Lettering</b>, Blow-Off Valve, illus. <span class="righttext"><a href="#Page175">175</a></span></li> -<li class="level1">Drawings, desc. <span class="righttext"><a href="#Page171">171</a></span></li> - -<li><b>Light</b>, and Sense of Seeing<span class="pagenum" id="Page291">[291]</span> -<span class="righttext"><a href="#Page254">254</a></span></li> -<li class="level1">Experiment with, illus. <span class="righttext"><a href="#Page255">255</a></span></li> -<li class="level1">Laws of <span class="righttext"><a href="#Page252">252</a></span></li> - -<li><b>Line</b>, def. <span class="righttext"><a href="#Page82">82</a></span></li> -<li class="level1">To Divide into Equal Parts <span class="righttext"><a href="#Page89">89</a></span></li> - -<li><b>Linear Perspective Drawing</b> <span class="righttext"><a href="#Page247">247</a></span></li> - -<li><b>Lines</b>, def. <span class="righttext"><a href="#Page45">45</a></span></li> -<li class="level1">Note <span class="righttext"><a href="#Page65">65</a></span></li> -<li class="level1">Parallel, def. <span class="righttext"><a href="#Page83">83</a></span></li> - -<li><b>Link Motion</b>, Stephenson’s, illus. <span class="righttext"><a href="#Page225">225</a></span></li> - -<li><b>Longitudinal</b>, def. <span class="righttext"><a href="#Page46">46</a></span></li> - -<li><b>Lucas, Theo.</b>, Acknowledgement <span class="righttext"><a href="#Page23">23</a>, -<a href="#Page266">266</a></span></li> - -<li class="startletter"><b>Marking Measurements</b> on Drawings -<span class="righttext"><a href="#Page243">243</a></span></li> - -<li><b>Mechanical Drawing</b> <span class="righttext"><a href="#Page137">137</a>, <a href="#Page247">247</a></span></li> -<li class="level1">Elevation <span class="righttext"><a href="#Page138">138</a></span></li> -<li class="level1">Examples <span class="righttext"><a href="#Page143">143</a></span></li> -<li class="level1">Procedure <span class="righttext"><a href="#Page141">141</a></span></li> - -<li><b>Minerva</b>, Free-hand Sketch of <span class="righttext"><a href="#Pageiii">iii</a></span></li> - -<li><b>Miter-Wheel</b> <span class="righttext">desc. <a href="#Page199">199</a>, <a href="#Page204">204</a>, illus. -<a href="#Page204">204</a></span></li> - -<li><b>Model</b>, def. <span class="righttext"><a href="#Page46">46</a></span></li> - -<li class="startletter"><b>Nonagon</b>, def. <span class="righttext"><a href="#Page47">47</a></span></li> - -<li><b>Numbering</b> Drawings, Office Rules for <span class="righttext"><a href="#Page194">194-5</a></span></li> - -<li><b>Numerals</b>, illus. <span class="righttext"><a href="#Page173">173</a></span></li> - -<li class="startletter"><b>Oblique</b>, def. <span class="righttext"><a href="#Page46">46</a></span></li> - -<li><b>Oblique Lines</b> <span class="righttext">How to Draw, <a href="#Page32">32</a>, <a href="#Page58">58</a>, -illus. <a href="#Page59">59</a>, <a href="#Page63">63</a></span></li> - -<li><b>Oblong</b>, def. <span class="righttext"><a href="#Page46">46</a></span></li> - -<li><b>Obtuse Angle</b>, def. <span class="righttext"><a href="#Page42">42</a></span></li> - -<li><b>Obtuse-Angled Triangle</b>, def. <span class="righttext"><a href="#Page50">50</a></span></li> - -<li><b>Octahedron</b>, def. <span class="righttext"><a href="#Page48">48</a></span></li> - -<li><b>Octagon</b>, def. <span class="righttext"><a href="#Page47">47</a></span></li> -<li class="level1">To Describe on a given straight line <span class="righttext"><a href="#Page95">95</a></span></li> -<li class="level1">To Inscribe in a circle <span class="righttext"><a href="#Page96">96</a></span></li> - -<li><b>Oil Can</b>, illus. <span class="righttext"><a href="#Page77">77</a></span></li> - -<li><b>Optic Nerve</b>, illus. <span class="righttext"><a href="#Page253">253</a></span></li> - -<li><b>Optics</b>, in Drawing, def. <span class="righttext"><a href="#Page252">252</a></span></li> - -<li><b>Outline Picture</b>, desc. <span class="righttext"><a href="#Page152">152</a></span></li> - -<li><b>Oval</b>, def. <span class="righttext"><a href="#Page46">46</a></span></li> -<li class="level1">How to Draw an <span class="righttext"><a href="#Page71">71</a></span></li> - -<li><b>Overall</b>, def. <span class="righttext"><a href="#Page46">46</a></span></li> - -<li class="startletter"><b>Paper</b>, Fastening Drawing on<span class="pagenum" id="Page292">[292]</span> -<span class="righttext"><a href="#Page184">184</a></span></li> -<li class="level1">Rule or Scale <span class="righttext"><a href="#Page242">242</a></span></li> -<li class="level1">Sensitized, desc. <span class="righttext"><a href="#Page188">188</a></span></li> -<li class="level1">The Right Side of <span class="righttext"><a href="#Page241">241</a></span></li> - -<li><b>Parallel</b>, def. <span class="righttext"><a href="#Page46">46</a></span></li> - -<li><b>Parallel Lines</b>, def. <span class="righttext"><a href="#Page83">83</a>, <a href="#Page252">252</a></span></li> -<li class="level1">To Draw <span class="righttext"><a href="#Page88">88</a></span></li> -<li class="level1">In Perspective <span