/ I ^"^ ft? . PREFACE This book was begun as a proprietary publication, but as it lon developed beyond the scope of such a work it was turned to a scientific handbook for general use by the exclusion from le text of everything of an advertising nature, and by the addi- fn of what seemed to be the most desirable technical infor^a- n available. It is believed that the work will be of use in jbmoting the progress of the knitting industry. I 1 WILDMAN MFG. CO. Norristown, Pa. I T> m CONTENTS Topics only. See lists of illustrations and of tables following this, and index at back of book. Page Preface {[{ Conventions 1 Abbreviations 2 Suggestions for a course of reading (with subdivisions, which see) 2 Yarn diameter 12 Elements of knitting (with subdivisions, which see) 14 Practical variations from knitting rules (with subdivisions, which see) 34 Explanation of formulas for regular rib fabrics 36 Explanation of regular flat fabric formulas — loop-wheel . . ' 45 Yarn-cut rules 49 Yarn-gauge rules 51 The relation of the diameter of the yarn to the needle spacing 53 Width of flattened tube of fabric for different numbers of needles and yarn 57 Width of fabric from different machines 63 Production of circular knitting machines (with subdivisions, which see) qq Relative production of different types of knitting machine . 84 Weight per square yard formula — derivation 89 Determining weight per square yard by weighing 95 Two-thread knitting (with subdivisions, which see) 95 Twist in flat knit fabric made with self-feeding needles (with subdivisions, which see) 101 Twist in rib fabric 112 Summary regarding twist of knit fabrics (with subdivisions, which see) 1 13 ^6t 116 Space allotment in knitting mills (with subdivisions, which see) Hy V vi Contents Page Relation of machine gauge and cut , 124 Gauge, different standards 125 Needles per inch of hosiery machines and ribbers measured from back to back of needles 128 Range of fabrics from the same gauge or cut 138 Yarn for flat cotton fleece goods 138 Sinker bur 140 Lander bur 146 Cast-off bur 147 Trouble, cause and remedy — spring-needle loop-wheel. . . . 150 Tuck-stitch figures — latch-needle 153 Vertical patterns in latch-needle knitting 155 Names of cams 160 Adjusting in general 160 Putting needles into ribber 161 Hooking fabric on ribber 164 Ribber take-up 166 Locating sources of trouble in rib knitting 167 Stitch adjustment 168 Adjusting the yarn carrier 171 Rib knitting — trouble, cause and remedy 171 Yarn counts (with subdivisions, which see) 187 Counts used for different kinds of yarns (with subdivisions, which see) 189 Explanation of convenient equations for determining the number of yarn in the constant weight counts 190 Single equivalent of two or more yarns 192 Explanation of yarn-transformation table 193 Yarn rules for different yarn counts 193 Figure designing with pattern wheels (with subdivisions, which see) 199 Economics of knitting (with subdivisions, which see) 249 Minimum weight per square yard 263 Theory of knit fabrics (with subdivisions, which see) 266 Theory of knit fabrics — general considerations 272 Ratio and proportion (with subdivisions, which see) 276 Measures 277 Mensuration (with subdivisions, which see) 286 Miscellaneous notes on belting (with subdivisions, which see) 290 Analogies between the flow of water and electricity 293 ILLUSTRATIONS List of contents (topics) precedes this. List of tables follows this. Index is at back of book. D Number Page Diagram of double tucks cleared by lap 46 246 of sample design 42 235 F Fabric, circular, ribbon structure 4 202 figured, sample 41 232 flat, back 2 17 face 1 16 with right-hand twist 5 107 range, from the same gauge or cut 1-2 138 regular relations ; . , . . 7 33 relation of wales and courses for stitches per foot constant 5 28 relation of width and breadth for stitches per foot constant 6 30 rib, effect of yarn twist on fabric twist 112 regular relations 2 270 relations for yarn variable 1 269 with wales spread apart 3 19 K Knots 275 L Loops, normal and twisted, outlines 4 106 M Machine, Machines, diagram of American circular ... 3 202 diagram of French circular 2 202 vii viii Illustrations Number Page Machine, types of circular . 1-8 204 type which does not twist yarn 7 110 type which twists yarn 6 109 N Needle, latch, with double-thread loops 2 100 spring, with double-thread loops 1 97 P Pattern developments: figure, divided ; two-division overlap right-hand . . 29 222 two-division under lap ; right-hand 30 222 incUned; overlap; right-hand 23 219 vertical; overlap; left-hand 26 222 over-lap; right-hand 24 219 underlap; left-hand 28 222 underlap ; right-hand 27 222 stripes, diagonal; overlap; right-hand 22 219 inclined; overlap; left-hand 25 222 overlap; right-hand 21 219 vertical 20 219 Pattern, exception to general rule 47-50 247 Pattern, exceptional, disposition of elements 51 248 Pattern lengths usable with 65 needles 40 229 Pattern models: figure, inclined; overlap; right-hand 13 218 vertical; overlap; right-hand 14 218 stripes, diagonal; overlap; right-hand 12 218 inclined; overlap; right-hand 11 218 vertical 10 218 Patterns, numerical, of five divisions, for cylinder needles equal to: one pattern division 32 225 two pattern divisions 33 225 three pattern divisions 34 225 four pattern divisions 35 225 six pattern divisions 36 225 seven pattern divisions 37 225 eight pattern divisions 38 225 nine pattern divisions 39 225 Illustrations ix Number Page Pattern positions, plan 226 Pattern, strip, detail 43 238 Presser model 44 240 reversed 55 240 positions 5 209 S Stitch, Stitches, double tuck 7 212 single tuck 6 211 successive tucks in the same course 8 213 tight rib 4 21 tuck block in a mixed field 9 215 very loose, flat fabric 1 264 Y Yarn-cut chart for latch-needle rib machine 50 Yarn delivery from bobbin and cone 2 104 Yarn diameter, determination , 13 Yarn diameter, relation to needle spacing 57 Yarn-gauge chart for spring-needle machine 52 Yarn twist illustrated by strip of paper coiled on pencil 1 102 TABLES Contents (topics) and list of illustrations precedes this. Index is at back of book. A Page Abbreviations 2 C Circles, circumferences and areas 280 Cuts, measured on needle line 130 F Fabric, Fabrics, flat, fundamental relations 45 flat, regular dimensions \ 48 formulas 46-47 rib, fundamental relations 36 regular formulas 38-39 dimensions. 40 weight per square yard 90-91 weight formula for different counts 94 transformations 93 width, proportion of machine width 65 tubular, width 59 Feeds and pattern divisions for 24 courses 235 G Gauge, definitions 127 I Inch, fractions, decimal equivalents 277 Inventions, knitting 265 K Knitting, latch-needle; trouble, cause and remedy 172 spring-needle; trouble, cause and remedy 150 xi xii Tables M Page Machine, body, latch-needle, performance 185 Motions, machines and fabric 204-205 N Needle, Needles, cylinder, for a 30 needle pattern 237 per inch, different gauges 126 measured on cam surface 175 simple factors for small machines 128 simple calculations . 129 spring, dimensions and data 149 in loop-wheel cylinders 154 leaded, weight per thousand 149 Numbers, squares, cubes, square roots and cube roots 278 P Power, electrical 294 for machines, auxiliary 121 latch-needle rib and winders 122 loop wheel 123 knitting mill 122-123 leather belt 289 proportionate distribution in knitting mill 123 transmitted by shafting 288 Production, calculations, hanks 69 hnear yards 68 pounds 69 square yards 68 factors, rib and flat 89 linear yards 76-77 loop- wheel, hanks ; . . 74 relative, rib and flat fabrics 85-87-88 rib fabric, hanks 73 pounds 72 rib tops, dozen pairs 82-83 square yards, general 79 regular fabric 81 winder, nutaper 114 upright, bobbin 115 Tables xiii R Page Ribber, Wildman, circumference 184 diameter 184 S Space, floor, in knitting mills 118 Stitches, maximum and minimum 186 T Trigonometric functions, natural 282 V Velocity of needles and yarn 159 Y Yarn-cut relations, rib 73 Yarn-gauge and yarn-cut rules for different counts 195 Yarn, Yarns, counts, convenient equations for determining. 191 counts, definitions '. 188 diameter and coils ' 196 proportion- of needle spacing 56 for flat cotton fleeced goods 139 latch-needle rib machine 163 loop-wheel machine 129 number and relative diameter and cube of diameter . . . 262 rules for different machines 53 single equivalent of two yarns 198 transformation constants 194 THE SCIENCE OF KNITTING CONVENTIONS The meaning of many of the technical terms used in this book is explained when they are brought into use, but the meaning of the most used terms and conventions is given here in order to make sure that they will be understood in case the explanation may not be with them when they are encountered. Cut is used instead of needles per inch, both because it is quite generally so used and because it is much shorter than needles per inch. The only objection to its use is that it might be confused with the word cut used to designate the size of yarn, but since the yarn cut is restricted, is really unnecessary, and is not used with reference to the machine, there is not much chance for confusion. On the contrary, there are good reasons for abandoning it in favor of a familiar substitute, such as the cotton number, and leaving the word cut for use entirely instead of needles per inch. Right Hand, applied to circular motion (or the result of it), means the direction of revolution of a right-hand screw when entering a solid body. Clockwise means the direction of motion of the hands of a clock, which for circular motion is the same as right hand. Left Hand is the reverse of right hand. Anti-clockwise is the reverse of clockwise. Forward means the direction of motion of whatever is the sub- ject of discussion — such as yarn, machine, fabric, etc. Backward means the reverse of forward. Number means yarn number in the cotton count unless otherwise specified. A Constant means a number which does not change, such as 3.1416, the number which expresses the ratio of the circum- ference of a circle to its diameter. A Variable means a number which does change. The age of anything is a variable, since it is constantly changing. 1 2 The Science of Knitting Gauge, applied to the needle spacing or to the fineness of cloth, means needles per inch and one-half, which is substan- tially the original meaning of the word as applied to knitting. Gauge, applied to needles, means the thickness of latch needles. There is] no rule for determining the gauge from this dimension, so tables have to be consulted for such information. Other dimensions of the needle, such as size of hook, length of latch, etc., correspond to an extent to the gauge, but have no fixed relation to it. For instance, a 48-gauge needle has a certain thickness and a fine hook, but the hook may be more or less fine. Diametral Revolutions means the product of the diameter in inches and the revolutions per minute of a revolving circle, such as a knitting machine, pulley or similar object. A 20- inch cylinder making 35 revolutions per minute is running at 20 X 35 = 700 diametral revolutions. dia Abbreviations Abbreviation Meaning + Increased by — Decreased by X Multiplied by -^ Divided by = Equals dia. Diameter r.p.m. Revolutions per minute . r.p.m. Diametral revolutions V Square root of i.e. That is e.g. For instance q.v. Which see. SUGGESTIONS FOR A COURSE OF READING If all knowledge of machine knitting were taken out of the world, and a perfect knitting machine, say a rib body machine for example, were set down in a knitting center, such as Leicester, England, or Utica, New York, with no more informa- tion than the assurance that it would knit cloth, it is safe to say that after repeated efforts to hook on the fabric and get it started, the machine would be so damaged and the operators so discouraged, that it would be pronounced an impossibility to make cloth on such a machine. Suggestions for a Course of Reading 3 Somewhat similarlj^, if a book announcing and demonstrating a system of knitting calculations is put into the hands of readers who do not even know that there is system in knitting, and most of whom are unfamiliar with mathematical demonstrations, such a book would not be very beneficial without an explanation of how to use it. Other important callings, civil engineering and mechanical engineering for examples, have their handbooks; but before the appearance of such books, the readers were prepared to un- derstand them by technical school and college instruction. Moreover, if the author of these knitting calculations fre- quently finds it necessary to take paper and pencil and carefully work out something which he himself has written in order to re- understand it, how much more will assistance be useful to one who has never heard of a knitting system and has never been prepared to understand one if it should appear. Although the above considerations show the advisabihty of helps in the use of this book, there are other reasons why sym- pathy for the knitter and his calling should prompt a fa,miliar attempt to improve both, in spite of the prevailing unsympa- thetic custom of disseminating cold facts without aids to the understanding of them. One reason is the value of machine knitting to the human race. The frame tender in an obscure little mill who longs for bigger and better things seldom realizes that he is doing as much knitting as fourteen thousand grandmothers with their hand needles, and just as the product of that hand knitting benefited his immediate family, so his work, thousands of times more, benefits members of his bigger human family so numerous and so far away that he can never know them. Another reason is the opportunity to benefit the knitter as a class. Who is there with any experience in the industry who has not known of a knitter's leaving his home town for a better opening, and then drifting back with the remark, " Yes, the wages were better, but the machines ran the other way and the yarn count was different, and I couldn't catch onto it." What a commentary! A knitter at home and not abroad! Suppose the mechanic said, " I am a machinist in Saratoga County but not elsewhere." What kind of a machinist would he be? For what reason is a knitter's knowledge limited to one locality, when the machinist's, the carpenter's, the mason's is universal. 4 The Science of Knitting For no reason. It is unreasonable. For what cause, then? Because the fundamentals have not been offered to him. Intimate acquaintance with the knitter and his surroundings shows the need of these appeals for improvement notwithstanding the fact that such appeals are unconventional and sure to be misunderstood by some who regard an offer of better educa- tional facilities as an imputation of ignorance. The error of such a position should be evident from the fact that the enlight- enment of the entire knitting world is ignorance compared to that of almost every other branch of human endeavor. It is what we retain which benefits us, not what we hear. A man might hear good sermons every Sunday of his life and good advice every week day, but if he retain nothing of either, he will not benefit thereby. Technical knowledge is not retain- able by the mere reading of it. The reader must take pencil and paper and put down in black and white the main truths if he is to be benefited by them. And while he is about it he might use a pen and indexed notebook and put those truths down where they will be readily available. Nystrom, in the preface to his handbook, put these words: " Every engineer should make his own pocket book, as he proceeds in study and practice, to suit his particular business." Nystrom's handbook has been superseded. Why? Largely because others made more complete handbooks from Nystrom's suggestion. And it is probable that this one sentence in Nystrom's book will be of more value to the world and live longer than all the rest of Nystrom's book put together, for the sentence will never become obsolete whereas the rest of the book will. Consequently, the knitter who does not begin the reading of this handbook by starting one of his own will miss not only the spirit and benefit of this book but he and the world will miss the benefit of his own book. What connects knitters all over the world? KJnit fabric. It may have been made by a Yankee, or a Frenchman, on a latch needle, or on a spring needle, on a round machine, or on a straight machine, — possibly^ an expert might tell some of the latter details, but every knitter recognizes the knit stitch itself, and every true knitter is attracted by it. Therefore, the way for broadening the knitter's horizon is through the fabric. But the fabric is made from yarn, so the beginning is there. This book does not treat of the composition of yarn, since such in- Suggestions for a Course of Reading 5 formation may be found in numerous books and since one idea of this book is not to repeat except where improvement seems evident. Yarn composition is important and should be studied elsewhere, but yarn diameter is mechanically the most impor- tant and is treated here in. a readily understandable way under Yarn Diameter The student should read this topic carefully and then apply the principles by determining the diameter of some yarn. If no hosiery yarn is at hand, a few pieces of soft cord, such as is used for tying bundles, will answer the purpose. Elements of Knitting The first part of this is plain sailing, but it is important since it defines the terms commonly used in knitting. The student should learn the application of the terms, such as needle wale, sinker wale, course, etc., and should form the habit of using them. Otherwise the descriptions which follow will not be readily understood. The first mathematical portion of the elements is the deriva- tion of the general rule Cut2 Yarn number = Constant This is one of the most important relations in knitting, so of course it is desirable that the student be able to derive it from the definitions of cut and number, since then he will not only understand it better, but will be able to conjure it up when he needs it. However, inability to derive the rule does not de- tract from its usefulness any more than does inabiUty to derive the rule for the horse power of a steam engine. Consequently, the derivation may be skipped by those who find it laborious, but the result should be thoroughly memorized. The latter part of the elements, that which contains the ex- planation of the underlying principles of knitting for (1) stitches constant, (2) yarn constant and (3) loops proportional to the diameter of the yarn, is very important. It is the theory of knitting put in language meant to be plain. It should be read with a pad and pencil at hand for working out the simple illus- trations in order to fix the principles; and should not be left until it is mastered since practically all that follows is dependent on it. 6 The Science of Knitting Practical Variations from Knitting Rules This is easy reading but highly important for several reasons. In the first place, mere book learning is even more deficient than mere practical learning. So the student of books is justly under the suspicion of impracticability until he has proven otherwise; and the best way in which he can prove otherwise is to admit freely his limitations. Therefore, the student should learn as early as possible how much allowance to make between theory and practice. He should put every principle to the severest test and should not depend on memory for the results of the tests but should put down on paper the discrep- ancies between the rules and the actual results, and should then derive the average maximum and minimum errors. These results should be kept with each formula, for no formula is com- plete without knowledge of its reliability. The formulas for regular fabrics are so new that only a little such knowledge is available for them, therefore the user must find the rest for himself. Relation of Machine Gauge and Cut This should be learned. Yarn-gauge Rules and Charts for Latch-needle Rib and Spring-needle Loop-wheel Machines These rules connect the fabric with the machine which makes it and, therefore, are highly important, but the allowable varia- tion from them is also important, so the charts showing the variations should be studied until the information in the charts can be properly applied. Formulas for Regular Rib Fabrics and Explanations: Formulas for Regular Flat Fabrics and Explanations These are the means of practical application of the theory of knit fabrics — rather the principles of knit fabrics — so the student should study them by working out examples with the formulas which are designated the most important in the ex- planations. Of course the Tabulations for Regular Fabrics belong with the formulas and should have the attention which they deserve. The student should understand thoroughly that although the principles of the formulas are on a substantial basis the constants used are a matter of choice. For instance, Suggestions for a Course of Reading 7 in his locality fabric which has courses to wales as 12 to 10 may be considered to represent best average practice. In such case the ambitious student may test his ability by working out a act of formulas for those conditions. The Relation of the Diameter of the Yarn to the Needle Spacing This is somewhat mathematical, but if found difficult the mathematics may be skipped. However, the results should be understood and considered. As a general rule, the machine which works the heaviest yarn in proportion to the needle spacing is technically the best machine. This indicates that it is desirable to find means of using heavy yarn, especially on those machines which are now restricted to comparatively light yarn. Of course, the practical problem involves retaining good needle velocity and a reasonable number of feeds, but any discovery which will throw hght on the subject is valuable. Width of Fabric from Different Machines This subject is much like the last. It may seem dry but it is useful. Range of Fabric from the Same Gauge or Cut This is an illustration of how much difference there may be in fabrics from the same number of needles per inch. Yet it has been customary to try to determine the cut from the fabric. It should be evident that the fabric rules given in this book pro- vide a more rational and accurate method for determining the needles per inch. Production of Circular Knitting Machines This gives the general considerations of the production question and deserves to be read thoroughly. Production — Methods of Calculating The student should take his pencil and paper and work through each method as it is given, then he should work each one through with the book closed, and finally he should work each one through with an entirely new set of conditions. Even then he will be fortunate if he remembers the methods suffi- ciently for application on the spot, since these methods are as easy to forget as they are important. A boiler maker who could 8 The Science of Knitting not calculate the capacity of his boilers, or an engine maker who could not calculate the capacity of his engines, would be re- garded as an ignoramus; yet the knitter, as a rule, cannot cal- culate the capacity of his machines, although this is one of the simple problems in knitting. Therefore, the student of knitting should learn the subject, not only because he may require it, but because it helps to put his calling on the higher plane where it should be. Relative Production of Different Types of Knitting Machines This is a highly important question and one which tests the reader's knowledge of what he has already read. It frequently happens that a cotton yarn company desires to install machinery to convert the yarn into fabric. What machines should be in- stalled to convert the most pounds or to produce the most yards? The knitter should be able to answer questions like these. If he studies this topic, he will be able to do so. Weight per Square Yard Formula — Derivation This formula is to knitting what the first law of gravitation is to the heavenly bodies. Astronomers used to be puzzled by the difference in motion between a planet and a comet, and by lesser differences in the motions of any two planets. But the first law of gravitation, namely, that bodies attract each other directly as their masses and inversely as the square of their distance, solved the whole problem; so that a law expressible in sixteen words bound the immeasurable universe together. Similarly the weight per yard formula binds all knit fabric together, for it states the conditions which control every piece of knit fabric. This derivation is simple arithmetic and it is so important that every knitter should learn it and be able to derive it at any time. Determining the Weight per Square Yard by Weighing Although this topic is intended for the manufacturer or analyst who will do enough weighing to warrant the cost of a die for cutting the fabric, it is useful to the student as well. If a die is not readily procurable, the student may cut out rectangular pieces of cloth, using for a pattern a piece of cardboard, say four inches square. Suggestions for a Course of Reading 9 Two-thread Knitting Twist in Flat Knit Fabric Made with Self-feeding Needles Twist in Rib Fabric Summary Regarding Twist of Knit Fabrics These are easy reading, but they should not be slighted be- cause they are easy. The student will find in them many principles which have much broader application than the titles indicate, and he should endeavor to understand those principles in order to extend their application himself. For instance, the subject of twist in knit fabrics and knitting yarn is as broad as its investigation has been narrow, so it offers a good field for study. Yarn Counts — General The knitter works with yam, so he is not thoroughly equipped for his occupation until he understands the methods of number- ing yarn. It is a sad reflection on our civilization that so much time has to be wasted in learning many different counts when a few would answer the purpose; but if the time consumed spurs the student to use his influence toward the adoption of two or three universal yarn counts, it will not be entirely lost. Yarn-count Definitions These should be memorized. Undoubtedly, some of the definitions will be forgotten in time, but if the student memo- rizes them when the subject is in hand, he is likely to retain a suflBciently clear idea of them to be of service in time of need. Counts Used for Dififerent Kinds of Yarns This old subject is treated briefly for the American knitter, since the usual treatise is either too voluminous or does not in- clude the local counts. The pitfalls of yarn numbering should be carefully learned, for it is frequently costly to specify the wrong number of yarn. Moreover, it is advisable to know something about the local yarn numbering when one goes to a new locality, since the knowledge dispels the to-be-expected sus- picion of provincialism. 