,transcriber's ,notes ,text printed in italics in the source document has been transcribed between underscores1 bold face text between equal signs4 ,small capitals have been replaced with ,,all ,,capitals4 ,more ,transcriber's ,notes may be found at the end of this text4 ,illustration ,illustration ,,self-,,help ,,mechanical ,,drawing ,,an ,,educational ,,treatise ,illustration 8,,learn ,,to ,,do ,a ,,thing ,,by ,,doing ,,it40--,,old ,,proverb ,,self-,,help ,,mechanical ,,drawing ,,an ,,educational ,,treatise ,illustration ,,by ,n4 ,,hawkins1 ,m4 ,e4 ,author of ,handbook of ,calculations1 etc4 ,new ,york3 ,,theo4 ,,audel ,,co41 ,publishers #aijb ,copyrighted by ,theo4 ,audel ,co4 ,new ,york #aijb ,this work is most kindly and respectfully dedicated to ,,the ,,coming ,,man who at the present time is undoubtedly devoting a goodly share of his spare time to the study of drawing4 ,illustration ,illustration3 ,,introduction ,preface4 ,it is because of a personal and practical experience of the advantage to be gained by the possession of a knowledge of drawing1 that the author is prompted to undertake the rather pleasant task of producing a self-help book relating to the subject4 ,since the days of youthful endeavor1 the author has passed through an extended experience of mechanical life1 and scarcely ever without chalk1 pencil or instrument in hand1 to illustrate by sketch or drawing1 the tools to be employed1 or to picture the finished product2 accordingly1 throughout this work1 words of explanation and the drawings will go together to aid the diligent student4 ,it has been said by an eminent writer1 that 8one workman is superior to another--other circumstances being the same--directly in proportion to his knowledge in drawing1 and those who are ignorant of it must in many respects be subservient to others who have obtained that knowledge40 ,it has been also said that no man is fitted to be foreman of a shop who cannot draw1 and it is generally true that no one will be appointed to that position1 except temporarily1 who does not possess some knowledge of the art1 either 8freehand0 or instrumental4 ,it is a question how far a good working knowledge of drawing can be attained without a teacher2 it is true that but few have become proficient without such aid1 but it is equally true that 8self-help0 has been the key note to all advancement4 ,the author received personal instruction in several ways and times1 at home1 in school1 in an architect's office1 and under an experienced mechanical engineer1 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 drawing4 ,it was a struggle and a battle to hold himself down to 8the board0 to the finish1 but it was a victory--one1 won over slothfulness and impatience1 and of such a nature as to warrant the use of the term 8self-help0 to the encouragement of others4 ,in conclusion two sentiments may be added2 if a good working knowledge of drawing is 8worth the while0 then1 #a1 the student should be thoroughly in earnest in acquiring it2 #b1 he should be willing to take sufficient time and give much hard study to gain the skill necessary for success4 ,this persistence is not irksome4 ,it carries its own reward1 and the results are definite and sure4 8,one step and then another1 and the longest walk is ended2 ,one stitch and then another1 and the largest rent is mended4 ,one brick upon another1 and the highest wall is made2 ,one flake upon another1 and the deepest snow is laid40 ,introduction4 ,drawing is one of the arts2 art relates to something to be done1 and art in the industrial and mechanical sense aims chiefly at utility1 and is governed by exact rules2 hence mechanical drawing--so-called--tends first to be useful and helpful1 and second to accuracy in execution1 including most minute details2 it aspires to the perfection of nature in adaptability of the means to the end4 ,drawing constitutes a universal language1 to acquire which is a matter of importance1 for by its use one is able to illustrate the form and dimensions of an object1 device1 or utility1 in very much less time1 and far more clearly1 than by a verbal description4 ,to a person who may not be able perfectly to understand the language of a country1 to be able to draw is an aid and a safeguard2 to use the words of ,sir ,joshua ,reynolds1 8the pencil speaks the language of every land40 ,in extensive iron works and metal-working establishments the designer and draughtsman is always in demand4 ,his services are indispensable and his position is a highly responsible one4 ,it becomes his special province to design improvements1 to furnish sketches and to make finished drawings2 to calculate strains1 strength1 power1 motion1 weight1 friction and durability4 ,all this and much more is the professional draughtsman's work4 ,in 8directory0 classification1 he who accomplishes such comprehensive results as above described is termed a 8,draughtsman10 but the word has as wide a meaning as 8,engineer10 which takes in civil1 mechanical1 naval1 sanitary1 steam and other engineering specialists4 ,so1 in drafting1 it includes the office boy employed in making blue prints1 it embraces the copyists1 tracers and assistants1 as well as the head draughtsman and chief engineer4 ,consequently the range is wide1 and the line hard to draw between draughtsmen who work with their hands1 and those who work with their brains4 ,it may be added that the best men are too frequently undervalued1 owing to the unavoidable difficulty in distinguishing the difference in true worth1 between the two widely separated classes4 ,it may be remarked that they only draw well who draw intelligently2 aptness in this1 as in many other virtues1 is a matter of slow growth1 8here a line and there a line0--it's the proper direction1 not the rate of progress1 that counts in the end4 ,there are several methods of drawing--#a1 ,free-hand2 #b1 ,instrumental2 #c1 ,geometrical2 #d4 ,perspective4 ,in the first the work1 also termed sketching1 is executed by pencil1 pen1 crayon1 or even paint-brush2 in the second the result is attained by the use of rule1 tee-square1 drawing pen1 etc42 this method is also denominated mechanical drawing1 and suggests the title of this volume4 ,the great usefulness1 not to say necessity1 of readiness in executing accurately1 drawings 8to scale10 is emphasized by the fact that now1 more than ever1 is all machinery designed1 and it may almost be said1 is 8built10 in the draughting room--this is a valuable hint relating to 8reading0 drawings4 ,it is wise1 as well as easy1 to begin at the beginning of things2 thus1 it is altogether the good part to mount a ladder by the first and second rounds rather than to attempt it by taking the third1 sixth1 ninth1 etc4--especially are first and second rounds the very best to start upon2 8,chalk-work10 is the first subject introduced1 next1 that of 8,free-hand40 ,these are the first steps leading upward in this most agreeable attainment--skill in illustrating and designing of objects1 tools1 and utilities4 ,a single word of advice before introducing the elementary work connected with mechanical drawing3 if the student should experience difficulty in mastering the diagrams and curves abounding in this book1 let him consult an experienced draughtsman or teacher1 who1 by a few strokes of a lead pencil1 can easily make them plain2 that knowledge--which cannot be printed or self-taught--termed the ,craftsman's ,art1 is communicated largely by personal telling and showing1 from man to man2 in drawing1 this help should be thankfully availed of1 when necessity arises4 ,,note4--,sketching is often in demand because there is no time for finished or careful drawings1 and the one who can draw a few lines in a moment to let a sudden necessity be known1 is the man of the hour4 ,all candidates for ,first ,class ,engineer's ,certificates in marine service in the navy have to undergo an examination in rough drawing2 this is intended not so much as a proof of the applicant possessing the capability of a draughtsman1 but in the event of any injury to the engines in his charge1 so that he may be able to send to his ,superintendent a rough drawing of the particular part1 properly dimensioned1 so that it could be worked from1 and time saved on the arrival of the ship at the port where the repairs are to be done4 ,illustration ,illustration3 ,,plan ,,of ,,the ,,work 8,no matter how thorough our education may have been at the first1 rules and formulas will slip from the memory1 and every day's experience gives additional evidence of the truth of the old adage that #8,,the ,,key ,,that ,,rests1 ,,rusts4'0--,,simpson ,,ballard4 ,the ,plan of the ,work4 ,the purpose or scope of this work may be briefly stated3 ,it is to aid the aspiring student in making the first advance towards a thorough and useful knowledge of drawing in its several divisions1 as elsewhere defined4 ,the method to be followed in presenting the subject will be the natural order clearly and simply defined1 as 8from the less to the greater40 ,the first subject to be discussed comes under the heading of chalk-work1 i4 e41 such drawings as can be executed on a blackboard1 a floor1 or even on more primitive surfaces1 such as a smooth stone or board4 ,this is indeed a lowly beginning1 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 drawing1 as to them it will revive the ambitions and first crude attempts made in the golden days of their youth4 ,let it be clearly understood by all1 and especially by those who wish to learn drawing1 that the study of this delightful art does not require any special qualification4 ,we need only ask one question3 ,have you learned to write8 ,if so1 be assured you may learn to draw1 but to all the same rule applies1 first the elements of the art1 and afterwards the more advanced study4 ,it is not expected that all should exhibit a decided taste for drawing1 for the possession of this is rather a gift of nature than the result of education2 but a knowledge of principles and a certain amount of executive ability may be obtained by every one of average capacity1 and whatever the natural power may be1 it will be increased and developed by exercise2 if the progress is steady and continuous and in the right direction1 success is sure to crown the work4 ,the second division of the book will be free-hand drawing1 i4 e41 that which is executed without instruments4 ,nothing to instruct has been spared in this important step in the path of advancement4 ,the illustrations accompanying the two opening sections have been made designedly elementary1 for there are many who have a taste for drawing and who have a desire to learn1 who from place of residence or other circumstances have not the opportunity of receiving the assistance of a master4 ,to such this book presents itself as a friend directing to the right road1 talking1 reasoning1 and explaining by the way4 ,the 8chalk-work0 and 8free-hand0 sections of the book relate to the foundations upon which all must rest who seek the aid to be derived from the art2 hence1 the following pages are written with a view to encourage all1 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 life4 ,at this point of attainment there arises a need to know the meaning of many words and phrases used by draughtsmen2 these are grouped alphabetically from ,a to ,z under the heading of1---- ,useful ,terms and ,definitions3 ,memorizing these few pages will be of benefit1 as an intimate knowledge of the language of the drawing office stamps a man as worthy of a hearing1 and assures attention to anything which he may write or say pertaining to the art4 ,after the ,definitions the subject explained will be the ,instruments and ,materials used in mechanical drawings2 following in due course appear ,geometrical and ,mechanical ,drawing1 ,gearing1 ,linear ,perspective1 ,projection1 ,shading1 ,tracing1 ,lettering1 ,drawing ,office ,rules1 ,reading ,drawings1 ,useful ,tables and a ,general ,index1 to which the student is referred4 ,a careful reading is requested to the following helpful note4 ,grateful acknowledgment is made to ,george ,perrott1 ,esq41 ,m4 ,e41 for practical and technical assistance throughout the work1 and to ,theo4 ,lucas1 ,engineer1 for text and illustrations in the portions of the book relating to ,linear ,perspective and ,projection4 ,,note4--,in ,,machinery ,prof4 ,chas4 ,h4 ,benjamin says1 referring to drawing1 under heading 8,how and what to study10 8444 ,i have so far said nothing about drawing1 for ,i do not think it of much use to learn that1 until you know what you want of it4 ,all this time that you have been studying mechanism you should have had a sketch book or pad of note paper1 and made free hand sketches of mechanical movements which interested you and of various machine details4 ,you should accustom yourself to use drawing as a means of expressing ideas1 just as you use written words1 so that it becomes a second nature to you to sketch anything you wish to remember or describe4 ,if you work from blue-prints in the shop1 or if you can borrow some to study1 this will help you to understand how a drawing is made4 ,you can get some drawing instruments at any time and begin to practice on drawing straight lines and circles1 so as to become familiar with the instruments4 ,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 least4 8,when you have become sufficiently familiar with the principles of drawing1 a book on mechanism will tell you how to draw gear teeth and cams1 and how to design various link motions4 ,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 thing2 it is of little use to be able to make a nice drawing unless you know what to draw and why4 8,drawing is a convenient tool as an aid in expressing to others the ideas which you wish to convey2 in all cases take the problems and the ideas from your every-day work and that which is around you2 your success will depend upon the close connection which you keep at all times between your acquired knowledge and your practical work40 ,general ,list of ,contents4 ,,introduction1 #a-bd ,,chalk ,,work1 #be-ch ,,preliminary ,,terms ,,and ,,definitions1 #ci-eb ,,freehand ,,drawing1 #ec-gh ,,geometrical ,,drawing1 #gi-ajj ,,drawing ,,materials ,,and ,,instruments1 #aja-acd ,,mechanical ,,drawing1 #ace-ahh ,,penciling1 #aci-adg ,,projection1 #adh-afd ,,inking ,,in ,,drawings1 #afg-agj ,,lettering ,,drawings1 #aga-age ,,dimensioning ,,drawings1 #agf-agi ,,shading ,,drawings1 #ahj-aha ,,section ,,lining ,,and ,,colors1 #ahb-ahe ,,reproducing ,,drawings1 #ahf-ahh ,,drawing ,,office ,,rules1 #ahi-aie ,,gearing1 #aig-bjh ,,designing ,,gears1 #bji-baf ,,working ,,drawings1 #bai-bbg ,,reading ,,working ,,drawings1 #bbh-bcj ,,patent ,,office ,,rules ,,for ,,drawings1 #bca-bcf ,,useful ,,hints ,,and 8,,points10 #bcg-bdd ,,linear ,,perspective1 #bde-bfe ,,personal1 ,,by ,,the ,,editor1 #bha ,,useful ,,tables1 #bfi-bhj ,,reference ,,index1 #bhc ,illustration3 ,,chalk-,,work ,the peculiarity of all art is that it cannot be communicated in writing alone1 craft is a term which is synonymous with art2 a craft requires manual dexterity which cannot be taught in books4 ,chalk ,work4 ,the blackboard has been well called the great weapon of the modern educator2 this is especially true in reference to instruction in an art dealing with lines1 curves and figures4 ,illustration3 ,fig4 #f4 ,many a man can chalk out on a blackboard1 or on a piece of sheet-iron1 or on the floor1 just what he wants to show1 and make his meaning very plain2 hence1 in every workshop1 and many other places1 a blackboard is more than useful1 and it has been said that no draughting office is complete without one4 ,fig4 #f represents a chalk-crayon4 ,illustration3 ,fig4 #g4 ,illustration3 ,fig4 #h4 ,figs4 #g and #h need no explanation1 as they represent two forms of the well-known blackboard4 ,chalk lines have this advantage--they are easily altered or rubbed out when not needed any longer4 ,the work executed upon a blackboard is mostly done by hand1 without aid from instruments2 a few tools1 however1 are useful--such as1 #a1 large wooden blackboard compasses holding a crayon1 which are made and sold by the trade in size twelve inches to thirty inches in length2 #b1 a straight-edge2 and #c1 some crayons4 ,with the compasses circles and part of the circle can be made1 and with the straight-edge the larger lines can be drawn4 ,these instruments are shown on page #bi1 and are1 #a1 compasses1 for holding chalk for making circles2 #b1 a tee-square2 #c1 a straight-edge2 #d1 a protractor for measuring angles2 #e1 a triangle #fj and #cj2 #f1 a brass holder for crayons4 ,blackboard ,drawing4--,the use of a blackboard comes principally and properly under the head of free-hand drawing1 but its importance is such that a separate division of the volume is assigned to it4 ,illustration ,thus1 chalk-work may be considered the first lesson in 8free-hand10 as all the examples can also be most profitably practiced with pencil and paper4 ,very rapid drawing upon the board should not be encouraged1 as it is likely not to be accurate enough2 again1 the board should be entirely free from grease4 ,cloths1 sponges or chamois skin rubbers may be used to erase or change the chalk marks4 ,vertical lines should be drawn from above downward2 short lines should be drawn with the fingers alone1 those somewhat longer with the hand1 using the wrist-joint2 the still longer lines with the forearm1 using the elbow-joint2 those longer yet with the whole arm1 using the shoulder-joint2 lines should always be drawn with a uniform motion1 slow enough for the eye to follow4 ,practice in chalk-work should alternate with sketching in a sketchbook and with geometrical drawing--to be hereafter described4 ,the student should practice a short time on the board1 at least once a week2 large sizes are the most profitable for the representations to be made2 when drawing in different directions the hand should be turned1 not the paper or board2 the hand should never be allowed to obstruct the sight1 hence the hand and fingers should be held in a position of freedom--with fingers not nearer than #a or #b inches from the board4 ,,note4--,the first lesson of any kind the author received in drawing was to make a straight line2 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 board2 this was a useful item of knowledge1 as proved by passing years4 ,a well-known artist1 in telling his early experience1 said3 8,the first thing ,i was taught was to draw a line1 divide it1 erect a perpendicular from its center1 and afterwards to divide the angle made by the perpendicular40 ,in answer to a question asking how long he was kept at the lines1 he replied1 8about two months--or a month or two10 indicating that even the longer time would have been well spent in learning to draw a straight line4 ,,preparatory ,,practice ,,in ,,drawing4 ,every visible object is bounded by lines which enable the observer to determine its shape4 ,if these lines are straight or curved1 the shape of the object is regular2 if broken1 the shape of the object is irregular4 ,the elements1 then1 of form are lines1 straight1 curved1 or broken1 and these1 therefore1 furnish the beginning of all instruction in free-hand or mechanical drawing4 ,,perpendicular ,,lines4 ,fig4 #ae shows six lines--upright and perpendicular1 with points or 8dots0 indicated at the top and bottom of each line2 to draw these1 proceed thus3 ,illustration3 ,fig4 #ae4 ,illustration3 ,fig4 #af4 ,the learner should stand with his right shoulder opposite the board1 and the weight of the hand and the arm should be allowed to fall naturally2 now1 make on the board two points1 one being six inches above the other1 these being merely 8dots10 shown at the ends of the lines1 figs4 #ae1 etc41 and made with two motions2 the line between the points should now be drawn not too quickly from the upper to the lower point2 three movements of the hand and arm complete the line2 to draw the other five lines the movements have simply to be repeated4 ,if the student pronounces to himself 8one10 8two10 8three10 at each motion1 it will be helpful2 in this exercise1 fig4 #ae1 the aim is to make six lines1 each line being parallel to the first4 ,again1 in the example1 it is intended that the lower point should be made first1 next the upper1 and lastly the line drawn from the upper to the lower point1 but the order may be reversed2 at one the upper point1 at two the lower1 at three the stroke upwards to complete the line4 ,,horizontal ,,lines4 ,to make these as shown in fig4 #af1 proceed as follows3 ,with the word one make a point1 with two another point six inches at the left1 with three draw a straight line from the left point to the right4 ,all added lines should be parallel3 for practice1 reverse the process thus1 one1 make a 8point10 at two another point at the right1 at three draw line to the left4 ,the student will note that the two motions--at the words one and two--are to fix the positions of the ends of the lines2 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 ladder4 ,illustration3 ,fig4 #ag4 ,illustration3 ,fig4 #ah4 ,,oblique ,,lines4 ,in drawing oblique straight lines as shown in fig4 #ag1 at the word one let the student make the lower point2 at the word two the upper1 a little to the right of the lower2 at the word three draw a line quickly from the upper to the lower point4 ,in pronouncing the words one1 two1 three1 let the student make the additional parallel lines4 ,as shown in fig4 #ah1 at the word one make the lower point2 at the word two the upper point1 a little to the left2 at the word three draw a line rapidly from the upper to the lower point1 and 8timing0 the process by repeating one1 two1 three1 make the additional parallel lines4 ,illustration3 ,fig4 #ai4 ,,broken ,,lines4 ,a broken line is composed of two or more straight lines at angles to each other 7see fig4 #ai74 ,to draw them begin 7saying7 one1 make a point2 two a point below at the left2 three1 a point above at the left2 four1 draw a line from the left hand point to the lower point2 at the word five1 from the lower point to the upper right hand point4 ,for practice draw numerous lines in the same way1 keeping them parallel to each other1 as shown in fig4 #bj4 ,illustration3 ,fig4 #bj4 ,illustration3 ,fig4 #ba4 ,illustration3 ,fig4 #bb4 ,illustration3 ,fig4 #bd4 ,illustration3 ,fig4 #bc4 ,illustration3 ,fig4 #be4 ,in example1 fig4 #ba1 the arrangement of the points is changed--let the student draw at the words1 as follows3 ,one1 a point2 two1 a point above at the left2 three1 a point below at the left2 four1 draw from the point at the left to the upper point2 five1 from the upper point to the lower right hand point2 continue to add parallel lines to complete the figure as shown4 ,figs4 #bb and #bc are given as examples to practice1 making first the points and then the connecting lines and afterward the parallel lines to complete the figures4 ,,curved ,,lines4 ,to draw curved lines1 as shown in fig4 #bd4 ,at the word one1 point2 at the word two1 point three inches directly above2 three1 at the same distance above again make a point2 now draw a curve as shown1 joining the middle point and the upper point2 now draw the curve as shown below it2 finally complete figure as shown4 ,illustration3 ,fig4 #bf4 ,illustration3 ,fig4 #bg4 ,illustration3 ,fig4 #bh4 ,illustration3 ,fig4 #bi4 ,illustration3 ,fig4 #cj4 ,figs4 #be to #cj are to be practiced1 making first the points and then connecting them by the curves to complete the figures4 ,when two or more students are working together1 with each having a blackboard1 the counting may be in concert--or a teacher could count for a class4 ,in these line examples care should be used in making them of uniform length4 ,there is a difference to be noted between a crooked line and a broken line1 the latter being a straight line and the former deviating from it4 ,square chalk crayons are the best for hand work1 as lines of an even or uniform width can be drawn with them4 ,a very fine effect is produced by using two thicknesses of chalk1 one being double the thickness of the other2 the heavy lines being used on the shade side of objects will produce a good effect1 giving thickness and body to the object4 ,round chalk crayons are used in the compasses to draw circles1 but hand lines drawn with them are not so neat as those produced with the square-shaped chalk4 ,to obliterate or remove the construction1 or false lines made on the blackboard1 a wooden handle two inches in diameter with a cone end #c or #d inches long1 covered with chamois skin or soft cloth tightly wrapped round the cone and fastened with a tack or drawing pin1 makes the best implement to erase lines not required1 the point of the cone will remove these without destroying the lines or curves which meet them4 ,sponges1 chamois skin or cloth rubbers are used to rub out the chalk drawings and clean the blackboard4 ,the best height for a diagram on the blackboard is not higher than the head1 nor lower than the elbow4 ,horizontal lines should be made from the left to the right2 the body and arm being moved with the hand1 and kept in the same relative position with it1 will steady the hand4 ,curved lines to the left should be drawn first1 enabling the eye to take in not only the curve in process of formation but that already made4 ,passing the crayon in the hand1 over the intended curve previous to marking it1 will guide the eye and give confidence to the hand in chalking the curve4 ,a proper distance from the blackboard is essential1 the face being about two feet away from it4 ,draw with the whole arm extended from the shoulder-joint1 not from the elbow or wrist4 ,illustration3 ,fig4 #ca4 ,illustration3 8,there are more ways than one of telling things3 by speech1 by writing1 by printing1 also by pictures and drawings40 ,knowles ,illustration3 ,,terms ,,definitions ,illustration3 ,,electra4 ,preliminary ,terms and ,definitions4 ,like all the arts1 drawing has a nomenclature of its own1 and nothing can be more helpful to the beginner than to know the name of things relating to the art of drawing4 ,this is a language almost peculiar to itself1 and used daily and hourly by many thousands of superintendents1 foremen and master mechanics1 as well as by owners1 designers and draughtsmen1 hence its introduction at this early stage4 ,,altitude4--,this is the elevation of an object above its base1 or the perpendicular distance between the top and bottom of a figure4 ,illustration3 ,fig4 #cc4 ,illustration3 ,fig4 #cd4 ,illustration3 ,fig4 #ce4 ,illustration3 ,fig4 #cf4 ,illustration3 ,fig4 #cg4 ,,angle is the difference in the direction of two lines which meet or tend to meet4 ,the lines are called the sides and the point of meeting1 the vertex of the lines4 ,to make an angle apparent1 the two lines must meet in a point1 as ,a ,b and ,a ,c1 which meet in the point ,a1 as shown in fig4 #cc4 ,angles are measured by degrees4 ,a ,degree is one of the three hundred and sixty equal parts of the space about a point in a plane4 ,angles are distinguished in respect to magnitude by the terms ,right1 ,acute and ,obtuse ,angles4 ,a ,right ,angle is that formed by one line meeting another1 so as to make equal angles with that other4 ,the lines forming a right angle are perpendicular to each other4 ,an ,acute ,angle is less than a right angle4 ,see ,fig4 #ce4 ,an ,obtuse ,angle is greater than a right angle4 ,see ,fig4 #cf4 ,obtuse and acute angles are also called oblique angles2 and lines which are neither parallel nor perpendicular to each other are called oblique lines4 ,the ,vertex or ,apex of an angle is the point in which the including lines meet4 ,an angle is commonly designated by a letter at its vertex2 but when two or more angles have their vertices at the same point1 they cannot be thus distinguished4 ,for example1 when the three lines ,a ,b1 ,a ,c1 and ,a ,d in fig4 #cg meet in the common point ,a1 we designate either of the angles formed1 by three letters1 placing that at the vertex between those at the opposite extremities of the including lines4 ,thus1 we say1 the angle ,b ,a ,c1 etc4 ,,apex4--,the summit or highest point of an object4 ,,arc4--,see circle4 ,,axis ,,of ,a ,,solid4--,an imaginary straight line passing through its center4 ,,axis ,,of ,a ,,figure4--,a straight line passing through the center of a figure1 and dividing it into two equal parts4 ,,base4--,the base of a solid figure is that on which it stands--the lowest part4 ,,bisect4--,to divide into two equal parts4 ,,bisector4--,a line which bisects4 ,illustration3 ,fig4 #ch4 ,,circle4--,a ,circle is a plane figure bounded by one uniformly curved line1 all of the points in which are at the same distance from a certain point within1 called the ,center4 ,the ,circumference of a circle is the curved line that bounds it4 ,the ,diameter of a circle is a line passing through its center1 and terminating at both ends in the circumference1 as ,a ,c ,b4 ,the ,radius of a circle is a line extending from its center to any point in the circumference4 ,it is one-half of the diameter4 ,all the diameters of a circle are equal1 as are also all the radii ,c ,d1 ,c ,b and ,c ,a4 ,an ,arc of a circle is any portion of the circumference1 as ,b ,d and ,a ,d4 ,semi-,circle4--,half a circle formed by bisecting it with a diameter1 as ,a ,c ,b4 ,fig4 #ch4 ,an angle having its vertex at the center of a circle is measured by the arc intercepted by its sides4 ,thus1 the arc ,a ,d measures the angle ,a ,c ,d1 and in general1 to compare different angles1 we have but to compare the arcs1 included by their sides1 of the equal circles having their centers at the vertices of the angles4 ,,circumscribe4--,to draw a line of figures about or outside1 such as a circle drawn around a square touching its corners or angles4 ,inscribe4--,to draw a line or figure inside or on the interior1 such as a circle drawn within a square touching its sides4 ,,concave4--,curving inwardly4 ,,cone4--,a solid body or figure having a circle for its base1 and its top terminated in a point or vertex4 ,,construction4--,the making of any object4 ,,contour4--,the outline of the general appearance of an object4 ,,convergence4--,lines extending towards a common point4 ,,convex4--,rising or swelling into a round form--the opposite to concave4 ,,corner4--,the point of meeting of the edges of a solid1 or the two sides of a plane figure4 ,,cross-,,hatches4--,in free-hand drawing the use of lines crossing each other to produce light and shade effects4 ,,curve4--,a line of which no part is straight4 ,reversed ,curve4--,one whose curvature is first in one direction and then in the opposite direction4 ,spiral ,curve4--,a plain curve which winds about and recedes1 according to some law1 from its point of beginning1 which is called its center4 ,,cylinder4--,a solid bounded by a curved surface and by two opposite faces called bases2 the bases may be any curved figures and give the name to the cylinder2 thus a circular cylinder is one whose bases are circles4 ,,cylindrical4--,having the general form of a cylinder4 ,,degree4--,the #cfjth part of a circle4 ,,describe4--,to make or draw a curved line2 to draw a plan4 ,,design4--,any arrangement or combination to produce desired results in industry or art4 ,to delineate a form or figure by drawing the outline--a sketch4 ,,develop4--,to unroll or lay out4 ,,diagonal4--,a right line drawn from angle to angle of a quadrilateral or many angled figure and dividing it into two parts4 ,,diameter4--,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 parts4 ,,edge4--,the intersection of any two surfaces4 ,,elevation4--,the term elevation1 vertical projection and front view--applied to drawings--all have the same meaning4 ,,face4--,one of the plane surfaces of a solid2 it may be bounded by straight or curved edges4 ,,finishing4--,completing a drawing whose lines have been determined by erasing unnecessary lines and strengthening and accentuating where this is needed4 ,,foreshortening4--,apparent decrease in length1 owing to objects being viewed obliquely2 thus a wheel1 when seen obliquely1 instead of appearing round1 presents the appearance of an ellipse4 ,,free-,,hand4--,executed by the hand unaided by instruments4 ,,generated4--,produced by4 ,,geometric4--,according to geometry4 ,,half-,,tint4--,the shading produced by means of parallel equidistant lines4 ,,hemisphere4--,half a sphere obtained by bisecting a sphere by a plane4 ,,horizontal4--,parallel to the surface of smooth water4 ,in drawing1 a line drawn parallel to the top and bottom of the sheet is called horizontal4 ,,inscribe4--,see circumscribe--its opposite4 ,,instrumental4--,by the use of instruments4 ,,line4--,a line has length1 only1 as ,a ,c2 a right line is a straight line1 the shortest line that can be drawn between two points1 ,a----,c4 ,straight4 ,one which has the same direction throughout its entire length4 ,curved4 ,one no part of which is straight4 ,broken4 ,one composed of different successive straight lines4 ,mixed4 ,one of straight and curved lines4 ,center4 ,a line used to indicate the center of an object4 ,construction4 ,a working line used to obtain required lines4 ,dotted4 ,a line composed of short dashes4 - - - - - - ,dash4 ,a line composed of long dashes4 -- -- -- ,dot and ,dash4 ,a line composed of dots and dashes alternating4 -- -- -- ,dimension4 ,a line upon which a dimension is placed4 ,full4 ,an unbroken line1 usually representing a visible edge4 ------ ,shadow4 ,a line about twice as wide as the ordinary full line4 ,a straight line is often called simply a line1 and a curved line a curve4 ,,longitudinal4--,in the direction of the length of an object4 ,,model4--,a form used for study4 ,,oblique4--,neither horizontal nor vertical4 ,,oblong4--,a rectangle with unequal sides4 ,,oval4--,a plane figure resembling the longitudinal section of an egg2 or elliptical in shape4 ,,overall4--,the entire length4 ,,parallel4--,having the same direction and everywhere equally distant4 ,,pattern4--,that which is used as a guide or copy in making things4 ,flat4 ,one made of paper or other thin material4 ,solid4 ,one which reproduces the form and size of the object to be made4 ,,perimeter4--,the boundary of a closed plane figure4 ,,perpendicular4--,at an angle of #ij4 ,,perspective4--,view2 drawing objects as they appear to the eye from any given distance and situation1 real or imaginary4 ,,plan4--,plan1 horizontal projection and top view have the same meaning4 ,,plane ,,figure4--,a part of a plane surface bounded by straight or curved lines1 or by both combined4 ,illustration3 ,fig4 #ci4 ,,polygon4--,a plane figure bounded by straight lines called the sides of the polygon4 ,the least number of sides that can bound a polygon is three4 ,polygons bounded by a greater number of sides than four are denominated only by the number of sides4 ,a polygon of five sides is called a ,pentagon2 of six1 a ,hexagon2 of seven1 a ,heptagon2 of eight1 an ,octagon2 of nine1 a ,nonagon1 etc4 ,diagonals of a polygon are lines joining the vertices of angles not adjacent4 ,the ,perimeter of a polygon is its boundary considered as a whole4 ,the ,base of a polygon is the side upon which the polygon is supposed to stand4 ,the ,altitude of a polygon is the perpendicular distance between the base and a side or angle opposite the base4 ,illustration3 ,fig4 #dj4 ,a ,quadrilateral is a polygon having four sides and four angles4 ,a ,parallelogram is a quadrilateral which has its opposite sides parallel4 ,the side upon which a parallelogram stands and the opposite side are called respectively its lower and upper bases4 ,a ,rectangle is a parallelogram having its angles right angles4 ,a ,square is an equilateral rectangle1 fig4 #da4 ,illustration3 ,fig4 #da4 ,illustration3 ,fig4 #db4 ,illustration3 ,fig4 #dc4 ,illustration3 ,fig4 #dd4 ,illustration3 ,fig4 #de4-di4 ,a ,rhomboid is an oblique-angled parallelogram4 ,a ,rhombus is