class="righttext"><a href="#Page251">251</a></span></li> - -<li><b>Parallel Perspective Drawing</b>, illus. <span class="righttext"><a href="#Page260">260</a> to -<a href="#Page263">263</a></span></li> - -<li><b>Parallel Rule</b> <span class="righttext">desc. <a href="#Page115">115</a>, illus. -<a href="#Page114">114-5</a></span></li> - -<li><b>Parallelogram</b>, def. <span class="righttext"><a href="#Page47">47</a></span></li> -<li class="level1">To Construct <span class="righttext"><a href="#Page93">93</a></span></li> - -<li><b>Pasting Drawing Paper</b>, “Points” <span class="righttext"><a href="#Page243">243</a></span></li> - -<li><b>Patent Office Drawings</b> <span class="righttext"><a href="#Page235">235</a>, illus. -<a href="#Page236">236</a></span></li> -<li class="level1">Rules of Great Britain <span class="righttext"><a href="#Page236">236</a></span></li> -<li class="level1">Rules of U. S. <span class="righttext"><a href="#Page233">233</a></span></li> - -<li><b>Patterns</b>, def. <span class="righttext"><a href="#Page46">46</a></span></li> -<li class="level1">Numbering, from drawings <span class="righttext"><a href="#Page194">194</a></span></li> - -<li><b>Pedestal</b>, illus. <span class="righttext"><a href="#Page178">178-9</a></span></li> - -<li><b>Pen</b>, Hand holding, illus. <span class="righttext"><a href="#Page166">166</a>, <a href="#Page169">169</a>, -<a href="#Page170">170</a></span></li> - -<li><b>Pencil</b>, Function of a <span class="righttext"><a href="#Page142">142</a></span></li> -<li class="level1">How to Cut, illus. <span class="righttext"><a href="#Page57">57</a></span></li> -<li class="level1">How to Hold, illus. <span class="righttext"><a href="#Page54">54</a>, <a href="#Page59">59</a>, -<a href="#Page60">60</a></span></li> -<li class="level1">How to Use <span class="righttext"><a href="#Page56">56</a></span></li> - -<li><b>Pencil-Compasses</b>, desc. <span class="righttext"><a href="#Page143">143</a></span></li> -<li class="level1">How to Hold <span class="righttext"><a href="#Page143">143</a></span></li> - -<li><b>Penciling</b>, desc. and illus. <span class="righttext"><a href="#Page139">139</a></span></li> -<li class="level1">“Points” <span class="righttext"><a href="#Page143">143</a>, <a href="#Page240">240</a></span></li> - -<li><b>Pencil Lines</b>, How to Make <span class="righttext"><a href="#Page119">119</a></span></li> - -<li><b>Pencils</b>, Sharpening Points of <span class="righttext"><a href="#Page143">143</a>, -<a href="#Page241">241</a></span></li> - -<li><b>Penknife</b>, illus. <span class="righttext"><a href="#Page52">52</a></span></li> - -<li><b>Pens</b>, Drawing, illus. <span class="righttext"><a href="#Page129">129</a></span></li> -<li class="level1">Lettering and Figuring, illus. <span class="righttext"><a href="#Page172">172</a></span></li> - -<li><b>Pentagon</b>, def. <span class="righttext"><a href="#Page47">47</a></span></li> -<li class="level1">To Inscribe in a circle <span class="righttext"><a href="#Page94">94</a></span></li> - -<li><b>Perimeter</b>, def. <span class="righttext"><a href="#Page47">47</a></span></li> -<li class="level1">Of a Polygon, def. <span class="righttext"><a href="#Page47">47</a></span></li> - -<li><b>Periphery of a Wheel</b>, def. <span class="righttext"><a href="#Page200">200</a></span></li> - -<li><b>Perpendicular</b>, def. <span class="righttext"><a href="#Page47">47</a>, <a href="#Page252">252</a></span></li> - -<li><b>Perpendicular Lines</b>, How to Draw <span class="righttext"><a href="#Page31">31</a>, <a href="#Page61">61</a>, -<a href="#Page62">62</a></span></li> - -<li><b>Perrott, Geo.</b>, Acknowledgement <span class="righttext"><a href="#Page23">23</a>, -<a href="#Page266">266</a></span></li> - -<li><b>Personal</b>, Note from the Author <span class="righttext"><a href="#Page266">266</a></span></li> - -<li><b>Perspective Drawing</b><span class="pagenum" id="Page293">[293]</span> <span class="righttext">def. -<a href="#Page47">47</a>, illus. <a href="#Page250">250</a></span></li> -<li class="level1">Definitions of Terms used in <span class="righttext"><a href="#Page249">249</a></span></li> -<li class="level1">Geometrical Terms used in <span class="righttext"><a href="#Page248">248</a></span></li> -<li class="level1">Of a Bridge, illus. <span class="righttext"><a href="#Page249">249</a></span></li> -<li class="level1">Scale or Approximate <span class="righttext"><a href="#Page257">257</a></span></li> -<li class="level1">Vanishing Point, illus. <span class="righttext"><a href="#Page251">251</a></span></li> -<li class="level1">Water Reflection, illus. <span class="righttext"><a href="#Page246">246</a></span></li> - -<li><b>Perspective</b>, Linear, def. <span class="righttext"><a href="#Page247">247</a></span></li> - -<li><b>Perspective Plane</b>, def. <span class="righttext"><a href="#Page250">250</a></span></li> - -<li><b>Picture Plane</b>, desc. <span class="righttext"><a href="#Page255">255</a></span></li> -<li class="level1">In Drawing, illus. <span class="righttext"><a href="#Page249">249</a>, -<a href="#Page250">250</a></span></li> -<li