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 COPYRIGHT DEPOSIT. 
 
HANDBOOK 
 
 FOR 
 
 Carpet Measurers, Cutters 
 and Salesmen 
 
 INCLUDING 
 
 TOPICS OF GENERAL INTEREST TO THE TRADE 
 
 WITH ILLUSTRATIONS AND DIAGRAMS 
 
 BY 
 
 JOHN W. LIND 
 
 GEORGE LYNDOE 
 
 The American Carpet and Upholstery Journal 
 
 Hartford Building, 41 Union Square, West 
 
 New York City 
 
 1905 
 
LiBSARY Of 30NGKESS 
 Two Dopies rfeuaveu 
 
 JUL 6 1905 
 
 jouynipu tntry 
 -fHcUflS '/<?OS 
 
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 , 7 /</ 
 
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 Copyright, 1905 
 By JOHN W. LIND 
 
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PREFACE, 
 
 Although intended as a guide to Carpet Measurers, 
 especially for those who lack experience, the information 
 and hints contained in the following pages are likely to 
 be of benefit to carpet cutters, layers, salesmen, and 
 others connected with the house-furnishing business. 
 
 For those who have been long doing this work, claim- 
 ing experience, it is a matter of importance to have a 
 system and know just what measurements would be su- 
 perfluous, how to do the work in the quickest and 
 surest manner — in a word, to become thoroughly versed 
 in their calling. Many of the rules and problems given 
 here are the outcome of a long experience aided by a pre- 
 vious training in drawing and surveying. 
 
 Years ago it used to be the custom to cut and fit carpets 
 at the house and then return them to the store to be sewed. 
 Some of the large New York stores often take two hun- 
 dred orders for carpets in a single day. Manifestly it 
 would be impossible to do work in the old way. Now, 
 however, the room or spaces to be carpeted, literally 
 speaking, are brought to the cutter at the store by the 
 measurer, who, if he understands his business, so meas- 
 ures the most irregular room or space that it can be 
 reproduced with perfect accuracy when struck out on the 
 cutting floor of the carpet workroom. 
 
 It is the aim of the writer to show how this can be done, 
 using the most practical methods. 
 
 iii 
 
iv PEEFACE 
 
 The diagrams are not only typical but actual examples, 
 and from them one can get an idea of the complexities met 
 with in modern houses. 
 
 Though a general understanding of mensuration and 
 plane geometry is recommended, the possession of this 
 knowledge is not essential. There are several problems, 
 however, which every carpet measurer should be able to 
 solve, and to become competent, something more than 
 rudiments should be known. The most important and 
 useful of these problems are explained and will be re- 
 ferred to as occasion demands. 
 
 To err is human. Nevertheless, none of us like to make 
 mistakes, and, what is more, we ought constantly to guard 
 against them by checks of various kinds. Mistakes on 
 the part of the carpet measurer or cutter are especially 
 costly, and a man's value to his employers is usually de- 
 termined largely by his accuracy.. 
 
 It is hoped that careful perusal of the following pages 
 will insure to the benefit even of those who only occasion- 
 ally make such mistakes, and do a service by helping to 
 reduce these to a minimum. 
 
CONTENTS 
 
 PAGE 
 
 Introduction vii 
 
 PART I 
 
 Implements of the Carpet Measurer 
 
 The Measuring Tape 1 
 
 The Pocket Eule 1 
 
 The Awl 2 
 
 The Chalk Line 2 
 
 The Pencil 3 
 
 PART II 
 Hints on Drawing' the Plan 4 
 
 PART III 
 Suggestions to Measurers 7 
 
 PART IV 
 
 Practical Hints on Measuring 
 
 To Measure a Hall and Hall for Tracker 15 
 
 To Measure Stairways 15 
 
 To Measure a Church 18 
 
 To Measure a Theater 18 
 
 To Measure a Boa t 21 
 
 To Measure a Large Obstructed Space 21 
 
 To Measure Any Irregular Room 24 
 
 To Measure a Window or Room Whose Sides or Corners 
 
 are Inaccessible 25 
 
 To Measure a Room or Rooms from the Outside without 
 
 Entering It. 27 
 
 To Measure for a Tracker 32 
 
 To Measure for a Carpet to be Bound 33 
 
 PART V 
 
 Typical Diagrams and Measurements Explained 34 
 
 v 
 
vi CONTENTS 
 
 PAET VI 
 
 PAGE 
 
 Simple Geometrical Problems 
 
 To Bisect a Line 55 
 
 To Bisect an Angle 55 
 
 To Draw a Line Parallel to a Given Line 55 
 
 To Erect or Let Fall Perpendiculars 56 
 
 To Find the Center of a Circular Window 58 
 
 To Find the Foci Points of an Ellipse 61 
 
 PAET VII 
 Common Arithmetic 
 
 Examples in Arithmetic and Short Methods 62 
 
 Vulgar Fractions 65 
 
 Duodecimals 73 
 
 Decimals and Decimal Fractions 75 
 
 Proportion, or Bule of Three 78 
 
 Square Root 81 
 
 PART VIII 
 To Estimate on Carpets 
 
 Mensuration of Plane Surfaces 83 
 
 Triangle 90 
 
 Trapezoid 87 
 
 Trapezium 91 
 
 Any Polygon 92 
 
 Circle 94 
 
 Circular Arc 102 
 
 Ellipse 103 
 
 PART IX 
 
 Hints on Matching and Cutting Carpets 108 
 
 PART X 
 
 A Short Treatise on Carpets — The Different Grades, and How 
 
 Made 117 
 
CONTENTS vii 
 
 PAET XI 
 
 PAGE 
 
 Suggestions to the Layer 124 
 
 PART XII 
 
 To Measure for Shades, Draperies, and Awnings 
 
 To Measure for Window Shades 130 
 
 To Measure for Laces, Draperies, and Sash Curtains 131 
 
 To Measure for Portieres 131 
 
 To Measure an Archway 131 
 
 To Measure for Awnings 133 
 
 PART XIII 
 
 Table of Cutting Lengths 135 
 
INTRODUCTION 
 
 The difference in the amount of work handled by the 
 carpet trade in the dull and busy season is so great, it is 
 extremely difficult to have available at all times sufficient 
 skilled help. 
 
 It is, therefore, frequently necessary to call on men in 
 the business, not familiar with the mechanical part of the 
 trade, to help out the workroom force. The result, as 
 may be expected, is misfit carpets. These mistakes, com- 
 ing as they do in the busy season, disarrange so to speak 
 the smooth running of the machinery, and are con- 
 sequently both costly and annoying. 
 
 To eliminate as far as possible such mistakes, and assist 
 those with limited experience, has been the main object in 
 publishing this book. It has been written by a man 
 thoroughly experienced, and the work explained in a 
 practical manner, making it possible for the student in a 
 few hours to gain knowledge which otherwise would take 
 years to acquire. 
 
 Recognizing its value, I heartily recommend this book 
 to the carpet trade. 
 
 George Lyndoe. 
 
 ix 
 
PART I 
 IMPLEMENTS OF THE CARPET MEASURER 
 
 THE TAPELINE 
 
 A fifty-foot tape is the length best fitted for the work 
 of carpet measuring, and one of the best standard 
 makes only should be used. As, however, even these 
 will vary in time, and as we remember that the line used 
 by the measurer is not the one used by the cutter, it 
 will be seen how important it is to compare the two 
 frequently, or, better still, to test them by a steel tape 
 or some measured distance laid out on the floor, say 
 twenty-five feet in length, and marked every 12 inches 
 with fine brass screws, the slots of which mark the feet. 
 This will always be available to the cutter and measurer 
 alike, and when several lines are in use those found in- 
 correct should be discarded, as it is cheaper to buy a 
 new line than to replace a misfit carpet. It will be found 
 convenient to have a few holes punched in the line and 
 small eyelets inserted, say at the 1, 3, 6, and 21-foot 
 marks. 
 
 THE RULE 
 
 The rule is used chiefly as a straight edge for drawing 
 the plan, for measuring under furniture or in other places 
 where use of the tapeline is impracticable. When line 
 
2 CARPET-MEN'S MANUAL 
 
 and rule are used in combination care should be taken to 
 add the length of the rule to the readings on the line. To 
 avoid the error of this omission it is best to bring the 
 mark on the line corresponding to the length of the rule 
 up to the end of the latter, and then fasten it, then pick 
 up the rule, which also diminishes the chances of leav- 
 ing it behind. The eyelets mentioned above will prove 
 useful for inserting the awl at one of these points as a 
 safeguard against injuring the tape. A rule made with 
 a beveled edge having a 1-4 and 1-2 inch scale will be 
 found convenient, especially when measuring from 
 architects' plans or drawing to a scale. 
 
 THE AWL 
 
 This instrument is used to fasten the end of the tape- 
 line to the floor by inserting point through the small hole 
 next the ring. It should have a fine removable point, 
 which if broken can be renewed. A pocket awl made by 
 C. Wood is a very practical tool for this work. It has a 
 hood or socket made to slip over the awl point and so pro- 
 tects the person carrying it from injury. The hood also 
 is used as a wrench when changing points. It is always 
 at hand, as it is never removed from the main tool except 
 for this purpose. 
 
 THE CHALK LINE 
 
 This may be any ordinary twisted or woven line; the 
 finer it is the better as it makes a finer mark and takes up 
 less room. In addition to these tools a pair of dividers 
 will be found useful. 
 
IMPLEMENTS 
 
 THE LEAD PENCIL 
 
 Pencils best adapted to drawing are black, Nos. 2 and 
 3, according to whether the paper is smooth or rough. 
 The lead should be sharpened in the shape of a wedge, 
 thus producing strength and durability and making an 
 even black line. Black, No. 3, sharpened round is best for 
 writing in the figures. 
 
PART II 
 DRAWING THE PLAN 
 
 On entering the room to be measured, take an eye sur- 
 vey, noting the relative size of the sides. If there are two 
 or more adjoining rooms observe whether the walls are in 
 the same straight line, or whether the walls in one room 
 project beyond those of the others, also if doors have sills 
 or not, or if sliding whether rod is at the top or bottom. 
 Then begin in the room nearest the front, using, if no 
 other means are at hand, the wall or floor as a drawing 
 board, making front of plan at top of paper, and draw 
 the outlines of the room as near to scale as possible. 
 Draw all projections and recesses, show slants and curves 
 of sides, if any. Mark plan at windows with a " W," 
 doors with a " D," entrance with an " E." Note if there 
 is a fireplace and whether open or not. If measuring for 
 rugs, it is also necessary to note registers and radiators, 
 their exact size and distance from walls. Pass to the next 
 room and proceed as before. If adjoining, draw it the 
 thickness of the wall from the first, draw closets if any, 
 in short, reproduce on paper the floor of each room as it 
 appears and in proper location with reference to each 
 other, thus making a complete ground plan of the whole. 
 In taking a diagram of any large house, such as an apart- 
 ment house or hotel, where the rooms over the ones be- 
 low are about the same shape and size, it will save time 
 
 4 
 
DRAWING THE PLAN 5 
 
 by having a sheet of paper for each floor placed one over 
 the other, then by bearing hard on the pencil each under- 
 lying paper will have traced upon it the plan, which only 
 needs going over with pencil to finish. When measuring 
 theaters, churches, or boats, where curves, projections 
 and recesses predominate, it is advisable to draw the 
 plan to scale. This can be done by first measuring the 
 place, marking the figures on the floor, afterwards draw- 
 ing the plan from these figures, using any convenient scale 
 as 1-4 or 1-2 inch to the foot, or else drawing each line to 
 scale as fast as measured. (Avoid copying plans, as 
 mistakes are apt to follow.) It will take a little more 
 time, but you will be repaid by being certain that your 
 pans are correct, for if any measures are wrong the 
 plan will not prove. It is also less difficult to cut, or 
 figure from such a plan, and the breadths can be laid 
 out or estimates given with great exactness. When a 
 plan is to be made of several adjoining rooms, some of 
 which may be dark or with rough walls, begin by mak- 
 ing a light freehand sketch of each room, after which a 
 smooth surface where the light is good can be selected 
 o finish the plan. If all lines running in the same direc- 
 tion are drawn before turning the paper to draw the 
 others, an advantage will be gained in speed. 
 
 After the plan is drawn, which should be done with 
 even, black, heavy lines, draw fine light lines to repre- 
 sent other measures which are to be taken, such as angles, 
 or cross, and square measures, etc. This diagram will 
 give something tangible to work from at the start. 
 
 It part of the floor space is to be covered by a rug and 
 the rest with filling, or if it has been arranged to run the 
 
6 CABPET-MEN'S MANUAL 
 
 border any particular way, this should be shown on the 
 plan by sketch and figures, and then submitted to cus- 
 tomer for approval. Moreover, if any instructions are 
 given by customer or suggestions advanced by measurer 
 and accepted by the former, such directions should be 
 written on the plan and repeated to the customer before 
 leaving the house. The importance of this part of a meas- 
 urer's work cannot be emphasized too strongly, as fail- 
 ure to do it, or an attempt at committing to memory 
 such instructions, will eventually cause trouble. When 
 it is required to measure for cocoa or rubber mats, 
 which, on account of irregularity of shape, have to be 
 made to order, a paper pattern should be taken and sent 
 to the factory, and a copy of same kept at the store. 
 Do not forget to mark the top of the pattern. 
 
PART III 
 SUGGESTIONS TO MEASUEEES 
 
 The first aim of the prospective carpet measurer 
 should be accuracy. To attain this, all his work should 
 be done with the greatest possible exactness. Measure 
 all rooms so that they can be reproduced, or " struck 
 out.'' Measures should be taken to an eighth of an inch 
 when carpets are to be bordered, but even when plain, 
 close measures will often assist the cutter in the difficult 
 task of covering a space with barely enough goods. 
 Negligence in this respect at the start is apt to foster 
 habitual carelessness later on. If a customer resides 
 far from the store, or measures are taken before the 
 carpet is selected, border measures should invariably be 
 taken. Make it a point to take such measures only as 
 will bring the best results, and do not fill the plan with a 
 lot of unnecessary measures, taken in a haphazard way, 
 that prove nothing. On the other hand, no measures 
 should be omitted that will serve to check the work. 
 It is far better to have too many measures than not 
 enough. Make a close study of the different methods 
 of measuring given in the following pages, and apply 
 them in drawing imaginary floor spaces, or copy the 
 several diagrams given, using rule and dividers. 
 Proficiency and self-reliance will be the immediate re- 
 sult. Never waste time figuring out where you can stop 
 
 7 
 
8 CAKPET-MEN'S MANUAL 
 
 a breadth or put in a piece, as you will then interfere 
 with the work of the cutter. Instead give him the ac- 
 curate measures and the exact shape of the floor. You 
 are the architect of the business, the cutter is the builder ; 
 he knows what material he has to work with, while you do 
 not, therefore give the proper instructions and leave the 
 rest to him. 
 
 The difference between measuring for bordered and 
 plain carpets will now be shown. 
 
 For a border carpet all the wall lines, together with 
 diagonal, or square measures, should be taken in order 
 to assure a perfect fit. In a plain carpet all the waste is 
 left on, to be turned under or cut off by the carpet layer. 
 It is, therefore, unnecessary to give as many measures 
 as when carpet is to fit exactly. The measures given 
 should, nevertheless, be exact and so taken that any slant 
 of the sides can be determined by the cutter. Thus in a 
 rectangular room length and width only are necessary; 
 in a room of trapezoidic shape, Fig. 1, Part VIII, length 
 of the parallel sides and the perpendicular distance be- 
 tween them are given. On a floor like a trapezium, Fig. 3, 
 Part VIII, the greatest length, length of the sides to 
 which this line is parallel, the perpendicular distance be- 
 tween them, together with the greatest width, are taken. 
 And in general such measures are taken as will divide the 
 floor into the necessary number of triangles and trape- 
 zoids, Fig. 4, Part VIII. The measures given in these 
 figures are all that are necessary for plain work or esti- 
 mates, and it will be noticed that, although all wall lines 
 are not measured, they can, nevertheless, be struck out 
 if required. It is, of course, understood that, whether 
 
SUGGESTIONS TO MEASURERS 9 
 
 plain or bordered, all recesses should be taken. In the 
 busy season in large cities, where measurers often are 
 expected to take from twenty to forty orders a day, 
 several minutes may be saved in each house, in the case 
 of a plain carpet, by taking only such measures as are 
 necessary for plain work. Cutters, however, should not 
 attempt to cut borders from plain measures, since if an 
 order is changed the room can easily be remeasured. If 
 more rooms are measured than the order calls for, give 
 the reasons for taking them, whether for selection, ad- 
 ditional order, etc., plainly written in each diagram or 
 elsewhere on the plan. 
 
 As many cutters find it convenient to strike out the 
 plan, working from straight lines marked on the floor, 
 perpendicular or at right angles to each other, it will be 
 of aid if measures are taken from similar base lines. 
 Several methods of how to erect or let fall perpendicular 
 lines are explained in this book, and the measurer can 
 use the one he finds most convenient. Measurers, how- 
 ever, should never rely entirely on what is known as 
 square measures, but use cross measures also to check 
 their work. A plan of any room can be reproduced if 
 measures are taken on any known line of perpendicular 
 offsets to corners or projections without measuring the 
 walls at all. These offsets when connected by straight or 
 curved lines, as the case may be, form the true wall lines, 
 but a single wrong measure which a cross measure 
 would check, might not be detected until too late. 
 
 No matter how used to any particular system a cutter 
 may be, he never fails to appreciate the value of cross 
 or diagonal measures. 
 
10 CARPET-MEN'S MANUAL 
 
 After the plan is drawn, begin at the entrance side of 
 the room to measure. If this side is not straight make it 
 such by snapping chalk line on the floor parallel, or at 
 right angles, as the case may require, Diag. 38, to the di- 
 rection in which the breadths according to the measurer's 
 judgment or customer's dictation should run. From this 
 chalk line as a base, measure both ways across the room, 
 also the whole width for a check. Now fasten the end of 
 the tapeline at the rear end of the room and measure, in 
 the direction the breadths are to run, the length from 
 end to end along wall or chalk line. Pull the tapeline 
 sufficiently taut to take out any kinks it may contain, 
 then pass along and note the reading, recording them on 
 diagram. Read figures on tape again, and glance at the 
 preceding figures to avoid making the common error of 
 taking six for nine or vice versa. If any recesses or pro- 
 jections occur along the line, note down the figures on the 
 tape opposite each, Diag. 5. After releasing the tape, use 
 it to measure depths and length of recesses before pro- 
 ceeding further, or if depth of recess is not greater than 
 the length of your rule use this, in which case the depth 
 should be taken when the recess is located. If the en- 
 trance side is not a straight line, and there are more than 
 four sides to the room all running in different directions, 
 snap two chalk lines on the floor perpendicular to each 
 other, if possible, and as long as they can be, Diags. 38 and 
 45, then, by measuring these lines and noting the point of 
 intersection, two base lines are established from which 
 all other measures may be taken. It is not necessary that 
 these base lines should be at right angles, but if not the 
 angle or slant they make with each other should be ascer- 
 
SUGGESTIONS TO MEASURERS 11 
 
 tained by- measures from line to line between any two 
 known points, Diags. 38, 45 3 and 5. If the room is too 
 large or obstacles exist preventing measures being taken 
 from two base lines, Diags. 4 and 5, strike out with the 
 chalk line a four-sided figure as large as possible and 
 from the four sides, as base lines, take the necessary off- 
 sets. Theaters, churches, boats, and lodge rooms should 
 be measured from the center in both directions, and the 
 whole width also should be taken to check the work. 
 
 When measures are taken of circular, or, as they are 
 more commonly called, swell windows, Diags. 34 to 44. the 
 measurer should first ascertain whether it is a segment; 
 i. e., a part of a circle, or a part of an ellipse, Diag.41,or 
 any other conic section, Diag. 45. To do this, try and 
 find the center by any of the methods given in this book. 
 The distance from this point to any part of the swell is 
 called the radius, and should always be given on the 
 plan together with the height or longest perpendicular 
 distance from the chord, or opening of the swell, to the 
 wall. The two measures combined will always check the 
 work, whereas, if the radius only is given, or the cutter 
 is left to find it from measures given of the height alone, 
 or distance from center to chord, any errors in these 
 measurements will cause corresponding error in length of 
 the circumference or swell without being discovered. If 
 after trial no such center can be found, then the swell is 
 no part of the circle and perpendicular offsets must be 
 taken from one or more measured straight lines drawn 
 from a common point or points on the circumference, 
 across it, or to points of opening of swell, or both (see 
 Diags. 37, 41, and 45). Again, the depth of the swell may 
 
12 CARPET-MEN'S MANUAL 
 
 be so shallow that the center would be far back in the 
 room, Diags. 37 and 38. In this case it will save time to 
 snap a chalk line across the swell, lay the tape over it and 
 measure offsets at right angles to it, with the rule or 
 tape, 6 or 12 inches apart, Diag. 37. The cutter can then 
 produce the swell by finding the radius, the different off- 
 sets serving as a check, or he can lay out the offsets and 
 with a flexible rod or thin strip of wood and chalk connect 
 the ends of the offsets. 
 
 It may happen sometimes that the walls are so ob- 
 structed with furniture, that to get accurate measures 
 would necessitate disturbing the latter with the risk of 
 damage to wall or furnishings, removal of the latter 
 causing annoyance to customer or wasting too much time. 
 Cases of this kind are not frequent, but, nevertheless, 
 happen, and as a measurer ought to be prepared for any 
 emergency, Diags. 7 and 8 can be studied to advantage. 
 
 In Diag. 7, the furniture, i. e., a what-not, dresser, and 
 bookcase, happened to be so arranged that it was im- 
 possible to get at the walls, and as the lady expected com- 
 pany she was unwilling to have anything moved. On in- 
 vestigation, however, it was found that the corners were 
 accessible by placing the rule under the furniture. Meas- 
 ures were taken as in Diag. 7, and the carpet, which 
 was a bordered Wilton, cut and made and when laid 
 proved a perfect fit. The lady, who in the meantime had 
 been greatly worried, as she felt partly responsible for 
 not allowing the furniture to be moved, was very much 
 pleased with the carpet, and after that had great faith in 
 the ability of the workmen of that store. 
 
 Often a man is sent to measure a house only partly 
 
SUGGESTIONS TO MEASUREES 13 
 
 finished, perhaps with only the studdings up, and in such 
 cases only approximate measures should be taken, in 
 order that sufficient goods may be reserved or estimates 
 given. Of course, border measures should not be at- 
 tempted, as alterations in construction of rooms would 
 result in a misfit carpet, and the measurer would have no 
 excuse, as he had no right to turn in a diagram based on 
 guesswork. 
 
 The measurer is often called upon to give an estimate 
 of the number of yards required, or the cost of the carpet. 
 Although it is preferable not to volunteer giving esti- 
 mates, it is sometimes difficult to refuse a customer's re- 
 quest, especially when the goods are to be sent C. 0. D., 
 as the customer may desire to know approximately the 
 amount of money to have on hand. When there is com- 
 petition for the order or the customer is in no hurry to 
 have the carpet delivered, the figures given may be the 
 means of holding or losing the order. 
 
 The measurer, therefore, should be able to give esti- 
 mates, but always with the explanation that they are only 
 approximate, as he has no way of knowing what loss there 
 would be in matching the figure. It is taken for granted 
 that the measurer is acquainted with the common rules 
 of arithmetic, otherwise, the examples given in this book 
 will be a great help. The estimate should always be 
 written on the plan for future reference. It is customary 
 to figure the yards net and then add from one foot to half 
 a yard for each breadth ; it is better to figure liberally as 
 the measurer then will be on the safe side. 
 
 The measurer should always endeavor to write small 
 plain figures. In the diagrams they should be placed in 
 
14 CAKPET-MEN'8 MANUAL 
 
 a continuous line and as nearly opposite the point 
 measured as possible. Eemember also to name or des- 
 ignate each room or space measured, that the layer may 
 have no difficulty in locating the same. Moreover, try to 
 do your work in such manner that it will be easily un- 
 derstood by all who shall have occasion to refer to the 
 diagrams. 
 
PART IV 
 PRACTICAL HINTS ON MEASURING 
 
 HALL MEASURES 
 
 In measuring front halls, begin at the entrance, as the 
 carpet is usually rolled toward the rear in cutting. For 
 the same reason all halls above the first ought to be 
 measured from rear to front. Position of the stair should 
 always be shown, to prevent cross-joins being placed 
 where most conspicuous. All door recesses, however 
 slight, should be given, because it may save waste of 
 material and unnecessary labor for the carpet layer. 
 
 HALL TRACKERS 
 
 To give the best effect a tracker should be placed in 
 the center of the hall, but as it is not always desirable to 
 have it cut to conform to the shape of the hall it is well 
 to measure the entire floor, and then show by sketch and 
 proper figures the position of tracker on the plan (see 
 diagram of halls). 
 