10 The Science of Knitting Single Equivalent of Two or More Yarns — Formula The equation for two yarns should be thoroughly learned, even if the demonstration is too difficult. Moreover, the equa- tion should be practiced until proficiency in its use is attained. When the knitter is asked what the equivalent of a ten and six yarn is and has to admit that he does not know and can- not find out without a table, his admission is a sad commen- tary on his knowledge. Explanation of Yarn-transformation Table — Yarn-transformation Table These should be mastered. Some may say that they have a parallel column transformation table with which they are familiar. That is all right for whoever does not use yarn every day, but the knitter should be able to transform between the counts which he uses without the aid of a table. He may be looking for a position some day, and the prospective employer may ask him a simple transformation question, just as a sea- man is asked to box the compass as a slight evidence of his knowledge. If he says that he does not know but must go home and look in a book to find out, he is likely to be advised to go home and stay there. Very many of the usual yarn trans- formations are solvable almost or entirely mentally, and it gives standing to a knitter to be able to answer such questions on the spot. It is not to be expected that all of the constants will be learned, but if a knitter uses cotton, worsted and mill- spun yarn, he should be able without looking at a book or a memorandum to make any transformation between the cotton count, worsted count, and whatever local count is used. Figure Designing with Pattern Wheels Although this is generally regarded as belonging more to loop- wheel knitting than to general knitting, still the principles are broad even if the application is somewhat restricted. More- over, the mental training obtained by mastering such problems is highly beneficial. The man who is content to have all of his information brought to him ready for use will become depend- ent just like the man who requires all of his food brought to him. But those who exercise either their minds or their muscles — and preferably both — for what they get are independent, as all rational beings should be. Suggestions for a Course of Reading 11 Minimum Weight per Square Yard This is an illustration of the purely theoretical. Fabric of the kind discussed is never seen. Naturally, some think that time spent in discussing it is lost. But such people would be surprised if they would learn how much our present knowledge of common affairs has been increased by discussing the in- finitely great and the infinitely small. Yet neither will ever be reached here. However, from those unattainable boundaries it is possible to work back and derive much practical information. It is so with the minimum weight per square yard; it sets a limit which assists in determining the attainable weights. But better still it shows how reasoning can be applied to knitting for its advancement as well as to anything else. Moreover, the knitter should not leave such reasoning for the so-called theo- rists. The knitter has the same kind of a brain as the theorist and frequently a better opportunity to use it, and he should exercise the opportunity. Vertical Patterns j This topic is something like Figure Designing in that it is certainly beneficial as a study, even if the opportunity does not occur for its application. " Economics of Knitting Economical knitting is what every knitter is striving for, since, if he does not get pretty near to it, competition will drive him out of business. Therefore, it ought to be of interest and value to know definitely just what roads lead to economy in- stead of groping around in the dark for them. Economics of Knitting points out those roads. The subject may seem dry. So are the economics of almost every industry. But by such dry subjects is progress made. Theory of Knit Fabrics This is not intended for practical knitters since they have already learned it from the Elements of Knitting. It is for those who want to get quickly at the reason for the knitting system which this book proclaims. It is a line of departure for those who feel prompted to express agreement or disagree- ment. The author hopes that all such will carry out their promptings with as much fidelity as has been exercised in devel- 12 The Science of Knitting oping the system itself, since only by such criticism can the truth be reached. The object of this book is to show the truth, and those who support its truths or correct its error j will be fur- thering that object. The Remainder of the Book This needs no introduction other than the index and table of contents. The knitter should remember, however, that although the tables are for him as well as for those who are not knitters, still he should not be dependent on the tables, since if he has followed these suggestions he already knows formulas enough to enable him to derive hundreds of tables. These tables are merely some of those rules worked out for cases which might arise, in order to save the time of working them out when the cases do arise. So the rule is the main thing. Moreover, the knitter can carry the rule in his head,'but not the table. There- fore, he should keep the rules in his head and be able to apply them whenever it is necessary. YARN DIAMETER It is the custom to use the yarn number in knitting cal- culations, which is right as far as it goes, since the number ex- presses the inverted weight per unit length of the yarn and is, therefore, useful, very much as the weight per foot of shafting is useful. But if a machinist were required to construct something with shafting and had to work ^by the weight per foot instead of the diameter, he would be sadly inconvenienced. Yet this is the condition under which the knitter has worked — a condition which is responsible for much confusion and waste. The knitting machine is insensible to the weight of yarn, but it is very sen- sitive to undersized or over-sized yarn. Of course, the weight has a relation to the diameter, but this relation is so affected by the composition, twist, and hygroscopicity of the yarn that it is not reliable for determining the diameter except when these and other disturbing conditions are alike. Although the number of the yarn is useful and therefore de- sirable for knitting purposes, the diameter or an equivalent is much more desirable, since the width of the fabric, the cut of the machine, the length of the stitch, and other important features are dependent on it. Yarn Diameter 13 It is generally considered that the actual or sensible diameter — the diameter which the machine experiences — is almost im- possible to determine. In weaving, calculations are made with diameters derived from the specific weight of the material, cotton, wool, etc., as the case may be, but these diameters are less than the sensible diameter. Moreover knitting — especially in America — has not yet reached the calculating stage, so what- ever diameters are used must not only be such as the. machine experiences but must be convenient of access and simple to handle. Method for the determination of the coils per half-inch of the yarn, from which the diameter of the yarn, the diameters per inch, and the yarn number may be calculated. A means of meeting all these requirements is illustrated herewith. Almost every one has a watch-chain bar. Make a very slight nick in the bar half an inch from the nearest side of the band. Wind the yarn in question around the bar out to the mark, say five slightly separated coils at a time, pressing each five coils toward the band, so that they come firmly to- gether, but are not compressed too tightly. Then one-half divided by the number of coils gives the diameter of the yarn. But it is not necessary to make the division since the number of 14 The Science of Knitting coils is as reliable to work with as the diameter and is much more convenient. By this means, from what follows and with only a piece of yarn, say eight inches in length, the knitter may determine the cut to use, the stitches per foot, the number of the yarn and other useful information. Moreover, skill in coil- ing the yarn may be acquired with less practice than is required for the use of a reel and balance. The novice should not be discouraged if the yarn number obtained by this method does not exactly agree with the number obtained by reeling, for it has already been shown that the diameter does not always cor- respond with the number, so it must follow that the number does not always correspond with the diameter. Consequently failure to get the correct number by counting the coils is not necessarily proof that either the method or the application of it is faulty. * Of course there are with this method, as with every other, sources of error, opportunities for carelessness, etc. such as chancing on an exceptionally light or heavy piece of the yarn, or pressing the coils differently, or using a rough or sticky bar; but with ordinary caution this method affords the knitter an exceedingly simple guide which is far ahead of what has for- merly been available. In the following discussion the yarn diameter and the coils are obtained with a bar. The coils per one-half inch are gen- erally used since the coils per inch are too many to count readily and no advantage is gained by using them, except for more elaborate calculations than the knitter is likely to make. Ob- viously the number of coils per half inch is half the number of coils per inch. So in order to prevent confusion, the coils per half inch are so stated, or as " one-half coils per inch," whereas " coils " means coils per inch. ELEMENTS OF KNITTING Definition of Knitting. — Knitting is making fabric on more than one needle by interlooping a thread or several parallel threads. The Loop is the Element. — Since the fabric is made up of a succession of loops, the element of the fabric is the loop. Course. — Successive loops in any one thread form a course, except in warp knitting where the loops formed at one time form a course. Elements of Knitting 15 [ Length of Course. — In circular knitting a course follows a continuous helical path in the tube of fabric from beginning to 3nd, so its length is inconveniently great; consequently the length is taken as one complete circuit of the fabric, and suc- cessive circuits are regarded as separate courses. First Course. — The first course may be formed in any one of many ways, such as wrapping the yarn once around each needle in succession, or may be in a fabric previously knit. Formation of Loop. — In the latter case a needle is inserted through each one of the original loops and yarn is thereby drawn through the original loops to form the next course which is held on the needles until the operation is repeated, and so on. Needle Loop. — The yarn lies in the plane of the fabric in what is called a snake curve, and the loops which are drawn through the previously formed loops are called the needle loops because they rest on the needle. Sinker Loop. — But since the yarn is continuous there must be corresponding connecting loops of opposite curvature; these ^re called sinker loops, because in the original knitting machine during the feeding of the yarn they rested against thin plates called sinkers. Wale. — A row of adjoining loops in different courses is called ja wale or rib. Stitch. — A stitch- is really the combination of loops from adjoining threads forming a fixed part of the fabric, and the duplication of which forms the whole fabric. But a stitch is frequently considered to be the length of yarn from any point to an adjoining corresponding point, e.g. from the middle of a sinker loop to the middle of the next sinker loop. Top and Bottom of Loop and Fabric. — The needle loop is considered to be the top of the stitch and the sinker loop the bottom. Correspondingly the bottom of the fabric is that which is knit first and the top is that which is knit last. Length and Width of Fabric. — The extent of the fabric along the courses is limited by the number of needles, but along the wales it is unlimited except by the supply of yarn, so the length of the fabric is taken as the length of a wale, and the width, as the length of a course, except in tubular fabrics in which half the length of a single course is taken — that is, the flattened width of the tube. 16 The Science of Knitting Suppositions. — For the discussion of the elementary prin- ciples of knitting, the yarn is considered round and flexible to bending but not to compression. The machine is considered to be ideal, i.e. perfect in its operation and without limitations as Width ~ of Wale 4 diameters Illustration 1. Face of plain flat fabric. A, A, needle loops, B, B, sinker loops. to length of stitch, size of needle, etc. The practical qualifica- tions are given subsequently. Illustrations of Knit Stitch. — Illustration 1 shows a face view and Illustration 2 shows a back view of three wales, marked 1, 2, 3, of plain flat (not ribbed) knitting. Elements of Knitting 17 Width of Wale and of Fabric. — A wale at its widest part is nade up of a loop bent over two threads side by side, and since :hese are all the same thread, the diameters are all the same, so. .he width of the wale is four diameters. Illustration 2. Back of plain flat fabric. But the wales touch at their widest portion so The entire width of the fabric = width of wale X number of wales = 4 dia. of yarn X number of wales = 4 dia. of yarn X number of needles. 18 The Science of Knitting The half width or flattened width of the tube = 2 dia. of yarn X number of needles = 2 dia. of yarn X dia. of machine X 3.14 X cut = 6.28 dia. of yarn X dia. of machine X cut. From this it follows that the width of the fabric is dependent not only on the diameter of the machine but on the cut and on the diameter of the yarn. This is actually demonstrated in regard to the cut by some small mills which have only a few diameters of machines, but make a wide range of garment sizes by using cylinders and dials of different cuts in the same machine. It is evident also that if yarn of smaller diameter is used, the width of the fabric will be proportionally less. This may be counteracted by increasing the diameter of the machine with the same cut, as is well known, or by using a cylinder and a dial of correspondingly finer cut. Since dia. of yarn = Coils per i inch' Needles Width of flattened tube of fabric = ^^rr^ r-^ — t- Coils per ^ men i.e. The flattened width of the tube of plain fabric from a circular machine equals the number of needles divided by the number of coils of yarn per half inch. . _ 3.14 X dia. of machine X cut^ ' Coils per \ inch i.e. The flattened width of the tube of plain fabric from a circular machine equals 3.14 multiplied by the diameter of the needle line multiplied by the cut and divided by the coils of yarn per half inch. Width of Course. — A visible course is narrower than the height of a stitch, since the loops overlap by approximately a diameter both at the top and at the bottom. Moreover, the width of the course is determined by the length of yarn in the stitch as well as by the diameter, instead of by the diameter alone as is the case with the wale. Courses and Wales per Inch. — Courses are generally com- pared by the number per inch, as are also the wales, but since the width of the fabric is proportional to the number of wales, the width is generally used instead of the wo^les per inch. Elements of Knitting 19 Stitches per Foot. — The length of yarn in the stitch is ex- bressed by the number of stitches per foot of yarn, since this is X convenient unit. It should be remembered, however, that the ength of the yarn in the stitch increases as the stitches per foot decrease — just as the wales per inch decrease when the width Df the wale increases. These are what are called inverse re- lations — that is, one goes up when the other goes down. There kre many such in knitting, and they must be kept in mind in Drder to comprehend the subject. Face and Back. — Each of the loops of the plain fabric is Irawn through another one toward what is considered the face Illustration 3. Rib fabric with wales spread apart. )f the fabric. This throws the tops and the bottoms of the loops m the back, as Illustration 2 shows, and makes the appear- mce of the back different from that of the front, or face. Rib Fabric. — Now consider the loops of every other wale to )e drawn through to the back instead of the front. Then Illus- 20 The Science of Knitting tration 1 will appear like Illustration 3, except that wales 1 and 3, coming together, will leave wale 2 entirely on the back. The face of the cloth will appear just the same as before, and the back will appear just like the face, since the tops and bottoms of the loops will be hidden between the front and back wales. Curling of Edges of Flat Fabric, — The objectionable curling of the edges of flat fabric is due to the accumulated straighten- ing out of the yarn in the stitches, which tendency is all in one direction in any one place — toward the face at the ends and toward the back at the sides — since the loops are all formed alike. But in rib fabric, where every alternate stitch in ai course is drawn in the reverse direction, the tendency to straighten does not accumulate but counterbalances, therefore the fabric does not curl at the edges. Raveling Flat and Rib Fabric. — It will also be noticed that the flat fabric may be raveled from either end, so that it is difficult to tell the top from the bottom when it is not on the machine; whereas the rib fabric cannot be raveled at the end which came off the needles first — the lower end, Illustration 3 — because the end thread is wound around the next thread instead of being merely looped through it. Comparative Width of Flat and Rib Fabric. — If the same number of needles is used, the rib fabric will be half as wide as the plain fabric, since half of the wales lie on the back. The courses will not be changed. Elasticity of Flat and Rib Fabric. — It is evident from the preceding that rib knitting is substantially flat knitting with every other wale facing inward, and since the wales on the in- side overlap those on the outside, rib fabric is only half as wide as flat fabric made of the same yarn and with the same total number of needles. In other words, rib fabric of the same width as flat fabric made of the same yarn has twice as many wales to stretch ; consequently it .has twice the elasticity from this fact alone. Moreover, when rib fabric is stretched, the front and back wales tend to get into line between each other, and so supply still more elasticity than has just been mentioned. Double Sets of Needles. — In rib machinery the needles are divided into two sets; one for knitting the face and the other for knitting the back. These sets are distinguished by various names, but in circular latch-needle machinery the needles which knit the back are generally called dial needles, and those which Elements of Knitting 21 knit the face are generally called cylinder needles. Since for plain rib fabric the same number of needles is used in each set, and since the cylinder needles generally knit the face of the cloth, the number of cylinder needles is used to designate the fineness of the fabric or the machine, and it is understood that the same number of dial needles is also used. Stitches per Foot. — The above designation makes the length bf a rib stitch include both a cylinder and a dial stitch, so that :thirty-two stitches per foot of yarn means thirty-two cylinder kt itches and thirty-two dial stitches, or what would be sixty-four |stitches in plain flat fabric. Illustration 4 shows a front view and an edge view of a tight ■ib stitch. The following is evident: TIGHT RIB STITCH EDGE VIEW Height Smch Illustration 4. Dimensions of Rib Stitch. — The width of the wale is four diameters, as has already been shown. The thickness of the fabric is four diameters. The height of the stitch is four diameters. Stitches of Different Fabrics of the Same Characteristics are Proportional to the Diameter of the Yarn. — From the above it follows that the stitch is proportional to the diameter of the yarn, for if the diameter is doubled, every dimension of the stitch will 22 The Science of Knitting be doubled, including the length of yarn in the stitch. In other words, corresponding stitches are proportional to the diameter of the yarn. The student should fix this thoroughly in his mind. A good way of so doing is to look at Illustration 4 through a reading glass held at different distances from the illustration. The size of the stitches will increase and decrease just as the diameter of the yarn does. Note that these different sized stitches seen through the glass are corresponding stitches — that is, the tightest for any given diameter of yarn. But the rule holds for any other corresponding stitches regardless of their length. Fabrics of Different Characteristics have Disproportionate Stitches. — However, for stitches which do not correspond, whereas the width and thickness must he proportional to the diameter of the yarn, the length of yarn in the stitch and consequently the height of the stitch are not proportional. If the stitches are not proportional, the fabrics are different. So the converse of the rule is true; that is, in dissimilar fabrics the lengths of yarn in the stitches are not proportional to the di- ameters of the yarn. Relation of Yarn Diameter and Needle Spacing. — Suitable yarn is that which the machine most economically converts into the most desirable fabric. The diameter of the yarn is proportional to the spacing of the needles. A convenient proof of this is found in the fact that ordinarily the width of the fabric is proportional to the width or diameter of the machine. From this it follows that when the number of needles is increased (i.e. when the cut is made finer) the width of the wales must be proportionally decreased or else the fabric would be made wider. Proofs of Relation of Yarn Diameter and Needle Spacing. — The diameter of the yarn is proportional to the width of the vrale. Consequently, the diameter of the yarn is reduced in proportion to the spacing of the needles. This important re- lation of the diameter of the yarn to the needle spacing was made - public by Gustav Willkomm, who observed it from a comparison of the needle spacing of hosiery frames and the yarn diameter; it was much later independently observed from a comparison of the gauge and corresponding yarn diameter of American and Canadian practice; and was soon after announced to be a general relation dictated by the characteristics of knit fabrics and conformed to by the machine manufacturers or users. l^Elements of Knitting 23 Relation of Yam Diameter and Needle Spacing is Elastic. — Since all practical machines will knit successfully yarn differ- ing in diameter within a wide range, there is naturally room for a difference of opinion regarding the proportion of yarn diameter to needle spacing, but ivhatever proportion is selected for any one kind and cut of machine is equally suitable on all the other cuts. The proportions used here are from quite extensive practice and are useful, but should not be taken as final. Indeed, from the principles previously explained and from the application of them, explained hereafter, the knitter may derive his own pro- portions. Formulas of Yarn and Cut Relation. — For instance, we have the rule that for corresponding fabrics Dia. yarn Needle spacing and remembering that = a constant, , , , . (1) . The cut = „ ,, ^ r- , . . . (2) Needle spacmg > we have Needle spacing = ^^^ . ...... (3) Substituting in (l)r the value of needle spacing in (3) we have Dia. yarn X Cut = a constant (4) That is, as the diameter of the yarn increases, the cut de- creases and vice versa. To use this rule with the coils instead of the diameter, substitute ^ ., for diameter of yarn which gives .R-rr- = a constant. Similarly, j=^-^, ^-^ — r- = a constant. Coils -^ Coils per ^ inch Suppose the knitter is running satisfactorily 12 cut machines and the yarn shows 51 coils in half an inch. Then for his con- ditions Constant = Cut =. 1? = _i_ . Coils per | inch 51 4.25 Consequently, his rule for such conditions is Cut = 27oc X coils per ^ inch. 24 The Science of Knitting If he runs heavier or lighter yarn, the constants for such con- ditions may be derived in the same manner. The rule is ap- plicable to all knitting machinery, but the constant is different for different types of machine because differences in structure limit the size of the yarn to be used. Spring-needle machines with jack sinkers, such as the Cotton and the Fouquet types, can use heavy yarn and, consequently, a very wide range of yarn. Spring-needle fixed-blade loop-wheel machines are restricted to light yarn. Circular latch-needle machines have a nar- rower range than loop-wheel machines, and the use of two sets of needles generally restricts the range still more. Con- stants for several types of machines are given elsewhere. Relation of Yarn Number and Diameter, and Machine Cut The cotton number of yarn is the number of yards in one pound divided by 840. Or7Tt is the number of 840 yard hanks in a pound. Hank is the name given to a fixed length of yarn. The hank of actual yarn is generally coiled and twisted, since it is too long to handle otherwise. Those who are familiar with yarn numbering have no trouble in realizing that the yarn number is 1 -f- the weight of a hank; since if each hank weighed half a pound, there would be two hanks to the pound, and the yarn would be number two, which is the same as dividing 1 by |, the weight of the hank. However, those who are not familiar with yarn numbering sometimes have difficulty in grasping the hank idea, and even those who are familiar with the subject some- times become confused when they try to figure out the relation of the diameter to the number. The following analogy may make the matter clearer. Suppose that instead of soft fuzzy twisted material, yarn is hard and smooth and round like a lead pencil, but still continuous in length. Then suppose that the yarn num- ber is the number of one-inch pieces in a pound, since it is easier to imagine a one-inch piece than an 840-yard piece. If one inch of a certain piece weighed one-tenth of a pound, then it would take ten pieces to weigh a pound, so that yarn would be number ten. The number ten could also be obtained by dividing 1 by the weight of one inch, the standard length. Consequently, Weight of / ^ -■-■■..■■_■■ . Elements of Knitting 25 In other words, the number equals one divided by the weight of a piece one inch long. Therefore, the diameter is the only di- mension which can be changed, since the length is fixed, namely 1 inch. But the weight is proportional to the square of the diameter. That is to say, if the diameter is doubled, the weight is made four times as much; but two multiplied by two equals four, so the proportional weight after doubling the diameter may be obtamed by multiplying the diameter by itself, i.e. by squaring it. But when the diameter increases, the weight does the same, consequently, the number decreases. Therefore a thick piece of yarn has a smaller number than a thin piece. This brings the illustration to the desired point, which is that tin: yarn numbers are inversely proportional to the squares of the yarn diameten^s. Inversely means inverted, or upside down. Con- sequently, to get the relative numbers of yarn square their diameters and turn the squares upside down, that is, for each yam divide one by the diameter squared. These squared diam- eters turned upside down will be to each other as the yarn numbers. This holds just as true of the pieces of actual ^yarn as it does of the imaginary pieces of smooth round wood, for it makes no difference whether the diameter can be measured readily, or whether the standard length is long or short, the yarn numbers are inversely proportional to the squares of the yarn diameters. Expresse'd in a formula this is Constant No. = ^^n;^- Transforming, ^. , Constant .(.>. Dia.2 = ^r^ (5) No. But from equation (4) Dia. X Cut = Constant, ^. , Constant ,n\ Constant Constant (6) -(5) No. = Cut^ ' Inverting Cut2 No. = Constant Note that the constants are not changed since their actual values are not yet required. 26 The Science of Knitting In other words, the number of the yarn is proportional to the square of the cut. This deduction was originally made by Gustav Willkomm. It follows naturally from his observation that the diameter of the yarn is proportional to the needle j spacing. i Foundation Principles. — It has been shown from considera- tion of the individual rib stitch that stitches — and consequently fabrics — of the same characteristics are in every respect pro- portional to the diameter of the yarn from which they are formed and conversely that when the proportion of the height of the stitch to the diameter of the yarn is changed, the characteristics of the stitch and consequently of the fabric are changed. Since these are the foundation principles of knit fabrics, they should be thoroughly understood. The dependence of these basic prin- ciples on the diameter of the yam makes the diameter of the yarn the foundation fact in knitting. There are other facts considered elsewhere, but the diameter leads in importance. Changing the Characteristics of the Fabric. — To return to the foundation principles of the fabric it will be noticed that there are as a rule with any one kind of yarn only two factors which may be changed, that is, the diameter of the yarn and the length of yarn in the stitch, each of which influences the height of the loop and con- sequently the number of courses per inch; also that the width of the wale and the thickness of the fabric are proportional to the diameter of the yarn and independent of the length of the stitch except for extremes which are considered elsewhere. Three General Cases. — For this discussion the following combinations are considered : 1. Stitches per foot of yarn constant, yarn diameter varied. 2. Stitches per foot of yarn varied, yarn diameter constant. 