class="level1">In Perspective, illus. <span class="righttext"><a href="#Page258">258</a></span></li> - -<li><b>Pinion-Wheel</b>, desc. <span class="righttext"><a href="#Page201">201</a></span></li> - -<li><b>Piston Rod</b>, desc. <span class="righttext"><a href="#Page223">223</a></span></li> - -<li><b>Pitch Circle</b> in Gearing <span class="righttext"><a href="#Page200">200</a></span></li> - -<li><b>Pitch Line</b>, Drawing the <span class="righttext"><a href="#Page209">209</a></span></li> -<li class="level1">In Gearing <span class="righttext"><a href="#Page200">200</a></span></li> - -<li><b>Plan</b>, def. <span class="righttext"><a href="#Page47">47</a></span></li> - -<li><b>Plan of the Work</b> <span class="righttext"><a href="#Page21">21</a></span></li> - -<li><b>Plane</b>, in Perspective, def. <span class="righttext"><a href="#Page249">249</a></span></li> - -<li><b>Plane of the Picture</b>, def. <span class="righttext"><a href="#Page250">250</a></span></li> - -<li><b>Plane Surface</b>, def. <span class="righttext"><a href="#Page49">49</a></span></li> - -<li><b>Point</b>, def. <span class="righttext"><a href="#Page82">82</a></span></li> - -<li><b>Point of Sight</b>, in Perspective Drawing <span class="righttext"><a href="#Page251">251</a></span></li> - -<li><b>Points</b>, relating to Chalk Drawings <span class="righttext"><a href="#Page36">36</a></span></li> -<li class="level1">To be observed in Sketching <span class="righttext"><a href="#Page141">141-2</a></span></li> -<li class="level1">Useful Hints and <span class="righttext"><a href="#Page170">170</a>, -<a href="#Page239">239</a></span></li> - -<li><b>Polygon</b>, def. <span class="righttext"><a href="#Page47">47</a></span></li> - -<li><b>Polyhedron</b>, def. <span class="righttext"><a href="#Page48">48</a></span></li> - -<li><b>Postulate</b>, def. <span class="righttext"><a href="#Page83">83</a></span></li> - -<li><b>Pounce</b>, How to Use, desc. <span class="righttext"><a href="#Page170">170</a>, -<a href="#Page186">186</a></span></li> - -<li><b>Preface</b> <span class="righttext"><a href="#Page13">13</a></span></li> - -<li><b>Preparatory Practice</b> in Drawing <span class="righttext"><a href="#Page30">30</a></span></li> - -<li><b>Prism</b>, def. <span class="righttext"><a href="#Page49">49</a></span></li> - -<li><b>Problems</b>, def. <span class="righttext"><a href="#Page83">83</a></span></li> -<li class="level1">Geometrical <span class="righttext"><a href="#Page86">86</a></span></li> - -<li><b>Produce</b>, def. <span class="righttext"><a href="#Page49">49</a></span></li> - -<li><b>Profile</b>, def. <span class="righttext"><a href="#Page49">49</a></span></li> - -<li><b>Projection</b>, Backward, illus. <span class="righttext"><a href="#Page153">153-4</a></span></li> -<li class="level1">Def. <span class="righttext"><a href="#Page49">49</a></span></li> -<li class="level1">Cylindrical Outline, desc. <span class="righttext"><a href="#Page159">159</a></span></li> -<li class="level1">Cylindrical Surface, illus. <span class="righttext"><a href="#Page161">161</a></span></li> -<li class="level1">Forward<span class="pagenum" id="Page294">[294]</span> <span class="righttext">desc. -<a href="#Page152">152</a>, illus. <a href="#Page155">155</a></span></li> -<li class="level1">Hexagon Nut, illus. <span class="righttext"><a href="#Page160">160</a></span></li> -<li class="level1">Marking Dimensions <span class="righttext"><a href="#Page150">150</a></span></li> -<li class="level1">Lines of Sight <span class="righttext"><a href="#Page150">150</a></span></li> -<li class="level1">Scaling and Measuring in <span class="righttext"><a href="#Page149">149</a></span></li> -<li class="level1">Sight-Lines, illus. <span class="righttext"><a href="#Page151">151</a></span></li> -<li class="level1">Sloping Surface, desc. <span class="righttext"><a href="#Page159">159</a></span></li> -<li class="level1">Spur-Wheel, desc. <span class="righttext"><a href="#Page162">162</a></span></li> - -<li><b>Projection Drawing</b>, desc. <span class="righttext"><a href="#Page148">148</a></span></li> -<li class="level1">Illus. <span class="righttext"><a href="#Page149">149</a>, <a href="#Page151">151</a>, -<a href="#Page153">153</a>, <a href="#Page154">154</a>, <a href="#Page155">155</a>, <a href="#Page157">157</a>, -<a href="#Page158">158</a>, <a href="#Page160">160</a>, <a href="#Page161">161</a>, <a href="#Page163">163</a></span></li> -<li class="level1">Principles of <span class="righttext"><a href="#Page148">148</a></span></li> -<li class="level1">Spur-Wheel, illus. <span class="righttext"><a href="#Page163">163</a>, -<a href="#Page212">212</a></span></li> - -<li><b>Proportional Dividers</b>, illus. <span class="righttext"><a href="#Page120">120</a></span></li> - -<li><b>Proportions</b> of Teeth of Wheels <span class="righttext"><a href="#Page210">210</a></span></li> - -<li><b>Proposition</b>, def. <span class="righttext"><a href="#Page83">83</a></span></li> - -<li><b>Protractor</b>, desc. <span class="righttext"><a href="#Page128">128</a></span></li> - -<li><b>Pulley and Friction Clutch</b>, illus. <span class="righttext"><a