 TO MEASURE A STAIR 
 
 Begin at the top and measure down across tread and 
 over risers, and then to check the measurements and 
 ascertain number of pads wanted, count the number of 
 steps. If all the straight treads are of the same depth, 
 
 15 
 
16 CARPET-MEN'S MANUAL 
 
 the length of one step (tread and riser) multiplied by the 
 number of steps will give the length of carpet provided 
 the stair is straight. If winding add six feet for a four- 
 feet or under square landing, or, if no landing, three feet 
 for each turn, — if the stair is in several parts, and 
 divided by landings, measure each section separate (see 
 diagram of stair). If the stair itself is winding, begin at 
 the top and run the tape down next the baseboard to the 
 beginning of the first winding tread, then across the 
 corner of the wind to the nosing of the next straight 
 tread, in such manner that the distance of the tape from 
 the baluster will be equal to the width of the straight 
 step, then down to the bottom. If the stair is to be 
 covered entire, measure the width of the straight step, 
 and the perpendicular distance from the tape to the 
 corner of the wind — also note the readings on the tape at 
 the two points from which the line crosses the corner. 
 If the steps vary in width, let tape remain, and with an 
 extra line or rule measure across the steps as they in- 
 crease or diminish in width and note the position of each 
 cross-measure so taken on the long tape (see diagram of 
 stair). Always give the exact length of the stair and let 
 the cutter add allowance for slipping. There is no more 
 reason for the measurer to add to this measure than there 
 is for him to add to any other measure taken in the house. 
 The only time this allowance should be considered by him 
 is when giving estimates, and then the length of one step 
 is to be added to each breadth. It is as well, however, to 
 have an understanding with the cutter on this point, as it 
 is the custom in some stores for the measurer to add this 
 allowance, while in others again it is left to the cutter. 
 
DIAGRAM 1. 
 
18 CAKPET-MEN'S MANUAL 
 
 TO MEASURE A CHUKCH LIKE DIAGRAM 1 
 
 Find center line of room. If possible snap chalk line 
 across it from wall to wall, if not, as far as it will go. 
 Measure on this line, beginning at the center, on one side 
 mark off every 27 inches, on the other every 36 inches, or, 
 if width of carpet is known, lay off the breadths on one 
 side, and on the other offset marks to corners, aisles, and 
 pews; measure such breadths or offsets from marks on 
 chalk line both ways. If pews intervene, as in front of 
 altar, snap chalk line perpendicular to center line as far 
 as it will go, from ends set other perpendicular lines and 
 so on until a straight line will clear the circumference of 
 inner circles, measure as before, laying off breadths on 
 one side and offsets on the other, and always measure 
 from line on which such marks are made. By proceeding 
 thus the room can be struck out, or carpet cut direct from 
 plan, and figures can be more readily perused, as the plan 
 will not be crowded. In pews if one or both ends slant, 
 measure the longest diagonal, if ends make the same 
 angle with front or back of pew measure the longest side. 
 
 TO MEASURE A THEATER — DIAGRAM 2 
 
 After center of room is found, which in this plan is 
 ascertained by finding middle of center door, or by 
 measuring from door to door each side of the center door, 
 or by lining up the posts, lay out center line CD and from 
 the end, touching back of seats, snap chalk lines at right 
 angles as far as possible in both directions, as AB. 
 From the center, on this line, mark off breadths on one 
 
20 CABPET-MEN'S MANUAL 
 
 side, and offsets to aisles and corners of seats, etc., on the 
 other, — from end of the last breadth or offset draw other 
 lines parallel to AB, and continue as before to end of 
 line and again produce lines parallel to the last and so on, 
 first back of orchestra circle, then back of orchestra stalls, 
 and last in front of orchestra. Draw on your paper a line 
 to represent the line AB, but extend it to the full width 
 of the paper, bisect this line, from the center lay off 
 all the breadths to scale, counting from the center line to 
 wall. Through these marks draw, lightly, perpendicular 
 lines parallel to each other the full length of paper. Now 
 measure to the offset marks and lay these down on the 
 paper according to scale. After all offset marks have 
 been laid down draw light lines through these marks upon 
 which set length of offsets, also to scale, measured from 
 AB in both directions. Fold paper back on center line, 
 connect offset ends, first lightly, then by bearing hard 
 enough on the pencil to show trace on folded part of 
 paper, straighten it out and go over tracing marks with 
 pencil and the plan is complete. The length of breadths 
 can be ascertained from scale and will be a check on your 
 work. The breadths should now be measured from the 
 chalk line both ways and recorded on the corresponding 
 lines on the plan, also measure boxes from entrance side 
 and wall ; the work is now finished unless carpet is to go 
 in front of seats, in which case measure each row and 
 number same. 
 
 Note in this theater both sides of the house are alike, 
 this is not always the case however, but if any difference 
 exists it will easily be noticed before the plan is finished; 
 when corrections can be made. 
 
PRACTICAL HINTS ON MEASURING 21 
 
 TO MEASURE A BOAT — DIAGRAM 3 
 
 Chalk line as long as possible fore and aft parallel to 
 keel or center line of boat. On this line lay off marks 
 for offsets to curved sides every two feet, also to corners 
 of houses, stairs, radiators, gang-ways, and all stationary 
 objects, working from aft forward. Measure distance of 
 chalk line from center line and draw these two lines on 
 paper, laying off the offset marks on the paper to scale, 
 together with all measures taken of offsets and gang- 
 ways. Fold paper back on center line, connect ends of 
 offsets by straight or curved lines as the case may be. 
 Bear hard enough on the pencil to mark folded part of 
 paper, and proceed as in Diag. 2 to get a correct plan. 
 Lay tapeline on the opposite side in the same position and 
 at the same distance from the center as chalk line, and 
 walk along it, comparing as you go the recorded measures 
 with the tape. Number and measure all staterooms. 
 For a check, lay rule on plan and measure length and 
 width, which should correspond to the different measures 
 taken for length and width. Observe the least conspic- 
 uous place for cross-joins, as the carpet for convenience 
 in handling may have to be cut in several sections and 
 the places for joining such sections should be located 
 on the plan. Indicate also the forward and after part 
 of the boat. 
 
 TO MEASURE A LARGE OBSTRUCTED SPACE — STORE PLAN, 
 
 DIAGRAM 4 
 
 Chalk line from A to any point B so it will clear all 
 obstructions, extend it to the wall if possible, from A to D 
 extended, from D to C and wall. Thus making as large 
 a four-sided figure as possible inside the counters. From 
 
-&&Mr 
 
 DIAGRAM 3. 
 
PRACTICAL HINTS ON MEASURING 23 
 
 A take cross measure to C, or to any other part of CD as 
 far from D as possible. From these four chalk lines or 
 
 DIAGRAM 4. 
 
 extensions take offsets to walls, counters, and shelves. 
 From CD and AD take measures to locate posts and radi- 
 
24 
 
 CARPET-MEN'S MANUAL 
 
 ator; give diameters of same. Measure and record the 
 chalk lines and the distances of the points from which the 
 
 square measures are taken. 
 
 HOW TO MEASUKE IRREG- 
 ULAR ROOMS DIAGRAMS 
 
 5 AND 6 
 
 Almost any irregular 
 space can be measured by 
 these methods. 
 
 Lay out the space 
 ABCD as large as possi- 
 Measure this space accurately, and 
 
 DIAGRAM 5. 
 
 ble, with chalk lines 
 determine the slant of its 
 sides by cross measures. 
 Then from the sides of this 
 figure take offsets to the 
 different corners. Locate 
 the points on the chalk 
 lines where the offsets are 
 taken. Measure from lines 
 AB and BD to posts, 
 then all the wall lines. 
 
 diagram 6 
 
 Chalk lines from A to B 
 and a, from B to b. From 
 D to d and C, from C to c. 
 On AB and DC select 
 the points m, n, o, and p. 
 Measure Am, An, AB, Aa, 
 A2, Al, and Ac. Measure 
 
 DIAGRAM 6. 
 
PEACTICAL HINTS ON MEASUBING 
 
 25 
 
 Bb, B2, Bl. Proceed in the same manner from D and C. 
 Measure the offsets ma, nb, od, pc, all the short offsets, 
 across the door, mantel, and depth of hearth, and thick- 
 ness of walls at the doors, A, D and C, B. 
 
 To Measure a Window or Room the ivalls of ivhich are 
 inaccessible — Diagram 7. — On any convenient part of 
 
 line AF draw a semicircle. 
 Give radius of this circle, also 
 the distance from center to the 
 points A and F. Lay your 
 rule or a straight narrow stick 
 on the floor, push it up to the 
 corner to be measured and let 
 it remain. Fasten tape at the 
 center of the circle, bring it 
 diagram 7. over the rule or stick, move 
 
 each to the right or left until the edges are parallel and 
 in a continuous line. Now make a mark on the circum- 
 ference at the further edge of the tape as a, b, c, d, e, f, 
 proceed in like manner at each corner, adding length of 
 rule or stick to measure on tape. Measure and record 
 the straight length Ba, Bb, Be, Ef, Ec, and Ed. 
 
 To strike out this ivindoiv. — From the given point C on 
 AF, and with the given radius, describe the semicircle. 
 From B and E, lay off the given measures Ba, Bb, etc. 
 Fasten chalk line at center of circle, bring it over the dif- 
 ferent points on the circumference and snap it. Make 
 these chalk lines the length previously taken to the cor- 
 ners. Connect the ends of the chalk lines. 
 
 // the corners are inaccessible or the space is a circular 
 window or room — Diagram 8. — On the line AF, Diag. 
 8, erect a square with any convenient side, the longer the 
 
26 
 
 CARPET-MEN'S MANUAL 
 
 DIAGRAM 8. 
 
 better. With a long straight edge, or rule and tape, as in 
 the preceding example, measure from wall across the 
 square, marking the sides of the square where the 
 straight edge or line crosses it. Measure and record the 
 
 corners C and B, from A or F, 
 also the length Bb, Be, Bd, 
 etc., etc. 
 
 N 
 
 TO CONSTRUCT 
 
 From the given point B or 
 C, and with the given length 
 of side, erect the square BCDE. From B, C, D, or E 
 lay out the offset marks, from b and across CD at c snap 
 chalk line continued. Proceed in like manner with the 
 other offsets. On these chalk lines lay out the lengths 
 as taken, connect with a pliable rod, or find radius as in 
 Problem 7. 
 
 To Measure a Window where the true corners owing to 
 moldings are inaccessible — Diagram 9. — Snap chalk line 
 parallel to the wall 
 lines and so that they 
 will clear all projec- 
 tions, thus producing 
 with the chalk line a 
 space inside the true 
 window ; this space 
 should now be meas- 
 ured as shown in the various diagrams, to determine the 
 length and true directions of the sides. From the bound- 
 aries of this figure measure to the baseboards and into 
 the recesses, which will give the true window. 
 
 DIAGRAM 9. 
 
PRACTICAL HINTS ON MEASURING 27 
 
 How to Measure a Room or Rooms from the outside 
 ivithout entering a house. — It sometimes happens that 
 the measurer when he arrives at the house he is to meas- 
 ure finds it closed, leaving him to choose between wait- 
 ing an indefinite time or returning a second and perhaps 
 a third time. If the order calls for a plain carpet or an 
 estimate, and the room is so situated that the floor can 
 be seen from the outside through the window, the length 
 and width of the room can be ascertained near enough 
 for all practical purposes by the following methods. 
 
 FIKST METHOD. SEE FIGUKE 1 
 
 Measure out from the wall any distance, say one or 
 two feet, record this distance, the thickness of the wall 
 and the distance of your eye from the floor when stand- 
 ing erect. Now place yourself over the measured mark 
 in such a manner that the further end of the floor can be 
 seen. Assume an upright position so that a plumb line 
 dropped from your eye will come directly over the mark. 
 Next take your rule, place the outer edge of one-half 
 against your face so that it will be plumb with the ground. 
 Sight along the upper edge of the other half, moving it 
 up or down on its hinge until the bottom of the baseboard 
 or end of floor is seen in line with 
 rule. Now place rule flat on the 
 paper, taking care not to change 
 the angle or opening made by the figure i. 
 
 two halves of the rule. With a 
 
 finely pointed pencil draw the angle on the paper as 
 CBD. 
 
 With a scale i inch to the foot, measure from B towards 
 
28 CARPET-MEN'S MANUAL 
 
 C a distance equal to the known distance of your eye from 
 the floor, from C erect a line at right angles to BC, pro- 
 long it until it intersects BD. CD is then the distance 
 from the plumh line to end of floor. From C on CD 
 measure off the recorded distance of plumb line from 
 inside of wall as Cm. mD measured on the same scale 
 will be the length required. 
 
 Note. This as well as the following methods are based 
 on geometrical truths, and the only obstacle to perfect 
 accuracy are : first, the difficulty of getting the true angle, 
 or in other words to sight the rule right while holding the 
 other part perpendicular over the mark; second, pos- 
 sibility of not getting the distance from eye to floor cor- 
 rect, and third, uncertainty as to the thickness of the wall. 
 These difficulties, however, can be reduced with practice. 
 The writer has frequently come within half an inch of the 
 true distance. 
 
 SECOND METHOD 
 
 Another method, better than the preceding, is to place 
 the lower part of the rule against the window pane or 
 frame, bring end of upper half to your eye. Sight along 
 the upper edge, moving the lower half of the rule up or 
 down on the window glass, or the sighting part up or 
 down, keeping the other pressed against the glass until 
 the bottom of baseboard, or end 
 of floor is on a line with edge of 
 rule. Now without moving the 
 rule make a mark on the glass 
 or frame at the upper end of 
 
 the lower part of the rule. Remove the rule carefully 
 and place it flat on the paper as before. Draw the angle 
 
PRACTICAL HINTS ON MEASURING 29 
 
 on the paper as ABC. Prolong AB indefinitely, on BC, 
 from B lay off to scale the distance BC, eqnal to distance 
 of mark on glass or frame from floor, using as scale one- 
 fourth inch to the foot. From C, and at right angles 
 with CB, draw a line intersecting the prolonged AB in 
 D. From C lay off to the same scale Cm, equal to the 
 thickness of wall from glass, or if rule was held on frame 
 or wall, the thickness of wall. mD measured on the same 
 scale is the length required. 
 
 Note. It will be noticed that using this method no 
 difficulty is experienced in holding the lower part of the 
 rule perpendicular to the ground, as it rests against the 
 glass or frame of the window, and if a lead pencil is split, 
 the lead taken out and the wood again joined and a piece 
 of it tied to each end of the upper part of the rule to 
 sight by, or a little chalk or sulphur is rubbed on the ends 
 for sights, the difficulty of getting the angle correctly 
 will be partly overcome. The higher the eye is from the 
 floor, the better the results obtained. 
 
 The third method will be readily understood by study- 
 ing the illustration. 
 
 FIEST METHOD 
 
 Bring A to the eye and sight along AB, AC being plumb 
 with the ground and over the mark. In drawing angle, 
 lay AC on line representing the height of eye from floor. 
 
 SECOND METHOD 
 
 Bring C to the eye and sight along CA, AB being 
 pressed against window. In drawing angle, lay AB on 
 line representing the height of A from the floor. 
 
30 
 
 CABPET-MEN'S MANUAL 
 
 THIRD METHOD 
 
 Attach plumb line to B, bring A to the eye, sight along 
 AC, when point is in sight tip rule, and lay finger on 
 plumb line. In drawing angle lay plumb 
 line on line drawn to represent height of eye 
 from floor. 
 
 TO MEASURE THE WIDTH 
 
 Suppose you measure the 
 
 length of the room by one of 
 
 v v the preceding methods from the 
 
 A S 
 
 T> 
 
 front piazza, and you now 
 want to observe the width of 
 the room from the same 
 place, proceed as follows: If 
 the room has two or more 
 front windows select two 
 points on the glass or sash 
 or frame as far apart as pos- 
 sible, as A and B, Fig. 3. 
 Measure and draw this dis- 
 tance on paper to scale J inch to the foot. 
 From this line erect a perpendicular mn, 
 equal to the length of the room. Through n 
 draw a line parallel to AB. Now hold your 
 rule horizontally on the window with 
 the hinge on B, moving the other half 
 
 :x 
 
 and sighting along it across the room 
 until the further corner is in line. 
 
PRACTICAL HINTS ON MEASURING 31 
 
 \" 
 
 VTJ,. 
 
 /<~*.%v 
 
 \ 
 
 FIGURE 3. 
 
 Remove the rule to the paper, place it so that the point 
 of the angle when drawn will come on the point B, the 
 ^ ^ part of the rule held against the 
 
 window, on line AB, and with 
 a finely pointed pencil draw the 
 angle CBA, or the line CB. Now 
 place rule at A and proceed in 
 like manner to get the angle 
 DAB ; place the rule again on the 
 paper at A, and draw the line 
 AD. The distance between the 
 intersecting points C and D, 
 measured on the J inch scale, is 
 the width required. If there is only one window available, 
 that will suffice, but it is evident that the further the points 
 A and B are apart the more accurate will be the result. 
 
 Any number of rooms can be thus measured by the 
 above methods from one point, if the floor and corners 
 can be seen, as, observe 
 Fig. 4, where the length 
 AB will be the same for 
 each triangle and only 
 the angles change, or in 
 Fig. 5, where the dis- 
 tance AB is the same 
 for all the triangles 
 and only the horizontal 
 angles change. If the 
 height of the ceiling 
 
 above the eye can be determined, the ceiling may be ob- 
 served in place of the floor with the same result. Other 
 
 Via.* 
 
 ^" ,* ^' 
 
 a_^ 
 
 "Tvs-5 
 
 TT^7]JX 
 
 JLcLJLxl 
 
 Mil 
 
 FIGURES 4 AND 5. 
 
32 
 
 CARPET-MEN'S MANUAL 
 
 'MDO* 
 
 method of finding the length and width conld be given, 
 but as they would require the use of instruments they 
 
 need not be explained 
 here. 
 
 Find by measurement 
 the center of doorways 
 from which the tracker 
 is to run, from these cen- 
 ters snap chalk lines in 
 the desired direction, un- 
 til they intersect. On 
 each of these lines erect 
 perpendiculars crossing 
 them, mark off half the 
 width of tracker each 
 side of center line, 
 through these points 
 produce chalk lines 
 which will represent the 
 trackers, chalk line from 
 C and F perpendicular 
 to AB and EH. Meas- 
 ure AB, AD, CE, also 
 DF, HG, HE ; these are 
 all the measures neces- 
 sary if the tracker is to 
 be in two parts, if in one 
 take the additional meas- 
 ure on center line from 
 
 DIAGRAMS 10 AND 11. b 10 IV. 
 
PRACTICAL HINTS ON MEASURING 33 
 
 CARPET TO BE BOUND DIAGRAM 11 
 
 Take a piece of stiff wrapping paper, place it on the 
 floor one edge against the molding. Take the dividers 
 and with one of its feet on the paper, the other touching 
 the molding, follow the curves of the same, tracing the 
 outlines on the paper; cut away the paper between this 
 line and wall and this will give a mold which can be 
 further improved by putting in place and going over it 
 with pencil. Now square up the edges running from the 
 walls and mark upper side of paper pattern. Mark floor 
 to represent the paper. Measure room as for a bordered 
 carpet, taking all necessary measures very accurately. 
 Locate marks on floor representing the patterns by meas- 
 urements on the plan. 
 
PART V 
 
 TYPICAL DIAGRAMS AND MEASUREMENTS 
 EXPLAINED 
 
 The following diagrams have been selected from a large 
 collection, and represent the average shapes of rooms, 
 together with some more rarely encountered, but pro- 
 duced to show a correct and practical way of measuring 
 any irregular room. Each diagram is explained, and it 
 will be noticed that the chalk line is brought into frequent 
 use. This is recommended, because if the chalk line is 
 relied on at the start, the measurer will learn to be 
 methodical and consequently find his work easier. The 
 tape, if held taut, may serve in place of the chalk line if 
 this is not at hand, and, with a pencil or piece of chalk, 
 make a mark on the floor along the edge of the tape. In 
 some of the diagrams the measures are given, in others 
 they are omitted, as it is desirable to have the student 
 take his own measures, using any scale in doing so, and 
 from these measures reproduce the plan. Thus not only 
 giving practical exercise in the use of the scale, but also 
 a better understanding of what measures are required 
 to reproduce the diagram. The fine lines represent chalk 
 lines, the dotted lines, measures, and the arrow heads 
 points from and to which measures are taken. 
 
 Diagrams 26, 27, 28, and 29 represent the same room 
 measured in four different ways. 
 
 a4 
 
DIAGRAMS AND MEASUREMENTS 35 
 
 In Diags. 26 and 27 chalk lines are used; it is called 
 the ' ' square ' ' system, because the chalk line is supposed 
 to be laid out perpendicular, or at right angles to the side 
 of the room from which we start, and all measures taken 
 from this chalk line being at right angles to it. 
 
 In Diags. 28 and 29 no chalk lines are used; it is 
 known as the triangular system, measures being taken in 
 such a manner as to divide the room into a series of 
 triangles, one side at least being a wall line. 
 
 By a combination of the two systems it is possible to 
 save time both in measuring and striking out the plan, 
 at the same time bringing the possibility of an error 
 down to a minimum. When using the last system tri- 
 angles having too obtuse or too acute angles should be 
 avoided, because in striking out the plan, the nearer the 
 arcs cross each other at right angles, the more definite 
 will be the point of intersection. In all cases of tri- 
 angulation a length and width measure should be taken 
 for a check, but not used for striking out the plan. 
 
 In Diag. 29 measures could be taken from A to C, D, 
 E, and F, and from B to H, G, and F, then GD and BE 
 will be checks, but it can also be struck out with two 
 measures less as shown in diagram. 
 
 diagram 12 
 
 Chalk lines from M to N and C to F. Measure width 
 LH, RS, and Gg. Fasten tape at m, on MN. Measure 
 to f on CF, noting angular points and offsets, with your 
 rule measure offsets from tape to M, K, H, and F, meas- 
 ure Aa, Bb, and from MN to both stairs, or if the line will 
 clear from end to end, fasten line at A, noting the corners 
 and taking offsets as before. 
 
A *> 
 
 DIAGRAMS 12, 13, AND 14. 
 
DIAGRAMS AND MEASUREMENTS 37 
 
 DIAGRAM 13 
 
 Measure from A to B, D to C, from F to f , c and E, C 
 to H. From entrance to A, d and f and to B, D, and F, 
 from c to h and H, E to G and curves. 
 
 diagram 14 
 
 Measure DF, Gg, gH, Cc, and AB, from D to c and AB, 
 also CA, from DF to g, c, and B. 
 
 diagram 15 
 
 Extend RO with chalk line from to K and R to r, mn 
 to P, chalk line from m and V perpendicular to mn and 
 QV. 
 
 Measure MN, NK, Nn, pP, pQ, Vr, VL, from A to M 
 and N, from W to K, P, 0, R and r, from v to r, L, all the 
 wall lines and cross measures. 
 
 diagram 16 
 
 Chalk line from S to H parallel to EF, and from H per- 
 pendicular to it, prolong MN and OP both ways, from 
 a and m draw lines perpendicular to them, measure across 
 curves, offsets, straight walls, angles, and all measures 
 as shown by dotted lines. 
 
 DIAGRAM 17 
 
 Extend Bb to any point as c, with chalk line from c 
 snap second line to DE so it will touch the corner C. 
 
 Measure from H to G and g, from c to C and d, from 
 B to b and c, from d to D and E. All wall lines and take 
 cross measures as shown by dotted lines. 
 
DIAGRAMS 15, 16, AND 17. 
 
DIAGRAMS AND MEASUREMENTS 
 
 39 
 
 DIAGRAM 18 
 
 Chalk line from A to B across swell, bisect and 
 measure depth of it to W ; measure from each end of this 
 
 line A and B to wall at 
 stair C and D; measure 
 width of hall from wall to 
 baluster. 
 
 diagram 19 
 Prolong AB to C ; bisect 
 BC with DE; from E on 
 
 DIAGRAM 18. 
 
 curve draw EE both ways 
 parallel to AC, chalk line 
 from G through f to F per- 
 pendicular to Ee, from M 
 perpendicular to GF, from 
 S perpendicular to xM, pro- 
 long it to N, from T and 
 P perpendiculars to NSM. 
 Measure AB, AC, entrance 
 to c, E, F, and e. Aa, ab, 
 DE, offsets at c and F. 
 Ff, Fx, FG 5 with offset to 
 both curves. XM and off- 
 sets every six inches. MN, 
 MS, Mp, Mn with offsets as before 
 to curves, also QR. 
 
 DIAGRAM 19. 
 
 pP, pQ, with 
 
 offsets 
 
40 
 
 CAKPET-MEN'S MANUAL 
 
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 L^a^; .' 
 
 
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 STAIR MEASURE 
 
 Always Count the Steps 
 Going Up 
 
 DIAGRAM 20 
 
 Begin to measure 
 from the top, as you 
 can do it quicker going 
 down than up. Measure 
 the length and width of 
 each part of the stair 
 and landing separate 
 and mark the parts top, 
 bottom, and landing. 
 Give number of steps. 
 
 diagram 21 
 
 Measure from top of 
 stair to second landing, 
 also the width of this 
 part, and landing. 
 Measure from wall on 
 second landing over and 
 to the bottom of middle 
 part. Take width of 
 first landing, and length diagrams 20, 21, 22, 23, 24, and 25. 
 from wall over landing 
 
 to bottom of first part. Give number of steps and land- 
 ings. 
 