an equilateral rhomboid1 fig4 #db4 ,a ,trapezium is a quadrilateral having no two sides parallel1 fig4 #dc4 ,a ,trapezoid is a quadrilateral in which two opposite sides are parallel1 and the other two oblique1 fig4 #dd4 ,a ,,polyhedron is a solid bounded by planes4 ,there are five regular solids which are shown in figs4 #de1 #df1 #dg1 #dh and #di4 ,a regular solid is bounded by similar and regular plane figures4 ,fig4 #de4--,the tetrahedron1 bounded by four equilateral triangles4 ,fig4 #df4--,the hexahedron1 or cube1 bounded by six squares4 ,fig4 #dg4--,the octahedron1 bounded by eight equilateral triangles4 ,fig4 #dh4--,the dodecahedron1 bounded by twelve pentagons4 ,fig4 #di4--,the icosahedron1 bounded by twenty equilateral triangles4 ,,prism4--,a solid whose bases or ends are very similar plane figures1 and whose sides are parallelograms2 prisms are called triangular1 square1 etc41 according as the bases are triangles1 squares1 etc4 ,,produce4--,to continue or extend4 ,,profile4--,an outline or contour4 ,,projection4--,the view of an object obtained upon a plane by projecting lines perpendicular to the plane4 ,,quadrant4--,the fourth part2 a quarter2 the quarter of a circle4 ,,quadrisect4--,to divide into four equal parts4 ,,section4--,a projection upon a plane parallel to a cutting plane which intersects any object4 ,the section generally represents the part behind the cutting plane1 and represents the cut surfaces by diagonal lines4 ,,sectional4--,showing the section made by a plane4 ,,shadow4--,shade and shadow have about the same meaning4 ,,solid4--,a solid has three dimensions--length1 breadth and thickness4 ,,sphere4--,a solid bounded by a curved surface every point of which is equally distant from a point within called the center4 ,,surface4--,the boundary of a solid4 ,it has but two dimensions--length and breadth4 ,surfaces are plane or curved4 ,a ,plane ,surface is one upon which a straight line can be drawn in any direction4 ,a ,curved ,surface is one no part of which is plane4 ,the surface of the sphere is curved in every direction1 while the curved surfaces of the cylinder and cone are straight in one direction4 ,the surface of a solid is no part of the solid1 but is simply the boundary of the solid4 ,it has two dimensions only1 and any number of surfaces put together will give no thickness4 ,illustration3 ,fig4 #ej4 ,illustration3 ,fig4 #ea4 ,illustration3 ,fig4 #eb4 ,illustration3 ,fig4 #ec4 ,illustration3 ,fig4 #ed4 ,,symmetry4--,design4 ,a proper adjustment or adaptation of parts to one another and to the whole4 ,,trisect4--,to divide into three equal parts4 ,,triangle4--,a triangle is a polygon having three sides and three angles4 ,tri is a ,latin prefix signifying three2 hence a ,triangle is literally a figure containing three angles4 ,a ,scalene ,triangle is one in which no two sides are equal4 ,see fig4 #ej4 ,an ,isosceles ,triangle is one in which two of the sides are equal4 ,see fig4 #ea4 ,an ,equilateral ,triangle is one in which the three sides are equal4 ,an ,equiangular ,triangle is one having its three angles equal4 ,an ,acute-,angled ,triangle is one in which each angle is acute4 ,a ,right-,angled ,triangle is one which has one of the angles a right angle4 ,see fig4 #ec4 ,an ,obtuse-,angled ,triangle is one having an obtuse angle4 ,fig4 #ed4 ,equiangular triangles are also equal sided1 and vice versa4 ,,vertical4--,upright or perpendicular4 ,vertical and perpendicular are not synonymous terms4 ,,vertex4--,see ,angle1 ,quadrilateral1 ,triangle4 ,the vertex of a solid is the point in which its axis intersects the lateral surface4 ,,view4--,see ,elevation4 ,views are called front1 top1 right or left side1 back1 or bottom1 according as they are made on the different planes of projection4 ,they are also sometimes named according to the part of the object shown1 as edge view1 end view1 or face view4 ,,working ,,drawing4--,one which gives all the information necessary to enable the workman to construct the object4 ,illustration ,illustration3 ,,freehand ,,drawing ,illustration3 ,fig4 #ee4 ,free-,hand ,drawing4 ,a free-hand drawing is executed with the unaided hand and eye1 without guiding instruments or other artificial help4 ,it is necessary to be known that all drawing required cannot possibly be done by rule and compass1 but that some portions must be drawn 8free-hand10 trusting to the eye alone4 ,hence1 it is important that the student should be able to sketch at sight from objects he may see1 or to draw roughly1 with a piece of chalk or a pencil1 pieces of mechanism required to be represented4 ,practice in free-hand should go along with mechanical drawing as progress is made1 and thus cultivating both branches equally4 8,a simple sketch will often10 as has been rather roughly said1 8express more than yards of talk40 ,even a slight sketch refreshes the memory1 and in the case of the preparation of a complete set of drawings1 with a view to the making of a thoroughly finished mechanical drawing1 the proper course to pursue is1 to make a general sketch1 letter the various parts for reference1 and then prepare a series of detailed sketches1 similarly lettered1 and diffuse with dimensions4 ,everyone1 whatever his specialty1 feels to-day that the ability to sketch rapidly and clearly is among the absolute necessities for correct and prompt transactions of business1 in giving and executing orders and doing business with persons outside his profession4 ,mistakes and misunderstandings may be averted by means of rough sketches taken at the time and shown for confirmation2 this also saves assistants from getting into trouble1 especially if they pin the sketch to the order1 for reference1 in case of the arising of any dispute4 ,these are a few of the advantages of knowing how to sketch quickly and correctly4 ,in 8free-hand0 any sort of pencil is better than none1 but there is a considerable advantage in having a good serviceable article--a pencil not too soft nor too hard1 and one which will retain its point for some little time4 ,fig4 #ee shows the approved position in which the pencil should be held while sketching4 ,the pencil should be held firmly between the thumb and first finger of the right hand2 press the second finger against the pencil at the opposite side to the thumb pressure1 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 steadiness4 ,the motion of the pencil is produced from the movement of the fingers and thumb1 principally in the vertical strokes1 and the horizontal strokes are produced by fingers and thumb1 combined with a wrist or elbow motion2 the oblique lines and curves are produced with a free movement1 with nothing cramped or confined about the finger joints4 ,,position4 ,it should be observed that nothing is more prejudicial to good execution than the habit of leaning over the paper1 which ought to be placed on a surface sufficiently inclined to bring every portion equally under the eye1 thus obviating the necessity of leaning forward4 ,all support to the figure should be obtained by resting on the left arm1 the right being left free for work4 ,by attention to these rules that awkwardness of position1 so detrimental to a good figure1 will be avoided4 ,it is better to have the light on the left hand1 as in this direction the shadow of the pencil does not interfere with the view of the drawing4 ,illustration3 ,fig4 #ef4 ,,how ,,to ,,cut ,a ,,pencil4 ,hold the pencil firmly in the left hand1 as in the drawing1 allowing about an inch to project beyond the fingers1 and turn it gradually as the knife removes the wood4 ,the knife should be held so that the blade alone projects beyond the fingers1 and the part of it nearest the handle used for cutting4 ,the pencil should be placed against the inside of the thumb of the right hand1 as in the drawing 7fig4 #ef71 and the wood removed by slight shaving4 ,the lead should not be cut at the same time as the wood1 but rested on the thumb and pared gently afterwards2 by attention to these directions the pencil will be economized4 ,,how ,,to ,,draw ,,straight ,,lines4 ,before a line is drawn1 the point at which it is to commence and the point where it is to end1 should be known2 and let it be distinctly understood that this judgment of the eye1 and placing of points1 should invariably precede the drawing of every line4 ,the first effort should1 therefore1 be to produce a line of points exactly parallel with the upper edge of the paper1 and at equal distances from each other4 ,commence with point ,a and place the point ,b carefully level with it1 now place a slip of paper against these points in the original1 mark their distance apart1 and see if the same proportion has been given in your copy2 if not1 make the necessary correction4 ,proceed with the next point1 examine it1 and so on to the end of the line4 ,when this is complete1 examine each point in succession1 to try if it is at the same distance from the top of the paper2 when this is correct1 proceed to draw the first level line4 ,hold the pencil as in the drawing1 fig4 #eg1 keeping the elbow near the side2 join ,a to ,b by one light1 steady stroke1 produced by a movement of the wrist1 and add stroke upon stroke until the line is of the required depth4 ,continue this process to the end of the line of points4 ,now place the point ,d at the right distance below the ,a1 proceed with the points for another line as before1 and continue the lines until the paper is covered4 ,in producing the stroke the pencil should not be jerked1 or any stop be made between the points1 but the movement should be even throughout1 and it is much better to produce each line by several soft strokes1 as the repetition of delicate lines induces lightness of touch and freedom of hand2 and it is also no small advantage that lines thus produced are more easily removed by the ,india rubber1 should they require correction4 ,,to ,,draw ,,the ,,first ,,oblique ,,line4 ,prepare three rows of points down the side of the paper1 on the left hand2 examine them to see that they are at equal distances from the side and from each other2 hold the pencil as in the drawing1 fig4 #eh1 move the elbow a little from the side1 and join the points ,a and ,b with one light line1 produced by a movement of the fingers and thumb1 repeating the strokes until the line is of the requisite depth2 proceed to join ,b to ,c1 taking care previously to bring the hand a little down the paper1 as the line from ,a to ,c is too long to be produced from one position4 ,when the three rows of points are filled1 make another set1 examine them and proceed as before4 ,by these means the paper will be covered with oblique lines1 and if the points have been placed exactly1 the sheet will have a neat and regular appearance4 ,,note4--,the drawings of hands are introduced to show the positions for holding the pencil1 and are not intended for copying4 ,illustration3 ,fig4 #eg4 ,illustration3 ,fig4 #eh4 ,it is a common1 and at the same time highly injurious habit1 to draw this line by a movement of the wrist1 the fingers remaining rigid4 ,this may be detected by watching the action of the thumb2 if it bends as the line is produced1 all is right2 but if it does not the wrist is at work4 ,,to ,,draw ,,the ,,upright ,,or ,,perpendicular ,,line4 ,this line demands the greatest attention1 and any care bestowed upon it will be amply repaid in the after studies4 ,commence by placing a line of points down the side of the paper1 examine them very carefully to see that they are all the same distance from its edge1 hold the pencil as in the drawing1 fig4 #ei1 move the elbow well out from the side1 and join the points by a movement of the fingers and thumb4 ,when one line is complete1 place the points for the next1 and examine them from the edge of the paper1 not from the line just drawn4 ,proceed in this manner until the paper is covered4 ,there is in most cases a tendency to place the points for this line in a slightly inclined direction1 as in writing1 though in some instances the tendency is the opposite1 a thoroughly correct eye in this respect being a rare gift3 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 eye4 ,,to ,,draw ,,the ,,second ,,oblique ,,line4 ,prepare three rows of points down the side of the paper1 examine them for correctness of position1 hold the pencil as in the drawing1 fig4 #fj1 remove the elbow as far as possible from the side1 and join the points by a movement of the fingers and thumb1 and continue the exercise until the paper is covered4 ,illustration3 ,fig4 #ei4 ,illustration3 ,fig4 #fj4 ,it will be noticed that each change in direction of the line to be drawn1 has been accompanied with a corresponding change in the position of the elbow and wrist4 ,the following simple rule will assist the memory when placing the hand for any given line2 the pencil should be held so that it may form a ,t with the line to be drawn3 ,illustration ,for the horizontal line1 elbow near the side4 ,illustration ,for the first oblique1 elbow a little removed4 ,illustration ,for the perpendicular1 elbow more removed4 ,illustration ,for the second oblique1 elbow most removed4 ,illustration3 ,finger and thumb lines4 ,wrist lines4 ,finger and thumb lines4 ,wrist lines4 ,it may also be interesting to notice1 with regard to the movements by which lines are produced1 that they are divided into two systems2 the first is that of the wrist1 which includes the horizontal1 and lines in nearly the same direction2 the second is that of the fingers and thumb1 by which all other lines are formed4 ,the following diagram exhibits the two systems and their various lines grouped1 and it will be observed that there is a space marked 7a7 between the two sets1 which may be considered neutral ground4 ,lines in this direction may be produced by either movement1 as may be most convenient1 but it will always be found that these lines are the most trying to the hand4 ,,on ,,figures ,,formed ,,of ,,straight ,,lines4 ,before commencing this subject1 let it be clearly understood that future success will1 in a great measure1 depend upon the amount of care bestowed upon it4 ,the aim should be to obtain absolute accuracy1 and for this end the copies should be tested by the most careful measurements1 and corrected until they are true with the originals1 but it should be distinctly understood that these measurements are only to be made after the eye and hand have done their best4 ,,note4--,to some it may appear that too much time and care has been bestowed on mere lines1 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 bold1 free and masterly character2 and with regard to shading1 which is simply an aggregation of good lines1 it is only by such a practiced hand its most charming effects can be produced4 ,fig4 #ff3 ,place the points ,a1 ,b4 ,examine them to see that they are the same distance apart as in the original1 and that they are level2 place the point ,c exactly under ,a1 and make ,a ,c equal in distance to ,a ,b2 now place the point ,d opposite ,c and under ,b2 try the distances between each point to see that they are the same2 divide each side by a point half way1 and then draw the lines4 ,fig4 #fg3 ,repeat the last figure and add the lines ,a and ,b1 taking great care that the points for them are correctly placed4 ,fig4 #fh3 ,commence with the square as before2 then join the half-way points4 ,fig4 #fi3 ,after the square is drawn1 place the points ,a and ,b at the right height above the half-way points1 and ,c1 ,d at the proper distance from the corners1 then draw the figure4 ,fig4 #gj3 ,the greatest care should be taken with the squares for this and the following figure1 as the slightest error in them will destroy the symmetry of the drawing within2 when the square is completed1 join the opposite corners1 and place on the crossed lines the points ,b1 ,c1 ,d1 ,e2 examine these to see that they are each at the same distance from the centre ,a1 and that this distance is equal to the space from ,a to the sides of the square2 when all are proved to be correct1 complete the figure4 ,illustration3 ,fig4 #ff4 ,illustration3 ,fig4 #fg4 ,illustration3 ,fig4 #fh4 ,illustration3 ,fig4 #fi4 ,illustration3 ,fig4 #gj4 ,illustration3 ,fig4 #ga4 ,fig4 #ga3 ,repeat the last drawing with1 if possible1 greater exactness1 and outside the octagon place the points ,a1 ,b1 ,c1 ,d1 etc42 examine each of these points to see that they are all at the same distance from the centre1 and then complete the figure4 ,,on ,,curved ,,lines4 ,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 curve4 ,the straight lines given in the exercises are valuable1 not only as a guide to the position of the hand1 but as an assistance to the eye when forming the curves or examining them after they are produced4 ,illustration ,the direction given for drawing a straight line was to form it by one steady movement from point to point1 without any jerk or stop by the way4 ,this instruction requires to be changed for the curve1 which is better produced by several short strokes1 thus3 ,illustration or by overlapping lines1 any outside bits being cleared away with ,india rubber4 ,these exercises will test the drawing power and try the patience of the pupil1 but they are worthy of all the care which can be bestowed1 which in future efforts will meet with its full reward4 ,fig4 #gf3 ,draw first the square as directed in the previous lesson1 join the points ,a1 ,b1 ,c and add the short lines at ,e and ,f1 proceed with the curve ,a ,b1 drawing it with faint lines at first1 and adding stroke upon stroke until the required depth is obtained2 the curve ,a ,c is more difficult to produce1 in consequence of the formation of the hand2 it should1 therefore1 be drawn in shorter pieces1 joining them together afterwards by over strokes4 ,illustration3 ,fig4 #gf4 ,illustration3 ,fig4 #gg4 ,fig4 #gg3 ,draw the square and straight lines first1 then add the curves1 taking care to give the greatest fullness at the right place4 ,fig4 #gh3 ,draw the square and straight lines1 proceed with the curves1 taking care to make each of the same proportion4 ,figs4 #gi and #hj3 ,the ovals contained in these figures are simply foreshortened circles1 and as such forms are of frequent occurrence in sketching from objects1 in bridges1 wheels1 ends of timber1 etc41 they should be carefully studied2 the greatest difficulty is to turn the narrow ends1 and prevent their looking like corners4 ,for this purpose it is better to draw the short curves first1 thus3 ,illustration and then join the longer sides to them4 ,fig4 #ha3 ,if this figure can be drawn correctly1 a great success has been achieved2 the circle is a most difficult form to delineate1 and without system could not be accomplished4 ,draw the square and straight lines within it with great care1 examine each point of the octagon to see that it is at the same distance from the centre1 and then draw the circle4 ,,examples ,,for ,,practice4 ,several figures1 #hc to #if1 representing more or less familiar parts of machines1 utilities1 etc41 are introduced for practice in free-hand1 but-- ,it must be noted that even in free-hand the wise student will occasionally use the straight edge and compasses1 so as to make his first attempts fairly creditable4 ,many good draughtsmen have begun by simply copying such figures and illustrations as are used throughout this volume and other similar sources2 perhaps there is nothing better for practice or training than the copying and reproducing of samples of good mechanical drawings1 yet it must always be remembered that advancement in free-hand must be made in the line of less to greater efforts1 and that the why and wherefore will be constantly asked by the aspiring student2 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 represented4 ,illustration3 ,fig4 #gh4 ,illustration3 ,fig4 #gi4 ,illustration3 ,fig4 #hj4 ,illustration3 ,fig4 #ha4 ,fig4 #hc is a section1 or end view of a bar of angle iron2 the student will find helpful practice in attempting this figure2 he may be allowed to use a straight-edge in drawing the lines1 but no measurements2 the work should be tested on completion by a rule1 or better by penciling from the original on tracing paper1 and comparing the free-hand with the copy1 when the defective proportions1 if any1 will be clearly exhibited4 ,fig4 #hd is a section of tee iron1 and fig4 #he is a section of channel iron4 ,these three figures on page #ge should be practiced alternately1 although seeming similar in shape4 ,fig4 #hf is a side and end view of an angle plate shaded4 ,fig4 #hg is a wrench shaded4 ,examples of bolt ends are shown in the two next numbers2 fig4 #hh exhibits the common square-head bolt1 and fig4 #hi the hexagon or six-sided bolt-head2 these are also examples of straight-line shading4 ,fig4 #ij is a lathe-dog1 and shows an example of curved shading2 fig4 #ib is an engine crank1 and an example of straight and curved shading2 fig4 #ia is a screw clamp4 ,fig4 #ic is a section of boiler plates riveted together2 a caulking tool is also shown4 ,in the example1 fig4 #id--;a hand-wheel--the principal difficulty1 even for the most advanced student in free-hand1 will be in drawing the circles2 a coin1 if convenient1 can be used to scribe about1 in drawing these2 the other parts can afterwards be filled in around the circle4 ,fig4 #if is introduced for practice in penciling and shading2 the figure represents a water-wheel on a stone pier4 ,the familiar oil can is shown in fig4 #ie4 ,these all are excellent objects for practice4 ,illustration3 ,fig4 #hc4--;,fig4 #hd4--;,fig4 #he4 ,illustration3 ,fig4 #hf4 ,illustration3 ,fig4 #hg4 ,illustration3 ,fig4 #hh4--;,fig4 #hi4--;,fig4 #ij4--;,fig4 #ia4 ,illustration3 ,fig4 #ib4 ,illustration3 ,fig4 #ic4 ,illustration3 ,fig4 #id4 ,illustration3 ,fig4 #ie4 ,illustration3 ,fig4 #if4 ,illustration3 ,,geometrical ,,drawing ,illustration ,geometrical ,drawing4 ,geometry is the science of measurement2 it has been known for more than three thousand years2 many lives have been devoted to its development1 and it exists to-day as the foundation of all mathematics4 ,geometrical drawing is the art of representing1 to the eye1 the problems 8worked out0 by geometricians1 and the importance of a knowledge of geometrical drawing is paramount4 ,the student will find that the figures delineated and explained in the next few pages constantly occur in mechanical drawing4 ,says ,walter ,smith1 ,state ,director of ,art ,education in ,massachusetts1 8,i have never known a case where a student did not progress more satisfactorily in his studies after a course of practical geometry40 ,the elementary conceptions of geometry are few3 #a4--;,a point4 #b4--;,a line4 #c4--;,a surface4 #d4--;,a solid1 and #e4--;,an angle4 ,all of which elements are used in mechanical drawings4 ,from these1 as data1 a vast number of mathematical problems have been deduced2 of which a few of the most elementary will be illustrated in this work2 but these few will repay the attention of the student4 ,in 8freehand0 drawing the crayon and pencil are used2 in geometrical drawings the dividers1 as shown in illustration1 fig4 #ig1 together with a rule1 are all that is necessary to accomplish the work4 ,a problem is something to be done1 and geometry has been defined as the science of measurement2 the relation between geometry and mechanical drawing is very close1 hence the term 8geometrical problem40 ,illustration3 ,fig4 #ig4 ,illustration3 ,fig4 #ih4 ,before proceeding with the examples1 a few elementary statements belonging to the science of geometry are presented2 these will be useful to the student1 not only while 8doing0 the problems1 but in many cases of every-day--future--experience4 ,geometry is one of the oldest and simplest of sciences2 it may be defined as the science of measurement2 geometry is the root from which all regular mathematical calculations issue4 ,it has claimed the best thought of practical men from the times of the ,greeks and ,romans two thousand years ago2 they derived their knowledge of the science from the ,egyptians1 who in turn were indebted to the ,chaldeans and ,hindoos in times beyond any authentic history2 hence it was under the operations of the laws explained in geometry1 that the pyramids of ,egypt and the temples of ,greece were constructed1 as well as the engines of war and appliances of peace of ancient times4 ,a point is mere position1 and has no magnitude4 ,a line is that which has extension in length only4 ,the extremities of lines are points4 ,a surface is that which has extension in length and breadth only4 ,a solid is that which has extension in length1 breadth and thickness4 ,an angle is the difference in the direction of two lines proceeding from the same point4 ,illustration ,lines1 ,surfaces1 ,angles and ,solids constitute the different kinds of quantity called geometrical magnitudes4 ,parallel lines are lines which have the same direction2 hence parallel lines can never meet1 however far they may be produced2 for two lines taking the same direction cannot approach or recede from each other4 ,illustration ,an ,axiom is a self-evident truth1 not only too simple to require1 but too simple to admit of demonstration4 ,a ,proposition is something which is either proposed to be done1 or to be demonstrated1 and is either a problem or a theorem4 ,a ,problem is something proposed to be done4 ,a ,theorem is something proposed to be demonstrated4 ,a ,hypothesis is a supposition made with a view to draw from it some consequence which establishes the truth or falsehood of a proposition1 or solves a problem4 ,a ,lemma is something which is premised1 or demonstrated1 in order to render what follows more easy4 ,a ,corollary is a consequent truth derived immediately from some preceding truth or demonstration4 ,a ,scholium is a remark or observation made upon something going before it4 ,a ,postulate is a problem1 the solution of which is self-evident4 ,let it be granted-- ,i4 ,that a straight line can be drawn from any one point to any other point2 ,,ii4 ,that a straight line can be produced to any distance1 or terminated at any point2 ,,iii4 ,that the circumference of a circle can be described about any center1 at any distance from that center4 ,the common algebraic signs are used in ,geometry1 and it is necessary that the student in geometry should understand some of the more simple operations of algebra4 ,as the terms circle1 angle1 triangle1 hypothesis1 axiom1 theorem1 corollary and definition are constantly occurring in a course of geometry1 they are abbreviated as shown in the following list3 ,addition is expressed by ,subtraction is expressed by - ,multiplication is expressed by ,equality and ,equivalency are expressed by ,greater than1 is expressed by ,less than1 is expressed by ,thus ,b is greater than ,a1 is written ,b ,a ,b is less than ,a1 is written ,b ,a ,a circle is expressed by ,o ,an angle is expressed by ,l ,a right angle is expressed by ,r4 ,l ,degrees1 minutes and seconds are expressed by ,a triangle is expressed by ,the term ,hypothesis is expressed by 7,hy47 ,the term ,axiom is expressed by 7,ax47 ,the term ,theorem is expressed by 7,th47 ,the term ,corollary is expressed by 7,cor47 ,the term ,definition is expressed by 7,def47 ,the term ,perpendicular is expressed by ,the difference of two quantities1 when it is not known which is the greater1 is expressed by the symbol ,thus1 the difference between ,a and ,b is written ,a ,b ,,geometrical ,,axioms4 #a4 ,things which are equal to the same thing are equal to each other4 #b4 ,when equals are added to equals the wholes are equal4 #c4 ,when equals are taken from equals the remainders are equal4 #d4 ,when equals are added to unequals the wholes are unequal4 #e4 ,when equals are taken from unequals the remainders are unequal4 #f4 ,things which are double of the same thing1 or equal things1 are equal to each other4 #g4 ,things which are halves of the same thing1 or of equal things1 are equal to each other4 #h4 ,the whole is greater than any of its parts4 #i4 ,every whole is equal to all its parts taken together4 #aj4 ,things which coincide1 or fill the same space1 are identical1 or mutually equal in all their parts4 #aa4 ,all right angles are equal to one another4 #ab4 ,a straight line is the shortest distance between two points4 #ac4 ,two straight lines cannot enclose a space4 ,problems in ,geometrical ,drawing4 ,illustration3 ,fig4 #ii4 ,,example #a4--,to bisect 7cut in two7 a straight line or an arc of a circle1 ,fig4 #ii4 ,from the ends of ,a ,b as centers1 describe arcs cutting each other at ,c and ,d1 and draw ,c ,d1 which cuts the line at ,e or the arc at ,f4 ,,ex4 #b4--,to draw a perpendicular to a straight line1 or a radial line to a circular arc1 ,fig4 #ii4 ,operate as in the foregoing problem4 ,the line ,c ,d is perpendicular to ,a ,b2 the line ,c ,d is also radial to the arc ,a ,b4 ,illustration3 ,fig4 #ajj4 ,illustration3 ,fig4 #aja4 ,,ex4 #c4--,to draw a perpendicular to a straight line1 from a given point in that line1 ,fig4 #ajj4 ,with any radius from any given point ,a in the line ,b ,c1 cut the line at ,b and ,c4 ,next1 with a longer radius1 describe arcs from ,b and ,c1 cutting each other at ,d1 and draw the perpendicular ,d ,a4 ,second ,method1 ,fig4 #aja4 ,from any center ,f above ,b ,c1 describe a circle passing through the given point ,a1 and cutting the given line at ,d2 draw ,d ,f1 and produce it to cut the circle at ,e2 and draw the perpendicular ,a ,e4 ,illustration3 ,fig4 #ajb4 ,third ,method1 ,fig4 #ajb4 ,from ,a describe an arc ,e ,c1 and from ,e1 with the same radius1 the arc ,a ,c cutting the other at ,c2 through ,c draw a line ,e ,c ,d and set off ,c ,d equal to ,c ,e1 and through ,d draw the perpendicular ,a ,d4 ,illustration3 ,fig4 #ajc4 ,illustration3 ,fig4 #ajd4 ,,ex4 #d4--,to draw a perpendicular to a straight line from any point without it1 ,fig4 #ajc4 ,from the point ,a with a sufficient radius cut the given line at ,f and ,g2 and from these points describe arcs cutting at ,e4 ,draw the perpendicular ,a ,e4 ,if there be no room below the line1 the intersection may be taken above the line2 that is to say1 between the line and the given point4 ,second ,method1 ,fig4 #ajd4 ,from any two points ,b ,c at some distance apart1 in the given line1 and with the radii ,b ,a1 ,c ,a1 respectively1 describe arcs cutting at ,a ,d4 ,draw the perpendicular ,a ,d4 ,illustration3 ,fig4 #aje4 ,illustration3 ,fig4 #ajf4 ,,ex4 #e4--,to draw a parallel line through a given point1 ,fig4 #aje4 ,with a radius equal to the given point ,c from the given line ,a ,b1 describe the arc ,d from ,b1 taken considerably distant from ,c4 ,draw the parallel through ,c to touch the arc ,d4 ,second ,method1 ,fig4 #ajf4 ,from ,a1 the given point1 describe the arc ,f ,d1 cutting the given line at ,f2 from ,f1 with the same radius1 describe the arc ,e ,a1 and set off ,f ,d1 equal to ,e ,a4 ,draw the parallel through the points ,a ,d4 ,illustration3 ,fig4 #ajg4 ,when a series of parallels are required perpendicular to a base line ,a ,b1 they may be drawn as in fig4 #ajg through points in the base line set off at the required distances apart4 ,this method is convenient also where a succession of parallels are required to a given line ,c ,d1 for the perpendicular may be drawn to it1 and any number of parallels may be drawn on the perpendicular4 ,illustration3 ,fig4 #ajh4 ,illustration3 ,fig4 #aji4 ,,ex4 #f4--,to divide a line into a number of equal parts1 ,fig4 #ajh4 ,to divide the line ,a ,b into1 say1 five parts4 ,from ,a and ,b draw parallels ,a ,c1 ,b ,d on opposite sides2 set off any convenient distance four times 7one less than the given number71 from ,a on ,a ,c1 and on ,b on ,b ,d2 join the first on ,a ,c to the fourth on ,b ,d1 and so on4 ,the lines so drawn divide ,a ,b as required4 ,second ,method1 ,fig4 #aji4 ,draw the line at ,a ,c1 at an angle from ,a1 set off1 say1 five equal parts2 draw ,b #e1 and draw parallels to it from the other points of division in ,a ,c4 ,these parallels divide ,a ,b as required4 ,illustration3 ,fig4 #aaj4 ,,ex4 #g4--,upon a straight line to draw an angle equal to a given angle1 ,fig4 #aaj4 ,let ,a be the given angle and ,f ,g the line4 ,with any radius from the points ,a and ,f1 describe arcs ,d ,e1 ,i ,h1 cutting the sides of the angle ,a and the line ,f ,g4 ,set off the arc ,i ,h1 equal to ,d ,e and draw ,f ,h4 ,the angle ,f is equal to ,a as required4 ,illustration3 ,fig4 #aaa4 ,,ex4 #h4--,to bisect an angle1 ,fig4 #aaa4 ,let ,a ,c ,b be the angle2 on the center ,c cut the sides at ,a ,b4 ,on ,a and ,b as centers describe arcs cutting at ,d dividing the angle into two equal parts4 ,illustration3 ,fig4 #aab4 ,,ex4 #i4--,to find the center of a circle or of an arc of a circle4 ,fig4 #aab4 ,draw the chord ,a ,b1 bisect it by the perpendicular ,c ,d1 bounded both ways by the circle2 and bisect ,c ,d for the center ,g4 ,illustration3 ,fig4 #aac4 ,illustration3 ,fig4 #aad4 ,,ex4 #aj4--,through two given points to describe an arc of a circle with a given radius1 ,fig4 #aac4 ,on the points ,a and ,b as centers1 with the given radius1 describe arcs cutting at ,c2 and from ,c1 with the same radius1 describe an arc ,a ,b as required4 ,second1 for a circle or an arc1 ,fig4 #aad4 ,select three points ,a1 ,b1 ,c in the circumference1 well apart2 with the same radius describe arcs from these three points cutting each other1 and draw two lines ,d ,e1 ,f ,g1 through their intersections according to ,fig4 #ajg4 ,the point where they cut is the center of the circle or arc4 ,,ex4 #aa4--,to describe a circle passing through three given points1 ,fig4 #aad4 ,let ,a1 ,b1 ,c be the given points and proceed as in last problem to find the center ,o1 from which the circle may be described4 ,this problem is variously useful2 in finding the diameter of a large fly-wheel1 or any other object of large diameter when only a part of the circumference is accessible2 in striking out arches when the span and rise are given1 etc4 ,illustration3 ,fig4 #aae4 ,,ex4 #ab4--,to draw a tangent to a circle from a given point in the circumference1 ,fig4 #aae4 ,from ,a set off equal segments ,a ,b1 ,a ,d1 join ,b ,d and draw ,a ,e1 parallel to it1 for the tangent4 ,illustration3 ,fig4 #aaf4 ,,ex4 #ac4--,to draw tangents to a circle from points without it1 ,fig4 #aaf4 ,from ,a with the radius ,a ,c describe an arc ,b ,c ,d1 and from ,c with a radius equal to the diameter of the circle1 cut the arc at ,b ,d1 join ,b ,c1 ,c ,d1 cutting the circle at ,e ,f1 and draw ,a ,e1 ,a ,f1 the tangents4 ,illustration3 ,fig4 #aag4 ,,ex4 #ad4--;,between two inclined lines to draw a series of circles touching these lines and touching each other1 ,fig4 #aag4 ,bisect the inclination of the given lines ,a ,b1 ,c ,d by the line ,n ,o4 ,from a point ,p in this line draw the perpendicular ,p ,b to the line ,a ,b1 and on ,p describe the circle ,b ,d1 touching the lines and cutting the center lines at ,e4 ,from ,e draw ,e ,f perpendicular to the center line1 cutting ,a ,b at ,f1 and from ,f describe an arc ,e ,g1 cutting ,a ,b at ,g4 ,draw ,g ,h parallel to ,b ,p1 giving ,h1 the center of the next circle1 to be described with the radius ,h ,e1 and so on for the next circle1 ,i ,n4 ,illustration3 ,fig4 #aah4 ,illustration3 ,fig4 #aai4 ,,ex4 #ae4--,to construct a triangle on a given base1 the sides being given4 ,first4 ,an equilateral triangle1 ,fig4 #aah4 ,on the ends of a given base ,a ,b1 with ,a ,b as a radius describe arcs cutting at ,c1 and draw ,a ,c1 ,c ,b4 ,second4 ,triangle of unequal sides1 ,fig4 #aai4 ,on either end of the base ,a ,d1 with the side ,b as a radius describe an arc2 and with the side ,c as a radius1 on the other end of the base as a center1 describe arcs cutting the arc at ,e2 join ,a ,e1 ,d ,e4 ,this construction may be used for finding the position of a point ,c or ,e at given distances from the ends of a base1 not necessarily to form a triangle4 ,illustration3 ,fig4 #abj4 ,illustration3 ,fig4 #aba4 ,,ex4 #af4--,to construct a square rectangle on a given straight line4 ,first4 ,a square1 ,fig4 #abj4 ,on the ends ,b ,a as centers1 with the line ,a ,b as radius1 describe arcs cutting at ,c2 on ,c describe arcs cutting the others at ,d ,e2 and on ,d and ,e cut these at ,f ,g4 ,draw ,a ,f1 ,b ,g and join the intersections ,h ,i4 ,second4 ,a rectangle1 ,fig4 #aba4 ,on the base ,e ,f draw the perpendiculars ,e ,h1 ,f ,g1 equal to the height of the rectangle1 and join ,g ,h4 ,illustration3 ,fig4 #abb4 ,,ex4 #ag4--,to construct a parallelogram of which the sides and one of the angles are given1 ,fig4 #abb4 ,draw the side ,d ,e equal to the given length ,a1 and set off the other side ,d ,f equal to the other length ,b1 forming the given angle ,c4 ,from ,e with ,d ,f as radius1 describe an arc1 and from ,f1 with the radius ,d ,e cut the arc at ,g4 ,draw ,f ,g1 ,e ,g4 ,or1 the remaining sides may be drawn as parallels to ,d ,e1 ,d ,f4 ,illustration3 ,fig4 #abc4 ,,ex4 #ah4--,to describe a circle about a triangle1 ,fig4 #abc4 ,bisect two sides ,a ,b1 ,a ,c of the triangle at ,e ,f1 and from these points draw perpendiculars cutting at ,k4 ,on the center ,k1 with the radius ,k ,a draw the circle ,a ,b ,c4 ,illustration3 ,fig4 #abd4 ,,ex4 #ai4--,to describe a circle about a square1 and to inscribe a square in a circle1 ,fig4 #abd4 ,first4 ,to describe the circle4 ,draw the diagonals ,a ,b1 ,c ,d of the square1 cutting at ,e2 on the center ,e with the radius ,e ,a describe the circle4 ,second4 ,to inscribe the square4 ,draw the two diameters ,a ,b1 ,c ,d at right angles and join the points ,a ,b1 ,c ,d to form the square4 ,in the same way a circle may be described about a triangle4 ,illustration3 ,fig4 #abe4 ,,ex4 #bj4--,to inscribe a circle on a square1 and to describe a square about a circle1 ,fig4 #abe4 ,first4 ,to inscribe the circle4 ,draw the diagonals ,a ,b1 ,c ,d of the square1 cutting at ,e2 draw the perpendicular ,e ,f to one side1 and with the radius ,e ,f describe the circle4 ,second4 ,to describe the square4 ,draw two diameters ,a ,b1 ,c ,d at right angles1 and produce them2 bisect the angle ,d ,e ,b at the center by the diameter ,f ,g1 and through ,f and ,g draw perpendiculars ,a ,c1 ,b ,d1 and join the points ,a ,d and ,b ,c where they cut the diagonals to complete the square4 ,illustration3 ,fig4 #abf4 ,,ex4 #ba4--,to inscribe a circle in a triangle1 ,fig4 #abf4 ,bisect two of the angles ,a ,c of the triangle by lines cutting at ,d2 from ,d draw a perpendicular ,d ,e to any side1 and with ,d ,e as radius describe a circle4 ,illustration3 ,fig4 #abg4 ,,ex4 #bb4--,to inscribe a pentagon in a circle1 ,fig4 #abg4 ,draw two diameters ,a ,c1 ,b ,d at right angles cutting at ,o2 bisect ,a ,o at ,e1 and from ,b with radius ,b ,e cut the circumference at ,g ,h and with the same radius step round the circle to ,i and ,k2 join the points to form the pentagon4 ,illustration3 ,fig4 #abh4 ,,ex4 #bc4--,to construct a hexagon upon a given straight line1 ,fig4 #abh4 ,from ,a and ,b1 the ends of the given line1 describe arcs cutting at ,g2 from ,g with the radius ,g ,a describe a circle4 ,with the same radius set off the arcs ,a ,c1 ,c ,f and ,b ,d1 ,d ,e2 join the points so found to form the hexagon4 ,illustration3 ,fig4 #abi4 ,,ex4 #bd4--,to inscribe a hexagon in a circle1 ,fig4 #abi4 ,draw a diameter ,a ,c ,b2 from ,a and ,b as centers1 with the radius of the circle ,a ,c cut the circumference at ,d1 ,e1 ,f1 ,g1 and draw ,a ,d1 ,d ,e1 etc41 to form the hexagon4 ,the points ,d ,e1 etc41 may be found by stepping the radius 7with the dividers7 six times round the circle4 ,illustration3 ,fig4 #acj4 ,,ex4 #be4--,to describe an octagon on a given straight line1 ,fig4 #acj4 ,produce the given line ,a ,b both ways and draw perpendiculars ,a ,e1 ,b ,f2 bisect the external angles ,a and ,b by the lines ,a ,h1 ,b ,c1 which make equal to ,a ,b4 ,draw ,c ,d and ,h ,g parallel to ,a ,e and equal to ,a ,b2 from the center ,g ,d1 with the radius ,a ,b1 cut the perpendiculars at ,e ,f1 and draw ,e ,f to complete the hexagon4 ,illustration3 ,fig4 #aca4 ,,ex4 #bf4--,to convert a square into an octagon1 ,fig4 #aca4--;,draw the diagonals of the square cutting at ,e2 from the corners ,a1 ,b1 ,c1 ,d1 with ,a ,e as radius1 describe arcs cutting the sides at ,g1 ,h1 etc41 and join the points so found to complete the octagon4 ,illustration3 ,fig4 #acb4 ,,ex4 #bg4--,to inscribe an octagon in a circle1 ,fig4 #acb4 ,draw two diameters ,a ,c1 ,b ,d1 at right angles2 bisect the arcs ,a ,b1 ,b ,c1 at ,e1 ,f1 etc41 to form the octagon4 ,illustration3 ,fig4 #acc4 ,,ex4 #bh4--,to describe an octagon about a circle1 ,fig4 #acc4 ,describe a square about the given circle ,a ,b1 draw perpendiculars ,h and ,k1 to the diagonals1 touching the circle to form the octagon4 ,or1 the points ,h1 ,k1 etc41 may be found by cutting the sides from the corners1 by lines parallel to the diagonals4 ,illustration3 ,fig4 #acd4 ,,ex4 #bi4--,to describe an ellipse when the length and breadth are given1 ,fig4 #acd4 ,on the center ,c1 with ,a ,e as radius1 cut the axis ,a ,b at ,f and ,g1 the foci1 fix a couple of pins into the axis at ,f and ,g1 and loop on a thread or cord upon them equal in length to the axis ,a ,b1 so as when stretched to reach the extremity ,c of the conjugate axis1 as shown in dot-lining4 ,place a pencil or drawpoint inside the cord1 as at ,h1 and guiding the pencil in this way1 keeping the cord equally in tension1 carry the pencil round the pins ,f1 ,g1 and so describe the ellipse4 ,,note4--,the ellipse is an oval figure1 like a circle in perspective4 ,the line that divides it equally in the direction of its great length is the transverse axis1 and the line which divides the opposite way is the conjugate axis4 ,second ,method4 ,along the straight edge of a piece of stiff paper mark off a distance a c equal to ,a ,c1 half the transverse axis2 and from the same point a distance a b equal to ,c ,d1 half the conjugate axis4 ,place the slip so as to bring the point b on the line ,a ,b of the transverse axis1 and the point c on the line ,d ,e2 and set off on the drawing the position of the point a4 ,shifting the slip1 so that the point travels on the transverse axis1 and the point c on the conjugate axis1 any number of points in the curve may be found1 through which the curve may be traced4 ,see fig4 #ace4 ,illustration3 ,fig4 #ace4 ,trigonometry4 ,trigonometry is that portion of geometry which has for its object the measurement of triangles4 ,when it treats of plane triangles1 it is called ,plane ,trigonometry2 and as the engineer will continually meet in his studies of higher mathematics the terms used in plane trigonometry1 it is advantageous for him to become familiar with some of the principles and definitions relating to this branch of mathematics4 ,the circumferences of all circles contain the same number of degrees1 but the greater the radius the greater is the absolute measures of a degree4 ,the circumference of a fly wheel or the circumference of the earth have the same number of degrees2 yet the same number of degrees in each and every circumference is the measure of precisely the same angle4 ,the circumference of a circle is supposed to be divided into #cfj degrees or divisions1 and as the total angularity about the center is equal to four right angles1 each right angle contains #ij degrees1 or #ij1 and half a right angle contains #de4 ,each degree is divided into #fj minutes1 or #fj2 and for the sake of still further minuteness of measurement1 each minute is divided into #fj4 ,in a whole circle there are1 therefore1 #cfj #fj #fj #a1bif1jjj seconds4 ,the annexed diagram1 fig4 #acf1 exemplifies the relative positions of the ,sine1 ,co-sine1 ,versed ,sine1 ,tangent1 ,co-,tangent1 ,secant and ,co-secant of an angle4 ,illustration3 ,fig4 #acf4 ,these may be defined thus3 ,,definitions4 #a4 ,the ,complement of an arc is #ij minus the arc4 #b4 ,the ,supplement of an arc is #ahj minus the arc4 #c4 ,the ,sine of an angle1 or of an arc1 is a line drawn from one end of an arc1 perpendicular to a diameter drawn through the other end4 #d4 ,the ,cosine of an arc is the perpendicular distance from the center of the circle to the sine of the arc2 or1 it is the same in magnitude as the sine of the complement of the arc4 #e4 ,the ,tangent of an arc is a line touching the circle in one extremity of the arc1 and continued from thence1 to meet a line drawn through the center and the other extremity4 #f4 ,the ,cotangent of an arc is the tangent of the complement of the arc4 ,the ,co is but a contraction of the word complement4 #g4 ,the ,secant of an arc is a line drawn from the center of the circle to the extremity of the tangent4 #h4 ,the ,cosecant of an arc is the secant of the complement4 #i4 ,the ,versed ,sine of an arc is the distance from the extremity of the arc to the foot of the sine4 ,for the sake of brevity1 these technical terms are contracted thus3 for sine ,a ,b1 we write sin4 ,a ,b2 for cosine ,a ,b1 we write cos4 ,a ,b2 for tangent ,a ,b1 we write tan4 ,a ,b1 etc4 ,illustration3 ,,instruments ,,and ,,materials ,illustration3 ,fig4 #acg4 ,drawing ,materials and ,instruments4 ,drawing tools or instruments are contrived solely for mechanical drawing2 aside from this use they are perfectly worthless1 hence the quality of these special utensils is a matter of the first consideration to the earnest student4 ,there are several degrees of excellence to be found in the make-up of drawing instruments and materials2 it may be remarked with truth that 8any kind are good enough1 and the best none too good10 i4 e41 a learner in this delightful art should not stop at the lack of goodness or the low grade existing in his 8tools10 but rather do the best work possible with the means at hand4 ,however1 in order that acceptable work may be accomplished1 fairly good instruments should be procured4 ,the advice of some one experienced in the use and care of draughting tools should be sought before purchasing4 ,a drawing board1 a single sheet of paper and a pencil is the simplest 8outfit0 to be thought of2 to this small beginning may be added1 soon afterwards1 an inexpensive pair of compasses1 a ,t-square and a couple of triangles2 a vast range of work can be executed with these few tools4 ,nothing else will be needed to do fine work except1 perhaps1 one or two pairs of better compasses and a few sweeps or means of drawing irregular curves2 all these had best be purchased separately2 for in buying a 8box of instruments10 it may contain some articles which are not desired1 or that are of a wrong size1 or even duplicates of those already possessed4 ,illustration3 ,fig4 #ach4 ,an outfit recommended by the author of 8,reed's ,hand ,book0 is as follows4 ,large compasses with movable leg4 ,a pair of dividers4 ,bow pencil4 ,bow pen4 ,pencil leg for large compasses4 ,pen leg for large compasses4 ,drawing pen4 ,louis ,rouillon1 ,b4 ,s41 ,instructor of ,drawing in ,pratt ,institute1 ,new ,york1 recommends the following3 ,compasses1 #e inches1 with needle point2 pen pencil and lengthening bar4 ,drawing pen1 #d inches4 ,t-square1 #bd-;inch blade4 #de-;degree triangle1 #i inches4 #cj and #fj degree triangle1 #i inches4 #a ,scroll4 ,dixon's ,v4 ,h4 pencil4 #ab-;inch boxwood scale1 flat1 graduated inch the entire length4 ,bottle of liquid ,india ink1 four thumb-tacks1 pen and ink eraser4 #bj sheets drawing paper1 #aa #ae inches1 and a drawing-board about #af #bc inches will also be necessary2 students can usually make the board themselves for less money than it can be bought4 ,,note4--,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 time4 ,nothing can be so productive of distress to a person drawing as to have his tools getting out of order1 joints one day too tight1 next day too slack1 points getting blunt or perhaps turning up altogether2 if needle points1 then the needles slip up1 and drawing spoiled2 in fact1 the purchaser can be annoyed in numberless different ways4--,w4 ,h4 ,,thorn4 ,illustration3 ,fig4 #aci4 ,illustration3 ,fig4 #adj4 ,,the ,,drawing ,,board4 ,a drawing-board should be made of well seasoned pine of a convenient size1 say #bc #af1 which will take half a sheet of imperial paper1 leaving -inch margin all around4 ,the working surface of the board--or its front side--should be perfectly smooth1 but instead of being flat it should have a very slight camber1 or rounding1 breadthways1 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 it4 ,the four edges of the board need not form an exact rectangle1 as much valuable time is often wasted in the attempts to produce such a board2 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 angles1 or square to each other4 ,an ,english authority recommends the use of two drawing-boards1 #db inches long and #cj inches wide1 made of plain stuff1 without cleets1 #a inches thick--seasoned--with edges perfectly straight and at right angles to each other4 ,with two boards1 one may be used for sketching and drawing details and the other for the finished drawing4 ,the board should be inch in thickness1 and fitted at the back1 at right angles to its longest side1 with a couple of hardwood battens1 about #b inches wide and inch thick2 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 temperature4 ,this latter purpose1 however1 is only effected by attaching the battens to the back of the board in the following manner3 444 ,at the middle of the length of each batten--which should be one inch less than the width of the board--a stout1 well-fitted wood screw is firmly inserted into it1 and made to penetrate the board for about inch1 the head of the screw being made flush with the surface of the batten2 on either side of the central screw1 two others1 about #c inches apart1 are passed through oblong holes in the battens1 and screwed into the body of the board until their heads are flush with the central one2 fitted in this way the board itself can expand or contract lengthwise or crosswise1 while its surface is prevented from warping or bending4 ,illustration3 ,fig4 #ada4 ,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 strip2 this is cut or sawn apart at about every inch to admit of contraction2 this strip serves as a guide to the stock of the drawing square1 allowing an easy sliding movement4 ,to produce really good work in the shape of a mechanical drawing1 one perfect straight edge only is required on a drawing board1 and that the left one1 which is always known as the working-edge2 but for the convenience of being able to draw a long line across the board at right angles to its lower edge1 this edge is made truly square with that on the left side of the board4 ,the details for building these drawing boards are given1 because they are easy to be made by one who understands the use of a few wood-working tools2 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 them4 ,fig4 #ada represents the board which has been described in the text1 with provisions for the contraction and expansion2 the very dark lines are intended to represent the ebony insertions--as described4 ,fig4 #adj represents a plain pine board with dovetailed battens4 ,illustration3 ,fig4 #adb4 ,fig4 #adb represents the common means used to attach or secure slightly or temporarily the drawing paper to the drawing board2 these are called thumb-tacks1 and are usually forced through the paper into the wood by the hand1 whence they are easily detached4 ,these are made to have as slight a projection as may be1 so as not to interfere with the free movement of the tee-square4 ,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 it2 this is effected by various kinds of drawing pins or thumb-tacks4 ,the best kind for this purpose have a head as thin as possible without cutting at its edges1 slightly concave on the under side next the paper1 and only so much convex on its upper side as will give it sufficient thickness to enable the pin to be secured to it2 better use four or more small pins along the edge of a sheet of paper1 than use one clumsy1 badly made pin at each end4 ,illustration3 ,fig4 #adc4 ,illustration3 ,fig4 #add4 ,fig4 #adc and fig4 #add represent a pair of plain trestles or horses in common use for supporting large size drawing boards4 ,this pattern is found frequently in the laying-out shop4 ,fig4 #ade and fig4 #adf represent adjustable horses or trestles--these are designed1 primarily1 for office use4 ,as will be seen by viewing the illustration1 the upper part is supported by two hard-wood sliding pieces2 these are provided with strong pins and numerous holes1 and pass through the frame of the trestle1 as shown1 so that the upper portions can be arranged at any angle convenient to the draughtsman1 as he lies over his work or stands by it4 ,illustration3 ,fig4 #ade4 ,illustration3 ,fig4 #adf4 ,fig4 #acg is introduced to exhibit the paper attached to the drawing board with the thumb-tacks1 and with the ,t-square and set-squares arranged to commence work2 the paper should not extend to the edges of the board2 three1 four or more tacks may be used on each edge of the sheet of paper1 instead of two1 as shown in illustration4 ,illustration3 ,fig4 #adg4 ,a most convenient--and except for its extreme lightness1 which is not good in a drawing stand--a most admirable device is shown in fig4 #ach4 ,the drawing table is simply a drawing board with folding legs2 these are made from hard-wood1 while the top is made of soft1 seasoned pine1 with square corners2 while the device is strong and well braced1 it can be folded and easily carried about--all as shown in the illustration4 ,illustration3 ,fig4 #adh4 ,,the ,,tee-,,square4 ,this is an instrument in the form of a letter ,t1 as shown in the figures #adi and #aej2 the two parts are known as stock and blade2 the horizontal part of the letter 7,t7 is the stock1 and the vertical part the blade--hence the name1 ,t-square2 to form the square1 the two parts are joined together in such a way as to make them exactly at right angles to each other2 the stock1 which is applied to the working edge of the drawing board1 being about one-third the length of the blade1 and about three times its thickness4 ,illustration3 ,figs4 #adi and #aej4 ,to be perfect in construction1 a tee-square should be as light as is consistent with its necessary strength and stiffness of parts2 it should be made of suitable material easily manufactured1 put together1 and repaired1 and withal as truly correct as is possible to be made4 ,such a square is represented in fig4 #adh2 it has a taper blade1 which is generally about double the width where secured to the stock as it is at the end4 ,illustration3 ,figs4 #aea and #aeb4 ,the manner in which the stock is united to the blade determines its adaptability or otherwise to the use made of it2 in some the stock is rectangular in section1 and the blade mortised into it2 in others the blade is dovetailed and let into the stock for the whole of its thickness4 ,,adjustable ,,bladed ,,square4 ,in cases where many parallel lines have to be drawn1 of lengths beyond the capabilities of ordinary set-squares1 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 adjustable bladed tee-square1 or one whose blade can be set at any desired angle4 ,the blade of such a square should be tapered as in illustration1 but shaped at its wide end as shown1 and having a stock wide enough to allow for the surface required in the washers of the fittings necessary to make the blade adjustable4 ,these fittings1 though requiring to be well made and neatly finished1 are not expensive or difficult to make1 as they consist merely of two washers1 a square-necked bolt1 and a fly nut4 ,the tee-square1 as shown1 has four parts3 #a1 blade2 #b1 fixed head2 #c1 shifting head2 #d1 swivel4 ,the head is held firmly by the left hand to the left edge of the drawing board1 and the blade serves as a straight-edge for horizontal lines that may extend the whole length of the paper4 ,it can be used for either horizontal1 or1 by reversing to the bottom of the board1 for vertical lines2 and1 by turning it over1 so that the shifting head is against the edge of the drawing board instead of the fixed head1 lines at different angles may be drawn4 ,the length of the blade should be the length of the drawing board2 if it is shorter1 inconvenience will be experienced when lines the whole length of the board are wanted4 ,,triangles1 ,,or ,,set-,,squares4 ,set-squares are invariably used in connection with the tee-square1 as shown in fig4 #adh4 ,the illustrations below show several patterns of the device2 by these1 vertical lines1 triangles1 squares and hexagonal1 octagonal and twelve-sided figures1 diagonal section lines1 etc41 can be easily drawn4 ,for ordinary purposes1 a triangle or set-square with angles of #de may be #d inches long and the other #h inches in length1 but a six-inch set-square having angles #ij1 #de and #de1 and an eight-inch one having angles of #ij1 #fj and #cj1 will be found sufficient for all purposes2 there are other triangles used specially for making letters4 ,illustration3 ,fig4 #aec4--;,fig4 #aed4--;,fig4 #aee4--;,fig4 #aef4 ,in practice the triangles or set-squares are slid along the edge of the blade1 and need not be any thicker than it4 ,,parallel ,,rule4 ,illustration3 ,fig4 #aeg4 ,this instrument is used to mark lines which are neither horizontal nor vertical 7usually these are drawn by the square and set-square71 and which are parallel to one another2 by adjusting the edge of the parallel ruler to a line1 it can be extended or opened out 7or vice-versa closed71 and the line or lines drawn will be parallel or equally distant from the base or first line it was set by4 ,see fig4 #aeg4 ,fig4 #aeh is a parallel ruler1 constructed with two rollers fixed on a rod so that they move the same distance1 carrying the ruler parallel to the starting line4 ,illustration3 ,fig4 #aeh4 ,,note4--,it has been said that 8a workman may be known by his tools10 but the statement must be taken with a good deal of allowance4 ,some workmen may possess a very fine set of tools and never use them1 because they have not the ability or inclination to learn how2 especially is this the case with drawing instruments4 ,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 drawing2 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 materials1 he is capable of showing good qualifications in other lines1 and the more skilled he is in one the easier can he acquire skillfulness in another1 if he applies the same amount of energy1 thought and interest as he did to acquire skill in the first4 ,,section ,,liner4 ,fig4 #aei shows an improved section liner which can be adjusted to any angle1 and will space the parallel lines at any desired regular distance4 ,illustration3 ,fig4 #aei4 ,,irregular ,,curve ,,or ,,scroll4 ,irregular curves1 or1 as they are sometimes termed1 sweeps1 represented by figs4 #afj-aff1 are used for curves that cannot be put in by the other instruments4 ,they are very useful when elliptical or parabolic curves are desired1 in preference to circles or arcs of a circle4 ,they are much used in design and architectural drawing4 ,they are made of thin hardwood or rubber1 and sometimes of horn4 ,illustration3 ,figs4 #afj-aff4 ,illustration3 ,fig4 #afg4 ,illustration3 ,fig4 #afh4 ,curves are irregular lines2 a circle is a regular line4 ,if a curve is to be passed through a number of predetermined points it should be first sketched in lightly1 free-hand2 a section of the scroll is then applied to the curve so as to embrace as many points as possible2 only the central points of those thus embraced should be inked in2 this process is continued until the desired curve is completed4 ,curves are made of various material1 pearwood1 cardboard1 xylonite1 hard rubber1 and a strip of soft lead is sometimes used1 which may be easily adjusted to the curve required4 ,the curves generally used in mechanical drawing are shown on previous page4 ,fig4 #bjh1 page #acd1 is a logarithmic spiral curve4 ,it is mathematically constructed and contains every curve within the limit of its size4 ,,ellipses4 ,an ellipse is a geometrical figure1 and can be drawn as described in geometrical problem #bi1 page #if2 many drawing offices keep sets of hard rubber ellipses1 to economize time constructing them4 ,illustration3 ,fig4 #afi4 ,illustration3 ,fig4 #agj4 ,,drawing ,,pencils4 ,these are instruments for marking1 drawing or writing1 formed of graphite1 colored chalk or materials of similar properties1 and having a tapering end1 inclosed1 generally1 in a cylinder of softwood4 ,fig4 #afg represents a ruling pencil2 its point is a parallelogram or of a wedge shape4 ,in ruling1 the length view rests against the square2 its shape gives considerable strength to the lead and allows the making of a very fine line4 ,fig4 #afh differs in the point of the pencil shown1 as may be observed in the illustration4 ,a pencil that is hard is best for mechanical drawing2 one that will retain a good point for some considerable time4 ,pencil lines should be made as light as possible2 the presence of lead on the surface of the paper tends to prevent the ink passing to the paper1 and in rubbing out pencil lines the ink is reduced in blackness1 and the surface of paper is roughened1 which is a disadvantage4 ,as little erasing or rubbing out as possible should be done4 ,,dividers ,,and ,,compasses4 ,these instruments1 while they appear alike1 have a separate use3 the dividers are used to space off distances and dimensions2 especially are they necessary in reading drawings made to scale4 ,compasses are used for describing circles1 curves1 etc41 dividers are used for marking out spaces4 ,two forms of the dividers are shown in figs4 #afi and #agj2 the simplest1 plainest form is shown in fig4 #afi2 these are used for rough spacings2 fig4 #agj represents a pair of dividers fitted with an adjustable screw controlled by a steel spring in one leg2 by this a very exact measurement can be made4 ,fig4 #agj is intended to exhibit what is called a 8hair-spring divider40 ,,proportional ,,dividers4 ,these dividers differ from the ordinary ones shown in figs4 #afi and #agj in that they are provided with four steel points1 one pair of which being set to the full dimension will be reproduced by the other pair1 but in a smaller1 or reduced size4 ,fig4 #aga are 8bisecting0 dividers1 being proportional dividers1 which1 when open1 one end measures double the distance of the other4 ,fig4 #agb are proportional dividers2 the points at one end are capable of being changed1 to measure practically any desired proportion at the other end1 by altering the position of the pivot where the legs cross one another4 ,the lower connecting link is a micrometer adjustment1 for minute measurements4 ,fig4 #agc are proportional dividers which are marked for the proportions of lines and radii of circles1 being provided with a rack movement for adjustment4 ,fig4 #agd represents three-leg dividers1 used for taking the position of three points2 this instrument is very useful in finding the position of a point in a figure4 ,illustration3 ,fig4 #aga4--;,fig4 #agb4--;,fig4 #agc4--;,fig4 #agd4 ,illustration3 ,fig4 #age4--;,fig4 #agf4--;,fig4 #agg4--;,fig4 #agh4--;,fig4 #agi4 ,,compasses4 ,compasses consist of two pointed legs2 they are instruments for describing circles or for--sometimes--measuring figures1 in absence of dividers4 ,fig4 #age represents compasses fitted as dividers4 ,compasses should have jointed legs1 which will allow the points to be placed at right angles to the paper1 whatever the size of the circle to be drawn4 ,compasses should not be used for circles which are too large to allow the points to be thus placed2 a lengthening bar is generally provided1 which greatly increases the diameters of circles which may be drawn by this attachment2 it is shown in fig4 #agf4 ,one leg of the compasses is usually provided with a socket to which are fitted three points3 a divider point1 fig4 #agi2 a pencil point1 fig4 #agg2 and a point1 fig4 #agh1 carrying a special pen for the inking of circles4 ,each of these points is generally provided with a joint1 so that it may be placed at right angles to the paper4 ,the other leg should be jointed2 it is often provided with a socket which receives two points1 one a divider point1 and the other carrying a needle point4 ,such an instrument may be used as dividers for spacing1 or as compasses for penciling or inking circles4 ,the joint at the head of the compasses 7see fig4 #age7 is the most important feature4 ,it should hold the legs firmly in any position1 so that in going over a circle several times only one line will result4 ,it should allow the legs to move smoothly and evenly1 and should be capable of adjustment4 ,illustration3 ,fig4 #ahj4--;,fig4 #aha4--;,fig4 #ahb4--;,fig4 #ahc4--;,fig4 #ahd4 ,as shown in fig4 #agd1 one leg has a hinge or joint1 and a needle point1 which can be regulated by a thumb screw2 the other leg has a socket or recess into which interchangeable parts can be inserted4 ,the four figures to the right of the compasses show the parts which are provided with shanks or insertion pieces4 ,fig4 #ahj and fig4 #aha represent compasses specially used for making small circles1 and work too minute for the larger instruments described above4 ,to do work of this nature easily a pair of spring dividers are frequently used4 ,this instrument has one point attached to a spring1 which is regulated by a screw1 so that very slight changes in the space may be made with ease4 ,compasses specially used for putting in fine circles and dimensions are called 8bows40 ,when a pen point it is a 8bow pen10 with a pencil point a 8bow pencil10 and if with needle point a 8bow dividers40 ,fig4 #ahj is a 8bow dividers01 this fitted with screw for fine adjustment in one leg1 fig4 #aha1 is called a 8hair-spring bow dividers02 for small details1 bows with steel spring legs without any joint are used2 these are called 8steel-spring bows40 ,illustration3 ,fig4 #ahe4--;,fig4 #ahf4--;,fig4 #ahg4 ,,spring ,,bows4 ,these were originally developed from the common form of compasses1 with a single spring leg2 later1 the demand for smaller sizes made changes necessary1 and spring bows are now made symmetrical1 both sides of the bow being made to 8spring40 ,fig4 #ahb are spring dividers4 ,fig4 #ahc is a spring pencil4 ,fig4 #ahd is a spring pen4 ,in these figures it will be seen that the two threads1 a right and a left1 are moved with one central thumbscrew2 in the figs4 #ahe to #ahg a single screw is used4 ,in choosing spring bows1 care must be exercised to select a sufficiently strong1 stiff spring1 as the relation between spring pressure and thumbscrew is important4 ,,beam ,,compasses ,,and ,,trammels4 ,in fig4 #ahh is shown a set of beam compasses1 together with a portion of the wooden rod or beam on which they are used4 ,illustration3 ,fig4 #ahh4 ,the latter1 as will be seen by the section drawn to one side1 ,a1 is in the shape of a ,t4 ,this form has considerable strength and rigidity4 ,beam compasses are provided with extra points for pencil or ink work1 as shown4 ,while the general adjustment is effected by means of the clamp against the wood1 minute variations are made by the screw1 ,b1 shifting one of the points1 as shown in the figure4 ,this instrument is quite delicate1 and1 when in good order1 is very accurate4 ,it should be used only for fine work on paper1 and never for scribing on metal4 ,illustration3 ,fig4 #ahi4 ,a coarser instrument1 and one especially designed for use upon metal1 is shown in fig4 #ahi1 and is called a trammel4 ,there are various forms of this instrument1 all being the same in principle4 ,the engraving shows a form in common use4 ,a heavier stick is used with it than with the beam compasses1 and no other adjustment is provided than that which is afforded by clamping against the stick4 ,in the illustration1 a carrier at the side is shown1 in which a pencil may be placed4 ,some trammels are arranged in such a manner1 that either of the points may be detached and a pencil substituted4 ,a trammel1 by careful arrangement1 can be made to describe very accurate curves1 and hence can be used in place of the beam compasses in many instances4 ,for all coarse work it is to be preferred to beam compasses4 ,it is useful for all short sweeps upon sheets of metal1 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 tool4 ,the length of rods for both beam compasses and tramels1 up to certain limits1 is determined by the nature of the work to be done4 ,the extreme length is determined by the strength and rigidity of the rod itself4 ,it is usually convenient to have two rods for each instrument1 one about #a or #b feet in length and the other considerably longer--as long as the strength of the material will admit4 ,,drawing ,,scales4 ,scales are proportioned rules or mathematical instruments of wood1 metal1 etc41 on which are marked lines and figures for the purpose of measuring sizes and distances4 ,it is usual to make scales in the proportion of parts of an inch equalling a foot2 the most generally adopted scale for machine drawing is one and a half inches1 equalling one foot2 that is1 twelve-eighths of an inch 7each eighth of an inch representing one inch72 there is no fixed rule in the choice of a scale1 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 utilized4 ,when objects are of moderate proportions they may be represented full size2 but when large1 the drawings must be smaller4 ,standard scales for mechanical drawings are 1 1 and full size4 ,these scales are often written #f #a ft42 #c #a ft42 #a #a ft41 and #a ft4 ,illustration3 ,fig4 #aij4 ,illustration3 ,fig4 #aia4 ,instead of selecting one of the scales named or one found upon the ordinary scales used by draughtsmen1 drawings may be made to any scale whatever4 ,thus1 if any object is to be represented in a certain space1 a scale should be constructed which will cause the whole of the object to be shown4 ,drawing to ,scale4--,the meaning of this is1 that the drawing when done bears a definite proportion to the full size of the particular part1 or1 in other words1 is precisely the same as it would appear if viewed through a diminishing glass4 ,the two-foot rule shown in fig4 #aib is the most useful instrument for the comparison of linear dimensions--it can be used as a scale of one-twelfth1 or #a inch equal to a foot1 #ab inches #ab feet1 it being divided into portions or spaces1 each of which is subdivided into halves1 quarters1 eighths and sixteenths2 frequently in the latter class of two-foot rules there are graduations of scales1 and it is then also called a draughting scale4 ,fig4 #aij represents a flat scale1 graded so that one inch represents a foot--th size--etc41 as shown4 ,fig4 #aia represents a triangular scale 7broken74 ,the triangular scale should read on its different edges as follows3 ,three inches and #a to one foot1 #a and to one foot1 and to one foot1 and to one foot1 and to one foot1 and one edge read sixteenths the whole #ab of its length4 ,fig4 #aij shows such a scale broken4 ,an explanation of the #a and side will suffice for all4 ,where it is used as a scale of #a to one foot1 each large space1 as from #j to #ab or #j to #a1 represents a foot1 and is a foot at that scale4 ,there being #ab in one foot1 the twelve long divisions at the left represent inches2 each inch is divided into two equal parts1 so from #j to one division at the left of #i is #i and so on4 ,the #a and scales being at opposite ends of the same edge1 it is obvious that one foot on the #a scale is equal to two feet on the scale1 and conversely1 one foot on the scale is equal to six inches on the #a scale2 and #a being equal to one foot1 the total feet in length of scale will be #ab2 at to #a foot the total feet will be #bd4 ,in working to regular scales1 such as 1 1 or size1 a good plan is to use a common rule1 instead of a graduated scale4 ,there is nothing more convenient