href="#Page224">224</a></span></li> - -<li><b>Punching Press</b> <span class="righttext">illus. <a href="#Page222">222</a>, desc. -<a href="#Page223">223</a></span></li> - -<li class="startletter"><b>Quadrant</b>, def. <span class="righttext"><a href="#Page49">49</a></span></li> - -<li><b>Quadrilateral</b>, def. <span class="righttext"><a href="#Page47">47</a></span></li> - -<li><b>Quadrisect</b>, def. <span class="righttext"><a href="#Page49">49</a></span></li> - -<li class="startletter"><b>Rack and Pinion</b>, desc. <span class="righttext"><a href="#Page205">205</a></span></li> - -<li><b>Radius of a Circle</b> <span class="righttext"><a href="#Page43">43</a></span></li> - -<li><b>Reading Working Drawings</b>, desc. <span class="righttext"><a href="#Page229">229</a></span></li> - -<li><b>Rectangle</b>, def. <span class="righttext"><a href="#Page48">48</a></span></li> -<li class="level1">To Construct a <span class="righttext"><a href="#Page92">92</a></span></li> - -<li><b>Reproducing Drawings</b>, desc. <span class="righttext"><a href="#Page186">186</a></span></li> - -<li><b>Reverse Curve</b>, def. <span class="righttext"><a href="#Page44">44</a></span></li> - -<li><b>Rhomboid</b>, def. <span class="righttext"><a href="#Page48">48</a></span></li> - -<li><b>Rhombus</b>, def. <span class="righttext"><a href="#Page48">48</a></span></li> - -<li><b>Right-Angle</b>, def. <span class="righttext"><a href="#Page42">42</a></span></li> -<li class="level1">Triangle, def. <span class="righttext"><a href="#Page50">50</a></span></li> - -<li><b>Robinson, A. W., M. E.</b>, note, Office Rules <span class="righttext"><a href="#Page191">191</a></span></li> - -<li><b>Rolling-Circle</b> in Gear-Wheel <span class="righttext"><a href="#Page200">200</a></span></li> - -<li><b>Rule</b>, Area of a Circle, To find the <span class="righttext"><a href="#Page271">271</a></span></li> -<li class="level1">Circumference of a Circle, To find the <span class="righttext"><a href="#Page271">271</a></span></li> -<li class="level1">Cylinder, To find the contents of a <span class="righttext"><a href="#Page271">271</a></span></li> -<li class="level1">Diameter of a Circle, To find the <span class="righttext"><a href="#Page271">271</a></span></li> -<li class="level1">Illus. <span class="righttext"><a href="#Page82">82</a></span></li> -<li class="level1">Inscribed Square, To find side of an <span class="righttext"><a href="#Page271">271</a></span></li> -<li class="level1">Parallelogram, To find the area of a <span class="righttext"><a href="#Page271">271</a></span></li> -<li class="level1">Pyramid or Cone, To find the contents of a <span class="righttext"><a href="#Page271">271</a></span></li> -<li class="level1">Radius of a circle, To find the<span class="pagenum" id="Page295">[295]</span> -<span class="righttext"><a href="#Page271">271</a></span></li> -<li class="level1">Sphere, To find the contents of a <span class="righttext"><a href="#Page271">271</a></span></li> -<li class="level1">Square, To find the side of an equal <span class="righttext"><a href="#Page271">271</a></span></li> -<li class="level1">Trapezoid, To find the area of a <span class="righttext"><a href="#Page271">271</a></span></li> -<li class="level1">Triangle, To find the area of a <span class="righttext"><a href="#Page271">271</a></span></li> -<li class="level1">Two-foot <span class="righttext">desc. <a href="#Page127">127</a>, <a href="#Page128">128</a>, illus. -<a href="#Page128">128</a></span></li> -<li class="level1">Wedge, To find the contents of a <span class="righttext"><a href="#Page271">271</a></span></li> - -<li><b>Rules</b> for Drawing Office <span class="righttext"><a href="#Page191">191</a></span></li> -<li class="level1">Wheels, To find proportions of <span class="righttext"><a href="#Page209">209</a></span></li> - -<li class="startletter"><b>Sand Paper</b>, Removing surface of paper -<span class="righttext"><a href="#Page168">168</a></span></li> - -<li><b>Scale</b>, Drawing to, desc. <span class="righttext"><a href="#Page126">126</a></span></li> - -<li><b>Scale Drawings</b>, To read <span class="righttext"><a href="#Page230">230</a></span></li> - -<li><b>Scale</b>, Flat, illus. <span class="righttext"><a href="#Page127">127</a></span></li> -<li class="level1">Triangular, illus. <span class="righttext"><a href="#Page127">127</a></span></li> - -<li><b>Scalene Triangle</b>, def. <span class="righttext"><a href="#Page50">50</a></span></li> - -<li><b>Scale or Approximate Perspective</b> <span class="righttext"><a href="#Page257">257</a></span></li> - -<li><b>Scale Rule</b>, for Proportions of Teeth <span class="righttext"><a href="#Page214">214</a></span></li> - -<li><b>Scales</b>, Drawing, desc. <span class="righttext"><a href="#Page126">126</a></span></li> - -<li><b>Scholium</b>, def. <span class="righttext"><a href="#Page83">83</a></span></li> - -<li><b>Screw-Thread</b>, U. S. Standard Gauge <span class="righttext"><a href="#Page280">280</a></span></li> - -<li><b>Scroll or Curve</b>, desc. <span class="righttext"><a href="#Page117">117</a></span></li> -<li class="level1">Universal