DIAGRAMS AND MEASUREMENTS 
 
 41 
 
 DIAGRAM 22 
 
 Measure from top of stair to landing, and from wall 
 of landing to A, B, and bottom of stair. Give width of 
 stair and landing, also distance from corner of baluster 
 to corner of wall. 
 
 diagram 23 
 
 From top of stair to A, B, C, D and bottom, give width 
 of stair, and distance from corners of baluster to corners 
 of walls. 
 
 diagram 24 
 
 Measure from A at top of stair following mopboard 
 down to the beginning of concave curve B. Move the 
 line over to the opposite side, and measure from C at 
 the beginning of the convex curve to the bottom, and then 
 the different widths of steps shown on the tape. 
 
 diagram 25 
 Measure the concave or longest side of the stair. 
 
 diagram 26 
 
 From any point L on 
 EF snap chalk line, LK, 
 on the floor as near 
 square as possible to EF. 
 Select and mark the two 
 points b and a. Measure 
 EL, EF, LK, La, Lb and 
 FK, bD, aC, bG, aH, FG, 
 GH, KA, BA, BC, CD, Dc, 
 Df, DE, and fm. Strike 
 out in the same order. diagram 26. 
 
42 
 
 CABPET-MEN'S MANUAL 
 
 
 
 J> 
 
 
 
 
 
 
 ^ 1 
 
 / 1 
 
 
 fv 
 
 \ 
 
 
 "* - ^X 
 
 / i 
 
 
 a. 
 
 
 
 
 
 "^. 
 
 •V 
 
 
 
 
 
 
 
 
 ■F 
 
 \ 
 
 \i 
 
 
 
 
 USE THE FOLLOWING} SYS- 
 TEM WHEN MEASUR- 
 ING FOR ESTIMATES 
 
 DIAGRAM 27 
 
 From corner E snap 
 chalk line at right angles 
 to EF, or as near as pos- 
 sible. Parallel to this 
 line and at the distance 
 KA, snap another chalk 
 line LA. On these two 
 lines select and mark 
 points a, b, c and d, op- 
 posite corners C, D, H, and G, measure LK, EK, Ea, Eb, 
 aC, bD, KA, EL, EF, LA, Lc, Ld, cH, dG, FG, GH, HA, 
 AB, BC, CD, and DE in the order named. 
 
 Note in Diag. 26 the chalk line is not at right angles to 
 EF, but its true direction is given by the diagonal measure 
 FK. The points a and c are selected so that one off- 
 set, Db and Ha on opposite sides of the chalk line are at 
 right angles to it. The measures bD and bG taken with- 
 out removing the awl, so are aC and aH. 
 
 DIAGRAM 27. 
 
DIAGRAMS AND MEASUREMENTS 
 
 43 
 
 ' v^ 
 
 \ , ^ • 
 
 
 V- 
 
 / \ 
 
 $ 
 
 ' \ 
 
 X ^ 
 
 % 
 
 v 
 
 \ 
 
 N&- ' 
 
 \ 
 
 x ' 
 
 V 
 
 x/ 
 
 /■"o* v 
 
 '• 
 
 DIAGRAM 28 
 
 With a convenient 
 length on the tape and 
 A as a center, describe 
 an arc, with B as center 
 and the same radius 
 describe an arc cutting 
 the first in a point as O. 
 Fasten the tape at O 
 and measure to all the 
 corners. Measure all 
 diagram 28. wall lines. 
 
 To reproduce. Snap a chalk line, on which lay the 
 length AB. From A and B as centers and AO as radius 
 locate 0. Fasten tape at and with the recorded 
 measures as radius de- 
 scribe arcs for each cor- 
 ner. With A as center 
 and AH as radius de- 
 scribe an arc cutting the 
 one already drawn at H. 
 Proceed in like manner 
 all around the room, 
 working from A to E and 
 from B to D. 
 
 diagram 29 
 
 Take the measures 
 
 from points and in the order named. From A to B, C, D, 
 
 F, and H. From B to C and E. From C to D and H. 
 
 From D to G, from H to G, from G to F, from F to E. 
 
 DIAGRAM 29. 
 
44 
 
 CARPET-MEN'S MANUAL 
 
 v Dli\0.30 3 
 
 To reproduce. Snap chalk line, on which lay the length 
 AB. From A, B, and the other points as found, and with 
 
 the length of the respec- 
 tive sides, describe arcs, 
 proceeding in the order 
 ^^"yf named above in taking the 
 measures. 
 
 diagram 30 
 
 Measure from A to m, n, 
 and D,from A to F. From 
 C to A, F, and D. From 
 F to D. From m to B and 
 C, from n to C and B 
 and from B to C construct 
 in the same order. 
 
 DIAGRAM 30. 
 
 DIAGRAM 31 
 
 Snap chalk line from A 
 to F across opening of 
 window, measure from A 
 to s, n, m; s and F, from 
 A to G, from H to G, F 
 and A, from G to D, P, 
 and F, from S to D and B, 
 from m to D. From S to 
 C and E and from n to C, 
 measure BC, CD, and DE. 
 Construct in same order. 
 
 DIAGRAM 31. 
 
DIAGRAMS AND MEASUREMENTS 
 
 45 
 
 DIAGKAM 32 
 
 Measure from A to B, m, o, C and H, from P to K, C, 
 and A. Snap chalk line from A to C, on it set distance 
 
 KP, measure from n to K, 
 from C to M and H. 
 Measure from B to D, m 
 to D, D to F, o to F, and 
 M to F. Measure across 
 and locate the hearth. 
 Measure HL for a check. 
 Construct in the same 
 order. 
 
 
 
 1 i%~ 
 
 
 
 \ 
 
 1 
 
 
 
 
 \ 
 
 1 
 
 
 
 
 
 
 
 
 
 s 
 
 
 
 
 s 
 
 N 
 
 
 s 
 
 
 
 
 v 1 
 
 ' s 
 i 
 
 ■3MPvdJa 
 
 s 
 
 \ 
 
 \ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 \ 
 
 
 
 j '>v 
 
 1 
 
 V 
 
 
 
 1^ -/- ^\- 
 
 _ L. 
 
 *•» «. i 
 
 _ 
 
 
 DIAGKAM 32. 
 
 DIAGRAM 33 
 
 Chalk line from A to 
 measure from C to A, 
 and D 
 
 B, 
 
 B, 
 
 DIAGKAM 33. 
 
 From A to m, n, B, X, and D, from B to D and 
 Y, from M to X, n to Y, and last XY. 
 
46 
 
 CARPET-MEN'S MANUAL 
 
 DIAGRAM 34 
 
 Prolong FA with chalk line on it 
 from F to m, set distance EC, 
 measure from F to A, E, and 
 C, from m to B and C, from 
 C to D and E, from E to 
 D, and DH, for check. 
 Find center of cir- 
 cular window 
 measure radi- 
 os, depth nw, 
 and mn. 
 
 diagram 35. 
 Chalk line from c 
 to F, and from C 
 perpendicular to AD, 
 measure from A to c 
 s, H, P, and D, also to 
 B, from B measure 
 to C and perpendicu- 
 lar to CH, measure 
 HK, HC, and DC, 
 measure the inside 
 opening of the swell 
 locate center and meas- 
 sure radius, depth sw 
 and thickness of wall. 
 
 DIAGRAM 35. 
 
DIAGRAMS AND MEASUREMENTS 
 
 47 
 
 .. $ 
 
 / 4 
 
 / } 
 / 
 
 Kn 
 
 i 
 
 t 
 
 **> 
 
 < * 
 
 \ 
 
 4 — I 
 
 
 DIAGRAM 36 
 
 Chalk lines from A and 
 H to B and D. Let fall a 
 perpendicular from junc- 
 tion of concave and convex 
 part of swell as m, n to b, c. 
 Find center of circle, Prob. 
 7, Me tli. 2. Measure Aa,Ab, 
 Ac, Ad, AB. Measure Sb, 
 
 DIAGRAM 36. 
 
 Kk by laying the rule or 
 tape so as to bisect the 
 angles abn, Lkm, measure 
 He, Hf, Hg, HD, also wall 
 lines and offsets. 
 
 diagram 37 
 Chalk line from A to B, C 
 to D in parlor, take offsets 
 every 12 in. from A to B, ° 
 also at b, p, r, and s on CD. 
 Locate doorway from C, 
 mantel from D; give depth 
 of same; measure length 
 and breadth of room. 
 
 diagram 38 
 dining room 
 Chalk lines from M to h. 
 
 DIAGRAMS 37 AND 38. 
 
48 
 
 CARPET-MEN'S MANUAL 
 
 From A to B parallel with CD in parlor, and from A to 
 any point P, locate and measure offsets a, b, c, f , g, 1, p, 
 r, and s. Measure BP, mn, h, o, all walls in room and 
 window, pp and the whole length from line mh to AB in 
 parlor. 
 
 HALL 
 
 Measure Aa, Ab, Ac, Be, Bf, BD, BA, eg, cd, and Dd. 
 Give thickness of wall at parlor door. 
 
 diagram 39 
 
 Chalk line from A at 
 right angles to AF, touch- 
 ing opposite wall at B. 
 Find center of circle by 
 Prob. 7, Meth. 2. Chalk line 
 from center perpendicu- 
 lar to AB, chalk line from 
 E perpendicular to ED. 
 
 Measure Aa, Ab, Ac, Ad, 
 and AB, measure radius, 
 offsets cW and dK, locate 
 window recesses by meas- 
 uring from a to g, a to N, also KL and KM, measure E 
 to S and b, and SF, also from e and f to Eb, measure 
 from E to k, 1, and D, and depth of door, De, Df, DB, DC, 
 EF, and FA. 
 
 DIAGRAM 40 
 
 Find center of circle, Prob. 7, Meth. 2, 3 or 4, chalk line 
 from A perpendicular to AE, or if more convenient from 
 a to B, across the swell. In the former case, set the short- 
 est distance of the center C from side AB, from A to M, 
 
 DIAGRAM 
 
DIAGRAMS AND MEASUREMENTS 
 
 49 
 
 in the latter, bisect aB and set ow perpendicular thereto. 
 
 Measure radius, depth of 
 swell, aA, aB, AB, AD, 
 BF, EF, EA, ED, DB. 
 
 Note. If the distance CO 
 or CM is known the center 
 is located and this meas- 
 ure with the radius forms 
 a check, but as the depth 
 OW or MK should be 
 given, if possible, this sub- 
 tracted from the radius 
 gives OC or OM, and the 
 diagram 40. depth OW added to the 
 
 chord AB gives length of swell nearly if semicircle or less. 
 
 DIAGKAM 41 
 
 Chalk line from A to B, 
 also from A and B to any 
 point C. Measure from A 
 and B towards C every 12 in. 
 offsets from chalk line to 
 swell, using near edge of 
 tape or rule in doing so. 
 Measure depth CF, cross 
 measures, and wall line. 
 
 DIAGRAM 42 DIAGKAM 41. 
 
 Chalk line from B to C, fasten line at B and with any 
 convenient length strike an arc. Ring at C, and the same 
 or any other length, strike an arc cutting the former, 
 from this point, 0, measure to all corners in window, also 
 
CARPET-MEN'S MANUAL 
 
 locate and 
 
 of window, 
 
 . CH, cross 
 
 TVtW V 
 
 DIAGRAM 42. 
 
 to this line snap chalk line 
 from r and n. Measure 
 Ah, Am, Ap, Ag, AB, also 
 Ha, Hx, HK, measure pn, 
 mr, locate and measure off- 
 sets, sides, and chalk lines. 
 In room measure as in 
 window of Diag. 42. using 
 any two corners to start 
 from; or draw perpen-^ 
 dicular line from B to FGr, 
 and measure offsets from 
 it to corners; measure 
 wall lines. 
 
 Note. The method of 
 taking all the cross meas- 
 ures from one point is the 
 
 measure offsets and sides 
 In room measure BC and 
 measure from A to D and 
 E, F to C and B and rest 
 of room as before. Or meas- 
 ure window, taking cross 
 measures from B and C to 
 corners, not forgetting off- 
 sets, or measure as in Diag. 
 43. whichever way is most 
 convenient. 
 
 diagkam 43 
 Chalk line from h to g; 
 
 DIAGRAM 43. 
 
DIAGRAMS AND MEASUREMENTS 
 
 51 
 
 quickest as the ring end of the tape does not have to be 
 shifted either when measuring 
 or striking out the room. 
 
 diagram 44 
 
 Chalk line from B to D, D 
 to F, A to F, C to D. Find 
 center of circle by Prob. 7, 
 Meth. 3. Measure and 
 locate window recesses 
 as per Diag. 39, give M 
 depth of same, all wall 
 lines, chalk lines, cross 
 
 DIAGRAM 44. 
 
 measures AD 
 and offsets. 
 
 and BF, 
 
 DIAGRAM 45 
 
 Let fall perpendicular 
 from B to straight line 
 across doorway, across 
 this line BA, at right 
 angles to it, snap chalk 
 line from J, touching 
 FE, chalk line from B to E and d to b. From a and c 
 to swell, join them by another line, wx, on this last line 
 mark points for offsets every 6 or 12 in., do the same on 
 cW, and aX, also on JN, BA, BE, to corners and swell. 
 
 DIAGRAM 45. 
 
52 CARPET-MEN >S MANUAL 
 
 Take cross measures aW, cX, from W to e, a to b, all chalk 
 lines, offsets, wall lines, and depth of mantel and door. 
 
 diagram 46 
 
 All the measures necessary in this room are to find the 
 lengths of the diameters AB and CD. As it is difficult 
 sometimes to locate these lines, the center not being 
 *^~~^__^^ known, proceed as follows: 
 
 // I ^>L Snap any two chalk lines par- 
 />C i \ allel to each other on the floor, 
 
 ^L^^y^^^^°r.^^A H B as EF and GrH. Bisect these 
 W i^Ll/ I lines in K and L, through K and 
 
 ^v i Ty* ^ draw a l me > meeting the 
 
 <^^ _ j j £*£ curved wall in M and N. Bisect 
 
 ^ MN in O, the center of the 
 
 diagram 40. room. With O as a center and 
 
 any convenient length in the tapeline as a radius, touch 
 and mark the baseboard or floor at the points 1, 2, and 3. 
 Through draw lines parallel to lines joining the points 
 1 and 2, 2 and 3, these lines are the axes or diameters re- 
 quired. To make sure that the room is an ellipse, or to 
 strike out the plan, proceed as in Prob. 8. If not an 
 ellipse measure as in the window of Diag. 45. 
 
 diagkam 47 
 
 In this plan the parlor, reception hall, two bedrooms, 
 and two passages are to be carpeted, and it is necessary 
 to locate the rooms exactly as well as give correct meas- 
 ures. Start at any prominent part, say in the parlor, at 
 the door AB erect a line perpendicular to AB, extend as 
 far as it will go on both sides; from this line snap DO 
 
DIAGRAMS AND MEASUREMENTS 53 
 
 at right angles thereto, also line to reception hall. De- 
 termine the direction of this line by a line ran, on ok in 
 the reception hall erect another perpendicular, prefer- 
 ably at the longest point of the hall, as it will then be the 
 
 e~± 
 
 DIAGRAM 47. 
 
 transfer axis if the room is an ellipse, from r and s on DO 
 and OC erect other perpendicular lines running to pas- 
 sages. Find center of circular room by any of the three 
 methods, locate mantel and window seats as in Diag. 45, 
 
54 CARPET-MEN'S MANUAL. 
 
 by offsets, or as in Diag. 39, measure AB, On, OS, OC, also 
 Or, OD, and OM, OP, Ok, measure length of bedrooms and 
 width from chalk line in both directions, measure lines 
 running through passages and offsets thereto, also walls 
 in same, measure reception hall as in Diag. 46. or window 
 in Diag. 45. 
 
PART VI 
 
 SIMPLE GEOMETRICAL PROBLEMS 
 
 PKOBLEM 1 
 
 To Divide a Given Line into Tivo Equal Parts. 
 
 From A and B as centers and any length on your tape 
 as a radius, describe arcs cutting each other in M and N. 
 
 Draw the line MCN and it will cut 
 the given line into two equal parts. 
 It will also be perpendicular to AB. 
 
 x 
 
 * 
 
 PROBLEM 2 
 
 To Divide a Given Angle, ABC, 
 into Two Equal Parts. 
 
 problem l. From B as a center with any 
 
 radius describe the arc AC. From A and C with one and 
 the same radius, describe arcs in- 
 tersecting in M. Draw a line from B 
 to M and it will bisect the angle as 
 required. 
 
 problem 3 
 
 To Draw a Line Parallel to a Given & 
 
 Line and at a Given Distance. problem 2. 
 
 Let AB be the given line. From any two points as M 
 
 55 
 
56 CARPET-MEN'S MANUAL 
 
 and N in the line AB, with a radius equal to the given 
 distance describe the arcs R and 0. Draw CD to touch 
 these arcs without cutting them. This will be the 
 parallel required. 
 
 peoblem 4 
 
 When the Parallel Line is to 
 Pass through a Given Point, C. 
 
 m ^~n~ From any point N in the line 
 
 problem 3. £B ^^ no as a rac ii us describe 
 
 the arc CM. From the center C and with the same 
 radius describe the arc SN. Take the straight distance 
 from C to M and apply it from N to S. Through C and 
 S draw DE, the parallel required. 
 
 problem 5 
 To Erect a Perpendicular from a 
 Given Point, A, on a Given A - 
 
 Line > BC ' PROBLEM 4. 
 
 Case 1 
 
 When the point is near the middle of the line. On 
 
 each side of the point, A, set off any two equal distances, 
 
 as AM and AN, with M and N as 
 
 ^^ centers and any radius greater than 
 
 MA, describe two arcs intersecting 
 
 in R. Through A and E draw the 
 
 line AR, and it will be the perpendic- 
 
 . .3 l w ,._Lui — , H i c u, , ular required. 
 
 Method 1 
 
 PROBLEM 5. 
 
 When the point is near the end of 
 the line or on it, with the center A and any radius, 
 describe the arc MNS; with the same radius or length 
 lay off on the arc from M and N the distances MN and 
 
SIMPLE GEOMETRICAL PROBLEMS 
 
 57 
 
 NS. Again, with N and S as centers, describe arcs in- 
 tersecting in R. Then draw AR. 
 
 Method 2 
 From any point M as a center 
 with the radius or distance MA 
 on tape draw an arc cutting the 
 
 METHOD 1. 
 
 method 2. From A 
 
 radius describe an arc MN, with 
 M as center and the same radius 
 describe an arc at N. N as center 
 and the same radius describe arc 
 at R. Through MN" draw a straight 
 line cutting arc at R, join R and A, 
 which gives the perpendicular. 
 
 given line in N and A. Through 
 M and N draw a straight line, cut- 
 ting the arc in R ; lastly draw AR, 
 which is the perpendicular 
 
 Method 3 
 
 as a center and any 
 
 METHOD 4. 
 
 M 
 METHOD 3. 
 
 Method 4 
 From any scale of equal parts 
 on the tapeline, set off from R to 
 B three such parts, with R as cen- 
 ter and four parts as radius swing 
 an arc. B as center and five parts 
 as radius, describe an arc cutting 
 the former in A. A line drawn 
 from R to A is the perpendicular. 
 
58 CARPET-MEN'S MANUAL 
 
 Note. This method is commonly used by carpet measurers 
 and is correct if the tape used is true, but as three different 
 lengths are used, if only one is out, the line will not be a per- 
 pendicular, and should it vary only \ of an inch at 3 ft. 
 it would at 25 ft. be about five inches out of square. Of 
 course, any length most convenient can be used, as (1 ft. 
 6 in., 2 ft., and 2 ft. 6 in.) or (three, four, and five,) or 
 
 (six, eight, and ten.) 
 
 problem 6 
 
 From a Given Point, A, to Given Line, BC, to Let Fall 
 
 a Perpendicular. 
 
 With the center at A and any radius describe an arc 
 
 cutting BC at M and N. With M and N as centers and 
 
 the same or any other radius describe arcs inter- 
 
 a secting in R, draw ADR for the 
 
 perpendicular. 
 
 Case 2 
 
 When the point is nearly op- 
 posite the point of the line. 
 
 From A draw any line AM 
 to meet BC. Bisect AM at N, 
 problem 6. with N as center and radius AN 
 
 describe an arc cutting BC in D. Draw >J£ 
 
 AD, the perpendicular required. _^^ * 
 
 problem 7 Method 1 A 
 
 To find the Center of a Given Circle « V C 
 
 or Part of a Circle. CAgE 2 
 
 With any radius and any point on the circumference 
 
 >%L 
 
SIMPLE GEOMETRICAL PROBLEMS 59 
 
 as at A, describe an arc, with the same radius and another 
 point as B describe an arc cutting the former in two 
 places C and D, from C and through 
 D draw a line CDO and it will pass 
 through the center. In like man- 
 ner draw another line EHO and it 
 will cross the first at the center *] 
 required. 
 
 Method 2 
 
 When a window is in the form of problem 7. 
 
 a circle mark any three points on the circumference as 
 
 ABC. Take A as a center and a 
 length on the tape greater than 
 half the length AB, describe an 
 arc MN. With B as a center and 
 the same radius swing another 
 arc cutting the former in M and 
 N. Again with B as center and 
 a little more than half the dis- 
 tance from B to C describe an 
 arc RS, C as center and the same radius describe an arc 
 cutting the former at RS. Through RS and MN draw 
 straight lines which will cross at the center. 
 
 Method 3 
 
 Bisect AB and erect a perpendicular 
 which when prolonged will pass through 
 the center. Draw a line from A to any 
 point on the circumference, the nearer the middle of it 
 
60 
 
 CARPET-MEN'S MANUAL 
 
 the better, bisect this line and draw a perpendicular from 
 it, crossing DC at the center required. 
 
 Method 4 
 
 Bisect AB and draw a line perpendicular through the 
 middle of it ; on this line lay your tape, 
 touching with its 20 ft. mark the wall 
 at D, the big numbers running towards 
 C, (the eyelet at 21 ft. mark recom- 
 mended before will here come in handy 
 for your awl). Tighten the tape on 
 the line; go back and pull up the awl, 
 
 taking care not to disturb the line ; fasten the ring end of 
 
 the line at A; bring it over the 
 
 part of the tape already laid out ; 
 
 move it up or down until the 
 
 marks on both parts touching 
 
 each other correspond ; when 20 is 
 
 subtracted from the first part, if 
 
 the tape is true, the marks will 
 
 come together at the center re- 
 quired. This method is recom- 
 mended when a carpet is on the 
 
 floor, as then it is sometimes difficult to get a chalk line 
 
 to show. 
 
SIMPLE GEOMETRICAL PROBLEMS 61 
 
 Method 5 (see Circular Arc) 
 
 To Construct an Ellipse 
 
 Let it be required to describe an ellipse whose diam- 
 eters or axes are 12 and 8 feet respectively. Draw a line 
 
 AB equal to the longest axis 12 
 feet, bisect and draw a line CD 
 through the bisecting points; on 
 ]p this line lay off the length of the 
 short axes, half on each side from 
 AB. Take half the length of the 
 long diameter on your dividers or 
 tape as a radius and with the points C or D as centers 
 describe an arc cutting AB in x and y. The points x and 
 y are then the two foci points. Place a pin or tack at 
 each of these points, also one in C or D. Fasten the end 
 of an inelastic cord or string to the tack at x, bring it 
 around the tack at C, pull it taut and fasten the other end 
 to the tack at y. Now pull out the tack at C and replace 
 it with a pencil or piece of chalk, and, keeping a steady 
 tension on the string, move the pencil as far as possible 
 first on one, then on the other side of the long diameter 
 and trace the elliptic curve. 
 
 Or mark half the length of the 
 long diameter as AO on a long 
 straight edge, then lay this a 
 straight edge on the short diam- 
 eter, first mark A at C, and mark 
 off the short diameter OC from 
 A. Place the two marks 00 so they will always touch 
 the two diameters. And the mark A will trace the curve. 
 
 «. 
 
PART VII 
 
 COMMON ARITHMETIC 
 
 Simple Addition 
 
 In adding up one or more columns of figures never add 
 a single figure at a time. Every figure must be seen and 
 used but not pronounced, therefore in memorizing keep 
 your mind free from words, and do not say three plus five 
 plus nine equals seventeen, but simply three, five, nine 
 seventeen. Commence at the bottom of the right-hand 
 column and add upwards, then by writing the carrying 
 figure at the top of the next column and so on, we have the 
 advantage of being able to leave our work in the middle of 
 the operation and return at leisure to finish it without 
 going over the figures already added. In the following 
 example only part of the answer is written to illustrate 
 the advantage of this method. 
 
 23 
 
 Ex. 1. 352 Proof. Add each column sep- 
 
 564 arately as before and to the 30 
 
 812 right, mark down the sum of ^5 
 
 529 each column so they will ad- jjj 
 
 287 vance one figure from right to 3180 
 
 636 left. 
 
 ~~80 
 
COMMON ARITHMETIC 63 
 
 Second Method. Proof. Find the excess of 9's in each 
 horizontal line, then by adding all the excesses together 
 and dividing the sum by nine, the remainder should be 
 the same as the remainder of the sum of the digits in the 
 total sum divided by nine. The operation should be per- 
 formed mentally, but to illustrate, the figures are written 
 in the following example. 
 
 3+5+2=10—9=1 
 5+6+4=15—9=6 
 8+1+2=11—9=2 
 5+2+9=16—9=7 
 2+8+7=17—9=8 
 6+3+6=15—9=6 
 
 3+1+8+0=12—9=3,30—27 3 
 
 Shoet Methods in Multiplication 
 
 To multiply any two figures by 11 : 
 
 Rule. Place the sum of the two figures between them 
 for the answer. If the sum is more than ten, increase the 
 left hand figure by one. 
 