3. Stitches per foot of yarn and yarn diameter varied so that the stitches per foot multiplied by the yarn diameter equals a constant — i.e., the stitches per foot increase just as the diameter decreases. What Determines Good Fabric. — Nos. 1 and 2 are readily understood. No. 3 is the condition for fabrics of different fine- ness but of the same characteristics. In other words, if a lot of machines from the coarsest to the finest were started in a com- munity of practical knitters and the fabrics were compared after the machines were in commercial operation, it would be found that the product of the stitches per foot of yarn multiplied by the Elements of Knitting 27 yarn diameter would be one and the same constant for all of the fabrics, of com'se with slight variations. The reasons for this are that in any one community there is an idea of what char- acteristics are required for good fabric, whether coarse or fine, so the yarn and stitch would be so adjusted as to give these characteristics on the different cut machines, with the result that the product of the stitches per foot of yarn and the diameter of the yarn would be a certain constant, for this is the condition for fabrics of different fineness but of the same characteristics. Consequently, the third combination is the most important one, for it represents average knitting conditions, whereas combina- tions 1 and 2, which range from the extreme of impracticability [Of operation to that of instability of fabric, represent abnormal [conditions generally and average conditions only between the limits of the range. However, their consideration is necessary in order to understand the subject. Stitches per Foot Constant and Yam Diameter Varied. {The 'first case.) — It is found by experiment that when the stitch is kept constant and the diameter of the yarn is varied, the courses^ and iwales per unit of length change so that their product is a con- stant quantity. For instance, suppose that at a certain stitch and with a certain yarn the wales and courses are each 10 per inch. Then the product of the wales and courses is 100. If now the size of the yarn fs either increased or diminished, the prod- uct of the courses and wales will still remain 100. But it has already been shown that the width of the wale changes in pro- portion to the diameter of the yarn, from which it is possible to determine the change in the wales, after which the change in the courses may be determined by dividing the number of wales per inch into the constant product of the wales and the courses. Suppose that the yarn is increased in diameter 10 per cent. Then the width of the wale will also be increased 10 per cent. Relation of Wales and Courses. — Consequently, the number of wales per inch after the change will be 10 divided by 1.1, which is 9.09. Now divide 100, the constant product, by 9.09, the new Inumber of wales, which gives 11, the new number of courses. JThis relation may be represented graphically as in Illustration 5, I which shows a piece of cross-section paper with courses laid off on the left scale upward from the zero at the lower left comer, and wales laid off at the bottom from the same starting point toward the right. A horizontal line from the 10-course mark 28 The Science of Knitting meets a vertical line from the 10-wale mark, making a square in the lower left corner of the paper, and a curve passes through the upper right corner of the square. This curve contains the intersections of all of the hues whose product is 100. The points in it are found by assuming different numbers of wales and divid- ing them into 100 to get the corresponding courses. After the la n "^ \ s V \ N \ It) s N S V,, s s 8 S > c< jur ses pe rii ict 6 5 i. S> 1 2 1 W de 3P ;r Inc 1 L 10 11 12 13 U Illustration 5. All rectangles with one corner at zero and the diagonally opposite corner in the curve contain the same number of stitches. This is the case with knit fabric when only the size of the j'arn is changed. That is to say, for fabris from any machine, when only the yarn size is changed, the number of stitches per unit of area remains constant. In other words, changing only the yarn size makes no change in the number of stitches per square inch. curve is obtained, when the number of courses (or wales) is known, the corresponding number of wales (or courses) is readily- found by following the known number out to the curve and then j reading the desired number from the other scale For instance, . it has just been determined that after an increase in the diam- eter of the yarn of 10 per cent the number of wales per inch has Elements of Knitting 29 changed from 10 to 9.09. Start from 9.09 wales and follow the dotted line out to the curve and then to the left to the course scale which it intersects at 11, the corresponding number of courses. Product of Wales and Courses Dependent on Stitches per Foot of Yam. — It should be borne in mind that this curve holds only for one set of conditions of not only stitch but kind of yarn and machine. Change in any of these factors moves the curve toward or from the origin (the zero), but does not alter its form. For instance, if the stitch is made tighter — that is, if the number of stitches per foot is increased — then the curve will be moved farther to the right and upward, but it wall be obtainable in the same way, namely, by dividing the constant product of wales and courses by the number of wales, which number is obtainable from the diameter of the yarn, and then marking the intersections of the corresponding wales and courses. The constant product is so far best obtained by experiment with the machine and the kind of yarn in question. Diameter of Yam and Stitches per Foot of Yam Determine Characteristics of Fabric for any one Kind of Yam. — It should be explained here that theoretically the machine has nothing to do wuth these considerations, but it has become so common to consider the dimensions of the fabric, i.e., wales, courses, etc., dependent on the machine, that confusion is likely to result from, a sudden departure from that idea. A little reflection wull show at once how erroneous the idea is. Hand knitting preceded machine knitting, and with hand needles there was not — nor is to-day — any such thing as needle spacing, consequently, there is no such thing as cut or gauge, and yet a big variety of yarn numbers and lengths of stitch were and are usable with hand knitting. This was evidently forgotten when machine knitting became common; and from the fact that a certain degree of fine- ness of fabric came from a certain degree of fineness of machine, the notion became popular that the cut of the machine deter- mined the fineness of the fabric. This notion really has its foundation in the limitations of the machine rather than in its adaptation to any particular work. It is possible to conceive of an infinitely fine, but infinitely strong, needle drawing a very long loop in a very large roving, which roving would determine the width of the loop entirely independent of the needle. However, in practice there are no infinitely strong needles, so we do not 30 The Science of Knitting meet such ideal machines. Consequently the diameter of the yarn has to be proportional to the needle spacing, from which has come the mistaken conclusion that the spacing of the needles determines the fineness of the fabric, whereas it is really deter- t mined by the diameter of the yarn. 1 s ^ _. _ 1 '' V ~^ s ~ 1 1 \ ~" \ ~ — 1 s ~ s ~ ~ ,() ^ ■~ ■ N >, ~ ~ 8 i arc ,s ^ V — « ~ ,7 — 1 .6 \ r"" ~ n ~ ~ ~ ,4 ~~ ~ ~ — ~ ~ ,s "~ .s ~ ~ ,1 1 Ya rds 1 1 1 1 J ~ ~ ~ .1 .2 .3 •i .5 .« 7 .8 <) 1 f) 1 1 1 ■> 1 ■? Illustration 6. All rectangles with one corner at zero and the diagonally opposite corner in the curve have the same area. These rectangles represent the changes which take place in the fabric for changes in the diameter of the yarn, but no change in the number of needles, number of knitted courses, and number of stitches per foot of yarn. In other words, on a certain number of needles with a fi^ed length of loop, knit a certain number of courses with different sized yarn and every resulting piece of fabric will just fit under a curve of this character. Relation of Width and Height of a given Piece of Fabric. — The relation of the wales and courses for stitches constant and yarn variable was shown on page 28. The relation of the width and height of a given piece of knit fabric for the same conditions may be similarly shown. Suppose that a piece of fabric is knit so Elements of Knitting 31 ;hat it is just one yard square. Moreover, suppose that the only ihange to be made is in the diameter of the yarn. Illustration 6 ihows a chart similar to Illustration 5, except laid off on both 5cales in yards and tenths of yards. The square enclosed by the jcale lines and the two lines drawn from 1 to the curve represents ihe square yard of cloth just mentioned. The curve is so drawn :hat it will contain the upper right corner of all rectangles whose Area is one. Now make another piece of cloth the same as before, 3ut with yarn 10 per cent larger in diameter. Since all conditions jxcept the size of the yarn are the same, there will be the former iotal number of wales and courses. It is known that t.he wales A^ill be wider in proportion to the increased diameter of the yarn, 30 this piece of fabric will be 1.1 yards in width. The height baay be obtained by working through the wales and courses. The lew number of wales per inch will be in the proportion of — = ).909. Consequently, the new number of courses per inch will 3e in the proportion of ■ = 1.10. But since the number of u.yoy ) jourses is not changed, the height of the fabric will be 1 yard X ~ = 0.909. The product of the width, 1.10, and the height, ).909, is 1, consequently the piece of fabric will still contain one ;quare yard, so that when it is drawn on the chart, its upper right ;omer will be in the curve as shown by the dotted lines. Com- paring the wale and course chart, 5, with the square yard chart, ), the observer sees that one is the reverse of the other, but that n each case the product of the dimensions is a constant. Production in Square Yards. — From the above it follows that vhen the stitch is constant and the yarn is variable, the product Df the width and the height of a piece of fabric (with the same lumber of stitches) is constant. Therefore, the production in iquare yards of a knitting machine with stitches constant is inde- oendent of the yarn, for what is gained in width by the use of arger yarn is lost in length by the drawing together of the :;ourses. Moreover, a square yard contains a constant length of yarn. Length of Yam in a Square Yard of Fabric. — From the above, and since the (cotton) number of yarn is inversely proportional to the weight of a constant length, the weight per square yard goes jp as the number of the yarn goes down, i.e., the product of the sveight per square yard and the number of the yarn is a constant. 32 The Science of Knitting Proportioning "Weight per Square Yard and per Dozen Gar- ments. — When it is desired to change the weight of piece fabric per yard, or goods per dozen, the change of yarn may be calcu- lated by the simple rule Present weight X present yarn -h desired weight = desired yarn. However, with garments care must be exercised to cut the same number of yards, which means that if the size of the yarn ia increased, the sizes must be cut from smaller diameters of ma- chine. It must be remembered, also, that the characteristics of the fabric will be changed, since the same characteristics are obtained only when the length of yarn in the stitch is proportional to the diameter of the yarn, which is the same as to say that the product of the diameter of the yarn and the stitches per foot of yarn is a constant. Diameter of Yarn Constant, Stitches per Foot of Yarn Varied. — The Second Case. Experiments show that the courses vary in some proportion to the stitches per foot, that is to say, as the stitches per foot are increased the courses increase. The wales, of course, remain constant. Therefore, the weight per yard is increased, but not in the proportion in which the courses are increased, because the increase in the stitches per foot lessens the length of yarn in a course. Consequently the increase in weight per yard is a slow differential between the gain in weight due to increased courses and the loss due to decreased length of yarn in a course. No simple expression for this change in weight has yet been found. Regular Fabrics. — The Third Case, that in which the product of the stitches per foot and the diameter of the yarn is constant, is illustrated, regarding the wales, courses and stitches by Illustration 7, with wales on the left scale and courses on the bottom scale. Several curves representing the constant prod- ucts of wales and courses for different stitches are shown. The 45-degree diagonal drawn through the origin upward to the right is the dividing line for wales equal to courses. It will be noticed that as the wales increase the courses increase equally, but the stitches per foot must increase also. This fabric is looser than is generally considered desirable in America, where the courses and wales are in the proportion of about 12.5 to 10, which pro- portion is used in this book. The line representing it is just below the diagonal. However, the selection of any proportion Elements of Knitting 33 s largely a matter of choice. The main fact is that for corre- ponding fabrics the stitch must be proportional throughout, rhis simple condition makes possible the use of a remarkable lumber of simple equations which are useful for showing not only "1 ( 1" 1 2 isfe4- X^ .^'^''^ V. ^Z y ,.:^bet?"3oU^ iSgl --IjhLZ y^ ; "X£^^?tfopv ^ ^ ^^\z ^^ ' '^'^ ■^' zt "^ % % rtf^z 4^ ^ Jl ^^ ^ ^ ^ o%»:^ \?^^/ ■ ^a?? L -5 V \-^! y ,%-* ^'^ ife s 3^ s -t -S^ ^^ ^ V J ^ ^^ ^ ^ ^;?^^ ^ 'a: ^t k. ^^ ^^ s^z NW/ '^ X 5 ^ ^ ::^^ s>^ 'lri_ ^ b- !^ ^ ^Z Nj, ^^1^ '^ ~L. ^ ^v^ \7 ^^^ ^^ ' < '-4 5 ^ / !S>_ -^ '^ Sv ifc ^^ '"lal^ t 5 V^ >v "^"a ^^ ^'^ ■Mfo k ^. /\ >- ^^ N, >*> '('"'•^ \. ^7 ZK 7 s ' s. .^ "^^v 'vitd 5 '^^zir .^. "■ ■ "^.vo :>i^ i^'^-s ^ li "^ ^ ^^ >' ^v V ^- '^ v^ *(iji>< A y ^ ■^' ^tv I^5> •^'H; ~T7 y^ ^^G^ W-J, v>'c^ !' '• z ^7 ^v ^2:^ ^^^ .. i>^rv^ ' 7 y ^ -^^ "^Ji •t*;<>^ I Z 7 ,.^'^>^ it -T ""3^^%* A/ <.<€'^ ^^ 'io^y !_ 7 .'^ ,«Vj> ■^^^w ,1.6- 'oJ— ' 7 >^ 1^'' ^-=o5it7~i?i,>y' ' 7a^^-'^^ *> o^ ^ I 77\Wr' * IZ7 :;:' IT IT X ^ TZZ^ -Ht--+^ ^ ^ IT X - H '^± ,.T^ I^ ^ +.._ 11 6 « I 8 » lull 12 IJH 15 10 tilt) 19 2U^1'J::;:j 24 '.'^20 27 28 ^'JW;11;>;j;M 44 »j;i6 37 48 ;<'J 40 414^43 41 4^46 47 «• Courses Illustration 7. vhart. showing the relation of wales, courses, and stitches in fabrics of the same characteristics, rhe wales per inch increase as the diameter of the yarn decreases, rhe courses per inch are proportional to the wales per inch, rhe stitches per foot of yarn are proportional to the wales per inch. ihe proportionate results of a change, but also the concrete re- mits, so that knitting moves from a rule-of-thumb stage — rather a. no-rule stage — to one of comparative certainty. Elsewhere are yiven fairly complete sets of rules showing the relations of all of the ordinary dimensions used in knitting. They are based on the 34 The Science of Knitting principles just explained and on constants derived from measure- ment of some 200 samples of ribbed fabric made of carded mule- spun hosiery yarn. Among the important rib-fabric relations may be noted here the following, although the reader is referred to page 36 which gives the conditions on which the relations are based, and to pages 38 and 39 which give enough relations for ordinary requirements. Some Relations of Regular Rib Fabrics. — Cut of machine = ^ -_ t^. j 8.57 Dia. oi yarn Stitches per foot of yam = ^ ^ . t^. ? • 2.14 Dia. of yarn Courses per inch = „ , „ . j . 3.2 Dia- OI yarn Wt. per square yard = 38 Dia. of yarn. Production, pounds per feed per 10 hours = 57,772 (Dia. of yarn.)^. Production, square yards per feed, per 10 hours = 1520 Dia. of yarn. PRACTICAL VARIATIONS FROM KNITTING RULES It is unnecessary to tell knitters that knitting is not an exact science. They know this so well that they have become ex- tremists on the subject, so that they are inclined to discredit all rules. Consequently, before a rule receives practical considera- tion it is necessary for the sponsor to proclaim that he knows there are exceptions to it in spite of the adage that there are exceptions to all rules. So the practical variations which follow are mentioned with the double object of meeting the above necessity and of pointing out where exceptions may be most expected . The Shape of Yam. — Yarn is supposed to be round; but it may be almost any other shape, except angular or absolutely flat. Soft yarn is frequently preferable for knitting, and the softness is usually obtained by slack twist; so that instead of a compact cylindrical mass like that of six-cord thread, the yarn consists of a bundle of fibers slackly twisted together and easily susceptible to pressure distortions. However, the general form is cylindrical, and the. fabric formed from it corresponds closely to what is expected from cylindrical elements, so it is permissible to consider the yarn cylindrical, if allowances are made for dis- tortion from the cylindrical form. This distortion is practically Practical Variations from Knitting Rules 35 proportional for similar conditions. For instance, suppose that owing to compression the width of a fabric is 10 per cent less than that calculated on the assumption that the thread is cylindrical. Then that proportion, 10 per cent less, is appli- cable to fabrics on other cuts made of the same kind of yarn with a stitch proportional to the diameter of the yarn. In I other words, results based on cylindrical yarn are valuable as ' proportions, even when distortion of the yarn prevents use of the absolute values, provided the distortion is caused by simi- lar conditions. Resilience or Resistance to Bending. — The structure of the knit stitch depends on resistance to bending, the force of which keeps the wales together in normal fabrics. Evidently this I for(« depends on the kind and condition of the fiber, the twist , of the yarn and other factors. Also, it depends on the curva- I ture to which the yarn is subjected. An abrupt curve is re- sisted more than an easy one. The normal knitting curve has a radius of approximately 1^ diameters of yarn. If the loop is so long that this radius is much increased, there will nbt be I enough force to hold the loops closed, so that the width will increase rapidly, the elasticity will decrease and the fabric wiU become shapeless. At the other extreme of stitch, that is very tight, the curvature is shortened by lengthwise ten- ' sion on the yarn which hugs the loops together, and nar- rows the fabric so that the loops lose theii' natural easy curves. The rules are not intended to apply to such fab- rics, since they are so " sleazy " on the one hand and so " boardy " on the other that they comprise an insignificant part of knitting. Most yarn used in knitting is susceptible of a sufficiently short bend to bring the wales together, but it can be realized that spring wire would not take such a bend, and that yarn of a wiry nature would take a bend between that of wire and that of soft cotton yarn. Accordingly, it is to be expected that ! fabrics made from wiry yarn will be wider than those made from the same size of soft cotton yarn. Sizing, dyeing, bleaching — in short, treatment of almost any kind — alters the bending property of yarn, so that allowance should be made therefor, when acciu-acy is required. Stitch Distortion. — The popular impression is that the machine forms the stitch somewhat as a die forms a coin. But, 36 The Science of Knitting ideally, the machine should draw through each other, loops of a proper length depending on the diameter of the yarn, and leave those loops to take the form dictated by their elasticity In actual practice there exists a wide range of stitches, from the j ideal to those pulled far out of shape. This distortion may be caused by excessive take-up tension, by too tight a stitch for the yarn and cut, by improper clearing of the loops, etc. Some of these distortions are quite permanent, such as the widening of the fabric by a spread dial stitch; whereas others are not, such as the narrowing due to take-up tension, which narrowing dis- appears more or less quickly, according to the treatment to which the fabric is subjected after knitting. There are other causes which make the actual results differ from the rules and for which allowance must be made when unusual accuracy is required. But knitting is no exception in this regard. Excepting mathematics, no science is exact, and knitting occupies an intermediate ground among the sciences (or scientific arts), since it is not so exact as some but more exact than others. Moreover, it will improve in exactness since the relations of cause and effect of these disturbing factors may be determined just as the general principles of knitting have been determined, so that rules may be made for the proper allowance under given conditions. I EXPLANATION OF FORMULAS FOR REGULAR RIB FABRICS These formulas are based on the following relations : Yarn number = • 6 Stitches per foot of yarn = 4 Cut. Yarn diameter 1 21 VNo. Courses -r- Wales = 1.25. Tensile strength of thread = 6000 (diameter) .2 Diametral revolutions per minute = 700 (35 r. p.m. of a 20-inch cyl). This table is meant for the practical knitter, so the explana- tion is addressed especially to him. Explanation of Formulas for Regular Rib Fabrics 37 The extreme left-hand column, No. 1, gives details of rib fabric about which the knitter should have definite knowledge. The other columns contain simple equations which give that knowledge expressed in as many different ways as the knitter may need, and many more than are ordinarily necessary. There- fore, it is essential that he should know which are the most im- f portant. A brief review of some of them will help him to decide. ( Consider first the column headed ^ Coils (No. 2) which means the number of close coils of yarn per half inch, such as it is > recommended to practice getting by coiling the yarn on a watch- chain bar. The importance of learning this simple method of determining the size of yarn should be understood. If a geolo- gist is given a little piece of rock he is supposed to be able to tell what it is and what can be done with it without asking a lot of questions about it. But if the knitter is given a piece of yarn, he has to ask what number it is, or ask for a larger piece and a yard stick (or reel) and scales before he can do anything ; but guess about it, and even after he does know the number, he I is more learned than . the average knitter if he can tell ,what fabric knit from it will look like, how much it will weigh per yard, how many pounds and square yards can be produced per day, etc. This |-Coil column puts all this information right I into his hands, provided he puts the formulas into practice, for it takes practice^ to use formulas accurately, just as it does to shoot on the wing accurately. The knitter who does not use his formulas before he needs them will not make a better showing than the hunter who has not yet fired ofT his gun. It is hoped that every knitter who is interested will get a note book, put in it the |-Coil column (No. 2) and the No. column (No. 5) and put them to the test by coiling a piece of the yarn he is knitting, working out the results by the formulas and then comparing the theoretical results with the actual results. Only in this way can he learn one of the most important things about a practical formula, that is, the allowance to make in using it. One or two trials are not sufficient. Many are needed, but whoever makes them will be well repaid, for he can thereby get in a few days a fund of extremely useful knowledge much of which has heretofore been unavailable, and the balance of which has been obtainable only by years of experience. The following explanations may be of use. They are given in order, starting at the head of the f-Coil colunm (No. 2). The first two equations are self evident. 38 The Science of Knitting FORMULAS FOR 1 h Coils Coils Dia. No. Cut Stitches per foot of yarn Wales per in. Courses per in. Wt. per sq. yd. §1 Lbs. Its Sq. ^M Yds. Tensile strength along wales, pounds per inch width, T Tensile strength along courses, pounds per inch width, t 2 § Coils 3 Coils 4 Dia. 5 No, 6 Cut 7 Stitches per ft. of yarn h Coils Coils 2 1 2 Dia. 10.5 VNo. 4.2865 Cut 1.0716 S. 2x1 Coils Coils 1 Dia. 21 v^No. 8.573 Cut 2.1433 S. 1 1 Coils Dia. 1 1 1 2x1 Coils 21 ^No. 8.573 Cut 2.1433 S. (h Coils)2 110.25 Coils2 441 1 441 Dia.2 No. Cut2 6 Stitches^ 96 ^ Coils 4.2865 Coils 8.573 1 2.4495 v^No. Cut Stitches 4 8.573Dia. i Coils 1.0716 h Coils 2 Coils 2.1431 1 9.798 VNo. 4 Cut Stitches 2.14325 Dia Coils 4 1 4 Dia. 5.25 VNo. 2.1431Cut Stitches 1.866 § Coils 1.6 Coils 3.2 1 6.5625 V No. 2.679 Cut Stitches 1.4932 3.2 Dia. 18.987 i Coils 37.98 Coils 37.98 Dia. 1.808 VNo. 4.43 Cut 17.72 Stitches 14,443 57,772 Coils2 57,772 Dia.2 131 No. 786 Cut2 12,576 Stitches2 (i Coils)2 760.1 h Coils 1520.2 Coils 1520.2 Dia. 72.39 VNo. 177.31 Cut 709.241 Stitches 3000 k Coils 6000 -Coils 6000 Dia. 285.7 699.8 Cut 2799 Stitches 937.5 i Coils 1875 Coils 1875 Dia. 89.29 Vno. • 218.7 Cut 874.7 Stitches The quantities at the left of the table are Explanation of Formulas for Regular Rib Fabrics 39 EGULAR RIB FABRICS 8 9 Courses per inch 10 Wt. per yd. 11 12 Production, 1 feed, 10 hours Tensile strength along wales, pounds per inch width, T Tensile strength along j courses, 1 pounds per inch width, t Wales per inch Pounds Sq. yds. 2 Wales 1.6 Courses 18.987 120.17 760.1 Sq. yds. 3000 T 937.5 t Wt. sq. yd. V Pounds 4 Wales 3.2 Courses 37.98 240.36 1520.2 Sq. yds. 6000 T 1875 t Wt. sq. yd. V Pounds 1 Wt. sq. yd. 37.98 Sq. yds. 1520.2 T 6000 t 1875 1 V Pounds 4 Wales 3.2 Courses 240.36 Wales2 27.~56 Course 52 43.06 3.269 131 Pounds 5240 81,625 rp2 7973 i2 (Wt. per j'd.)2 (Sq.yds.)2 Wales 2.1431 Courses 2.679 4.43 28.035 177.31 Sq. yds. 699.8 T 218.7 t Wt. per yd. V Pounds ..866 Wales 1.4932 Courses 17.72 112.14 709.24 Sq. yds. 2799 T 874.7 H Wt. per yd. "^ Pounds Wales Courses 1.25 9.495 60.08 380.05 Sq. yds. 1500 T 468.75 t Wt. per yd. V Pounds 1.25 Wales Courses 11.868 75.105 475 1875 T 585.9 t Wt. per j'd. ^ Pounds Sq. yds. 9.495 Wales 11.868 Courses Wt. Sq. yds. 40.04 T 157.9 t 49.34 ■^ Pounds 6.3305 3610 Wales2 5641 Courses^ 40.075 Wt.2 Pounds (Sq.yds.)2 623.48 <2 60.92 40.04 380.05 Wales 475 Courses 40.04 Wt. 6.3245 V P Yds. T 3.947 T t 1.2335 1500 Wales 1875 Courses 157.9 Wt. 24.97 v'p 3.947 Sq. yds. 3.2 ( 468.75 Wales 585.9 Courses 49.34 Wt. 7.804 Vp 1.2335 X Sq. yds. T 3.2 t , J spr&ssed in terms of those at the top. 40 The Science of Knitting <^C20000000000000000000000000000 9 o «> ■ 02 A^ »CCOOOOOOC005t^0005C^100->*HT-< r- •* «o o CO oi iM o> r^ ■* o „, » ^. „-. -,^-,. „ ^^ ,-, -*io«icoooo«oot^eoooeooo»oooort.t>-«o-^oco 5^00I>'COlO'— IC505t:^CCt>"T-lt^(M00iOC.0-^-^OOC:'>-lOTt<0-105.-<«5OOOt^COt^t^OOCOOOt^OO>-i OCO— iO0500t^';OCDlO'«tl-^C0CCC— Ci— II— I OOt^CO«0';OiOiOlOiO-*->tlTj(M*< 1--. oc r- <» ' ( t-^ (>? •"^ •<*< Tj* -Tf lO to o So 2 3 j2^ 3 .^ iO-HOO»Ocot^t:^«Sl^iOM<-*r^eo>ocDi— i-«5iO-«*l001C30CCiC^Cl-^05iOC^CSOOOOC2COr-C^t— (N05iOC^Cl«OCC»-l051r^»OCO»-l0500<:OiO-^C>J'— I T-(05t^CC''OiO-^irOCC(MC-lT-(.-i^^000003Ci05050500aOOOOOOOOOC30 CS|,_,rtT-<7-c^rt^.-irt^^rti-i.-->OCS100-5f'05COt— CJCOOO >-(C0'*T»<»O->*<«DCOiO»i5'^C0C*l«00I^00t-~»0'— I C*-00 (MC>!T''^>o'0»0"5»o»c»cio»o«5 Explanation of Formulas for Regular Rib Fabrics 41 Diameter of Yam. — This is useful to know, although it is not expected that the practical knitter will do much calcu- lating with the diameter, since the coils per half inch are more convenient. Nimiber of Yam. — This is very important, but the user should remember that it does not always give the exact number which is obtained by weighing. Of what use is it then? Of much more use than the regular number, which is of use prin- cipally for the pounds production and pounds per yard, whereas the number determined by the diameter is the one which con- cerns the running of the machine, the wales, the courses, the width of the fabric, and the square-yard production, all of which are of far more importance to the knitter than the others. Count the coils in half an inch, multiply them together, and divide by 110. The quotient is the cotton number of the yarn. Do not worry about the decimal point, for experience will show whether the yarn is 2, 20, or 200. Practice by taking one short piece of yarn and coiling it several times to see what the average error is. One coil in twenty, over or under, is not enough to worry about. Some yarns cannot be coiled satisfactorily, such as thrown silk and very loosely-twisted worsted. But probably 95 per cent of the yarns used can be satisfactorily coiled, so the method should not be abandoned on account of its hmitations until a superior one is found. Notice that in the above calculation which gives the final result, a covenient approximation to the exact constant is used, namely, 110 instead of 110.25, which practice should be followed in every such case. But when these formulas are used for the derivation of other formulas the exact constants should be used in order to avoid discrepancies between the derived formulas. Cut. — The correct cut (needles per inch) for a given yarn is a very important question in knitting. Formerly, before it could be answered at all, the number of the yarn had to be known, and not only that, but it had to be expressed in the yarn count with which the knitter was familiar. Then he could give an idea of the cut on which to use it in the light of his experience, but if the yarn did not happen to be just the number which he had used, he was very likely to misjudge since the number of yarn is very misleading as to its size. What knitter is there, who in order to find the relative size of two yarns, would go to the trouble of extracting the square roots of 42 The Science of Knitting the numbers and comparing the reciprocals of the square roots? Not one in a hundred. Yet that is the simplest way of com- paring the sizes of yarns. No wonder that the knitter in his search for simplicity should get the erroneous notion that the cut should be proportional to the yarn number. This seems reasonable, since the yarn gets finer as the number increases. But it has made trouble for lots of knitters who have tried to follow it, since when the user counted that in going from a No. 10 to a No. 40 he was getting yarn only one-fourth as large, in reality, it was half as large, and was breaking needles to an extent not indicated by the rule. But here is a rule — cut from ^ coils — which makes the yarn diameter proportional to the size of the spaces through which the yarn has to go, which rep- resents good average practice, and which is applicable without yarn numbers at all, provided a little piece of the yarn is at hand. It frequently happens that a knitter is shown a sample of yarn too small to reel and is asked if it is adaptable to his machines. Here is a method of answering the question quickly and decisively. Divide the coils in half an inch by 4.29 and the quotient is the cut which is generally used for knitting such yarn economically. Stitches. — The stitches per foot of yarn, although not much used, are important and sometimes indispensable. A knitter is told to start some machines and having done so is criticized for not having used a different length of stitch. Probably neither he nor his critics were at fault, but each had been brought up to a different standard of fabric. Here, however, is a standard based on sufficiently wide observation to make it defensible. Of course, after the machines are started and it is decided what kind of fabric is required for the particular con- ditions, the stitch should be changed accordingly, but in the absence of special orders the knitter should have good reasons for what he does. Not only this rule for the stitches per foot but the other rules as well, are useful as a basis of understand- ing between the knitter and his superior. It is not essential that either agrees to the constants used. Indeed, it is expected that the rules will be modified to meet the local requirements, but in their present shape they mark a line from which an agreed departure may be made. One cause of serious confusion in the knitting business has been this lack of a common ground for understanding between a knitter from