Curve, illus. <span class="righttext"><a href="#Page134">134</a></span></li> - -<li><b>Secant of an Arc</b> <span class="righttext"><a href="#Page99">99</a></span></li> - -<li><b>Section</b>, def. <span class="righttext"><a href="#Page49">49</a></span></li> -<li class="level1">Drawing <span class="righttext">illus. <a href="#Page163">163</a>, desc. -<a href="#Page160">160</a></span></li> - -<li><b>Sectional</b>, def. <span class="righttext"><a href="#Page49">49</a></span></li> - -<li><b>Section-Liner</b>, illus. <span class="righttext"><a href="#Page116">116</a></span></li> - -<li><b>Section Lines</b> in Drawings <span class="righttext"><a href="#Page240">240</a></span></li> - -<li><b>Section-Lining</b>, Cast-iron, etc., illus. <span class="righttext"><a href="#Page182">182</a></span></li> -<li class="level1">Cog-Wheel, illus. <span class="righttext"><a href="#Page183">183</a></span></li> - -<li><b>Section-Lining Drawings</b> <span class="righttext">desc. <a href="#Page182">182</a>, illus. -<a href="#Page183">183</a></span></li> -<li class="level1">Wheel Hub, illus. <span class="righttext"><a href="#Page184">184</a></span></li> - -<li><b>Selecting Drawing Instruments</b> <span class="righttext"><a href="#Page103">103</a>, -<a href="#Page240">240</a></span></li> - -<li><b>Semi-Circle</b>, def. <span class="righttext"><a href="#Page43">43</a></span></li> - -<li><b>Sensitized Paper</b>, desc. <span class="righttext"><a href="#Page188">188</a></span></li> - -<li><b>Set-Square</b>, illus. <span class="righttext"><a href="#Page102">102</a>, <a href="#Page114">114</a></span></li> - -<li><b>Shading Curves</b>, illus. <span class="righttext"><a href="#Page181">181</a></span></li> - -<li><b>Shading Drawings</b> <span class="righttext"><a href="#Page180">180</a></span></li> - -<li><b>Shadow</b>, def. <span class="righttext"><a href="#Page49">49</a></span></li> - -<li><b>Shadow Line</b>, def. <span class="righttext"><a href="#Page46">46</a></span></li> - -<li><b>Shadow Lines</b>, “Points” <span class="righttext"><a href="#Page241">241</a></span></li> - -<li><b>Sharpening Pencils</b><span class="pagenum" id="Page296">[296]</span> -<span class="righttext"><a href="#Page57">57</a></span></li> - -<li><b>Shop Drawings</b>, Office Rules <span class="righttext"><a href="#Page192">192</a></span></li> - -<li><b>Sight</b>, Point of, in Perspective Drawing <span class="righttext"><a href="#Page252">252</a></span></li> -<li class="level1">Sense of <span class="righttext"><a href="#Page254">254</a></span></li> - -<li><b>Sight Lines</b> in Projection, illus. <span class="righttext"><a href="#Page157">157</a></span></li> - -<li><b>Sine</b> of an Arc <span class="righttext"><a href="#Page99">99</a></span></li> - -<li><b>Skew-Gearing</b>, desc. <span class="righttext"><a href="#Page203">203</a></span></li> - -<li><b>Sketch Books</b>, desc. <span class="righttext"><a href="#Page142">142</a></span></li> -<li class="level1">Office Practice <span class="righttext"><a href="#Page194">194</a></span></li> - -<li><b>Sketches</b>, details <span class="righttext"><a href="#Page142">142</a></span></li> - -<li><b>Sketch</b>, Free-hand, Advantage of <span class="righttext"><a href="#Page55">55</a></span></li> - -<li><b>Sketching</b> <span class="righttext">desc. <a href="#Page141">141</a>, note <a href="#Page17">17</a></span></li> -<li class="level1">Points to be observed in <span class="righttext"><a href="#Page141">141</a></span>-2</li> - -<li><b>Sloping Surface</b> in Projection <span class="righttext">desc. <a href="#Page159">159</a>, illus. -<a href="#Page166">166</a></span></li> - -<li><b>Solid</b>, def. <span class="righttext"><a href="#Page49">49</a>, <a href="#Page83">83</a></span></li> - -<li><b>Solid Pattern</b>, def. <span class="righttext"><a href="#Page47">47</a></span></li> - -<li><b>Speed of Gears</b> <span class="righttext"><a href="#Page208">208</a></span></li> - -<li><b>Sphere</b>, def. <span class="righttext"><a href="#Page49">49</a></span></li> - -<li><b>Spiral Curve</b>, def. <span class="righttext"><a href="#Page44">44</a></span></li> - -<li><b>Spring Bows</b> <span class="righttext">illus. <a href="#Page122">122</a>, <a href="#Page123">123</a>, desc. -<a href="#Page124">124</a></span></li> - -<li><b>Spur-Gear</b> <span class="righttext">desc. <a href="#Page201">201</a>, illus. <a href="#Page211">211</a></span></li> - -<li><b>Spur Mortise-Wheel</b>, illus. <span class="righttext"><a href="#Page202">202</a></span></li> - -<li><b>Spur-Wheel</b>, desc. <span class="righttext"><a href="#Page199">199</a>, <a href="#Page216">216</a></span></li> -<li class="level1">How to Draw <span class="righttext"><a href="#Page209">209</a></span></li> -<li class="level1">Illus. <span class="righttext"><a href="#Page198">198</a></span></li> -<li class="level1">Projection <span class="righttext">desc. <a href="#Page162">162</a>, illus. -<a href="#Page163">163</a></span></li> -<li class="level1">Teeth of cast-iron, desc. <span class="righttext"><a href="#Page202">202</a></span></li> - -<li><b>Square</b>, def. <span class="righttext"><a href="#Page48">48</a></span></li> -<li