 Ex. 1. 11X25=2+5=7; then 275 the answer. 
 Ex. 2. 11X79, 7+9=16, then 869 is the answer. 
 
 To multiply more than two figures by 11 : 
 Rule. Write the first right hand figure; prefix to this 
 the sum of the first and second, then the sum of the second 
 and third etc. Then write the left hand figure. Carry 
 when necessary. 
 
 Ex. 3. 56879X11=625669. 
 
64 CAKPET-MEN'S MANUAL 
 
 CKOSS MULTIPLICATION 
 
 A Rapid and Practical Method 
 
 Ex. 4. Multiply 45X34=1530. 
 
 Explanation. We first say 4X5=20 (always reserve 
 carrying figure) write down and carry 2, next 4X4= 
 16+2 (the carrying figure) =18+3X5=33, write down 3 
 and carry 3, next 4X3=12 plus 3=15, write it down and 
 the product is complete : 1530. 
 
 Ex. 4. Multiply 465 by 382. 465 
 
 382 
 
 177630 
 
 The frequent use of this method tends to increase the 
 ability of retaining large sums in the head ; after a little 
 practice great speed in multiplying two numbers may be 
 attained. 
 
 TO MULTIPLY ANY NUMBER BY NINES 
 
 Ex. 5. Multiply 9999 by 5634=56334366 answer. 
 
 Explanation. Write down the multiplier, less one, and 
 subtract the multiplier less one from the number of nines. 
 
 TO MENTALLY MULTIPLY ANY TWO SUMS FROM 10 TO 20 
 
 Ex. 6. Multiply 15X12. 
 
 Explanation. We first say 2X5=10, next 2+5 and one 
 to carry=8, place in the mind the figure 1, and after it 8 
 
COMMON ARITHMETIC 65 
 
 and or 180. Try it and you have increased your multi- 
 plication table from 12 to 20. Carry if any. 
 
 To multiply by 5. Annex one cipher and divide by 2. 
 
 To multiply by 25. Annex two ciphers and divide by 4. 
 
 To multiply by 50. Annex two ciphers and divide by 2. 
 
 To multiply by 125. Annex three ciphers and divide 
 by 8. 
 
 To multiply by 250. Annex three ciphers and divide 
 by 4. 
 
 Vulgar Fractions 
 
 A fraction means a part of anything. If an apple be 
 cut into eight equal parts, each part will be called an 
 eighth of the whole apple and is written -§. This £ is a 
 fraction. If we had three or five or seven of these pieces 
 of the apple we would represent it by § or f or £ as the 
 case might be. All these are fractions. A Vulgar Frac- 
 tion is always represented by two numbers (at least), one 
 over the other and separated by a small horizontal line. 
 The number above the line is called the numerator, the 
 number below the line the denominator. 
 
 The denominator tells us into how many parts the 
 whole has been divided, and the numerator tells us how 
 many of these parts we have. Thus in the above fraction 
 |, the 8 shows that the apple has been divided into 8 
 equal parts and the 3 shows that we have 3 of those pieces 
 or parts of the apple. 
 
 A Proper Fraction is one whose numerator is less than 
 its denominator as f, f or +. An improper fraction is 
 one whose numerator is more than its denominator as 
 h h or J; | means more than a whole one, because I must 
 
66 CARPET-MEN'S MANUAL 
 
 be a whole. Then f will be 3 thirds plus 3 thirds plus 2 
 thirds or 2f and this form is called a mixed number. 
 
 A single fraction is a simple expression for any num- 
 ber of parts of the integer. 
 
 A compound fraction is the fraction of a fraction as \ 
 off, toff, etc. 
 
 Any whole number may be expressed like a fraction by 
 writing 1 under it as f . 
 
 The common measure of tivo numbers is that number 
 which will divide each of them without a remainder. 
 Thus 3 is the common measure of 12 and 15; and the 
 greatest number that will do this is called the greatest 
 common measure. 
 
 A number, which can be measured by two or more num- 
 bers, is called their common multiple and if it be the least 
 number which can be measured, it is called their least 
 common multiple, thus 30, 45, 60, and 75 are multiples of 
 3 and 5, but their least common multiple is 15. 
 
 problem 1 
 
 To find the greatest common measure of two or more 
 numbers. 
 
 Rule. If there be two numbers only, divide the greater 
 by the less, and this divisor by the last remainder, and so 
 on ; always dividing the last divisor by the last remainder, 
 till nothing remains, then will the last divisor be the 
 greatest common measure required. 
 
 When there are more than two numbers, find the 
 greatest common measure of two of them as before, and 
 of that common measure and one of the other numbers 
 and so on, through all the numbers to the last, then will 
 
COMMON AEITHMETIC 
 
 67 
 
 the greatest common measure last found be the answer. 
 If 1 happens to be the common measure, the given num- 
 bers are prime to each other and found to be incom- 
 mensurable. 
 
 Ex. 7. What is the greatest common measure of 3168, 
 2860, and 1980? 
 
 Operation: 
 
 1 
 
 44 44)1980=45. 
 
 44 is the greatest common measure required. 
 
 3168 
 2860 
 
 2860 
 
 2772 
 
 308 
 264 
 
 88 
 88 
 
 308 
 
 88 
 
 44 
 
 
 PROBLEM 2 
 
 To find the least common multiple of two or more 
 numbers. 
 
 Rule. Divide by any number that will divide two or 
 more of the given numbers without a remainder and set 
 the quotients, together with the undivided numbers, in a 
 line beneath. 
 
 Divide the second line as before ; and so on until there 
 are no two numbers that can be divided; then the con- 
 tinued product of the divisor and quotients will give the 
 multiple required. 
 
 Example. What is the common multiple of 3, 5, 8, and 
 10? 
 
 5)3, 5, 8, W 
 
 2)3, 1, 8, 2r Then 5X2X3X4=120, the answer. 
 3, 1, 4, 1, 
 
68 CAKPET-MEN'S MANUAL 
 
 Reduction of Vulgak Fractions 
 
 Reduction of vulgar fractions, is done by changing them 
 from one form to another, in order to prepare them for 
 the operation of addition, subtraction, etc. 
 
 Case I. To reduce fractions to their lowest term 
 
 Bute. Divide the numerator and denominator of the 
 given fraction by any number that will divide both of 
 them without a remainder and these quotients again in 
 the same manner and so on until it appears that there is 
 no number greater than 1 which will divide them, and 
 the fraction will be reduced to its lowest term. Or, divide 
 both terms by the greatest common measure, and the 
 quotient will be the terms of the fraction required. 
 
 Example. Reduce Hi to its lowest terms 
 
 • ttt-H=i*> tt-H=ib the answer. 
 Or thus. Greatest common measure=48, 48)it$=f- 
 
 Note. Any number ending with an even number or a 
 cipher, is divisible by 2. Any number ending with 5 or 
 is divisible by 5. If the right hand figure of any number 
 be 0, the whole is divisible by 10. If the two right hand 
 figures are divisible by 4, the whole number is divisible 
 by 4. If the three right hand figures are divisible by 8 
 the whole number is divisible by 8. If the sum of the 
 digits constituting any number be divisible by 3 or 9 the 
 whole is divisible by 3 or 9. 
 
 When numbers, with the sign of addition or subtraction 
 
COMMON AEITHMETIC 69 
 
 between them, are to be divided by any number, each of 
 the numbers must be divided. Thus : 
 
 But if the numbers have the sign of multiplication be- 
 tween them, only one of them must be divided. Thus : 
 
 3X8X10 _ 3X4X10 _ 1X4X10 __ 1X2X10_ 20 
 
 2X6 ~~ 1X6 ~~ 1X2 ~~ 1X1 T~ " 
 
 To Reduce a Fraction of Any Denomination to One 
 Having a Desired Denominator 
 
 Rule. Multiply the old numerator with the new denom- 
 inator. Divide the product by the old denominator; the 
 quotient is the new numerator of the fraction with the 
 desired denominator. 
 
 Example. How many quarters are equal to f ? f X4=20, 
 
 24 
 
 20-^-8=^ • 
 4 
 
 How many 12ths are equal to T W 12X25=300-r- 
 100=A. 
 
 Example. The length of a room is given as 15-3 meas- 
 ured by a surveyor 's tape 10 inches to the foot. To what 
 length on the cutter's tape does it correspond? 
 
 AXl2=AV^10=^f=3f inches, and 15 feet 3f is the 
 length on the cutter 's tape nearly. 
 
 How to Add Fractions 
 
 Find the sum of | and |. 
 
 Explanation. 4X5=20; 3X9=27; 20+27=47, which is 
 
70 CAKPET-MEN'S MANUAL 
 
 the numerator of the answer, and the product of the 
 denominators 4X9=36, the denominator of the answer, ££• 
 
 Find the sum of |, f , and f. 
 
 Multiply 2 by 8 of the denominators by 2 in the numera- 
 tor equals 32, next 2X3 (denominators) =6 by 5 (numera- 
 tor) =30, next 3X8 (denominators) =24 by 1 (numerator) 
 =24, 32+30+24=86, the numerator of the answer, and 
 2X3X8 (the denominator) =48, the denominator of the 
 answer ff=lif • Or, find the least common multiple of 
 the denominators. 
 
 Divide this multiple by each denominator, and multiply 
 the quotient by the numerator, the product is the numera- 
 tor of each fraction, the sum of which will be the numera- 
 tor of the answer, with the least common multiple as 
 denominator. 
 
 Example. Add |, f, and f as before. 
 
 Here it is found that 24 is the smallest number which 
 can be divided by 2, 3, and 8 without leaving a remainder ; 
 it is therefore called the least common dividend or 
 multiple. 
 
 2 in 24=12, 12X1=12, first numerator. 
 
 3 in 24=8, 8X2=16, second numerator. 
 8 in 24=3, 3X5=15, third numerator. 
 
 Sum of the numerators =43. The numerator of the 
 answer. 
 
 Least common multiple=24. The denominator of the 
 answer. 
 
 To Subtract Fractions 
 
 From f take f . 
 
COMMON AKITHMETIC 71 
 
 Explanation. Multiply 3 (numerator) by 3 (denomi- 
 nator) =9. 
 
 Multiply 2 (numerator) by 4 (denominator) =8. 8 
 from 9 leaves 1, the numerator of the remainder. The 
 product of the denominators 4X3=12 is the denominator 
 of the answer. 
 
 Multiplication of Fractions 
 
 Rule. Change all the factors to the form of fractions. 
 Eeduce crosswise and multiply straight, then the prod- 
 uct of all the numerators is the numerator, and the prod- 
 uct of all the denominators, the denominator of the 
 answer. 
 
 Example, ix 108 ; ix±p=48. 
 
 Example. 2ffX2«x7, ttx||xf=8x7=56. 
 
 How much is | of f of I of 14? |xlxlx^=W=10A. 
 
 Division of Fractions 
 Eeverse the divisor and proceed as in multiplication. 
 
 2 
 
 Example. }^-li=i^-|, reverse the i then ixS?=f. 
 
 Second Method 
 
 Draw two parallel lines and write the dividends on the 
 upper line, and divisors on the lower. Multiply the num- 
 bers outside the lines for the numerator and those on the 
 inside for the denominators of the answer. Always 
 cancel factors common to both terms. 
 
72 CARPET-MEN'S MANUAL 
 
 Example. Divide i of f by f of f 
 1 3 
 
 2 8 
 ^ 5 
 4 ^ 
 
 2 
 
 24 3 
 80HU) 
 
 Multiplication of Mixed Numbers. General Rule 
 
 To multiply any two mixed numbers. Find the prod- 
 uct of the whole numbers and the product of the frac- 
 tions, and add to this amount the product of the lower 
 fraction by the upper whole number, and the upper 
 fraction by the lower whole number. Multiply 21| by 
 15f 
 
 Explanation. An outline of the operation is here given, 
 but in practice the partial product should be added 
 mentally as they occur. 
 
 21* 
 
 _15+ 
 
 315 =21X15 
 3 =*of21 
 3 =i of 15 
 
 Answer=32l3V 
 A Practical Business Method 
 
 As it is only necessary to get the answer to the nearest 
 cent, when it is less then one-half, drop it ; and when one- 
 half or more call it one cent. By this method entire dis- 
 
COMMON AEITHMETIC 73 
 
 regard of fractions in the partial product renders a mis- 
 take or error almost impossible. 
 
 Multiply 11JX9 
 
 Explanation. J X 11=31 ; call it 4 because it is nearer 4 
 than 3. 
 
 iX9=2J ; call it 2. 
 
 4+2=6 plus the product of the whole number 99=105. 
 
 Hi 
 
 _9i 
 
 105= Answer. 
 
 Duodecimals 
 
 Duodecimals are so called because they decrease by 
 twelves, from the place of feet towards the right hand. 
 Feet are sometimes marked with a comma at the top 
 thus ', inches with two commas ", and parts of inches with 
 three commas '". 
 
 KULE 
 
 1. Under the multiplicand write the same names or 
 denominations of the multiplier; that is, feet under feet, 
 inches under inches, parts under parts. 
 
 2. Multiply each term in the multiplicand, beginning 
 at the lowest, by the feet in the multiplier, and write each 
 result under its respective term, observing to carry a unit 
 for every 12 from each lower denominator to its next 
 superior. 
 
 3. In the same manner multiply every term in the 
 multiplicand by the inches in the multiplier and set the 
 
74 CARPET-MEN'S MANUAL 
 
 result of each term one place removed to the right of 
 those in the multiplicand. Proceed in like manner with 
 all the rest of the denominations if there be any; and the 
 sum of all the lines will be the product required. Or the 
 denominations of the particular product will be as fol- 
 lows : When feet are concerned the product is of the same 
 denomination with the term multiplying feet. When feet 
 are not concerned, the name of the product will be ex- 
 pressed by the sum of the indices of the two factors. 
 
 Example. Find the number of square feet in a rug, 
 sixe 10 ft. 4| in.X7 ft. 8£ in. 
 
 10' 
 
 7 
 
 4" 9'" 
 8 6 
 
 72 
 6 
 
 9 3 
 11 2 
 5 2 4 6 
 
 80' 1" 7"'= (80+ A+A of tV square feet) or 80 square 
 feet and 19 square inches, the answer. 
 
 To find the number of square feet in a rubber mat, size 
 4' 5"X5' 7". 
 
 4' 5' 
 5 7 
 
 22 1 
 2 6 11 
 
 24' 7" 11"'=(24+A+H of A square feet)=24 T ¥t 
 square feet, or 24 feet 95 inches 
 square, or 24£ square feet, nearly. 
 
COMMON ARITHMETIC 75 
 
 Decimal Fkactions 
 
 A decimal fraction is a part of a whole which has been 
 
 divided into 10, 100, 1,000, etc., number of parts. It is 
 
 commonly expressed by writing the numerator only, with 
 
 a point before it called the separatrix or decimal point, 
 
 thus: 
 
 .l=one tenth. 
 
 .01=one hundredth. 
 
 .001=one thousandth. 
 
 .0001= one ten- thousandth. 
 
 Ciphers on the right of the decimals do not alter their 
 value. But ciphers on the left and after the decimal 
 point diminish the value in a tenfold proportion for every 
 cipher. 
 
 The use of decimals in figuring is very convenient, 
 particularly when dollars and cents constitute one of the 
 factors. 
 
 Addition of Decimals 
 
 Rule. Set the numbers under each other according to 
 the value of their places, as in whole numbers, or so that 
 the decimal points shall stand each directly under the pre- 
 ceding. Then add as in whole numbers, placing the 
 decimal point in the sum directly under the other points. 
 
 Examples. 
 
 
 r237 
 
 
 f0.56 
 
 25.23 
 
 
 1.25 
 
 3.056 
 
 
 0.002 
 
 Add^ 163.113 
 
 AdcH \ 
 
 
 0.045 
 
 
 3.652 
 
 
 428.444 
 
 7.564 
 
76 CABPET-MEN'S MANUAL 
 
 SUBTKACTION OF DECIMALS 
 
 Rule. Set the less number under the greater in the 
 same manner as in addition. Then subtract as in whole 
 numbers and place the decimal point in the remainder 
 directly under the other points. 
 
 Examples. 365.24 2,986 
 
 2.153 0.213 
 
 363.087 2.773 
 
 First answer is, three hundred and sixty-three whole 
 and eighty-seven thousandths. 
 
 Second answer is, two whole and seven hundred and 
 seventy-three thousandths. 
 
 Multiplication of Decimals 
 
 Rule. Set down the factors under each other and 
 multiply as in whole numbers. In the product from 
 right to left point off as many figures as there are deci- 
 mals in both factors. 
 
 If there are not so many figures in the product as there 
 ought to be decimals, prefix the proper number of 
 ciphers to supply the defect. 
 
 Example. Multiply 43.35 by 0.156=6.7626. 
 
 Ex. 2. 4.25X4.5=19.125. 
 
 When decimals are to be multiplied by 10, 100, 1,000, 
 etc., move the decimal point one, two, three, or more 
 places to the right. 
 
COMMON AEITHMETIC 11 
 
 Example. Multiply 3,25 by 10=32,5=Thirty-two whole 
 and five-tenths. 
 
 Division of Decimals 
 
 Divide as in whole numbers, point off for decimals in 
 the quotient from left to right as many figures as the 
 decimals in the dividend exceed those in the divisor. 
 
 Example. Divide 81.4025 by 32.561=2.5. 
 
 32.561)81.4025(2.5 
 65.122 
 
 16.2805 
 16.2805 
 
 To divide by 10, 100, 1,000, etc., move the decimal point 
 one, two, three, or more places from right to left. 
 
 To Reduce Vulgar Fractions to Decimals 
 
 Attach any number of ciphers to the numerator and 
 divide this by the denominator, being sure to have a figure 
 in the answer for each cipher attached. 
 
 Example. Reduce i to a decimal. 4)100=0.25. 
 
 How much is f of a foot reduced to decimals? 8)50= 
 0.625. 
 
 THE FOLLOWING TABLES SHOW VULGAR FRACTION AND THEIR EQUIVALENT 
 
 DECIMALS 
 
 * 
 
 of 
 
 an 
 
 inch 
 
 =0032 
 
 i 
 
 of 
 
 an 
 
 inch 
 
 =0.25 
 
 fof 
 
 an 
 
 inch 
 
 =0.625 
 
 tV 
 
 • 
 
 
 " 
 
 =0.0*3 
 
 8 
 
 f 
 
 ' 
 
 
 '« 
 
 =0.375 
 
 S i 
 
 
 " 
 
 =0.75 
 
 1 
 
 f 
 
 
 
 
 =0.125 
 
 1 
 
 "5 
 
 « 
 
 
 
 =0.5 
 
 7 < 
 
 
 < < 
 
 =0.875 
 
78 
 
 CARPET-MEN'S MANUAL 
 
 12 INCITES OR ONE FOOT THE WHOLE NUMBER 
 
 £=0.0104 
 
 1=0.073 
 
 6=0.5 
 
 sV of a foot or f inches =0.032 
 
 £=0.0208 
 
 1=0.083 
 
 7=0.583 
 
 T V " " | " =0.063 
 
 1=0.0313 
 
 2=0.167 
 
 8=0.667 
 
 i " '* H " =0.125 
 
 i=0.0417 
 
 3=0.25 
 
 9=0.75 
 
 f " '« 4£ " =0.375 
 
 f=0.0521 
 
 4=0.333 
 
 10=0.833 
 
 f " " 7$ " =0.625 
 
 1=0.0625 
 
 5=0.417 
 
 11=0.917 
 
 | " " 10$ " =0.875 
 
 ONE YARD OR 36 INCHES THE WHOLE NUMBER 
 
 1 ill.: 
 
 2 ius.: 
 
 3 ins.: 
 
 4 ins.: 
 
 5 ius.: 
 
 6 ins.: 
 
 7 ins. : 
 
 8 ins.: 
 
 9 ins.: 
 
 :0.028 
 :0.056 
 
 =0.083 
 
 :0.111 
 
 :0.139 
 :0.167 
 :0.194 
 
 : 0.222 
 
 :0.25 
 
 10 ins. 
 
 11 ins. 
 
 12 ins. 
 
 13 ins. 
 
 14 ins. 
 
 15 ins. 
 
 16 ins. 
 
 17 ins. 
 
 18 ins. 
 
 =0.278 
 
 :0.306 
 
 :0.333 
 
 :0.361 
 
 :0.389 
 
 :0.417 
 
 : 0.444 
 =0.472 
 
 :0.5 
 
 19 ins. 
 
 20 ins. 
 
 21 ins. 
 
 22 ins. 
 
 23 ins. 
 
 24 ins. 
 
 25 ins. 
 
 26 ins. 
 
 27 ins. 
 
 :0.528 
 :0.556 
 :0.583 
 =0.611 
 :0.639 
 :0.667 
 :0.694 
 :0.722 
 =0.75 
 
 28 ins. 
 
 29 ins. 
 
 30 ins. 
 
 31 ins. 
 
 32 ins. 
 
 33 ins. 
 
 34 ins. 
 
 35 ins. 
 
 36 ins. 
 
 :0.778 
 : 0.806 
 :0.833 
 =0.861 
 :0.889 
 
 :0.917 
 
 :0.944 
 :0.972 
 
 :1 
 
 i= 4$ ins. =0.125 
 i=9 ins. =0.25 
 f=13$ ins. =0.375 
 $=18 ins.=0.5 
 1=22$ ins. =0.625 
 f=27 ins. =0.75 
 1=31$ ins. =0.875 
 T V=2J- ins. =0.063 
 ■&=!$ ins. =0.032 
 
 Proportion, or the Rule op Three 
 
 In problems to be solved by the rule of three, three 
 quantities are given to find the fourth. 
 
 The following is a form of simple proportion: 
 If we call the unknown quantity x ; 2 is to 4 as 6 is to 
 x and is written 2 : 4=6 : x. It is here seen that the prob- 
 lem is composed of four terms of which 2 and x are called 
 the outside terms, 4 and 6 the inside terms. Now if the 
 unknown quantity, x, is one of the outside terms its value 
 is equal to the products of the inner terms divided by the 
 other outside term, but if x is an inside term, then its 
 value is equal to the product of the outside terms divided 
 by the other inside term. Thus in the above analogy x= 
 
 4x6 
 
 — - — ±s 12 and by substituting the unknown quantity x 
 
COMMON ARITHMETIC 79 
 
 by the found term 12 we have 2 is to 4 as 6 is to 12, and 
 I =¥=2. 
 
 Ex. If it takes 12 yards of f carpet to cover a room, 
 how many yards of f carpet will cover the same room? 
 
 12 yards f wide 
 x yards f wide 
 
 x : 12-t : | then x =%gi = 16 yards. 
 
 Rule. Write the terms belonging to the statement in 
 one line, under it write the terms of the question, so that 
 terms of the same name will come under each other. If 
 from the nature of the question the answer is direct, the 
 term involved, on the same line with the unknown will be 
 one of the inside terms, but if the answer is indirect the 
 term will have an outside place, or in the first case the in- 
 volved term will stand second ; in the second case it will 
 stand first, the unknown are always placed last on the 
 right hand side. 
 
 Example. If 9 men in 4 days working 8 hours per day 
 can do a piece of work ; how many days will it require for 
 7 men to do the same job by working 5 hours per day? 
 Explanation: 
 
 Statement, 9 men, 4 days, 8 hours 
 Question, 7 men, x days, 5 hours 
 7 :9=4 :sr * 
 5 :8=x:y 
 
 (7X5) :(9X8)=4 :y and 
 Learly. 
 
 Formulate the questions and answers in the following 
 
 ^ 9X8X4 Ql , 
 
 y= 7x5 =8i days nearly. 
 
80 CABPET-MEM'S MANUAL 
 
 manner. If 9 men can do the work in 4 days ; how many 
 days will it take 7 men to do it? Answer : more days, less 
 men. The answer is indirect and the lower term 7 will 
 come outside or in first place. Again, we say, if it takes 
 4 days by working 8 hours per day, how long will it take 
 working 5 hours per day? Answer: more days, less 
 hours. Again the answer is indirect and 5 will be the 
 outside term. 
 
 Example. Five men laid a house of carpets in 6 days ; 
 how many men will it require to lay the same house of 
 matting in 4 days, when it consumes imore time to lay 
 the latter? 
 
 Explanation : 
 
 5 men, 6 days, 1 hard 
 x men, 4 days, H harder 
 
 4 :6 =5 :x- 
 
 1 :lj=^:y 
 
 4X1 :6Xli=5 :y 
 
 y= =10 men, the answer. 
 
 If 5 men can do the work in 6 days -; how many men will 
 it require to do it in 4 days? More men, less days; an- 
 swer is indirect and 4 will be outside term. Again, if 5 
 men can do it in 6 days when it is 1 hard ; how many men 
 will it take to do it when it is i harder. More men, harder 
 work. Answer is direct and li will come in second 
 place and be an inside term. In the first question x was 
 the unknown, but was found. In the second, y is the un- 
 known to be found, 
 
COMMON ARITHMETIC 81 
 
 Square Root 
 
 Definition. To extract the square root from a number, 
 is to find the number which multiplied by itsell gave as a 
 product the present number. 
 