one section of the Explanation of Formulas for Regular Rib Fabrics 43 country and a superintendent from another, so that the knitter frequently had to go back where he came from. Wales per Inch. — These are useful in determining what the fabric will look like, since the fineness of fabric is considered to be represented by the wales per inch. The wales are practically independent of the stitches and of the cut. Courses per Inch. — These depend on both the diameter of the yarn and on the stitches per foot, with the result that they are not subject to very close calculation, since a httle error in the yarn diameter or in the stitches per foot of yarn makes a considerable change m the courses. However, it is sometimes desirable to be able to tell what number of courses to expect. Weight per Yard. — This is seldom used, except in the piece- goods business, probably because the means of obtaining it have been inconvenient. However, the tables and rules given in this book remove much of the difficulty, so there is now no good reason for not giving the weight per yard the attention which it deserves. It is useful in determining how many square ^ards make up a dozen of goods, and after that in determining the change in weight per dozen resulting from a change in weight per yard. Regular rib fabric made of No. 13 yarn (38 coils per !ialf inch) weighs about half a pound to the square yard, as the equation shows (18.987 -^ coils per one-half inch). Suppose it is pade into garments weighing 7 pounds to the dozen. Unless f.he trimming is unusually heavy, it may be neglected. Then jor the purposes of the mill, one dozen of the goods contains I' H- 0.50 = 14 square yards of fabric. Now, suppose the mill j;an buy at a bargain a lot of yarn coiling 36 to the half mch, ibout one number heavier; 19 ^ 36 = 0.53, the weight per quare yard, which multipHed by 14 equals 7.42, which shows hat if this yarn is used it will make the goods nearly half a •ound per dozen heavier, provided the regular stitch is used. Stitches = ^ Coils -^ 1.07.) Many other problems Hke this, .'hich should be calculated instead of guessed, may be cal- ulated by the use of the simple rule for the weight of regular ib fabrics. Production in Pounds per Ten Hours per Feed. — This is an xtremely useful formula, since the ordinary method of working ut production is too laborious for a busy knitter, yet he is ■equently asked how many pounds per day can be produced 44 The Science of Knitting with yarn like a given sample. Divide 14,443 by the coils in half an inch squared; or divide 14,443 by the coils in half an inch and then divide the quotient by them again. Suppose there are 30 coils per half inch. The square of 30 is 900. The quotient of 14,443 -i- 900 is 16, the pounds production per feed per 10 hours actual running time. The other calcu- lation is 14,443 4- 30 = 4814, and divided by 30 again, equals 16. There is no allowance for lost time, but none need be made if the user knows that his machines are running somewhat above the expected 700 diametral revolutions per minute. If they are running around 770, a lost time allowance of 10 per cent is made by increased speed, so 16 pounds per feed may be taken as final. On the other hand, if the knitter wants to get the production down fine, he may get the exact lost time and the exact diametral revolutions and correct the 16 pounds per feed by the methods explained elsewhere. To be very exact he should use the production derived from the number of the yarn, Column 5, because the number is more reUable when weight is concerned, whereas the coils are more reliable when size is concerned. The pounds-production formula is a good one to try on skep- tics. Almost every one knows that rules are of different degrees of reliability. For instance, weather forecasts frequently go wrong, but the rule that every one must die is quite reliable. So it is with knitting rules. The rule for the number of courses per inch may go wide of the mark, but the pounds-production rule is absolute (provided no mistake has been made in its derivation). It is amusing, therefore, to hear some knitter remark, " Well, I tried that production rule, and it was wrong, just as I thought it would be." That is, the calculated and actual results disagreed, so the natural conclusion was that the rule must be wrong. But the rule is absolute, so the assumed factors were wrong. In other words, the experimenter did not get the speed, the yarn number, the stitch, and the time with the accuracy which he expected of the rule, so he jumped at the conclusion that the rule was wrong, thereby confessing his own error. If such mistakes are made in the use of absolute rules, they may also be made in the use of the rules which are admittedly approximate, so that these rules may be made to ap- pear less reliable than they really are. Explanation of Regular Flat-fabric Formulas. — Loop-wheel 45 Square Yards Production. — This is sometimes called for, so the mitter should be prepared to give it, although it is much less ised than the pounds production. Government contracts sometimes specify tensile strength. For 'sxplanation of the strength formulas see Theory of Knit Fabrics. Column No. 3 gives the quantities just discussed in terms of he coils per inch for use in calculations, but the knitter need iot trouble with these since the coils per half inch are more convenient for him. Column No. 4 is also for theoretical calculations more than or practical problems. Column No. 5 is nearly or quite as necessary as Column S^o. 2, since the knitter should be able to know what he can do vith yarn which he has not seen, as well as with yarn of which le has a sample, provided, of course, that the twist or the ma- erial does not make it unsuitable for knitting. This column ;ives what Column No. 2 does but in terms of the yarn number, rhe remarks already made apply to this column, so it is not lecessary to repeat them. The other columns are useful to the investigator, analyst, md designer more than to the practical knitter, so he need not rouble with them, although in casually' reading them over he bay see one or more expressions adapted to his special require- Qents. DXPLANATION OF REGULAR FLAT-FABRIC FORMULAS.— LOOP- WHEEL These formulas are based on the following: Yarn number = ^^^ ■ . 40 Stitches per foot = 3.0983 Gauge. Yarn diameter 1 21 VNo. Courses 4- Wales =1.25. Tensile strength of thread = 6000 Dia^. Diametral revolutions per minute = 1000 (50 r.p.m. of a 20- inch cyl.) Fifty revolutions per minute of a 20-inch cylinder is lower peed than is used in many places, but since wool work and fine Formulas. — Loop-wheel 1 2 h Coils 3 Coils 4 Dia. 5 No. 6 Cut 7 Gauge i Coils Coils Dia. No. Cut Gauge Stitches Wales per in. Courses per in. Wt. per sq. yd. Pounds per 10 hrs. per feed Sq. yds. per 10 hrs. per feed Tensile strength along wales, pounds per inch width, T Tensile strength along courses, pounds per inch width, t \ Coils Coils 2 1 2 Dia. 10.5 Vno. 2.49 Cut 1.66 Ga. 2Xh Coils Coils 1 Dia. 21 VNq. 4.98 Cut 3.32 Ga. 1 1 Dia. 1 1 1 2X§ Coils Coils 21 VNo. 4.98 Cut 3.32 Ga. (1 Coils)2 110.25 Coils2 441 1 No. Cut2 17.78 Ga.2 40 441 Dia.2 i Coils 2.49 Coils 4.98 1 4.2165 VNo. Cut 1 Gauge 4.98 Dia. h Coils 1.66 Coils 3.32 1 6.3245 VNo. f Cut Gauge 3.32 Dia. § Coils .5358 Coils 1.0716 1 19.596 VNo. 4.6475 Cut 3.0983 Ga. 1.0716 Dia. 1 Coils 2 Coils 4 1 5.25 VNo. 1.245 Cut Gauge 1.2047 4 Dia. \ Coils 1.6 Coils 3.2 1 6.5625 Vno. 1.5563 Cut 1.0375 Ga. 3.2 Dia. 9.494 1 Coils 18.987 Coils 18.987 Dia. .904 VNo. 3.813 Cut 5.717 Ga. 17,755 (i Coils)2 71,020 Coils2 71,020 X Dia.2 161 No. 2862 Cut2 6440 Ga.2 1869 h Coils 3738 Coils 3738 Dia. 178 Vn^. 750.6 Cut 1125.9 Ga. 1500 ' i Coils 3000 Coils 3000 Dia. 142.86 VNo. 602.35 Cut 903.6 Ga. 937.5 h Coils 1875 Coils 1875 Dia. 89.29 VNo. 376.7 Cut 565 Ga. (46) The quantities at the left of the table dar Flat Fabrics 8 Stitches 1 9 Wales per in. 10 Courses per in. 11 Wt. per sq. yd. 12 Pounds per 10 hrs. per feed Sq. yds. per 10 hrs. per feed Tensile strength along wales, pounds per in. width, T Tensile strength along courses, pounds per in. width, t 58 Stitches 2 Wales 1.6 Courses 9.494 Wt. 133.25 1869 Sq. yds. 1500 T 937.5 t V Pounds 16 Stitches 4 Wales 3.2 Courses 18.987 Wt. 266.5 3738 Sq. yds. 3000 T 1875 t ^/Pounds 1 1 1 Wt. 18.987 Sq. yds. 3738 T 3000 t 1875 "^/Pounds 266.5 16 Stitches 4 Wales 3.2 Courses 3titche32 384 Wales2 27.56 Courses"^ 43.06 .81725 Wt.2 161 Pounds 31.684 20,411 y2 7970 (Sq. yds.)2 Stitches Wales 1.245 Courses 1.5563 3.813 Wt. 53.543 750.6 Sq. yds. 602.35 T 376.7 t 4.647.5 ^Pounds Stitches 1.2047 X Wales Courses 1.0375 5.717 Wt. 80.26 1125.9 Sq. yds. 903.6 T 565 t 3.0983 V Pounds Stitches 3.7325 X Wales 2.986 -X Courses 17.72 Wt. 248.7 3490 Sq. yds. 2799.5 T ^ 1749.6 t v'Pounds Stitches 3.7325 Wales Courses 1.25 4.747 Wt. 66.62 934.5 Sq. yds. 750 T 937.5 T 468.75 t V Pounds Stitches 1.25 X Wales Coufses 5.94 Wt. 83.27 1168.1 Sq. yds. 586 t 2.986 VPounds 17.72 4.747 Wales 5.94 Courses Wt. sq. yd. 196.85 Sq. yds. T 157.89 t 98.75 ^Pounds 14.036 Stitches 61,839 4438 Wales2 6935 Courses^ 197.06 Wt.2 Pounds (Sq. yds.)2 127.23 <2 49.57 5titches2 196.9 3490 934.5 Wales 1168.1 Courses 196.85 Wt. 14.032 X v^Pounds Sq. yds. 1.246 T 1.99 f Stitches 2799.5 750 Wales 937.5 Courses 157.89 Wt. 11.26 X v'Pounds Sq. yds. 1.246 T 1.6 « Stitches 1749.6 468.75 Wales 586 Courses 98.75 Wt. 7.038 X v^Pounds Sq. yds. 1.99 T 1.6 t Stitches jxpressed in terms of those at the top. (47) 48 The Science of Knitting Thick- ness. oooooooooooooooooooooooooooooc Production per feed, 10 hours, 1000 diametral r.p.m. 'A «0 C^OiCOCOCOCOC<3i002'0'-0->*->Tl-^-^-^-^-^COCOCOCCO'3C<5COCOeOOOCOCOCOCOCO r/3 a o a, cico <— looi— i«o-rtcoot^-*T-ia5t^iocC'— looot^ .l^t^«OC050»OlOiO»OU3"5Ttl-05 0COOOOt:^t^t^50CO«DiOiO>0 ■^COCCCOCOC^qC-lTH,-(T-li— l— l.-H>— l^H,-( la a- «^C0l:^C005»Ct^C0r^«SC<)l0Oi0»-il000Q0t^l0'-H«0OCC'^-*'«*-J>.t^lOiO-*l-lt^OCOCCirOeO ^1 ■>**liOOT-iCJ5CO-»t. -l05CO-*iOCOI>-0000050'— It-HC^JC^CO-^-^iOlOeOCOI^t^OOOOOSCiOO i-^,-Hrt.-Ht-H,-l,-<,-HrHrtCJMMCS|C^CSl(NC-Oi CO«OiOC5COOO'-(->tlOOOC«3 0iC<)050500t>.if5CO'— 05>0CvI COOOr^iOOOi-oOt^ONlOOOOCO'OI^CnOeOOt^OS^COiOl^OSOtM-^ Tj(Ttl»0i0»0OO«0I>.t^t-~I>.000000000005020>0505OOOOO'-i'-i.-i 0) M 3 (A O .<*iioi>.ooo50'-iMco->!f4 wjcot^ 0005 0.-H c*< loco r^ rHT-HT-s,-l,-l(MC^CSl(MC^) (MCMCl CSICS coco COCO CO COCO CO rH T-H i-H rt rt rt r-l rt rt,_| C<1CS|CV) (MMCa S 6 kdeot-ooosO'— i)02O-*c t^ 05 ooi-itht-i osootoio t^rtlrf5C:5COC003C^iOod-HT*CCO<»':Ot-l--t-00000000050>OS05C50CJOO^^-i-lr-i^lM<>) Thicknes- ses per in. Maximum No. of courses. i Coils per in. t-iO»O>Ot>-lOC1iOu0t— coo lOCO OOdOO OC-ir-»005C0 c^lOCO«D'-HlCiO'«tlOOOCO«OTtl<— ICOOS'-liM •>tH>.l--t-iOCM00COaD.050<>1COTtllOin00050i-ICqcO-*iraOt-00 05 0^ C^C^CMiMCOCOCOeOCOCO-*-^-^-*'<*lTj--<*<«OlMCO COC005C^1COO«005 05«0 (M>Ot^00l>-lO'-i c^c^(Mcqcococococococcrt<'*''<*<-^M<-»t<'*-*'*<>o>o>cmirt>oio»o»o>o Sxplanation of Regular Flat-fabric Formulas. — Loop-wheel 49 Dalbriggan are made at about that speed, and since a compara- :ively low speed has been taken for latch-needle rib machines, aamely, 700 diametral revolutions, the above loop-wheel speed s considered best for use here. Of course, flat-fleece machines 'un much faster than 1000 diametral revolutions, as do low- ?rade balbriggan machines, but it has been considered best to compromise on this speed rather than to use one which would bot be so general. If time would allow, the best method would be to work out a complete set of formulas for each different set Df established conditions. Until this is done, the reader must resort to modifying the conditions given, or to deriving his own formulas. The latter is much the better way, and it is not diffi- cult since the laws are very simple. Although this set of formulas is worked out especially for loop-wheel machines making flat work out of single cotton yarn, some of the formulas are applicable to other machines which conform to part of the conditions. For instance, the latch- needle automatic hosiery machine uses about the same weight of yarn as that used by the loop-wheel machine. Consequently the formulas for cut, stitches, weight per yard, and some others apply to the automatic hosiery machine, although of course the formula for pounds production does not, neither does that for yards production. The explanation of the rib formulas applies equally to the flat formulas, so the reader is referred to that explanation and especially to that portion which shows the importance of Col- umns 2 and 5. YARN-CUT RULES Chart for Latch-needle Rib Machine The cut or number of needles per inch is given on the left, the cotton number of the yarn is given at the bottom, and the three curves give the yarn number called for by the yarn rule, jnumber equals cut squared divided by a constant, with con- stants respectively 8, 6 and 4, reading do^Tiward on the chart. Consequently the heavy-yarn limit is supposed to be repre- sented by the highest curve, the average practice by the middle curve, and the limit for good fabric by the lower curve, although it is to be borne in mind that there is really no definite limit on the fine-yarn side. The observations of actual practice are represented by marks, 50 The Science of Knitting as follows: circles stand for single thread, crosses stand for double thread or more than double thread on coarse cuts, and crosses in squares stand for two-thread work where the dial had one-third the number of cuts that the cylinder had. Evidently, when the dial is cut coarser than the cylinder, the — - r " r ~ ~ - r [— r r r ~" ^ ^2 \y r-- y ^ y ' ^ ' l-^ A f [" ^ 1 - y " ' iy I ) -^ ■V Y " 12 r 1 , / ^^ y' ^ / ^ t / K ^ / y ^ ■^ ^ ' f . ■ / y ! f J /\ f ? ^ ^ 1 \ , A f-^ 8 - ^a ^ «-> / >/ > y U / J fi > y ' J ■^ 6 Y 7 A - / 6 , / / r LATCH NEEDLE RIB CHART » Two th read ( or more, on coarae cuta ) o Single thread B Dial cut less than cylinder cut, two thread ~ h r / / / / A / /J " J / J _ _ _ _ ^ ISSifrSie 9 101112ial«U16 WIS 19 20 212-.>23 2't25 2C::7 28 29M31;j£ »;i:i4 j;i;)6ilJ;M;i9 W'tl't2l;i'M«ii«4i48 Yarn, Cotton Number The relation between the yarn and the cut for latch-needle rib machines. The cut is on the left. The yarn number is at the bottom. The curves show the relations given by the rules for light, medium, and heavy yarn respectively. The crosses, squares, and circlea are from actual practice irrespective of the rules. rib rule does not hold, but the yarn may be much heavier. It is shown elsewhere that when the dial needles are removed entirely the yarn may be still heavier. Three illustrations are evident of the use of yarn much heavier than the rule calls for, i.e., 7 yarn for 8 cut, 9 yarn for 9| cut and Yarn-cut Rules 51 U yarn for 10 cut. However, all of these are the single equiva- lents of two threads, and show that it is practical to run two heavy threads where their single equivalent would not run. ^o the rule, Number = Cut^ -- 8, may be taken as a rehable commercial guide for the heavy limit, except on course cuts as is shown below. For 6 cut and coarser it is noticeable that the yarn is two thread. This is partially due to the practice where the observa- tions were made. But in spite of the use of multiple threads, svhich favors heavy combined yarn weight, still some of the ob- servations of actual practice fall below what any of the rules call or. This is true of all kinds of knitting machines so far investi- gated, consequently the yarn must be Ughter than that called or by the rule for coarse cuts, say for 5 cut and coarser. YARN-GAUGE RULES Chart for Spring-needle Loop-wheel Machine This chart gives a comparison of the yarn rules with actual practice, especially in order to show how much allowance should )e made in using the rules. The fuU lines represent the rules; and the squares, cu-cles and rosses represent the actual practice. The square designates wo-thread work with a short needle; the cross, two-thread v^ork with an ordinary needle; and the circle, single-thread V'ork with an ordinary needle. The significance of the chart may be understood from a pecimen yarn reading, say, 24 gauge, which is as follows: Condition Yarn (or single equivalent of two yarns) Heavy weight rule 9.6 Average rule 144 Light weight rule 19.2 Actual, two-thread, short needle 10, 12, 12.5 Actual, two-thread, ordinary needle ... 15 Actual, single-thread, ordinary needle . . 11.5,16 The following points are important : 1. For 10 gauge and coarser, actual practice is to use yarn ghter than the rule calls for, on account of the improper sign of coarse-gauge machines. Allowance should be made •r this by using a smaller constant for 10 gauge and under. 52 The Science of Knitting For instance, if average weight fabric is desired, such as would be represented in medium gauges by yarn equal to gauge squared divided by 40, then for 8 and 10 gauge, divide by 30, and for finer gauges, divide by 25 or 20, according to the adaptability of the machine. 1 40 — ■" "" — ~* "" — ■*■ '- ■~ "~ ■~ — — "■ / r- -G ►- "" ■~ ^ ■P / ^ 36 / ^ ^ , ^ '" ■ / ^ ^ ' Gauge-' / ° y ^ '' (iO / Gau'ge ''1 ^ a* 33 , _ _ _ ^ _ _ ^ — _ _ _ 46 ^ ^ — 3auj e' ^ -^ — - - - - ■M — - »- — — - — ~ — 7 «i — — t 3- — — ^ -y -' >- —30 ;:? ^ — — ~ ~ ■" ~ 31 "~ ■~ / y ' i-- , ~ "~ " / /■ ^ _ Z9 ■ / / / [— / / \ \* ^ _ _ / / r y" j;j(, " ■~ " r ^ G ^ ^ ^=i6 ~ ~ ~ ~~ ~ / J V X •-M / ° " '■ y ^2i ~ ~ ■" ~ ~ ~ 'I / /^ ^ /■ y > / k't ~ ■^ t n ^ y ^19 L UJ It / /' "7 ~ V / ^IB r / ' X - !^" / f / ^^10 ' n r / SPRING NEEDLE LOOP WHEEL CHART a Short Needle.Two Thread X Two Thread Single Thread 9" &)14 t y " ^ ~ f* 7 r ^!1 7 f- / " ~ / / / 11 ( 10 / / Y 1 1 ^ 8 / ' I '/ 1 - f / f » 1 1 1 \ i 1 I < 1 a 1 > 1 01 II 21 31 41 SI 6 1 71 91 9: 02 12 3 2 \ : i2 Ul 72 (J2 93 03 13 23 33 43 iV 6S la 83 941 Q4 14. l\ 34 44 &4 6i 741 Yarn, Cotton Number The relation between the yarn and the gauge for spring-needle loop-wheel circular machines. The gauge is on the left. The yarn number is at the bottom. The curves show the relations given by the rules for light, me- dium, and heavy yarn respectively. The crosses, squares, and circles are from actual practice irrespective of the rules. 2. Yarn equal to gauge squared divided by 60 seems to repre- sent well the practical heavy limit. In this comparison only one case exceeds it. Which is No. 5 yarn for 18 gauge. But this is the single equivalent of two yarns, and it is for a short needle, so it is extreme for an ordinary needle and single yarn. lelation of the Diameter of the Yarn to the Needle Spacing 53 3. The Ught weight rule, yarn equals gauge squared divided y 30, does not represent the light limit. This should be evi- ent from the fact that for light yarn it is not the diameter but he strength which principally determines the limit. This rule oes represent fairly well what is called light-yarn-short-stitch at work generally used for fine balbriggans. Such fabrics are lade in both odd and even gauges. It may be noticed that ke single-thread practice for gauges 27, 28, 30 and 31, much of J^hich is with high grade balbriggans, conforms closely to this file. Two-thread work follows the average rule or goes heavier scept for 14 gauge and coarser. Yarn Rules for Different Machines Average Circular .spring-need'.e rib No. = Circular latch-needle flat (work) No. = Straight jack sinker No. = Automatic hosiery machines No. = Circular spring-needle loop-wheel No. = Latch-needle rib ... No. = Cut2 10 Cut^ 13 Gauge - _ Cut2 56 ~ 24.89 Cutf 18 Gauged Cut2 40 Cut2 17.77 Approximate heavy limit Cut_2 39 Gauged Cut2 26.6 Cut2 60 HE RELATION OF THE DIAMETER OF THE YARN TO THE NEEDLE SPACING It should be evident that the yarn can be no wider than the Dace provided for it; and from this consideration, supported by 3servation of actual practice, Gustave Wilkomm long ago termined the average relation of yarn width to distance be- veen centers of needles to be as 1 is to 7.4 for flat fabric, his was the introduction of science into knitting; consequently, le relation of the size of the yarn to the needle spacing is storically the most important knitting consideration. But though the room for the yarn is of interest and of importance. 54 The Science of Knitting especially concerning the limit of the size of the yarn, other im- portant factors should have consideration. A bridge designed to carry only the expected load would break under an overload. Just so a machine designed only for normal yarn would " smash " needles at a bunch or knot, both of which are frequent in com- mercial yarn. On the other hand, the yarn is generally flattened against the needle during the sinking of the stitch, so that it is sometimes possible to feed yarn which otherwise seems too big. From these considerations and from the fact that manufactur- ers differ in the yarn-space allowance for an equal distance be- tween centers of needles, owing to the use of different-sized needles and sinkers, it is evident that for general purposes a more reliable basis of calculation is desirable. Clearly, observation of use is the best means of determining usage. A certain kind of barge might be designed to carry a cer- tain amount of load, but the best means of determining the capa- city of that kind of barge would be by comparing observations of actual loads under different conditions. A' load for smooth water might be about the calculated capacity, whereas for rough water it might be much less. The average capacity, which is the one desired, would be somewhere between the two just mentioned. So with the knitting machine the prospective user wants to know what size yarn he can safely run. Other- wise he might sell samples made of a trial lot of selected yarn, basing his knitting cost on the running of that yarn and then be under the necessity of delivering the goods from " bunchy " yarn with consequent extra cost for knitting, whereas if he had known what trouble would result, he could have made his samples with lighter yarn and so been better prepared to stand the overload due to an unexpected increase in the proportion of bunches. Indeed, there are so many such considerations which affect the size of the yarn with respect to the spacing of the needles that the only reliable means of allowing for them is by taking the results of actual practice. The constants oi the yarn-cut rules given in this book are so obtained and although more extensive observation may modify them, still they are useful as given. The form of these rules is yarn No. = —7^ , in which k is the constant, equal to 6 for latch-needle rib machines, 18 for auto- matic hosiery machines, etc, delation of the Diameter of the Yarn to the Needle Spacing 55 Since the formula contains the cut (which is the reciprocal of he needle spacing) and the yarn number, it gives all that is leeded except the relation of the number of the yarn to its liameter, which is provided for single cotton hosiery yarn by ^^' ^ 441Dia.2' The relation of the diameter to the cut can now be derived is follows: No.=^, (1) k 441 Z>2' No. = -r^,, (2) (i)-('^) ^ = 44rD^' '•^'- • • • (^> V(3) Cut 1 Vk 21 D' D = ^ .(4) 21 Cut That is, the diameter of the yarn equals the square root of the mru-cut-rule constant divided by twenty-one times the cut. Transforming (4), ^ z) X Cut = y^^, 21 Z)^^=^. (5) Cut 21 ..„, 1 . '^^ . . . . '• ' Now ^=^—7 is the needle spacing, i.e., in a ten-cut machine the leedles are spaced y^ inch apart. Consequently, D -r- p-— is he proportion of the needle spacing occupied by the yam, which •roportion equals ^ , so that the proportion of yarn diameter to ■eedle spacing is the square root oj the yarn-cut-rule constant 'ivided by 21. Formula (4) for the loop-wheel machine becomes 1 D = 4.98 Cut 1 X ' 4.98 '" Cut = say, i X Needle Spacing. 56 The Science of Knitting Consequently, the yarn-diameter-cut formula for any machine shows the proportion of needle spacing occupied by the yarn diameter. The following table gives the above mentioned rela- tions for several types of knitting machine. 1 2 3 Square root of yarn- 4 5 Propor- tion of needle Names of machines Yarn-cut rules cut rule con- stant spacing occupied by yarn diameter 21 vl Vik Vk 21 Hosiery, automatic Cut2 ~ 18 4.2425 4.948 .202 Latch- needle flat Cut2 -4- 13 3 . 6055 5.824 .17167 Latch- needle rib Cut2 -=- 6 2.4495 8.573 .11663 Spring-needle loop-wheel . . . Cut2-^ 17.77 4.2155 4.982 .20072 Spring- needle rib Cut2 -f- 10 3.1623 6.640 . 15059 Rule for flattened width \ of tube same as diam- > Cut2^ 11.17 3.342 6.284 .15913 eter of needle line. ) Straight jack-sinker ma- ) chine ) Cut2-T- 24.98 4.989 4.209 ^ .23745 Rule for fabric same i width as length of ? Cut2-=- 27.56 5.25 4 .25 needle line ' Rules are given also for machines which produce fabric as wide as the machine, a rule for the circular machine and a rule for the flat machine. From this it is seen that for the circular machine, yarn with diameter ^-^ of the needle spacing makes fabric as wide as the machine when the tube is flattened. Consequently, finer yam makes fabric narrower than the ma- chine and heavier yarn makes fabric wider than the machine. With the straight jack-sinker machine evidently the yarn must be I of the needle spacing to make fabric as wide as the machine, since four diameters make a wale and the width of the wale must equal the needle spacing in order to have the fabric as wide as the machine (on the needle line) . Yarn according to the aver- age rule is -^-^ of the needle spacing, which is very near to j. Width of Flattened Tube of Fabric 57 This diagram shows graphically what Column 5 shows numeri- cally. o o o O Yarn which makes iwp W.Flat Auto Hosiery Jack Sinker Fabric as wide as Straight Machine o O O O r nj DiK o • TVT ■D\. Yam which makes Tube ^ »t r-n ^ L.N. Rib SpnngN.Rib ., ,. , ., ,. L.N.Flat as wide as dia.of Machine rhe distance between adjacent lines represents the distance from center to center of needle (in one set, for rib machines) . rhe circles show the proportional diameter of yarn used on the machines named under them. ) When the same-sized yarn is used on these different machines, the cut is inversely proportional to the diameters of these circles, so the latch-needle rib machine requires the coarsest cut. WIDTH OF FLATTENED TUBE OF FABRIC FOR DIF- FERENT NUMBERS OF NEEDLES AND YARN As is demonstrated elsewhere, the theoretical width of the abric does not depend directly on the diameter of the cylinder Dut on the diameter of the yarn and on the number of needles n the cylinder. The actual width differs from the theoretical »vidth according to the extent of compression of the yarn, the iistortion of the stitch, and the inaccuracy in determining the >^arn diameter. Therefore, allowances must be made accord- ng to these conditions. In order to facilitate making these illowances, the numbers of needles used vary by twentieths, ^g., 200, 210, 220, etc. Consequently, if it is desired to make m allowance of 10 per cent more than the theoretical width, it nay be done without calculating by reading the width two columns farther to the right than the nearest number of needles, [f the allowance is to be 10 per cent less, the reading should be wo columns to the left of the nearest number of needles. In- ismuch as exact results are not to be expected, the division of he needles by twentieths is close enough for practical pur- 58 The Science of Knitting poses, since by using the number in the table nearest to the desired number the error cannot be over 2| per cent, which is closer than the diameter of the yarn can be measured. It would be desirable to have a table from which the width of the fabric might be read at once, but this is an impossibility in the present state of knowledge. However, experience indicates that in any one mill with any one type of machine and kind of yarn, the variation from the theoretical width is quite regular, say 5 per cent or 10 per cent over or under. The variations from the table appear to be about as follows: Small ribbers with a well-closed dial stitch .and good take-up tension, 10 per cent less than the theoretical. Rib body machines, without fabric ring, 10 per cent more than the theoretical. Rib body machines, with fabric ring, same as the theoretical. Loop-wheel flat-work machines, 10 per cent less. Automatic hosiery machines, normal stitch, same as table. Small latch-needle machine, fiat work, very tight take-up tension, 30 per cent less. Large latch-needle machine, flat work, 10 per cent less. Cardigan lies out wider than corresponding plain rib from 43 per cent to 91 per cent, average 66 per cent. Tuck lies out wider than corresponding plain rib from 42 per cent to 65 per cent, average 53 per cent. Consequently, to get the width of either tuck or cardigan, determine the width of the plain rib fabric according to the table and the machine as given above, and then add, say 50 per cent for tuck, and 70 per cent for cardigan. The above suggestions are not to be taken as final, since much more observation will be necessary for forming definite conclusions. Therefore, whoever has frequent need of de- termining the width of the fabric from the yarn and the number of needles should derive his own allowances by recording the differences' between the table and the actual fabric, and then using the average difference for an allowance to be applied to the table. For instance, if the average of a number of obser- vations is 10 per cent less than the table, and the extremes are 5 per cent either way, then the user may count with some certainty on coming within 5 per cent of the actual if he discounts the table by 10 per cent. Do not depend on memory for the determination of the correction, for gross errors are sure to result. Width of Flattened Tube of Fabric lOCMOit^cOirSCOOJ.— i-^005C:OOOOt^O«C'0-<*<->*<-<*#CC503C500 coi-icobP-eotoiO'^-^cocococ^iCM'-ii-HOOOOscncnooooco -rtit-COCMM>OOOCMl^CO■*lC0C0CMCMT--ll--l^OOOO5O0>000000^-■l>•t>;t>; a.i-o_i,_icoco-Hir5.