class="level1">To Convert into an Octagon <span class="righttext"><a href="#Page95">95</a></span></li> -<li class="level1">To Describe about a Circle <span class="righttext"><a href="#Page94">94</a></span></li> -<li class="level1">To Inscribe in a Circle <span class="righttext"><a href="#Page93">93</a></span></li> - -<li><b>Standards</b>, for U. S. <span class="righttext"><a href="#Page278">278</a></span></li> -<li class="level1">Office Rules for <span class="righttext"><a href="#Page193">193</a></span></li> - -<li><b>Steady Rest</b>, Scale, illus. <span class="righttext"><a href="#Page228">228</a></span></li> - -<li><b>Straight Line</b>, def. <span class="righttext"><a href="#Page46">46</a></span></li> -<li class="level1">To Draw a Perpendicular to a <span class="righttext"><a href="#Page86">86</a></span></li> -<li class="level1">Drawing Figures of <span class="righttext"><a href="#Page66">66-7-8</a></span></li> -<li class="level1">How to Draw a <span class="righttext"><a href="#Page57">57</a>, <a href="#Page59">59</a></span></li> -<li class="level1">To Bisect a <span class="righttext"><a href="#Page86">86</a></span></li> - -<li><b>Steel</b>, Section-Lining, illus. <span class="righttext"><a href="#Page182">182</a></span></li> - -<li><b>Steel Gears</b>, Economy of <span class="righttext"><a href="#Page216">216</a></span></li> - -<li><b>Surface</b>, def. <span class="righttext"><a href="#Page49">49</a>, <a href="#Page82">82</a></span></li> - -<li><b>Symbols</b>, representing Materials <span class="righttext"><a href="#Page193">193</a></span></li> - -<li class="startletter"><b>Table</b> of Areas of Circles<span class="pagenum" id="Page297">[297]</span> -<span class="righttext"><a href="#Page273">273-277</a></span></li> -<li class="level1">Bolts, Standard Sizes of <span class="righttext"><a href="#Page280">280</a></span></li> -<li class="level1">Circular Measure <span class="righttext"><a href="#Page272">272</a></span></li> -<li class="level1">Circumferences of Circles <span class="righttext"><a href="#Page273">273-277</a></span></li> -<li class="level1">Contents <span class="righttext"><a href="#Page24">24</a></span></li> -<li class="level1">Decimal Equivalents <span class="righttext"><a href="#Page269">269</a></span></li> -<li class="level1">Diameters of Circles <span class="righttext"><a href="#Page273">273-277</a></span></li> -<li class="level1">Land Measure <span class="righttext"><a href="#Page272">272</a></span></li> -<li class="level1">Metric Equivalents <span class="righttext"><a href="#Page270">270</a></span></li> -<li class="level1">Pipe, Standard Sizes of Welded <span class="righttext"><a href="#Page279">279</a></span></li> -<li class="level1">Roman Figures <span class="righttext"><a href="#Page272">272</a></span></li> -<li class="level1">Solid Measure <span class="righttext"><a href="#Page272">272</a></span></li> -<li class="level1">Wire Gauges <span class="righttext"><a href="#Page278">278</a></span></li> -<li class="level1">Useful for Draughtsmen <span class="righttext"><a href="#Page266">266-280</a></span></li> - -<li><b>Tangent</b> of an Arc, def. <span class="righttext"><a href="#Page99">99</a></span></li> -<li class="level1">To Draw a, to a Circle <span class="righttext"><a href="#Page91">91</a></span></li> - -<li><b>Tee-Iron</b>, illus. <span class="righttext"><a href="#Page75">75</a></span></li> - -<li><b>Tee-Square</b>, Adjustable, desc. and illus. <span class="righttext"><a href="#Page113">113</a></span></li> -<li class="level1">Desc. <span class="righttext"><a href="#Page112">112</a></span></li> -<li class="level1">How to Use, illus. <span class="righttext"><a href="#Page111">111</a>, -<a href="#Page147">147</a></span></li> -<li class="level1">Illus. <span class="righttext"><a href="#Page102">102</a>, <a href="#Page112">112</a></span></li> -<li class="level1">Points about <span class="righttext"><a href="#Page242">242</a></span></li> - -<li><b>Teeth in Bevel Gears</b>, desc. <span class="righttext"><a href="#Page204">204</a></span></li> - -<li><b>Terms and Definitions</b>, Preliminary <span class="righttext"><a href="#Page41">41</a></span></li> - -<li><b>Test-Pieces</b>, Use of, in Blue Prints <span class="righttext"><a href="#Page188">188</a></span></li> - -<li><b>Tetrahedron</b>, def. <span class="righttext"><a href="#Page48">48</a></span></li> - -<li><b>Theorem</b>, def. <span class="righttext"><a href="#Page83">83</a></span></li> - -<li><b>Thumb-Tack</b> <span class="righttext">illus. <a href="#Page109">109</a>, desc. <a href="#Page110">110</a></span></li> - -<li><b>Tints and Colors</b>, desc. <span class="righttext"><a href="#Page184">184</a></span></li> - -<li><b>Title and Date</b>, on Sketches <span class="righttext"><a href="#Page142">142</a></span></li> - -<li><b>Title, Date, Scale, etc.