 Rule. Separate the number under the root mark into 
 classes, the whole number to the left, and the decimals (if 
 any exist) to the right from the decimal point, with two 
 figures in each class. Now take the first root figure, such 
 that its square will be equal to, or just less than, the num- 
 ber in the first class. Subtract this square from the first 
 class, and to the right of the remainder write down the 
 next class and separate the last right hand figure from the 
 rest by a comma. Next form a divisor of twice the found 
 root and use this divisor to divide the number formed by 
 the remainder and the first figure of the second class. 
 The quotient is written to the right of the divisor, after 
 which this new divisor is multiplied by the last root figure. 
 The product is subtracted from the first remainder. To 
 the right of this second remainder write down the figures 
 of the third class, and proceed in like manner until there 
 is no remainder, or by adding two ciphers to the right of 
 each remainder the desired number of decimals are 
 obtained in the root. 
 
 Example. Extract the square root from 104976. 
 
82 CARPET-MEN'S MANUAL 
 
 Explanation: 
 
 Here 3 is the first root figure, 3 times 
 
 3=9; put 9 under 10 (the first class) 
 3 \ 71 0' 49 '76=3^4 and subtract# The rema i nder i s 
 
 1, write down 49 (second class) 
 
 62 
 644 
 
 14'9 
 
 -L2 4 and point off the last right hand 
 
 ~25T6 figure 9 from the 14. Multiply the 
 
 257 6 fi rs t root figure 3 by 2 and write the 
 
 product 6, to the left of 149. Six 
 
 in 14=2; 2 is the next root figure; 
 
 put it down to the right of 3 in the root, and to the right 
 
 of 6 opposite the 149. Multiply this 62 by 2, the second 
 
 root figure=124, write it under 149 and subtract. To 
 
 the remainder 25 prefix the next class 76 and point off 
 
 the 6. Multiply 32 by 2 and write the product to the left 
 
 of 257'6. 64 in 257 goes 4 times. 4 is the next root 
 
 figure, write it to the right of 2 and 64 and multiply this 
 
 644 by 4 and write the product under the 257'6, which, 
 
 there being no remainder, will finish the operation and 
 
 give the root 324. Prove 324X324=104976. 
 
PART VIII 
 TO ESTIMATE ON CARPETS 
 
 In times of keen competition, estimates have to be 
 made on the smallest margin of profit. The success of a 
 business venture depends, therefore, to a certain extent 
 on the ability of the man doing the estimating. Nine 
 times out of ten, everything else being equal, the one sub- 
 mitting the lowest estimate gets the job, and although 
 the contract must of necessity show a profit, the real gain 
 frequently will come through future orders, as a person of 
 true economical ideas will have his work done where he 
 is sure of honest treatment and satisfactory workman- 
 ship. Haphazard and careless estimating will bring the 
 same results as other work done in this manner. A friend 
 of the writer once remarked, when asked to what he 
 attributed his success in business : l ' I give first credit 
 to the man who did my estimating, for by his shrewdness 
 my first large order was secured ; secondly, to my work- 
 men, whose good workmanship recommended my busi- 
 ness until now orders flow in while estimates are rarely 
 called for." 
 
 As it is necessary to know the length of figure or de- 
 sign in order to determine the point at which a carpet 
 will cut to match, so it is equally important to know the 
 length of space the carpet is to cover in order to deter- 
 mine the waste. Thus a carpet with a 48-inch pattern for 
 
 83 
 
84 CABPET-MEN'S MANUAL 
 
 a floor measuring 15 ft. 10 in., would have no more waste 
 than would be necessary for a turn-under, or two inches, 
 on each breadth, whereas the same pattern would waste 
 one-half yard on each breadth for a floor fourteen feet six 
 inches long. Again, take a nine-inch pattern for the room 
 fifteen feet ten inches in length and the waste will be 
 eight inches on each breadth, because in order to make 
 it match the carpet must be cut where the figure repeats 
 itself. Drop patterns have two cutting points, one, half 
 the distance between the full length of the design, and 
 the other where the figure is repeated, and in order to 
 match such a carpet with the least possible waste, one 
 breadth is dropped down beyond the others in cutting; 
 this drop which is equal to half the length of the design, 
 will, therefore, be additional waste. Hence, it is obvious 
 that in order to give an accurate estimate, not only must 
 the length of figure and length of room be known, but 
 also the character of the design. It is also evident that 
 the largest patterns do not always mean the greatest 
 waste. 
 
 If more than one room is to be covered with a carpet 
 of the same design the different lengths may be added 
 together and estimated on as if for one carpet. Enough 
 waste, however, must be allowed for each room to give 
 sufficient turn-under. The table of cutting lengths on 
 the last pages, has been computed for different length 
 patterns from twelve to fifty- three inches, and will be 
 found of practical use. 
 
 To apply these tables, first measure the full length of 
 the design and ascertain if it is a " set " or a " drop " 
 pattern- Then, having in mind the length of the room, 
 
TO ESTIMATE ON CARPETS 85 
 
 enter the table and column with the length of the pat- 
 tern at the top, and if it is a " drop " pattern, the first 
 number found, which corresponds to, or just exceeds, the 
 length of the room, will show the cutting point. The let- 
 ter S or M in the margin and on the same horizontal line 
 will indicate whether the carpet cuts to a set or match 
 at this length. But, if it is a " set " pattern, i. e., a pat- 
 tern with only one cutting point, the length at which the 
 carpet will cut to match can only be found on the same 
 horizontal line with the letter S. 
 
 Example. A carpet with a 28-inch " drop " pattern 
 is bought for a room 16-3 long. Which is the nearest 
 cutting point, and will it cut to a " set " or " match " 
 at this length! 
 
 In the column under 28" we find 16' 4" as being nearest 
 to the length of the room, and looking at the margin we 
 find the letter S, which indicates that the carpet will cut 
 to a " set " at this point, and, of course, a " set " pat- 
 tern will cut the same length. Now take the same length 
 pattern for a room 17' 4" long, and we find that the 
 "drop" pattern cuts to a match at 17' 6." But the 
 " set " pattern will only match at 18' 8". 
 
 Sometimes it is required to submit estimate from a 
 small sample from which it is difficult to determine 
 whether the pattern is " drop " or " set." If, how- 
 ever, the sample is turned nap out, and the two selvages 
 brought together, this difficulty is easily overcome. 
 
 The width multiplied by the length gives the area of 
 any rectangular space, but when estimating for carpets 
 the breadths and their proper alignment have to be con- 
 sidered. Therefore, first find the number of breadths 
 
86 
 
 CARPET-MEN'S MANUAL 
 
 required, by dividing the width of room by the width of 
 one breadth of carpet. If, however, there should be a 
 fraction, and such fraction is less than one-half, a breadth 
 half the length of the room can be split and the ends 
 sewed together, i. e., cross- joined. When this is to be 
 done the customer, if present, should be consulted, 
 as some object to a cross- join, with the probable mis- 
 match of one part, or for other reasons they may prefer 
 to have the breadths left whole. If only a few inches are 
 lacking, a breadth of sufficient length can be split into 
 several strips wide enough to cover, an allowance of one 
 or two inches should be made for turning under the raw 
 edge. Attention to similar details is often the means of 
 gaining the customer's confidence. For convenience the 
 following table of widths for from one to twelve breadths 
 f goods, with f , f , and J border added to each side, are 
 given. 
 
 8 9 10 11 12 
 
 | goods . . . . 
 f body and f border. 
 | body and f border. 
 | body and ^border. 
 
 2.3 
 6.0 
 5.3 
 3.9 
 
 4.6 
 8.3 
 7.6 
 6.0 
 
 6.9 
 
 10.6 
 9.9 
 
 9.0 
 12.9 
 12.0 
 10.6 
 
 11.3 
 15.0 
 14.3 
 12.9 
 
 13.6 
 17.3 
 16.6 
 15.0 
 
 15.9 
 19.6 
 18.9 
 17.3 
 
 18.0 
 21.9 
 21.0 
 19.6 
 
 20.3 
 24.0 
 23.3 
 21.9 
 
 22.6124 9 
 26.3 28.6 
 25.6j27.9 
 24.0126.3 
 
 27.0 
 30.9 
 30.0 
 
 28.6 
 
 To find number of yards required for a rectangular 
 floor. 
 
 Rule. Multiply length of room by number of breadths, 
 the product gives the number of yards net, if length is 
 taken in yards and fraction thereof. If in feet and inches 
 divide the product by three for the answer. 
 
 Note. If 3 breadths are considered, the length in feet 
 and fraction will express the quantity in yards. Thus 
 
TO ESTIMATE ON CAEPETS 
 
 87 
 
 12' 3"=12i yards, 12' 6"=12i yards, 12' 9"=12f yards, 
 etc. 
 
 If the floor has the form of a trapezoid, i. e., has 
 only one pair of opposite sides parallel, as in Fig. 1, 
 and the difference in length of the 
 parallel sides is slight, it can be esti- 
 mated by regarding it as a rectangle. 
 But, if the difference is great, as for 
 example, in a room 15' 9" wide, one side 
 of which measures 18' 0" and the op- 
 posite side 12' 0", it would make a dif- 
 ference of about six yards and would 
 have to be considered if figuring 
 against others. 
 There are three practical ways of determining the 
 quantity required to cover any floor, viz.: 
 
 First by Construction; that is to say, by drawing the 
 floor plan to scale, then the length of each breadth is 
 easily found by measuring with the same scale used in 
 constructing the plan. No matter how irregular a floor 
 may be this method can always be depended on, and the 
 larger the scale used the better results obtained. Half 
 an inch to a foot is a convenient scale. The same meas- 
 ures are required to produce the plan on paper to scale, 
 as would be used in striking out the plan on the floor, the 
 rule and dividers being substituted for the tape. 
 
 Second, by finding the drop or difference in length of 
 the breadths, and adding or subtracting, as the case 
 may be, these several drops to or from the length of the 
 first breadth. 
 
 Third, by the rules of mensuration modified by the 
 
88 
 
 CABPET-MEN'S MANUAL 
 
 necessity of considering the figure and match of the pat- 
 tern which require that the ends of each breadth be cut 
 off square, thus adding so much waste to the geometrical 
 area of the space covered. 
 
 The first method is general and can be used in all cases, 
 and is withal so simple that further explanation is 
 deemed unnecessary. 
 
 SECOND METHOD 
 
 To find the drop in a trapezoid, Fig. 1 
 Rule 1. Divide the difference in length of the two paral- 
 lel sides by the number of breadths, the quotient giving 
 the difference in length of breadths. 
 
 In a right-angle triangle 
 Rule 2. Divide the length by the number of breadths 
 contained in the base or width. 
 
 Ex. 1. What will be the difference in length of breadths 
 required for a floor like Fig. 1 ? 
 
 Here the sides are 12' 0" and 18' 0". Difference=6' 
 0"=72 inches. End of room 15' 9"=seven breadths. 72 
 inches divided by 7 gives a quotient of 10J inches=drop. 
 Ex. 2. How many yards f plain carpet 14-inch pattern 
 is required to cover a floor like Fig. 1, with and without 
 allowing for waste in matching? 
 Entrance side=12' 0" 
 Plus the drop=0 10J 
 
 1st breadth 
 
 =12 10J 
 
 and cuts 12' 10" 
 
 2d 
 
 -13 8i 
 
 " " 14 
 
 3d 
 
 =14 6J 
 
 " " 15 2 
 
 4th " 
 
 =15 5 
 
 " " 16 4 
 
 5th " 
 
 =16 3J 
 
 " " 16 4 
 
 6th " 
 
 =17 H 
 
 " " 17 6 
 
 7th " 
 
 =17 llf 
 
 " " 18 
 
TO ESTIMATE ON CARPETS 89 
 
 Number of yards, net, 107' ll"-^3=36; waste allowed, 
 110' 2"-^3=37 yards. 
 
 Note: When this method is used always write down 
 the length of the several breadths, one under the other, 
 then compare the number and the width of the room to 
 make sure no breadths are omitted. When adding, draw 
 a line across top of column and above this place the carry- 
 ing figure, thus making it possible if interrupted to re- 
 sume the work where left off. 
 
 THIRD METHOD 
 
 Rule 3. Multiply half the sum of the two parallel sides 
 by the number of breadths. To the product add half their 
 difference. 
 
 Ex. 3. Find how many yards is required to cover a 
 floor like Fig. 1 by this method. 
 
 Longest side 
 Shortest side 
 Sum . . 
 Half sum 
 Half difference 
 
 18' 0" Half sum . . . . = 5 yards 
 12 Number of breadths = 7 
 
 = 30' 0" Product ...'..= 35 yards 
 
 = 15 Half difference . . = +1 
 
 = 30 Number of yards, net = 36 yards 
 
 As it is better not to figure too close on account of some 
 small difference in length of pattern which may occur in 
 different rolls of the same pattern, if one foot is added 
 to each breadth for a 14-inch pattern, the last method 
 will make the estimate 38 J yards and give ample allow- 
 ance. 
 
90 
 
 CARPET-MEN'S MANUAL 
 
 When the floor is in the form of a right-angle triangle. 
 
 FIRST METHOD BY CONSTRUCTION 
 
 Draw side AB to scale and equal to 15.6 
 (see Fig. 2). From point A erect AC per- 
 «*pendicular to AB and equal to 13.6. Join 
 B and C. On AC mark off the 
 width of the breadths; from 
 these marks draw lines parallel 
 to AB. Measure AB for the 
 first breadth and each line from 
 AC to BC for the following 
 breadths. 
 
 FIGURE 2. 
 
 SECOND METHOD 
 
 Ex. 4. Drop of breadth to be deducted=6)15' 6"= 
 2' 7". 
 
 First breadth =15' 6" 
 
 Second 
 
 =12 11 
 
 Third 
 
 =10 4 
 
 Fourth 
 
 = 79 
 
 Fifth 
 
 = 52 
 
 Sixth 
 
 = 27 
 
 
 3)54' 3 
 
 
 THIRD METHOD 
 
 Rule 4. Multiply half the length by the number of 
 breadths, or vice versa. To the product add half the 
 length. 
 
TO ESTIMATE ON CAEPETS 
 
 91 
 
 Ex. 5. 
 
 2)15'6= T 9' 
 
 Breadths = 6 
 
 46' 6" 
 Half the length =+ 7 9 
 
 3)54' 3' ' = 18tV yards, net. 
 
 Note. When in a triangular room, as above, the 
 width requires five breadths of carpet, the length of the 
 side in feet and inches gives the number of yards re- 
 quired. Thus a floor in the form of a right-angle tri- 
 angle, Fig. 2, the end measures 11' 3" and the length 
 18' 9", here it requires 18f yards of carpets § yard width. 
 
 When the floor has the form of a trapezium, Fig. 3. 
 
 BY THE SECOND METHOD 
 
 FIGURE 3. 
 
 Drop on BE=11 inches 
 " " EC=6'8" 
 
 J by Problem 2. 
 
 Then the 1st breadth 
 
 =15' 5"+ 11 "=16' 4" 
 
 2d " 
 
 =10' 4"+ 11"=17' 3" 
 
 3d " 
 
 =17' 3"+ 11"=18' 2" 
 
 4th " 
 
 =18' 2"+ 11"=19' 1" 
 
 5th " 
 
 =19' 1"+ 11"=20' 0" 
 
 0thsameas5th=19' 1"+ 11"=20' 0" 
 
 7th breadth 
 
 =20' 0"-6' 8"=13' 4" 
 
 8th " 
 
 =13' 4"-6' 8"= 6' 8" 
 
 ^ Number of yds., net, nearly =130.10-i-3=43t 
 
 THIRD METHOD 
 
 Rule 5. Divide the room into a trapezoid and a tri- 
 angle. Estimate each separately and take the sum. 
 
92 
 
 CARPET-MEN'S MANUAL 
 
 Ex. 7. 
 
 In trapezoid ABED : 
 
 _/15.5+20.0\ , /20.0-15.5\ ftA , iA „ QA1 -, 
 of \ + l 1=90 10 or30£yds. 
 
 In triangle DEC : 
 
 3X20 20 
 
 ~~ 2~~ + T 
 
 40' 0" or 13i yds. 
 
 And in the whole room ACEB, net sum nearly 43! yds. 
 
 Note. If length of pattern is known and added to each 
 breadth in the second method, the exact number of yards 
 can be found. Drop and length of pattern should be 
 added mentally for practice. 
 
 When the floor is an irregular polygon, Fig. 4. 
 If the room has more than four sides all different in 
 length, with no square corners. 
 
 Ex. 7. How many yards of 
 | plain Brussels (with and with- 
 out allowance for matching) are 
 required to cover a floor like Fig. 
 4, length of pattern 15" ? 
 
 BY THE SECOND METHOD. 
 
 Drop on CD =2' 8" 
 " " DE = 2' 0' 
 " " FE=4' 0" 
 " " AF= 9V 
 
TO ESTIMATE ON CARPETS 
 
 93 
 
 Drop . 
 Drop. 
 
 let 
 Breadth 
 
 15' 11" 
 on CD 
 
 +2' 8" 
 on AF 
 
 19' 4f 
 
 2d 
 Breadth 
 
 19' W 
 CD" 
 
 +2' 8' 
 AF 
 
 22' 10' 
 
 3d 
 
 Breadth 
 
 22' 10' 
 CD 
 
 + 2' 8' 
 
 AF 
 +0'9V 
 
 26' 3^ 
 
 4th 
 Breadth 
 
 26' 3^ 
 
 O'O" 
 AF 
 
 27' 1" 
 
 5th 
 Breadth 
 
 27' 1" 
 DE 
 
 -2'0' 
 AF 
 
 +0'9V 
 
 6th 
 Breadth 
 
 25'IOV 
 DE" 
 
 -2 0" 
 
 23' 10" 
 
 7th 
 Breadth 
 
 23' 10' 
 DE 
 
 -2' 0' 
 FE 
 
 -4' 0' 
 
 17' 10' 
 
 8th 
 Breadth 
 
 17' 10" 
 
 DE 
 
 -2' 0" 
 
 FE 
 -4' 0" 
 
 11' 10' 
 
 9th 
 Breadth 
 
 11' 10" 
 
 DE 
 
 -2' 0" 
 FE 
 
 -4' 0" 
 
 5' 10" 
 
 1st breadth 
 
 _ 19' 4i" 
 
 and cuts at 20' 0' 
 
 2d 
 
 - 22 10+ 6 
 
 U i 
 
 
 ' 23 9 
 
 3d 
 
 - 26 3+10 
 
 a i 
 
 
 ' 27 6 
 
 4th " 
 
 = 27 1+3 
 
 <t ( 
 
 
 1 27 6 
 
 5th " 
 
 = 25 10+ 9 
 
 (< ( 
 
 
 1 27 6 
 
 6th " 
 
 = 23 10+ 6 
 
 11 ' 
 
 
 1 25 
 
 7th " 
 
 = 17 10+ 6 
 
 u t 
 
 
 ' 18 9 
 
 8th " 
 
 = 11 10+ 6 
 
 U i 
 
 
 1 12 6 
 
 9th " 
 
 = 5 10+ 6 
 
 <( i 
 
 
 ' 7 6 
 
 3)180' 9"=60£ yds., net. 3)189'10"=63i yds. to match. 
 
 Note. The figures added to the second column denote 
 the distance each breadth has to be dropped below the 
 
 lines AF and FE in order to find 
 the match. 
 
 BY THE THIRD METHOD 
 
 Rule 6. Make the floor into a 
 rectangle by affixing triangles 
 whose hypotenuses or longest 
 sides will form sides of the room. 
 Multiply the length of this rec- 
 tangle by the number of breadths. 
 From the product subtract the 
 quantity in each triangle reduced 
 by half its height. 
 
 FIGUKB 4. 
 
94 
 
 CARPET-MEN'S MANUAL 
 
 Note. If there are three breadths on the base of the 
 triangle subtract the height of the triangle from the 
 square of the room. 
 
 Ex. 8. How many yards of J plain Brussels will it take 
 to cover a floor like Fig. 4? Greatest width BE=20' 0". 
 Greatest length FH.+GD=27' 8". 
 
 Triangle on CD. 
 
 DG =11' 10" 
 
 BC =- 3 11 
 
 Triangle on DE. 
 Half DG = 5' 11" 
 
 Breadths on GE= 6 
 
 HalfCM=7' 11" -5-2=3' 11F 
 
 Breadths on BG = 3 
 
 35' 6" 
 HalfDG =-5 11 
 
 11' 10i" 
 Half CM =-3 11| 
 
 3)29' 7" =9f yds. 
 Triangle on AF. 
 
 3)7' ll"=2f~d. 
 
 Triangle on FE. 
 Half FH =7' 11" 
 Breadths on HE= 4 
 
 Half An =1' 11" 
 Breadths on BH= 5 
 
 9' 7" 
 Half An -1 11 
 
 31' 8" 
 HalfFH = -7 11 
 
 3)7' 8"=2£yds. 
 Yards in rectangle =83£ 
 
 3)23' 9"=8 yds. 
 
 " " triangles=—2S 
 
 " on the floor =60^ net. 
 
 Note. If the bevels or slants are alike on any two op- 
 posite sides, so that the cut of end can be used in any of 
 the triangles, then the area without the half length de- 
 ducted is the number of yards in the triangle. 
 
 When the room is in the form of a circle. 
 Find the length of the several breadths by the follow- 
 ing: 
 
TO ESTIMATE ON CARPETS 
 
 95 
 
 Rule 7 
 
 FIGURE 
 
 Take the difference between 
 the square of the radius and 
 the square of the number of 
 breadths required less one, in 
 feet and fractions thereof , count- 
 ing from the center. The square 
 root multiplied by two, is the 
 length of the breadth sought. 
 
 To find the number of yards 
 required : 
 
 Rule. To the length of the center breadth or breadths, 
 which are always equal to the length of the diameter, add 
 the length of the breadths found on each side. 
 
 Ex. 1. What is the length of the 2d, 3d, and 4th breadth 
 from the center one, in a circular room (Fig. 5), radius= 
 
 10 ft.? 
 
 Second breadth=2 VlO 2 — (3.4i) 2 =18.10. 
 
 Third breadth =2 Vl0 2 -(5.7i) 2 =16.6. 
 Fourth breadth=2 <v/l0 2 -(7.10i) 2 =12.4. 
 Ex. 2. How many yards of f plain carpet is required 
 for a circular room, radius=10 feet as above? 
 
 Center breadth =20' 0" 
 
 First from center breadth =20' 0" 
 Second " " " =18 10 
 
 Third " " " =16 6 
 
 Fourth " " " =12 4 
 
 67' 8" X 2= 135' 4" 
 155' 4" 
 
96 CARPET-MEN'S MANUAL 
 
 155' 4", or 51| yards net, is the number of yards re- 
 quired for the whole room. 
 
 Ex. 3. How many yards of f plain Brussels does it re- 
 quire for a circular room (Fig. 6), radius=6' 9"$ 
 
 FIGURE 6. 
 
 1st breadth = diameter =13' 6" 
 
 2d " =2 V (6.9) 2 -(2' 3') 2 =12 9 
 3d " =2 V(6.9) 9 -(4' 6V=10 1 
 
 Number of yards on one side of the diameter =3(3' 4"=12f yards. 
 Number of yards on the other side = +36 4 =12$ yards. 
 
 And in the whole room =72' 8"=24i yards, net. 
 
 Ex. 4. How many yards of f body and § border are re- 
 quired for a circular room (Fig. 6), radius=8' 7i"H 
 
 Radius, . . . =8' 7£" 
 
 Width of border, . . = -1 10| 
 
 Radius of circle inside the border, = 6' 9" 
 
 Number of yards of f carpet, . = 24£. See Ex. 3. 
 Number of yards of f carpet, . = +18{. See (5) the circle. 
 
 Total number of yards, . = 42^ 
 
 No allowance made for matching either body or border. 
 
TO ESTIMATE ON CARPETS 97 
 
 The usefulness of the preceding rules will appear when 
 applied in solving the following problems. By knowing 
 the different methods, the most irregular floor can be 
 accurately estimated with ease. In order to explain the 
 work in full, it was necessary to write figures, which in 
 general practice are mentally applied. 
 
 Ex. 1. How many yards of f plain Brussels is required 
 to cover a floor like Diag. 31! No allowance for match- 
 ing. 
 
 BY THE SECOND METHOD 
 
 Explanation, 
 
 Drop on BC=lli" for each foot or 2' 2" for each 
 breadth. See Mule 1. 
 
 Drop on DE=12y for each foot or 2' 4" for each 
 breadth. 
 
 Beginning at the entrance side. 
 
 1st b 
 
 ■readt 
 
 h, 
 
 = 
 
 17' 
 
 & 
 
 2d 
 
 a 
 
 =17' 6"+r 
 
 11'= 
 
 19 
 
 5 
 
 3d 
 
 a 
 
 = 19 5 +2 
 
 2 = 
 
 21 
 
 7 
 
 4th 
 
 u 
 
 = 21 7 +2 
 
 2 = 
 
 23 
 
 9 
 
 5th 
 
 it 
 
 = 23 9 + 
 
 4 = 
 
 24 
 
 1 
 
 6th 
 
 a 
 
 
 = 
 
 24 
 
 1 
 
 7th 
 
 u 
 
 
 = 
 
 24 
 
 1 
 
 8th 
 
 u 
 
 = 24 1 - 
 
 9 = 
 
 23 
 
 4 
 
 9th 
 
 u 
 
 = 23 4 -2 
 
 4 = 
 
 21 
 
 
 
 10th 
 
 u 
 
 = 21 4 -2 
 
 4 = 
 
 19 
 
 
 
 = 217' 10" 
 
 Deduct length of hearth, = — 7 
 
 3)210' 10" 
 Number of yards net, = 70i nearly. 
 