-ir— cciOt^'*CMC5»ocMC2<»cC'-i05r^»occ tio»0-*C<5CMCMi-l»-lOOOC5O05000000t^r-. I— t^«0«05D«D lOCMC^l'^OOCMOOCOOt^'^'— 'OSCO'^CMOSO'^'— 'Oit— eO'l'CO'-; S 2 6 lOOt^QOOO'-HCMCC-'J'iOCO 0002OCM'*< "* I* •. CO o CO CO § US Ui CO CO o o CD OO r^ Oi us t^ ■* CD CO 00 o CO 03 00 us CO us eo CO CO CO CO 00 00 t^ t^ CD CD CO US Ui us US us •* ■^ ■* ■* ■* ■^ eo CO eo CO CO CO CO CO o o 00 o eo "5 C. CD CD »C lO us ■<*< -* Tft ■^ ■^ 'i* •<*< CO CO eo CO CO CO CO CO CO CO CO CO CO CO CO r-l OS CD oo 05 eo US 00 CO CO CO o 00 CD 00 CO CO CO 05 •I* CO CO CO o OS OS o OS 00 CO CD CD <5 us I>. CO CO Ui "5 IC •^ ■* ■* ■TJH •^ TJH CO CO eo CO CO CO CO eo CO (M c* CO CO (N ■<1< to 00 00 o CO OJ CI 05 t^ us CO eo t^ B o 05 05 OO CD 00 us 03 eo eo 05 o us OS us 00 CD 00 CO o CO CO us '^ CO CO ITS »c lO '*< •!< •^ CO eo CO eo eo CO CO CO CO CO CO CO CO CO CO CO s O CO to C35 t^ 00 03 CO CO 05 00 t- CO s ■<*< CO eo t^ s CO OS 00 t^ CO CO us us 00 us CO CO CO >o >o ■* Ttl ■* -* -* eo CO co CO CO eo CO CO CO CO CO CO CO CO CO CO CO CO OS CO l>. CO o CO 05 GO CO o 05 03 CO CD us us us ^ CD CO t^ § 8 OJ s Oi us us eo CO o eo CO 73 *"* to »0 US us Tt< ■* >* -* CO CO CO eo CO eo eo eo eo eo CO *< -<*< CO CO CO CO § 03 00 CO CD CO us eo us CO eo CO I*' § § M lO m -^ ■* •^ •<*< CO CO CO CO CO CO CO eo CO CO CO CO CO CO CO CO eo e CO eo CO CO e. CD o "S 05 eo o eo eo >* o 1-1 o s § s 03 CO eo CO us us CO eo 00 eo ^ CO 00 eo eo eo « o i-H CO CO 1-1 1-1 us CO l^ 00 Oi o eo eo eo s CO 00 CO u eo eo ^ CO CO 00 o eo •^ Width of Flattened Tube of Fabric 61 -a a o a or 1 oo to o oo t>. CI CI 02 o CI CO OS s CO lO CO CO 00 r^ CO o oo ^ ■* OS OS CO CD CO CO o 00 CM 00 ci O OS oo »0 OS OS CO OS lO .-1 ^ ^ d d d r^ t^ C 00 UO C-ti OS OS OS o OS CI oo oc CO o CO o CM o o CI OS 00 O CI oo o CD CO CO •* o t^ CI ■ o o ai OS "-i CD CO •-' oo d 05 od CI CO od 00 CO CI CO o CJ OS 00 00 CO 00 CO OS ic. 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Therefore, the distance from center to center f adjoining needles is jr-: ' If tiie wale is the same width as the istance from center to center of adjoining needles, then the fabric all be just as wide as the machine, i.e., just as wide as the length f needle hne taken to produce it. But the wale is as wide as )ur times the diameter of the yarn. Therefore, the condition )r fabric as wide as the machine is 4 Dia. = -p^r— f Cut Dia. = 4 Cut Consequently on a straight machine if the diameter of the yarn is lual to one divided hy four times the cut, the fabric will be as mide s the needle line is long. The rule for the number of yarn to make fabric as wide as le machine is derived as follows: From above, ^ Dia. = . ^ ^ , (1) 4 Cut ut Dia. = \^ (2) 21 VNo. J) - (1) ^ ^ quarmg No. = 4 Cut 21 VNo. Cut = 5.25 VNo. Cut2 27.56 Which is to say, on a straight machine if the number of the yarn equal to the cut multiplied by itself and divided by 27.56, the ',bric will be as wide as the needle line is long. The same considerations apply to the circular machine, with le added one that reduction must be made from the circular ) the flat shape, since the diameter of the machine is used in- ead of the circumference to express its size. If the rule just ven were followed, the fabric would lie out about f ^s wide J the diameter of the machine, because it would be half as wide 64 The Science of Knitting as the distance around the circumference of the machine. Con- sequently, the yarn should be only about two-thirds of the diameter which is required by the straight machine. That diameter is 1 (1) Dia. = 4 Cut The ratio of the circumference of the circle to the diameter is 3.1416, so the diameter of the yarn should be multiplied by 2 „ -, ■ ., ^. in order to make the doubled width of the cloth the d.l4lD same as the diameter of the machine. 1 9 1 X 4 Cut 3.1416 6.283 Cut Consequently, on a circular machine if the diameter of the yarn equals one divided by 6.283 times the cut, the width oj the flattened tube of fabric will equal the diameter of the needle line. But the diameter of the yarn = -==^ J 21 VNo. *^^^^^«^^' 6-:28lcut = ^IV^; or Cut = 3.342 VNo. Cut2 No. = 11.17 Or, in words, on a circular machine if the number of the yarn is equal to the cut multiplied by itself and divided by 11.17, the icidth of the flattened tube of fabric will equal the diameter of the needle line. However, the size of the yarn is generally determined by more important considerations than the width of the fabric, such as its adaptability to economical knitting, the weight and appearance of the fabric, etc., so the rules based on general practice are the ones which should be used until other rules are shown to be as good. The demonstrations just given are not only useful for showing the general relation of the width of fabric and size of machine, but they may be used to calculate the width when the ordinary yarn rules are known. Width of Fabric from Different Machines 65 The general form of the yarn rule is Cut2 No. =^. Extract the square root of both sides of the equation 3ut from (2) (3) - (4) /^r- . Cut Vk VNo. = 1 21 Dia. yarn Cut (3) (4) 21 Dia. yarn V/c But it is well known that the width of fabric from any one dnd of machine is independent of the cut, since the same width )f fabric is expected from any one diameter regardless of the Hosiery, automatic Latch- needle, flat Latch- needle, rib Spring- needle, loop-wheel Spring- needle, rib General rule for fabric same width as circular machine Circular machines Rule Cut2 18 Cut" 13 Cut2 6 Cut2 17.77 Cut2 10 Cut^ 11.17 Constant 18 13 6 17.77 10 11.17 VConstant 4.2425 3.6055 2.4495 4.2155 3.1623 3.42 Width of fab- ric (double) 4- dia. of needle line 1.27* 1.08 .73 1.26 .95 1 Straight machines Straight jack-sinker . General rule for fabric same width as flat machine Cut2 24.89 Cut" 27.56 24.89 27.56 4.989 5.25 Width of fab- ric (single) -r- length of needle line .95 Normal stitch. 66 The Science of Knitting cut, so the cut may be regarded as constant. Then the equa- tion shows that the diameter of the yarn is proportional to the square root of the yarn-rule constant. Consequently, the width of fabric from different machines is proportional to the square roots of their yarn-rule constants. But we already know the rules for fabric of the same width as the machines; for in- stance, for circular machines with yarn No. = j~-^ the fabric is just as wide as the machine. For latch-needle rib machines the regular constant is 6. The square root of 6 is 2.45 and the square root of 11.17 is 3.324. Since the square roots of the constants express the width of the fabric, and since 3.324 rep- resents unit width, the width of fabric to be expected from latch- needle rib machines is as 2.45 is to 3.324 or 0.73. The table on page 65 shows this as well as the widths to be expected from other machines. THE PRODUCTION OF CIRCULAR KNITTING MACHINES Units of Production. — The production may be given in com- mon units of measure, such as pounds, square yards, linear yards, etc., or in trade units, such as dozen garments, dozen pairs, etc.; but to use trade units intelligently requires a knowl- edge of the pounds or yards in each such unit, so for common use it is best to give the production in common units. Pound is the Simplest Unit. — The pound is the simplest unit since it is the easiest to measure and since the length and breadth of the fabric do not have to be considered. Production Factors. — The production in pounds depends on the following variables: needle velocity, number of feeds, weight of yarn, length of stitch and actual running time — five in all. Explanation of Diametral Revolutions. — Needle velocity is generally expressed as revolutions per minute, to which it is proportional for a- given diameter, i.e. if one 20-inch machine runs 20 r.p.m. and another 40 r.p.m., the needle velocity of the second cylinder is twice that of the first. But this method of expressing the velocity necessitates stating the diameter in every case, so it is better to express the velocity in diametral revolutions per minute (dia. r.p.m.) which is the product of the diameter in inches and the revolutions per minute. A 20-inch machine running 20 r.p.m. has a needle velocity of 20 X 20 = 400 dia. r.p.m. This is especially convenient for knitting ma- I The Production of Circular Knitting Machines 67 ihines, in which the needle velocity is generally constant for iifferent diameters, since it not only faciUtates calculating the aroduction but enables determining the speed of different- sized machines. Diametral-revolutions Constant for Knitting Machine. — Suppose a particular kind of work is tried on a 20-inch machine ind is found to run best at 20 r.p.m. Then 20 X 20 or 400 is bhe speed in dia. r.p.m. for all of the machines; according to sv'hich a 10-inch should run 400 -^ 10 = 40 r.p.m., and a 16-inch, iOO ^ 16 = 25 r.p.m. For these and other reasons the needle velocity is expressed in dia. r.p.m. and 700 is taken as a fair average for rib work, except automatic work on small machines For which 420 is taken. Conditions for High Velocity. — Generally, good conditions of yarn, machine and attendance favor good needle velocity and vice versa. Light yarn and a fairly loose stitch favor good velocity, since bunches and knots have room to pass between the needles without causing trouble. Each manufact^urer should determine for himself the best speed for his conditions. Advisable to Start Low. — It is advisable to start low and then gradually work up to the point where the cost of knitting per unit of production is the least. Maximum Number of Feeds Generally Used. — The number of feeds is generally the greatest that can be used on the machine or for the pattern required. Selection of Yam Number. — The weight of yarn is limited to an extent by the cut and after that by the weight of the goods, the cost of the goods, etc. Since cotton is the most used knitting material, the number of the yarn is generally given in the cotton count. Number of Yam Proportional to Square of Cut. — The number of the yam is proportional to the square of the cut or gauge, i.e. if the cut is made twice as fine, the yarn number should be four times as fine. Possible Variation of Yam. For latch-needle rib machines the variation in the yarn number for a given cut is generally not over twice the heaviest. In other words, if No. 8 is about as heavy as is practical. No. 16 would be about the light limit. It is of course understood that the extreme light limit is the lightest thread that will hold together during the formation of the stitch, but the fabric so made would be worthless. 68 The Science of Knitting bO a o 3 o o •rH I d a> a ^ O CO a ;^ OQ O 73 0) CO c3 o 5 g .S o >-' 3 00 § oT <^ a o p^ ^ ^ -<3 'X ^ go CO (D « 03 . •*-> o X O Oh r^ SH 03 j:3 03 O • 1—1 O 13 o j-i Oi cc o o O -J=3 o3 o ^^ H - to U CO CO a O- 0) c;i 03 o3 c^ X X t^ X T3 X S X Oh o '^ -^ ^ rt o3 § -^^ a W) ^ O a 02 CD o3 ^- (-! CO o o< o. S '^ 03 o3 <+H 0) ^ Oh 03 o. 3 o o X a, X 03 S-i ■— 1 TJ a> 1 Cm O -id d -1-3 o3 -d fe .g X (0 M <3i -^ PIH ^ 0) O) II p^ o X s X d ^(^ ;h' ■-s X X M ^ 00 o3 ^ X -a -1 lO o rt ^ CO lO *:: X X (M ^ ^ CO T— 1 -* 1— 1 l3 CO 03 X 5 OlN tH nH 05 (A o P4 X a d o -♦J o o Cm o d o -^i d ^ fM X X 44 CQ d ns 03 ^ II fe ^d o X to ■1 s 0) X t-l d 4* tn' X 1 X CO 1—4 GO X CO y 3 O T*4 /\ d o o Oh _d -t-3 CO X CO X o lO d (D o 1—1 «M rH Cm O .s CO ^ 03 X 'S o a 00 70 The Science of Knitting Stitches per Foot of Yarn and Courses per Inch. — The length of stitch is best expressed by the number of cyhnder needles per one foot of yarn. The number of courses per inch is frequently used, but the production in pounds cannot be calculated from the courses because it is not known how much yarn is required to make a given number of courses. One foot of yarn takes up from 3 inches to 5 inches of needles in a latch-needle rib machine. For cuts from Nos. 4 to 14 inclusive and yarn = ■ ^^, one foot of yarn fills about 4 inches of needles for a good fabric, so 4 inches is taken as the average. When the yarn is lightened, the stitch is generally tightened and vice versa. Causes of Lost Time. — The running time of course depends on the number of hours m the working day, on the conditions of yarn, attendance, and machine, whether stop motions are used, etc. Generally, the greater the number of feeds, the greater will be the stoppage from yarn defects and for replacement of bobbins or cones. Estimates of stoppage run from 10 per cent to 20 per cent. Factors of Linear Yard Production. — The production in linear yards is dependent on the speed, feeds, and courses per inch. It is obtained by calculating the number of courses made per day by the machine and then dividing this number by the number of courses in a yard of the fabric. The production in hanks is found by calculating the number of yards of yarn used by the machine per day, dividmg it by the number of yards in a hank, and dividing the result by the num- ber of the yarn. The production in square yards is equal to the number of stitches made per unit of time divided by the number of stitches per square yard; but since the latter is inconvenient to get, the stitches per square inch are used and multiplied by 36 X 36 = 1296, the number of square inches in a square yard. Explanation of General Rib-fabric Production Table in Pounds Page" 72 This table gives the production in pounds for 10 hours actual running time for^all factors variable except stitches, which are taken at 9.8 VNo., that is, one foot of yarn occupies four inches of needles. To use the table multiply together the diameter of the cylinder in inches, the revolutions per minute and the feeds: select the Production 71 number at the top of the table nearest to this product and read the answer under it opposite the number of the yarn used. Example. — How many pounds of fabric will be produced in ten hours under the following conditions? Diameter of cylinder 16 inches, Revolutions per minute 44, Feeds 8, Yarn No. 11 cotton, Multiply together the diameter, the revolutions per minute, and the feeds 16 X 44 X 8 = 5,632. See the table on page 72 The nearest number at the top of the table is 5,400, and under it, opposite No. 11 yarn is 91.75. Discount this, say 20 per cent for lost time, which gives 73.4 pounds. The average production of spring-needle circular loop-wheel flat work is 1.23 times that given in the table. For instance, such a machine under the above conditions would, in 10 hours actual time, produce 91.75 X 1.23 = 113 pounds. Production Table in Hanks for Rib Machine — Example Page 73 How many pounds of fabric will be produced in a 10-hour day by a 6-feed, 18-inch machine running 50 r.p.m. and using No. 10 cotton yarn. The diametral revolutions are 18 X 50 = 900. The constant for 900 dia. r.p.m. and 6 feeds is 908.75, which divided by 10, the yarn number, = 91, the pounds pro- duction for 9 hours, which under good conditions may be taken as the production for a 10-hour day. If the yarn is two thread get either (1) the production for the equivalent single-thread or (2) the total of the productions for each thread. For instance, what is the pounds production per 10-hour day of a 4-feed machine making 700 diametral revo- lutions per minute and using a No. 8 yarn and a No. 24 yarn at each feed. (1) The equivalent single yarn is ^ — r— x = -5^ = 6. The ii4 -\- O oZ constant for 700 diametral r.p.m. and 4 feeds is 471.2, which divided by 6 = 78.6, the pounds production. 72 The Science of Knitting (2) The production for each thread is 471.2 -^ 8 =59 471.2 4- 24 = 19^ 78.6. Total production. General Rib-fabric Production Table in Pounds For explanation see pages 70 and 71 Production. Pounds of rib fabric per 10 hours actual running time Yarn No. 5 Diameter X r.p.m. X Feeds 500 1200 1900 2600 97.2 3300 4000 4700 5400 6100 6800 7500 18.69 44.86 71.03 123.35 149.52 175.7 201.85 228.00 254.20 280.35 6 15.58 37.38 59.19 81.00 102.80 124.60 146.4 168.22 190.00 211.80 233.65 7 13.35 32.05 50.74 69.43 88.12 106.80 125.5 144.20 162.90 181.60 200.30 8 11.68 28.04 44.39 60.75 77.10 93.46 109.8 126.16 142.52 158.87 175.23 9 10.32 24.76 39.20 53.64 68.08 82.52 96.97 111.40 125.95 140.30 154.73 10 9.35 22.43 35.52 48.60 61.68 74.76 87.85 100.94 114.00 127.10 140.19 11 8.50 20.39 32.29 44.18 56.07 67.97 79.86 91.75 103.65 115.54 127.43 12 7.79 18.69 29.60 40.50 51.40 62.30 73.21 84.11 95.02 105.90 116.80 13 7.19 17.25 27.32 37.38 47.45 57.51 67.58 77.64 87.70 97.77 107.95 14 6.68 16.02 25.37 34.72 44.06 53.40 62.75 72.10 81.44 90.78 100.13 15 6 23 14.95 23.68 32,40 41.12 49.84 58.57 67.29 76.01 84.73 93.46 16 5.84 14.02 22.20 30.38 38.55 46.73 54.91 63.08 71.26 79.44 87.85 17 5.50 13.20 20.89 28.59 36.28 43.98 51.68 59.37 67.07 74.76 82.46 18 5.19 12.46 19.73 27.00 34.27 41.54 48.81 56.07 63.34 70.61 77.89 19 4.92 11.80 18.69 25.58 32.47 39.35 46.24 53.12 60 00 66.90 73.78 20 4.67 11.21 17.75 24.30 30.84 37.38 43.92 50.46 57.00 63.55 70.09 21 4.45 10.68 16.91 23.14 29.37 35.60 41.83 48.06 54.29 60.52 66.75 22 4.25 10.20 16.14 22.09 28.04 33.98 39.93 45.88 51.82 57.77 63.72 Yarn No. 8200 8900 9600 10,30C 11,000 11,700 12,400 13,100 13,800 14,500 5 306.50 332.70 358.90 385. OC 411.20 437.40 463.50 489.70 515.90 542.10 6 255.45 277.25 299.05 320.85 342.70 364.50 386.30 408.10 429.90 451.70 7 219.00 237.65 256.35 275.05 293.75 312.45 331.15 349.85 368.55 387.20 8 191.60 207.95 224.30 240.65 257.00 273.40 289.70 306.10 322.40 338.80 9 169.16 183.60 198.05 212.50 226.95 241.40 255.85 270.27 284.70 299.15 10 153.26 166.35 179.43 192.51 205.60 218.70 231.80 244.85 257.95 271.05 11 139.33 151.22 163.12 175.00 186.90 198.80 210.70 222.60 234.50 246.40 12 127.70 138.60 149.50 160. 4C 171.35 182.50 193.15 204.05 215.00 225.95 13 117.90 127.95 138.00 186. 9C 158.15 168.23 178.30 188.35 198.40 208.50 14 109.47 118.80 128.15 137. 5C 146 85 156.20 165.55 174.90 184.25 193.60 15 102.17 110.90 119.60 128.34 137.07 145.80 154.52 163.25 171.96 180.70 16 95.80 103.97 112.15 120.32 128.50 136.70 144.86 153.04 161.22 169.40 17 90.16 97.86 105.55 113.24 120.95 128.64 136.34 144.04 151.73 159.43 18 85.16 92.42 99.70 106.95 114.23 121.50 128.77 136.05 143.30 150.58 19 80.67 87.56 94.44 101.33 108.22 115.10 122.00 128.87 135.76 142.65 20 76.63 83.17 89.71 96.25 102.80 109.34 115.88 122.42 128.96 136.50 21 72.98 79.21 85.44 91.67 97.91 104.13 110.36 115.80 116.40 129.05 22 69.66 75 62 81.56 87.51 93.46 99.41 105.35 111.30 117.25 123.20 Production 73 Production Table in Hanks for Rib Machine For example see bottom of page 71 Constants which dividedby the cotton number of the yarn give the production of latch-needle circular rib knitting machines in pounds per 9 hours actual time. The stitches per foot of yarn are four times the cut. R.p.m. Dia. r.p.m. Feeds (20 in.) 1 2 3 4 20 400 67.31 134.63 201. <:5 269.27 25 500 84.14 168.30 252. r. 336.60 30 600 100.97 201.95 302. 9. i 403.90 35 700 117.80 235.61 353.42 471.20 40 800 134.63 269.27 403.90 538.53 45 900 151.46 302.92 454.38 605.85 50 1000 168.29 336.59 504.88 673.17 5 6 7 8 20 400 336.60 403.90 471.20 538.55 25 500 420.73 504.90 589.00 673.20 30 600 504.90 605.85 706.80 807.80 35 700 589.00 706.80 824.65 942.40 40 800 673.15 807.80 942.40 1077 .)00 45 900 757.30 908.75 1060.20 1211.60 50 1000 841.45 1009.70 1178.00 1346.30 9 10 11 12 20 400 605.90 673.15 740.50 807.80 25 500 757.30 841.45 925.60 1009.70 30 600 908.77 1009.70 1110.70 1211.70 35 700 1060.20 1178.00 1296.00 1413.60 40 800 1211.60 1346.30 1481.00 1615.60 45 900 1363.10 1514.60 1666.00 1817.50 50 1000 1514.50 1682.90 1851.20 2019.50 13 14 15 16 20 400 875.20 942.50 1009.70 1077.00 25 500 1094.00 1178.00 1262.00 1346.30 30 600 1312.70 1413.70 1514.60 1615.60 35 700 1531.40 1649.30 1767.00 1885.00 40 800 1750.30 1885.00 2019.50 2154.00 45 900 1969.00 2120.50 2272.00 2423.40 50 1000 2187.90 2356.10 2524.30 2692.70 1 Cut Yarn Cut Yarn 3 1.5 9 13.5 4 2.7 10 16.7 5 4.2 11 20.2 6 6.0 12 24.0 7 8.2 13 28.2 8 10.8 14 32.7 74 The Science of Knitting Production Table in Hanks for Loop-wheel Machine Constants which divided by the cotton number of the yarn give the produc- tion of spring-needle circular loop-wheel knitting machines in pounds per ten hours actual time. The stitches per foot are three times the gauge. R.p.m. (20 in. cyl.) Dia. r.p.m. Feeds | 1 2 3 4 5 6 7 8 9 10 70 60 50 40 30 20 10 1400 1200 1000 800 600 400 200 223 193 160 128 97 65 32 447 383 320 256 192 129 64 670 575 480 384 290 193 95 893 765 640 510 385 255 128 1115 965 800 640 480 325 160 1337 1145 960 766 575 385 194 1560 1340 1115 894 670 450 224 1783 1530 1275 1020 767 510 255 2000 1720 1435 1148 860 575 290 2230 1920 1600 1280 960 640 320 Example. — What is the production in pounds per day of a 6-feed spring-needle circular loop-wheel machine 15 inches in diameter, running 60 revolutions per minute and knitting No. 10 cotton yarn? The diametral revolutions per minute are 15 X 60 = 900. The table does not give this, but does give 800 and 1,000, and since what is desired is halfway between these, take half of the hanks given under 6 feeds and opposite 800 and 1,000. That is, half of 960 + 766 = I X 1726 = 863. This number of hanks, 863, divided by the yarn. No. 10, gives 86.3, the pounds pro- duction for 10 hours actual running time. Discount this by the proportion of lost time, or by one-tenth, if the lost time is not known. The actual production then for good conditions is 86.3 X 0.9 = 77.7. For two-thread work see two-thread example for rib-produc- tion table in hanks, bottom of page 71 and top of page 72. For fleeced-underwear fabric obtain the face production by either two-thread method, pages 71 and 72, and double it to allow for the weight of the backing. Production Table Linear Yards — Explanation Pages 76 and 77 If the number of courses of fabric made in an hour is known and this number is divided by the courses per yard, the quotient will be the linear yards produced per hour. Since the number of courses per inch depends both on the diameter of the yarn and on the stitches per foot of yarn, as well as on other con- Production 75 litions, a table to meet all of the requirements would be both )ulky and costly. However, the courses produced by the nachine may be easily calculated, and if the courses per inch ire counted in the sample in question, if at hand, or taken from he guide table herewith, and divided into the courses produced )y the machine, the linear yards may be obtained satisfactorily rom a comparatively small table, such as the one on page 76. The table is based on the following calculations: The courses per hour = r.p.m. X feeds X 60 . (1). The courses per linear yard = courses per inch X 36 . (2). The linear yards per hour = (1) -r- (2) r.p.m. X feeds X 60 36 X courses per inch _ 1.667 X r.p.m. X feeds courses per inch constant courses per inch ^ The table shows the constants for different revolutions per ninute of circular machines or strokes per minute of straight nachines and for different numbers of feeds. The constants nust he divided by the courses per inch to get the linear yards. 5ince the production-in linear yards is independent of the diam- eter of the machine, except as it affects the revolutions per ninute, the diameters are given merely as an alternative guide or use for latch-needle machines when the revolutions per ninute are not known. Deduction should be made from the esult obtained, in proportion to the time lost. Production, Linear Yards Pages 76 and 77 Example. — How many linear yards, per 10-hour day, of fabric laving 24 courses per inch, will be produced by a 4-feed machine unning 100 r.p.m.? In the table opposite 100 r.p.m. and under t feeds is the constant 667, which divided by 24, the number >f courses, gives 27.8, the linear yards per hour, actual time, jince the machine has only four feeds, the lost time may be ionsidered 10 per cent in the absence of definite information, rhen the day will consist of 9 hours actual running time, o the actual production in linear yards per day will be 17.8 X 9 = 250. 76 The Science of Knitting Production, Linear Yards For explanation see bottom of page 74 Constants which divided by the number of courses per inch give the production of knitting machines in linear yards per hour. R.p.m. of 1 circular machine. Feeds Dia. Strokes per min. of straight machine 1 2 3 4 5 6 7 1 700 1167.0 2333.0 u 564 940.0 1880.0 u 462 770.0 1540.0 2310. u 400 666.7 1333.0 2000. 2 350 583.3 1167.0 1750. 2i 311 518.3 1037.0 1555. 2h 280 466.7 933.3 1400. 21 255 425.0 850.1 1275. 3 233 388.3 776.7 1165. 3J 215 358.3 716.7 1075. 3^ 200 333.3 666.7 1000. 1333. 3i 187 311.7 623.4 935. 1247. 4 175 291.7 583.3 875. 1167. 4i 165 275.0 550.0 825. 1100. 1375. 4i 156 260.0 520.0 780. 1040. 1300. 4f 147 245.0 490.0 735. 980. 1225. 5 140 233.3 466.7 700. 933. 1167. 5i 133 221.6 443.3 665. 887. 1108. 1333. 1552. 5i 127 211.7 423.3 635. 847. 1058. 1270. 1482. 51 122 203.3 406.7 610. 813. 1017. 1220. 1423. 6 117 195.0 390.0 585. 780. 975. 1170. 1365. 7 100 166.7 333.3 500. 667. 833. 1000. 1167. 8 88 146.7 293.3 440. 587. 733. 880. 1027. 9 78 130 260.0 390. 520. 650. 780. 910. 10 70 116.7 233.3 350. 467. 583. 700. 817. 11 64 106.7 213.3 320. 427. 533. 640. 747. 12 58 96.7 193.3 290. 387 483. 619. 677. 13 54 -90.0 180.0 270. 360. 450. 540. 630. 14 50 83.3 166.7 250. 333. 417. 500. 583. 15 47 78.3 156.7 235. 313. 392. 470. 548. 16 44 73.3 146.7 220. 293. 367. 440. 513. 17 41 68.3 136.7 205. 273. 342. 410. 478. 18 39 65.0 130.0 195. 260. 325. 390. 455. 19 37 61.7 123.3 185. 247. 308. 370. 431. 20 35 58.3- 116.7 175.. 233. 292. 351. 408. 21 33 55.0 110 165 220. 275. 330. 385. 22 32 53.3 106.7 160. 213. 267. 320. 373. 23 30 50.0 100.0 150. 200. 250. 300. 350. 24 29 48.3 96.7 145. 193. 242. 290. 338. Production, Linear Yards 77 If the number of courses is not known, but the cut is known, then from the guide table take the number of courses opposite the cut. Excepting the diameter column and the cut table the figures apply to any knitting machine, either circular or straight. R.p.m. of circular Feeds machine. Dia. Strokes per min. of straight machine 8 9 10 11 12 13 14 15 16 1 700 u 564 u 462 n 400 Guide table 2 350 Cut Coiirsea 2\ 311 6 16 21 280 7^ 19 21 255 8 21 3 233 9 24 3i 215 10 27 3^ 200 11 29 3i 187 12 32 4 175 13 35 4i 165 14 38 4^ 156 41 147 5 140 5i 133 5h 127 51 122 6 117 1500. 7 100 1333. 1500. 8 88 1173. 1320. 1467. 9 78 1040. 1170. 1300. 1430. 10 70 933. 1050. 1167. 1283. 1400. 11 64 853. 960. 1067. 1173. 1280. 1387. 12 58 773. 870. 967. 1063. 1160. 1257. 1353. 13 54 720. 810. 900. 990. 1080. 1170. 1260. 1350. 14 50 667. 750. 833. 917. 1000. 1083. 1167. 1250. 1330. 15 47 627. 705. 783. 862. 940. 1018. 1097. 1175. 1253. 16 44 587. 660. 733. 807. 880. 953. 1027. 1100. 1173. 17 41 547. 615. 683. 752. 820. 888. 957. 1025. 1093. 18 39 520. 585. 650. 715. 780. 845. 910. 975. 1040. 19 37 493. 555. 616. 678. 740. 802. 863. 925. 987. 20 35 467. 525. 583. 642. 700. 758. 817. 875. 933. 21 33 440. 495. 550. 605. 660. 715. 770. 825. 8.80. 22 32 427. 480. 533. 587. 640. 693. 747. 800. 853. 23 30 400. 450. 500. 550. 600. 650. 700. 750. 800. 24 29 387. 435. 483. 532. 580. 628. 677. 725. 773. 78 a .2 ♦J > 'C Q to P4 H a o u :3 o u >» I V CO 0) -f^ o a^ „ o a ■bi)-s ^ 03 CO X 03 O 02 _ . , >. 03 O M ^ =3 g 03 =• =^ a W)-^ c^ 03 j^ q=| 3 ^ -C 03 bc o -♦J 03 a 03 1^ ^ -, 3 J2 ■^ 03 fl :S -S j2 § '^ '^ '^ S O 03 03 •-H t^ rj rs .3 "i r, ^ .s -5 So I' ^ 03 r3 ^ 02 03 'g ^ O J ^ a;3 -^ bc P a g -d >> o •^ o 7^ O c3 S •^ O fl fl O The Science of Knitting a fl CO 03 CO 03 fG 02 "^ O 03 cr 03 a 03 03 CO O O Oi O ft| tH ,-H 03 a 02 03 u 03 c3 cr 02 03 a, 02 0) C3 03 O 03 O X o ft X X a i ftQ M CD CO 1— ( 1— I 03 ■«:*^ TfH l-i 03 CO 03 03 ^ ^ ft fl X CO 00 X X o -(-3 •3 X X X X 02 02 73 73 03 03 03 03 fe fe fe -a 03 ft QQ 73 >H 02 73 03 03 73 03 03 X) m OQ 03 fc^ _r 03 bc . -§ _r J gj ^ ^ 8 "^ -03 ft =3 S 03 ft 2 -+^ - "-< 03 2 <13 § -3 a? .« 03 .h 03 03 03 02 1> ^ •^ ^ .5 03 '^^ 3 >3 « 03 03 03 J ^ 03 -Q o •- ' ft ^ C M a ^ ^ 03 03 -" X -d 73 O "*^ <13 . ^ > S ."S 03 03 "^ 03 TJ ^ 02 03 o ^ s > o >• 03 o 73 03 S -^ CO ^ 03 ^ -d F-S --H >i a 03 03 ^ O 03 t>, fl d 03 J^ t4_ C 03 Jh w ti "^ £2 Q a O 03 T3 ^ 03 03 a S 73 03 ^ tn o3 73 a =3 fl 0) a tn 4j ^ -S «2 S }S 03 ;5 o !=! 1^ ?S ^ W) f^ >> 03 ^ "" - - - -^ ^ O 03 03 03 o3 O fG -" r-i r-i > 03 ^ 02 O 73 ft 03 ft .9 3 «3 02 -tJ X! o Production Table, Square Yards, Wales and Courses Known 79 n o t a s I j> _a> 8 .ti >< u o O 03 IS ^'^ « n e3 ^ I- 3 °.^ 3 „ ^^ S^ TS S3 >. a. a 2 -^ «^ "tJ .2 S ® c n c ^ © .i: a -3 -^ o "^ ® S S ^ fl c ^ 2 « °^ ^ «J ^ cr g -- CO T3 IS « o - « o -5 t2 '-3 « ja -a 3 « cr ■> «5 °" -^ +3 TO ^ .S w -f <- ""^ ^ o) a> .s X m S- a O > cs «o J^COiO-*0000000000 »o C^OCOCOOOOOOOOOCO iC'-i50rt!C>CMt^(MOOCOOOCCC5'«l< ■^ O t-^ 05 O im' m" lO CD 00 oT ^ 05 -^ ^ ^ ^ ,_ rt i-c ,-( (M CI C^J •<*< «oc^t--ccooooooooooc r^c:3C^>or-otciooo-HoocoGOO Ml-~-Hi0O'^0C(MC0»-l»0CT>C000 "*ict^ooor.