</b>, Office Rules for <span class="righttext"><a href="#Page192">192</a></span></li> - -<li><b>Title Page</b> <span class="righttext"><a href="#Pagevii">vii</a></span></li> - -<li><b>Tracing-Cloth</b>, desc. <span class="righttext"><a href="#Page186">186</a></span></li> - -<li><b>Tracings</b>, Office Rules for Keeping <span class="righttext"><a href="#Page195">195</a></span></li> -<li class="level1">Tinted and Shaded, desc. <span class="righttext"><a href="#Page184">184</a></span></li> - -<li><b>Trammels</b>, desc. and illus. <span class="righttext"><a href="#Page125">125</a></span></li> - -<li><b>Trapezium</b>, def. <span class="righttext"><a href="#Page48">48</a></span></li> - -<li><b>Trapezoid</b>, def. <span class="righttext"><a href="#Page48">48</a></span></li> - -<li><b>Trestles</b>, Drawing-Board, desc. and illus. <span class="righttext"><a href="#Page110">110</a></span></li> - -<li><b>Triangle</b>, def. <span class="righttext"><a href="#Page50">50</a></span></li> -<li class="level1">To Describe a Circle about a <span class="righttext"><a href="#Page93">93</a></span></li> - -<li><b>Triangle, or Set-Square</b>, desc. and illus. <span class="righttext"><a href="#Page114">114</a></span></li> -<li class="level1">How to Use<span class="pagenum" id="Page298">[298]</span> <span class="righttext">desc. -<a href="#Page147">147</a>, illus. <a href="#Page166">166</a></span></li> - -<li><b>Triangles</b>, illus. <span class="righttext"><a href="#Page102">102</a></span></li> -<li class="level1">To Construct <span class="righttext"><a href="#Page92">92</a></span></li> - -<li><b>Trigonometry</b>, principles and def. <span class="righttext"><a href="#Page98">98</a></span></li> - -<li><b>Trisect</b>, def. <span class="righttext"><a href="#Page50">50</a></span></li> - -<li><b>Trundle Wheel</b> <span class="righttext">desc. <a href="#Page201">201</a>, illus. <a href="#Page208">208</a></span></li> - -<li><b>Two-foot Rule</b>, illus. <span class="righttext"><a href="#Page128">128</a></span></li> - -<li class="startletter"><b>U. S. Standards</b>, Pipes <span class="righttext"><a href="#Page279">279</a></span></li> - -<li><b>Upright Lines</b>, How to Draw <span class="righttext"><a href="#Page61">61</a></span></li> - -<li><b>Useful Tables for Draughtsmen</b> -<span class="righttext"><a href="#Page269">269</a>-<a href="#Page280">280</a></span></li> - -<li class="startletter"><b>Valve</b>, Blow-off <span class="righttext">desc. <a href="#Page174">174</a>, illus. -<a href="#Page175">175</a></span></li> - -<li><b>Valve Gear</b>, or Link Motion, illus. <span class="righttext"><a href="#Page225">225</a></span></li> - -<li><b>Vanishing Point</b>, def. and illus. <span class="righttext"><a href="#Page251">251</a></span></li> -<li class="level1">In Drawing, illus. <span class="righttext"><a href="#Page250">250</a></span></li> -<li class="level1">In Perspective Drawing <span class="righttext"><a href="#Page252">252</a></span></li> - -<li><b>Varnish</b>, Shellac, for Drawings <span class="righttext"><a href="#Page241">241</a></span></li> - -<li><b>Versed Sine</b> of an Arc <span class="righttext"><a href="#Page99">99</a></span></li> - -<li><b>Vertex</b>, def. <span class="righttext"><a href="#Page51">51</a></span></li> -<li class="level1">Of an Angle, def. <span class="righttext"><a href="#Page42">42</a></span></li> - -<li><b>Vertical</b>, def. <span class="righttext"><a href="#Page51">51</a>, <a href="#Page251">251</a></span></li> - -<li><b>Vertical Lines</b>, in Perspective <span class="righttext"><a href="#Page257">257</a></span></li> - -<li><b>Vertical-Plane</b>, def. <span class="righttext"><a href="#Page249">249</a></span></li> - -<li><b>View</b>, def. <span class="righttext"><a href="#Page51">51</a></span></li> - -<li><b>Visual Ray</b> in Perspective Drawing <span class="righttext"><a href="#Page256">256</a></span></li> - -<li><b>Visual Rays of Light</b> <span class="righttext">desc. <a href="#Page252">252</a>, illus. -<a href="#Page255">255</a></span></li> - -<li><b>Vulcanite</b>, Section-Lining, illus. <span class="righttext"><a href="#Page182">182</a></span></li> - -<li class="startletter"><b>Water Reflection</b> in Perspective Drawing, illus. -<span class="righttext"><a href="#Page246">246</a></span></li> - -<li><b>Wheel</b>, Bevel, A, illus. <span class="righttext"><a href="#Page203">203</a></span></li> -<li class="level1">Crown, illus. <span class="righttext"><a href="#Page208">208</a></span></li> -<li class="level1">Helical, A, illus. <span class="righttext"><a href="#Page207">207</a></span></li> -<li class="level1">Hub, Section-Lining, illus. <span class="righttext"><a href="#Page184">184</a></span></li> -<li class="level1">Internal Gear, desc. <span class="righttext"><a href="#Page201">201</a>, -<a href="#Page207">207</a></span></li> -<li class="level1">Miter, A, illus. <span class="righttext"><a href="#Page204">204</a></span></li> -<li class="level1">Proportions of the Teeth of a <span class="righttext"><a href="#Page210">210</a></span></li> -<li class="level1">Spur <span class="righttext">illus. <a href="#Page198">198</a>, desc. <a href="#Page199">199</a>, -<a href="#Page201">201</a></span></li> -<li class="level1">Worm, desc. <span class="righttext"><a href="#Page201">201</a></span></li> - -<li><b>Wood</b>, Section-Lining, illus. <span class="righttext"><a href="#Page182">182</a></span></li> - -<li><b>Working Drawing</b>, Bending Machine <span class="righttext"><a href="#Page220">220-1</a></span></li> -<li class="level1">Def.