for a mechanical draughtsman than to be able to readily resolve dimensions into various scales1 and the use of a common rule for fractional scales trains the mind1 so that computations come naturally1 and after a time almost without effort4 ,the protractor shown in fig4 #aic is an instrument for laying down and measuring angles on paper2 it is used in connecting with a scale to define the inclination of one line to another4 ,protractors have the degrees of a half circle marked upon them2 as the whole circle contains #cfj degrees1 half of it will contain #ahj1 one-quarter #ij1 etc4 ,hence1 protractors showing #ahj exhibit all that is needed4 ,to protract means to extend1 so this instrument is also useful in 8extending0 the lines of inclination at the circle4 ,illustration3 ,fig4 #aib4 ,illustration3 ,fig4 #aic4 ,,drawing-,,pens4 ,a special pen called a drawing-pen1 and also special ink1 are required to ink a drawing2 figs4 #aid and #aie represent two sizes of drawing-pens--one being best adapted for fine work1 and the other for coarse or heavy line work4 ,the points1 as will be observed in the illustration1 are made of two steel blades which open and close as required for thickness of lines by a regulating screw4 ,illustration3 ,fig4 #aid4 ,illustration3 ,fig4 #aie4 ,a good drawing pen should be made of properly tempered steel1 neither too soft nor hardened to brittleness4 ,the nibs should be accurately set1 both of the same length1 and both equally firm when in contact with the drawing paper4 ,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 lines1 but otherwise as broad and rounded as possible1 in order to hold a convenient quantity of ink without dropping it4 ,the lower 7under7 blade should be sufficiently firm to prevent the closing of the blades of the pen1 when using the pen against a straightedge4 ,illustration3 ,fig4 #aif4 ,illustration3 ,fig4 #aig4 ,the spring of the pen1 which separates the two blades1 should be strong enough to hold the upper blade in its position1 but not so strong that it would interfere with easy adjustment by the thumbscrew4 ,the thread of the thumbscrew must be deeply and evenly cut so as not to strip4 ,an important requisite after the pencil lines have been put in is ink1 with which to line the drawing4 ,this should be of the best that can be procured4 ,the pen is filled by dropping the ink between the blades1 or nibs1 while held in a nearly vertical position1 as shown in fig4 #aif4 ,liquid ,india ink can be procured in bottles with glass tube feeders1 which are very good1 and keep the hands and fingers free of the ink4 ,fig4 #aig is a sectional view of such a bottle and 8filler10 or feeder4 ,this generally answers all requirements1 but the dry ink of good quality1 in sticks or bars1 cannot be surpassed1 although it requires skill for its preparation4 ,fig4 #aih represents a sloping dish or 8tile0 for mixing1 which should be done with little pressure1 in clean1 filtered or distilled water1 care being taken to keep the liquid free of dust1 which obstructs the free flow of the ink in the pens4 ,illustration3 ,fig4 #aih4 ,the bars of ,india ink are shown1 as they are imported1 in figs4 #aii to #bjb4 ,pure ,india or ,china ink is only made in those countries1 because the special wood from which it is prepared is found only in those regions4 ,so-called ,india inks1 made of lampblack and animal glue1 are only imitations2 therefore ,india ink should be purchased from a reliable importing house--shape is little guarantee of quality4 ,illustration3 ,fig4 #aii4--;,fig4 #bjj4--;,fig4 #bja4--;,fig4 #bjb4 ,illustration3 ,fig4 #bjc4 ,soft gray vulcanized rubber 7fig4 #bjc7 should be used for cleaning drawing paper2 for erasing any portion of a line in pencil1 a piece of prepared white vulcanized rubber is the best1 small in size and of rectangular shape 7see fig4 #bje74 ,illustration3 ,fig4 #bjd4 ,illustration3 ,fig4 #bje4 ,illustration3 ,fig4 #bjf4 ,illustration3 ,fig4 #bjg4 ,an ink eraser is made of a composition of rubber and ground glass1 and it should be used as sparingly as possible on drawings1 as it roughens the paper and removes the gloss from its surface 7see fig4 #bjd74 ,steel ink erasers are useful in removing defects1 overrun lines1 joint of lines if swollen1 etc42 they have a fine point and can be used to advantage with a little practice2 they are used with a scratching1 not a cutting1 motion 7see figs4 #bjf1 #bjg74 ,,drawing ,,paper4 ,the first thing to be considered in selecting drawing paper is the kind most suitable for the proposed plan4 ,paper may be purchased in sheets #bb #cj inches1 that make four exercise sheets #aa #ae inches2 this may be of several grades and tints4 ,the qualities that constitute good paper are strength1 uniformity of thickness and surface1 neither repelling nor absorbing liquids1 admitting of considerable erasing without destroying the surface1 not becoming brittle nor discolored by reasonable exposure or age1 and not buckling when stretched1 or when ink or color is applied4 ,the sizes and names of paper made in sheets is as follows3 ,cap #acag ins4 ,demy #aebj ,medium #agbb ,royal #aibd ,super ,royal #aibg ,imperial #bbcj ,atlas #bfcd ,double ,elephant #bgdj ,antiquarian #cjec ,for large drawings paper is made in rolls4 8,detail paper0 is especially made for marking out new designs2 it is made in rolls #cf1 #db and #ed inches wide2 it has excellent erasing qualities and takes ink and color with facility4 ,when working by artificial light it is desirable that the paper be of a light-brown color1 which is less trying to the eyes than a pure white4 ,if it is a shop drawing or sketch not to be preserved1 use detail paper1 which is the most economical and will stand a great deal of handling without becoming soiled4 ,if it is a detailed plan1 finished drawing or a picture1 use the best white drawing paper to be obtained1 so that your drawings can be preserved indefinitely without danger of fading1 which is due either to the paper being poorly made and discoloring with age1 or being of poor fiber and absorbing the ink or color1 and the drawing consequently losing its brightness4 ,after deciding on the size of paper most suitable for the work1 then carefully select the paper embracing the most qualities of value for the proposed drawing4 ,illustration3 ,fig4 #bjh4 ,illustration3 ,,mechanical ,,drawing ,illustration3 ,fig4 #bji4 ,mechanical ,drawing4 ,in distinction to 8free-hand10 mechanical drawing is executed almost entirely by the use of the instruments previously described2 hence its other term1 instrumental drawing4 ,to define it particularly it may be said that1-- ,mechanical drawing is the correct reproduction of any figure or part of a machine1 whether of full size or reduced in the proportion of one part to another2 it also comprises the art of delineating the interior parts which are hidden from view in solid bodies4 ,a mechanical drawing is the vehicle for conveying the ideas of the designer to those who are to embody them in wood and metal1 and the considerations which should govern its production are those which affect its clearness and legibility or those which facilitate reference to it4 ,drawings consist of plans1 elevations and sections2 plans being views on the top of the object in a horizontal plane2 elevations1 views on the sides of the object in vertical planes2 and sections1 views taken on bisecting planes1 at any angle through an object4 ,drawings in true elevation or in section are based upon flat planes1 and given dimensions parallel to the planes in which the views are taken4 ,two elevations taken at right angles to each other fix all points1 and give all dimensions of parts that have their axis parallel to the planes on which the views are taken2 but when a machine is complex1 or when several parts lie in the same plane1 three and sometimes four views are required to display all the parts in a comprehensive manner4 ,a man must have either a natural talent for hand-drawing or years of experience1 before he can produce a sketch and 8dimension0 it1 fit to work from2 hence the elementary character of the examples given for practice4 ,a 8pretty0 drawing is not expected from a beginner2 it should always be borne in mind1 that correctness of dimensions and general clearness1 rather than elaborate finish1 are what will save the battle in the days of competition4 ,mechanical drawings should be made with reference to all the processes that are required in the construction of the work1 and the drawings should be responsible1 not only for dimensions1 but for adaptation to fitting1 forging1 pattern-making1 moulding1 and so on4 ,every part laid down should have something to govern it that may be termed a 8base0--some position which1 if understood1 will suggest size1 shape and relation to other parts4 ,searching after a base for each and every part and detail1 the draughtsman should proceed upon a regular system1 continually maintaining a test of what is done4 ,a mechanical drawing consists chiefly of three views3 #a4 ,the plan or top view4 #b4 ,the side elevation4 #c4 ,the end elevation4 ,in addition to the above1 drawings are used to show interior portions of the figure2 these are termed 8sections10 and they may be taken where any plane crosses another4 ,,note4--,the word elevation1 as applied to mechanical drawings1 means simply a view2 hence a side elevation is a side view1 or an end elevation is an end view4 ,the word plan is employed in place of the word top2 hence a plan view is a top view or a view looking down upon the top of the piece4 ,a general view means a view showing the machine put together or assembled1 while a detail drawing is one containing a detail1 as a part of the machine or a single piece disconnected from the other parts of the whole machine4 ,penciling4 ,illustration3 ,fig4 #baa4 ,it is very nearly true1 as has been said1 that every mechanical drawing is1 in the first instance1 penciled2 if this is so1 then more work is done with the pencil than with the pen2 therefore the first attention of the student of mechanical drawing should be directed to the following instructions for penciling a drawing4 ,with all necessary materials in hand1 and in good order for the beginning of a drawing1 the first thing to do is to pin the paper on the board quite square4 ,to do this effectively1 lay the paper flat and put on the ,t-square with its head at the left side of the board2 slide the square up nearly to the top1 and arrange the paper level with the blade2 with the right hand hold the paper still and move the square down a little2 now1 pin the top of the paper with thumb-tacks4 ,next1 pressing the square lightly to the paper1 slide it down to the bottom and pin that part of the paper to the board4 ,the paper must not project outside or over the edges of the board1 and the pins or tack-heads should be forced down flush with the paper1 so as not to interfere with the free movement of the tee-square up and down the board as occasion may require4 ,the accuracy of the work depending upon their condition1 it is first needful to see that the pencil and pencil compasses are properly sharpened4 ,reference is made to valuable directions contained on pages beginning with #ee1 under the heading of 8,free-hand ,drawing10 to which may be added that-- ,all lines should be drawn with the pencil slightly inclined in the direction in which it is moved4 ,any and all lines not needed in the finished drawing should be erased at one time after the final lines have been determined1 for the surface of the paper is soiled very quickly when worked upon after erasures have been made4 ,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 strengthened1 in order that the final lines may be left in perfect condition4 ,to show where the lines meet or terminate it is needful that all pencil lines pass the actual ending place1 making a distinct intersection4 ,this does not apply to 8inking in0 the lines1 but rather to prevent the over-drawing of the ink lines1 because the edge of the rule and the pen itself obstruct or partly cover the view of the line1 it is very liable to pass over or beyond the required point in inking the lines1 which must not occur4 ,in the preliminary operation of producing a regular mechanical or instrumental drawing1 it is necessary to make a 8sketch10 in pencil1 of the object to be represented4 ,the ,,american ,,machinist has given in a few words the order to be followed1 in effecting the best results2 we quote1 as follows3 8,in making a free-hand sketch of an object from the model it is well to observe the following order3 ,look the model over carefully and determine the number of views necessary to illustrate it fully1 drawing the same1 free-hand1 in their proper relation to each other1 on sketching paper4 ,look the sketch over carefully to see that nothing has been omitted1 and put on dimension lines1 after which scale the model carefully and put on dimensions4 ,do not put in the dimensions at the same time the dimension lines are drawn2 have all the dimension lines in place before attempting to insert dimensions4 8,follow the same order in making the drawing with instruments as was used in making the sketch2 that is1 draw the views in their proper relation to each other1 put in dimension lines1 then dimensions1 and lastly notes and title4 ,if section drawing is made1 do not draw section lines in pencil40 ,,points ,,to ,,be ,,observed ,,in ,,sketching4 #a4 ,especial attention is to be paid to outlines--edges of plane surfaces are lines2 when a line is made it represents the edge or outside of something4 #b4 ,learn to be accurate before being rapid4 #c4 ,a sketch should be intelligible to any one1 even if they are unacquainted with drawing4 #d4 ,horizontal and vertical lines and a few curves will enable one to make almost any simple sketch4 #e4 ,it must be also remembered in making drawings from actual measurement that the instruments are not in the first place employed2 the rough sketch is first made and then it is converted into a drawing4 ,the draughtsman makes a rough sketch entirely by the hand and eye1 measures the various parts1 and jots down the measurements in his sketch2 after this he reduces the whole to the desired scale1 and proceeds to make his mechanical drawing4 #f4 ,let the sketch book be the constant companion of the student2 it may be advantageously filled with outlines of machine or other work suitable for preservation1 to be made into finished drawings1 or for reference4 ,sketches are often valuable for reference as aids in originating new designs4 #g4 ,a sketch1 when possible1 should have all the dimensions written upon it1 but-- #h4 ,sketches in shop practice should not take the place of working-drawings2 the latter have a check upon them in being drawn to a scale--hence the figures written upon them and dimensions by scale must agree4 #i4 ,place title and date on each sketch--no matter how seemingly unimportant--for future reference4 #aj4 ,practice sketching at every favorable opportunity4 ,there is no necessity for detail at first--simply the outlines of the article and its parts4 #aa4 ,sketch-books1 with paper bound in cloth covers1 are utilized for bold1 off-hand sketches by experienced draughtsmen1 but a single sheet of paper1 used on both sides1 is not unworthy of service in an emergency--or even the blank side of a letter may be available4 ,sketching-blocks1 or paper 8pads10 #d #f1 or more1 in size1 and containing #dh sheets1 are sold by stationers1 and are found to be most convenient to have in hand and for practical use4 ,portfolio-envelopes1 made of extra length paper 7manila7 are useful in filing away sketches and drawings4 ,the size #aj #ae is used for ,united ,states ,patent ,office drawings4 ,the function of the pencil--in mechanical drawing--is to make a path for the pen to follow4 ,if it were possible to make a drawing with all its lines ending at the proper place1 at the first time1 there would be no necessity for using the pencil4 ,one is obliged1 however1 so to use the pencil that all lines pass beyond the actual ending place1 thus making a distinct point for the drawing pen to stop at4 ,the pencil should be pressed to the paper just enough to make a clean1 fine line1 and no more2 once over the path is sufficient1 if the line is visible and true4 ,to sharpen drawing pencils1 #a1 use a fine file1 after taking off enough of the wood with a knife2 #b1 make a conical point for the free-hand drawing pencils and a chisel point for ruling and marking distances4 ,pencil compasses are instruments where one leg is provided with a pencil point4 ,fig4 #bji shows the mode of manipulation of those shown in fig4 #ahj and fig4 #aha4 ,the pencil compass is held by the projection above the joint between the thumb and first finger1 which enables it to be rotated by a movement of the finger without causing any undue pressure on the points4 ,should much pressure be applied1 there is a tendency to force the point or center through the paper1 making an ugly center mark2 at the same time the pressure tends to break off the pencil point4 ,these few illustrations from fig4 #bab to fig4 #bai are made designedly simple1 so that they may be utilized in 8free-hand0 work1 for which they are good practice1 as well as serving for examples in mechanical drawing4 ,illustration3 ,figs4 #bab4 ,figs4 #bab1 showing a spool or bobbin1 exhibit three views1 viz43 front elevation or plan1 and section2 both are drawn with simple lines1 the end elevation by circles4 ,illustration3 ,fig4 #bac4--;,fig4 #bad4 ,figs4 #bac and #bad are two side views of a hexagon head bolt4 ,figs4 #baf and #bag are a square head bolt--two side views and end view4 ,figs4 #bah and #bai are a front and edge view of a forked or double joint4 ,illustration3 ,figs4 #bae4 ,figs4 #bae show three views of a file handle2 the front view and section are practice for compound curves and curved lines meeting straight ones2 all these are capable of being produced by instruments4 ,moreover1 many of the views and illustrations used to instruct and explain machine tools and other devices in other parts of the volume1 are drawn so that they may be used also as examples in advanced instrumental practice4 ,this is a 8hint0 to the diligent and painstaking student worthy of remembering4 ,illustration3 ,fig4 #baf4--;,fig4 #bag4--;,fig4 #bah4--;,fig4 #bai4 ,the designing and drawing of arcs and whole circles occupy a large proportion of space in nearly all mechanical drawings4 ,the making of a complete circle is a matter of no great difficulty1 but the beginning and termination of parts of circles require both judgment and considerable practice4 ,to aid the student these two illustrations of circles are introduced4 ,to draw fig4 #bbj with a pencil1 using the upper edge of the blade of the ,t-square as a guide1 draw a center line1 ,a ,b1 mark on it a distance of #d inches1 space this into half inches1 using the dividers and making the points with it2 then with the pencil compasses or bow pencil1 which must be held as shown on page #bji1 and rotated from left to right1 or clockwise1 draw a series of circles through these points1 tangent to one another or all touching at ,a1 care being taken that the pencil lines exactly meet at ,a1 and also cut the divided points as shown in the illustration4 ,for fig4 #bba divide the center line as before1 and draw the semi-circles on it ,a ,b1 ,b ,c1 meeting at ,b1 and ,c ,d1 ,d ,e1 etc4 ,illustration3 ,fig4 #bbj4 ,illustration3 ,fig4 #bba4 ,now from center ,b draw circles ,a ,c1 ,c ,e1 meeting in ,c1 and so on with the circles1 arcs or segments2 success in drawing this figure depends on the correct spacing of the center line in the first instance into equal parts4 ,the ,t-square should be used for drawing horizontal lines only4 ,its head should always be placed upon the left edge of the board4 ,vertical lines should be drawn by the use of a triangle placed upon the ,t-square and not by means of the ,t-square only2 because the edges of a board are seldom at right angles to each other1 and the blade of the ,t-square is often not at right angles to the head1 so that lines at right angles to each other will not result from the use of the ,t-square upon all edges of the board4 ,only the upper edge of the ,t-square should be used1 as the edges are often not quite straight or parallel4 ,the #de triangle has two angles of #de and one of #ij4 ,the #cj and #fj triangle has an angle of #cj1 one of #fj1 and one of #ij4 ,by placing these triangles upon the ,t-square1 lines at any of these angles with a vertical or horizontal line may be drawn4 ,drawings finished in ink are much more effective and desirable than pencil drawings2 but as a good inked drawing cannot be made except upon an accurate pencil drawing1 students should begin with the pencil1 and should not use ink until they are able to produce satisfactory results in pencil4 ,projection4 ,the word projection means to throw forward1 and in ordinary machine drawing it is the projecting or throwing forward of one view from another view4 ,in drawings the lines in one view or plan may be availed of to find those of others of the same object1 and also to find their shape or curvature as they would appear in the other representations2 this is called projection-drawing4 ,fig4 #bbb is the illustration as shown in fig4 #bab on page #adc1 with the addition of dotted projection line1 which illustrates the method of throwing forward the section and the end view of the object2 these two views are procured from the plan or first figure1 as shown in fig4 #bbb4 ,fig4 #bbd represents the square bolt and nut shown in fig4 #baf1 and the mode of projecting is similarly shown by dotted lines4 ,fig4 #bbc shows file handle shown in fig4 #bae and the mode of projecting4 ,illustration3 ,fig4 #bbb4 ,illustration3 ,fig4 #bbc4 ,illustration3 ,fig4 #bbd4 ,the principles upon which 8projection0 in drawing is based1 are illustrated in the following examples and text3 ,as a real object can be scaled with a foot rule1 so a drawing must permit of scaling and measuring4 ,this measuring may take place as with the real object in full size or the drawing may1 for the sake of convenience1 be reproduced and measured in a reduced scale1 as half1 or in still smaller sizes4 ,sometimes it may prove convenient to enlarge the drawing to twice the natural size of the object1 as a means of making it stand out more clearly than the real size would accomplish4 ,for practical purposes1 it is productive of economy of time to mark the dimensions of height and width or depth on the drawing in figures1 to avoid the scaling4 ,this marking of the dimensions is best done at the time of making the drawing1 while the conception of the object is clear4 ,to convey a correct impression of the object1 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 length2 for this1 it must be assumed that the eye of the observer is equally distant from all points of a plane through the nearest point1 or one of the axes of the object1 and that the lines of sight are all parallel to each other and square to this plane4 ,in fig4 #bbe these lines of sight are seen as directed toward one side of a cube or block2 it will be readily understood1 however1 that in this way nothing is visible and accessible for scaling and dimensioning except this front face of the block1 thus1 a determination of the dimensions of only height and width would be possible1 while the dimension of depth is entirely undetermined4 ,illustration3 ,fig4 #bbe4 ,it is thus necessary to get a view of the block from another side2 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 view4 ,fig4 #bbf shows how the lines of sight would strike the object in the three directions4 ,if these lines should be rays of light1 some of them would pass by the body until they squarely strike the large plane surfaces1 ,i1 ,,ii1 ,,iii2 naturally the rays of light on the faces of the object will be retained1 and cannot strike the plane surfaces1 thus leaving dark shadows of exactly the same outlines as the block2 these would be exact drawings of the faces1 and if by some means they can be fixed and retained on the plane they can be completely measured and dimensioned4 ,this throwing forward of the outline of the object in different views on the planes is called projection of the object1 and furnishes a highly important means of fixing the outlines and dimensions in the three main directions of height1 width and depth2 evidently1 the light rays passing by the front face may not all reach the plane of projection1 but they may be retained by protruding parts of the object behind the front face4 ,these protruding parts naturally would also be projected on the plane in the same manner as the main body of the block4 ,these projections of the protruding part are plainly visible in plane ,,ii and plane ,,iii1 while the part would not be drawn in outline in plane ,i4 ,it may be imagined1 however1 that the greater thickness of the body in the direction of the protruding part would intensify also the shadow1 thus outlining the face of the protruding part in plane ,i4 ,it is apparent that these three projections are all needed1 but as drawing is all done in one single plane1 the three projections will for the sake of convenience have to be brought into a single plane4 ,this can be realized if plane ,,ii is swung around axis ,o ,z and plane ,,iii around axis ,o ,y1 until all three surfaces are in one single plane1 which would then appear as shown in fig4 #bbg4 ,it is also possible to assume transparent planes in front of the body and extend the parallel lines of sight forward instead of backward4 ,thus an outline picture will be created on each of the three planes ,i1 ,,ii1 ,,iii in fig4 #bbh1 in a manner similar to fig4 #bbf4 ,for drawing purposes1 all three views again have to be brought into a single plane1 which is done by swinging ,,ii around ,o ,z1 and ,,iii around ,o ,y in the same manner as fig4 #bbg was evolved from fig4 #bbf4 ,it will be noted that in fig4 #bbi plane ,,iii is now above ,i and plane ,,ii on the left-hand side of ,i1 while in fig4 #bbg they were below and at the right-hand side of plane ,i4 ,as the swinging of the top and side planes takes place around the edges of the front plane ,i two systems may thus be distinguished1 according to the position of plane ,i in regard to the object4 ,fig4 #bbf thus represents the system of backward projection1 while fig4 #bbh represents the system of forward projection4 ,either system can have1 however1 the plane ,,ii at the right- or left-hand side edge1 while plane ,,iii may be attached to the top or bottom edge of plane ,i2 it is readily understood that a number of combinations are possible for each system1 as it is not necessary to adhere absolutely to one rule4 ,the system of forward projection is the one generally practiced and further examples are all executed by this system1 meaning that the planes are always between the observer and the object4 ,illustration3 ,fig4 #bbf4 ,illustration3 ,fig4 #bbg4 ,illustration3 ,fig4 #bbh4 ,for the clearness of the drawing1 it is desirable to have all corners1 edges and outlines appear in such solid lines as they appear to the eye4 ,if1 therefore1 certain sharply defined outlines occur on one side more than on the opposite one1 it is most desirable to take the view against the side that has the most definitely marked outlines4 ,if the opposite side should show a number of wholly different features1 it may prove even desirable to show this side also1 thus gaining four views instead of the usual three1 and so obtain a more complete understanding of the shape of the object1 besides giving increased facilities for dimensioning each part of the body4 ,this additional view may be taken from the sides1 as well as up or down1 thus making a maximum of five views possible by which the outside of the object may be delineated4 ,fig4 #bcj 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 faces4 ,it is not necessary1 however1 to resort to five views in such a case as is represented in fig4 #bcj1 as the only differing feature1 the circular space in ,,iii bottom1 might be shown in ,,iii top by dotted lines1 and the difference of ,,ii right might be shown in ,,ii left1 also by dotted lines4 ,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 views4 ,illustration3 ,fig4 #bbi4 ,so far the projections and views have only represented the outlines of the object2 it may often be desirable1 however1 to show central holes or other perforations or variations of sections2 in this case it is possible to imagine the object cut in slices1 by planes1 through certain well defined axes1 or other lines of distinctive importance1 and then take a view of this sectional plane with its newly created intersections or sharply marked outlines2 thus1 a section may often take the place of the third1 fourth or fifth view to great advantage4 ,illustration3 ,fig4 #bcj4 ,it is not always possible to get a view against a face or side of the object1 but1 with irregularly shaped bodies or under special conditions1 it may be necessary to take a view of corners1 sloping planes1 curved or irregularly shaped surfaces4 ,fig4 #bca shows a hexagonal nut in the three normal projections2 from the top view it is readily seen that the front view shows the side of the hexagon in a contracted scale1 and that therefore the scaling and dimensioning for the horizontal direction have all to be done in the top or plan view2 the front and side views convey1 however1 the dimension of height correctly1 and these are therefore the right places for scaling and dimensioning in the vertical direction4 ,fig4 #bca shows how a cylindrical outline appears in the three views2 the hole in the nut presents itself as circular in the top view1 while it appears in the front and side views as a rectangle4 ,for simple objects1 it is unnecessary to show the edges of the planes1 and the three views are grouped1 as regards distances and positions1 as most convenient for the execution of the drawing4 ,where sloping surfaces are of irregular form1 it may be necessary to employ help lines for their full determination in the three views4 ,fig4 #bcb shows how the surface that is produced by a slanting cut through a cylinder would appear in the three views4 ,the help lines are placed in the top view in eight equal divisions around the circumference of the cylinder4 ,these division lines are shown by dotted lines on the cylinder in the front and side views4 ,their intersections1 with the sloping cut in the front view1 furnish also the height of the corresponding points for the side view4 ,illustration3 ,fig4 #bca4 ,by progressive determination of points1 lines and surfaces1 even the most complicated bodies can be completely represented for their reproduction in any application to mechanical or industrial purposes4 ,illustration3 ,fig4 #bcb4 ,the spur wheel shown on page #afc is an example of projection drawing4 ,the wheel is illustrated in three views3 fig4 #bce is a side view1 or elevation2 fig4 #bcd is a front elevation2 fig4 #bcc is a section view on ,c ,d4 ,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 ,c ,d1 cutting the plane of view and showing the interior shape at ,c ,d4 ,the side elevation1 fig4 #bce1 is projected from the front elevation1 fig4 #bcd1 by drawing parallel lines from the edges in the front view across its face4 ,in actual drawing practice the figures should be made about three times larger than the example1 and as follows3 ,for the front elevation draw the center lines ,a ,b1 ,c ,d1 and from their point of intersection as a center1 with the compasses draw the inner circle or hole1 also the pitch line ,e ,e4 ,with the dividers space this line into nineteen equal divisions2 each point on this line will be the center of a tooth1 and the distance from one point to the next one is the pitch of the tooth4 ,now1 with the dividers mark off the thickness of tooth at each side of these points on pitch line2 with the compasses draw the outer circle for points of teeth1 the inner circle for the root of teeth1 and circles for thickness of rim and hub2 also circles representing the fillets at rim and hub4 ,for clearness and to prevent confusion these lines are shown on one-half the wheel only1 terminating in center line ,c ,d2 all the lines of the front elevation are now complete excepting the teeth4 ,in the drawing office it is unusual to delineate all the teeth in a gear wheel1 the lines without the teeth as now completed being deemed sufficient1 giving all particulars2 however1 to prevent the error of mistaking the circles it is well to represent one or two teeth on the drawing4 ,illustration3 ,fig4 #bcc4--;,fig4 #bcd4--;,fig4 #bce4 ,in the example1 proceed and complete the entire wheel1 taking on the compasses a radius equal to the pitch of the tooth2 set them on the pitch line at the point ,g1 already spaced for thickness of tooth1 draw line ,h from pitch line to root of tooth2 proceed similarly all around the circle1 completing one side4 ,next1 reverse the operation and draw the corresponding side of the root of tooth4 ,now take a radius equal to half the space between teeth and the thickness of tooth on pitch line1 and1 with center in pitch line1 as shown at ,i1 draw the outside or addendum of tooth1 ,j2 it will be apparent that the reverse addendum of the tooth next adjoining can be formed at the same time1 with one setting of the compasses2 finish all the teeth similarly2 the front elevation will thus be completed4 ,fig4 #bcc is an excellent example of sectional drawing1 to be executed as follows3 ,first draw the center line ,l ,m of fig4 #bcc1 lay off at each side of it half the breadth of face and of the hub2 now project1 from center line ,c ,d1 in the front elevation1 fig4 #bcd1 with the ,t-square the upper and lower teeth1 the fillets1 the chamfers1 the hub and center hole1 also dot in the pitch line ,f ,f1 take the radii and draw the fillets and chamfers2 draw section lines and the view will appear as shown in fig4 #bcc4 ,fig4 #bce is a side elevation of fig4 #bcd1 and is a fine sample of projection1 to be executed as follows3 ,proceed similarly as for fig4 #bcc1 projecting the lines from the outside edges of the front elevation1 instead of from the center line ,c ,d as in last figure1 and the end elevation will be as shown in fig4 #bce4 ,the student will be assisted in understanding this working drawing by consulting the pages under the heading of 8,gearing40 ,illustration3 ,,lettering1 ,,inking ,,section ,,lining ,illustration3 ,fig4 #bcf4 8,inking ,in0 ,drawings4 ,when a drawing is completely finished in penciling1 it should next be 8inked in0 for preservation4 ,care should be used that the pen may be perfectly clean2 the pen should be held nearly vertical1 leaning just enough to prevent it from catching on the paper2 the pen should be held between the thumb and first and second fingers1 the knuckles being bent1 so that it may be at right angles with the length of the hand4 ,the ink should be rubbed up fresh whenever it is about to be used1 for it is better to waste a little time in preparing ink slowly than to be at a continual trouble with pens1 which will occur if the ink is ground too rapidly or on a rough surface4 ,to test ink1 a few lines can be drawn on the margin of a sheet1 noting the shade1 how the ink flows from the pen1 and whether the lines are sharp4 ,after the lines have dried1 cross them with a wet brush2 if they wash readily1 the ink is too soft2 if they resist the water for a time and then wash tardily1 the ink is good4 ,care must be exercised not to overload the pen with ink1 and1 like the pencil1 the pen should always be moved from left to right and from the bottom to the top of the board4 ,when inking1 both 8nibs0 of the pen point must rest evenly on the paper and the pen be pressed only lightly against the ,t-square4 ,never ink any portion of a drawing until the penciling is complete4 ,in inking long1 fine lines it is well to go over each line twice1 without moving the ,t-square1 trying not to widen the line on the second passage2 also see that the pen contains ink enough to finish a line1 as it is difficult to continue with the same width of line after re-filling4 ,to produce finished drawings1 it is necessary that no portion should be erased1 otherwise the color applied will be unequal in tone2 thus1 when highly finished mechanical drawings are required1 it is usual to draw an original and to copy it4 ,where sufficient time cannot be given to draw and copy1 a very good way is to take the surface off the paper with fine sand-paper before commencing the drawing2 if this be done1 the color will flow equally over any erasure it may be necessary to make afterwards4 ,the rules of procedure in drawing the lines in 8inking0 are1 #a1 ink in the small circles and curves2 #b1 ink in the larger circles and curves2 #c1 then all the horizontal lines1 beginning at the top of the drawing and working downward2 #d1 next ink in all the vertical lines1 commencing at the left and moving back to the right2 #e1 draw in the oblique lines2 #f1 all the center lines and dimension and reference lines4 ,the figuring and lettering should be always done with ,india ink1 thoroughly black2 the last lines to be drawn are the section lines4 ,the reason why irregular curves and arcs of circles are inked in first is1 that it is easier to draw a straight line up to a curve than to take a curve up to a straight line4 ,in practice1 the flat side of the drawing-pen is laid against the tee-square or ruler2 the taper of the blade of the pen is sufficient to throw the point enough away from the edge to prevent blotting2 the pen is drawn from left to right and from the bottom to the top of the board4 ,this is shown in fig4 #bcg1 intended to represent 8short work0 with the drawing-pen4 ,the wrist is shown resting upon the blade of the square4 ,illustration3 ,fig4 #bcg4 ,illustration3 ,fig4 #bch4 ,in a similar figure1 #bch1 the position of the hand holding the pen indicates the best relative posture for inking long lines4 ,in one of these illustrations the work is executed principally by the wrist--in the other by the arms and fingers working together4 ,the pen should be held with even pressure against the straight-edge or curve4 ,if the pressure varies1 the blades will spring and the width of the line will change4 ,the blades should be of such length that both will bear equally upon the paper when the pen is inclined slightly1 so as to bring the inner blade near the straight-edge2 the angle of the pen should not be changed while drawing any line4 ,when the inking is finished1 the whole drawing may be cleaned by rubbing it with bread which is not greasy or so fresh as to stick to the paper4 ,if the paper is much soiled it may be necessary to use an eraser4 ,a soft pencil eraser should be used and great care taken that the ink lines are not lightened and broken by it4 ,to avoid the necessity of using an eraser upon a finished drawing1 instruments and paper must be kept free from dust and dirt4 ,the triangles and ,t-square should be cleaned often1 by rubbing them vigorously upon rough1 clean paper4 ,pounce is a powder used to prevent blotting in rewriting over erasures2 it is held in a bag or small box with a perforated lid for convenience in sprinkling on paper2 when used it should be distributed evenly with a piece of chamois1 and the surplus or loose particles removed before applying the ink4 ,a drawing is made to be read1 and the skill in inking1 as in 8free-hand0 and in penciling1 does not consist so much in the fineness of the lines as in their clearness4 ,lettering ,drawings4 ,lettering is an important part of making drawings1 the object aimed at being to identify any portion by reference letter or letters2 thus in fig4 #bci the line ,a ,c describes the line extending from ,illustration3 ,fig4 #bci4 ,any information which cannot be expressed in the drawing is always expressed by lettering1 and it is desirable to confine the lettering of drawings to one or two standard alphabets that are plain and distinct1 and the principles of which are easily acquired4 ,these conditions are fulfilled in the ,gothic fonts shown on page #agc4 ,both letters and figures must be carefully made and of uniform proportion2 it is well to 8lay out0 these by regular measurement before permanently inking them4 ,letters should not be less than one-eighth of an inch in height and penciled carefully before inking4 ,on page #agc are printed two forms of numerals and letters of the alphabet2 it is recommended that these be used both for practice in free-hand and for regular office work4 ,for easy reference1 letters should not be crowded nor allowed to interfere with one another2 they should be drawn neatly1 avoiding all lines of the drawing2 plain letters are always used on mechanical drawings1 whether for title1 scale1 reference1 etc4 ,arrow-heads1 figures and letters should be in black1 and made with a writing pen4 ,a pen with a ball point is preferable1 giving an equal thickness of line1 no matter in which direction the stroke is made4 ,illustration3 ,fig4 #bdj4 ,neat1 well-lettered drawings go far towards establishing a high standing for the aspiring draughtsman4 ,all lettering should be done free-hand1 first with the pencil1 sharpened to a fine round point1 and afterwards written in ink4 ,for this purpose common writing pens are best to be used2 fig4 #bdj represents the several numbers of the approved ,gillott's pens adapted to this purpose4 ,in lettering1 it is well1 for a guide for size and location1 to draw1 with a round-pointed pencil1 two horizontal lines just the height the letters are to be2 the letters are also best made with careful use of the instruments1 rather than free-hand4 ,in order to letter systematically1 it is a good plan to start with the middle letter of the inscription and work in both directions2 making too prominent letters should be avoided1 plain and distinct letters being most desirable4 ,finally1 with an ordinary writing pen1 trace over the penciling in ink2 the pencil guide lines being erased after the letters are inked in completes the operation4 ,illustration ,an important matter in connection with lettering a drawing is the location of the letters2 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 described4 ,when single letters are used1 they should be inked in before the shade or section lines are drawn4 ,fig4 #bda is an example introduced to show the method of lettering a descriptive mechanical drawing4 ,the figure shows a 8blow-off valve0 of approved design drawn in section2 the letters designate the several parts2 the reading to accompany the lettering is as follows3 ,a--,inlet communicating with annular passage 7,c7 to admit steam1 which blows off scale and sediment from seat 7,e7 before disc 7,l7 comes in contact with same4 ,b--,plug to permit passage of rod to clean out blow-off pipe4 ,c--,annular steam passage around casing 7,d7 and communicating with inlet 7,a74 ,d--,removable bronze casing1 in which plug 7,l7 fits snugly4 ,e--,removable bronze seat ring1 which also holds casing 7,d7 in place4 ,j--,slot in casing 7,d7 arranged to discharge sheet of steam from ,c1 which1 blowing across seat 7,e71 cleans off scale and sediment before contact with disc 7,l74 ,k--,non-rotating washer to prevent loosening of locknut 7,h7 when opening valve4 ,l--,reversible disc1 having two ,babbitt-metal seating faces 7,f7 7,f74 ,illustration3 ,fig4 #bda4 ,dimensioning ,drawings4 ,to 8dimension0 working drawings is to place measurements upon the parts represented1 to enable the workman to proceed without measuring the drawing itself4 ,these dimensions should be placed so as not to interfere with nor crowd the lines of the drawing1 nor yet interfere with one another4 ,arrow-heads are used at the extreme points of measurement1 the figures are generally inserted midway between the arrows2 a dot and dash line reaches from the figure to the arrow-heads1 as shown below4 ,illustration ,when the dimension is short these lines are omitted and the dimension is placed outside the drawing1 thus ,illustration and connected by a curved line2 at other times it is found needful to place arrow-heads outside the drawing and the measurement inside4 ,illustration ,when the dimension is long and narrow it is usual to carry the dimensions under the drawing by dotted and dash lines1 as shown below4 ,illustration ,arrow-heads and figures should be drawn free-hand with a common writing pen4 ,usually dimensions are given in inches1 up to #bd inches1 as it is found less confusing2 for instance1 if written #a #a it may be mistaken for #aa2 if written #ac no mistake could be made4 ,again1 #a #j may be mistaken for #aj2 if written #ab it would not2 in addition to being more distinct1 it occupies less space on the drawing4 ,in large measurements there is more room for the figures1 and1 therefore1 they can be spaced further apart--in feet and inches4 ,all figures should be made of a fairly large size4 ,vertical dimensions should read from the right hand1 thus1 as shown3 ,illustration ,measurements of importance1 such as the diameter of a circle1 the pitch or distance apart of rivets and bolts1 etc41 should be marked in figures on the drawing4 ,when rough or unfinished work is mixed with machined or finished portions1 it is usual to mark ,f1 or 8fin410 after the latter dimension4 ,in practice1 at times1 instead of dimensions reference letters are used1 thus3 ,illustration3 ,d diam4 of shaft1 #b inches4 ,l length of bearing1 #c inches4 ,t thickness of collar1 inch4 d diam4 of collar1 #c inches4 ,generally it is preferable to give the diameters of turned and bored work on a section1 instead of an end drawn separately2 confusion is sometimes caused by a number of radial dimensions4 ,fig4 #bdb and fig4 #bdc are introduced to show the principal measurements required in practical work1 and the usual way in which such dimensions are marked when ordering parts of machinery4 ,fig4 #bdb is a pedestal1 or metal frame2 three views are shown1 the center figure being an elevation1 the lower figure is the plan of the base1 the upper figure is a view of the top1 on which is bolted the bearing block1 it being on the outside of the center figure4 ,the essential measurements are marked by letters4 ,h is the vertical height from base to the seat of bearing block3 ,l being the length1 and ,w the width of the base2 ,p is the length between checks1 and ,b the width of seat for bearing block2 ,c is the distance from center to center of the holding down bolt holes1 and ,t is the depth of the holes in the base2 ,k is the distance from center to center of the bolt holes in the top for bearing block4 ,fig4 #bdc is a hanger1 or metal bracket1 and shows the center figure or elevation1 the plan of the top and the plan of the seat for bearing block1 which is bolted on the interior of the center figure4 ,h is the vertical distance from the top to the seat for bearing block2 the other measurements required are marked by letters similar to figure #bdb4 ,now1 one of the important matters in connection with dimensioning a drawing is the location of the figures4 ,one rule1 whose utility cannot be gainsaid1 is that they should be so located that they can be altered or erased without damage to the lines of the drawing1 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 machine4 ,illustration3 ,fig4 #bdc4--;,fig4 #bdd4 ,shading ,drawings4 ,to produce an effect1 drawings are shaded2 that is1 shadow lines about twice the width of the regular line are drawn according to a recognized rule1 which always represents the same peculiarity of form in the same way4 ,in working drawings light lines only are permitted2 shade lines are wider than the working lines1 and in reading scale measurements the extra thickness of line would make a difference4 ,instead of representing the shadow as it is really cast by the object1 the edges which cast the shadow are determined1 and all the views are treated as if the light came from behind and from the left1 downwards1 at an angle of #de to the horizontal line1 as shown by the arrows in figs4 #bde to #bdh4 ,illustration3 ,fig4 #bde4--;,fig4 #bdf4--;,fig4 #bdg4--;,fig4 #bdh4 ,the lower and right-hand outlines of projecting parts will cast shadows1 and the student should make them of extra width4 ,fig4 #bdi3 ,in shading curves1 divide the center line as before 7see page #adf7 and describe circles from center1 ,d2 these lines are not to be shaded in penciling1 but when inking4 ,the figures represent two rings1 ,a and ,c1 and spaces1 ,b and ,d4 ,the outside of a surface is shaded according to circle #a1 and the inside surface according to circle #b4 ,this will give the desired shading1 but it makes a drawing incorrect1 and therefore shading is not used in working drawings4 ,this shading is accomplished by inking the circle first with regular width of line2 then with the same radius remove the point of compasses from the true center1 placing it outside1 according to the desired position of the shaded line1 and describe an arc of a circle4 ,in fig4 #bej divide center line as before2 with the #de triangle or set square1 draw through the center the diagonals shown by dotted lines2 and through the points ,a1 ,b1 ,c1 etc41 draw the perpendiculars1 cutting the diagonals2 from the points of intersection draw the horizontal lines1 completing the squares4 ,illustration3 ,fig4 #bdi4 ,illustration3 ,fig4 #bej4 ,now1 take a radius of half an inch1 and in the corner of each square draw with the bow-pencil a circular arc meeting the pencil lines exactly2 with the bow-pen ink in the arcs first1 then ink carefully the lines joining with the arcs2 all lines must be of the same width2 put in the shade on arcs and lines as in fig4 #bdi2 and1 finally1 erase the pencil lines at corners1 etc4 ,section-,lining4 ,cross-hatching has been defined in the 8preliminary definitions0 to drawing2 this term represents the practice of drawing diagonal lines representing the interior of an object1 shown as a piece cut in half or when a piece is broken away4 ,this is done to make more of the parts show1 or to exhibit more clearly the nature of the materials2 hence section lining and cross-hatching tell the same thing1 i4 e41 the drawing of diagonal lines1 usually at an angle of #de1 to show that the object is broken away and the interior designed to be represented4 ,illustration3 ,cast iron4 ,fig4 #bea4 ,illustration3 ,wrought iron4 ,fig4 #beb4 ,illustration3 ,steel4 ,fig4 #bec4 ,illustration3 ,composition4 ,fig4 #bed4 ,illustration3 ,vulcanite4 ,fig4 #bee4 ,illustration3 ,wood4 ,fig4 #bef4 ,illustration3 ,leather4 ,fig4 #beg4 ,illustration3 ,brick4 ,fig4 #beh4 ,illustration3 ,fig4 #bei4 ,figs4 #bea to #beh1 inclusive1 show the section lining and cross-hatching by which it is customary to represent the various materials entering into a construction4 ,in fig4 #bei is outlined a representation of a section of a cog-wheel2 section #a being the wood cogs2 #b1 the iron wheel1 and #c the wedges at the root of the gear4 ,it would be impossible to convey the same ideas by ordinary plan or elevation drawing2 all the objects on the same page are more clearly represented by the use of section lines or cross-hatching4 ,sectioning is executed by drawing a series of parallel lines about inches apart4 ,lay the #de triangle on the upper edge of the ,t-square and draw the top-most line of the sectioning4 ,then slide the triangle along the ,t-square for each successive line4 ,the sectioning should be inked in without previous penciling and the lines should be finer than the lines of the general drawing4 ,various devices are in use for mechanically equalizing the distances in section lining1 but the trained eye is the most practical method4 ,when two abutting pieces are sectioned1 the section lining on one piece slants in an opposite direction to that on the other4 ,to draw an object to be sectioned on both sides of its center line1 only one side is sectioned1 while the other side is drawn in full4 ,sections are necessary in nearly all machine drawings2 they are usually taken horizontally or vertically1 but they may be taken in any direction2 the position of a section should be shown by a line upon the object2 this line is called the cutting plane4 ,in fig4 #bfa is shown the hub of a wheel1 it is also a sample of work for practice4 ,illustration3 ,fig4 #bfj4 ,illustration3 ,fig4 #bfa4 ,fig4 #bfj shows the mode of representing two different materials in one plane1 or a section may be represented by the darker portion1 and the lighter shaded portion being a surface resting on the section4 ,fig4 #bfa shows the section of a shaft surrounded by the surface of a wheel4 ,,tints ,,and ,,colors4 ,for special purposes of illustration drawings are made which must be tinted4 ,in such cases the paper must be expanded and stretched evenly all over its surface2 otherwise when the moist tint is applied the paper will wrinkle and get out of shape2 to do this cut the paper at least half an inch less in size than the drawing board2 lay the paper face down1 turn up a margin or edge of about three-fourths of an inch all round1 then dampen the paper with a sponge and clean water2 allow it to soak for a few minutes until it is evenly dampened or moistened all over1 turn the paper upside down 7face up74 ,apply strong paste to the under side of the margin all round2 rub down1 on the drawing-board1 working from the center of the board outwards so as to exclude the air and prevent creases or furrows4 ,the board is then inclined and left to dry slowly2 make sure that the paper is all well pasted and every part of the edges attached to the board4 ,if tracings are required to be tinted or shaded1 the color may be applied before the tracing is cut off1 or what is more usual1 the color may be applied on the back of the tracing2 then there is no liability to wash out the lines4 ,mechanical drawings are seldom tinted1 but are mainly produced in ,india ink4 ,where1 however1 a fine effect is desired1 working drawings are colored1 so as to show at a glance the material of which the different parts are to be made4 ,the colors required are few but should be of the best quality4 ,besides ,india ink the following water-colors are generally used3 #a1 ,neutral-tint4 #b1 ,prussian ,blue4 #c1 ,chrome ,yellow4 #d1 ,gamboge4 #e1 ,raw ,sienna4 #f1 ,carmine4 #g1 ,vermillion4 #h1 ,venetian ,red4 #i1 ,sepia4 #aj1 ,indigo4 ,these come in hard cakes4 ,certain colors and tints represent different metals and materials as follows3 ,wrought ,iron--,prussian ,blue4 ,steel--,carmine and ,prussian ,blue1 mixed to give a purple shade4 ,steel ,casting--,same as the above darkened by ,venetian ,red4 ,cast-,iron--,neutral ,tint made of ,india ,ink1 indigo1 mixed with a little carmine4 ,brass--,gamboge or ,chrome ,yellow4 ,babbitt--,emerald ,green2 sometimes light mixture of ,india ,ink4 ,copper--,purple ,lake4 ,it is sometimes found necessary to prepare a highly finished and shaded drawing of the work in hand4 ,such elaborations1 in fact1 are much admired by the uninitiated1 although the complete shading of the drawing is no criterion as to the scientific value of the machine4 ,an illustration of this is told in the note4 ,,note4--,a consulting engineer had to lay before a board of directors plans of horizontal engines for their consideration4 ,one of these drawings was of a very superior machine1 but being only depicted lineally was at once rejected by them1 for a highly finished representation of a very inferior apparatus4 ,the engineer1 wishing to induce the board to decide for the best1 suggested that the matter should be postponed to a future day1 and in the meantime had the drawing of the superior machine highly colored and finished4 ,at the next meeting the directors unanimously decided that this was the very one which they preferred and had chosen4 ,reproducing ,drawings4 ,when once finished1 one or more copies of drawings are frequently required2 these are produced1 #a1 by blue printing1 as described before2 #b1 by tracing4 ,a tracing is a mechanical copy of a design or drawing1 made by reproducing its lines as seen through a transparent medium--as tracing-cloth or tracing-paper4 ,tracing-cloth is a thin linen fabric1 coated with size2 this is called tracing-lines2 tracing-paper is so prepared as to be transparent1 so that it will receive marks either in pencil or with pen and ink4 ,tracing-cloth must be fastened to the board1 over the drawing1 by pins or other tacks2 moisture or dampness should be carefully avoided and the drawing done on the smooth side of the cloth4 ,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 waste1 chamois1 or similar material1 but the pounce should be thoroughly removed--by washing--before applying the ink4 ,in making tracings the same order is followed as described under the section 8,inking0--to repeat3 #a1 ink in the small circles and curves2 #b1 ink in the larger circles and curves2 #c1 then all the horizontal lines1 beginning at the top of the drawing and working downward2 #d1 next ink in all the vertical lines1 commencing at the left and moving back to the right2 #e1 draw in the oblique lines2 #f1 all the center lines red 7carmine71 and dimension and reference lines in blue 7,prussian blue7 or vice versa4 ,the figuring and lettering should always be done with ,india ink1 thoroughly black4 ,,blue ,,printing4 ,copies of drawings or parts representing details and measurements are frequently needed for the office1 pattern shop1 machine and blacksmith shop1 etc4 ,these copies are best made by printing on sensitized or specially prepared paper1 from tracings drawn on transparent cloth or paper1 as hereabove described4 ,the original design may be guarded with the utmost care for long preservation1 but the blue prints1 so called1 are for ready reference and use without much regard to the length of time they are to be in existence4 ,the usual practice is to carefully trace from the drawing on transparent cloth or paper an exact reproduction of it1 filling in all detail lettering and sizes or figured dimensions4 ,this tracing is fixed in a frame similar to a picture frame1 with the side on which the drawing is made next to the glass3 #a1 place the sensitized side of the paper 7which has been prepared previously7 against the back of the tracing2 #b1 fix soft padding against the back of the paper and fasten it up so that both paper and tracing are compressed firmly against the glass1 permitting no creases or air spaces between them4 ,illustration3 ,fig4 #bfb4 ,this should be done in a darkened room2 #c1 expose for three to six minutes1 according to the intensity of the sun2 #d1 take the sensitized paper out of the frame and quickly wash well in clean running cool water1 and the drawing will appear in white lines on blue ground2 #e1 hang the print up by one edge so that the water will run off and the print will soon dry and be ready for use4 ,,test-,,pieces4 ,to make good blueprints1 being guided only by the appearance of the exposed edge of sensitized paper1 requires considerable experience4 ,very often1 especially on a cloudy day1 the edge looks just about right1 but when taken out of the frame and given a rinsing1 it is only to find that the print looks pale because it should have been allowed to remain exposed for a longer period4 ,now simply take a small test-piece of the same paper 7say about #d inches square7 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 exposed1 and cover these samples with a piece of glass about #d inches square4 ,as a general rule1 we can find a place on top of the frame for the testing-piece1 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 appearance1 the novice can get just as good results as the experienced hand without danger of failure4 ,,black ,,process ,,copying4 ,this is accomplished by specially sensitized paper by which a fac-simile of the original drawing can be made2 that is1 black lines upon white ground4 ,it also avoids the objection to the blue print paper of shaded drawings which show light and shade reversed4 ,the prints made by the process are said to be absolutely permanent and can be altered1 added to or colored the same as original drawings4 ,the sensitized paper is sold ready for use1 but it can be prepared by dissolving two ounces of citrate of iron and ammonium in eight ounces of soft water2 keep in a dark bottle1 also1 one and one-third ounces of red prussiate of potash in eight ounces of water2 keep in another dark bottle2 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 paper1 similar to envelope paper1 let it dry and put away in a dark place until required for use4 ,illustration3 ,,drawing ,,office ,,rules ,drawing ,office ,rules4#a #a ,,note4--,a4 ,w4 ,robinson1 ,m4,e41 ,montreal1 must have all credit for these admirable rules and regulations4 ,they bring into a single focus the whole science and art of mechanical drawing4 ,there are drawing offices where from ten to nearly one hundred people are busily employed in making new plans and sketches by the hundreds1 and where thousands of completed drawings are filed for reference or for changes1 as these are needed in the shop management4 ,to be introduced for the first time into such a company is a trial for the 8new man0 both of nerve and manners1 and a test as well of skill2 nothing helps more at such a time than an acquaintance with the rules and routine of the office1 for the old saying holds good in a drawing office1 of 8doing in ,rome as the ,romans do40 ,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 hand4 ,,size ,,of ,,drawings4 #a4 ,the standard size shall be #bc inches by #cf inches1 subdivided into half1 quarter and eighth sheets4 #b4 ,full-size drawings shall be reserved1 as far as possible1 for general views and parts not capable of being shown on smaller sheets4 #c4 ,all shop detail shall1 as far as possible1 be shown on quarter and eighth sheets4 ,,character ,,of ,,drawings4 #d4 ,detail drawings shall1 as far as possible1 classify the different kinds of works1 such as castings1 forgings1 shafts1 levers1 piping1 etc4 ,different kinds of work shall not be shown on the same detail drawing4 #e4 ,all shop drawings liable to repetition shall be traced and blue-printed4 ,all temporary details1 requiring only one copy1 may be made on sketch sheets and press copied4 #f4 ,a shop drawing is to be considered as an order or instruction to the shop1 and not merely as a statement or illustration4 ,for this purpose it must convey clearly and distinctly all the information necessary to make the article4 #g4 ,every dimension necessary to the execution of the work is to be clearly stated by figures on the drawing1 so that no measurements need to be taken in the shop by scale4 ,all measurements to be given with reference to the base or starting point from which the work should be laid out1 and also with reference to center lines4 #h4 ,all figured dimensions on drawings to be plain1 round vertical figures1 not less than one-eighth inch high1 and formed by a line of uniform width and sufficiently heavy to insure printing well4 ,no thin1 sloping1 or doubtful figures1 or diagonal-barred fractions will be tolerated4 ,all figured dimensions below two feet to be expressed in inches4 #i4 ,all center lines to be alternate dot and dash in fine black line4 ,all dimension lines to be double dot and dash1 with a central space for the figure1 and of such strength as to show on blue-print more faintly than lines of drawing4 ,lines of drawing to be bold and clearly defined in proportion to the scale1 and may be shade-lined by making the right-hand and bottom lines heavier4 ,no ornamental shading or other 8frills0 allowed on shop drawings4 #aj4 ,every drawing1 whether whole or half-sheet1 shall have the title1 date1 scale and number of the sheet stamped in lower right-hand corner1 and the quarter and eighth sheets printed on top4 #aa4 ,the name of the drawing1 as given in the title1 is invariably to consist of two divisions in one line separated by a hyphen4 ,the first division is to state the general name of the thing or machine1 and the second name is to clearly designate the part or parts represented 7or if a general view should so state74 ,the wording of titles should be submitted to the chief engineer or head draughtsman for approval4 #ab4 ,each drawing shall bear the name of the draughtsman and examiner1 the surname being used without initials4 #ac4 ,drawings of piping details shall be made in diagram form1 using standard symbols4 #ad4 ,all detail parts for standard or repetition work shall be shown unassembled as far as possible4 ,,drawing ,,symbols4 #ae4 ,detail shop drawings should state3 7a7 ,the pattern number of every casting in plain figures of larger size than the dimension figures4 7b7 ,the material of which the parts are made1 using symbols as follows3 ,c4,i4--,cast iron4 ,w4,i4--,wrought iron4 ,m4,s4--,machinery steel4 ,h4,s4--,hammered steel4 ,bs4--,brass4 ,bbt4--,babbitt4 ,bz4--,bronze4 ,c4,r4,s4--,cold rolled steel4 ,other materials write full name4 7c7 ,finished surfaces will be indicated by 8f0 written on the line or surface to be finished4 ,when not so marked it is understood that the part is to be left black or rough4 ,in cases where finish might be presumed but not required1 follow the figured dimensions by the word 8cast10 if a casting1 and 8rough10 if a forging4 ,,standards4 #af4 ,the following standards shall be strictly adhered to as given in the tables noted3 7#a47 ,table of standard diameters of shafting and key seats4 7#b47 ,table of standard stock sizes of rounds4 7#c47 ,table of standard stock sizes of flat steel4 7#d47 ,table of standard clearance fits4 7#e47 ,table of standard symbols for notation of riveting4 7#f47 ,table of standard symbols for pipe fittings4 ,also such other standards as may be adopted from time to time4 ,,numbering ,,of ,,drawings4 #ag4 ,drawers and filing cases shall be numbered consecutively4 ,drawers shall contain #ajj sheets each1 and filing cases #bjj sheets each1 and to be fully indexed4 ,drawings shall be numbered by a number indicating both drawer number and serial number in the drawer--thus1 #g1fjd is the fourth sheet in drawer #gf1 etc4 #ah4 ,drawing numbers shall be checked off the index as required1 and the index posted up in uniform handwriting by the clerk4 #ai4 ,standard size drawings shall be kept in drawers and quarter and eighth sheets in filing cases4 ,all drawings shall be indexed by an index sheet kept in each drawer or case4 ,,checking4 #bj4 ,all drawings must be approved before being traced4 ,when tracing is completed it will be given immediately to the chief draughtsman1 who will have a preliminary print made and carefully checked1 before being used4 ,,patterns4 #ba4 ,all patterns shall bear the number of the drawing on which they are first detailed1 followed by a serial letter1 according to the number of patterns on the drawing4 #bb4 ,standard patterns used repeatedly and liable to be ordered from in repairs must not be changed4 ,other patterns may only be changed when absolutely necessary and by order4 ,when so changed they will bear the original number and letter1 followed by ,a for the first change1 ,b for the second change1 and so on thus3 #dhfj ,,ab is the second change in pattern #dhfj ,a4 ,,sketch ,,books4 #bc4 ,each draughtsman will be supplied with a sketch book by the company1 in which he shall make all his notes1 calculations and data referring to his work1 and under no circumstances shall notes of value be made on loose sheets4 ,each entry should invariably be commenced with the subject and date1 and full notes made of data on which the calculations were based1 and the results obtained clearly stated4 ,these books are to remain the property of the company4 ,,in ,,general4 #bd4 ,changes in drawings1 sketches or order lists issued to the shop shall only be made when authorized by the chief engineer1 or1 in his absence1 by the chief draughtsman1 and when so authorized shall be made by the order clerk4 #be4 ,the names of all similar parts in order lists and drawings are to be uniform4 #bf4 ,tracings must be kept in safe1 for blue-printing purposes only4 ,office copies of blue-prints must be used for references4 #bg4 ,no drawing1 print or photograph shall be taken from office without permission4 ,,numbering ,,working ,,drawings4 ,there are a great many different systems used in indexing drawings1 most of which have some good points1 but very few are sufficiently elastic to cover a wide field4 ,a plan based upon the decimal system of notation is very simple1 and1 as there is no practical limit to the number of subdivisions1 it can be expanded indefinitely4 ,following are the main outline features of the system as adapted to the needs of drawing offices belonging to large works4 ,the main division numbers1 #jjj1 #ajj1 #bjj1 #cjj1 etc41 are used respectively for all plans and general sheets referring to the division concerned4 #ajj includes general plans covering more than one department1 and all small-scale plans with cross references to departments covered4 ,the class or tens divisions contain general drawings of the subdivisions1 the subclasses or units divisions being limited to details only4 ,further subdivisions would probably be necessary in some cases4 ,a card index with cross references and written by someone who knew what to do is an essential part of the system4 ,illustration3 ,,gearing ,,and ,,design ,illustration3 ,fig4 #bfc4 ,gearing4 ,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 drawing4 ,the diagrams are intended for exercises in drawing1 i4 e41 to be redrawn as parts of practice2 the text is to be studied not only for the good to be gained from the study of gearing1 but as an example of the way in which written or printed descriptions are necessary to explain a subject illustrated by drawings4 ,a gear is primarily a toothed wheel2 gearing is a train of toothed wheels for transmitting motions2 there are two chief sorts of toothed gearing1 viz41 spur gearing and bevel gearing4 ,a spur wheel has teeth around the edge pointing to the center2 commencing at the center1 a spur wheel may be said to consist of a hole1 square1 octagonal or round1 for its axle or shaft2 a hub2 the web1 body or arms2 a rim1 and the teeth2 see fig4 #bfc4 ,a spur wheel has teeth on its circumference which run parallel to its shaft2 wheels as shown in fig4 #bga are termed helical wheels2 these are similar to spur wheels except their teeth are arranged upon different angles to the shaft4 ,a bevel is a slant or inclination of a surface from a right line1 hence a bevel wheel is one whose teeth stand beveling or at an oblique angle to the shaft1 or towards the center2 see fig4 #bfg4 ,miter wheels are bevel wheels of the same size1 working at right angles with one another2 see fig4 #bfh4 ,the diameter of both spur and bevel wheels is measured and calculated neither from the outside nor from the bottom of the teeth1 but on the pitch circle4 ,when we speak of the diameter of a spur or bevel wheel1 we mean the diameter of the pitch circle1 without any reference to the form of tooth4 ,the addendum circle of a toothed wheel is as shown in illustration1 fig4 #bfd2 addendum means 8something added10 and1 as shown in the figure1 it is the part added beyond the pitch 8line0 or circle4 ,illustration3 ,fig4 #bfd4 ,the pitch line is the most important one in gearing2 the 8pitch line0 or 8pitch circle0 is supposed to be the working circle4 ,this is shown in ,p--,p in fig4 #bgd4 ,the periphery of a wheel is the extreme circumference1 as ,n in fig4 #bgd4 ,all parts of gear-wheels consist of portions1 to which have been given generally accepted names4 ,fig4 #bfd shows the 8addendum circle0 and the 8pitch line0 as marked4 ,the teeth and rim are shown in white1 and the other portions are indicated by the names4 ,the