->(>r-^iotCooor-HC-r r^05-H-5jt^Oi0^tO-*>«t^0005'-< 1— I^H»-1*— It-H^^i-H^^CQ CSI lOt^OlOC^-^iOOOOOOOiO cooocscoior^oc^-^cooo-^co^o coaOi— icO'Cr^OC^i-^ccoO'-HcO'O CO ■^ od oT >-<" c^f CO TjT lo i-C Gc oT - OOOOOOOOOOOOOO COOOOlMrtlCOOOOC^'^COaOCC^ co-<*roOO'-i(MCCTt<>-'5CDt^ o ■^eOCOt-^0C05O'— iC^CO'^iOCO C3 05iO-H00-.COU5-*-i*CCIM'^OOOOOI>^CO) cJcO-^lOCOt^OOOSO'-l'— l*<>Ot^OOO'— 'CO-^COt^OsOC^lCO C^ CO ■^'" -^ O CO t^" Old CO Os" O" ^" C-f CO t>- 00'-ICCCOOO»-'-^t^OCO>nOOOO C0i0C0t^0CO'-lC^'^'-iOO>«lM_C»CC-^"<»<^ocot~t»ooa5030<— 1 «o C0C0-*»«C0t^0C05O'-COCO«Ot^l^000505 »o t^eoic-«*oot^ccio C^CO-*'iOC01^CX)0500'-i2'-ipe^t^ -^(>qCOCDCDt^t:^0000 5?q55ooS^^ococoo5c,(MlMC'3COCOCO->*"-*'<*< 1C0'«*<>0C0 Approx- imate stitches CO »oos-^Ooococot^ioc^r^-00O5»-lC/No. VNo. Cut2 354.62 Cut 750.6 Cut 24 yarn 12 cut (18 gauge) 24 yarn 12 cut (18 gauge) 10.92 10.92 29.56 29.56 6.71 19.9 36.3 62.5 .62 1.83 1.23 2.12 86 The Science of Knitting combination for the latch-needle rib machine; and (3) the relative production, considering that of the rib machine as 1. Then all this is repeated with the production of the rib feed doubled, in order to show roughly the relative production per machine (cylinder), since in practice the number of feeds used per machine is about two to one, in favor of the rib machine. It should be remembered that when the yarn is alike the cut of the machines is different, and when the cut is alike the yarn is different; so when 24 yarn is the basis of comparison, the rib machine is 12 cut and the loop-wheel machine 31 gauge, whereas when the cut is 12 (18 gauge), the yarn on the loop-wheel machine is No. 8 and on the rib machine 24. Not only the actual production, but the proportional pro- duction also may be obtained from the formulas, as is illustrated by the pounds production per feed for yarn the same (24), Comparing rib to fiat, the formula constants are 131 to 161, the actual pounds are 5.46 to 6.71, and the relative pounds are 1 to 1.23; these are all in the same proportion. The comparison of production per machine shows the rib machine to lead in pounds for the same yarn as 100 to 62, but to fall behind in the yardage as 100 to 183. The loop-wheel machine leads for the same cut both in pounds and yards. Although the comparison just made is useful when the formulas fit the conditions, it is desirable to understand the reasons why the production of one type of machine differs from another. The general principles may be shown by taking the production of one machine and modifying it according to the given conditions until it shows the production of the other machine. For simplicity the reduction will be made from the latch-needle rib machine to the loop-wheel flat-work machine. Although the factors involved are comparatively simple, still confusion is Hkely to result if the production in pounds is not considered separately from the production in square yards, so the production in pounds will be considered first, under the two general cases: (1) the same yarn; (2) the same cut. Then the production in square yards will be considered in the same order. Relative Production of Different Types of Knitting Machines per Feed Latch-needle Rib Compared to Loop-wheel Spring-needle Flat- work Machine Pounds, yarn the same. ilelative Production of Different Types of Knitting Machines 87 Factors which Affect the Difference in Production Assumed 35 to 50 or 1 to 1.43 Rib to Flat Needle Velocity. Length of yarn fed in equal needle travel Cut Stitches Formulas ?:M?5VNo. to 9.798 VNo. 4.2165 VNo. 19.596 VNo. or 1 to .86 Relative Production Calculation f\"elocity) (Length yarn) Rib. 1 X 1.43 1 X 0.86 1 Pounds. Cut the Same. Additional Factor. = 1.23 pounds production per feed of fiat to 1 of rib for yarn the same. Rib to Flat , Diameter of Yarn . Formulas . to 8.573 Cut ^" 4.98 Cut or 1 to 1.72. Relative Production Calculation (Velocity)(Length yarn)(Dia. yarn squared) Rib. ix^x5fxHBxif = 3.65 pounds pro- duction per feed of flat to 1 of rib for cut the same. The relative velocity needs no explanation, since it is clear that if all other conditions are the same, a machine which runs faster than another will produce more fabric. Now in this case there is one factor other than the velocity to be considered, which factor is the relative length of yarn which is drawn in by each machine for an equal needle travel. It is evident that if machines A and B are of the same cut and have the same needle velocity, but A is running at 30 stitches per foot of yarn and B at 40 stitches, then B has to run farther in order to use a foot of yarn, and the distance it has to run as compared to A is as 40 is to 30. Therefore, when each runs an equal distance, the relative lengths of yarn consumed will be as 1 ^ 30 is to 1 -T- 40, which is the same as 40 is to 30. Conse- quently, the length of yarn consumed by two machines of the same cut and needle velocity is inversely proportional to their respective stitches per foot of yarn. If the machines have the same needle velocity and stitches 88 The Science of Knitting per foot of yarn, but A has a finer cut, then A will draw the yarn in faster, since it will draw more stitches during an equal travel. And since the machines to be compared are frequently of different cut, it is desirable to have a means of comparison which will take into consideration both the stitches per foot of yarn and the cut. This means can be worked out as follows. The stitches per foot divided by the cut give the distance in inches which each machine must travel in order to draw in an equal length of yarn. Therefore, the reciprocal of this, that is, the cut divided by the stitches, gives the relative length of yarn drawn in for an equal needle travel. Consequently, the length of yarn consumed by each of two machines of the same needle velocity hut different cuts is proportional to the cut divided hy the stitches per foot of yarn, respectively. .., The length-of-yarn factor used is worked out according to the last statement, which factor together with the velocity factor shows that when a latch-needle rib machine produces one pound per feed a loop-wheel flat-work machine, using the same yarn, produces 1.23 pounds. This was shown before by a comparison of the results obtained with the formulas, but this method shows how it may be determined without the formulas, provided the relative cuts, stitches, and velocities are known. When the yarn used on the two machines is different, the problem is just the same as before with the exception that the added factor of diameter of yarn squared has to be used since the machine using the heavier yarn will produce more in the proportion of the square of the diameter. Square yards. — Yarn the same. (See Factors, page 87.) Relative Production Calculation (Velocity) (Width of Fabric) 1 43 1 72 Rib. 1 X -^ — X ~— =2.46 square-yards production ^ ■'• per feed of flat to 1 of rib for yarn the same. Cut the same. Relative Production Calculation (Velocity) (Dia. yarn squared) Rib. 1 X -J— X ~r- X ~r- = 4.23 square-yards produc- ■'• ^ ■'• tion per feed of flat to 1 of rib for cut the same. Weight Per Square Yard Formula — Derivation 89 The following tabulation shows the method_of working out the relative production in square yards. It is noticeable at once that the length of yarn is not a factor in the square-yards production, but that the machine velocity and yarn diameter are factors. The reason for this may be understood with the aid of the following tabulation of the rel- ative machine conditions for the two different cases. Dia. cyl. Cut Dia. yarn Num- ber of needles R.p.m. Width of fabric Yarn same ( ?;}\ ( Flat Cut same \^}^ ( Flat 1 1 1 1 1 1.72 1 1 1 1 1 1.72 1 1.72 1 1 35 50 35 50 1 1.72 1 1.72 Evidently the diameter of the machine does not change, but since, for yarn the same, the cut does change, the number of needles must also change. Consequently, for the same yarn the machine with the more needles makes the wider fabric, and with the same number of needles the machine with the heavier yarn makes the wider fabric. This shows how it is that the yarn diameter affects the square-yards production. When the yarn IS the same, the fabric is wider in proportion to the number of needles, which is proportional to the cut, which is proportional to the diameter of yarn which the machine would use with an equal cut. Therefore, the square-yards production of the machine with the finer cut is increased in proportion to the diameter of yarn which is used with an equal cut. But when the cut is the same, the flat machine uses yam which, according to the rule for corresponding fabrics that the dimensions of an individual stitch are proportional to the diameter of the yarn, makes the fabric both wider and longer for an equal number of stitches; consequently, the square-yards production is increased in proportion to the square of the diam- eter of the yarn. WEIGHT PER SQUARE YARD FORMULA —DERIVATION The weight in pounds of a square yard of cloth is evidently the number of stitches in a yard divided by the number of stitches in a pound. The number of stitches in a yard is: 90 The Science of Knitting CO coco CO coco coco Tj<^ -* ^^ ,}<^ ^^ ^ io>o «oio io>o S S JS ?2;* 5g J:;0S 3z2 M^ '^ «="^ °oS^ o^ CM Jo^ §S ^t^ CO CO coco CO coco TjtTt< ^r)< t}< tj<,h ^Tt< lO«5 lO loio iO»C lOio ^ SJ t: S "^ S '^ lo «e coco t^ >o a> -HO os-* cm oooo osco r:; £2 SS 99 ?5'-1 <^*S »o«= J^ 0005 ^ cm co ■* S SS- oo S CO CO coco CO CO T»< •^ 05 05 t- ^— 1 t;^ car- jqo 05CM lo coo cMco lOO CO oooo TJ< •^■^ ^"^ "^"^ >0 u^fcO »0»0 iO»0 »0 lOCO 2 — £2 S:J? 12 oo> K® "^"^ ^^ "'^ ^^^ ooco oo C2r:;;:;^S^S'::;«o£3'^^"''='5'M>oooocM-!j0 iclo O CO (O t^ CO lO lO 1-1 lO I>- 00 CO ■^ >o es CO OOt^ lO SjO C^ Tt< CO So I^ CO O C5 t^ 05 00 -^ CO 05 UO CO CM CO Oq t^ T-H lO - 05 O CM CO >0 coco kOio ioco CO coco coco t- O CM 00 !>• 00 CO CO oo O M CO coco CM "-H 05 CO O CO CO 05 T-l tH -^ lO O l:^ CO 00 ■* Tfi CM U503CM>OCOt^t— J>.CO»0 ^ CO 05 -H CO lO t^ 03 i-H CO ^lo "O coco coco COt^ t^ 00 CO lO "O 0» CO-* oo lO -^ rtl CO CM -H M 00 .-H CM ^ C5 CO -H COO CO lO t^ 00 -** "^ — ' -" (» O CM »0 t-- O CM -^ coco -*l Tt< ■>*< iC >0 lO to CO CO t>- o. t-- t^ t^ t2<^'^COOO"*COOCOIr^C<100»0 S ^ r:^ °£ N "^ coco xji rt oo CO 00 •<*< -^ lO lO lO »c >o CO !>. t^ !>. oo oooo T-H CO 't* 00 CM eo t^ CO y »n CO ™ t~-- O O CO 0> CM O lO l>- CO •^ r-l CO t-- T-H lO 0> CO t^ t^ 00 00 00 CJS »C O CO lO CM CM ■* O ■<*< 00 "^ "^ ■* CO 05 1*1 t--. 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The area of the disc cut with this size die is 2.405 inches. The weight per square inch = , and since there are 1296 square inches in a square yard, the w • u^ A Wt. of disc ^^ ,_^_ Weight per square yard = — — X 1296 = Wt. of disc X 538.8. The balance may be graduated in any unit, such as grains or pounds, as long as it is remembered that the result is in the same unit. As a rule it is convenient to use the pound, both because the goods are generally classified by the number of pounds per dozen, and because the cotton yarn unit of weight is the pound. However, convenience is the principal guide in selecting both the unit of weight and the size of the disc. When accuracy is required, several discs should be cut at one time, in order to get a greater area to weigh, as well as a better aver- age, if the cuttings are from different portions of the fabric, as they may readily be if the fabric is folded with that intention. Also a comparison of the weights of these different discs shows the variation in the weight of the fabric. Of course, when a sample of the fabric is at hand and the yarn and stitches per foot are known, the weight per square yard may be calculated by use of the formula, so that there is no need of weighing; but when the yarn number or the stitches per foot are not known, either one may be obtained from the formula (trans- formed) after the weight per yard is determined by weighing. TWO-THREAD KNITTING Advantages. — Among the advantages of two-thread knitting over single-thread may be mentioned the following: 1. The possibility of obtaining heavier fabric on any one cut, since two threads may be knit more readily than a single thread of the weight of the two threads. 2. Decreased trouble in knitting, owing to the facts that knots and bunches are smaller, that weak places in one yarn are not ^^ The Science of Knitting likely to part (since the other yarn carries the load), and that even if one yarn does part, the other generally keeps the fabric on the needles. 3. Improved appearance of the fabric, since inequalities in the yarn tend to compensate, and to make clearer work than one yarn of as good quality as the two yarns. 4. More durable fabric, since both threads in a stitch are not 80 likely to break as a single thread, even though the single thread be somewhat larger. Disadvantages. — Among the disadvantages are the following: 1. When the yarn is of the same kind, the cost is greater, since double spinning is required. 2. When the machine continues running after one thread breaks, a large piece of fabric may be spoiled. 3. The number of threads is doubled, so the stoppage for lost ends is doubled. 4. Less elasticity. Plating. — If the work is plated, i.e., if one thread shows on the face of the goods and the other does not, then there are the further advantages that the appearance of the goods is much smoother, and that the thread which does not show may be of less expensive material than the other. Generally Advisable to Plate Two-thread Work. — The smooth appearance is due to the avoidance of twisted threads in the stitches. Therefore, it is advisable to plate two-thread work, whether it is required to hide one thread or not Conditions for Plating. - The conditions for plating are to keep the threads from twisting around each other before entering the needle and in a fixed relative position after they enter it. If these requirements are remembered, the principal difficulties of plating are surmountable by the exercise of observation and judgment Testing with One Feed and Contrasting Colors. - A good plan for adjusting the machine is to start only one feed with the kind and size of yarn to be used, as nearly as possible, but in contrast- ing colors, say black and white. It will be at once evident which thread comes on the face, and if it is not the right one, it may be transposed; also the quality of the plating will be very clear If it is poor, the machine should be turned very slowly and the action of the yarn observed in order to locate the place where the yarns twist around each other. Two-thread Knitting 97 Locating Causes of Defects. — As a rule the twisting is over- come or reduced by keeping the yarns from touching each other up to the time they enter the needles, and after that by keeping control of them, either by tension or otherwise. Separating the Threads in Feeding. — The first thing to do then with any machine is to conduct the yarn to the needles by separate paths, for if two yarns follow the same path, they are sure to twist around each other. Even when they enter the needles they should do so through separate holes in the guide or carrier; or if there is not room for two holes, as is sometimes the case with fine-gauge loop- wheel machinery, the two threads should be kept separate by being guided to the hole at different angles, or by some other such means. Machines Considered. After the yarn has reached the needles the treatment depends very much on the type of machine which is used. The spring-needle flat-work machines and latch-needle rib machine are considered here. Illustration i. — Illus- tration 1 shows a diagram of a spring-beard needle with the old loop about to cast off over a new double loop con- sisting of a black and white thread. As shown, the illustration applies to vertical-needle machines, such as the loop-wheel machine, but it may be turned so that the needle lies horizon- tally with the beard up, when it serves for most machines of the jack-sinker type. Illustration 1. Double-thread loops on spring needle. The thread in the head of the needle appears on the back of the fabric. 98 The Science of Knitting .>. ufTu ^^^^^ ^" ^P"^S ^^^^1^- - It ^ill be noticed that the black thread, cotton say, is in the head of the needle, and that the white one, say wool, is under it (behind it, if the needle is horizontal); also that in the up-coming stitch the black or cotton thread is on the back. If the positions of the threads in the heads of the needles are reversed, then they will be reversed in the fabric also Therefore, it is not only necessary to feed the yarns to the needles in the correct relative position but to keep them there which latter requirement is sometimes difficult, especially with loop-wheel machines. Yarn Difficulties. — The composition and twist of the yam are sources of trouble, so the most used materials, namely wool and cotton, should be considered. In the first place there is the tendency of the yarn to untwist, which tendency is generally more pronounced in wool than in cotton. Then in the loop-wheel machine there is a rolling motion imparted by the sinker-bur blade which increases the tendency to twist. Rolling by Rotary Sinker. - Moreover, there is opportunity to twist, not only when the yarns are feeding over the sinker, but after they get under the needle beard, for the cramp of the needle must be sufficiently open to receive small bunches at least, so it cannot clasp the yarn tightly enough to hold it securely in place Helps to Spring-needle Plating. - Some of the helps to good plating on spring needles may be understood from the preceding- that IS, needle cramp as close as is permissible, yarns about of a size, and anythmg which will prevent twistmg of the yarns in the uncontrolled space between the sinker and the cast-off. Treatment of Yam. — Among the artificial means of preventing twisting IS deadening the yarn by emulsionizing, dampening oilmg, etc.; but a better way, although not always available, is to use a gauge of machine as fine as is consistent with good running so that the stitch may be fairly long, since the loops keep their position much better when the gauge is well filled and the loop is long. Short Stitches Twist the Most. - This is illustrated by the custom of using eveners or dividers on loop-wheel machines which knit fine yarn with a tight stitch, and of not using them with heavy yarn and a long stitch. Silk and Worsted. -When it is impractical to use yarn of about the same size, as is generally the case in knitting a silk face and a worsted back, where the cost of an equal-size silk yarn Two-thread Knitting 99 would be prohibitive, then deadening the yarn must often be resorted to. Casting-ofE from Spring Needle. — Suppose that the two threads are kept in the correct relative position until they get to the cast-off. This is one of the troublesome places, especially in loop- wheel knitting. By reference to Illustration 1, it will be seen that the old loop has to move up over the new double one without disturbing its own structure or the relative position of the yarns in the new loop. With a needle as closely cramped as the one shown the new loop is comparatively safe, but such a close cramp is impractical; moreover, as the old loop comes up, the black thread on the back is likely to be rolled through upon the face by the friction against the new loop. This is aggravated not only by the upward pull of the fabric, but by the crude action of the cast-off blade. Comparison of Jack Cast-off and Rotary Cast-off. — Conse- quently, machines in which the fabric draws at right angles to the needles and in which jack cast-offs are used, do better plating as far as casting-off is concerned. Moreover, they do better work as far as sinking the stitch is concerned, since they are generally equipped with jack sinkers which place the yarn in position and then retire direc4;ly, instead of retiring with a rolling motion as does the fixed bur blade. One important factor which counts in favor of the plating on jack-sinker machines is practice, for where jack-sinker machines are used two-thread fabrics are much more common, so that jack-sinker knitters have opportunity to become more expert in this kind of work. Two Sinker Burs. — Before leaving the loop-wheel machine mention should be made of the use of two sinkers for plating. Owing to the fact that the needle drives the sinker bur, it is inadvisable to overload the latter, and since two-thread wotk is generally made heavier than single-thread work of the same gauge, it is not uncommon to divide the work of sinking between two burs, in which case the first to feed the needle carries the thread which goes on the back of the fabric. Short Stitch for Concealed Yam., — This practice enables mak- ing the stitch of the back thread tighter than that of the face thread, which is frequently done and seems to be warranted by the evidently shorter path occupied by the thread on the back of the fabric. With two sinkers the feed occupies additional space, so that 100 The Science of Knitting the number of feeds per cyhnder is more restricted; and there is increased danger of the yarn dropping out of the needles owing to the increased distance from the first sinker to the cast-off; but there is the advantage that with differently colored yarns, checks and vertical stripes may be made by blocking certain spaces in the face sinker, which floats the face thread on the back of the fabric and lets the back color show through on the face. Illustration 2. Double-thread loops on latch needle. The thread nearest the point of the hook is hidden in the fabric. The dial needle is not shown. Illustration 2. — Illustration 2 shows a latch needle which has just drawn a double loop for ribbing and which is about to clear the old loop over the new loop. Position of Thread in Latch Needle. — It will be noticed that in this case the thread which is hidden is toward the latch, or outside, as the needle generally stands; that this thread is hidden between the back and the face instead of being left exposed on the back; and that its path is much shorter than that of the Twist in Flat Knit Fabric Made With SeK-feeding Needles 101 other thi'ead, which probably accounts for the practice of using tension on it in order to improve the plating; although it is doubtful if much difference can be made in the length of yarn fed, since the construction of the machine makes nearly equal lengths imperative. Two Holes in Carrier. — A good way of keeping the yarns apart before they reach the needles is to use two holes in the carrier, one in the usual position feeding to the inside, and the other feeding out of the bottom of the carrier. In this case it is advisable to withdraw the dial needle sooner than is usual, in order to avoid the danger of catching the dial latch in the hole in the bottom of the carrier. With the threads separated in this way good plating of the cylinder stitches is obtained. Plating Inside of Rib Fabric. — If plating of the dial stitches also is desired, the tension must be kept on the loops with proper cam arrangement until the dial stitches are cleared. If this re- quirement is met, the yarn to be hidden will slide up ii^to the head of the dial needle and occupy the position nearest the latch just as it does in the cylinder needle. Tracing Trouble. — The causes of defective plating may frequently be located from an examination of the fabric con- taining the defectSs Reversal of the yarn before it gets into the needles is generally indicated by a streak along a course. Re- versal in clearing the stitch is generally indicated by appear- ance of the back thread at the edge of the wales at irregular intervals, except when the needle has something to do with the trouble, when the wale will show the defect throughout its length. TWIST IN FLAT KNIT FABRIC MADE WITH SELF-FEEDING NEEDLES The yarn generally comes to the knitter on cones. So the subject of twist begins for him with the cone. It will be con- ceded that the yarn on this cone has a certain amount of twist, either right-hand or left-hand as the case may be. It does not matter whether part of that twist was put into the yarn in con- ing it or not. This is as true of a bobbin as it is of a cone. Right-hand Twist. — Right-hand twist is such that if the yarn could be turned into metal, it would look and act like a right- hand screw; that is, by turning it into a board in the direc- tion of the hands of a clock it would draw itself into the wood. 102 The Science of Knitting Motion in this direction is called clockwise because it is like that of the hands of a clock. Left-hand Twist. — Yarn with left-hand twist, if solidified, would have to be turned in the opposite direction in order to make it enter the board, which direction is called anti-clockwise because it is opposed to that of the hands of a clock. Point of View does not Affect Direction of Twist. — Turning the yarn end for end does not alter the appearance of the twist, so its direction can always be recognized. Extent of Twist. — The extent of the twist is designated by the number of turns per inch, just as is that of a screw thread. Illustration 1. Strip of paper pulled lengthwise from a pencil on which it had been coiled in an anti-clockwise direction. The twist in the paper is right-hand, and there are as many twists as there were coils. Similarly, right-hand twist is put into yarn when it is pulled off a cone on which it was wound in an anti-clockwise direction. Suppose that the piece of yarn is one inch long and has no twist. Then if one end is held and the other is given five complete revolutions, the yarn twist is five to the inch. When released, the yarn will shorten somewhat, so that the twist of that par- ticular piece will be more than five to the inch since then there will be less than an inch of yarn. The actual twist of this piece of yarn or of any piece is the number of complete turns in a given length divided by that length. For instance, if there are twenty turns in two inches, the twist is 20 -t- 2, or 10 to the inch. Determining Extent of Twist. — A convenient method of determining the number of turns is to cut a known length, say two inches, and hold one end while the other end is untwisted and each turn is counted until the strands are straight. The number of turns divided by the length gives the extent of the twist. Twist in Flat Knit Fabric Made With Self-feeding Needles 103 Twist of Yarn is Affected by Delivery from Package. — Con- sider that the yarn is on the knitting machine, but not yet threaded to run into the needles. As it comes off the cone its extent of twist is changed. Take a pencil and roll a strip of paper around it. Then draw the strip off the pencil endwise as shown in Illustration 1. The strip will have as many twists in it as there were turns around the pencil and the direction of the twist will depend on the du-ection in which the paper was rolled. Stand the pencil with its' point upw^ard, and regard it from the point. Then, as is shown, the paper was wound anti- clockwise, and, evidently, the twist put in the strip is right-hand. How Cones are Wound. — Now, yarn is generally wound on cones as this strip of paper was wound on the pencil, so when yarn is drawn off from the nose of a cone, it is given one right- handed twist for every complete turn around the cone. Con- sequently, if the yarn already had right-hand twist, that is increased, and, conversely, if it had left-hand twist, th^t is reduced. How Bobbins are Wound. — Bottle bobbins from upright winders are generally wound in the direction opposite to that of the cone. Consequently, when yarn unwmds from a bottle bobbin from the ordmary winder, left-hand twist is put into it to the extent of one turn for every length around the bobbin. If the yarn is right-hand twist, then that is reduced, whereas if it is left-hand twist, it is increased. Illustration 2. — Illustration 2 shows a bottle bobbin and a cone and how the yarn unwinds from each. The arrows en- circlmg the yarn show the direction of the twist which is put into the yarn by the unwinding, provided the free end of tlie yarn is kept from turning. From this it follows that the yarn near the cone or bobbin is actually twisted in the reverse direc- tion of that shown by the arrows. If this is not perfectly clear, reference may be made to Illustration 1 which shows how the yarn is twisted coming from the cone. The yarn coming from the bobbin is twisted in the reverse direction. It should be noted that one turn of twist in the yarn is made for each com- plete turn of yarn around the bobbin, or cone. The average diameter of these packages is about four inches, so one average turn around the package is roughly one foot. Feeding the Yam Makes it Revolve. — Now, thread the yarn into a machine with self-feeding needles, such as latch-needle 104 The Science of Knitting machines for fiat work, rib work or hosiery. It will be found that when the yarn is running into the needles, it revolves in the direction in which a corresponding screw would revolve when being screwed into a piece of wood. In other words, yarn with right-hand twist turns clockwise when running from the ob- server toward the machine, and left-hand-twist yarn revolves A Direction of twist caused ty unwinding i,e, left handed Direction of twist caused by unwinding i.e. right handed Illustration 2. anti-clockwise. Moreover, the rate of turning is quite rapid, sometimes amounting to one turn in less than an inch of the yarn travel. Yam Twist Most Important in Making it Revolve. — From this it is evident that the influence of the twist of the yarn itself has much more to do with its revolving when entering the machine than the direction of its unwinding from the cone. Illustration of Yarn-feeding Conditions. — The explanation of this may be determined by considering the conditions and a somewhat similar case. The yarn is drawn into the old loop at the rate of about five feet per second. For a similar case, sup- pose a wire cable to be inserted in a snugly fitting hole in a Twist in Flat Knit Fabric Made With Self-feeding Needles 105 piece of wood and then pulled through from the farther side at the rate of five feet per second. Of course, the cable would re- volve in the direction dictated by its twist. That is, a cable with right-hand twist, viewed from the entering side of the board, would revolve clockwise, and one with left-hand twist would revolve anti-clockwise. To carry the illustration still further, suppose that instead of drawing the cable through a closely fitting hole in a board it be Illustration 3. Illustration of loop distortion caused by the twist in the yam. Owing to the inclination of the fibers, the portion marked B slides forward in the loop E in front of loop A. Consequently, loop E is farther forward in the drawing than loop D, so that in the fabric loop E is higher than loop D and causes left-hand twist in the fabric. Therefore, the twist of the fabric matches the twist of the yarn. Then the rope irawn through a closely fitting loop in a rope, svould tend to twist the cable as just described. Rule for Revolution of Yarn in Feeding. — Consequently, when ^arn is drawn into a stitch, it isTevolved according to its twist. Illustration 3 shows the influence of the twist on the revolution 106 The Science of Knitting A. Normal loops. B. Loops obtained with left-hand twist yarn, and caus- ing left-hand twist fabric. Loops obtained with right-hand twist yarn, and causing right-hand twist fabric. Illustration 4. Twist in Flat Knit Fabric Made With Self-feeding Needles 107 of the yarn as it enters the machine. The hook of the needle has just drawn a new loop through an old one. The yarn has left- hand twist as is shown. The part of the loop which entered the needles first (A) is back of the part which entered last (B), which was drawn in at a velocity of about five feet per second and had to drag a considerable length through the old loop, whereas the other side had but little, if any, dragging to do. Close observation will show that the direction of inclination of the strands of yarn in both the new loop and the old one through which it was drawn tends to slide the entering yarn forward toward the observer, and then to revolve it as it w^ould a left-hand screw in entering. The revolving of the yarn takes some of the twist out of the yarn which is being looped and transfers it to the yarn which is being fed. The moving forward of the entering yarn displaces the loops in a way which produces twist in the fabric, as will be shown. Flat-fabric Twist caused by Revolving of Yam in Feeding. — It is evident that B is farther forward than A, but C corre- sponds to B, so C is farther forward than A. Consequently, Illustration 5. Plain flat knit fabric with right-hand twist caused by right-hand-twist yam. when the loops are turned upward as they are seen in the face of the actual fabric, loop E will be higher than loop D. That is, with left-hand-twist yarn the left-hand needle loops are high- est, and, conversely, with right-hand-twist yarn the right-hand needle loops are highest. Illustration 4 shows the meaning and result of having one needle loop higher than the other. At A two adjoining needle loops are shown in normal position. Fabric with loops like this is not twisted by the causes under discussion. 