<span class="pagenum" id="Page299">[299]</span> -<span class="righttext"><a href="#Page51">51</a></span></li> -<li class="level1">Illus. <span class="righttext"><a href="#Page218">218</a>, <a href="#Page220">220</a>, -<a href="#Page221">221</a>, <a href="#Page222">222</a>, <a href="#Page223">223</a>, <a href="#Page224">224</a>, -<a href="#Page225">225</a>, <a href="#Page226">226</a>, <a href="#Page228">228</a></span></li> -<li class="level1">Bumping Post, illus. <span class="righttext"><a href="#Page226">226</a></span></li> -<li class="level1">Points, etc. <span class="righttext"><a href="#Page243">243</a></span></li> -<li class="level1">Power Punching Press <span class="righttext"><a href="#Page222">222</a></span></li> -<li class="level1">Numbering a, Office Rules for <span class="righttext"><a href="#Page195">195</a></span></li> -<li class="level1">To Read a <span class="righttext"><a href="#Page229">229</a></span></li> - -<li><b>Working Drawings</b>, desc. <span class="righttext"><a href="#Page219">219</a>, <a href="#Page227">227</a></span></li> - -<li><b>Worm-Gear</b>, desc. <span class="righttext"><a href="#Page206">206</a></span></li> - -<li><b>Worm-Wheel</b> <span class="righttext">desc. <a href="#Page201">201</a>, illus. <a href="#Page206">206</a></span></li> -<li class="level1">Speed of a <span class="righttext"><a href="#Page216">216</a></span></li> - -<li><b>Wrench</b>, illus. <span class="righttext"><a href="#Page75">75</a></span></li> - -<li><b>Wrist-Lines</b>, illus. <span class="righttext"><a href="#Page64">64</a></span></li> - -<li><b>Wrought-Iron</b>, Section-Lining, illus. <span class="righttext"><a href="#Page182">182</a></span></li> - -</ul> - -<hr class="full" /> - -<div class="tnbot" id="TN"> - -<h2>Transcriber’s Notes</h2> - -<p>Inconsistent and unusual spelling, capitalisation and hyphenation have been retained, unless mentioned below. The -discrepancies between the General List of Contents and the structure of the text have not been corrected.</p> - -<p>Depending on the hard- and software used to read this text and their settings, not all elements may display as intended. -Where scales are given for illustrations, these can, of course, not be relied upon for measurements.</p> - -<p>The numbering of illustrations in the book is inconsistent. Illustrations that have no numbered captions may or may not -be counted; this has not been standardised, except as listed below. Missing illustration numbers have been added only where -they are referenced in the text. The illustrations referred to in the text as Figs. 242 and 243 are captioned Fig. 243 and -244.</p> - -<p>Page 65-69 and Figs. 66-71: the text uses upper case reference letters, the illustrations lower case, which has not been -standardised.</p> - -<p>Page 84, table of symbols: the source document uses letters (O and L) rather than symbols for circle and angle.</p> - -<p>Page 94, Bisect two of the angles <i>A C</i> of the triangle: presumably the unmarked point A is in the lower left-hand -corner of the illustration.</p> - -<p>Page 113, The tee-square, as shown, ...: there is no illustration with the relevant reference numbers; probably the -reference is to Fig. 151/152.</p> - -<p>Page 239, rough irregular lines, as in fig. 134, on page 131: there is no Fig. 134 on page 131; page 134 nor page 131 -show the rough irregular lines. Several other illustrations in the book do show such lines.</p> - -<p>Index: the order of entries is as printed in the source document.</p> - -<p class="blankbefore75">Changes made:</p> - -<p>Illustrations and Notes have been moved out of text paragraphs.</p> - -<p>Some obvious minor punctuation and typographical errors have been corrected silently.</p> - -<p>In some tables the ditto symbol („) has been replaced with the dittoed text; the use of × and x in -multiplications and dimensions has been standardised to ×.</p> - -<p>Page 48: Figure numbers 45-49 added to illustration.</p> - -<p>Page 89: and on <i>B</i> on <i>B I</i> changed to and on <i>B</i> on <i>B D</i>.</p> - -<p>Page 177: D = diam. of collar changed to d = diam. of collar.</p> - -<p>Page 193: Bbt.--Babbit. changed to Bbt.--Babbitt.</p> - -<p>Page 203: as described on page 191 changed to as described on page 199.</p> - -<p>Page 214: 4 tenths measured at the 2′ line changed to 4 tenths measured at the 2″ line.</p> - -</div><!--TN--> - -<div style='display:block; margin-top:4em'>*** END OF THE PROJECT GUTENBERG EBOOK SELF-HELP MECHANICAL DRAWING ***</div> -<div style='text-align:left'> - -<div style='display:block; margin:1em 0'> -Updated editions will replace the previous one—the old editions will -be renamed. -</div> - -<div style='display:block; margin:1em 0'> -Creating the works from print editions not protected by U.S. copyright -law means that no one owns a United States copyright in these works, -so the Foundation (and you!) can copy and distribute it in the United -States without permission and without paying copyright -royalties. 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