circular pitch line1 as opposed to the diametral pitch1 is the same as the pitch circle4 ,it is a line which bisects all the teeth of a toothed wheel4 ,the rolling circle is the same as the circular pitch line4 ,diametral means pertaining to a diameter or the length of a diameter2 hence a diametral pitch is a system of measures or enumeration based upon the diameter instead of the circular pitch line2 it is used very generally in spacing for fine tooth gear4 ,wheels of this description usually have their teeth cut in a gear-cutting machine1 i4 e41 medium and fine tooth gears4 ,illustration3 ,fig4 #bfe4 ,a cog wheel is the general name for any wheel which has a number of cogs placed around its circumference4 ,when the teeth of a wheel are made of the same material and formed of the same piece as the body of the wheel1 they are called teeth2 when they are made of wood or some other material and fixed to the circumference of the wheel1 they are called cogs2 see fig4 #bfe4 ,a pinion is a small wheel4 ,when two toothed wheels act upon one another1 the smaller is generally called the pinion4 ,the terms trundle and lantern are applied to small wheels having cylindrical bars instead of teeth4 ,the teeth in pinions are sometimes termed leaves2 in a trundle1 staves4 ,see fig4 #bgc4 ,the wheel which acts is called a leader or driver2 and the wheel which is acted upon by the former is called a follower or the driven4 ,when a screw or worm revolves in the teeth of a wheel1 the latter is termed a worm wheel or worm gear2 see fig4 #bgj4 ,when a pinion acts with a rack having teeth1 we speak of rack and pinion4 ,when the teeth are on the inside of the rim1 and not on the periphery1 the wheel is termed an internal gear2 see fig4 #bgb4 ,two wheels acting upon one another in the same plane are called spur gear2 the teeth are parallel with the axis4 ,when wheels act at an angle1 they are called bevel gear4 ,friction gear-wheels are those which communicate motion one to the other by the simple contact of their surfaces4 ,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 together4 ,grooved friction wheels are used to give greater cohesion than can be obtained by the plain surface4 ,fig4 #bfc shows a pair of spur-wheels in gear4 ,the dotted circles which meet are the rolling circles1 called the 8pitch line0 or 8pitch circle40 ,illustration3 ,fig4 #bff4 ,a spur mortise wheel is similarly shown in fig4 #bff2 it is very like in appearance to a spur wheel2 it differs essentially in that the teeth are separate cogs1 fixed in singly to the rim2 see also fig4 #bfe1 page #bja4 ,,note4--,the teeth of spur wheels cast from a pattern must of necessity be larger at one side than at the other1 because the teeth must have taper to permit the extraction of the pattern from the mould2 therefore1 in fixing wheels to gear1 the large side of one should meet the smaller side of the other2 should the two large sides come together the teeth will meet only at the large side1 and the teeth will probably break away from the excessive strain on that point4 ,skew gearing are bevel wheels working out of center2 the teeth do not form radial lines from the wheel center4 ,fig4 #bfg shows a pair of bevel wheels in gear as described on page #aii4 ,a bevel mortise wheel1 i4 e41 one having cogs inserted in its rim instead of teeth4 ,illustration3 ,fig4 #bfg4 ,a bevel wheel and pinion must be made to suit one another by both having teeth forming together an angle of #ij1 therefore they are pairs1 or proportioned in the number of teeth one to the other4 ,any other proportion used would not exactly gear and would be termed a 8bastard0 gear4 ,illustration3 ,fig4 #bfh4 ,fig4 #bfh represents a pair of miter wheels in gear2 it will be noted that the shafts1 when connected1 will be at right angles to each other1 the wheels being in all particulars of the same dimensions2 the figure answers the purpose of a much longer description1 if given in words4 ,a miter-wheel can easily be known by putting a square upon the face of the teeth1 which are always at an angle of #de with one another1 irrespective of size4 ,a miter-wheel is a particular kind of bevel-wheel1 the bevel being limited to an angle of #de in each wheel4 ,the curve of the teeth in bevel-gears1 when correctly formed1 changes constantly from one end of the tooth to the other1 therefore bevel-gears whose teeth are produced with a forced cutter are not theoretically correct4 ,fig4 #bfi represents a rack and pinion3 the teeth in this form of gear are shaped similarly to those in the spur wheel1 shown on page #aih1 with the difference that the teeth of one are on a circle and on the rack are made on a straight line4 ,illustration3 ,fig4 #bfi4 ,a flange or addition to the end of a tooth and the rim connecting them together is used to strengthen the teeth4 ,this extends from the root to pitch line when the wheel and pinion are both flanged3 if only one is flanged it extends from the root to the addendum4 ,illustration3 ,fig4 #bgj4 ,fig4 #bgj illustrates a worm and a worm wheel1 sometimes called screw gears4 ,this is a slow but powerful method of transmitting power1 one revolution of the worm only moving the wheel the distance of one tooth and space4 ,a worm gear is a spur wheel with teeth at an angle to the axis1 so as to work with a worm which is a screw1 or has teeth shaped in the form of a spiral wound round its circumference2 the screw or worm is called an endless screw1 because it never comes to a stopping place in the circumference of the wheel4 ,illustration3 ,fig4 #bga4 ,fig4 #bga represents a gear with helical teeth4 ,it is similar to a spur wheel1 and is used in place of same in heavy and slow moving machinery1 the formation of teeth preventing--in large measure--the jar or concussion noticeable in common spur gears4 ,in recent years the speed at which gearing is run has been greatly increased4 ,a striking instance is that of a pair of cast-iron helical wheels1 #f ft4 #c in4 diameter1 #ab in4 wide1 making #bbj revolutions per minute1 the speed of the pitch line being #d1cai feet per minute2 these wheels are running continuously and with little noise4 ,there is also a cut gear in a mill in ,massachusetts1 #cj feet in diameter1 and the speed of pitch line is #d1fgj feet per minute4 ,illustration3 ,fig4 #bgb4 ,an internal or annular gear wheel is one in which the faces of the teeth are within and the flank without the pitch circle1 hence the pinion operates within the wheel4 ,see fig4 #bgb4 ,in internal geared wheels there is almost an entire absence of friction and consequent wear of the teeth1 as compared to ordinary spur gearing4 ,fig4 #bgc shows a crown-wheel which has pin teeth which are fixed by one end only1 on its side face and gear into a trundle wheel4 ,illustration3 ,fig4 #bgc4 ,a trundle wheel has no teeth1 properly speaking4 ,instead of teeth1 it has pins as shown on illustration1 fig4 #bgc1 arranged like the rungs of a ladder between two walls4 ,see page #bja4 ,trains of ,gears4--,when two wheels mesh--that is1 engage with each other--as in fig4 #bfc1 one axle revolves in the opposite direction to the other2 but when internal gears mesh as shown in fig4 #bgb1 the shafts revolve in the same direction2 three or more gears running together are often called a train of gears4 ,maximum speed of gears under favorable conditions for safety is comparatively-- ,ordinary cast-iron wheels1 #a1hjj feet per minute4 ,helical cast-iron wheels1 #b1djj feet per minute4 ,mortise wood cog wheels1 #b1djj feet per minute4 ,ordinary cast-steel wheels1 #b1fjj feet per minute4 ,helical cast-steel wheels1 #c1jjj feet per minute4 ,cast-iron machine cut wheels1 #c1jjj feet per minute4 ,it is not1 however1 advisable to run gears at their maximum speeds1 as great noise and vibration are caused4 ,designing ,gears4 ,this section is introduced into the work for a double purpose2 #a1 as an exercise in drawing2 #b1 as a study in accurate measurements4 ,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 drawing4 ,some sample rules are given in the following pages to aid in calculations relating to gears1 and still others are given under the section 8,useful ,rules and ,tables0 at the end of the volume2 these are to be carefully studied4 ,to accurately divide the pitch circle of a gear wheel by hand requires both patience and skill4 ,on the accuracy of spacing lies the essential requisite of a good gear wheel4 ,the drawing in plate1 fig4 #bgd1 illustrates a pair of spur wheels1 shown in gear1 the office instructions for which being3 8,required1 a detail plan of a pair of spur wheels2 dimensions3 wheel1 #gf teeth1 #c inches pitch1 #g-;inch eye1 #f arms2 pinion1 #ai teeth2 scale1 #a inches #a foot40 ,the drawing1 as illustrated1 is the result of the above instructions1 all pencil lines being removed1 and this result is worked out as follows3 #gf teeth #c inches1 pitch #bff inches in circum4 #g ft4 #j in4 diam4 #c ft4 #f in4 radius2 with this measurement as represented on scale1 draw line ,p ,p on drawing4 ,this is called the pitch line4 ,draw next diameter line1 produce or extend this diameter line for pinion1 and with radius of #aj 7#ai teeth #c7 from pitch line of wheel1 draw pitch line of pinion4 ,take any point in this pitch line of wheel1 mark off #c inches as represented on scale1 mark this around the pitch line1 it will be the center of each of the #gf teeth2 then the breadth of thickness of each tooth 7 pitch #j4dge7 must be marked from these centers1 then mark from ,p ,l1 length of tooth to point 7 pitch #j4ce7 and ,p ,l to root 7 pitch #j4d71 draw circles for outside of teeth ,n and root of tooth ,o2 now with compass set to the pitch 7#c7 of the wheel1 draw the outer portion from pitch line of tooth4 ,the radius will center in the pitch line of next tooth where thickness of tooth has been marked2 after finishing outer portion of both sides of teeth1 set the compass from center of tooth with radius to the thickness marked on pitch line and draw the portion of tooth from pitch line to root4 ,now mark off with dividers and draw thickness of rim 7 pitch #j4e71 divide this line into six parts1 draw radii for centers of arms2 draw the bore hole #g and the thickness of metal for hub same as pitch4 ,on radii lines of arms1 draw the breadth of arm at rim 7 pitch and thickness of tooth71 increase in breadth approaching the center 7#a per foot71 draw the thickness of feather of arm 7 pitch #j4ce72 draw web on inside of rim 7 pitch #j4cge72 fill in arcs for the joining of arms in rim and hub 7radii pitch #j4h7 and feather to rim and hub 7radii pitch #j4cg74 ,proceed in similar manner1 completing the teeth of pinion1 and when pencil lines are all in1 ink the drawing1 erasing all needless lines4 ,p ,p shows the pitch line2 ,b1 thickness of tooth2 c1 breadth of space2 ,a1 the pitch2 ,e1 clearance at root2 ,n1 the addendum of tooth2 ,o1 the root of tooth2 ,h1 length of tooth from pitch line to point2 ,i1 length of tooth pitch line to root2 ,g1 whole length of tooth2 ,f1 thickness of rim2 ,j1 web or feather on rim2 ,k1 breadth of arm2 ,l1 thickness of feather2 ,m1 hub1 or thickness round the eye4 ,,note4--,it must be remembered that no fixed standard has ever been agreed upon for these proportions1 and workshops differ considerably in practice4 ,illustration3 ,fig4 #bgd4 ,the number of teeth1 their proportions1 pitch and diameter of pitch circle are frequently determined on the 8,manchester0 principle4 ,this system originated in ,manchester 7,eng471 and is now generally used in the ,united ,states for determining diameters and number of teeth1 which1 of course1 regulate speeds4 ,the principle is not applicable to large wheels1 but is limited in its application to small wheels1 or wheels having 8fine pitch10 as will be seen in the following explanation1 which is introduced as very useful and indispensable knowledge for the acquisition of the student in mechanical drawing4 ,illustration3 ,fig4 #bge4 ,the 8pitch0 of teeth has already been stated to be the distance from center of one tooth to the center of another on the 8pitch line10 measured on the chord of the arc4 ,in determining the number of teeth or pitch of wheels on this principle1 the pitch is reckoned on the diameter of the wheel1 in place of the circumference1 and distinguished as wheels of 8#d pitch10 8#f pitch10 8#h pitch10 etc4 ,in other words1 this means that there are four1 six1 or eight teeth in the circumference of the wheel for every inch of diameter4 ,in designing gears to transmit power the stress on a tooth is calculated2 it determines the breadth or width and also the thickness of the tooth on pitch line2 the space between the teeth is in proportion to the thickness of tooth1 and the thickness of both combined 7one tooth and one space71 measured on the pitch line or circle1 is the pitch of the wheel4 ,from the pitch all the proportions and measurements for the sizes and strength of the parts of the wheel are taken by rule1 and a symmetrical form is produced4 ,in machine drawing the practice is to represent wheels by circles only2 the teeth are never shown except on enlarged details and then only in very rare instances2 the circles drawn are always the pitch lines or the rolling points of contact of the wheels4 ,the addendum circle is seldom if ever used in practical drawing4 ,should it be necessary to show it in an exceptional case1 the circle would be represented by 8dotted0 line4 ,the shape of tooth and mode of constructing it1 as practiced in drawing offices1 differs from the true theoretical curve of the tooth1 although very minutely4 ,in all calculations for the speed of toothed gears the estimates are based upon the pitch line1 the latter standing in the same place as the circumference of a pulley4 ,to find the diameter of a gear-wheel multiply the number of teeth by the pitch1 divide by #c4adaf4 ,to find the pitch of a gear-wheel multiply the diameter by #c4adaf and divide by the number of teeth4 ,to find the number of teeth in a gear-wheel multiply the diameter by #c4adaf and divide by the pitch4 ,the breadth of wheels1 where practicable1 should be at least three times the pitch4 ,illustration3 ,fig4 #bgf4 ,fig4 #bgf shows a scale for proportions of teeth2 it is divided into tenths and used thus3 ,say wheel is #b pitch1 then from pitch circle to addendum will be #c tenths1 and from pitch circle to root of tooth will be #d tenths measured at the #b line on scale1 and so on4 ,the decimal proportions already given in example1 page #baj1 are adopted in many workshops4 ,many others use the proportions approved of by ,sir ,william ,fairbairn1 which are3 ,table of proportion of gears3 ,depth of tooth above pitch line 4#ce of the pitch4 ,depth of tooth below pitch line 4#dj of the pitch4 ,working depth of tooth 4#gj of the pitch4 ,total depth of tooth 4#ge of the pitch4 ,clearance at root 4#je of the pitch4 ,thickness of tooth 4#de of the pitch4 ,width of space 4#ee of the pitch4 ,the diameter of a wheel or pinion is invariably the diameter measured on pitch circle1 except it is specially described otherwise1 thus the diameter 8over all10 etc4 ,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 leaving1 as they rotate or roll together on their pitch circles4 ,the curve of teeth outside the pitch circle is called 8the face10 and the curve from pitch circle to root is called 8the flank40 ,the difference between the width of a space and the thickness of a tooth is called clearance or side clearance4 ,the play or movement permitted by clearance is called the backlash2 clearance is necessary to prevent the teeth of one wheel becoming locked in the spaces of the other4 ,wheels are in gear or geared together when their pitch lines engage1 i4 e41 when the pitch circles meet4 ,wheels to be geared together must have their teeth spaced the same distance apart1 or in other words1 of the same pitch4 ,the teeth of spur wheels are arranged on its periphery parallel to the wheel axis1 or shaft on which it is hung4 ,the teeth of a bevel wheel or bevel gears are always arranged at an angle to the shaft4 ,when the teeth of bevel gears form an angle of #de they are called miter wheels4 ,miter wheels to gear must be of equal sizes4 ,a crown wheel is a disc that has teeth which are on its side face2 that is1 teeth on a flat circular surface all parallel to the axis of the wheel4 ,a rack has teeth on a flat surface or plane all parallel to one another4 ,a gear cut by machine is called a cut gear4 ,it has teeth with less clearance than cast wheels1 which are not so true or perfect1 and therefore require more clearance4 ,a worm with even a light load is liable to heat and cut if run at over #cjj feet of rubbing surface travel4 ,the wheel teeth will keep cool1 as they form part of a large radiating surface2 the worm itself is so small that its heat is dissipated slowly4 ,a worm throws a severe end thrust or strain on its shaft4 ,steel ,gears4--,there is great economy in the use of cast-steel over cast-iron in gears2 the average life of the former is nearly twice as great as of cast-iron gears4 ,and1 apart from their longer life and efficiency1 there is less danger of breaking4 ,the most accurate teeth1 strongest and most uniform in wearing1 are to be found in steel gears cut from solid stock1 or made by cutters of proper shape4 ,fig4 #bge shows an elevation and a vertical section of a spur wheel4 ,from these views the various parts in spur gears can be better understood1 as they are represented here in combination1 and the wheel in its entirety4 ,,aa is the horizontal center line1 ,,bb1 ,,bb the vertical center lines1 ,,ii and ,,ii the pitch lines1 ,n thickness of tooth1 ,o space of tooth1 ,d total depth of tooth1 ,c breadth of face1 ,f diameter on pitch line1 ,p diameter over all1 ,g diameter of hub1 ,e diameter of hole1 ,h depth of hole1 ,l thickness of rim1 ,m thickness of web4 ,much has been and still is being written on gearing4 ,no general rule is followed by the writers2 the elementary principles given will enable the student to master spur gearing1 and bevel and combinations of many kinds of wheels will afterwards be found easier to delineate than the numerous lines seem to indicate4 ,illustration3 ,,working ,,drawings ,illustration3 ,fig4 #bgg4 ,working ,drawings4 ,from the 8plans0 made in the office are produced 8working drawings0--which represent in detail the work to be done to exact measurement and of material1 as indicated1 by the pattern-maker1 the foundry1 the forge1 the shop1 and finally1 by the erector of the completed mechanism4 ,how to satisfactorily fulfill the directions contained in these drawings1 representing only a part of the work1 so that it will fit1 with needed accuracy1 to all other parts of the design1 is the task before each separate worker4 ,it is by means of this division of the process of manufacture through these drawings1 that scores and hundreds of men can be employed at the same time upon a single engine or machine2 thus1 while handwork has been superseded by machines in many quarters1 the art of drawing has not been narrowed nor diminished1 for no drawings or designs have yet been made by machinery1 nor are they likely to be4 ,it is thus that a good designer and draughtsman 8projects0 or extends himself1 to the advantage of many fellow workers4 ,the drawing1 fig4 #bgg1 shows a simple form of pillar crane3 it consists of an upright cast-iron pillar1 which is bolted on a cap stone1 under which is the foundation plate not shown in the drawing2 the boom is of rolled steel1 supported by steel tie rods1 and provided with rollers at the base2 the hoisting gear is shown in broken lines and circles2 all as seen in the drawing4 ,illustration3 ,fig4 #bgh4--;,fig4 #bgi4 ,illustration3 ,fig4 #bhj4 ,figs4 #bgh1 #bgi and #bhj show a drawing of a 8hydraulic beam bending machine0 in three views2 fig4 #bhj is a plan1 fig4 #bgh is an end elevation1 and fig4 #bgi a side elevation1 and a portion of the latter in section shows the interior construction4 ,,note4--,these three views are a practical illustration of drawings for a machine of the following dimensions3 this machine has a bed #c #e feet in area1 with #bg holes in each side for the bending pins4 ,the frame and cylinders are made of cast iron1 the rams of machinery steel1 and the slides for holding the bending blocks1 of steel casting4 ,the distance between the bending blocks is #ag inches4 ,the cylinders are copper lined1 #h inches diameter1 and the rams have a #f-;inch stroke4 ,the rams1 which are independent and single acting1 are returned by counterweights placed as shown under the table4 ,the cylinders can be operated independently from either side of the machine by an arrangement of valves and levers4 ,the machine complete weighs about #g1ejj lbs4 ,illustration3 ,fig4 #bha4--;,fig4 #bhb4--;,fig4 #bhc4 ,the drawing1 page #bbb1 shows three views of a power punching press4 ,fig4 #bhb is a side elevation4 ,fig4 #bhc a front elevation4 ,fig4 #bha a vertical sectional view2 from these views the proportion1 general arrangement and disposition of the automatic devices can be easily understood2 it may be well to call particular attention to the automatic clutch on the top shaft and the tripping device4 ,illustration3 ,fig4 #bhd4 ,this drawing1 fig4 #bhd1 shows a side elevation in section of a self-adjusting piston-rod packing4 ,a is the gland1 ,b is the piston rod1 ,c is a brass sleeve which contains the packing ,d1 ,e is the cylinder cover1 ,f is a coil spring4 ,it will be seen that the spring ,f 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 follower4 ,all as shown in the drawing4 ,the drawing1 fig4 #bhe1 shows a sectional view of a large pulley fixed on a 8quill10 or hollow shaft3 the driving shaft passes through the hollow shaft and is attached to the friction clutch shown at the right-hand end2 this friction clutch drives the hollow shaft and pulley4 ,illustration3 ,fig4 #bhe4 ,fig4 #bhf shows the mechanism1 called the link-motion1 employed to reverse an engine1 or to enable it to be run in either direction4 ,many forms of link-motion have been devised1 but the ,stephenson form1 as shown in the figure1 is1 however1 the one in almost universal use4 ,illustration3 ,fig4 #bhf4 ,this drawing shows shading and the mode of figuring the parts for identification4 ,illustration3 ,fig4 #bhg4--;,fig4 #bhh4--;,fig4 #bhi4 ,figs4 #bhg to #bhi represent a bumping-post for the end of railway tracks1 reproduced on an enlarged scale from the columns of the ,engineering ,news4 ,in addition to the lettering and dimensions1 admirably shown in the drawings1 the following description is appended to show how printed text and mechanical drawings mutually aid in practical--or commercial--usage4 ,the unique feature of the arrangement shown1 is that the center line of the post does not coincide with the track1 thus adapting itself to the nature of the blows of a car-bumper1 as received in the single-post style of the mechanism4 ,,bumping ,,post ,,for ,,railway ,,tracks4 ,the post is a #ae-;in4 steel ,i-beam1 resting on a base plate -in4 thick1 and supported by anchor rods #a ins4 diameter1 with upset ends held by nuts on a heavy forging bolted to the top of the post4 ,these rods extend forward and outward to clear the rails1 and then pass vertically through a #d #f-;in4 angle iron crosstie1 and an ordinary wooden tie1 extending down to an anchor block or deadman buried in the ground #f ft4 below the top of the rail4 ,vertical braces or spreaders are fitted between the anchor timber and a longitudinal timber under the ties1 so as to prevent the loosening of the anchor rods when the post is struck4 ,the rods are held in position against the rails by steel forgings bolted to the rail with #a-;in4 turned bolts4 ,an oak striking block1 #ab #ab ins41 #c ft4 long1 is bolted between angle iron brackets on the face of the post4 ,illustration3 ,fig4 #bij4 ,front ,view4 ,fig4 #bia4 ,side ,view4 ,scale1 #c in4 #a ft4 ,to ,read ,working ,drawings4 ,one of the advantages resulting from a knowledge of practical draughting is1 that it enables a mechanic to read a drawing when given him as a guide for his work4 ,it is getting every day more general among draughtsmen to figure exactly and minutely every part of their drawings which are made to a scale4 ,drawings are almost always made 8finished size10 that is1 the dimensions are for the work when it is completed4 ,consequently all the figures written on the different parts indicate the exact size of the work when finished1 without any regard to the size of the drawing itself1 which may be made to any reduced and convenient scale4 ,even in full size drawings this system of figuring is not objectionable4 ,it is a system which should be followed whenever a drawing is made 8to work to10 for it allows the workman to comprehend at a glance the size of his work and the pieces he has to get made4 ,figuring makes a drawing comprehensible even to those who cannot make drawings4 ,a working drawing should be made1 primarily1 as plain as possible by the draughtsman2 second1 the workman should patiently and carefully study it1 so that it is thoroughly understood4 ,in studying a drawing1 the object it is intended to represent should be made as familiar as possible to the mind of the student1 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 in1 that he may see1 mentally1 the whole4 ,the following is a description of reading drawings when dimensions are not figured4 ,here we have a piece of machinery represented by fig4 #bij1 and the information we have is that it is to scale1 three inches one foot4 ,now1 with scale and dividers1 we can arrive at its actual dimensions4 ,measurements should be first taken with the dividers from the drawing1 and then the dividers applied to the scale to which the drawing is made2 this scale is always marked on the working drawing2 if the dividers are set to the length of the base of the example1 fig4 #bij1 they will measure1 on an ordinary two-foot rule1 three and three-fourths inches1 but if applied to the three-inch scale they will read one foot three inches1 the actual length of the part2 the 8reading0 is from the scale2 thus1 in both figures the drawings are 8three-inch scale40 ,now1 #c inches is one-fourth of a foot1 hence #c #d #a ft4 #c in41 the full size1 and so on for all parts of the drawing4 ,fig4 #bia shows a side view of the 8steady rest10 illustrated in front elevation1 fig4 #bij2 from the scale as before we get the sizes2 the two views combined give length1 breadth and thickness of the parts4 ,in some figures it is necessary to show end views1 also section views1 to enable all measurements to be read from the drawing4 ,illustration3 ,,patent ,,office ,,drawings ,patent ,office ,drawing ,rules4 ,u4 ,s4 ,,patent ,,office ,,rules4 ,,as ,,applied ,,to ,,preparation ,,of ,,drawings4 ,each applicant for a patent is required by law to furnish a drawing of his invention whenever the nature of the case admits of it4 ,the drawing must be signed by the inventor or the name of the inventor may be signed on the drawing by his attorney-in-fact1 and in either case must be attested by two witnesses4 ,the drawing must show every feature of the invention covered by the claims4 ,when the invention consists of an improvement on an old machine1 the drawing must exhibit1 in one or more views1 the invention proper1 disconnected from the old structure1 and also1 in another view1 so much only of the old structure as will clearly show the connection of the invention with the old machine4 ,several editions of the patent-drawings are printed1 the smallest of which is about #c #d inches1 so that the drawing must be so made that it will stand a reduction of about one-fourth4 ,this work is done by the photo-lithographic process1 and therefore the character of the original drawing must be brought as nearly as possible to a uniform standard of excellence suited to the requirements of the process4 ,,note4--,these rules will be found most useful to many readers of this work--hence their introduction at this point4 ,nearly #ej1jjj patents are 8applied for0 in the ,united ,states every year4 ,the following rules are given by the ,patent ,office for guidance3 #a4 ,drawings must be made upon pure white paper of a thickness corresponding to three-sheet ,bristol board4 ,the surface of the paper must be calendered and smooth4 ,india ink alone must be used1 so as to secure perfectly black and solid lines4 #b4 ,the size of a sheet on which a drawing is made must be exactly #aj #ae inches4 ,one inch from its edges a single marginal line is to be drawn1 leaving the 8sight0 precisely #h #ac inches4 ,within this margin all work and signatures must be included4 ,one of the shorter sides of the sheet is regarded as its top1 and measuring downwardly from the marginal line1 a space of not less than #a inches is to be left blank for the heading of title1 name1 number and date4 #c4 ,all drawings must be made with the pen only4 ,every line and letter1 signature included1 must be absolutely black4 ,this direction applies to all lines1 however fine1 to shading1 and to lines representing cut surfaces in sectional views4 ,all lines must be clean1 sharp1 and solid1 and they must not be too fine or crowded4 ,surface shading1 when used1 should be open4 ,sectional shading should be made by oblique parallel lines about of an inch apart4 ,solid black should not be used for sectional or surface shading4 #d4 ,drawing must be made of the fewest lines possible1 consistent with cleanness4 ,the plane upon which a sectional view is taken should be indicated by a broken or dotted line4 ,heavy lines on the shade side of objects should be used1 except where they tend to thicken the work and obscure letters of reference4 ,the light is always supposed to come from the upper left hand corner at an angle of #de degrees4 #e4 ,the scale to which a drawing is made should be large enough to show the mechanism without crowding4 ,the number of sheets used must never be more than is absolutely necessary4 ,illustration3 ,fig4 #bib4 #f4 ,the different views should be consecutively numbered4 ,letters and figures of reference must be carefully formed4 ,they should1 if possible1 measure at least one-eighth of an inch in height4 ,if the same part of an invention appears in more than one view of the drawing it must always be represented by the same character4 #g4 ,the signature of the inventor is to be placed in the lower right-hand corner of each sheet1 and those of the witnesses at the lower left-hand corner4 ,the title should be written with pencil on the back of the sheet4 ,drawings should be rolled for transmission1 never folded4 ,on page #bce1 fig4 #bib exhibits a reproduction of a patent office drawing1 used in connection with specification papers in an application for a ,united ,states patent4 ,,english ,,practice4 ,the rules for patent drawings in ,england are practically the same as in the ,united ,states2 the paper sizes are1 however1 different4 ,they must be on sheets of one of the two following sizes 7the smaller being preferable71 #ac inches at the sides by #h inches at the top and bottom1 or #ac inches at the sides by #af inches at the top and bottom1 including margin1 which must be one-half an inch wide4 ,if there are more figures than can be shown on one of the smaller-sized sheets1 two or more of these sheets should be used in preference to employing the large size4 ,when an exceptionally large drawing is required1 it should be 8continued0 on subsequent sheets4 ,there is no limit to the number of sheets that may be sent in4 ,illustration3 ,,practical ,,points ,illustration3 ,fig4 #bic4 ,see page #bdd4 ,useful ,hints and 8,points40 ,many of these 8points0 are repetitions1 with but little variation from the way they have been previously stated2 they are thus repeated to emphasize their practical worth4 ,a good draughtsman leaves his work in such a state that any competent person can without difficulty ink in what he has drawn4 ,the criterion of a good set of drawings is that with a properly prepared specification they are complete in themselves and require no explanation4 ,a 8break0 in a figure or object in a drawing is shown in rough irregular lines1 as in fig4 #acd1 on page #aca2 this is useful when the paper is not large enough to show the whole4 ,never use a sloping line in writing fractions on a drawing4 ,the objection arises from the fact that such a dimension as #a1 if written with the inclined line1 unless very distinctly executed1 may be read as 4 ,in inking do not draw the lines further than you wish them to go1 but in penciling it is well to extend the lines1 free up4 ,never use a scale for a ruler4 ,do not overload the pen with ink4 ,having filled the pen1 nearly close the nibs and try the width of the line on a piece of paper or the margin of the drawing4 ,never refill or lay the pen aside without first cleaning it4 ,the application of the science of geometry to the drawing-board is absolutely necessary to success1 for the reason that the whole fabric of mechanical drawing rests on the principles of geometry1 which is well termed the science of measurements4 ,section lines should be the last inked and always without previous penciling4 ,center lines are necessary in working drawings4 ,in choosing ,t-squares1 care should be exercised to see that the head slides up and down the left-hand side of the board easily1 and that when pressed against the board with the left hand there is no 8slogging0 of the blade up or down1 or in other words1 that the head is bearing firmly for its whole length against the board4 ,the best place for the title of a drawing is said to be the upper left-hand corner2 this facilitates the filing of the sheet4 ,never use a soft pencil except for finishing in shadow lines4 ,the rubber should always be kept clean4 ,great care should be taken to keep drawing boards out of the way of heat or damp1 as these cause the wood to warp4 ,circles and curves are to be 8inked in0 before straight lines4 ,first ink the smallest and afterwards the larger curves4 ,do not press heavily on the pencil so as to cut the paper1 but draw lightly1 so that the mark can be erased and leave no trace1 especially if the drawing is to be inked4 ,the draughtsman should commence his work at the top of the paper1 keeping the lower part covered over until he needs to use it4 ,shade lines should be avoided in all working drawings1 as their use interferes with accurate measurements4 ,to make ink stick to the tracing cloth1 with a woolen cloth rub some powdered chalk or pounce over the surface on which the ink lines are to be drawn1 then wipe the surface clean and use a good quality of ink4 ,for striking small circles a small bow pen should be used4 ,to fix lead pencil marks on sketches so that they cannot be readily erased1 sponge them with milk carefully skimmed1 then lay blotting paper over them and iron with a hot flat-iron4 ,to have the ink preserve its fluidity and to keep out all dirt and dust1 keep the cover on the ink slab2 the mistake is often made of putting too liberal a supply of water in ink well1 which causes a waste of both time and ink2 no more should be prepared than to meet immediate requirements4 ,always draw on the right side of the sheet1 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 paper2 note which side is the smoothest and has the least number of blemishes on it2 this is the right side to draw on4 ,as to sharpening pencils1 it is always best to cut a chisel point on the pencil used for drawing1 and put a circular point on the pencils in the bow pencil and pencil leg4 ,the chisel point makes a finer line and lasts much longer than a round point4 ,the varnish used in many large drawing-rooms is simply white shellac dissolved in alcohol2 it requires a little experience to mix these to a proper consistency1 but this is soon acquired4 ,never sharpen your pencil over the drawing4 ,a center line of a drawing is the line upon which the figure