108 The Science of Knitting At B the left-hand loop was higher than the other one, so if the bases of the loops are kept horizontal as shown, which corre- sponds to keeping the courses horizontal in the fabric, then, evidently, the fabric has left-hand twist. On the contrary, if the right-hand loop was higher as at C, the fabric has right-hand twist. This right-hand twist is shown more fully in Illustration 5. Rule for Flat-fabric Twist. — From the preceding it follows that yarn with left-hand twist produces fabric with left-hand twist, and yarn with right-hand twist produces fabric with right- hand twist, or the twist of the fabric is like the twist of the yarn. An interesting question is how much, if any, does the direction of motion of the machine affect the twist of either the yarn or the fabric? Evidently one end of the yarn is in the cloth and the other is in the cone. The cone does not revolve with respect to the yarn and only in the case of some one-feed circular machines does the yarn revolve with respect to the cone. Effect of Machine Motion on Fabric Twist. — A case of this kind is shown in Illustration 6, which is of a one-feed circular ribber in which the cams revolve anti-clockwise (the conventional direction of motion for such machines). Since the yarn enters the hole in the center of the end of the stud and comes out of the side of the stud, and since the stud revolves, whereas the cones are stationary, it is evident that for each revolution of the machine it must put one turn of twist in the yarn. The arrow in Illustra- tion 6 shows the direction of motion of the machine, from which it is evident that the twist put in the yarn is left-hand. Some Machines Twist Yarn Slightly. — Consequently, in a machine of this kind the twist put in the yarn is right-hand if the yarn carrier turns clockwise and left-hand if it turns anti- clockwise. This is also true of the ribber with dogless attach- ment when the cone does not revolve with the yarn carrier. In general, it is true of all machines in which either the carrier (yarn guide) or cone revolves in respect to the other, i.e., in machines in which the cone is stationary and the carrier revolves, or in machines in which the carrier is stationary and the cone revolves. Some Machines do not Twist Yarn. — When both the cone and carrier revolve together, as in Illustration 7, then the direc- tion of motion of the machine does not affect the twist of the yarn. This comes under the general rule that when the cone and carrier do not revolve with respect to each other, then neither the DIRECTION OF MOTION OF YARN CARRIER Illustration 6. Type of machine which twiats yarn. (109) Illustration 7. Type of machine which docs not twist yarn. (110) Twist in Flat Knit Fabric Made With Self-feeding Needles 111 direction of motion of the machine nor the relative motion of the different parts of the machine affect either the twist of the yarn or the twist of the fabric. Illustration 7 shows a ribber of the revolving cam type in w^hich the carrier and the cone are station- ary with respect to each other, although they both revolv^ with respect to the head base. The result is the same whether the cams revolve one way or the other or w^hether the cams are stationary and the needles revolve one way or the other. This is contrary to the notions of some knitters and knitting-machine manufacturers who advocate a particular direction of motion, or a particular type of machine on account of alleged beneficial action on the twist of the yarn. Machine Motion does not Determine Direction of Yam Revolution in Feeding. — The fallacy of these arguments may be quickly shown by observing a knot traveling toward the needles during the making of the heel or toe on an automatic hosiery machine. If the yarn has right-hand twist, the knot will revolve clockwise viewed from behind and will continue to revolve so in spite of the fact that the needles revolve first in one direction and then in the other. This is equally true whether the machine be of the revolving cylinder type or of the more common revolving cam type. Fabric Twist Independent of Machine Motion. — Regarding the effect of the direction of motion of the machine on the twist of the fabric, reference to Illustration 3 shows that it matters not which of the two loops is formed first as far as the resulting twist in the fabric is concerned, for if the right-hand loop is formed last, the side of the loop on the extreme right will be drawn back- ward instead of forward toward the observer, so the illustration holds true for either case. Naturally, a corresponding conclusion would apply to right-hand-twist yarn as well. Consequently, the direction of motion of the machine has no effect on the twist of the fabric. From this it folio w^s that it makes no differ- ence whether the cams or the needles revolve with respect to the head base, since by any combination only two directions for the formation of the stitch are available and it has just been shown that neither one of these directions has any effect on the twist of the fabric. Minor Causes of Fabric Twist. — However, it is practically certain that the take-up tension, the j'-arn tension, the angle at which the yarn is fed and many such details combine to affect the 112 The Science of Knitting twist of the fabric in ways and to an extent which cannot readily be generaHzed. Moreover, the cause of what little twist there is in rib fabric seems to manifest itself slightly in flat goods also. This is explained under the title twist in rib fabric, which twist is opposite to that of the yarn of which it is composed. Conclusion. — Consequently, in flat fabric there are generally at least two opposite tendencies; namely, the marked one just described which is to twist in the direction of the yarn twist, and a slighter tendency to twist in the opposite direction. Ob- servations so far indicate that the former generally prevails, but if it is quite weak, then the twist of the fabric becomes op- posite to that of the yarn, but there is no inclination of the wales accompanying it. More- over, the effect is generally so slight as to be unobjectionable. TWIST IN RIB FABRIC Twist in rib fabric is due to a slight untwisting of the yarn instead of to stitch distortion. If the stitch is long, there is a greater length of yarn in it to on rib fabric twist. The yarn is untwist, SO the effect in the right-hand twist, which tends to fabric is more noticeable. The manner in which the un- twisting of the yarn affects the fabric may be understood by considering one face stitch with the top or round portion upward as in the illustration. The two sides of the loop lie approximately parallel as they enter the next lower loop. " Suppose that the twist of the yarn is right-hand. Then the visible strands or fibers will be inclined upward to the right like the threads of a right-hand screw. Consequently, if any of the twist comes out, the bottom of the stitch must turn to the right, and every stitch in the fabric Illustration o! one eflfect of yarn twist straighten, and to throw the bot- tom of the stitch to the right as shown by the dotted lines, which puts left-hand twist in the fabric. Summary Regarding Twist of I\iiit Fabrics 113 twisting thus puts left-hand twist in the fabric for the wales will then be inclined upward to the left. In other words, the twist of the fabric is opposite to that of the yarn composing it. This can be illustrated nicely by running one cone of left- hand- twist yarn with a set of right-hand-twist yarn. The course made by the left-hand-twist yarn being distinctly different from the other courses, produces the loop effect of an improperly adjusted cylinder stitch cam, but close examination will show the stitches of this course to be twisted opposite to those of the other courses. Obviously, the weaker the twist in the yarn the slighter will be the twist in the fabric, and it can be reduced by running to- gether two equal threads of equal but opposite twist. SUMMARY REGARDING TWIST OF KNIT FABRICS General The direction of motion of the cylinder and the cams with re- spect to each other or with respect to the head base is immaterial. When the yarn carrier revolves with respect to the yarn- supply package, there is a slight tendency to twist the yarn right-hand if the motion of the carrier is clockwise and left-hand if the motion is anti-clockwise, but this tendency is so slight that it is negligibre, even on very small-sized machines on which it is the greatest. The yam is twisted in coming from the package, right-hand if unwound clockwise and left-hand if unwound anti-clockwise; and the extent of twist is inversely proportional to the length of one complete coil; but, at most, it is insuflficient to affect materially either the yarn or the fabric. WTien yarn is being drawn by a self-feeding needle, it re- volves clockwise if the yarn twist is right-hand and anti-clock- wise if left-hand, and thereby transfers some of the twist from the yarn which is forming the loop to the yarn which is just entering. The tendency is strong in hard yarns w^ith well- defined strands. This helps to account for the persistent kink- ing of some yarn when running into the machine. Rib Work The revolving of the yarn in entering seems not to affect the twist of the fabric, but the natural tendency of the yarn in the loops to untwist makes rib fabric twist slightly opposite to the twist of the yarn. 114 The Science of Knitting Winder Capacity, in Pounds per Spindle per 9 Hours Actual Time Nutaper, 1250 r.p.m. Cotton Worsted Cut Araer. Amst. Cohoes Silk dram Yarn 195 293 546 count Y^ Y Y 1.17 Y 1.87 Y 3.7 Y .64 Y Y means yarn number 1.0 195 293 546 1.2 1.9 3.7 .6 1.2 162 244 455 1.4 2.2 4.4 .8 1.4 139 209 390 1.6 2.6 5.2 .9 1.6 122 183 341 1.9 3.0 5.9 1.0 1.8 108 163 303 2.1 3.4 6.7 1.2 2.0 98 147 273 2.3 3.7 7.4 1.3 2.3 84 126 234 2.7 4.4 8.6 1.5 2.7 73 110 204 3.1 5.0 9.9 1.7 3.0 65 98 182 3.5 5.6 11.1 1.9 3.5 56 84 156 4.1 6.5 13.0 2.2 4.0 49 73 136 4.7 7.5 14.8 2.6 4.5 43 65 121 5.3 8.4 16.7 2.9 ■ 5 39 59 109 5.9 9.4 18.5 3.2 6 32 49 91 7.0 11.2 22 3.8 7 28 42 78 8.2 13.1 26 4.5 8 24 37 68 9.4 15.0 30 5.1 9 22 33 61 10.5 16.8 33 5.8 10 19.5 29 55 11.7 18.7 37 6.4 11 17.7 27 50 12.9 21 40 7.0 12 16.3 24 46 14.0 22 44 7.7 13 15.0 23 42 15.2 24 48 8.3 14 13.9 21 39 16.4 26 52 9.0 15 13 20 36 17.6 28 56 9.6 16 12.2 18.3 34 18.7 30 59 10.2 17 11.5 17.2 32 19.9 32 63 10.9 18 10.8 16.3 30 21.1 34 67 11.5 19 10.3 15.4 29 22.2 36 70 12.2 20 9.8 14.6 27 23.4 37 74 12.8 21 8.3 14.0 26 24.6 39 78 13.4 22 8.9 13.3 25 25.7 41 81 14.1 23 8.5 12.7 24 26.9 43 85 14.7 24 8.1 12.2 23 28.1 45 89 15.4 25 7.8 - 11.7 22 29.3 47 93 16.0 26 7.5 11.3 21 30.4 49 96 16.6 27 7.2 10.9 20 31.6 51 100 17.3 28 7.0 10.5 19.5 32.8 52 104 17.9 29 6.7 10.1 18.8 33.9 54 107 18.6 30 6.5 9.8 18.2 35.1 56 111 19.2 Allowance should be made for lost time according to the quality of yarn and skill of help, which vary so much that a general rule is not given. Winder Capacity 115 Capacity in Pounds per Spindle of Upright Bobbin Winder, 300 r.p.m. of Main Shaft, for 9 Hours Actual Time Yarn count Cotton 166 Y Worsted 249 Y Cut 465 Y Amer. Yxl Amst. Yxl. 59 Cohoes YX3.19 Silk dram Yx.545 Y means yarn number 1.0 166 249 465 1.0 1.6 3.2 .55 1.2 138 207 388 1.2 1.9 3.8 .65 1.4 119 178 332 1.4 2 2 4.5 .76 1.6 104 156 291 1.6 2.5 5.1 .87 1.8 92 138 258 1.8 2.9 5.7 .98 2.0 83 125 233 2.0 3.2 6.4 1.09 2.3 71 107 200 2.3 3.7 7.4 1.27 2.7 62 93 174 2.7 4.2 8.5 1.45 3.0 55 83 155 3.0 4.8 9.6 1 63 3.5 47 71 133 3.5 5.5 11.2 1.91 4.0 42 62 116 4.0 6.4 12.8 2.18 4.5 37 55 103 4 5 7.2 14.3 2.45 5 33 50 93 5 8.0 15.9 2.72 6 28 . 42 78 6 9.5 19.1 \3.27 7 24 36 66 7 11.1 22 3.81 8 21 31 58 8 12.7 26 4.36 9 18 28 52 9 14.3 29 4.9 10 16.6 25 47 10 15.9 32 5.5 11 15.1 23 42 11 17 5 35 6.0 12 13.8 21 39 12 19.1 38 6.5 13 12.8 , 19.2 36 13 20 41 7.1 14 11.9 17.8 33 14 22 45 7.6 15 11.1 16.6 31 15 24 48 8.2 16 10.4 16.0 29 16 25 ■ 51 8.7 17 9.8 15.6 27 17 27 55 9.3 18 9.2 13.8 26 18 29 57 9.8 19 8.7 13.1 25 19 30 60 10.3 20 8.3 12 5 23 20 32 64 10.9 21 7.9 11.9 22 21 33 67 11.4 22 7.6 11.3 21 22 35 70 14.7 23 7.2 10.8 20 23 37 74 12.5 24 6.9 10.4 19.4 24 38 78 13.0 25 6.6 10.0 18.6 25 40 80 13.6 26 6.4 9.6 17 9 26 41 83 14.2 27 6.1 9.2 17.2 27 43 86 14.7 28 5.9 8.9 16.6 28 45 89 15.3 29 5.7 8.6 16.0 29 46 93 15.8 30 5.5 8.3 15.5 30 48 96 16.3 32 5.2 7.8 14.5 32 51 102 17.4 34 4.9 7.4 13.7 34 54 108 18.5 36 4.6 6.9 12.9 36 57 .115 19.6 38 4.4 6.6 12.2 38 60 120 20.7 40 4.2 6.2 11.6 40 64 127 21.8 Allowance should be made for lost time according to the quality of yarn and skill of help, which vary so much that a general rule is not given. 116 The Science of Knitting SUMMARY REGARDING TWIST OF KNIT FABRICS — CONTINUED Flat Work The revolving of the yarn in entering tends to twist the fabric the same as the yarn of which it is composed. When twist from this cause does not occur, there is generally a slight twist opposite to the twist of the yarn, due to the cause just men- tioned in connection with rib work. SET The original underwear mills in America carded and spun their own yarn, and the size of the mill was expressed by the number of sets of cards. A set of machinery was considered to be: 1 set of cards; 1 mule; 2 spring-needle knitting tables, with 2 four-feed cylinders each, i.e. 16 flat feeds in all; prepara- tory and finishing machinery to match, according to the special conditions, which were too diverse for general classification. Soon, however, the use of larger cards, the efforts to increase production, the introduction of the latch-needle machine, the use of fine bought cotton yarn instead of mill-spun woolen yarn — all these and other conditions — made the term set as applied to a knitting mill so indefinite that its use decreased. However, there are still many knitting mills which spin their own yarn; and there is much knitting information expressed in the set unit, so a knitter should know not only what a set is but also how much allowance to make in the use of it. Results of quite extensive investigations of knitting mills making their own yarn exclusively or nearly so, on woolen cards, show a set of machinery — for 48 inches of card width, either actual or reduced from other size cards — to range as follows : 1 set 48-inch cards; mule spindles, 240 to 325; winder spindles, 20 to 40; flat feeds, 14 to 25; sewing machine settings, 6 to 12; preparatory machinery, cuff-knitting machinery, and finishing machinery (other than that mentioned) to correspond. Among the other machines, which cannot be classified by the set because one is sufficient for a number of sets, may be mentioned a press, a washer, and a hydro-extractor. In ad- dition there are means for final drying, such as drying forms or dry pipes, brushers, dyeing and bleaching apparatus, and some Space Allotment in Knitting Mills { )ortant machinery according to the work done am i s used. I cost of a set of knitting machinery is $10,000, wi I on of 30 per cent either way. cost of mill buildings per set is $7000, with consid .tion, frequently on the low side, since popular opinio ti «t any kind of building was good enough for a knitting The cost of the site varies so much that generahzatioi not be made. In some cases the land is " thrown in " as as power is paid for. The horse power required, as is shown w* where in the book, is about 18 per set. used, the engine is non-conder for heating, washing, and dr per set per year will supplv requirements, if the exh some live steam used du i stallations increase the ( cent. When exhaust stea ing, and drying, about fift^ those purposes. There i? and power installations It is difficult to det' water used is seldom an idea of it. Large mill for childrei and ladies' ribbed vests; dyed, and bleached, uset draulic elevators, and pre 1000 gallons of water ar year. SPACE ALLOTS. The figures are from me operation, and are useful for or for estimating on the real estate of underwear. The per set figures are probably the i afford means of comparison on nearly eq units for proportioning the space accordin capacity of the mill. The Science of Knitting I^^OJ, CO CO 00 UO C*| *l OS O t^ OS aaiiog 5§ o «o O fO t^ OS >C (N C^ O t^ in CO t>- o cq t^ CO r>. t^ -^ OS CO lO CO CO (M ■>*< O CO r-l -I-' OJ w o .2, Tf) C 03 a o > 'So f& O t/J -^j IB m ;3 03 o tn a U) 02 CD O 03 Space Allotment in Knitting Mills 119 Mill A was built for the manufacture of percentage flat goods, but was running on men's fleeces when inspected. Mill B was built for the manufacture of woolen underwear and still made some in fine gauges, but the bulk of its output was men's cotton fleeces. Mill C was designed for making woolen underwear, but was running exclusively on men's fleeces, turning out from 300 to 350 dozen per day. Mill D was designed for a general variety of goods, and was making children's fleeces, men's flat cotton underwear, and ladies' ribbed vests. All of the mills sold through commission houses. None of them was equipped with rib machinery exclusively; but this would not make much difference in the space allotment, so the figures may be taken for ribbed-underwear mills making their own yarn, as well as for flat-goods mills, either woolen or cotton. Explanation of the per Set Allotment ^ Storage. — That of mills A and C was not obtained, but from 500 to 1000 square feet seems advisable, according to the amount of stock to be carried. Mill B had more room than it used. Picking. — Mill D picked and garnetted all of its waste, and had room to spare, which accounts for its large space allotment. None of the other mills worked up its own rag waste. Mill C had more room than it needed. Carding. — The figures run close together, but it should be remembered that ail of the yarn used was not spun, so slightly more yarn-making space would probably be desirable for a mill making all of its own yarn. In such a case 2000 square feet for yarn making is reasonable, and an approximate rule for dividing it up into picking, carding, and spinning is as 1 is to 2 is to 3. Spinning. — Mill C had some spare room. See paragraph on Carding for remarks on total yarn space which apply to Spinning as well. Winding and Knitting. — Mill C was crowded. A fair al- lowance is 600 square feet when flat cuff frames are used, and 500 when not. The proportion of winding to knitting space is about as 1 is to 2. Washing. — An allowance of 200 is generally sufficient. Mill B had more than was required. 120 The Science of Knitting Drying. — This space depends on the method or methods used for drying, or whether any is done at all. In rare cases washing and drying are not done. In the mills in question the horizontal-dry-pipe method was used. Mill B has also a drying room for the use of drying frames, which accounts for the larger space in that mill. When drying frames and drying lofts are used exclusively, the space may run as high as 1000 square feet and over, although 500 is a better average. The use of drying ovens decreases the space and heat needed for drying. Seaming and Finishing. — Mill A had waste room. A fair division when cuff looping is done is 1 to 2 for seaming to finishing. When looping is not done, the proportion of seaming and the total space may be less. An allowance of 1100 square feet is fair average practice for the total when looping ia done. Napping. — This was an afterthought, since fleeces became popular after these mills were built and the machine or machines were generally put wherever convenient. The space for Mill B is too small, since all of its product was not napped. The small garment brushers are not included in napping. They were scattered in different places when used. Packing. — All of these allowances are large, and properly some of each should be classified as storage of finished goods, but these two departments are so closely connected that it is difficult to locate the dividing line. Storage. — This space is excessive, owing to the facts that Mill B had been designed for a larger number of sets than was installed, and Mill C had been just recently enlarged but the new machinery was not yet in place. An allowance of 800 square feet is considered ample; 600 is considered an average. Machine Shop. — This space is generally limited by con- venience. Office. — The close relationship here shown to the capacity is reasonable since all of the mills had the same method of sell- ing, and the accounting methods would probably be much alike. Boiler. — Mill A had waste room, and Mill D had a com- pact battery. The average is between the two. Engine. — Mill A had waste room. Miscellaneous. — The extent of this is more a matter of accident than design. Horse Power Required by Various Machines 121 Space Conclusion A total allowance of 7000 square feet per set of 48-inch cards is a fair average allowance, and 4000J seems to be about the minimum. It will be evident that there is quite a divergence in the space allowances, not only in the departments but' in the mills as a whole. This is to be expected; since knitting as an industry is comparatively new in America; since the mills have generally been a growth from a small original mill, often unsuited to the purpose; and since the design of knitting mills presents so many perplexing problems that designers have not found it profitable to devote to it the time necessary for its development. Al- though success in the knitting business depends on a great many factors more important than too much or too little space, still the space factor is overlooked only at expense which should go to profit and which will ultimately go there when the ^extent of the loss is realized. Every 100 square feet of floor space costs about $10.00 per year to maintain, which is interest at 6 per cent on a capitalization of $167.00. On the other hand, if the space is insufficient to allow expedition in the conduct of the business, or if it is so poorly arranged as to require more than necessary hands to convey the work, the cost mounts up quickly. Experience indicates the advisability of the use of automatic con- veyors more than at present; passageways large enough to avoid congestion, but no larger; storage so arranged as to be available for either raw stock or finished goods ; and room for enlargement in at least one direction, and preferably more than one. HORSE POWER REQUIRED BY VARIOUS MACHINES USED IN KNITTING MILLS ^^ Horse Power Picker, wool or bur 4 -6 Picker, rag . .'. 7 - 9 ( 2 Beater 4 -6 Lapper < 3 Beater 3 -10. 5 r 4 Beater 6 -16 Set cards 1 -2 Mule spindles per 100 4- .7 Winders, upright, say 30 spindles 1 Hydro extractor 2 -4 Sewing machines, 5 1 The above is from " Manual of Power " by Samuel Webber, published by D. Appleton & Co. and other sources. 122 The Science of Knitting Latch-needle Rib Machines By test Horse Power Hanger friction, including belts for 4 body machines or 7 ribbers 273 Body machine, 9 feed, without shafting . . .443 " " with shafting and motor 546 (One motor to about 50 body machines) Ribber, 2 feed, without shafting 31 " '' with shafting and motor.. .394 (One motor to 50 ribbers) Winder, 40 spindle, without shafting 44 40 " with shafting 713 Details are as follows: Knitting machines, Wildman, running at about 800 dia. r.p.m.; shafting, Ijf" dia., running at 340 r.p.m.; hanger bearings, 8" X 1x1" babbitted and with ring oilers. POWER FOR KNITTING MILLS Results in indicated horse power of tests in two mills making men's cotton fleeced underwear and making their backing yarn on wool cards. 1 Belted shafting load Average load including shafting. Full load including shafting Average machinery load less belted shaft- ing load Full machinery load less belted shafting load 3 Sets 48-in. cards Total 14.97 39.4 50.2 24.43 35.23 Per set 5 13.1 16.7 8.15 11.75 10.5 Sets 48-in. cards Total 86.75 127.6 210.3 85.85 123.55 Per set 8.25 12.15 20 8.17 11.75 Power for Knitting Mills 123 Generalization of Above Mill with less than 5 sets 48-in. cards Machinery load without shafting . . Shafting load Total load Mill with 5 or more sets 48-in. cards: Machinery load without shafting . . Shafting load Total load Average 8.15 _5 13.15 8.15 8.25 16.40 Full 11.75 _5 16.75 11.75 8.25 20.00 Subsequent information from other mills confirms the above, except that for general practice in mills of say 8 sets or over, 18 indicated horse power per set is nearer the average total load. Spring-needle Loop-wheel Knitting Machines Delivered horse power to run circular spring-needle loop-wheel knitting machines, averaging 6^ feeds per cylinder, 26-gauge cotton flat work, 1200 diame- tral revolutions per minute. - llOcyls. Per cyl. Per table r with shafting 33 15 18 .30 .14 .16 .60 .27 .33 no cylinders' 1 shafting alone overhead and under tables 14 to 16 without above-men- •^ tioned shafting Proportionate Distribution of Power in a Ejiitting Mill Making Its Own Yarn Winding Knitting (including rib cuflfs and borders) Seaming Finishing Washing Yarn making Per cent horse power 6.1 22 6.6 12 4.5 48.8 100.0 124 The Science of Knitting RELATION OF MACHINE GAUGE AND CUT The term cut is used to designate the needle spacing of circu- lar latch-needle machines, generally with the number of cylinder needles per inch, measured on the circumference of the cylinder. A 12-cut machine has twelve cylinder needles per inch of the outside cylinder circumference generally measured on the cam surface. The dial needles are not involved. For instance, the 12-cut machine might have a dial cut to match the cylinder, or cut half as fine, or have no dial at all. Such details are de- scribed in other ways than by the general word cut. This is reasonable since only one side of the cloth is seen at a time — generally the face or cylinder side — and the fineness of the cloth is judged by the number of wales per inch (or other unit) made on the cylinder needles. The use of dial needles does not necessarily change this number of wales, since the dial stitches lie back of the cylinder stitches instead of between them. The term gauge is used to designate the needle spacing of spring-needle machines, generally in connection with the num ber of needles per inch-and-one-half of the needle line. An 18-gauge machine has 18 needles per inch-and-one-half of the needle line, whether curved or straight, or whether with one or two sets of needles. Evidently an inch-and-a-half is one-half greater than an inch, so gauge is one-half greater than corresponding cut, e.g. 12 cut and 18 gauge stand for the same number of needles per inch. 2 Therefore, Cut = Gauge X 5 > 3 and Gauge = Cut X « • This applies to the fabric as well as to the machine; but spring-needle fabric is generally wider than latch-needle fabric made with the same number of needles per inch, since heavier yarn is generally used on spring-needle machines. The relation of the yarn numbers for different machines may be determined by coniparison of their respective yarn formulas. For latch-needle circular rib machines Yarn = (^^ (1) Gauge 125 For spring-needle circular loop-wheel machines yarn=(«2;£^. ...... (2) For machines with the same number of needles per inch 3 Gauge = Cut X ^ • Substituting this value for gauge in (2), (^^^ 2-J I ^^^*^' 9 Yarn = ^—^^ = -^^ = —Cut'. Yarn = ^^ ). (3) 160 Dividing (1) by (3) Cut2 Yarn for latch-needle rib fabric _ 6 _ 1^0 _ Yam for spring-needle flat fabric 9 Cut^ 54 ~ ' ' ^ * 160 Therefore the number of the yarn for latch-needle rib machines is three times the number for spring-needle ' flat-work machines having the same number of needles per inch. If 10 yarn is right on 21 gauge, 30 yarn will be right on 14 cut. That is, the diameter of the yarn is about 1.73 greater for spring-needle flat- work machines than for latch-needle rib machines. GAUGE Different Standards The table gives the number of needles per English inch for the gauge given in the extreme left-hand column. For in- stance, 126 The Science of Knitting 18-gauge in French, coarse French, fine Saxon EngUsh, split Enghsh, soHd Enghsh, three needle American, New England Viennese is needles per English inch 10.98 16.46 19.38 6.00 12.00 18.00 9.00 17.39 Needles per English Inch French English American Ga, Saxon Vien- nese Groa. Fin. Split Solid 3 Needle New England 4 2.439 4.306 1.333 2.667 4 2 3.865 5 3.049 5.382 1.667 3.333 5 2.5 4.830 6 3.659 6.458 2 4.000 6 3 5.797 7 4.268 7.535 2.333 4.667 7 3.5 6.763 8 4.878 8.611 2.667 5.333 8 4 7.729 9 5.488 9.688 3 6.000 9 4.5 8.695 10 6.098 10.76 3.333 6.666 10 5 9.662 11 6.707 11.83 3.667 7.330 11 5.5 10.63 12 7.317 12.92 4 8.000 12 6 11.59 13 7.927 13.99 4.333 8.666 13 6.5 12.56 14 8.537 15.07 4.667 9.333 14 7 13.53 15 9.146 16.15 5 10.00 15 7.5 14.49 16 9.756 17.22 5.333 10.67 16 8 15.46 17 10.37 15.55 18.30 5.667 11.33 17 8.5 16.43 18 10.98 16.46 19.38 6 12.00 18 9 17.39 19 11.58 17.38 20.45 6.333 12.67 19 9.5 18.36 20 12.20 18.29 21.53 6.667 13.33 20 10 19.32 21 12.80 19.21 22.61 7 14.00 21 10.5 20.29 • 22 13.41 20.12 23.68 7.333 14.67 22 11 21.25 23 14.02 21.04 24.76 7.667 15.33 23 11.5 22.22 24 14.63 21.95 25.83 8 16.00 24 12 23.19 25 15.24 22.93 26.91 8.333 16.67 25 12.5 24.15 26 15.85 23.78 27.99 8.667 17.33 26 13 25.12 27 16.46 24.70 29.06 9 18.00 27 13.5 26.09 28 17.07 25.61- 30.14 9.333 19.07 28 14 27.05 29 17.68 26.52 31.22 9.667 19.33 29 14.5 28.02 30 18.29 27.44 32.29 10 20.00 30 15 28.98 31 28.35 10.333 20.67 31 15.5 29.95 32 29.27 10.667 21.33 32 16 30.92 33 30.18 11 22.00 16.5 31.88 34 31.10 11.333 22.67 17 32.85 35 32.01 11.67 23.33 17.5 36 12 24.00 18 37 12.333 24.67 18.5 38 12.667 25.33 19 39 13 26.00 19.5 40 13.333 26.67 20 Gauge 127 bO 9 o ^ 03 bi 9 c 0) bfl j; § § < nea. mach inery, a J3 M M ^ ^ § i s'l s 3 ?