98 CARPET-MEN'S MANUAL 
 
 BY THE THIKD METHOD. 
 
 RULE 5, 
 
 8 th breadth X24' 0"= 
 
 = 192' 
 
 0" 
 
 1st 
 
 
 = 17 
 
 6 
 
 10th 
 
 
 = 18 
 
 9 
 
 
 228' 
 
 3" 
 
 Triangle on BC 
 « " « DE 
 
 = 5' 0" 1 
 = 5' 0" \ = 
 
 -ir 
 
 0" 
 
 Length of hearth 
 
 =7'0"j 
 
 
 
 3)211' 3" 
 Number of yards, 70i net. 
 
 Ex. 2. How many yards of f plain carpet is required 
 for room, Diag. 34? 
 
 Explanation. Figure from the entrance side, and begin 
 by ascertaining the different lengths in the swell. See 
 Rule 7. 
 
 The center is 11" from the entrance side continued, the 
 distance from the center to the second left breadth 
 is, t herefore, 2' 3" +ll" = 3' 2", hence its length is 
 = 2 V(p' 5' / ) 2 -(3' 2") 2 = 9' 0". The distance from the center 
 to the first breadth is 11", therefore its length is 
 =2a/(5' 5") 2 -(ll") 2 =10' 6". 
 
 There are 3 breadths to the right of the entrance side 
 running into the swell. The first of these is 14' 3"+ 
 4' 5"=i8' 8" long; the second of these is 18' 8" long. 
 The third breadth comes 4' 6"-ir=3' 7" from the center, 
 therefore its length is 5' 5"- V(5' 5") 2 -(3' 4")' i =l'4" less 
 than the second, or 17' 4". In triangle CED we have 14| 
 yards. See note on triangle, Rule 4. 
 
TO ESTIMATE ON CARPETS 99 
 
 The estimate will then be, 1st short breadth = 9' 0" 
 
 2d 
 
 1st long " 
 
 2d " 
 
 3d " 
 
 =10 6 
 =18 8 
 =18 8 
 =17 4 
 
 In triangle CED 
 
 3)74' 2" =24| yards 
 =+14i " 
 
 Number of yards, 
 
 net =39.0 " 
 
 Ex. 3. Estimate on Diag. 35 for f plain carpet. 
 
 BY SECOND METHOD 
 
 Explanation. First find the length of the several 
 breadths in the window. Second, find the drop on BC 
 and CD. 
 
 Beginning at the entrance side, we notice that the first 
 and fifth breadths in the window are short and the three 
 center breadths run through. First breadth in window 
 comes 6'0" — 2' 3" from the center, therefore its length 
 = 2V(4'5'') 2 -(3'9'') 2 =4'7''. Second breadth is6'0"-4'6" 
 from the center, and its length= / V / (4' 5") 2 — (1' 6") a + the 
 difference between radius and depth of swell =8' 6". 
 Tliird breadth=S' 9". Fourth breadths 9". Fifth 
 breadth is 9' 0" — 6' 0" from the center, therefore its length 
 
 = 2 V(4' 5") 2 -(3' 0") 2 =6' 6". 
 
 Drop on BC=S' 7"-J-3=l' 3" for each breadth. 
 
 Drop on DC=11' 0"-*-6' 5"=20±" for each foot, or 3' 11" for each breadth. 
 
 L-u: C*. 
 
100 CABPET-MEN'S MANUAL 
 
 1st breadth in room= 7' 6"+l' 3" =8' 9" 
 
 1st 
 
 2d 
 
 3d 
 
 4th 
 
 5th 
 
 5th 
 
 6th 
 
 window = 47 
 
 room = 8' 8" +1' 3"= 9'll"+2db'dthinwindow=18 5 
 
 " = 9' 11" +1' 3"=11' 2'+3d " " " =19 11 
 
 " =11' 2" - 8"=10' 6"+4th " " " =19 3 
 
 " =10' 6"-3'll"=6' 7" . . . .=66 
 
 window . . . .-. . . .=66 
 
 room= 6' 7"-3' 11" =28 
 
 3)86' 11" 
 Number of yards, net . . . . ' . = 29 
 
 DIAGRAM 35. BY THIRD METHOD. RULE 6 
 
 6 breadths X 11' (length of room), = 66' 0" 
 
 3 " in window, 8' 9" long=26' 3" 
 1 « a 4' 7" a = 4' 7" . 
 
 1 " " 6' 6" " = 6' 6" 
 
 Triangle on BC, = 3' 7" 
 
 " DC, =11' r 
 
 103' 4" 
 = -14 8 
 
 3)88' 8" 
 
 Number of yards net=29i nearly. * 
 
 Estimate the above by rules 4 and 5. 
 
 Scale and estimate the following diagrams by these 
 rules, using the different methods. 
 
 Diagrams 27, 36, 38, 40, and 43. 
 
 In the previous examples the carpets have been es- 
 timated without borders. To estimate on a carpet with 
 a border, we first subtract twice the width of the border 
 from the extreme length and width of the room, the re- 
 mainder is the length and width of the space to be covered 
 by the body of the carpet. The number of yards for this 
 
 * 2£ yards could be saved in this room by using waste for the 1st breadth in 
 window and 6th breadth in room. 
 
TO ESTIMATE ON CARPETS 101 
 
 space having been found by the preceding methods, the 
 distance around the room following wherever the outside 
 of the border is to go, found by adding the lengths of the 
 different sections of wall measured on the baseboard if 
 the room is to be all covered, gives the yards of border 
 required. To the sum of these two quantities there must 
 be added the waste necessary to match the figure in the 
 plain carpet and 9 inches for each miter as an allowance 
 for seams and matching the miters in the border. 
 
 THE CIRCLE 
 
 To find the area, radius, diameter, or circumference of 
 a circle, each from any other. 
 
 (1) 3.1416 times the square of the radius=area or . . tR*=A 
 
 (2) 3.1416 times the square of the diameter divided by 4= 
 
 area or K ^ 2 a 
 
 (3) Circumference divided by 4 times 3. 1416= area or . _~L = A. 
 
 (4) 3.1416 times the diameter = circumference or . . 7rD=C 
 
 (5) 3.1416 times twice the radius = circumference or . 2n\R=C 
 
 (6) Twice the square root of 3.1416 times the area=cir- 
 
 cumference or 2 VnA=G 
 
 (7) Circumference divided by 3. 1416= diameter or . — =D 
 
 TV 
 
 (8) Twice the radius = diameter or 2R=D 
 
 (9) Twice the square root of the area divided by 3.1416= /~£ 
 diameter or 2\/ -rr"=D 
 
 (10) Circumference divided by twice 3.1416=radius or . 5 — iA - ie ='R 
 
 «&Xo.l41o 
 
 (11) Square root of the area divided by 3.1416=radius or a /— =R 
 
 y^= : 
 
 (12) Half the diameter=radius ..... -^ =R 
 
102 
 
 CARPET-MEN'S MANUAL 
 
 Note. — A is area ; C is circumference ; D is diameter ; R is radius. 
 The sign »r is called P, and denotes the numerals 3.1416. 
 
 THE CIRCULAR ARC 
 
 How to find by calculation the chord or opening AB, 
 the height DP, the chord AD of half the arc, the radius 
 AC, and the arc ADB. 
 
 By a well-known property of 
 the right-angle triangle, namely, 
 that the square of the longest 
 side is equal to the squares of 
 the two shorter added together, 
 provided any two sides in the 
 triangles ADP and APC are known, the rest can always 
 be found. 
 
 (13) Thus, if given the radius and chord AB or its 
 half AP. Then VAC 2 -AP 2 =CP and CD-CP=DP ; and 
 VAP 2 +PD 2 =AD. 
 
 (14) Again when the radius and height PD are given, 
 then CD— DP=CP; and VCA 2 -CP 2 =AP. 
 
 (15) And when AP and PD are given, then as 
 
 PA 3 PA 3 
 
 DP : PA: :PA : CD+CP^p^ and 2CD=pp +PD, and 
 
 PA 3 
 
 pyr-+PD =Eadius. 
 
 (16) And when AD and AB are given then ADB 
 8AD-AB 
 
TO ESTIMATE ON CARPETS 103 
 
 THE ELLIPSE 
 
 To find the circumference of an ellipse. 
 
 (17) Rule. Multiply half the sum of the two diameters 
 by 3,1416 and the product is the circumference nearly. 
 
 TO FIND THE AREA OF AN ELLIPSE 
 
 (18) Rule. Multiply the product of the two semi-axes 
 by 3,1416 or multiply the product of the two diameters 
 by .7854. 
 
 To show the usefulness of the above rules as apper- 
 taining to the carpet business we will take the following 
 examples. 
 
 Ex. 1. How many feet of border are required to go 
 around a circular room, radius of which is 5 feet? 
 
 C=2*B,=2X3.1416X5=31' 5", or 10i yards nearly. 
 
 Ex. 2. How much will a circular rubber mat cost at 50c. 
 
 a square foot, diameter being 5 feet ? 
 
 *D 2 3.1416X25 10fi , , , xdr^oo 
 
 A = — : — = j =19.64 square feet and cost $9.82. 
 
 4 4 
 
 Ex. 3. The opening of a swell or circular window is 8 
 
 feet and the depth is 2 feet 6 inches. Find the radius. 
 
 — = — =4' 51" nearly. 
 
 2 2 
 
 Ex. 4. How many yards of border are required to go 
 
 around a circular window, Fig. 7, opening AB 16' 0" 
 
 and depth DP=4' 1". We first find the chord AD= 
 
 a/AP 2 +PDW64+16.8=9.0. (13). Then ADB= 
 
 8AD-AB 8X9-16 56 10 , , />1 , . ,.„ 
 s = ^ =-« =18 8 or 61 yards nearly. (16) 
 
104 CARPET-MEN'S MANUAL 
 
 Ex. 5. How many yards of border are required to go 
 around an elliptical-shaped room whose diameters are 
 24' 9' and 15' 3"? 
 
 Long diameter=24' 9" 3.1416 
 
 Short " =15 3 20 
 
 Sum =40' 0"-*-2 (17) 62.8320-5-3=21 yards nearly. 
 
 Half sum =20' 0" 
 
 Ex. 6. How many square feet in a mat of elliptical 
 shape, diameters being 6 and 4 feet! 
 
 1st method. Half long diameter =3 
 
 Half short " =2 3.1416 
 Product =6 6 
 
 18.8496 sq. ft. 
 
 2d method, or 6X4=24; 24x.7854=18.8496 sq. ft. 
 
 Note. When the diameter is 20 feet 
 or less call it yards, and add one. When 
 the diameter is more than 20 and less 
 than 40 add two yards to the number of 
 feet for yards, which will be near enough 
 in practice. 
 
 A short method of rinding the difference in quantity 
 of carpet of different widths : 
 
 GENERAL RULE 
 
 1. E educe the fractions to the same denomination. 
 
 2. If from the nature of the question, the answer should 
 be more, place the greater of the two fractions on the 
 right hand side of the smaller, but if it appear that the 
 
 Foe a Ciecle. 
 To find yards 
 of border. 
 
 r 
 
TO ESTIMATE ON CARPETS 105 
 
 answer should be less, place the greater fraction to the 
 left of the smaller fraction. 
 
 3. Take the difference between the numerators and 
 place it above the numerator on the left and cancel the 
 denominator. 
 
 Ex. 1. If it requires 12 yards of i carpet to cover a 
 room, how much will it take of J goods 1 
 
 Of course, it will take more carpet to cover the room 
 with the narrower goods if the carpet is sold by linear or 
 running yards; the i fraction will therefore be placed 
 on the right (the smaller fraction always remaining 
 stationary to better remember the rule). J, t- Now 3 from 
 4 (the two numerators) leave 1 ; place the 1 over the 3 and 
 
 cancel or draw a line across the 4 thus J- Answer is then 
 i more carpet of the | width, and as i of 12 is 4, 4 added 
 to 12 (the number of yards of i goods), gives 16, the num- 
 ber of yards required. 
 
 Now let us reverse the question, using the same 
 quantities. 
 
 If it requires 16 yards of f wide carpet to cover a room 
 how many yards will it take of t? This time it will take 
 less carpet, therefore we place the larger or f- on the left 
 
 and proceed as before : f, f . 4—3=1,$. Thus J less is the 
 answer. J of 16 is 4 and 16—4 equals 12 (the number of 
 yards of J goods) as before. Thus it will be seen that 
 in changing from J- to f add | to the given number of 
 yards. Changing from f to i subtract | from the given 
 number of yards. 
 
 If an order is received calling for an estimate on a 
 quantity of carpet made up we will say of | and f goods, 
 
106 CARPET-MEN'S MANUAL 
 
 it may be required to figure the quantity on a basis of so 
 much a square yard. First estimate the cost of f goods 
 required, then the cost of the border. Or, if the price of 
 both are the same, get the cost of the whole carpet at 
 once. Divide this sum by the number of square yards 
 the floor contains and the quotient will be the cost of the 
 carpet that will cover one square yard of floor space. 
 
 Ex. 1. A customer, undecided whether to have a 
 parquette floor laid or use a carpet, wants to know how 
 much more or less it will cost per square yard to cover a 
 room 12' 0"X15' 0", with J carpet at $1.00 per yard and 
 f border at .85 than to have a parquette floor at $1.75 a 
 square yard. 
 
 We find that it takes 15 yards of f goods at $1.00 per 
 yard=$15.00, 18 yards of f goods at 85 cents=$15.30, 
 making the carpet cost $30.30, and as the room contains 
 20 square yards of floor space it is evident that each 
 square yard will cost $30.30-^20, or $1.52, to cover with 
 the carpet ; which makes it 23 cents less per sq. yard than 
 the hardwood floor would cost. 
 
 Oilcloths and Linoleums 
 
 When estimating for oilcloths or linoleums the same 
 rules will govern as when estimating for carpets in gen- 
 eral, with the difference, however, that this kind of floor 
 covering is usually made in patterns which will permit 
 the cloth being cut without regard to top or bottom of 
 figure. When the goods are made only in certain widths 
 considerable waste will sometimes occur because the 
 width of the cloth may be much more than the width of 
 the room, and as seams lessen the wearing quality they 
 
TO ESTIMATE ON CARPETS 107 
 
 should be avoided as much as possible. As, however, the 
 customer may want to economize for the time being, and 
 only buy enough to cover the room regardless of seams, 
 it is very important that the salesman when writing out 
 the order should state what width of goods are kept in 
 stock, also to emphasize, when quoting the price, that it is 
 for the square yard, in order that there may be no mis- 
 understanding in the customer's mind. Unless the meas- 
 urer knows the width of the goods, he can neither esti- 
 mate accurately, nor answer the customer intelligently, 
 when suggestions as to cutting and piecing are requested. 
 As most linoleums and oilcloths have geometrical designs 
 it is often possible to economize by cutting the cloth 
 enough longer than the room to utilize the waste in filling 
 out the width and piece in jogs. If estimated this way a 
 full memorandum of instructions should be made on the 
 plan for the guidance of the cutter. 
 
PART IX 
 HINTS ON MATCHING AND CUTTING CAEPETS 
 
 It is not intended to treat at length the subject of 
 carpet cutting. Nor is it necessary, owing to the fact 
 that whereas the inexperienced measurer when doing his 
 work is left to his own resources, the new cutter, after ob- 
 serving others, will always have available advice, and the 
 foreman of the workroom who has full responsibility 
 naturally expects to be consulted in all cases demanding 
 special attention. As, however, questions may arise 
 where a general knowledge of cutting and matching 
 carpets would be required, a few hints on the subject will 
 be given, and the inexperienced measurer should seize 
 every opportunity to study the work done in the cutting 
 room. 
 
 The cutter on receiving the plan should first carefully 
 scrutinize it to make sure that all necessary measures are 
 given, and when in doubt as to the correctness of the plan 
 have the measures verified before proceeding further. 
 Having received what appears to be a correct plan, the 
 next step is to determine in which direction to run the 
 breadths, with particular reference to figure, shading, 
 and effect of sweeping on pile of fabric. Sometimes 
 this question is decided by the customer, and, if so, the 
 measurer has marked the plan accordingly with an arrow. 
 
 108 
 
MATCHING AND CUTTING CARPETS 109 
 
 Otherwise it is left to the cutter's judgment. There are 
 no set rules governing this point, consequently there exists 
 among cutters some diversity of opinion as to the proper 
 way of running the breadths and pointing the figures. 
 Ninety-nine out of every hundred carpets which have 
 come under the observation of the writer, and which have 
 been cut by many different men, have given satisfaction 
 by having the breadths and figures run as follows : 
 
 IN HALLS 
 
 Main halls if covered separately should have the 
 breadths and figures run from the entrance. All halls 
 above the first should have the breadths run the long way, 
 top of figure pointing to the front, or toward the second 
 stair if both are alike, or bottom of figure towards the 
 first stair, as the case may be. A stair having one width 
 only and showing an uncovered margin on each side, or 
 if covered with an uncut pile carpet such as Brussels, 
 Tapestry, etc., should have the figure point up always, 
 unless the parlor, hall, and stair be alike, and the stair so 
 situated as to spoil the effect on account of the figures 
 running in an opposite direction, in which case the figure 
 should run the same way as the parlor carpet. On a stair 
 covered entire with a cut pile carpet, such as a Wilton, 
 Axminster, etc., the carpet should be cut with the pile or 
 nap running downwards regardless of the figure, and in 
 this case if the main hall and stair are alike, with the 
 breadths running in one direction and stair carpet show- 
 ing from the front entrance, run hall carpet with figure 
 pointing same as the figure on the stair. 
 
110 CAEPET-MEN'S MANUAL 
 
 FRONT ROOM 
 
 If the difference in length and width is slight run 
 breadths to the front; if the difference is considerable, 
 run breadths the long way, in any case, with the nap 
 pointing towards the strongest light. 
 
 In front alcove rooms, the length of the room is deter- 
 mined regardless of the alcove, but of course the breadths 
 in the alcove are run the same as in the room of which it 
 is a part. 
 
 Back parlor and hall if connected with the parlor by 
 large swinging or sliding doors and carpeted with the 
 same pattern as the parlor, run breadths and design with 
 the parlor carpet. In rooms adjoining parlor and con- 
 nected with parlor by narrow doorways having sills, 
 run breadths the same as in the parlor, but if the dif- 
 ference in length and width is considerable run it the 
 long way of the room. When pile carpets are used, un- 
 less the difference in length and width of the room is very 
 great, run breadths with pile towards the strongest light. 
 
 In rear rooms run breadths the long way with figures 
 pointing towards the window if possible. 
 
 Having settled the above, we will now ascertain how 
 many widths are required, on which side to have the 
 selvage, and where short breadths or waste can be utilized. 
 We will start by measuring the width of the goods, be- 
 cause frequently the goods may run under or over 27 
 inches and if many breadths are required J of an inch 
 would in the former case make the carpet fall short, and 
 in the latter make the carpet cover a space which a 
 regular 27-inch carpet might or might not cover. 
 
MATCHING AND CUTTING CAEPETS 111 
 
 The selvage side can be easily determined if we remem- 
 ber never to place cross- joins or piecings where they will 
 be conspicuous, as in doorways or at the head or bottom 
 of stairs. A stair which is to be covered entire requiring 
 a part of a breadth, should have the piecing done on the 
 wall side, and in rooms or halls, if any let-ins occur along 
 the selvage side, like door or window recesses, run the 
 selvage across, and cover with waste or short breadths, 
 being particular, however, to have the pieces match. 
 
 We will next consider how to run it if the carpet has a 
 border. There is perhaps no question of more impor- 
 tance to the carpet measurer, and as it is to the interest of 
 all concerned that this matter should be settled at the 
 house to the customer's satisfaction, by answering the 
 following questions we can come to conclusions that 
 should govern us in giving our opinions. 
 
 1. Why is the border made? 
 
 To give a finish to the carpet and by contrast bring out 
 the harmony of design. 
 
 2. Will the carpet look as well without the border as 
 with it? 
 
 In general no, sometimes yes; if by fitting the border 
 around the room it has to be cut so as to mar the beauty of 
 the pattern or if the space is so small that the border will 
 predominate and give it a crowded and patched appear- 
 ance, the carpet would look better perhaps without the 
 border, although according to the answer of our first 
 question it would certainly look better with it at least in 
 the majority of rooms. 
 
 Does it take more yards by using the border? Yes, as 
 the carpet and border alike are sold by the running yard, 
 
112 CARPET-MEN'S MANUAL 
 
 and as most borders are narrower than the body, it fol- 
 lows that to cover a given space, more yards are needed 
 with a border than without, the difference varying ac- 
 cording to the size and shape of the room, width of border 
 and length of pattern; the average difference when a f 
 border is used is about five yards; this ought not to be 
 considered, however, if by using the border we add to the 
 decorative value of the carpet, for, after all, the principal 
 function of a floor covering is to give an air of comfort 
 and refinement to a room. 
 
 Would it spoil the carpet for use in another room by 
 having a border 1 
 
 If a carpet is made to fit a room exactly the chances are 
 very small of its fitting any other room without first 
 being made over. Carpets as a rule are not put down to- 
 day to be taken up to-morrow, and if the customer owns 
 the house, the carpet may remain down for years, hence 
 its appearance in that room should have first considera- 
 tion. It is not necessary, however, to have the border fol- 
 low the outline of the room in order to make the carpet 
 look well, as it will look better frequently to have the 
 border cut square. Indeed, the opportunity of making 
 use of a square carpet with a border in another room is 
 better than if the carpet had no border, as a filling which 
 is always procurable can be used as a surround for the 
 carpet, which is centered as a rug. A plain filling to 
 match shade of carpet can always be procured, whereas 
 often it is extremely difficult if not impossible to match 
 the carpet with body or border of the same pattern. 
 This is of special importance to persons living in flats or 
 apartments and liable to move at any time. 
 
MATCHING AND CUTTING CABPETS 113 
 
 From the above we may deduce the following rules: 
 Show as much border as possible, but show body in pro- 
 portion. Have border follow outlines of the room with 
 as few miters as possible, recesses of less dimensions 
 than the width of the border to be covered with the body 
 carpet, or filling. Never stop a border unless it can be 
 done and made to look finished. 
 
 We will next ascertain how much longer than the 
 room the carpet will have to be cut in order to match. 
 This is essential before cutting into the goods because 
 the number of yards on ticket or stock book may seem 
 sufficient, but owing to waste in matching the quantity 
 may fall short of what is required to cover the space. 
 
 Starting from any prominent part of the pattern meas- 
 ure off the length of the room as shown on plan. The 
 first repetition of this part of the figure beyond this 
 length will be the cutting point, the difference represent- 
 ing the waste on that breadth. If, however, it should be 
 difficult to detect the cutting point by studying a single 
 breadth mark off the length of the room from the end of 
 the breadth, then bring the end of the carpet up to this 
 mark in such a way that the figures on both breadths will 
 run in the same direction, move the end up until the 
 figures match, or to a point where the figures come op- 
 posite. If it should waste too much on the left side try 
 the right. 
 
 Sometimes the pattern is such that in order to match it 
 more than one roll is required, but these designs are rare. 
 
 "We can determine the cutting point by adding the 
 length of the pattern a sufficient number of times to make 
 the same equal or just exceed the length of the room, or, 
 
114 CABPET-MEN'S MANUAL 
 
 in drop patterns, if the length of the figure is multiplied 
 by a whole number, the product will show where the car- 
 pet cuts to a u set," as it is called, and multiplying by 
 a fraction will show where it cuts to a match. Thus a 
 24-inch figure cuts to a set at 6, 8, 10 ft., etc., because 
 3X2=6, 4X2=8, 5X2=10, and so on. For the same rea- 
 son it would cut to a match at 7, 9, and 11 ft. because 
 3JX2=7; 4iX2=9, 5^X2=11. 
 
 Having ascertained that there are sufficient goods 
 strike out the plan, if the carpet is to be a border, or if the 
 room is irregular. If several adjoining rooms are to be 
 covered lay them out on the floor according to the plans, 
 and arrange the breadths so that the figures in the several 
 carpets will line with each other, and cut border so that 
 if it has a conspicuous figure, it will be centered at the 
 wall or window as the case may be. Match all miters as 
 well as possible and those that can't be matched place in 
 some obscure corner. If a border should come within a 
 few inches of covering the width of the room use filling to 
 match outside the border, if more than a few inches, it is 
 safer to cut the carpet to fit (unless ordered otherwise 
 by the customer) and use waste in doorways and window 
 recesses if any. 
 
 Wiltons and velvets are cut down flat and are sewed 
 together raw edge. Brussels and Tapestry borders are 
 cut with an allowance of one inch, to be turned back on 
 each side when sewed, unless made into rugs, when they 
 also should be cut down flat. All carpets thus cut should 
 have the seams covered with binding on the underside. 
 