is to be constructed2 the center line is the first line to be drawn4 ,the ,t-square belongs to the left side of the drawing-board1 and is operated by the left hand4 ,the right hand should be kept free for the purpose of picking up pencil1 pen and bows1 adjusting and marking off4 ,the left hand controls the ,t-square and the triangle that slides along the upper edge of the square2 the right hand is for the instruments4 ,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 does4 ,avoid rubbing out and constantly cleaning the drawing with ,india rubber2 if wrong lines are made or it is desired to make alterations1 the part to be changed should be rubbed out and completely re-drawn4 ,when using the bows see to it that the steel-pointed leg that is put down first on the paper1 to secure a center for a curve or a circle1 is a trifle longer than the pencil or pen leg4 ,to clearly indicate the position of a center which is to be used again1 lightly pencil a small circle about it2 never put the point of a pencil in the center hole to enlarge or blacken it2 the prick point made by the dividers and needle points should be no more than can be just seen1 hence the circle to be made as advised above4 ,illustration3 ,fig4 #bid4 ,be particular in having the legs of the dividers exactly the same length1 and sharp1 so that in pricking off distances1 and dimensions1 and centers1 the indent or hole made in the paper is as small as possible4 ,the term 8plane0 means a perfectly flat surface2 that is1 something which has length and breadth but no thickness4 ,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 8finished10 tool-finish1 or 8faced10 according to the degree of finish required4 ,the single letter f is frequently used4 ,avoid fingering the drawing sheet as much as possible2 in pointing to any part of the drawing use a pencil and not the finger4 ,remember that a drawing is made to be read4 ,the skill in inking does not depend on the fineness of the line1 but on its clearness4 ,a soft pencil should never be used on a mechanical drawing unless in rare cases when it is used for pencil shading2 the hardness or softness of pencils is denoted by letters4 ,never ink any portion of a drawing until the penciling is entirely finished4 ,stretching or pasting the paper to the board is very seldom resorted to1 for the reason that the mechanical drawings are to scale and the paper is natural when pinned to the board and more correct than if under a strain4 ,mechanical drawings are always required in practice right away1 and time would be wasted and lost in damping and pasting and drying again4 ,a working drawing1 whether made to a scale or not1 must have all the dimensions plainly written upon it1 for a workman should never be compelled to measure a drawing4 ,in marking off distances1 centers1 etc41 a fine needle point is useful2 the hole should not be punctured through the paper1 merely a prick point1 so that it will leave an impression1 which will not be obliterated by the use of rubber2 drawing-pens are often equipped with such a needle point in the end of the handle1 that is visible only when the pen is unscrewed from the handle2 but in the absence of one of this kind the point of the divider leg will be of use4 ,mechanical construction drawings represent a large amount of mental and manual work1 as well as a considerable cost in money2 hence1 they are of value quite as much as property which has been acquired by the expenditure of either labor or capital4 ,it is wise to keep copies of original designs and sketches1 as well as data and formul1 for record and comparison4 ,the best system for keeping drawings is to make them of certain standard sizes1 and to keep them flat1 unrolled1 in drawers1 numbered1 lettered and labeled4 ,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 diameter4 ,these are shown in fig4 #bid4 ,a puncture can be made near the top and1 when a new drawing or blue-print is inserted in this cylindrical case1 a cardboard tag can be looped through the puncture4 ,this label will give the title and number of drawings in that case4 ,a manuscript book methodically and neatly kept should tell immediately the number of the drawing and the case4 ,fig4 #bic is good for practice in line drawing and also as an optical illusion4 8,you look and are deceived4 ,at first glance you say1 #8,of course1 those two lines are curved4' ,you are mistaken4 ,they are exactly parallel4 ,in order to prove this hold them up edgewise to the eye4 ,it is1 of course1 the subsidiary lines which lead the vision astray4 ,it is a case of first impressions being quite wrong40 ,illustration3 ,,linear ,,perspective ,illustration3 ,fig4 #bie4 ,linear ,perspective4 ,it should be mentioned that this subject is outside the limits of mechanical drawing1 which only deals with objects that can be measured1 projected or dimensioned to an accurate scale4 ,but1 in rounding out the more formal subjects it is well to look a little outside the rigid lines of mechanics into the methods of nature1 for no system of teaching drawing is complete that does not include some explanations for sketching from nature--the objects being always around the student1 the eye always clear to see and the hand only needing the training to make permanent the impressions received4 ,the word perspective means to see through2 the word perspective being derived from the ,latin word perspicere1 to look through1 hence1 perspective is a science which teaches us to see correctly and enables us to represent the appearance of anything we may wish to draw2 care should be taken in perspective drawing1 to select objects interesting in themselves1 and the best specimens of their class1 so as to cultivate taste1 while they at the same time afford useful and instructive drawing lessons4 ,the meaning of the term linear perspective is a line view2 the previous examples have been composed of surfaces placed fronting the eye2 perspective is the science which treats of the changes of form produced by viewing them in various oblique positions4 ,the slightest alteration of position will change the appearance of an object2 this can be easily shown--for illustration take a coin1 the actual shape of which is a perfect round2 or1 strictly speaking1 a circle4 ,if we take the coin between the thumb and the first finger1 holding it in an upright position1 and exactly facing the eyes1 as in ,fig4 #bif1 it appears of its true form1 viz41 a circle4 ,if we alter its position1 balancing it upon the thumb1 in a level position1 with its edge directly opposite the eye1 as in ,fig4 #big1 its appearance is changed1 and what we know to be really a circle1 appears to us as a straight line4 ,illustration3 ,fig4 #bif4--;,fig4 #big4--;,fig4 #bih4 ,now1 still balancing the coin upon the thumb1 but changing its position with regard to the eye1 by holding it a little lower than in the last position1 that is slightly beneath the level of the eye1 as in fig4 #bih1 we see both the edge and the surface1 the coin now appearing neither a circle nor a straight line1 but a curved figure of an elliptical form4 ,thus the same coin held in three different positions has assumed three different shapes4 ,let us take two coins of the same size1 holding 7in the position shown at fig4 #bif7 one in each hand4 ,now1 closing one eye1 7which will make the experiment more clear71 hold one coin out at arm's length1 and the other at about the distance of a foot from the eye4 ,on comparing them1 we find that the coin which is further from the eye appears less than the nearer one4 ,we know that the coins are really equal in size1 yet one appears smaller than the other4 ,we thus see that when we change the position of an object1 we have as a consequence a change of appearance2 also that the change of appearance may affect both the shape and the size of the object4 ,these diversities of appearance may be remarked in everything around us4 ,we can observe them in the street by looking at a building from different points of view1 or by comparing the apparent sizes of the street lamps2 in the railway station1 by watching the arriving or departing train2 and at sea1 by noticing the vessels as they approach1 or as they retire1 ultimately vanishing from our sight in that line where the sea and sky appear to meet4 ,all these interesting variations of appearance are in strict accordance with the laws of ,,geometry and ,,optics4 ,the former subject has been enlarged upon beginning with page #ha of this work1 where a line1 a point1 an angle1 etc41 are defined2 other terms are explained at page #da and the following pages2 to these we add a few definitions essential to the subject4 ,a ,,plane is a surface which is perfectly even and flat2 to use a familiar illustration1 a plane is like the surface of a sheet of plate glass2 recollect particularly1 that a surface which is at all curved1 is not a plane4 ,the ,,ground-,,plane is the plane on which we stand2 the base-line is an imaginary line passing through the middle of the feet as we stand square and erect2 and the vertical plane is supposed to stand on the base-line and perpendicular to it4 ,illustration3 ,fig4 #bii4--,see page #bee4 ,planes are parallel to each other when they are throughout their entire surfaces the same distance apart4 ,illustration3 ,fig4 #cjj4 ,,the ,,perspective ,,plane is an upright square of glass1 usually framed like a picture1 with a base1 so that it can stand up alone4 ,this is placed between the eye of the spectator and the subject to be drawn1 and as the drawing is sometimes made directly upon it1 it is sometimes called the ,picture or the ,plane of the ,picture4 ,illustration3 ,fig4 #cja4 ,,horizontal means perfectly level1 like the surface of still water4 ,we must be careful to understand perfectly the difference between the terms 8level0 and 8even0 or 8flat40 ,a surface may be even or flat1 without being level4 ,thus the wall is even and flat1 but it is upright1 not level2 level means a fixed1 constant position4 ,in fig4 #cja a house is shown in perspective in which the line ,h ,l is the line of the horizon and ,v ,p is the1-- ,,vanishing ,,point4--,the vanishing point is familiarly represented by the rails on a trolley track on a straight road1 which seem to approach each other in the distance1 as shown in fig4 #cjb at ,v ,p4 ,illustration3 ,fig4 #cjb4 ,all parallel lines seen in perspective appear to meet in the same vanishing point4 ,the value of the vanishing point may be seen in the view of a wooden house1 fig4 #cjc1 where it 7,v ,p7 gives direction to the retiring lines of the roof1 side planks and door4 ,illustration3 ,fig4 #cjc4 ,,point ,,of ,,sight4--,this is that point in the eye where the lines or rays from the object cross each other1 as shown at ,p in fig4 #cje1 also in fig4 #bii at ,s4 ,,vertical means perfectly upright4 ,if we attach a piece of thread to a weight1 a small piece of lead for example1 and hold the thread with the lead hanging downwards1 the thread will fall in an upright or vertical position4 ,,parallel lines are said to be parallel to each other when they are throughout their whole lengths the same distance apart4 ,,perpendicular4 ,when one straight line1 meeting another1 makes the angles at the point of contact equal1 each of the angles is called a right angle1 and the lines are said to be perpendicular to each other4 ,remember especially that perpendicular and vertical have not the same meaning4 ,vertical means an unvarying upright position4 ,perpendicular means that one line or plane meets another line or plane at right angles4 ,the fig4 #bie on page #bdf is a study in perspective1 showing a water reflection4 ,as rays from every visible part of the object are reflected1 all following the same law1 the reflection will appear to the eye inverted1 and of the same size as the object4 ,the arch itself forms the upper half of a hollow cylinder1 and the reflection forms the lower half4 ,the reflection shows much more of the interior of the arch than can be seen directly4 ,the leaning tree1 the boy fishing1 and the receding banks1 all are seen in accordance with the laws of reflection and perspective4 ,,the ,,horizontal ,,line1 ,,the ,,point ,,of ,,sight ,,and ,,the ,,vanishing ,,points are the principal items4 ,these should be studied in every room and during every walk1 and the more pleasing accidents of form stored in the mind or committed to paper for future use4 ,illustration3 ,fig4 #cjd4 ,,optics1 the science of sight1 gives us the following laws3 #a4 ,that we see by the agency of light4 #b4 ,that light passes from objects to our eyes4 #c4 ,that light travels in straight lines1 which are called ,visual ,rays4 ,the human eye may be briefly described as a chamber of a spherical or globular form1 with a circular opening in front4 ,this circular opening is called the pupil1 and through it the visual rays pass to the interior of the eye4 ,the visual rays1 passing from space in all directions through the small pupil1 are received upon what may be called the interior wall of the globular chamber forming the eye 7see fig4 #cje74 ,this interior wall is called the retina1 and upon it the impressions of external objects are received1 just as they are received upon a screen in a dark chamber4 ,these impressions are conveyed by the optic nerve from the retina to the brain4 ,in front of the pupil is a segment of a small sphere1 composed of the cornea and the aqueous humor1 both of which are transparent1 and from their shape and density have a convergent effect upon the rays passing through them4 ,behind the pupil is the transparent crystalline lens1 which1 from its shape and its elasticity1 is a powerful agent in aiding the convergence of the rays1 and in bringing objects at various distances to a clear focus upon the retina4 ,illustration3 ,fig4 #cje4 ,the pupil has the power of contraction and dilation1 which is influenced by the quantity of light entering the eye1 but when it is dilated to the utmost its size is very small in comparison with the great chamber forming the body of the eye4 ,in fig4 #cje we have a rough sectional diagram of the eye and an object in front of it4 ,this object1 an arrow1 is seen by means of the visual rays proceeding from it1 the principal two of which are shown4 ,the visual ray from ,a passes through the pupil and is received upon the retina at a4 ,in the same way the visual ray from ,b passes through the pupil and is received upon the retina at b4 ,it will thus be seen that the impressions or images received upon the retina are inverted2 but1 by long reason and experience1 the mind has acquired the habit of determining the real positions of objects1 and does not1 though the image is so received1 imagine them to be upside down4 ,it will also be observed1 in the same way1 that that portion of an object which is upon the right will be pictured upon the retina upon the left1 and vice versa1 but the mind1 for the reasons before stated1 never imagines the object to be reversed4 ,this fact is another proof that1 as mentioned at the commencement of our study1 to see accurately is a matter of education and practice4 ,and first of ,optics2 it was asserted1 page #beb1 that we see by the agency of light which passes from objects to our eyes in straight lines which are called ,visual ,rays4 ,we see by the agency of light1 as all objects1 except such as may be styled self-luminous1 when placed in a dark chamber are not perceivable by us1 except by touch1 smell or hearing2 we cannot see them2 they are invisible4 ,but when1 by removing a shutter or igniting a flame1 we introduce something to the chamber which was not present when the chamber was dark1 we become at once conscious of the appearance of the object1 we perceive it by the sense of sight4 ,this something which must always be present to enable us to see1 is called ,light2 all objects are made visible to the sense of seeing by its agency4 ,without light1 natural or artificial1 it would be impossible to distinguish one object from another4 ,illustration3 ,fig4 #cjf4 ,that the ,visual ,rays pass from objects in straight lines to the eye may be proved by the following experiment 7see fig4 #cjf73--,pierce two screens with a large pin1 and place them so that the holes are in a straight line with a flame1 as the light of a candle or lamp4 ,on fixing the eye to one of these holes we are able to see the flame2 but if we slightly move the flame1 one of the screens1 or the eye1 the flame is no longer visible4 ,to be visible1 the flame1 the holes in the screens1 and the eye must all be in the same straight line4 ,see fig4 #cjf4 ,in fig4 #bii the picture plane is represented by the rectangle ,w ,x ,y ,z4 ,although the picture plane is here shown as a rectangle1 it may be of any shape or of any size4 ,the observer is at ,s1 looking through the picture plane at the cross ,r ,c ,o ,h4 ,the observer is standing upon a horizontal surface1 which is called the ground plane4 ,if we are in a room1 the window may be called a picture plane and the floor a ground plane4 ,the picture plane rests1 as it were1 upon the ground plane1 in a line which passes from ,y to ,z4 ,the two planes meet or intersect in this line1 which is called the ground line4 ,the ground line is sometimes called the picture line1 or the measuring line4 ,the visual rays1 by means of which the observer sees the cross1 will1 in their course from it to the eye1 pass through the picture plane4 ,these visual rays will intersect the picture plane in a number of points1 and if we mark the true positions of these points the result will be a perspective image of the cross4 ,the rays are shown passing from the cross to the eye of the observer1 and meeting the picture plane in points r1 c1 o1 h2 r being joined to o1 and c to h1 we have the perspective image of the cross as it would appear to the observer at ,s4 ,of course an infinite number of rays proceed from the cross to the eye of the observer2 but it is quite evident that we need only consider those proceeding from the extremities of the object4 ,scale or ,approximate ,perspective4 ,real1 or true perspective1 represents the object exactly as it is seen in nature1 where the parts that are far away from the eye of the observer appear smaller than those nearby4 ,occasions arise1 however1 in practical life1 with its numerous phases of industrial requirements1 where the convenience of showing the complete form of the object in a single view might preferably be coupled with the convenience of scale dimensions4 ,this has led to a modified perspective1 that sacrifices some of the accuracy in the appearance of the object to gain the advantage of scale dimensions2 this form of perspective may be distinguished by the name--approximate or scale perspective--which does not represent the object exactly as seen in nature1 but where those parts that are afar off are shown of the same size as those that are near by1 and where the lines that run out into space are parallel to each other and do not converge into a vanishing point4 ,to represent an object in perspective1 the horizon and the point of vision will have to appear in the drawing as the fundamental starting points4 ,three dimensions are distinguished for the fixing of an object in space from a certain reference point4 ,they are height1 breadth and thickness1 and are in their direction square to each other4 ,the height is the fundamental direction1 being derived from the direction of gravity1 that invariably extends to the center of the earth4 ,all directions in the perspective determination of an object are parallel to these4 ,vertical lines and planes point toward the center of the earth1 while horizontal planes1 including the directions of breadth and thickness1 are square to the vertical direction4 ,in this1 the principal visual ray extends in the direction of thickness4 ,for a clear understanding of perspective1 it must be firmly fixed in mind1 that for each prominent point of the object behind the picture plane1 a corresponding point lies in the picture plane1 in that position where a straight line or ray of sight that is going from the eye to the point of the object1 cuts through the picture plane4 ,suppose we could replace these rays of sight by thin1 visible threads of wire that would go through little holes in the picture plane1 we could then walk around this bundle of rays1 and by looking at it from three different directions1 we would get three different views of it4 ,we may look upon it from the top1 from the side or from the end1 where the bundle of rays all concentrate in the eye of the observer4 ,illustration3 ,fig4 #cjg4 ,figs4 #cjg and #cjh show1 in two cases1 how these three views would appear4 ,the end views are those where the perspective picture appears on the plane1 while the top and side views only show where the rays intersect the picture plane4 ,the top view shows how far1 for example1 point ,a is distant from a vertical line ,o ,z1 while the side view shows how far point ,a is below horizontal line ,o ,x1 which is at the same height above the ground as the eye of the observer1 ,o4 ,thus1 all points of the cube can be located on the picture plane1 and the outlines of the cube reproduced in perspective4 ,illustration3 ,fig4 #cjh4 ,modified arrangements are shown in figs4 #cji and #caj for parallel and angular perspective4 ,illustration3 ,fig4 #cji4 ,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-line1 which latter is the intersection of the picture plane with the level ground of the end or perspective view4 ,at the same time the eye of the observer is in one and the same vertical line for both views1 two vanishing points may be found in the horizon outside of the principal visual ray4 ,to find the position of these two vanishing points in the picture plane1 the modified top view1 fig4 #caj1 is used4 ,illustration3 ,fig4 #caj4 ,as all lines that end in a vanishing point must be parallel in reality1 this parallelism may be seen in the top view and lines through the eye of the observer1 parallel to the directions of the main lines of the object1 will cut the picture plane at the vanishing points4 ,through these two vanishing points the directions of two sets of lines are found1 the starting points of which are determined from the plane of measurement4 ,the third set of lines1 being vertical1 also appears vertical and parallel in the picture4 ,the position of each vertical line is found in the top view1 where the light rays from the observing eye to the ends of the vertical lines intersect with the picture plane4 ,projecting these points down upon the rays to the vanishing points produces the vertical lines in the picture4 ,for example1 in fig4 #caa1 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 object4 ,illustration3 ,fig4 #caa4 ,in fig4 #cab the eye of the observer is first placed directly opposite the object1 then it sees the object to the left but a short distance away1 while in the third figure the observer is farther away from the object4 ,in each case the picture plane and plane of measurement is at the front face of the cube4 ,illustration3 ,fig4 #cab4 ,illustration3 ,fig4 #cab 7second part74 ,for such simple objects1 it is not necessary to draw the top view at all4 ,the only reminder of the top view is the eye or point of vision1 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 ,m1 which is1 in this suppressed reproduction1 absolutely necessary1 in order to find the apparent position of the real corners behind the picture plane4 ,so far1 only square or sharp-cornered objects have been represented in perspective4 ,it is evident1 however1 that round objects can also be shown in linear perspective1 placing reference lines on the object and representing these as if they were real lines4 ,a cylinder is thus shown in fig4 #cac of which the end planes will appear very distinctly in sharp outlines4 ,illustration3 ,fig4 #cac4 ,vertically1 only the outlines of the cylinder1 as contrasted against space1 will appear as distinct outlines1 while the reference lines will not appear and are therefore shown only as dotted lines4 ,fig4 #cad shows the approximate or scale perspective with all the axes drawn and the corresponding angles and scales marked4 ,the outlines of the object running in these directions appear all parallel to the axes4 ,the approximate or scale perspective completely avoids all the difficulties of choosing a point of sight1 of having several views1 vanishing points and measurement points1 and thus offers a representative view1 with a great saving of time and labor4 ,particularly for mechanical purposes1 where an artistic impression is not called for1 it presents a distinct advantage over the true or real perspective4 ,illustration3 ,fig4 #cad4 ,illustration3 ,,tables ,,and ,,index ,illustration3 ,,mariners' ,,compass4 ,useful ,tables for ,draughtsmen4 ,,table ,,of ,,decimal ,,equivalents4 #hths1 #afths1 #cb;ds and #fdths of an ,inch4 #hths4 4#abe 4#bej 4#cge 4#ejj 4#fbe 4#gej 4#hge #afths4 4#jfbe 4#ahge 4#cabe 4#dcge 4#efbe 4#fhge 4#habe 4#icge #cbnds4 4#jcabe 4#jicge 4#aefbe 4#bahge 4#bhabe 4#cdcge 4#djfbe 4#dfhge 4#ecabe 4#eicge 4#fefbe 4#gahge 4#ghabe 4#hdcge 4#ijfbe 4#ifhge #fdths4 4#jaefbe 4#jdfhge 4#jghabe 4#ajicge 4#adjfbe 4#agahge 4#bjcabe 4#bcdcge 4#bfefbe 4#bifhge 4#cbhabe 4#ceicge 4#cijfbe 4#dbahge 4#decabe 4#dhdcge 4#eaefbe 4#edfhge 4#eghabe 4#fjicge 4#fdjfbe 4#fgahge 4#gjcabe 4#gcdcge 4#gfefbe 4#gifhge 4#hbhabe 4#heicge 4#hijfbe 4#ibahge 4#iecabe 4#ihdcge ,,table ,,of ,,decimal ,,equivalents ,of ,millimeters and ,fractions of ,millimeters4 mm4 ,inches4 4#jjjgi 4#jjaeg 4#jjbcf 4#jjcae 4#jjcid 4#jjdgb 4#jjeea 4#jjfcj 4#jjgji 4#jjghg 4#jjhff 4#jjide 4#jajbd 4#jaajb 4#jaaha 4#jabfj 4#jacci 4#jadag 4#jadif 4#jaege 4#jafed 4#jagcb 4#jahaa 4#jahij 4#jaifi 4#jbjdg 4#jbabf 4#jbbje 4#jbbhc 4#jbcfb 4#jbdda 4#jbebj 4#jbeih 4#jbfgg 4#jbgef 4#jbhce 4#jbiac 4#jbiib 4#jcjga 4#jcaej 4#jcbbh 4#jccjg 4#jcchf 4#jcdfe 4#jcedc 4#jcfbb 4#jcgja 4#jcghj 4#jcheh #a 4#jcicg #b 4#jghgd #c 4#aahaa #d 4#aegdh #e 4#aifhe #f 4#bcfbb #g 4#bgeei #h 4#cadif #i 4#cedcc #aj 4#cicgj #aa 4#dccjg #ab 4#dgbdd #ac 4#eaaha #ad 4#eeaah #ae 4#eijee #af 4#fbiib #ag 4#ffibi #ah 4#gjhff #ai 4#gdhjc #bj 4#ghgdj #ba 4#hbfgg #bb 4#hffad #bc 4#ijeea #bd 4#iddhh #be 4#ihdbe #bf #a4jbcfb #aj mm4 #a ,centimeter #j4cicg inches4 #aj cm4 #a ,decimeter #c4icg #aj dm4 #a ,meter #ci4cg #be4d mm4 #a ,english ,inch4 ,,rules ,,relative ,,to ,,the ,,circle4 ,the circle contains a greater area than any other plane figure bounded by an equal perimeter or outline4 ,,to ,,find ,,circumference-- ,multiply diameter by #c4adaf4 ,or divide diameter by #j4cahc4 ,,to ,,find ,,diameter-- ,multiply circumference by #j4cahc4 ,or divide circumference by #c4adaf4 ,,to ,,find ,,radius-- ,multiply circumference by #j4aeiae4 ,or divide circumference by #f4bhcah4 ,,to ,,find ,,side ,,of ,,an ,,inscribed ,,square-- ,multiply diameter by #j4gjga4 ,or multiply circumference by #j4bbea4 ,or divide circumference by #d4ddbh4 ,,to ,,find ,,side ,,of ,,an ,,equal ,,square-- ,multiply diameter by #j4hhfb4 ,or divide diameter by #a4abhd4 ,or multiply circumference by #j4bhba4 ,or divide circumference by #c4ede4 ,,square-- ,a side multiplied by #a4dadb equals diameter of its circumscribing circle4 ,a side multiplied by #d4ddc equals circumference of its circumscribing circle4 ,a side multiplied by #a4abh equals diameter ,a side multiplied by #c4ede equals circumference of an equal circle4 ,a side multiplied by #a4bgc equals circle inches ,,to ,,find ,,the ,,area ,,of ,a ,,circle-- ,multiply circumference by one-quarter of the diameter4 ,or multiply the square of diameter by #j4ghed4 ,or multiply the square of circumference by 4#jgieh4 ,or multiply the square of diameter by #c4adaf4 ,contents of cylinder area of end length4 ,contents of wedge area of base altitude4 ,surface of cylinder area of both ends length circumference4 ,surface of sphere diameter squared #c4adaf1 or diameter circumference4 ,contents of sphere diameter cubed 4#ebcf4 ,contents of pyramid or cone1 right or oblique1 regular or irregular area of base altitude4 ,area of triangle base altitude4 ,area of parallelogram base altitude4 ,area of trapezoid altitude the sum of parallel sides4 ,,roman ,,table4 ,i4 denotes ,one4 ,,ii4 ,two4 ,,iii4 ,three4 ,,iv4 ,four4 ,v4 ,five4 ,,vi4 ,six4 ,,vii4 ,seven4 ,,viii4 ,eight4 ,,ix4 ,nine4 ,x4 ,ten4 ,,xi4 ,eleven4 ,,xii4 ,twelve4 ,,xiii4 ,thirteen4 ,,xiv4 ,fourteen4 ,,xv4 ,fifteen4 ,,xvi4 ,sixteen4 ,,xvii4 ,seventeen4 ,,xviii4 ,eighteen4 ,,xix4 ,nineteen4 ,,xx4 ,twenty4 ,,xxx4 ,thirty4 ,,xl4 ,forty4 ,l4 ,fifty4 ,,lx4 ,sixty4 ,,lxx4 ,seventy4 ,,lxxx4 ,eighty4 ,,xc4 ,ninety4 ,c4 ,one hundred4 ,d4 ,five hundred4 ,m4 ,one thousand4 ,x4 ,ten thousand4 ,m4 ,one million4 ,,solid ,,measure1 ,,or ,,cubic ,,measure4 ,this is used in measuring bodies1 or things having length1 breadth and height or depth4 ,,table4 #agbh cubic inches 7cu4 in47 make #a cubic foot 7cu4 ft474 #bg cubic feet1 #a cubic yard 7cu4 yd474 #abh cubic feet1 #a cord 7,c474 ,,circular ,,measure4 #fj seconds 77 make #a minute 774 #fj minutes #a degree 774 #cfj degrees #a circum4 7,c474 ,the circumference of every circle whatever1 is supposed to be divided into #cfj equal parts1 called degrees4 ,a degree is of the circumference of any circle1 small or large4 ,a quadrant is a fourth of a circumference1 or an arc of #ij degrees4 ,a degree is divided into #fj parts called minutes1 expressed by the sign 771 and each minute is divided into #fj seconds1 expressed by 772 so that the circumference of any circle contains #ba1fjj minutes1 or #a1bif1jjj seconds4 ,,long ,,measure--,,measures ,,of ,,length4 #ab inches #a foot4 #c feet #a yard4 #e yards #a rod4 #dj rods #a furlong4 #h furlongs #a common mile4 #c miles #a league4 ,the mile 7#e1bhj feet7 of the above table is the legal mile of the ,united ,states and ,england1 and is called the statute mile4 ,tables of ,diameters1 ,circumferences and ,areas of ,circles4 -------------------------- ,diam4 ,area4 ,circum4 -------------------------- #j4j 4#a 4#jjghed 4#cadaf 4#b 4#jcadaf 4#fbhcb 4#c 4#jgjfhf 4#idbdh 4#d 4#abeff #a4beff 4#e 4#aigce #a4egjh 4#f 4#bhbgd #a4hhej 4#g 4#chdhe #b4aiia 4#h 4#ejbff #b4eacc 4#i 4#fcfag #b4hbgd #a4j 4#ghed #c4adaf 4#a 4#iejc #c4deeh 4#b #a4acaj #c4gfii 4#c #a4cbgc #d4jhda 4#d #a4ecid #d4cihb 4#e #a4gfga #d4gabd 4#f #b4jajf #e4jbfe 4#g #b4bfih #e4cdjg 4#h #b4eddg #e4fedi 4#i #b4hcec #e4ifij #b4j #c4adaf #f4bhcb 4#a #c4dfcf #f4eigc 4#b #c4hjac #f4iaae 4#c #d4aedh #g4bbeg 4#d #d4ebci #g4ecih 4#e #d4ijhg #g4hedj 4#f #e4cjic #h4afha 4#g #e4gbef #h4dhbc 4#h #f4aege #h4gife 4#i #f4fjeb #i4aajf #c4j #g4jfhf #i4dbdh 4#a #g4edgg #i4gchi 4#b #h4jdbe #aj4jeca 4#c #h4eecj #aj4cfgc 4#d #i4jgib #aj4fhad 4#e #i4fbaa #aj4iief 4#f #aj4aghh #aa4cjig 4#g #aj4geba #aa4fbci 4#h #aa4cdaa #aa4icha 4#i #aa4idef #ab4bebb #d4j #ab4effd #ab4effd 4#a #ac4bjbe #ab4hhje 4#b #ac4hedd #ac4aidg 4#c #ad4ebbj #ac4ejhh 4#d #ae4bjec #ac4hbcj 4#e #ae4ijdc #ad4acgb 4#f #af4faij #ad4deac 4#g #ag4cdid #ad4gfee 4#h #ah4jief #ae4jgif 4#i #ah4hegd #ae4cich #e4j #ai4fcej #ae4gjhj 4#a #bj4dbhb #af4jbba 4#b #ba4bcgb #af4ccfc 4#c #bb4jfah #af4fejd 4#d #bb4ijbb #af4ifdf 4#e #bc4gehc #ag4bghh 4#f #bd4fcja #ag4eibi 4#g #be4eagf #ag4ijga 4#h #bf4dbjh #ah4bbab 4#i #bg4ccig #ah4eced #f4j #bh4bgdc #ah4hdif 4#a #bi4bbdg #ai4afcg 4#b #cj4aijg #ai4dggi 4#c #ca4agbe #ai4gibj 4#d #cb4afii #bj4ajfb 4#e #cc4ahca #bj4dbjd 4#f #cd4baai #bj4gcde 4#g #ce4befe #ba4jdhg 4#h #cf4cafh #ba4cfbh 4#i #cg4cibh #ba4fggj #g4j #ch4dhde #ba4iiaa 4#a #ci4eiai #bb4cjec 4#b #dj4gaej #bb4faie 4#c #da4heci #bb4iccf 4#d #dc4jjhd #bc4bdgh 4#e #dd4aghf #bc4efai 4#f #de4cfdf #bc4hgfa 4#g #df4effc #bd4aijc 4#h #dg4ghcf #bd4ejdd 4#i #di4jafg #bd4hahf #h4j #ej4bfee #be4acbg 4#a #ea4ecjj #be4ddfi 4#b #eb4hajb #be4gfaa 4#c #ed4ajfa #bf4jgeb 4#d #ee4dagg #bf4chid 4#e #ef4gdej #bf4gjce 4#f #eh4jhhj #bg4jagg 4#g #ei4ddfh #bg4ccai 4#h #fj4hbab #bg4fdfj 4#i #fb4baad #bg4ifjb #i4j #fc4fagc #bh4bgdc 4#a #fe4jchh #bh4ehhe 4#b #ff4dgfa #bh4ijbg 4#c #fg4ibia #bi4bafh 4#d #fi4cigh #bi4ecaj 4#e #gj4hhbb #bi4hdea 4#f #gb4chbc #cj4aeic 4#g #gc4hiha #cj4dgcd 4#h #ge4dbif #cj4ghgf 4#i #gf4igfi #ca4ajah #aj4j #gh4ecih #ca4daei 4#a #hj4aahe #ca4gcja 4#b #ha4gabh #cb4jddb 4#c #hc4cbbi #cb4cehd 4#d #hd4idhg #cb4fgbf 4#e #hf4eija #cb4ihhg 4#f #hh4bdgc #cc4cjji 4#g #hi4ibjb #cc4faej 4#h #ia4fjhh #cc4ibib 4#i #ic4cacb #cd4bdcd #aa4j #ie4jccb #cd4eege 4#a #if4gfhi #cd4hgag 4#b #ih4ebjc #ce4aheh 4#c #ajj4bhge #ce4ejjj 4#d #ajb4jgjc #ce4hadb 4#e #ajc4hfhi #cf4abhc 4#f #aje4fhcb #cf4ddbe 4#g #ajg4eacb #cf4geff 4#h #aji4cehh #cg4jgjh 4#i #aaa4bbjb #cg4chej #ab4j #aac4jigc #cg4fiia 4#a #aad4iija #ch4jacc 4#b #aaf4hihg #ch4cbgd 4#c #aah4hbbi #ch4fdaf 4#d #abj4gfbh #ch4ieeg 4#e #abb4gahe #ci4bjii 4#f #abd4fhih #ci4fhda 4#g #abf4fgfi #ci4hihb 4#h #abh4fgif #dj4baba 4#i #acj4fiha #dj4ebfe #ac4j #acb4gcbc #dj4hdjg 4#a #acd4ghbb #da4aedi 4#b #acf4hdgh #da4dfij 4#c #ach4ibia #da4ghcb 4#d #ada4jbfa #db4jigc 4#e #adc4achh #db4daaf 4#f #ade4bfgb #db4gbeg 4#g #adg4daad #dc4jcih 4#h #adi4egab #dc4cedj 4#i #aea4gdfh #dc4ffha #ad4j #aec4ichj #dc4ihbc 4#a #aef4adej #dd4bife 4#b #aeh4cfgg #dd4fajf 4#c #afj4fjfa #dd4ibdh 4#d #afb4hfjb #de4bchi 4#e #afe4acjj #de4eeca 4#f #afg4daee #de4hfgc 4#g #afi4gafg #df4ahad 4#h #agb4jccf #df4dief 4#i #agd4cffb #df4hjig #ae4j #agf4gadf #dg4abci 4#a #agi4jghf #dg4dchj 4#b #aha4dehd #dg4gebb 4#c #ahc4heci #dh4jffd 4#d #ahf4bfej #dh4chje 4#e #ahh4fiai #dh4fidg 4#f #aia4acde #di4jjhh 4#g #aic4eibh #di4cbcj 4#h #aif4jffh #di4fcgb 4#i #aih4eefe #di4ieac #af4j #bja4jfai #ej4bfee 4#a #bjc4ehca #ej4egif 4#b #bjf4aaii #ej4hich 4#c #bjh4fgbd #ea4bjhj 4#d #baa4bdjg #ea4ebba 4#e #bac4hbdf #ea4hcfc 4#f #baf4dbdc #eb4aejd 4#g #bai4jcig #eb4dfdf 4#h #bba4fgjh #eb4gghh 4#i #bbd4cagf #ec4jibi #ag4j #bbf4ihja #ec4djga 4#a #bbi4fehc #ec4gbab 4#b #bcb4cebb #ed4jced 4#c #bce4jfah #ed4cdif 4#d #bcg4ghga #ed4ffcg 4#e #bdj4ebhb #ed4iggi 4#f #bdc4bhdi #ee4bibj 4#g #bdf4jegd #ee4fjfb 4#h #bdh4hdef #ee4ibjc 4#i #bea4fdid #ef4bcde #ah4j #bed4dfij #ef4edhf 4#a #beg4cjdc #ef4hfbh 4#b #bfj4aeec #eg4aggj 4#c #bfc4jbbj #eg4diaa 4#d #bfe4ijdd #eg4hjec 4#e #bfh4hjbe #eh4aaie 4#f #bga4gafd #eh4dccf 4#g #bgd4fdei #eh4gdgh 4#h #bgg4eiaa #ei4jfai 4#i #bhj4eeba #ei4cgfa #ai4j #bhc4ebhg #ei4fijc 4#a #bhf4ebaa #fj4jjdd 4#b #bhi4ebib #fj4cahf 4#c #bib4eecj #fj4fcbg 4#d #bie4eibe #fj4idfi 4#e #bih4fdgg #fa4bfaa 4#f #cja4gahf #fa4egeb 4#g #cjd4hjeb #fa4hhid 4#h #cjg4ijge #fb4bjce 4#i #caa4jbee #fb4eagg #bj4j #cad4aeic #fb4hcai 4#a #cag4cjhg #fc4adfj 4#b #cbj4dgci #fc4dfjb 4#c #cbc4fedg #fc4ggdc 4#d #cbf4heac #fd4jhhe 4#e #ccj4jfcf #fd4djbf 4#f #ccc4biaf #fd4gafh 4#g #ccf4ecec #fe4jcaj 4#h #cci4gidg #fe4cdea 4#i #cdc4jfih #fe4feic #ba4j #cdf4cfjf #fe4igcd 4#a #cdi4ffga #ff4bhgf 4#b #ceb4ihid #ff4fjah 4#c #cef4cbgc #ff4iaei 4#d #cei4fhji #fg4bcja 4#e #cfc4jejc #fg4eddb 4#f #bff4dced #fg4hehd 4#g #cfi4hcfa #fh4agbf 4#h #cgc4bebf #fh4dhfg 4#i #cgf4fhdh #fh4hjji #bb4j #chj4acbg #fi4aaej 4#a #chc4eifc #fi4dbib 4#b #chg4jgef #fi4gdcd 4#c #cij4egjg #gj4jege 4#d #cid4jhad #gj4cgag 4#e #cig4fjgh #gj4fheh 4#f #dja4aejj #ga4jjjj 4#g #djd4gjgh #ga4cadb 4#h #djh4bhad #ga4fbhc 4#i #daa4hgjg #ga4idbe #bc4j #dae4dgef #gb4beff 4#a #dai4jiic #gb4egjh 4#b #dbb4gcbg #gb4hhdi 4#c #dbf4chdh #gc4aiia 4#d #dcj4jebf #gc4eacc 4#e #dcc4gcfa #gc4hbgd 4#f #dcg4dced #gd4adaf 4#g #dda4aejc #gd4deeg 4#h #ddd4hhji #gd4gfii 4#i #ddh4fbgc #ge4jhda #bd4j #deb4chic #ge4cihb 4#a #def4afga #ge4gdbd 4#b #dei4ifjf #gf4jbfe 4#c #dfc4gfic #gf4cdjg 4#d #dfg4eidg #gf4fedi 4#e #dga4dceb #gf4ifij 4#f #dge4biaf #gg4bhcb 4#g #dgi4afcf #gg4eigc 4#h #dhc4jeac #gg4iaae 4#i #dhf4iedg #gh4bbeg #be4j #dij4hgci #gh4ecih 4#a #did4hjhg #gh4hedj 4#b #dih4geib #gi4afha 4#c #ejb4gbee #gi4dhbc 4#d #ejf4gjge #gi4gife 4#e #eaj4gjeb #hj4aajf 4#f #ead4gahe #hj4dbdh 4#g #eah4gdgf #hj4gchi 4#h #ebb4gibd #ha4jeca 4#i #ebf4hebi #ha4cfgb #bf4j #ecj4ibib #ha4fhad 4#a #ece4jbaa #ha4iief 4#b #eci4abhg #hb4cjig 4#c #edc4beba #hb4fbci 4#d #edg4ciaa #hb4ichj 4#e #eea4edei #hc4bebb 4#f #eee4gafc #hc4effd 