 Axminster and Moquettes should be cut with an al- 
 lowance of 1| inch, to be picked and turned under. And 
 
MATCHING AND CUTTING CARPETS 115 
 
 as a matter of fact, to make a first-class job, all carpets 
 surrounded by a border should have the surplus cut off 
 and the raw edge hemmed or overcast. Moquettes and 
 Axminsters should be plucked and hemmed to make a 
 good seam and prevent raveling. Some cutters turn 
 under this surplus on Brussels and Tapestries, but as the 
 carpet rarely can be made any larger owing to the length 
 of the border the only result of such turning under of 
 waste is to furnish a refuge for moths. Turning under 
 is also liable to show a ridge on the surface of the carpet 
 when laid, and, the under part if used afterwards will 
 contrast with the faded parts. 
 
 Cutting ivith a " drop " occurs when the pattern is 
 such that to make a match and save waste the figure is 
 dropped down one-half its length. To illustrate, suppose 
 six breadths are required to make the carpet. After the 
 cutting point is located cut three breadths through this 
 figure, draw down the fourth breadth until it matches 
 with the third. Cut off the (t drop " or part extending 
 beyond the third. Roll out this fourth breadth and cut 
 it the same length as the three first, cut the remaining 
 two, through the same figure and the same length as the 
 fourth. Now, place the fifth breadth between the second 
 and third, and the first in the place left by the fifth, and 
 the carpet is matched. If the carpet requires an odd 
 number of say five breadths, cut the first two to a set, drop 
 down the third, cut off the waste, make the fourth and 
 fifth breadth the same length and cut through the same 
 figure as the third; now let the first and fourth breadths 
 change places, and the whole carpet will match. Try the 
 inside end of the roll before cutting off the " drop," as it 
 
116 CARPET-MEN'S MANUAL 
 
 may save this waste. And when an odd number of 
 breadths are used cut the lesser number first, as that may 
 permit a saving on the last breadth. 
 
 All carpets after being sewed should have the seams 
 thoroughly pressed on the back; if any fullness appears 
 it may be taken out by the application of a wet cloth and 
 hot iron. The carpet should now be inspected by the 
 cutter, who will thus make sure that filling or piecings 
 are properly placed, and that the carpet is otherwise all 
 right before it leaves the store. 
 
 Carpets made in rug shape should be stretched face 
 down on the cutting floor and tacked to chalk lines pre- 
 viously laid out to represent the desired size of the rug. 
 It is then ready for the shrinking and sizing process, 
 which consists of sprinkling the carpet with a solution 
 of water and sizing, vigorously rubbing it with a broom, 
 after which it is left to dry. Be careful not to sprinkle 
 too much, as it may saturate and soil the surface. Care 
 should also be taken not to wet the end borders too much, 
 which would cause the corners to be drawn out of square 
 for the reason that the border will not shrink as much 
 in the width as it will in the length. All carpets similarly 
 treated should be shipped rolled around a pole face out. 
 
PART X 
 FLOOR COVERINGS 
 
 The following article is written for the benefit of those 
 not familiar with the different varieties of carpets at 
 present in the American market. For a complete treatise 
 on this subject the reader is referred to the " History and 
 Manufacture of Carpets," issued by the Review Publish- 
 ing Company, New York City. 
 
 The principal varieties of carpets sold and named in 
 order according to their grade are as follows : 
 
 Oriental Carpets. 
 
 Savonneries and Aubusson. 
 
 Hand-made and Chenille Axminsters. 
 
 Wiltons and Body Brussels. 
 
 Machine-made Axminsters and Moquettes. 
 
 Velvets and Tapestries. 
 
 Woollens (as all Ingrain carpets are called by the 
 trade) and Venetians. 
 
 The Oriental Carpets and Rugs may be divided into 
 three general classes — Turkish, Persian, and Indian. 
 These again are subdivided into different varieties, each 
 generally taking its name from the province or district 
 where made. Thus among the makes or weaves classed 
 as Turkish are: Ghiordez, Demerdji, Gulistan, Oushak, 
 Karabajh, Kazak, Kurdistan, Bergamo, Mossuls, Der- 
 
 117 
 
118 CARPET-MEN'S MANUAL 
 
 bends, Daghestans, Shirvans, and Anatolians. Bokharas, 
 Khivas, Guendjes, Samarkand, and Soumak, the last 
 five being Turkoman weaves. Among the best known 
 Persians are the Ferajhan, Sultanabad, Muskabad, 
 Gorovan, Tabriz, Kermanshah, Saruk, Meshed, Bijar, 
 Serebend, Sheraz, Senna, Khorassan and Herez, the last 
 five being made in small sizes. And among the Indian 
 rugs are such names as Mirzapore, Masulipitan, Amritzar, 
 Lahore, Hydarabad, and Pushmina. As the makes are so 
 numerous it requires a great amount of study and hand- 
 ling of these goods to get thoroughly acquainted with the 
 different qualities and makes. They are all made in one 
 piece, usually with a linen or hemp warp and filling, and 
 a pile consisting of tufts of colored wool knotted around 
 the warp by the weaver's fingers. 
 
 Savonnerie is a French carpet woven in one piece on a 
 high warp tapestry loom, the warp being of wool and the 
 weft of worsted threads, which are fastened by a double 
 knot on two threads of the warp. 
 
 Aubusson is also a French carpet made on a tapestry 
 handloom. The warp is cotton and the weft consists of 
 woolen yarns of the colors called for by the design. The 
 weft yarns are inserted in the warp by hand, the weaver 
 using a small bobbin in doing so. 
 
 Hand-made Axminsters have a warp of linen threads 
 with a pile of woolen tufts tied in by hand in Oriental 
 fashion. 
 
 The Chenille Axminster has a thick groundwork upon 
 which the woolen pile, previously formed into threads 
 resembling chenille, is woven to and fro across the ground- 
 work, and fastened upon it by threads of warp ; it has a 
 
FLOOR COVERINGS 119 
 
 cut or velvet pile. They are like the above mentioned 
 carpets, very elegant and quite expensive. 
 
 The Wilton, next in grade, is probably the most endur- 
 ing of all machine-made carpets. These are woven with 
 a thick, firm worsted pile upon, or rather, intermingling 
 with, a linen back. The worsted is entirely in the warp 
 and is woven over wires running across the breadths, 
 forming the pile in rows of loops ; as the wires, which have 
 a sharp, knife-like edge, are withdrawn the loops are cut, 
 leaving a velvet surface. Each color is represented by 
 threads of warp running the entire length of the web and 
 as they cease to be required on the surface they are 
 dropped and carried along in the warp, showing the 
 worsted on the back until again needed by the design on 
 the surface. The warp threads are wound on reels ar- 
 ranged on horizontal frames placed one above the other 
 back of the loom, each reel supplies one thread, and each 
 frame 260, this being the number in a 27-inch carpet. 
 The number of frames rarely exceeds five, never more 
 than six, the quality of carpet depending on the number 
 of frames employed and is determined by the number 
 of colors showing in a straight line lengthwise in the 
 carpet. Thus three-, four-, and five-frame Wilton and 
 Brussels. 
 
 The Brussels is woven with the pile in loops and the 
 worsted showing on the back, in the same manner as the 
 Wilton, except that the pile is not quite so thick and close, 
 about fifty per cent, less yarn being used. The loops re- 
 main uncut, the wires having a round instead of a sharp 
 edge. 
 
 Machine-made Axminsters and Moquettes have a cotton 
 
120 CABPET-MEN'S MANUAL 
 
 warp, cut worsted pile, and weft of hemp, forming the 
 back, and binder for the tufts. 
 
 The yarn composing the pile is wound on spools and 
 carried to the warp by an endless chain. The threads are 
 then grasped by a series of nippers drawn out and around 
 the binding or tufting thread, after which the heddles are 
 operated and the threads cut by two steel blades, thus 
 forming the tufts. 
 
 These carpets are known by different names, as Savon- 
 nerie, Saxony, etc. The method of manufacture being 
 essentially the same, differing in the number of tufts to 
 the inch, the Savonnerie having the tuft threads woven 
 side by side, whereas in the Saxony the tuft or binding 
 threads are separated by a filler of hemp. 
 
 The Velvet or Wilton Velvet have a very similar pile 
 to the Wilton, though there is usually a greater variety of 
 colors and a freer handling of design and shading. This 
 is because of the different manner of construction. The 
 pattern being first printed on the yarn warp, thread by 
 thread, then woven on a backing of hemp or jute yarn, a 
 cotton chain and a linen or cotton weft, which serves as a 
 binder for the loops. The velvet surface is obtained by 
 weaving the worsted warp over wires which when with- 
 drawn cut the loops as in the weaving of Wiltons. The 
 worsted does not show at all on the back, and thus it can 
 easily be distinguished from the Wilton, though to the 
 initiated a glance at the surface is sufficient for this 
 purpose. 
 
 Tapestry or Tapestry Brussels are made the same as 
 Velvets excepting that the loops are left uncut as in Brus- 
 sels carpets. It is distinguished from Brussels by the 
 
FLOOR COVERINGS 121 
 
 greater variety of colors in the design and by not show- 
 ing any worsted on the back. These carpets are graded 
 according to the number of warp threads in the width of 
 the fabric, this number varying in 27-inch goods from 
 about 180 in the low grade to 216 in the 10-wire carpets, 
 thus 10-, 9-, 8-wire Tapestry and Velvets. These car- 
 pets are also made by weaving the worsted warp undyed 
 or in a uniform basic color, after which the pile, cut or 
 uncut, is submitted to a color-printing machine, where 
 rollers, one for each color, and engraved according to pat- 
 tern, impress the desired design. 
 
 The Woolens comprise all the Ingrains carpets, such as 
 the three-plies, two-plies, and all the plain and unfigured 
 carpets. The three-plies are made of three separate 
 layers or thicknesses ingrained together. The two-piles 
 used to be called by various names, as Ingrains, Kidder- 
 minsters, Extra Superfines, etc., all meaning the same 
 thing, are composed of two layers or plies, and are usually 
 woven harder and more thoroughly ingrained than the 
 three-plies. The more general this ingraining or mixing 
 up of the plies, the more durable the fabric will be ; thus a 
 design showing large masses of unmingled color will not 
 wear as well as though thoroughly ingrained or inter- 
 woven with the plies beneath it. Both sides of these 
 carpets are equally serviceable, only the colors are 
 reversed. 
 
 The plain or unfigured woolens, usually called fillings, 
 are mostly used for groundwork on which to spread rugs, 
 or as a surround or filling on a floor partly covered by a 
 rug or carpet. 
 
 Venetian carpets are made with a worsted or cotton 
 
122 CARPET-MEN'S MANUAL 
 
 warp and jute filling. The warp is colored and makes the 
 figure effect. These carpets are used mostly for stairs 
 and halls. 
 
 Other floor coverings are the Mattings of China and 
 Japan, American-made Matting, known as Prairie or 
 Crex Matting. The Cocoa or Coir Matting, Oilcloths, 
 and Linoleums. 
 
 In the China Matting the warp is hemp, the weft of 
 straw, is generally woven in check patterns. 
 
 The warp of the Japanese Matting is of cotton, the 
 straw used for the weft finer, and the design more elab- 
 orate than in the Chinese Matting. 
 
 The Prairie Matting consists of a coarse grass weft and 
 a cotton warp ; this matting is made in different widths, 
 and in striped or plain designs. 
 
 Cocoa or Coir Mattings are made entire from the fiber 
 or husk of the cocoanut. These mattings are manufac- 
 tured by the natives in the countries where the cocoanut 
 palm grows; in America from imported fiber. These 
 goods also come in different widths. 
 
 Oilcloths consist of a burlap foundation heavily treated 
 to a sizing of liquid glue, rye flour, tapioca, or varnish. 
 One side is then covered with a mixture composed of 
 ocher, linseed oil, and benzine, the quality of cloth de- 
 pending on the number of coats thus received. When 
 dry it is rubbed smooth and submitted to a machine which 
 prints the pattern. 
 
 Linoleums are similar to oilcloths, though not so glossy, 
 but softer and less noisy to walk over. They are made 
 from a mixture of boiled linseed oil, cauri gum, resin, and 
 ground cork, rolled on a jute burlap foundation. The 
 
FLOOR COVERINGS 123 
 
 method of printing the pattern is almost similar to the 
 process employed in printing oilcloths. 
 
 In the making of Inlaid Linoleums the different parts 
 of the pattern are formed and colored separately; they 
 are then arranged according to design on a burlap back- 
 ing and a pressure applied until the coating and burlap 
 are thoroughly united, thus the pattern goes clear through 
 to the backing. 
 
 Interlock is another species of floor covering; it is com- 
 posed of rubber blocks and derives its name from the 
 manner these blocks are joined together. Each block 
 representing the whole or part of a pattern is dovetailed 
 or locked together when laid. It is about i inch in thick- 
 ness, very expensive but almost indestructible. 
 
PART XI 
 SUGGESTIONS TO THE LAYER 
 
 On the carpet layer depends to a certain degree the 
 successful termination of the measurer's and cutter's 
 skill. 
 
 To him is entrusted the completion of the work, and the 
 possibility of having an otherwise perfect job spoiled, by 
 a careless or incompetent layer, is sufficient reason for the 
 following few remarks. 
 
 Before attempting to lay the carpet, the room should be 
 cleared as far as possible of all movable furniture, after 
 which a careful inspection should be made of the floor to 
 make sure no loose tacks or other small objects remain, 
 which would cause unevenness on the surface after the 
 carpet is laid. 
 
 The entire carpet should now be spread on the floor, and 
 the correct position of filling or piecings for recesses or 
 jogs (if any) verified. Should there be any error caused 
 by the measurer, cutter, or otherwise, which can be easily 
 remedied by the layer, he should quietly rectify the same 
 before proceeding further. 
 
 The carpet being all right the lining is now spread in the 
 following manner : Turn back a part of the carpet as far 
 as possible, first, at the two corners (taking one at a 
 time), then at the middle, thus exposing a part of the floor 
 
 124 
 
SUGGESTIONS TO THE LAYER 125 
 
 upon which to spread as many strips of lining as the space 
 will allow. Carefully return the carpet to its first position 
 and repeat the operation on the other side or end of the 
 room. By handling the carpet as described above, the 
 chance of disturbing or wrinkling the lining, which would 
 result if the whole carpet was dragged over it, is thus 
 avoided. 
 
 If the carpet is plain, i. e., without a border, it should if 
 possible be laid from the front and entrance side of the 
 room, for the reason that these parts are usually the most 
 conspicuous and less liable to be covered with furniture. 
 It is therefore desirable to have the figures line up 
 straight at these parts of the room; this result would be 
 hard to obtain in some carpets if the start was made at the 
 rear and the carpet stretched towards the front. Be 
 careful, when turning under the carpet, to follow the 
 same figure or line of pile. 
 
 Of course, if all the recesses are at the rear wall, the 
 carpet considerably longer than the room, and the cus- 
 tomer desire the waste left on, it will save time, and cut- 
 ting into the carpet, by starting to lay at the rear, and 
 have the turn-under at the front. If good workmanship is 
 paramount, however, the surplus should be cut off and 
 only a few inches allowed for a turn-under. Bordered 
 carpets in rooms with bay or swell windows should in- 
 variably have the bay or swell laid first, for if the carpet 
 is cut tight it will be found extremely difficult to put 
 these parts in after the rest of the carpet has been 
 stretched. 
 
 Stair runners should be laid from the bottom by driving 
 a tack at each selvage as the work progresses, until the top 
 
126 CABPET-MEN'S MANUAL 
 
 is reached. Now straighten by line of pile and tack the 
 upper end securely, then work down by driving tacks 
 between the selvages on the tread at bottom of riser ; this 
 will thoroughly stretch the carpet, besides being the most 
 expeditious way. If it is a winding stair, the wind or 
 elbow part will have to be treated separately. 
 
 Oilcloth and linoleum should be cut larger than the 
 space for which it is intended ; it should be spread and cut 
 to fit in the space itself, as you cannot accomplish this 
 with success by measurement. It should be spread so as 
 to lie perfectly smooth, naturally, as it cannot be forced. 
 
 To obtain the best results these goods should be spread 
 on the floor of the cutting room for a few days after being 
 cut, and at the time of laying it should be trimmed so as to 
 leave $ of an inch margin all around ; this gives the goods 
 the necessary chance to expand. Use no tacks on oil- 
 cloths at time of laying or at any other time, unless it 
 becomes necessary to tack the seam. 
 
 Sometimes the ends are inclined to roll at the base- 
 board or in front of doors, this may be prevented by driv- 
 ing small tacks temporarily into the base or sill, or by 
 tacking a narrow strip of oilcloth on the edge of the sill ; 
 this will allow the cloth to work under as it expands. The 
 seams of linoleums may be cemented or bradded when 
 laid, otherwise treat same as oilcloth. 
 
 To lay mattings properly is more difficult than is 
 generally supposed. In irregular spaces, tower or bay 
 windows, straight seams can only be had by free use of 
 the chalk line. 
 
 Mattings are mostly laid with the knee-stretcher, except 
 in long spaces, or where the center is full ; in such cases 
 
SUGGESTIONS TO THE LAYER 127 
 
 the vise can be used to better advantage, as by this tool 
 the strain can be made gradual, whereas the jerk pro- 
 duced by the knee-stretcher would in many cases break 
 the warp. 
 
 If the matting is to be laid over lining, it will be ad- 
 vantageous to spread the lining the opposite way of the 
 matting ; where this is not convenient, it should be laid by 
 starting with a half width of lining, so that the seams of 
 the lining and matting will not come over each other, as 
 this will sometimes cause trouble, being too bulky for the 
 double-pointed tacks. 
 
 As only few rooms require just even widths, it becomes 
 necessary to split a width to fit; this can be accurately 
 done, no matter how irregular the baseboard is, by turn- 
 ing this breadth face down, pushing the selvage up against 
 the baseboard, and using the selvage of the last breadth 
 laid, as a straight edge ; this can easily be followed with 
 the shears, and with a little practice the required and 
 exact fitting width is thus produced; in turning the cut 
 piece face up the raw edge will come next the baseboard 
 and should be finished by tacking a narrow binding on, to 
 prevent fraying when sweeping. 
 
 China matting can be joined by pulling out the fiber 
 until the ends of the warp are about two inches long, then 
 turn the warp ends under and drive a double-pointed tack 
 over each ; place the other end similarly prepared close to 
 the first and tack in the same manner. This makes a 
 neat and substantial join. 
 
 Fine matting should be tacked the same way without 
 pulling out the fiber. On a slanting or circular base 
 where matting cannot be turned under, double-pointed 
 
128 CARPET-MEN'S MANUAL 
 
 tacks should always be driven on the warp, as these are 
 much more effective in holding the strain than ordinary 
 tacks. After the carpet is laid remove all scraps or pieces 
 of carpet and lining, be careful not to leave any loose tacks 
 scattered around the carpet, window sills, or furniture. 
 If the parties concerned are present they should be 
 asked to inspect the work and see if everything is satis- 
 factory. If any fault is found as to quality, shading, 
 waste, etc., over which the carpet layer has no control, 
 he should politely inform the customer that the store is 
 the proper place to make all complaints. The layer by 
 being pleasant and accommodating will frequently cause 
 the customer to overlook minor faults. 
 
 Note. When handling oilcloths and linoleums great 
 care should be taken not to break the surface, especially 
 in cold weather when the cloth is chilled, as it is then very 
 brittle. It should therefore be left in a warm room, away 
 from registers and stoves, a few days before being laid. 
 A printed notice containing this warning should be pasted 
 on the outside of each roll. 
 
PART XII 
 
 TO MEASURE FOR SHADES, DRAPERIES, AND 
 
 AWNINGS 
 
 This work, although belonging to a different part of the 
 house-furnishing business, may be considered as coming 
 within the field of the carpet measurer. Inasmuch as he 
 is frequently called on to take such measures, consider- 
 able expense can be saved both dealer and customer by 
 having one man measure for the carpets, shades, awn- 
 ings, and draperies; and where no special work of the 
 draper's art or awning man's skill is required, such meas- 
 ures, if taken accurately and according to the following 
 rules, will be sufficient for all purposes. 
 
 Shades are either placed on the casing, on the stop- 
 bead, or in the run of the window over the pulley. This 
 last place is recommended, as shades so placed will not 
 interfere with the hanging of draperies, and serve their 
 purpose equally well. If double shades are required 
 they can be placed one over the other in double brackets, 
 unless, as is sometimes the case, the window frames are 
 set in beyond the outside casing, in which case the second 
 shade can be hung between the jambs. If window 
 screens are so placed as to interfere with the workings 
 of an inside shade, the brackets must be placed either 
 on the casing or on the stop-bead, but no fixed rule can be 
 given and in the absence of specific instructions from the 
 customer the measurer will have to use his own discre- 
 
 129 
 
130 CARPET-MEN'S MANUAL 
 
 tion. To measure for shades use either tapeline or rule. 
 If tape is correct, which can easily be ascertained by 
 comparing it with a rule, its use has the advantage of not 
 being limited to one or two places on which to take the 
 measure, as is the case when the rule is used, and the 
 possibility of errors is minimized because no adding of 
 lengths is necessary. Hold the ring of the tape against 
 the stile of the window with the thumb of one hand, carry 
 the tape to the opposite between the thumb and forefinger 
 of the other hand, moving it up and down until the nail 
 of thumb or forefinger just touches the stile. Take very 
 exact measures for inside and stop-bead shades. If the 
 window is wider than the spread of your arms fasten the 
 tape with your awl. 
 
 For length, measure from the top of lower sash to sill, 
 and double your tape, or if the two sashes are of different 
 lengths, measure height of window between casings. 
 Outside shades should be measured so as to place the 
 bracket on a flat surface, and from one to two inches 
 from stop-bead; give the exact length of the shade from 
 bracket to sill, and let cutter make allowance for trim- 
 ming, hem, and extra length. 
 
 To Measure for Laces and Draperies 
 
 Make a floor plan of each room, suite or story, with 
 drawings of doors and windows to be decorated. Well- 
 defined outline sketches are all that is needed. The fol- 
 lowing measures will enable the drapery cutter to pro- 
 duce plans to scale from which almost any drapery can 
 be cut: Width between stop-beads, height of window 
 between casings, width of casing, length of window from 
 
TO MEASURE FOR SHADES 131 
 
 top of casing to sill and floor, projection of casing from 
 wall (return), and height of room. If a bay, give dis- 
 tance of window from corners. If a swell, give distance 
 between windows, together with such measures as are 
 required for circular or elliptical window (see diagrams). 
 
 To Measure for any Ordinary Curtain, with pole or 
 cornice, in the usual place across top of casing, only three 
 measurements are required, viz. : across the width of cas- 
 ing at top, from top of casing to floor, and projection of 
 casing from wall. (Return.) 
 
 For " French " or " Glass " Curtains, give width 
 between stop-beads and length between casings. For 
 sash curtains, give width between stop-beads and length, 
 three-fourths (J), or the whole of the lower sash. 
 
 To Measuke for Portieres 
 
 If portieres are to be hung outside on the casing, meas- 
 ure width of the whole casing or frame and length from 
 top of casing to floor. If inside, measure width of open- 
 ing between jambs and height of opening from floor. 
 
 To Measure an Archway 
 
 Measure the width where the pole is to be placed, then 
 from crown of arch to floor and from spring of arch to 
 floor. If a pole is to be fitted around the inside, or cor- 
 nice, to go outside, or a frame of any kind to fit the form 
 of arch, take a paper pattern of the space. 
 
 If the opening is too large for a pattern to be taken, 
 and it is not a segment of a circle enabling it to be laid 
 out by finding the radius, proceed as follows : 
 
132 
 
 CABPET-MEN'S MANUAL 
 
 Make a sketch of the opening to be measured, snap a 
 chalk line on the floor across the space and measure the 
 width of it on the floor. Draw marks across chalk line 
 every foot, beginning at the center and working both 
 ways. Fasten the end of your tape to the side of the 
 arch and only at such a distance from the floor that 
 when stretched taut and parallel to the floor the marks 
 on the tape will be directly over the corresponding marks 
 on the chalk line. The further the lines are apart the 
 better. 
 
 Fasten the tape in this position with tack or awl. Now 
 get two straight sticks or rods of such length that the two 
 
 combined will be longer 
 than the distance from 
 the floor to highest part 
 of arch. Place end of 
 rod on center mark on 
 ^ chalk line and hold it up 
 perpendicular so it will 
 traverse the tape at the 
 corresponding mark, hold 
 the second rod on the 
 first, with edges touching 
 the marks even, and move it up in contact with arch. 
 Grasp the two rods firmly and lay them on the tape for 
 length. Proceed in like manner across every foot mark 
 on tape, and record measure on sketch. (See Diag. 48.) 
 In this manner one man can do the work without steps or 
 ladder. The height of any room can be measured in this 
 way if sufficiently long sticks can be obtained. 
 
 
 
 
 
 
 
 T 
 
 
 
 
 
 «T 
 
 
 
 " '» T { 
 
 J\rcK 
 
 Woj 
 
 
 
 
 f f V '» 
 
 ff ?. .? 
 
 ,_/...< 
 
 r * « «• .' 
 
 
 DIAGRAM 48. 
 
TO MEASURE FOR SHADES 133 
 
 AWNINGS 
 
 The usual way of placing awnings is to fasten them on 
 the outside of the frame from one-half to one inch from 
 the opening of the window, and, where there are blinds, 
 so arranged that they can be left on if desired. The 
 custom as to length varies in different sections of the 
 country. In some cities the awnings are made to come 
 so low that the ends of the frame almost touch the win- 
 dow sill, while in other places the rule is to have the ends 
 of the frame fastened 3 inches below the upper half of the 
 window. In the former case the frame is made to slide 
 on rods fastened to the wall, so that when the awning is 
 up, the frame will fit close under the top of the window. 
 In the latter case the ends of the frame are hinged to the 
 window frame at a distance from the top of the window 
 equal to the projection of the frame. 
 
 The rods are also used if the projection of the frame 
 from the wall is greater than one-half the space, as in the 
 case where the awning is to be made as a canopy over a 
 door, and to raise the iron frame would bring its top too 
 high; the rods thus serve as guides for the ends of the 
 frame to slide on, bringing the top of the frame even with 
 the top of the space. Made in that way lines must be 
 attached to the ends of the frame and passed through 
 pulleys above, in order to raise the ends of the frame into 
 place when the awning is in use. 
 
 In either case only three measures are required, viz., 
 the greatest width of the opening, the length from top of 
 opening to where the frame is to rest when the awning is 
 in use, and the whole length of the opening. 
 
 Should the window be arched at the top take a paper 
 
134 CAKPET-MEN'S MANUAL 
 
 pattern, or take measures as in the previous article on 
 how to measure an archway. A door awning projecting 
 over a flight of stairs can be placed quite low down on the 
 door frame, provided it projects far enough to allow a 
 person ascending the steps to enter without interference. 
 
PART XIII 
 
 TABLE OP CUTTING LENGTHS. 
 
 Length of Figure in Inches. 
 
 fee 
 
 12" 
 
 13" 
 
 14" 
 
 15" 
 
 16" 
 
 17" 
 
 18" 
 
 19" 
 
 20" 
 
 21" 
 
 22" 
 
 23" 
 
 24" 
 
 25" 
 
 s... 
 
 9.0 
 
 8.8 
 
 9.4 
 
 8 9 
 
 9.4 
 
 8.6 
 
 9.0 
 
 9.6 
 
 8.4 
 
 8.9 
 
 9.2 
 
 9.7 
 
 8.0 
 
 8.4 
 
 M.. 
 
 9.6 
 
 9.2} 
 
 9.11 
 
 9.4} 
 
 10.0 
 
 9.2} 
 
 9.9 
 
 10.3} 
 
 9.2 
 
 9.7} 
 
 10.1 
 
 10.6} 
 
 9.0 
 
 9.4} 
 
 S... 
 
 10.0 
 
 9.9 
 
 10.6 
 
 10.0 
 
 10.8 
 
 9.11 
 
 10.6 
 
 11.1 
 
 10.0 
 
 10.6 
 
 11.0 
 
 11.6 
 
 10.0 
 
 10.5 
 
 M.. 
 
 10.6 
 
 10.3} 
 
 11.1 
 
 10.7} 
 
 11.4 
 
 10.7} 
 
 11.3 
 
 11.10} 
 
 10.10 
 
 11.4} 
 
 11.11 
 
 12.5} 
 
 11.0 
 
 11.5} 
 
 S .. 
 
 11.0 
 
 10.10 
 
 11.8 
 
 11.3 
 
 12.0 
 
 11.4 
 
 12.0 
 
 12.8 
 
 11.8 
 
 12.3 
 
 12.10 
 
 13.5 
 
 12.0 
 
 12.6 
 
 M.. 
 
 11.6 
 
 11.4} 
 
 12.3 
 
 11.10} 
 
 12.8 
 
 120} 
 
 12.9 
 
 13.5} 
 
 12.6 
 
 13.1} 
 
 13.9 
 
 14.4} 
 
 13.0 
 
 13.6} 
 
 S... 
 
 12.0 
 
 11.11 
 
 12.10 
 
 12.6 
 
 13.4 
 
 12.9 
 
 13.6 
 
 14.3 
 
 13.4 
 
 14.0 
 
 14.8 
 
 15.4 
 
 14.0 
 
 14.7 
 
 M.. 
 
 12.6 
 
 12.5} 
 
 13.5 
 
 131} 
 
 14.0 
 
 13.5} 
 
 14.3 
 
 15.0} 
 
 14.2 
 
 14.10} 
 
 15.7 
 
 16.3} 
 
 15.0 
 
 15.7} 
 
 S... 
 
 13.0 
 
 13.0 
 
 14.0 
 
 13.9 
 
 14.8 
 
 14.2 
 
 15.0 
 
 15.10 
 
 15.0 
 
 15.9 
 
 16.6 
 
 17.3 
 
 16.0 
 
 16.8 
 
 M.. 
 
 13.6 
 
 13.6} 
 
 14.7 
 
 14.4} 
 
 15.4 
 
 14.10} 
 
 15.9 
 
 16.7} 
 
 15.10 
 
 16.7} 
 
 17.5 
 
 18.2} 
 
 17.0 
 
 17.8} 
 
 S... 
 
 14.0 
 
 14.1 
 
 15.2 
 
 150 
 
 16.0 
 
 15.7 
 
 16 6 
 
 17.5 
 
 16.8 
 
 17.6 
 
 18.4 
 
 19.2 
 
 18.0 
 
 18.9 
 
 M.. 
 
 14.6 
 
 14.7} 
 
 15.9 
 
 15.7} 
 
 16.8 
 
 16.3} 
 
 17.3 
 
 18.2} 
 
 17.6 
 
 18.4} 
 
 19.3 
 
 20.1} 
 
 19.0 
 
 19.9} 
 20.10 
 
 S... 
 
 15.0 
 
 15.2 
 
 16.4 
 
 16.3 
 
 17.4 
 
 17.0 
 
 18.0 
 
 19.0 
 
 18.4 
 
 19.3 
 
 20.2 
 
 21.1 
 
 20.0 
 
 M.. 
 
 15.6 
 
 15.8} 
 
 16.11 
 
 16.10} 
 
 18.0 
 
 17.8} 
 
 18.9 
 
 19.9} 
 
 19.2 
 
 20.1} 
 
 21.1 
 
 22.0} 
 
 21.0 
 
 21.10} 
 
 S... 
 
 16.0 
 
 16.3 
 
 17.6 
 
 17.6 
 
 18.8 
 
 18.5 
 
 19.6 
 
 20.7 
 
 20.0 
 
 21.0 
 
 22.0 
 
 23.0 
 
 22.0 
 
 22.11 
 
 M.. 
 
 16.6 
 
 16.9} 
 
 18.1 
 
 18.1} 
 
 19.4 
 
 19.1} 
 
 20.3 
 
 21.4} 
 
 20.10 
 
 21.10} 
 
 22.11 
 
 23.11} 
 
 23.0 
 
 23.11| 
 
 S... 
 
 17.0 
 
 17.4 
 
 18.8 
 
 18.9 
 
 20.0 
 
 19.10 
 
 21.0 
 
 22.2 
 
 21.8 
 
 22.9 
 
 23.10 
 
 24.11 
 
 24.0 
 
 25.0 
 
 M.. 
 
 17.6 
 
 17.10} 
 
 19.3 
 
 19.4} 
 
 20.8 
 
 20.6} 
 
 21.9 
 
 22.11} 
 
 22.6 
 
 23.7} 
 
 24.9 
 
 25.10} 
 
 25.0 
 
 26.0* 
 
 S... 
 
 18.0 
 
 18.5 
 
 19.10 
 
 20.0 
 
 21.4 
 
 21.3 
 
 22.6 
 
 23.9 
 
 23.4 
 
 24.6 
 
 25.8 
 
 26.10 
 
 26.0 
 
 27.1 
 
 M.. 
 
 18.6 
 
 18.11} 
 
 20.5 
 
 20.7} 
 
 22.0 
 
 21.11} 
 
 23.3 
 
 24.6} 
 
 24.2 
 
 25.4} 
 
 26.7 
 
 27.9} 
 
 27.0 
 
 28.1$ 
 
 S... 
 
 19.0 
 
 19.6 
 
 21.0 
 
 21.3 
 
 22.8 
 
 22.8 
 
 24.0 
 
 25.4 
 
 25.0 
 
 26.3 
 
 27.6 
 
 28.9 
 
 28.0 
 
 29.2 
 
 M.. 
 
 19.6 
 
 20.0} 
 
 21.7 
 
 21.10} 
 
 23.4 
 
 23.4} 
 
 24.9 
 
 26.1} 
 
 25.10 
 
 27.1} 
 
 28.5 
 
 29.8} 
 
 29.0 
 
 30.2} 
 
 S... 
 
 20.0 
 
 20.7 
 
 22.2 
 
 22.6 
 
 24.0 
 
 24.1 
 
 25.6 
 
 26.11 
 
 26.8 
 
 28.0 
 
 29.4 
 
 30.8 
 
 30.0 
 
 31.3 
 
 M.. 
 
 20.6 
 
 21.1} 
 
 22.9 
 
 23.1} 
 
 24.8 
 
 24.9} 
 
 26.3 
 
 27.8} 
 
 27.6 
 
 28.10} 
 
 30.3 
 
 31.7} 
 
 31.0 
 
 32.3* 
 
 S... 
 
 21.0 
 
 21.8 
 
 23.4 
 
 23.9 
 
 25.4 
 
 25.6 
 
 27.0 
 
 2S.6 
 
 28.4 
 
 29.9 
 
 31.2 
 
 32.7 
 
 32.0 
 
 33.4 
 
 M.. 
 
 21.6 22.2} 
 
 23.11 
 
 24.4} 
 
 26.0 
 
 26.2} 
 
 27.9 
 
 29.3} 
 
 29.2 
 
 30.7} 
 
 32.1 
 
 33.6} 
 
 33.0 1 34.4A 
 
 135 
 
136 
 
 CARPET-MEN'S MANUAL 
 
 TABLE OP CUTTING LENGTHS. 
 
 Length of Figure in Inches. 
 
 
 26" 
 
 27" 
 
 28" 
 
 29" 
 
 30" 
 
 31" 
 
 32" 
 
 33" 
 
 34" 
 
 35" 
 
 36" 
 
 37" 
 
 38" 
 
 39" 
 
 S... 
 
 8.8 
 
 9.0 
 
 9.4 
 
 9.8 
 
 10.0 
 
 7.9 
 
 8.0 
 
 8.3 
 
 8.6 
 
 8.9 
 
 9.0 
 
 9.3 
 
 9.6 
 
 9.9 
 
 M.. 
 
 9.9 
 
 10.14 
 
 10.6 
 
 10.104 
 
 11.3 
 
 9.04 
 
 9.4 
 
 9.74 
 
 9.11 
 
 10.24 
 
 10.6 
 
 10.94 
 
 11.1 
 
 11.44 
 
 S... 
 
 10.10 
 
 11.3 
 
 11.8 
 
 12.1 
 
 12.6 
 
 10.4 
 
 10.8 
 
 11.0 
 
 11.4 
 
 11.8 
 
 12.0 
 
 12.4 
 
 12.8 
 
 13.0 
 
 M.. 
 
 11.11 
 
 12.44 
 
 12.10 
 
 13.3* 
 
 13.9 
 
 11.74 
 
 12.0 
 
 12.44 
 
 12.9 
 
 13.14 
 
 13.6 
 
 13.104 
 
 14.3 
 
 14.74 
 
 S... 
 
 13.0 
 
 13.6 
 
 14.0 
 
 14.6 
 
 15.0 
 
 12.11 
 
 13.4 
 
 13.9 
 
 14.2 
 
 14.7 
 
 15.0 
 
 15.5 
 
 15.10 
 
 16.3 
 
 M.. 
 
 14.1 
 
 14.74 
 
 15.2 
 
 15.8J 
 
 16.3 
 
 14.24 
 
 14.8 
 
 15.14 
 
 15.7 
 
 16.0* 
 
 16.6 
 
 16.111 
 
 17.5 
 
 17.104 
 
 S... 
 
 15.2 
 
 15.9 
 
 16.4 
 
 16.11 
 
 17.6 
 
 15.6 
 
 16.0 
 
 16.6 
 
 17.0 
 
 17.6" 
 
 18.0 
 
 186 
 
 19.0 
 
 19.6 
 
 M.. 
 
 16.3 
 
 16.104 
 
 17.6 
 
 18.1J 
 
 18.9 
 
 16.94 
 
 17.4 
 
 17.104 
 
 18.5 
 
 18.114 
 
 19.6 
 
 20.04 
 
 20.7 
 
 21.14 
 
 S... 
 
 17.4 
 
 18.0 
 
 18.8 
 
 19.4 
 
 20.0 
 
 18.1 
 
 18.8 
 
 19.3 
 
 19.10 
 
 20.5 
 
 21.0 
 
 21.7 
 
 22.2 
 
 22 9 
 
 M.. 
 
 18.5 
 
 19.14 
 
 19.10 
 
 20.64 
 
 21.3 
 
 19.44 
 
 20.0 
 
 20.74 
 
 21.3 
 
 21.104 
 
 22.6 
 
 23.14 
 
 23.9 
 
 24.44 
 
 S... 
 
 19.6 
 
 20.3 
 
 21.0 
 
 21.9 
 
 22.6 
 
 20.8 
 
 21.4 
 
 22.0 
 
 22.8 
 
 23.4 
 
 24.0 
 
 24.8 
 
 25.4 
 
 26.0 
 
 M.. 
 
 20.7 
 
 21.4J 
 
 222 
 
 22.114 
 
 23.9 
 
 21.114 
 
 22.8 
 
 23.44 
 
 24.1 
 
 24.94 
 
 25.6 
 
 26.24 
 
 26.11 
 
 27.74 
 
 S... 
 
 21.8 
 
 22.6 
 
 23.4 
 
 24.2 
 
 25.0 
 
 23.3 
 
 24.0 
 
 24.9 
 
 25.6 
 
 26.3 
 
 27.0 
 
 27.9 
 
 28.6 
 
 29.3 
 
 M.. 
 
 22.9 
 
 23.74 
 
 24.6 
 
 25.44 
 
 26.3 
 
 24.64 
 
 25.4 
 
 26.14 
 
 26.11 
 
 27.84 
 
 28.6 
 
 29.34 
 
 30.1 
 
 30.104 
 
 S... 
 
 23.10 
 
 249 
 
 25.8 
 
 26.7 
 
 27.6 
 
 25.10 
 
 26.8 
 
 27.6 
 
 28.4 
 
 29.2 
 
 30.0 
 
 30.10 
 
 31.8 
 
 32.6 
 
 M.. 
 
 24.11 
 
 25.104 
 
 26.10 
 
 27.94 
 
 28.9 
 
 27.14 
 
 28.0 
 
 28.104 
 
 29.9 
 
 30.74 
 
 31.6 
 
 32.44 
 
 33.3 
 
 34.14 
 
 S... 
 
 26.0 
 
 27.0 
 
 28.0 
 
 29.0 
 
 30.0 
 
 28.5 
 
 29.4 
 
 30.3 
 
 31.2 
 
 32.1 
 
 33.0 
 
 33.11 
 
 34.10 
 
 35.9 
 
 M.. 
 
 27.1 
 
 28. n 
 
 29.2 
 
 30.24 
 
 31.3 
 
 29.84 
 
 30.8 
 
 31.74 
 
 32.7 
 
 33.64 
 
 34.6 
 
 35.54 
 
 36.5 
 
 37.44 
 
 S... 
 
 28.2 
 
 29.3 
 
 30.4 
 
 31.5 
 
 32.6 
 
 31.0 
 
 32.0 
 
 33.0 
 
 34.0 
 
 35.0 
 
 36.0 
 
 37.0 
 
 38.0 
 
 39.0 
 
 M.. 
 
 29.3 
 
 30.44 
 
 31.6 
 
 32.74 
 
 33.9 
 
 32.34 
 
 33.4 
 
 34.44 
 
 35.5 
 
 36.54 
 
 37.6 
 
 38.64 
 
 39.7 
 
 40.74 
 
 S... 
 
 30.4 
 
 31.6 
 
 32.8 
 
 33.10 
 
 35.0 
 
 33.7 
 
 34.8 
 
 35.9 
 
 36.10 
 
 37.11 
 
 39.0 
 
 40.1 
 
 41.2 
 
 42.3 
 
 M.. 
 
 31.5 
 
 32.74 
 
 33.10 
 
 35.04 
 
 36.3 
 
 34.104 
 
 36.0 
 
 37.14 
 
 38.3 
 
 39.44 
 
 40.6 
 
 41.74 
 
 42.9 
 
 43.104 
 
 S... 
 
 32.6 
 
 33.9 
 
 35.0 
 
 36.3 
 
 37.6 
 
 36.2 
 
 37.4 
 
 38.6 
 
 39.8 
 
 40.10 
 
 42.0 
 
 43.2 
 
 44.4 
 
 45.6 
 
 M.. 
 
 33.7 
 
 34.10* 
 
 36.2 
 
 37.54 
 
 38.9 
 
 37.54 
 
 38.8 
 
 39.104 
 
 41.1 
 
 42.34 
 
 43.6 
 
 44.84 
 
 45.11 
 
 47.14 
 
 S... 
 
 34.8 
 
 36.0 
 
 37.4 
 
 38.8 
 
 40.0 
 
 38.9 
 
 40.0 
 
 41.3 
 
 42.6 
 
 43.9 
 
 45.0 
 
 46.3 
 
 47.6 
 
 48.9 
 
 M.. 
 
 35.9 
 
 37. 1} 
 
 38.6 
 
 39.104 
 
 41.3 
 
 40.04 
 
 41.4 
 
 42.74 
 
 43.11 
 
 45.24 
 
 46.6 
 
 47.94 
 
 49.1 
 
 50.44 
 
TABLE OF CUTTING LENGTHS 
 
 137 
 
 TABLE OP CUTTING LENGTHS. 
 Length of Figure in Inches. 
 
 
 40" 
 
 41" 
 
 42" 
 
 43" 
 
 44" 
 
 45" 
 
 46" 
 
 47" 
 
 48" 
 
 49" 
 
 50" 
 
 51" 
 
 52" 
 
 53" 
 
 s... 
 
 10.0 
 
 10.3 
 
 10.6 
 
 7.2 
 
 7.4 
 
 7.6 
 
 7.8 
 
 7.10 
 
 8.0 
 
 8.2 
 
 8.4 
 
 8.6 
 
 8.8 
 
 8.10 
 
 M.. 
 
 11.8 
 
 11.114 
 
 12.3 
 
 8.114 
 
 9.2 
 
 9.44 
 
 9.7 
 
 9.94 
 
 10.0 
 
 10.24 
 
 10.5 
 
 10.74 
 
 10.10 
 
 11.04 
 
 S... 
 
 13.4 
 
 13.8 
 
 14.0 
 
 10.9 
 
 11.0 
 
 11.3 
 
 11.6 
 
 11.9 
 
 12.0 
 
 12.3 
 
 12.6 
 
 12.9 
 
 13.0 
 
 13.3 
 
 M.. 
 
 15.0 
 
 15.44 
 
 15.9 
 
 12.64 
 
 12.10 
 
 13.14 
 
 13.5 
 
 13. 81 
 
 14.0 
 
 14.34 
 
 14.7 
 
 14.104 
 
 15.2 
 
 15.54 
 
 S .. 
 
 16.8 
 
 17.1 
 
 17.6 
 
 14.4 
 
 14.8 
 
 15.0 
 
 15.4 
 
 15.8" 
 
 16.0 
 
 16.4" 
 
 16.8 
 
 17.0 
 
 17.4 
 
 17.8 
 
 M.. 
 
 18.4 
 
 18.94 
 
 19.3 
 
 16.14 
 
 16.6 
 
 16.104 
 
 17.3 
 
 17.74 
 
 18.0 
 
 18.44 
 
 18.9 
 
 19.H 
 
 19.6 
 
 19.104 
 
 S... 
 
 20.0 
 
 20.6 
 
 21.0 
 
 17.11 
 
 18.4 
 
 18.9 
 
 19.2 
 
 19.7 
 
 20.0 
 
 20.5 
 
 20.10 
 
 21.3 
 
 21.8 
 
 22.1 
 
 M.. 
 
 21.8 
 
 22.2* 
 
 22.9 
 
 19.84 
 
 20.2 
 
 20.74 
 
 21.1 
 
 21.64 
 
 22.0 
 
 22.54 
 
 22.11 
 
 23.44 
 
 23.10 
 
 24.34 
 
 S... 
 
 23.4 
 
 23.11 
 
 24.6 
 
 21.6 
 
 22.0 
 
 22.6 
 
 23.0 
 
 23.6 
 
 24.0 
 
 24.6 
 
 25.0 
 
 25.6 
 
 26.0 
 
 266 
 
 M.. 
 
 25.0 
 
 25.?4 
 
 26.3 
 
 23.3} 
 
 23.10 
 
 24.44 
 
 24.11 
 
 25.54 
 
 26.0 
 
 26.61 
 
 27.1 
 
 27.74 
 
 28.2 
 
 28.84 
 
 S... 
 
 26.8 
 
 27.4 
 
 28.0 
 
 25.1 
 
 25.8 
 
 26.3 
 
 26.10 
 
 27.5 
 
 28.0 
 
 28.7 
 
 29.2 
 
 29.9 
 
 30.4 
 
 30.11 
 
 M.. 
 
 28.4 
 
 29.04 
 
 29.9 
 
 26.104 
 
 27.6 
 
 28.14 
 
 28.9 
 
 29.41 
 
 30.0 
 
 30.71 
 
 31.3 
 
 31.104 
 
 32.6 
 
 33.14 
 
 S... 
 
 30.0 
 
 30.9 
 
 31.6 
 
 28.8 
 
 29.4 
 
 30.0 
 
 30.8 
 
 31.4" 
 
 32.0 
 
 32.8 
 
 33.4 
 
 34.0 
 
 34.8 
 
 35.4 
 
 M.. 
 
 31.8 
 
 32.54 
 
 33.3 
 
 30.54 
 
 31.2 
 
 31.104 
 
 32.7 
 
 33.34 
 
 34.0 
 
 34.84 
 
 35.5 
 
 36.14 
 
 36.10 
 
 37.64 
 
 S... 
 
 33.4 
 
 342 
 
 35.0 
 
 32.3 
 
 33.0 
 
 33.9 
 
 34.6 
 
 35.3 
 
 36.0 
 
 36.9 
 
 37.6 
 
 38.3 
 
 39.0 
 
 39.9 
 
 M.. 
 
 35.0 
 
 35.10| 
 
 36.9 
 
 34.04 
 
 34.10 
 
 35.74 
 
 36.5 
 
 37.24 
 
 38.0 
 
 38.94 
 
 39.7 
 
 40.44 
 
 41.2 
 
 41.114 
 
 S... 
 
 36.8 
 
 37.7 
 
 38.6 
 
 35.10 
 
 36.8 
 
 37.6 
 
 38.4 
 
 39.2 
 
 40.0 
 
 40.10 
 
 41.8 
 
 42.6 
 
 43.4 
 
 44.2 
 
 M.. 
 
 38.4 
 
 39.34 
 
 40.3 
 
 37.74 
 
 38.6 
 
 39.44 
 
 40.3 
 
 41.11 
 
 42.0 
 
 42.104 
 
 43.9 
 
 44.74 
 
 45.6 
 
 46.44 
 
 S... 
 
 40.0 
 
 41.0 
 
 42.0 
 
 39.5 
 
 40.4 
 
 41.3 
 
 42.2 
 
 43.1 
 
 44.0 
 
 44.11 
 
 45.10 
 
 46.9 
 
 47.8 
 
 4S.7 
 
 M.. 
 
 41.8 
 
 42.84 
 
 43.9 
 
 41.24 
 
 42.2 
 
 43.14 
 
 44.1 
 
 45.04 
 
 46.0 
 
 46.114 
 
 47.11 
 
 48.104 
 
 49.10 
 
 50.94 
 
 S... 
 
 43-4 
 
 44.5 
 
 45.6 
 
 43.0 
 
 44.0 
 
 45.0 
 
 46.0 
 
 47.0 
 
 48.0 
 
 49.0 
 
 50.0 
 
 51.0 
 
 52.0 
 
 53.0 
 
 M.. 
 
 45.0 
 
 46.14 
 
 47.3 
 
 44.94 
 
 45.10 
 
 46.104 
 
 47.11 
 
 48.114 
 
 50.0 
 
 51.04 
 
 52.1 
 
 53.14 
 
 54.2 
 
 55.24 
 
 S... 
 
 46.8 
 
 47.10 
 
 49.0 
 
 46.7 
 
 47.8 
 
 48.9 
 
 49.10 
 
 50.11 
 
 52.0 
 
 53.1 
 
 54.2 
 
 55.3 
 
 56.4 
 
 57.5 
 
 M.. 
 
 48.4 
 
 49.64 
 
 50.9 
 
 48.44 
 
 39.6 
 
 50.74 
 
 51 9 
 
 52.101 
 
 54.0 
 
 55.14 
 
 56.3 
 
 57.44 
 
 58.6 
 
 59.74 
 
 S... 
 
 50.0 
 
 51.3 
 
 52.6 
 
 50.2 
 
 51.4 
 
 52.6 
 
 53.8 
 
 54.10" 
 
 56.0 
 
 57.2 
 
 58.4 
 
 59.6 
 
 60.8 
 
 61.10 
 
 M.. 
 
 51.8 
 
 52.114 
 
 54.3 
 
 51.114 
 
 53.2 
 
 54.44 
 
 L5.7 
 
 56.94 
 
 58.0 
 
 59.24 
 
 60.5 
 
 61.74 
 
 62.10 
 
 64.04 
 
6 1905