4#g #eei4ijbe #hc4hhje 4#h #efd4ajdd #hd4aidg 4#i #efh4cbbj #hd4ejhh #bg4j #egb4eeec #hd4hbcj 4#a #egf4hjdc #he4acgb 4#b #eha4jfij #he4deac 4#c #ehe4cdid #he4gfee 4#d #ehi4fdee #hf4jgif 4#e #eic4iegd #hf4cich 4#f #eih4bhdi #hf4gjhj 4#g #fjb4fbhb #hg4jbba 4#h #fjf4ihga #hg4ccfc 4#i #faa4cfah #hg4fejd #bh4j #fae4gebb #hg4ifdf 4#a #fbj4aehb #hh4bghh 4#b #fbd4ehjj #hh4eibi 4#c #fbi4jage #hh4ijga 4#d #fcc4dgjg #hi4bbab 4#e #fcg4icig #hi4eced 4#f #fdb4dbdc #hi4hdie 4#g #fdf4ibdf #ij4afcg 4#h #fea4ddjg #ij4dggi 4#i #fee4igbd #ij4gibj #bi4j #ffj4eaii #ia4ajfc 4#a #ffe4jhcj #ia4dbjc 4#b #ffi4ffai #ia4gcde 4#c #fgd4befe #ib4jdhg 4#d #fgh4hffh #ib4cfbh 4#e #fhc4dibh #ib4fggj 4#f #fhh4acde #ib4iiaa 4#g #fib4giai #ic4cjec 4#h #fig4dfej #ic4faie 4#i #gjb4aech #ic4iccf #cj4j #gjf4hehc #id4bdgh 4#a #gaa4eghf #id4efaj 4#b #gaf4cade #id4hgfa 4#c #gba4jffb #ie4aijc 4#d #gbe4hccf #ie4ejdd 4#e #gcj4fafg #ie4hahf 4#f #gce4daed #if4acbg 4#g #gdj4bbii #if4ddfi 4#h #gde4jfja #if4gfaa 4#i #gdi4ijfj #ig4jgeb #ca4j #ged4gfgf #ig4chid 4#a #gei4fdej #ig4gjce 4#b #gfa4echj #ih4jagg 4#c #gfi4ddfg #ih4ccai 4#d #ggd4cgab #ih4fdfj 4#e #ggi4caac #ih4ifjb 4#f #ghd4bfgb #ii4bgdc 4#g #ghi4bchh #ii4ehhe 4#h #gid4bbfj #ii4ijbf 4#i #gii4bbij #ajj4bafh #cb4j #hjd4bdgg #ajj4ecaj 4#a #hji4bhba #ajj4hdea 4#b #had4ccbb #aja4aeic 4#c #hai4cihj #aja4dgcd 4#d #hbd4dgif #aja4ghgf 4#e #hbi4egfh #ajb4ajah 4#f #hcd4fhih #ajb4daei 4#g #hci4hahe #ajb4gcja 4#h #hdd4ifbh #ajc4jddb 4#i #hej4abbi #ajc4cehd #cc4j #hee4bihf #ajc4fgbf 4#a #hfj4dijb #ajc4ihfg 4#b #hfe4figc #ajd4cjji 4#c #hgj4ibjb #ajd4faej 4#d #hgf4aehh #ajd4ibib 4#e #hha4daca #aje4bdcd 4#f #hhf4fhca #aje4eege 4#g #hia4ifhh #aje4hgag 4#h #hig4bgjc #ajf4aheh 4#i #ijb4ehgd #ajf4ejjj #cd4j #ijg4ibjc #ajf4hadb 4#a #iac4bfhh #ajg4abhc 4#b #iah4fcca #ajg4ddbe 4#c #ibd4jaca #ajg4geff 4#d #ibi4djhh #ajh4jgjh 4#e #icd4hbjb #ajh4chdi 4#f #idj4bdgc #ajh4fiia 4#g #ide4fija #aji4jacc 4#h #iea4adhf #aji4cbgd 4#i #ief4fbbh #aji4fdaf #ce4j #ifb4aabh #aji4ieeg 4#a #ifg4fahd #aaj4bfii 4#b #igc4acig #aaj4ehda 4#c #igh4fgfh #aaj4hihb 4#d #ihd4bbif #aaa4babd 4#e #ihi4gihj #aaa4ebfe 4#f #iie4chbb #aaa4hdjg 4#g #ajjj4ihba #aab4aedi 4#h #ajjf4eigg #aab4dfij 4#i #ajab4bbij #aab4ghcb #cf4j #ajag4hgfj #aac4jigc 4#a #ajbc4echg #aac4daae 4#b #ajbi4bagb #aac4gbeg 4#c #ajcd4iaac #aad4jcih 4#d #ajdj4fbab #aad4cedj 4#e #ajdf4cdfg #aad4ffha 4#f #ajeb4jhhj #aad4ihbc 4#g #ajeg4hddi #aae4bife 4#h #ajfc4fagf #aae4fajf 4#i #ajfi4djfj #aae4ibdh #cg4j #ajge4baja #aaf4bchi 4#a #ajha4jbii #aaf4eeca 4#b #ajhf4hfed #aaf4hfgb 4#c #ajic4gaff #aag4ahad 4#d #ajih4ehce #aag4dief 4#e #aajd4dffb #aag4hjig 4#f #aaaj4cfde #aah4abci 4#g #aaaf4bghf #aah4dchj 4#h #aabb4bjhc #aah4gebb 4#i #aabh4aech #aai4jffd #ch4j #aacd4aadi #aai4chje 4#a #aadj4jiah #aai4fidg 4#b #aadf4jhdd #abj4jjhh 4#c #aaeb4jibg #abj4cbcj 4#d #aaeh4aafg #abj4fcgb 4#e #aafd4aefd #abj4ieac 4#f #aagj4baah #aba4bfee 4#g #aagf4bhcj #aba4egif 4#h #aahb4cfih #aba4hich 4#i #aahh4dgbd #abb4bjhj #ci4j #aaid4eijf #abb4ebba 4#a #abjj4gbdf #abb4hcfc 4#b #abjf4hgdb #abc4aejd 4#c #abac4jcif #abc4dfdf 4#d #abai4bbjg #abc4gghh 4#e #abbe4dage #abd4jibi 4#f #abca4fcjj #abd4djga 4#g #abcg4hehb #abd4gbab 4#h #abdd4ajba #abe4jced 4#i #abej4cfag #abe4cdie #dj4j #abef4fcga #abe4ffcg 4#a #abfb4ibha #abe4iggi 4#b #abfi4bcdh #abf4bibj 4#c #abge4eegc #abf4fjfb 4#d #abha4hiee #abf4ibjc 4#e #abhh4bdic #abg4bcde 4#f #abid4cahi #abg4edhg 4#g #acja4jjdb #abg4hfbh 4#h #acjg4djeb #abh4aggj 4#i #acac4hbai #abh4diaa #da4j #acbj4bedc #abh4hjec 4#a #acbf4gjbd #abi4aaie 4#b #accc4affc #abi4dccf 4#c #acci4fdeh #abi4gdgh 4#d #acdf4adaj #acj4jfai 4#e #aceb4febj #acj4cgfa 4#f #acei4aghf #acj4fijc 4#g #acfe4gbaj #aca4jjdd 4#h #acgb4bgia #aca4cahf 4#i #acgh4hebi #aca4fbbg #db4j #ache4ddbd #aca4idfi 4#a #acib4jdgf #acb4bfaa 4#b #acih4ffhe #acb4egeb 4#c #adje4cjea #acb4hhid 4#d #adaa4iegd #acc4bjce 4#e #adah4fbed #acc4eagg 4#f #adbe4cjib #acc4hcah 4#g #adcb4jjhf #acd4adfj 4#h #adch4gbch #acd4dfjb 4#i #adde4dedf #acd4ggdc #dc4j #adeb4bjab #ace4jhhe 4#a #adeh4ifce #ace4djbf 4#b #adfe4gdae #ace4gafh 4#c #adgb4eceb #acf4jcaj 4#d #adgi4cddf #acf4cdea 4#e #adhf4afig #acf4feic 4#f #adic4jaje #acf4igcd 4#g #adii4hfgj #acg4bhgf 4#h #aejf4gcic #acg4fjah 4#i #aeac4fbgb #acg4iaei #dd4j #aebj4ecjh #ach4bcja 4#a #aebg4dejb #ach4eddb 4#b #aecd4chec #ach4hehd 4#c #aeda4ccfj #aci4agbf 4#d #aedh4cjbe #aci4dhfg 4#e #aeee4bhdg #aci4hjji 4#f #aefb4bhbf #adj4aaec 4#g #aefi4bjfc #adj4dbib 4#h #aegf4cbee #adj4gdcd 4#i #aehc4cgjf #ada4jege #de4j #aeij4dcac #ada4cgag 4#a #aeig4ejgg #ada4fheh 4#b #afjd4eiii #adb4jjjj 4#c #afaa4gjgg #adb4cadb 4#d #afah4hcac #adb4fbhc 4#e #afbe4igje #adb4idbe 4#f #afcc4abee #adc4beff 4#g #afdj4bifb #adc4egjh 4#h #afdg4dhbf #adc4hhdi 4#i #afed4fhdg #add4aiia #df4j #affa4ijbe #add4eacc 4#a #affi4acfj #add4hbgd 4#b #afgf4chec #ade4adaf 4#c #afhc4fejb #ade4deeg 4#d #afij4icjh #ade4gfii 4#e #afih4bbgb #adf4jhda 4#f #agje4ecib #adf4cihb 4#g #agab4hfgj #adf4gabd 4#h #agbj4baje #adg4jbfe 4#i #agbg4efig #adg4cdjg #dg4j #agcd4idde #adg4feej 4#a #agdb4ccea #adg4ifij 4#b #agdi4gdad #adh4bhcb 4#c #ageg4afce #adh4eigc 4#d #agfd4fjab #adh4iaae 4#e #aggb4jedf #adi4bbeg 4#f #aggi4ebcg #adi4ecih 4#g #aghg4jjhf #adi4hedj 4#h #agid4ejia #aej4afha 4#i #ahjb4jbed #aej4dhbc #dh4j #ahji4eegd #aej4gifd 4#a #ahag4ajej #aea4aaje 4#b #ahbd4ffhd #aea4dbdh 4#c #ahcb4bdge #aea4gchi 4#d #ahci4hdbc #aeb4jeca 4#e #ahdg4debh #aeb4cfgb 4#f #ahee4jgij #aeb4fhad 4#g #ahfb4gbaj #aeb4iief 4#h #ahgj4cghf #aec4cjig 4#i #ahgh4jeai #aec4fbci #di4j #ahhe4gdji #aec4ichj 4#a #ahic4ddeg #aed4bebb 4#b #aija4affb #aed4effd 4#c #aijh4ijbd #aed4hhje 4#d #aiaf4fedc #aee4aidg 4#e #aibd4dbah #aee4ejhh 4#f #aicb4bjea #aee4hbcj 4#g #aidj4jjdb #aef4acgb 4#h #aidg4hahi #aef4deac 4#i #aiee4fdic #aef4gfee #ej4j #aifc4died #aeg4jgif 4#a #aiga4cegb #aeg4cich 4#b #aigi4bcdh #aeg4gjhj 4#c #aihg4abhj #aeh4jbba 4#d #aiie4jcgj #aeh4ccfc 4#e #bjjb4ifag #aeh4fejd 4#f #bjaj4ijbj #aeh4ifdf 4#g #bjah4heha #aei4bghg 4#h #bjbf4hbii #aei4eibi 4#i #bjcd4hagd #aei4ijga #ea4j #bjdb4fbjf #afj4bbab 4#a #bjej4hhie #afj4eced 4#b #bjeh4hgdb #afj4hdie 4#c #bjff4ibde #afa4afcg 4#d #bjgd4iije #afa4dggi 4#e #bjhc4jgbc #afa4gibj 4#f #bjia4afig #afb4ajfb 4#g #bjii4bhbi #afb4dbjc 4#h #bajg4daah #afb4gcde 4#i #baae4eefc #afc4jdhg #eb4j #babc4gaff #afc4cfbh 4#a #baca4hibf #afc4fggj 4#b #badj4jhdc #afc4iiaa 4#c #badh4biag #afd4cjec 4#d #baef4eadi #afd4faie 4#e #bafd4gecg #afd4iccf 4#f #bagc4jjhb #afe4bdgi 4#g #baha4bghe #afe4efai 4#h #bahi4efdd #afe4hgfa 4#i #baig4hffa #aff4aijc #ec4j #bbjf4ahcd #aff4ejdd 4#a #bbad4eafe #aff4hahf 4#b #bbbb4hfec #afg4acbg 4#c #bbca4bbih #afg4ddfi 4#d #bbci4fajj #afg4gfaj 4#e #bbdh4jjei #afh4jgeb 4#f #bbef4dage #afh4chid 4#g #bbfd4hddh #afh4gjce 4#h #bbgc4bhgi #afi4jagg 4#i #bbha4gdff #afi4ccah #ed4j #bbij4bbaj #afi4fdfj 4#a #bbih4gaab #afi4ifjb 4#b #bcjg4baga #agj4bgdc 4#c #bcae4gchf #agj4ehhe 4#d #bcbd4bgei #agj4ijbf 4#e #bccb4hbhi #aga4bafh 4#f #bcda4cigf #aga4ecaj 4#g #bcdi4ihbj #aga4hdea 4#h #bceh4ehba #agb4aeic 4#i #bcfg4aigi #agb4dgce #ee4j #bcge4hbid #agb4ghgf 4#a #bchd4dgfg #agc4ajag 4#b #bcic4acif #agc4daei 4#c #bdja4hahc #agc4gcja 4#d #bdaj4eabf #agd4jddb 4#e #bdai4bbbg #agd4cehd 4#f #bdbg4idhe #agd4fgbf 4#g #bdcf4fhii #agd4ihfg 4#h #bade4ddga #age4cjji 4#i #bded4bbjj #age4faej ------------------------ ,,united ,,states ,,standard ,,sizes ,,of ,,wrought ,,iron ,,welded ,,pipe4 ---------------------------------------- ----------------- ,length ,length of pipe of pipe per per ,inside ,actual ,actual square square diam-outside ,inside,external,internal foot of foot of eter ,diam- ,thick- ,diam- circum- circum- outside inside nom4 eter4 ness4 eter4ference4ference4surface4surface4 ---------------------------------------- ----------------- 4#dje 4#jfh #j4bfi #a4bgb #j4hdh #i4ddj #ad4ae 4#ed 4#jhh #j4cfd #a4fif #a4add #g4jge #aj4ej 4#fge 4#jia #j4dic #b4aba #a4eeb #e4feg #g4fg 4#hdj 4#aji #j4fbb #b4feb #a4ieg #d4ejb #f4ac #a4jej 4#aac #j4hbd #c4bii #b4ehi #c4fcg #d4fce #a #a4cae 4#acd #a4jdg #d4acd #c4bib #b4ijc #c4fgi #a #a4ffj 4#adj #a4ch #e4bae #d4cce #b4cja #b4gfh #a #a4ij 4#ade #a4fa #e4ifi #e4jfa #b4jaj #b4cga #b #b4cge 4#aed #b4jfg #g4dfa #f4did #a4faa #a4hdh #b #b4hge 4#bjd #b4dfg #i4jcb #g4ged #a4cbh #a4edg #c #c4ej 4#bag #c4jff #aj4iif #i4fcf #a4jia #a4bde #c #d4j 4#bbf #c4edh #ab4eff #aa4adf 4#iee #a4jgg #d #d4ej 4#bcg #d4jbf #ad4acg #ab4fdh 4#hdi #j4idi #d #e4j 4#bdg #d4ejf #ae4gjh #ad4aec 4#gfe #j4hdh #e #e4efc 4#bei #e4jde #ag4dge #ae4hdi 4#fbi #j4geg #f #f4fbe 4#bhj #e4jfe #bj4hac #ai4jed 4#egg #j4fcj #g #g4fbe 4#cja #g4jbc #bc4ied #bb4jfc 4#eje #j4edd #h #h4fbe 4#cbb #g4iha #bg4jif #be4jgf 4#ddd #j4dgh #i #i4fhh 4#cdd #i4jj #cj4dcc #bh4bgg 4#cid #j4dbe #aj #aj4gej 4#cff #aj4jah #cc4ggb #ca4dge 4#cee #j4cha ---------------------------------------- ----------------- ---------------------------------------- ------ ,length of pipe con- ,weight,no4 of ,inside ,actualtaining per threads,length diam- ,ex- in- one foot per per- eter ternal ternal cubic of ,inch of fect nom4 area4 area4 foot4 length4 screw4screw4 ---------------------------------------- ------ 4#abi 4#jegbbejj4 4#bdc #bg #j4ai 4#bbi 4#ajdaache4 4#dbb #ah #j4bi 4#ceh 4#aiaf #gea4e 4#efa #ah #j4cj 4#eed 4#cjdh #dgb4d 4#hde #ad #j4ci 4#hff 4#eccc #bgj4j #a4abf #ad #j4dj #a #a4ceg 4#hfbg #aff4i #a4fgj #aa #j4ea #a #b4afd #a4dif #if4be #b4beh #aa #j4ed #a #b4hce #b4jch #gj4fe #b4fid #aa #j4ee #b #d4dcj #c4cee #db4cf #c4ffg #aa #j4eh #b #f4dia #d4ghc #cj4aa #e4ggc #h #j4hi #c #i4fba #g4chh #ai4dj #g4edg #h #j4ie #c #ab4eff #i4hcg #ad4ef #i4jee #h #a4jj #d #ae4ijaab4gcj #aa4ca #aj4gbh #h #a4je #d #ai4fceae4ici #i4jc #ab4dib #h #a4aj #e #bd4biiai4iij #g4bj #ad4efd #h #a4af #f #cd4dgabh4hhi #d4ih #ah4gfg #h #a4bf #g #de4ffcch4gcg #c4gb #bc4daj #h #a4cf #h #eh4dbfej4jci #b4hh #bh4cdh #h #a4df #i #gc4gaefc4fcc #b4bf #cd4fgg #h #a4eg #aj #ij4gfbgh4hch #a4hj #dj4fda #h #a4fh ---------------------------------------- ------ ,thread taper three-fourths inch to one foot4 ,all pipe below #a inches is butt-welded1 and proved to #cjj pounds per square inch2 #a inch and above is lap-welded and proved to #ejj pounds per square inch4 ,,standards ,,for ,,wire ,,gauges ,,in ,,use ,,in ,,the ,,united ,,states4 ,dimensions of ,sizes in ,decimal ,parts of an ,inch4 ---------------------------------------- ------------------- ,washburn ,number,american,birming- ,moen ,impe- ,u4 ,s4 ,number of or ,brown ham1 or,mfg4 ,co41 rial ,stubs' ,stand4 of ,wire ,stubs' ,worces- ,wire ,steel for ,wire ,gauge4 ,sharpe4 ,wire4 ter1 ,ms4,gauge4 ,wire4 ,plate4 ,gauge4 ---------------------------------------- ------------------- #jjjjjj 4444 4444 4444 4#dfd 4444 4#dfhge #jjjjjj #jjjjj 4444 4444 4444 4#dcb 4444 4#dcge #jjjjj #jjjj 4#df 4#ded 4#cich 4#djj 4444 4#djfbe #jjjj #jjj 4#djifd 4#dbe 4#cfbe 4#cgb 4444 4#cge #jjj #jj 4#cfdh 4#ch 4#ccaj 4#cdh 4444 4#cdcge #jj #j 4#cbdhf 4#cd 4#cjfe 4#cbd 4444 4#cabe #j #a 4#bhic 4#c 4#bhcj 4#cjj 4#bbg 4#bhabe #a #b 4#begfc 4#bhd 4#bfbe 4#bgf 4#bai 4#bfefbe #b #c 4#bbidb 4#bei 4#bdcg 4#beb 4#bab 4#be #c #d 4#bjdca 4#bch 4#bbec 4#bcb 4#bjg 4#bcdcge #d #e 4#ahaid 4#bb 4#bjgj 4#bab 4#bjd 4#bahge #e #f 4#afbjb 4#bjc 4#aibj 4#aib 4#bja 4#bjcabe #f #g 4#addbh 4#ah 4#aggj 4#agf 4#aii 4#ahge #g #h 4#abhdi 4#afe 4#afbj 4#afj 4#aig 4#agahge #h #i 4#aaddc 4#adh 4#adhc 4#add 4#aid 4#aefbe #i #aj 4#ajahi 4#acd 4#acej 4#abh 4#aia 4#adjfbe #aj #aa 4#jijgdb 4#ab 4#abje 4#aaf 4#ahh 4#abe #aa #ab 4#jhjhjh 4#aji 4#ajee 4#ajd 4#ahe 4#ajicge #ab #ac 4#jgaifa 4#jie 4#jiae 4#jib 4#ahb 4#jicge #ac #ad 4#jfdjhd 4#jhc 4#jhjj 4#jhj 4#ahj 4#jghabe #ad #ae 4#jegjfh 4#jgb 4#jgbj 4#jgb 4#agh 4#jgjcabe #ae #af 4#jejhb 4#jfe 4#jfbe 4#jfd 4#age 4#jfbe #af #ag 4#jdebeg 4#jeh 4#jedj 4#jef 4#agb 4#jefbe #ag #ah 4#jdjcjc 4#jdi 4#jdge 4#jdh 4#afh 4#je #ah #ai 4#jcehi 4#jdb 4#jdaj 4#jdj 4#afd 4#jdcge #ai #bj 4#jcaifa 4#jce 4#jcdh 4#jcf 4#afa 4#jcge #bj #ba 4#jbhdfb 4#jcb 4#jcage 4#jcb 4#aeg 4#jcdcge #ba #bb 4#jbecdg 4#jbh 4#jbhf 4#jbh 4#aee 4#jcabe #bb #bc 4#jbbega 4#jbe 4#jbeh 4#jbd 4#aec 4#jbhabe #bc #bd 4#jbja 4#jbb 4#jbcj 4#jbb 4#aea 4#jbe #bd #be 4#jagi 4#jb 4#jbjd 4#jbj 4#adh 4#jbahge #be #bf 4#jaeid 4#jah 4#jaha 4#jah 4#adf 4#jahge #bf #bg 4#jadaie 4#jaf 4#jagc 4#jafd 4#adc 4#jagahge #bg #bh 4#jabfda 4#jad 4#jafb 4#jadi 4#aci 4#jaefbe #bh #bi 4#jaabeg 4#jac 4#jaej 4#jacf 4#acd 4#jadjfbe #bi #cj 4#jajjbe 4#jab 4#jadj 4#jabd 4#abg 4#jabe #cj #ca 4#jjhibh 4#ja 4#jacb 4#jaaf 4#abj 4#jajicge #ca #cb 4#jjgie 4#jji 4#jabh 4#jajh 4#aae 4#jajaefbe #cb #cc 4#jjgjh 4#jjh 4#jaah 4#jajj 4#aab 4#jjicge #cc #cd 4#jjfcjd 4#jjg 4#jajd 4#jjib 4#aaj 4#jjheicge #cd #ce 4#jjefad 4#jje 4#jjie 4#jjhd 4#ajh 4#jjghabe #ce #cf 4#jje 4#jjd 4#jjij 4#jjgf 4#ajf 4#jjgjcabe #cf #cg 4#jjddec 4444 4444 4#jjfh 4#ajc 4#jjffdjfbe #cg #ch 4#jjcife 4444 4444 4#jjfj 4#aja 4#jjfbe #ch #ci 4#jjceca 4444 4444 4#jjeb 4#jii 4444 #ci #dj 4#jjcadd 4444 4444 4#jjdh 4#jig 4444 #dj ---------------------------------------- ------------------- ,,united ,,states ,,standard ,,sizes ,,of ,,bolts4 ------------------------------ ,,distance ,,across ,,distance ,,flats1 ,,across ,,thick- ,,diam- ,,square ,,corners1 ,,ness ,,eter4,,and ,,hex4 ,,hex4 ,,of ,,head4 ------------------------------ #a #a #a #a #a #a #a #a #a #a #a #a #b #a #b #b #a #a #b #b #a #a #b #b #a #a #b #b #a #a #b #c #a #a #b #c #a #b #c #c #a #b #c #d #a #b #c #d #a #b #d #d #b #c #d #e #b ------------------------------ ,,united ,,states ,,standard ,,screw ,,thread ,,gauge4 ,illustration3 ,fig4 #caf4 ,some ,things ,personal4 ,in the preparation of this work the idea of self-help has never been forgotten2 nothing has been held back or omitted which would1 in the author's opinion1 tend to advance the student in the draughtsman's art4 ,the volume contains the experience in practical drawing1 as related to engineering and mechanics1 of over one hundred years1 i4 e41 the author's1 ,mr4 ,perrott's and ,mr4 ,lucas' experiences added together exceed that period4 ,hence1 the work should be really helpful2 it has been aimed also to be entertaining and with easy tasks2 all the illustrations of the book are recommended as models for practice--they have been selected with that view4 ,moreover1 as between author and publishers1 the latter have agreed to issue the work in the most thorough style possible--as to paper1 printing and binding--and to sell it at a very generously low price1 considering all things4 ,with the closing words 8hail and farewell10 the author bids adieu 7,god be with you7 to the reader and the student4 ,illustration3 ,,beacon ,,light4 ,self ,hawkins' ,mechanical ,drawing4 ,help ,index4 ,,page ,acute ,angle1 def4 #db ,acute-,angled ,triangle1 def4 #ej ,addendum ,circle1 illus4 #bjj ,alphabets1 ,gothic1 desc4 #aga ,altitude1 def4 #da ,altitude of a ,polygon1 def4 #dg ,american ,machinist1 ,quotation from #ada ,angle1 def4 #da1 #hc ,to bisect an #hi ,to draw an #hi ,angle-,iron1 illus4 #ge ,angle-,plate1 illus4 #ge ,angular ,perspective ,drawing1 illus4 #bfj1 #bfe ,apex1 def4 #db ,apex of an ,angle1 def4 #db ,arc1 def4 #db ,complement of an #ii ,cosecant of an #ii ,cotangent of an #ii ,sine of an #ii ,supplement of an #ii ,tangent of an #ii ,versed ,sine of an #ii ,arc of ,circle1 ,to find the center of an #ij ,arcs1 ,drawing #adf ,illus4 #adf ,arrow-,heads1 how made #agb1 #agf ,axiom1 def4 #hc ,axis1 ,conjugate1 def4 #if ,of a ,figure1 def4 #dc ,of a ,solid1 def4 #db ,transverse1 def4 #if ,backlash in ,gearing #bae ,backward ,projection desc4 #aeb1 illus4 #aeb-c ,base1 def4 #dc ,of a ,polygon1 def4 #dg ,beacon ,light1 illus4 #bhb ,beam ,compasses desc4 #abd1 illus4 #abd ,bending ,machine1 ,hydraulic desc4 #bba1 illus4 #bbj-a ,benjamin1 ,prof4 ,chas41 8,how and ,what to ,study0 #bc ,bevel-,gear1 desc4 #bja ,bevel ,mortise ,wheel1 desc4 #bjc ,bevel ,wheel desc4 #aii1 illus4 #bjc ,bisect1 def4 #dc ,bisector1 def4 #dc ,blackboard1 illus4 and desc4 #bg ,blackboard ,drawing #bh ,blue ,printing desc4 #ahf1 illus4 #ahg ,test pieces #ahh ,blue ,prints1 ,office rules for #aif ,black ,process ,copying #ahh ,boiler-,plate1 ,riveted1 illus4 #gf ,bolt1 ,square-head1 illus4 #gf ,bolt and ,nut1 ,square-head desc4 #add1 illus4 #ade ,hexagon desc4 #add1 illus4 #gf1 #add ,bow-,dividers desc4 #abc1 illus4 #abb ,bow-,pencil1 desc4 #abc ,bows1 ,use of #bdb ,brick1 ,section ,lining1 illus4 #ahb ,broken ,lines1 ,how to ,draw #cc ,def4 #df ,bumping ,post1 illus4 #bbf ,calipers1 illus4 vi ,cast-,iron1 ,section-,lining1 illus4 #ahb ,caulking ,tool1 illus4 #gf ,center ,line1 def4 #df ,center ,lines1 ,in ,drawings #bdj-a ,in ,shop ,drawings #aib ,chalk-,crayon desc4 #bg1 illus4 #bg1 #cg ,chalk-,work #bg ,instruments for ,drawing1 illus4 #bi ,channel-,iron1 illus4 #ge ,checking ,drawings #aid ,circle1 def4 #dc ,to describe about a square #ic about a triangle #ic through two points #ij through three points #ij ,to find the center #ij ,to inscribe in a square #id in a triangle #id ,circles1 ,drawing desc4 #adf1 illus4 #adf ,circumference of a ,circle #dc ,circumscribe1 def4 #dc ,circular ,pitch ,line1 illus4 #bjj ,classifying ,drawings1 ,office ,rules for #aia ,clearance in ,wheel ,teeth #bae ,cog-,wheel def4 #bja1 illus4 #bja ,section ,lining1 illus4 #ahc ,coin1 ,perspective ,view of a1 illus4 #bdh ,color and ,tints #ahe ,compass1 ,mariners'1 illus4 #bfh ,compasses1 ,beam1 desc4 and illus4 #abd ,desc4 and illus4 #aba ,for holding chalk1 illus4 #bi ,how to hold1 illus4 #acf ,complement of an ,arc #ii ,composition1 ,section-,lining1 illus4 #ahb ,concave1 def4 #dd ,cone1 def4 #dd ,conjugate ,axis1 def4 #if ,construction1 def4 #dd ,line1 def4 #df ,contents1 ,table of #bd ,contour1 def4 #dd ,convergence1 def4 #dd ,convex1 def4 #dd ,copying ,drawings1 ,black ,process #ahh ,blue ,printing #ahf ,tracing #ahd ,copyright viii ,corner1 def4 #dd ,corollary1 def4 #hc ,co-secant of an ,arc1 def4 #ii ,co-sine of an ,arc1 def4 #ii ,co-tangent of an ,arc1 def4 #ii ,crane1 desc4 #bai ,working drawing of1 illus4 #bah ,cross-,hatches1 def4 #dd ,cross-hatching ,drawings #ahb ,crown ,wheel1 illus4 #bjh ,curve1 def4 #dd ,curved ,line1 def4 #df ,curved ,lines1 ,drawing1 desc4 #fi ,drawing ,figures of #gj1 #gb1 #gc ,how to ,draw #ce ,illus4 #gj ,curved ,surface1 def4 #di ,curve or ,scroll1 illus4 #aag ,cut ,gears1 desc4 #bae ,cylinder1 def4 #dd ,cylindrical1 def4 #dd ,cylindrical ,projection1 illus4 #afa ,dash ,line1 def4 #df ,decimal ,equivalents1 ,table of #bfi ,dedication ix ,definitions1 ,preliminary #da ,degree1 def4 #da1 #dd ,describe1 def4 #dd ,design1 def4 #dd ,symmetry in1 def4 #ej ,designing ,gears #bji ,detail ,drawings1 ,office ,rules for #aia ,develop1 def4 #de ,diagonal1 def4 #de ,diagonals of a ,polygon1 def4 #dg ,diameter1 def4 #de ,diameter1 ,of a ,circle #dc ,diameters of ,wheels1 ,how to ,measure #aii ,diametral ,pitch1 desc4 #bjj ,of ,gears #bab ,dimensioning ,drawings desc4 #agf1 illus4 #agg1 #agi ,dimension ,line1 def4 #df ,dimensions on ,drawings1 ,office ,rules for #aib ,dividers and ,compasses1 desc4 #aai ,dividers1 illus4 #hb1 #aai ,bisecting1 desc4 #aai ,bow1 illus4 #abb 8,point0 #bdb ,proportional desc4 #aai1 illus4 #abj ,spring ,bow1 desc4 #abd ,dodecahedron1 def4 #dh ,dot-and-,dash ,line1 def4 #df ,dotted ,line1 def4 #df ,draughtsmen1 ,useful ,tables for #bfi-bhj ,drawing1 ,blackboard #bh ,free hand #ee ,linear ,perspective #bdg ,parallel ,perspective #bfj-a ,projection1 desc4 #adh ,scale ,perspective #beg ,spur ,gear1 illus4 #afc1 #baa ,spur ,wheel1 desc4 #afb ,straight ,line ,figures desc4 #fe1 illus4 #ff-g-h ,symbols #aic ,the ,pitch ,line #bji ,to ,scale1 desc4 #abf ,working1 def4 #ea ,drawing-,board desc4 #ajg1 illus4 #ajb1 #ajf1 #ajh ,expansion and ,contraction of #ajh ,how to ,construct #ajg ,trestles1 illus4 #aaj1 #aaa ,drawing ,instruments1 desc4 #ajc ,how to ,select #ajd ,illus4 #aje ,outfit ,recommended #ajd ,drawing ,materials1 desc4 #ajc ,drawing ,office ,rules #aia ,drawing ,paper1 desc4 #acb ,erasing ,lines #adj ,fixing of1 illus4 #ajb ,fixing on the ,board #aci ,pasting #ahd 8,points0 #bdc ,patent ,office ,sizes #bcd ,sizes of #acc ,drawing ,pencils1 desc4 and illus4 #aah ,how to ,use #ef ,drawing ,pen1 ,filling with ink1 illus4 #acj ,drawing ,pens1 desc4 and illus4 #abi ,drawing-,pins1 desc4 #aaj ,drawing ,scales1 desc4 #abf ,drawings1 ,cleaning1 desc4 #afi ,color and ,finish1 note #ahe ,dimensioning1 desc4 #agf ,inking in1 desc4 #afg ,lettering1 desc4 #aga ,patent ,office ,rules for #bcc ,reproducing #ahf ,section-,lining1 desc4 #ahb ,shading desc4 #ahj1 illus4 #ahj1 #bbe ,size of1 ,office ,rules #aia ,tint and ,color1 desc4 #ahd ,drawing-,table1 desc4 #aaa ,folding ,legs1 illus4 #ajd ,edge1 def4 #de ,elevation1 def4 #de ,elevation and ,section1 ,spur ,wheel desc4 #baf1 illus4 #bab ,ellipse1 ,an1 desc4 #if1 #aah ,to describe when length and breadth are given #if ,envelopes1 ,portfolio1 desc4 #adb ,equiangular ,triangle1 def4 #de ,equilateral ,triangle1 def4 #ej ,erasing1 8,points0 on #bdb ,eye1 illus4 and desc4 #bec ,effect of ,light on #bec ,face1 def4 #de ,faced ,surfaces1 ,points1 etc4 #bdb ,figures1 ,drawing ,straight-line #fe ,numerals1 examples of #agc ,straight-line1 illus4 #ff ,file ,handle1 desc4 and illus4 #add ,finger and ,thumb ,lines1 illus4 #fd ,finished ,surfaces1 ,how to indicate #aic 8,points0 #bdb ,finishing1 def4 #de ,flanged-tooth ,wheel1 desc4 #bje ,flat ,pattern1 def4 #dg ,foreshortening1 def4 #de ,forward ,projection desc4 #aea1 #aeb1 illus4 #aee ,free-hand1 def4 #de ,free-hand ,drawing #ee1 #gh ,first ,lesson in #cj ,penciling1 illus4 #ed ,free-hand ,illustration1 a ,water ,wheel #gh ,friction-,clutch and ,pulley1 desc4 #bbd ,friction ,gear-,wheels1 desc4 #bja ,full ,line1 def4 #df ,gear1 def4 #aii ,gearing1 desc4 #aii ,drawing desc4 #afb1 illus4 #afc ,gearing and ,design #aig ,gears1 ,a ,train of1 desc4 #bjh ,speed of #bjh ,gear-,wheels1 ,spur1 illus4 #aih ,generated1 def4 #de ,geometric1 def4 #de ,geometrical ,axioms #hd ,geometrical ,drawing1 desc4 #ha ,problems in #hf ,geometrical ,signs #hd ,geometry1 defs4 #bdi ,elements of #ha ,gothic ,letters1 illus4 #agc ,grooved ,friction ,wheels1 desc4 #bja ,ground-,plane def4 #bdi1 #bee1 illus4 #bdi ,half-,tint1 def4 #de ,hand-,wheel1 illus4 #gg ,hanger1 illus4 #agi ,helical ,wheel desc4 #aii1 illus4 #bjg ,hemisphere1 def4 #de ,heptagon1 def4 #dg ,hexagon1 def4 #dg ,to ,construct a #ie ,hexagon-,head ,bolt1 illus4 #add ,hexahedron1 def4 #dh ,horizontal1 def4 #de1 #bej ,horizontal ,line1 in ,drawing1 illus4 #bej ,how to ,draw #cb ,in ,perspective #beb ,hypothesis1 def4 #hc ,icosahedron1 def4 #dh ,india ,ink1 desc4 and illus4 #aca ,dish or ,tile1 illus4 #aca ,india ,rubber ,eraser1 illus4 #acb ,use of #bdj ,ink1 ,preparing1 for ,drawings1 desc4 #afg ,test for ,good1 desc4 #afg ,ink ,eraser1 ,steel1 desc4 and illus4 #acb ,inking1 illus4 #aff1 #afi ,long ,lines1 illus4 #agj ,rules of ,procedure #afh ,short ,work1 illus4 #afi 8,inking in0 ,drawings1 desc4 #afg 8,points10 etc4 #bci1 #bdc ,patent ,office ,drawings #bcd ,inscribe1 def4 #de ,instrumental1 def4 #de ,instruments for ,chalk-work1 illus4 #bi ,internal ,gear1 desc4 #bja ,internal-,gear ,wheel1 illus4 #bjg ,introduction #ae ,isosceles ,triangle1 def4 #ej ,lantern-,wheel1 desc4 #bja ,lathe-,dog1 illus4 #gf ,lemma1 def4 #hc ,lettering1 ,blow-,off ,valve1 illus4 #age ,drawings1 desc4 #aga ,light1 and ,sense of ,seeing #bed ,experiment with1 illus4 #bee ,laws of #beb ,line1 def4 #hb ,to ,divide into ,equal ,parts #hi ,linear ,perspective ,drawing #bdg ,lines1 def4 #de ,note #fe ,parallel1 def4 #hc ,link ,motion1 ,stephenson's1 illus4 #bbe ,longitudinal1 def4 #df ,lucas1 ,theo41 ,acknowledgement #bc1 #bff ,marking ,measurements on ,drawings #bdc ,mechanical ,drawing #acg1 #bdg ,elevation #ach ,examples #adc ,procedure #ada ,minerva1 ,free-hand ,sketch of iii ,miter-,wheel desc4 #aii1 #bjd1 illus4 #bjd ,model1 def4 #df ,nonagon1 def4 #dg ,numbering ,drawings1 ,office ,rules for #aid-e ,numerals1 illus4 #agc ,oblique1 def4 #df ,oblique ,lines ,how to ,draw1 #cb1 #eh1 illus4 #ei1 #fc ,oblong1 def4 #df ,obtuse ,angle1 def4 #db ,obtuse-,angled ,triangle1 def4 #ej ,octahedron1 def4 #dh ,octagon1 def4 #dg ,to ,describe on a given straight line #ie ,to ,inscribe in a circle #if ,oil ,can1 illus4 #gg ,optic ,nerve1 illus4 #bec ,optics1 in ,drawing1 def4 #beb ,outline ,picture1 desc4 #aeb ,oval1 def4 #df ,how to ,draw an #ga ,overall1 def4 #df ,paper1 ,fastening ,drawing on #ahd ,rule or ,scale #bdb ,sensitized1 desc4 #ahh ,the ,right ,side of #bda ,parallel1 def4 #df ,parallel ,lines1 def4 #hc1 #beb ,to ,draw #hh ,in ,perspective #bea ,parallel ,perspective ,drawing1 illus4 #bfj to #bfc ,parallel ,rule desc4 #aae1 illus4 #aad-e ,parallelogram1 def4 #dg ,to ,construct #ic ,pasting ,drawing ,paper1 8,points0 #bdc ,patent ,office ,drawings #bce1 illus4 #bcf ,rules of ,great ,britain #bcf ,rules of ,u4 ,s4 #bcc ,patterns1 def4 #df ,numbering1 from drawings #aid ,pedestal1 illus4 #agh-i ,pen1 ,hand holding1 illus4 #aff1 #afi1 #agj ,pencil1 ,function of a #adb ,how to ,cut1 illus4 #eg ,how to ,hold1 illus4 #ed1 #ei1 #fj ,how to ,use #ef ,pencil-,compasses1 desc4 #adc ,how to ,hold #adc ,penciling1 desc4 and illus4 #aci 8,points0 #adc1 #bdj ,pencil ,lines1 ,how to ,make #aai ,pencils1 ,sharpening ,points of #adc1 #bda ,penknife1 illus4 #eb ,pens1 ,drawing1 illus4 #abi ,lettering and ,figuring1 illus4 #agb ,pentagon1 def4 #dg ,to ,inscribe in a circle #id ,perimeter1 def4 #dg ,of a ,polygon1 def4 #dg ,periphery of a ,wheel1 def4 #bjj ,perpendicular1 def4 #dg1 #beb ,perpendicular ,lines1 ,how to ,draw #ca1 #fa1 #fb ,perrott1 ,geo41 ,acknowledgement #bc1 #bff ,personal1 ,note from the ,author #bff ,perspective ,drawing def4 #dg1 illus4 #bej ,definitions of ,terms used in #bdi ,geometrical ,terms used in #bdh ,of a ,bridge1 illus4 #bdi ,scale or ,approximate #beg ,vanishing ,point1 illus4 #bea ,water ,reflection1 illus4 #bdf ,perspective1 ,linear1 def4 #bdg ,perspective ,plane1 def4 #bej ,picture ,plane1 desc4 #bee ,in ,drawing1 illus4 #bdi1 #bej ,in ,perspective1 illus4 #beh ,pinion-,wheel1 desc4 #bja ,piston ,rod1 desc4 #bbc ,pitch ,circle in ,gearing #bjj ,pitch ,line1 ,drawing the #bji ,in ,gearing #bjj ,plan1 def4 #dg ,plan of the ,work #ba ,plane1 in ,perspective1 def4 #bdi ,plane of the ,picture1 def4 #bej ,plane ,surface1 def4 #di ,point1 def4 #hb ,point of ,sight1 in ,perspective ,drawing #bea ,points1 relating to ,chalk ,drawings #cf ,to be observed in ,sketching #ada-b ,useful ,hints and #agj1 #bci ,polygon1 def4 #dg ,polyhedron1 def4 #dh ,postulate1 def4 #hc ,pounce1 ,how to ,use1 desc4 #agj1 #ahf ,preface #ac ,preparatory ,practice in ,drawing #cj ,prism1 def4 #di ,problems1 def4 #hc ,geometrical #hf ,produce1 def4 #di ,profile1 def4 #di ,projection1 ,backward1 illus4 #aec-d ,def4 #di ,cylindrical ,outline1 desc4 #aei ,cylindrical ,surface1 illus4 #afa ,forward desc4 #aeb1 illus4 #aee ,hexagon ,nut1 illus4 #afj ,marking ,dimensions #aej ,lines of ,sight #aej ,scaling and ,measuring in #adi ,sight-,lines1 illus4 #aea ,sloping ,surface1 desc4 #aei ,spur-,wheel1 desc4 #afb ,projection ,drawing1 desc4 #adh ,illus4 #adi1 #aea1 #aec1 #aed1 #aee1 #aeg1 #aeh1 #afj1 #afa1 #afc ,principles of #adh ,spur-,wheel1 illus4 #afc1 #bab ,proportional ,dividers1 illus4 #abj ,proportions of ,teeth of ,wheels #baj ,proposition1 def4 #hc ,protractor1 desc4 #abh ,pulley and ,friction ,clutch1 illus4 #bbd ,punching ,press illus4 #bbb1 desc4 #bbc ,quadrant1 def4 #di ,quadrilateral1 def4 #dg ,quadrisect1 def4 #di ,rack and ,pinion1 desc4 #bje ,radius of a ,circle #dc ,reading ,working ,drawings1 desc4 #bbi ,rectangle1 def4 #dh ,to ,construct a #ib ,reproducing ,drawings1 desc4 #ahf ,reverse ,curve1 def4 #dd ,rhomboid1 def4 #dh ,rhombus1 def4 #dh ,right-,angle1 def4 #db ,triangle1 def4 #ej ,robinson1 ,a4 ,w41 ,m4 ,e41 note1 ,office ,rules #aia ,rolling-,circle in ,gear-,wheel #bjj ,rule1 ,area of a ,circle1 ,to find the #bga ,circumference of a ,circle1 ,to find the #bga ,cylinder1 ,to find the contents of a #bga ,diameter of a ,circle1 ,to find the #bga ,illus4 #hb ,inscribed ,square1 ,to find side of an #bga ,parallelogram1 ,to find the area of a #bga ,pyramid or ,cone1 ,to find the contents of a #bga ,radius of a circle1 ,to find the #bga ,sphere1 ,to find the contents of a #bga ,square1 ,to find the side of an equal #bga ,trapezoid1 ,to find the area of a #bga ,triangle1 ,to find the area of a #bga ,two-foot desc4 #abg1 #abh1 illus4 #abh ,wedge1 ,to find the contents of a #bga ,rules for ,drawing ,office #aia ,wheels1 ,to find proportions of #bji ,sand ,paper1 ,removing surface of paper #afh ,scale1 ,drawing to1 desc4 #abf ,scale ,drawings1 ,to read #bcj ,scale1 ,flat1 illus4 #abg ,triangular1 illus4 #abg ,scalene ,triangle1 def4 #ej ,scale or ,approximate ,perspective #beg ,scale ,rule1 for ,proportions of ,teeth #bad ,scales1 ,drawing1 desc4 #abf ,scholium1 def4 #hc ,screw-,thread1 ,u4 ,s4 ,standard ,gauge #bhj ,scroll or ,curve1 desc4 #aag ,universal ,curve1 illus4 #acd ,secant of an ,arc #ii ,section1 def4 #di ,drawing illus4 #afc1 desc4 #afj ,sectional1 def4 #di ,section-,liner1 illus4 #aaf ,section ,lines in ,drawings #bdj ,section-,lining1 ,cast-iron1 etc41 illus4 #ahb ,cog-,wheel1 illus4 #ahc ,section-,lining ,drawings desc4 #ahb1 illus4 #ahc ,wheel ,hub1 illus4 #ahd ,selecting ,drawing ,instruments #ajc1 #bdj ,semi-,circle1 def4 #dc ,sensitized ,paper1 desc4 #ahh ,set-,square1 illus4 #ajb1 #aad ,shading ,curves1 illus4 #aha ,shading ,drawings #ahj ,shadow1 def4 #di ,shadow ,line1 def4 #df ,shadow ,lines1 8,points0 #bda ,sharpening ,pencils #eg ,shop ,drawings1 ,office ,rules #aib ,sight1 ,point of1 in ,perspective ,drawing #beb ,sense of #bed ,sight ,lines in ,projection1 illus4 #aeg ,sine of an ,arc #ii ,skew-,gearing1 desc4 #bjc ,sketch ,books1 desc4 #adb ,office ,practice #aid ,sketches1 details #adb ,sketch1 ,free-hand1 ,advantage of #ee ,sketching desc4 #ada1 note #ag ,points to be observed in #ada-b ,sloping ,surface in ,projection desc4 #aei1 illus4 #aff ,solid1 def4 #di1 #hc ,solid ,pattern1 def4 #dg ,speed of ,gears #bjh ,sphere1 def4 #di ,spiral ,curve1 def4 #dd ,spring ,bows illus4 #abb1 #abc1 desc4 #abd ,spur-,gear desc4 #bja1 illus4 #baa ,spur ,mortise-,wheel1 illus4 #bjb ,spur-,wheel1 desc4 #aii1 #baf ,how to ,draw #bji ,illus4 #aih ,projection desc4 #afb1 illus4 #afc ,teeth of cast-iron1 desc4 #bjb ,square1 def4 #dh ,to ,convert into an ,octagon #ie ,to ,describe about a ,circle #id ,to ,inscribe in a ,circle #ic ,standards1 for ,u4 ,s4 #bgh ,office ,rules for #aic ,steady ,rest1 ,scale1 illus4 #bbh ,straight ,line1 def4 #df ,to ,draw a ,perpendicular to a #hf ,drawing ,figures of #ff-g-h ,how to ,draw a #eg1 #ei ,to ,bisect a #hf ,steel1 ,section-,lining1 illus4 #ahb ,steel ,gears1 ,economy of #baf ,surface1 def4 #di1 #hb ,symbols1 representing ,materials #aic ,table of ,areas of ,circles #bgc-bgg ,bolts1 ,standard ,sizes of #bhj ,circular ,measure #bgb ,circumferences of ,circles #bgc-bgg ,contents #bd ,decimal ,equivalents #bfi ,diameters of ,circles #bgc-bgg ,land ,measure #bgb ,metric ,equivalents #bgj ,pipe1 ,standard ,sizes of ,welded #bgi ,roman ,figures #bgb ,solid ,measure #bgb ,wire ,gauges #bgh ,useful for ,draughtsmen #bff-bhj ,tangent of an ,arc1 def4 #ii ,to ,draw a1 to a ,circle #ia ,tee-,iron1 illus4 #ge ,tee-,square1 ,adjustable1 desc4 and illus4 #aac ,desc4 #aab ,how to ,use1 illus4 #aaa1 #adg ,illus4 #ajb1 #aab ,points about #bdb ,teeth in ,bevel ,gears1 desc4 #bjd ,terms and ,definitions1 ,preliminary #da ,test-,pieces1 ,use of1 in ,blue ,prints #ahh ,tetrahedron1 def4 #dh ,theorem1 def4 #hc ,thumb-,tack illus4 #aji1 desc4 #aaj ,tints and ,colors1 desc4 #ahd ,title and ,date1 on ,sketches #adb ,title1 ,date1 ,scale1 etc41 ,office ,rules for #aib ,title ,page vii ,tracing-,cloth1 desc4 #ahf ,tracings1 ,office ,rules for ,keeping #aie ,tinted and ,shaded1 desc4 #ahd ,trammels1 desc4 and illus4 #abe ,trapezium1 def4 #dh ,trapezoid1 def4 #dh ,trestles1 ,drawing-,board1 desc4 and illus4 #aaj ,triangle1 def4 #ej ,to ,describe a ,circle about a #ic ,triangle1 or ,set-,square1 desc4 and illus4 #aad ,how to ,use desc4 #adg1 illus4 #aff ,triangles1 illus4 #ajb ,to ,construct #ib ,trigonometry1 principles and def4 #ih ,trisect1 def4 #ej ,trundle ,wheel desc4 #bja1 illus4 #bjh ,two-foot ,rule1 illus4 #abh ,u4 ,s4 ,standards1 ,pipes #bgi ,upright ,lines1 ,how to ,draw #fa ,useful ,tables for ,draughtsmen #bfi-bhj ,valve1 ,blow-off desc4 #agd1 illus4 #age ,valve ,gear1 or ,link ,motion1 illus4 #bbe ,vanishing ,point1 def4 and illus4 #bea ,in ,drawing1 illus4 #bej ,in ,perspective ,drawing #beb ,varnish1 ,shellac1 for ,drawings #bda ,versed ,sine of an ,arc #ii ,vertex1 def4 #ea ,of an ,angle1 def4 #db ,vertical1 def4 #ea1 #bea ,vertical ,lines1 in ,perspective #beg ,vertical-,plane1 def4 #bdi ,view1 def4 #ea ,visual ,ray in ,perspective ,drawing #bef ,visual ,rays of ,light desc4 #beb1 illus4 #bee ,vulcanite1 ,section-,lining1 illus4 #ahb ,water ,reflection in ,perspective ,drawing1 illus4 #bdf ,wheel1 ,bevel1 ,a1 illus4 #bjc ,crown1 illus4 #bjh ,helical1 ,a1 illus4 #bjg ,hub1 ,section-,lining1 illus4 #ahd ,internal ,gear1 desc4 #bja1 #bjg ,miter1 ,a1 illus4 #bjd ,proportions of the ,teeth of a #baj ,spur illus4 #aih1 desc4 #aii1 #bja ,worm1 desc4 #bja ,wood1 ,section-,lining1 illus4 #ahb ,working ,drawing1 ,bending ,machine #bbj-a ,def4 #ea ,illus4 #bah1 #bbj1 #bba1 #bbb1 #bbc1 #bbd1 #bbe1 #bbf1 #bbh ,bumping ,post1 illus4 #bbf ,points1 etc4 #bdc ,power ,punching ,press #bbb ,numbering a1 ,office ,rules for #aie ,to ,read a #bbi ,working ,drawings1 desc4 #bai1 #bbg ,worm-,gear1 desc4 #bjf ,worm-,wheel desc4 #bja1 illus4 #bjf ,speed of a #baf ,wrench1 illus4 #ge ,wrist-,lines1 illus4 #fd ,wrought-,iron1 ,section-,lining1 illus4 #ahb ,transcriber's ,notes ,inconsistent and unusual spelling1 capitalisation and hyphenation have been retained1 unless mentioned below4 ,the discrepancies between the ,general ,list of ,contents and the structure of the text have not been corrected4 ,depending on the hard- and software used to read this text and their settings1 not all elements may display as intended4 ,where scales are given for illustrations1 these can1 of course1 not be relied upon for measurements4 ,the numbering of illustrations in the book is inconsistent4 ,illustrations that have no numbered captions may or may not be counted2 this has not been standardised1 except as listed below4 ,missing illustration numbers have been added only where they are referenced in the text4 ,the illustrations referred to in the text as ,figs4 #bdb and #bdc are captioned ,fig4 #bdc and #bdd4 ,page #fe-fi and ,figs4 #ff-ga3 the text uses upper case reference letters1 the illustrations lower case1 which has not been standardised4 ,page #hd1 table of symbols3 the source document uses letters 7,o and ,l7 rather than symbols for circle and angle4 ,page #id1 ,bisect two of the angles ,a ,c of the triangle3 presumably the unmarked point ,a is in the lower left-hand corner of the illustration4 ,page #aac1 ,the tee-square1 as shown1 4443 there is no illustration with the relevant reference numbers2 probably the reference is to ,fig4 #aea_/aeb4 ,page #bci1 rough irregular lines1 as in fig4 #acd1 on page #aca3 there is no ,fig4 #acd on page #aca2 page #acd nor page #aca show the rough irregular lines4 ,several other illustrations in the book do show such lines4 ,index3 the order of entries is as printed in the source document4 ,changes made3 ,illustrations and ,notes have been moved out of text paragraphs4 ,some obvious minor punctuation and typographical errors have been corrected silently4 ,in some tables the ditto symbol 77 has been replaced with the dittoed text2 some tables have been split or re-arranged4 ,the use of and x in multiplications and dimensions has been standardised to 4 ,page #dh3 ,figure numbers #de-di added to illustration4 ,page #hi3 and on ,b on ,b ,i changed to and on ,b on ,b ,d4 ,page #agg3 ,d diam4 of collar changed to d diam4 of collar4 ,page #aic3 ,bbt4--,babbit4 changed to ,bbt4--,babbitt4 ,page #bjc3 as described on page #aia changed to as described on page #aii4 ,page #bad3 #d tenths measured at the #b line changed to #d tenths measured at the #b line4