- 1 5 8 ^ ^ I Spring-needle fla ( Circular loop-wh Trick-needle loop- ^ 05 lO tn GO 00 J C5 O iS "SjS M CO CO CO CO >-i C 9 ?, M t-1 COCOCDCCCO^T-HtM '° < CI O -^ 02 o to bC c X CO o c3 0) a i=l IB .S o o o t-l-H o3 oT a;) So .S a-s ^ OJ T3 J -»^ -d ^ ^ ^ ,0 ^ "M 02 _0Q a 13 O) oT bC in c3 bC I o T5 O 2 o ^ bC o) CO a in S=i c3 C! 03 q; a o « O O bD bC ^ a bC a bC 1=1 03 bD o3 CO O 02 o O bC o bc t; .a^ ^ oT (N a M ^ '^ el bC a; -f? CQ -^ -H a 2 T3 o -^ d o ^ <^ ^ a ^ .^ «2 ^ a ^ d •I- o ^ W ^ ^ r^ ^ -^ _j-j CO ■♦J -g ^ bC d o a •a ^ ^ ^ "" n. 0) ^ CD ad CQ ^ o3 0) _. ^ d s :: .Jd O pd CO bD d bC 128 The Science of Knitting NEEDLES PER INCH OF HOSIERY MACHINES AND RIBBERS MEASURED FROM BACK TO BACK OF NEEDLES The cut or number of needles per inch of these machines is not much used, but the diameter of the cyHnder and the total number of needles is given instead to convey an idea of the fineness of the machine. Those who are not sufficiently famihar with such machinery to form a fair idea of the fineness from this information have to consult tables, which are given in some machine catalogues, or have to work out the cut by divid- ing the number of needles by 3.14 and then by the diameter. But since the division is generally shirked, since the tables are not always handy, and since comparatively few can remember the cuts for a wide range of sizes and needles, there is a general impression that it is possible to get along without knowing the cut. This impression is correct where experience and experiment are satisfactory guides, but it is impossible to establish a scientific basis of reckoning without knowledge of the cut or the needle spacing. The following table shows a simple and rememberable method of quickly calculating the cut with sufficient accuracy for all practical purposes. Dia. ofcyl. 2\ 2\ 2f 3 3^ 3^ 3f 4 4^ ^ .14 .13 .Hi .101 .10 .09 .081 .08 .07^ .07 Multiply the number of cylinder needles by the number under the diameter and the result will be the cut. It is unnecessary to bother with the decimal point since the cuts generally range from 3 to 20 so confusion cannot occur. For instance, a 3|-186-needle machine is one of the following cuts, because the rule says multiply by ten, 1.86, 18.6 or 186: but since 1.86 cut is infrequent and since 186 cut is absurd, the result to take must be 18.6. Accurately, the cut is 18.2. The error due to the use of the quick rule is 2 per cent on this size, 3 1, and on the 2| inch also. For the other sizes the error is 1 per cent or under. The table in the middle of page 129 gives examples worked out by short cuts. For the other sizes there is not much advantage to be gained by the use of shorter cuts than the multipliers given. These diameters are from back to back of needle. If the cam-surface diameter is used, take the multiplier of the next smaller size, which will give the cut as closely as is generally Yam for Loop- wheel Machines 129 required. For instance, what is the cut of a 160-needle ma- chine 4| inches in diameter on the cam surface? The multi- pHer for the next smaller size, 4|, is 7|, which gives 12 cut. The actual cut is 12.15. Dia. Needles Multi- plier Solution Actual cut Error 21 126 IH 126 Add 126, one-tenth Add 63, half of one-tenth 1449 14.5 -0.006 3 148 10^ 148 Add 74, half of one-tenth 1554 15.7 -.0104 31 136 10 136 13.2 + .021 3^ 128 9 128 Subtract 128, one-tenth 11.52 11.56 -.0104 31 146 Sh 146 Subtract 146, one-tenth 1314 Subtract 73, half of one-tenth 1241 12.4 + .0013 4 214 8 214 Subtract 428, one-fifth 1712 17 + .0053 il 138 7h 138 Subtract 345, one-quarter 1035 10 3 + .0013 Yam for Loop-wheel Machines Gauge Light Average Maximum Gauge Light Average Maximum 8 2.1 1.6 1.1 26 22.0 17.0 11.0 10 3.3 2.5 1.7 . 28 26.0 20.0 13.0 12 4.8 3.6 2.4 30 30.0 22.0 15.0 14 6.5 4.9 3.3 32 34.0 26.0 17.0 16 8.5 6.4 4.3 34 38.0 28.0 19.0 • 18 11.0 8.0 5.4 36 44.0 32.0 22.0 20 13.0 10.0 6.7 38 48.0 36.0 24.0 22 IS.O 12.0 8.1 40 54.0 40.0 26.0 24 19.0 14.0 9.6 130 The Science of Knitting O »0 OO Tfi c<5 00 (M '-JCJC«j00-^CX5O5lC«j O O l« 00 - <0 to >C to ..^ .^tt T«<" 00 00 CO 2S; CO CO 00 c^ ??s o 00 § <9 o c^i «o CO t>. to <0 CO to tfi .^ ■^" ^" ^' CO CO CO O to 00 CO to t^ 05 O o»i^coo6cot--.-^oo->*-CO00tO(MO5t^toC0l-H to to 05 O CO 05 COtOtO'^-«»rt<00COC0C0 00 2S22P^°0<=^>«O'^toio i— itog50coi>.»-05i— iio T-(tooi>-oooootocoe^o t^ O O to to ■■tl ■^" Tfi CO CO 00 00 CO toeotocooicooor-i^coo «D-tt<»o«OTfitooo^ COcOOOto»-lCT>CO-^(NoS t^ CO to to T^! ■^" Tt* CO co" CO eo" co M 00 t^ O -ooooooor- «OQp5J05-^t^t>.lOcOto «oioa)C^Ttooo5 00«DOCOC1050coSo5 O to to ■«^ Tj< CO CO CO CO IM ccoocoooootocqt^ OOtoOOOOi-li-ltOto^. ^t^COOSCOIMtOC^IC^ oooooooot^Tjicqo to to T»< -^ -^^ CO 00 00 CO «OOOtOO>toOt^tO OiC*^C0CO05COC0tO to to_^— ' >— I M CO O OO o> 1* 00 eo o> to OO o to T»< Tt< OO OO eo eo o o CO o eo c>« eo t^ -^ti -"i* to •<*» 05 c- o 05 eo O to o i>. eo i-i to M< M< OO eo eo ■^ ■^ CO CO eo C3 i-H o o CO 1-1 to i-< to to to -i* ■^ 05 to (M T»4 CO 00 eo T-i eo M to 00 00 O OS eo !>• 1-1 o »-< to 00 o ^ OO CO eo 00 eo t--. a> to to -H Oi to 00 eo o •umo -•iTO •BTQ ^ 00 a> -^ a CO N ^ to -«tl (M § to «^ to to to cO oi>t^ooo500rt(Meo >-c 05 t>;".iOMiH05S-5< 2 2 — 22 2S "^ P "-* "^ «^" t* "*' »o "5 to t^ i-W HM raw hH 1 i-W «)« "K »4« H|M B|< Cuts for Different Diameters and Slots 131 ^ o o »o t^ to to CO o 00 CM 00 on to o CO CO ■«1< Oi «0 C^ CO o OS CO CM ■^ CO o CM OS to • to eo CM cq o 03 05 00 r^ r^ CO CO CO to to to ■^ •^ •* ■* -<*< '* '-H <_, „ CM »0 CO o CM eo o eo o o 00 CM ^ o <_, to CM CO CM I^ C5 'i* r^ eo ^ on Oj CM -H CM CO OS s CM Tf< OS CO to to t~- oil «o t^ 05 CM CD "-^ CO CM CO CO <-> oo CO ■*! CM "-1 OS ,_, o 0» oo 00 t^ r>. CO CO to to to to ■* ■* -*< eo to t^ CO 00 «o ■«*< Tj< t^ o •^ OS to IXJ T»< CM OS t>. to CO "-I o 00 ,_! o 05 00 00 r>. CO CD CD to to to •^ ■^ ■"+1 Tfl ■^ ■^ CO 1— ' o o o o L-3 o CM o CO to 00 CM CI o to on •<* r^ to r- oo CM o OS on CO ■»t< h- CM o T—i CO oo t^ OS CO OS to CO to CM CM ■»t< on r^ 00 CO ■—I CM -^ 00 CM t^ eo 05 CO CO <-i 00 CO •«*" CM o OS t^ _l o 0> 00 i^ t^ CO CO to to to to ■^ ■«1< Ttl ■^ ■^ CO eo ^^ *^ o o o o oo o to o 00 CM r>. o on o on r- ■»f< CD CM ■^ 00 CO 05 CO o f^ r- CD to on •^ or) f^ CM OS 00 CO CO CM t^ CO Oi CM •^ CM CO CO r^ t^ t^ o 05 O CM CO o CO CM 00 to CM OS t^ to eo OS 00 CD ^3 a> 05 00 b» t^ CO CO to to to -«t< ■* •* •^ •>* CO CO CO o C5 IM t-- tn CO o 00 to 00 to to to to o C5 to to r^ t^ CO CO CO to CM t^ r^ cr> r^ CO 05 lO r^ C3 CO ■^ to ■ (-TS <-) m S5 CM 00 t>. o t^ «D t^ o •* 05 •^ o CO eo o 00 CD CO CM o r^ to (N o 05 00 00 r^ CO CO CO to «o to ->*< ■^ ■* Tf< ■^ CO CO CO '-^ '— ' O o "5 >0 CM o CM o CM ^ o to CO to •^ •»t< to r^ on to CD oo iO r-< 00 05 00 CM ■* on o CO CM CO to eo OS ■* C^J ■* CM on on ■<* eo to on oo OS CM CO CM 00 , t>. t>. ■^ -* «0 00 CM t^ CM 00 to CM o t^ ■>*< CM o OS t^ CO -* _l o a> 00 Jr^ t^ CO CO to to to ■* '^ ■^ TtH •>* eo CO CO eo '— < '-H O o 00 U5 O CM t-- o CO to to to o „ to to to r^ r^ CM CO 02 o CM CM ■^ CO to CO to r^ to to to «o eo CO rf *— ; CM 05 OS CM on CO CO on CO CM OS b- •^ ■—1 •-1 CO CD CO to '—1 t^ eo o 00 to CO OS 00 CO to CO ^H o 05 oo t^ t^ CO CO to to to •>* •* •* CO eo CO CO eo »-H ▼- ' o 00 CO CM O o CO CM CM to CM to ^ oo o o ■»f o o o to CM o CO to oo to ■* »-H O CM ■* CO ■<*< r^ ■^ to OS to •^ to r^ CD CM o r- ^-< OS 05 ^ ■«*< "-1 CO OS to CM OS CD ■ 00 00 1:^ t^ CO to to to ■^ •^ •^ TJ< ■^ CO eo eo CO eo o o 1^ O 00 o eo to o 00 00 to to to C5 CM CM <-) ^ to c^ ^ -CTl CO CM OS CO CM M< r^ oo 00 o t^ -H CO oo r^ vH 02 to CM CM CO CO o CD eo o «o 00 «o CO oo CM o '-< t^ ■<*< o 1X1 to eo 05 »>- CD •* eo CM o 05 00 t^ t^ CO CO to to to '^ -<1< •<*< '<1< CO eo CO eo eo eo o 00 o IC CO CM to o 00 o CM to o ■»t< to to CM lO (-> CO •* eo Oi CM •^ CM CO on CM en CM CM CM eo CO o to ■*! CO CM o o to o to CO o tn CO ■>*< CD O •<»< o CO CM OS CD ■* CM o 00 CO to CO CM i-H o 05 00 t^ t^ CD CO to to ■«1< "^ -* -o o «o ^ CO CO •^ CM to eo CM CO CM CO o o CO CO s CO CM ■^ on OS to in (M CO cu CM OS CO CO 00 CO ■o eo CM o OS 05 00 t>. CO CO kO to •«*< -* ■«»< ■* eo CO CO CO eo eo CM ej rlNi HM BM T** -*» n^^ -M WIP» mt T^ r^rt «!•» r** P (M (>) CM CM eo eo CO CO •««< ■^ •^ •^ to to to to CO CO CO CO 132 The Science of Knitting O 05 C<2 «0 Cfl O O 05 05 00 00 CD(MO5lOC<5O00lOC0 o o o o OOiOOCOlOlCOO-^t-IO'* SS{52'5Z?'^'^''=<^^<3^000^00000 00C3,-lloO3COOJUt.rtJ^,J(C^Sp:-*C§ i-(00050000Ir^t— t^ «0 <© CD lO lO »0 lO o o o ^™^ ^^ CO I - WW v.*^^ T— !>• {^ 1— I CO lO CO 00 OOCJOCO»OC• O CO .^~,^ -JcDcoooeoooooo > CO CO O OO «0 00 1-1 .a V a> v a o CO m2S'^°°°°*^'^'^"^^^"'"'"5«5 SS2S2SJ5PSooico.«ooo ■*«5 00'-|»OOM00iSc^C> ■•-I O 05 05 00 00 !>. t>. I>. «5 (N O oooot^05C5t~-t^h~ SS?SJ^SS22^<»«»'*Smoo2£o £322^2??2Mc»o-^^i>J COOCOCO>0»0 0>0-* °°. '^ °=. '=^. « ". « '^^. » ^ 2 S S ^ 2 § g •i-iooioooooo*t>^t>J <0 CO CO »0 lO lO lo" ■•*4 rjH »OCOt^O,)<05Tt." 1^' CO CO CO U5 IC »0 lO <*■ Tjt iii-§g8ggg§22gg2§2 >— I O 05 00 OO t— t-' CO CO CO iC »0 U5 ITS -.^i Tji Tti r-!ooocs,,j*co§p??^;gig2;gSo -^'-looiocooooti t^ »-H CO T— ( 1-H O 05 00 OO t>. t:^ C0c0c0i0ic>oi0rt<-»*cooic^jico5-.■ CD CD lO tei lO lO Tti Tti Tti Tft' t- lO ■ CO ■>*< SS22SS'=>i5<^<=> COGg»— IrHCDOSi-HOt^ t--cot^Ocooocoooio -H O 05 O 00 t^ t-^ CO CD CO lO ui >o >o -- — — ^ — ^OOlOi— ICOCO 'CCOI^->ti(MOlO»000 coiot^MOioooooeo "-HOOlOCOOOOCOUSCO O O O I^ SSfc=2S2.^S2e«!¥??oo ■* CO t>- ■<* ^53.?^r7^riJ2^:T^fO'^^''50oot^oooTtl ■^•^»OOOr-.CO-Ht^cOOt^i*(N«>t^lO'5l^ ■-lOOSOOOOt— "t--^CDcdco" U5«5»Ct(<-»*- cS c^ o5 ^ Ml— ICOCOO-*iOlOC^IOO ■'-o OO d o CO d o o CM oo' o oo 00 •>* oo' CM o 00 o CM CO !>.' CJ CO lO 00 d CI o CO d 00 CO o CO o CM OO d CO CO d o Cl CO t^ C5 lO ca o o oo t^ 00 o CO CO 00 CO o o CO t-' CI o CO 00 CO 00 o CO CO CO o CO OO d s OO d o o CI CO d CO 05 CO 00 lO lO ■<* CI oo' o 00 00 00 CM 1>1 CM CO CM d CI o CD CO d CO CO d CO o CO CO CO d o CO CO o d 05 00 o o CO »o 00 CI oo" o lO o QO 00 00 CM 00_ d CM CI o d CI CO CO o i o o o d CO 00 00 d o CO CO 05 CO OO CO CM o oo' o o o oo CO CO CI o CO 00 CM o o !>■' 00 CM CJ t^ CO CO CO 00 CM CM CO o CO :-::::: o (M CI 00 o CO o lO CO d o CO 05 CO en 00 00 CO lO t^ CI oo' o CI oo 00 CO CM t-' 00 o a> !>.' o 00 d 00 o C] CO d CO CO CO d 00 o CO d 00 o o o CO 00 d o CO OO d o OO d o o d »o 00 o oo -f oo' 00 § o !>.' 00 o o d o «o d CO CO CM d CO CO o d «o o •o o CO d o CI o d o CO d CM 00 o CO "*. 00 o CI o 00 en CO CO o CI CI o d o CO d o d 00 o d f OS d o o '.'.'.'■'■ c<\ o to cq o CI d o OO CO 00 d o d o 00 o o o CO Oo' o CO 00 1^ CI oo CO CO CO 00 d o 00 to CO »o CO CO 00 CM o d CO o o i : : : : ^. o o o CO d o d CO CO d 00 C4 CO 00 c? od o CO CO CO CO CO o CO o "0 d d CO CO CM d CI CO d o . . . : . o CO : : : : :K o CO OS o" o . lO CM o CO >o CO d o CO CO d d CI CO oo o 02 CO d 00 o t^ »o «o o o CO d o CO o d CI CO CD o 00 CO 00 OO OO CO CO 00 o o »o lO CM »o t^' o CI 00 CO o CM CO d CO CM CO o o CO 00 00 oo CO »o r4-* WW «M H-* C>1 C*< r4-t MM >o UO lO CO CO CO CO 134 The Science of Knitting a> d o 09 to s u Tf^joiftcocoeoosos ^^ooosoodoood ■^ t^ oooQ«5»oooeiOCOlOO-l^t~- O OOOOOCOOO»COOO>rt> CDTfHOCK|0S'»tl'-l-rtOCO^l^OOO» t— OTt<05'^0>»0'-IOOiOOU5«0"5CO«OCOeO Cuts for Different Diameters and Slots 135 lCOOOOOTt< -^ ^_ ' ■ ■ O '-n 00 lO 00 (M -^ C oo 00 t^ O O CO -^ t^ 40 O GO CD t^ 1-- O CO to 00 00 oo 00 1-H 00 OOOOOOfMOO c3 C^C-lCNj(MCOCOCOCO"^"^"»^rt*iOiOw^lOCDCO*OCO 136 The Science of Knitting (M ^ r^ O -H O r-l CO -^ 00 CO OS O CO l-H t^ c^q .-I ,-( O 00 o; r^ CO T^ — ' o o CO 0) CO t^ O CO 00 O 1^ CO 00 -^ 05 lO o «0 CO o CD CO c^ r^ ■ CO Tt* 05 OO C5 • t^ cq i>- CO 05 • ^ ^ d o d ■ o o o o o ■ *0 O »0 Tfi CO • C^ ■* 02 oo c • CO i-H CO Od CI • i-H ,-1 o o o> Q C O O O O CO Tf< -^ TJ< CO C-. CO 1—1 CO Ci CO o O lO O lO •— I 00 O ■* o o o (M T-H OO lO ■^ O O »C >-l 0291 .0145 22 .0290 1.48 .36 .013 .0696 .0406 .010 .0306 .0153 24 .0280 1.45 .32 .012 .0636 .0356 .010 .0256 .0128 26 .0260 1.31 .32 .009 .0586 .0326 .010 .0226 .0113 28 .0260 1.40 .30 .006 .0544 .0284 .009 .0194 '.0097 30 .0230 1.31 .25 .004 .0508 .0278 .009 .0188 .0094 32 .0220 1.28 .0476 .0256 34 .0220 .0447 .0227 36 .0200 1.17 .24 .003 .0422 .0222 .006 .0162 .0081 38 .0190 40 .0190 This table is based on average needle dimensions from a prominent spring-needle manufacturer, and on average blade thickness of a prominent loop-wheel machine. Both the needle company and the machine company emphasize the quite well- known fact that there are but few if any recognized standards for needle and sinker design. Therefore, this table is not to be taken as final, but rather as an initial basis from actual practice, with the help of which more refined tables may be made after the principles of needle and sinker design are better understood. Approximate Weight in Pounds per Thousand of Leaded Needles for Spring- needle Loop-wheel Machine 1 Gauge Pounds Gauge Pounds Gauge Pounds 12 15.0 20 8.1 28 5.7 14 11.7 22 7.3 30 5.4 16 10.2 24 6.6 32 5.2 18 9.1 26 6.1 34 5.0 150 The Science of Knitting Spring-needle Loop-wheel Knitting Trouble Cause Remedy Small hole with Rough or nicked blade is Polish or replace blade. single cut in in lander or cast-off. yarn. Sinker bur is too tight or too Readjust or replace loose, so that blade binds the sinker. yarn against the needle. Eyes of needles are too long or Shorten the beards or too low, so that the yarn cuts eyes, or use larger in the sinking of the stitch. sinker. Eyes of needles are too shal- Replace needles. low, so that the point of the beard is not covered. Beards are turned to one side Replace needles or re- or the other. pair the mold. Lander is set so tight or so Readjust or replace the loose that it cuts the stitch lander. against needles. Lander blades cut the stitch Readjust the lander or against the presser. presser, or both. Cast-off is so high as to break Depress the cast-off. the stitch. Clearing bur cuts the stitch Elevate clearing bur or against the leads or cylinder. move push down ahead. Push down is so far inward Move the push down that the stitch is pulled tight out or reduce take-up on the needle and is cut dur- tension. ing pushing down. A series of drop Yarn drops down off the sink- Elevate the guide, put stitches without er. (This is characterized tension on the yarn. a break in the by a tight thread crossing or use a blade with yarn. the hole.) a more prominent nib. Yarn at the sinker bur runs Lower the guide, or up over the beards. (This sinker, or shorten the is characterized by a loose beard. thread crossing the hole.) Yarn drops out from under Cramp the needle the beards between the beard, use the sta- sinker and the presser. tionary presser ex- (Characterized same as tending from under No. 2.) the sinker to the lander; dampen the yarn. Push down rolls the stitches Move the push down on the outside of beard. back from the nee- (Characterized same as dles, increase the No. 2.) take-up tension or use a wire tension against the cloth ahead of the push down and above it. 1 Trouble, Cause, and Remedy Spring-needle Loop-wheel Knitting 151 Trouble Cause Remedy Tears or long rag- Lander is too high. Lower the lander. ged holes or a Lander blades are too blunt. Use a new lander. series of them. Take-up is slack. Increase the take-up tension or use a ten- sion wire on the cloth above and behind the push down. Heel of the push down is too low. Push down bears on the lan- Elevate the push down. Move push down for- der. ward. Push down bears on the leads Elevate the push down. or the cylinder. Needles are rough or tarnished. Polish by running with a strong yarn and a loose stitch. Tucks in a verti- The needle beard is low so that Replace the needl^. cal line. the 3-arn is split and part re- mains on the outside of the beard. The needle is bent inwardly so Bend it outwardly. that it is not completely pressed. The needle is loose in the lead Replace if leaded, or re- or trick. new the leather if trick. The needle is weak, owing to Replace the needle. deficient temper, so that it bends away from the presser. A mote or seed is lodged in the Remove the obstruc- head of the needle, so that tion. the stitch will not cast-off readily. Single drop The sinker bur is clogged with Clean sinker bur. stitches. lint so that the beard is pressed down and the yarn cannot get under it. (If successive spaces are clogged a succession of drops will be caused.) ■ The sinker bur is so tight that Readjust the sinker or the blades brush a beard use one that runs down so that the yarn can- more freely. not get in under it. The yarn is dropping out from See " Series of drop under beard after leaving stitches without a sinker or running out of the break in the yarn." j'arn groove on the sinker 1 bur. 152 The Science of Knitting Spring-needle Loop-wheel Knitting Trouble Cause Remedy Rows of tight The gmde is clogged with lint. Clean the guide and stitches. This may make a number of polish the periphery courses of tight stitches be- of the hole or enlarge fore the yarn breaks or the the hole. lint pulls through and runs • into the needles. • Rough barrel. Replace bobbin. Coils pulled under Use quicker traverse or others. more tension in wind- Pull from ing. bobbin . Incorrect distance Elevate or depress bob- due to from thread eye. bin to point of freest delivery. Bobbin not under Place bobbin so yarn eye. delivery is uniform all around. Wrong position. See above. Friction on side of Use cone with more cone. taper, or increase Pull from speed of knitting ma- cone due' chine. to Knot or seed on Remove obstruction or side of cone. turn by hand until it is removed. ^ Underwinds. Improve the winding. Sinker bur cramped so that Readjust bur or replace the blades bind the needles with one properly de- and bend them inwardlj' so signed. that full stitch is not taken. Beards of the nee- The stop motion claw may be Draw the claw back. dles broken off. so close to the needles that it catches a high beard. The toe of the fiat presser is so Round the toe of the sharp that it gets in under a presser. high beard. The cast-off is so far through Move the cast-off in- the needles that it pushes wardly. the stitch out against the beards and breaks them off. ■ The presser is set so hard that Press lighter or farther the beard is pressed down toward the point of flat and breaks at the head the beard. or cramp. The guide is too close to the Move the guide out. needles. The sinker bur backs out for a Tighten the spring in bunch and does not return the sinker tube. fully to position. The guide strikes sinker caus- Move the guide away, ing it to over-reach. or if it is too flexible to retain its position against the tension of the yarn, use a heav- ier guide. Tuck-stitch Figures — Latch-needle 153 Spring-needle Loop-wheel Knitting Trouble Cause Remedy Needles breakinsc The lander bur is over-reach- Set the lander to run at the lead or ing so that blades buck tighter in the needles. trick. needles. . The presser is set so deep as Press lighter. to bend needles too much. The needles are too short. Use longer needles. Occurs when yarn is heavj- or wiry, and stitch is long as in knitting linen or ramie. The cast-off is set so tight as to Set the cast-off looker. snap the needles as they leave. Tucks made at The round presser is nicked by Turn down the presser. random. bruise or by striking the lander blades so that it acts as a tuck presser. A bent blade in the sinker Replace the blade. , is brushing down a needle beard occasionally so that the yarn comes up outside of the beard. . The cast-off blade is broken or Insert a blade. out so that the stitch is not cast off. TUCK-STITCH FIGURES — LATCH-NEEDLE The needles in latch-needle knitting machinery are operated jy carris, and the angles of these cams cannot be so steep as to operate one needle at a time, for if they were so steep, then the Dutts would be sheared off. But to produce tuck figure de- signs it is desirable to be able to make any one needle tuck or knit. Consequently, some other device than the cam is needed to operate the needles. The most used device is a wheel which takes the place of the final rise on the raising cam. The first part of the raising cam, which brings the needles to the tuck po.sition, is left just as in the ordinary machine. If the wheel had no cuts in its edge, the machine would knit plain fabric just as if the ordinary raising cam were used; for after the needle had been raised to the tucking position by the fixed cam, the butt would come to the fiat upper face of the wheel and be raised farther so that the needle would knit, as the angle of the 154 The Science of Knitting Needles in Tompkin's Spring-needle Leaded Cylinders Gauge Dia. 12 14 16 18 20 22 24 26 28 30 32 34 36 9 218 256 294 331 369 406 444 481 519 556 594 632 669 10 243 285 326 368 410 451 493 535 577 618 660 702 743 11 267 313 359 405 451 497 543 589 635 680 726 772 818 12 291 342 392 442 492 542 592 642 693 742 798 843 892 13 306 370 424 479 533 587 641 696 750 804 858 913 967 14 340 399 457 516 574 632 691 749 808 866 924 983 1041 15 364 427 490 553 615 677 740 803 866 928 990 1053 1115 16 389 456 523 589 656 723 790 856 924 990 1056 1124 1190 17 413 484 555 626 697 768 839 910 981 1052 1122 1194 1264 18 437 513 588 663 738 813 888 963 1039 1113 1189 1264 1339 19 462 541 621 700 779 858 938 1017 1097 1175 1255 1335 1413 20 486 570 653 737 820 903 987 1071 1155 1237 1321 1405 1487 21 510 598 686 774 861 949 1037 1124 1212 1299 1387 1475 1562 22 535 627 719 811 902 994 1086 1178 1270 1361 1453 1545 1636 23 559 656 751 847 943 1039 1135 1231 1328 1423 1519 1616 1711 24 583 684 784 884 984 1084 1185 1285 1386 1485 1585 1686 1785 25 608 713 817 921 1025 1129 1234 1338 1443 1547 1651 1756 1895 26 632 741 849 958 1066 1175 1283 1392 1501 1608 1717 1826 1934 27 656 770 882. 995 1107 1220 1333 1445 1559 1670 1783 1897 2008 28 681 798 915 1032 1148 1265 1382 1499 1617 1732 1849 1967 2083 29 705 827 948 1069 1189 1310 1432 1552 1674 1794 1915 2037 2157 30 729 855 980 1106 1230 1355 1481 1606 1732 1856 1981 2107 2231 31 754 884 1013 1142 1271 1401 1530 1660 1790 1918 2047 2178 2306 32 778 912 1046 1179 1312 1446 1580 1713 1848 1980 2113 2248 2380 33 802 941 1078 1216 1353 1491 1629 1767 1905 2042 2179 2318 2455 face of the wheel (not the edge) is just that of the higher part of the raising cam. But the object of the wheel is not to make all of the needles knit, but to make certain of them tuck This is accomplished by cutting grooves in the edge of the wheel, wide enough and far enough apart to let some needle butts enter. From this it follows that the wheel must revolve. In revolving it meshes with the butts just as a gear does with the teeth of another gear. The needles whose butts enter the spaces in the wheel are not raised above the tucking position, so they tuck; but the needle butts for which no spaces are provided ride up on the face of the wheel and are, consequently, raised so that these needles knit. • Suppose that one feed is used with a pattern wheel cut so as to catch every second butt in a space and the others on the face of the wheel. Then every needle which enters a space will tuck, and every one which does not will knit. If the number of Vertical Patterns in Latch-needle Knitting 155 needles in the cylinder is even, then the same needles will tuck every time around, and the machine will become loaded up; but if an odd number of needles is used, then the needles which tuck one time will clear the next, and so produce fabric con- taining diagonal tuck stitches. From this it is evident that the number of needles in the cylinder is determined to an extent by the arrangement of the cuts in the pattern wheel But if there are two feeds, then the second one may be provided with the regular cams and so clear all the tucks; or it may be provided with a pattern wheel so designed that each one will clear the tucks of the other. The number of feeds is not restricted to one or two, but may be any number which space will allow, and all or part of them may have pattern pressers according to the design to be made. The conditions to be met and ways to meet them are explained under the heading Figure Designing with Pattern Wheels. Machines such as the one just described, that is, with an odd number of cylinder needles (no dial) and two feeds, each with a knit-one-tuck-one pattern, are used for making incandescent mantles. Each wale consists of two tuck stitches followed by two plain stitches. VERTICAL PATTERNS IN LATCH-NEEDLE KNITTING Vertical effects in the fabric are generally caused by differ- ences in the needles. It is possible to obtain some vertical effects otherwise, as by an automatic striper changing every half-revolution of the machine, but very narrow effects could not be so obtained. It happens sometimes on a two-feed machine that a needle becomes roughened so that it does not clear, i.e., tucks, at one feed, but knits under the extra pull of the second loop at the other feed. Suppose it is a cylinder needle. Then it makes a verti- cal stripe one wale in width but with only half as many courses per inch as the rest of the fabric, because the thread which was taken where the needle tucked is not drawn through into the face but Hes back out of sight. Suppose this hidden thread is black and the other thread is white. Then the pattern is a white vertical stripe in a field of alternate black and white horizontal stripes one course in width. Several facts may be noted from this illustration. 156 The Science of Knitting 1. A vertical effect may be caused by making one wale differ- ent from another owing to a difference in its needle from the other's. Evidently these different needles might be spaced or grouped in different ways. 2. The yarn which is fed where a stitch is tucked is hidden, whereas the held loop is pulled through upon the face of the goods, 3. The number of courses in the tucked wale is 2> 3 or j of those in the plain wales according as the needle clears at the second, third or fourth feed. For instance, on single tuck the needle tucks at the first feed and clears at the second feed, so its wale has only ^ as many courses per inch as the plain rib fabric; and on double tuck the needle tucks at the first feed, then at the second and finally clears at the third, so its wale has i the number of courses per inch as the plain rib fabric. Now, if a needle can produce a different effect by accident, it can be intentionally made to produce a different effect. Two obvious methods of changing its action are (1) to unload it en- tirely by dropping its stitch, or (2) to load it up with one or more extra threads. The second method is the one involved in this discussion. The loading up of any one needle independently of the others is considered to the best advantage on a two-feed machine. It I is generally accomplished in one of two ways. 1. By the use of a long latch on the needle to be loaded. 2. By reduction of the travel of the needle to be loaded. The No. 1 method may be used with a single cam race, whereas the No. 2 method requires more than one cam race. Consider the No, 1 method used in an imaginary rib machine with ten needles and with two feeds, with black yarn at one feed, white yarn at the other feed and with long latches in four adjacent needles. The machine may have a dial or not. If it has a dial, the inside of the fabric will show black and white courses alternately. If it has no dial the alternate courses will still be black and white except that where the tucking occurs, the color which is kept out of the face will appear in the back. Set the raising cam at the black feed so that all of the latches clear, i.e., all knit, and set the raising cam at the white feed so that the four long latches do not clear, i.e., so they tuck. Then the six short latch needles will knit at each feed to make a gray field composed of alternate black and white courses, but the Vertical Patterns in Latch-needle Knitting 157 four long latch needles, instead of pulling the white yarn through upon the face of the goods, will merely hold it until the black feed is reached, when each will leave the white hidden by draw- ing another black loop through the black stitch it already has. The pattern will be a black vertical stripe of double length stitches, four wales in width, in a gray field composed of alter- nate black and white courses. Now elevate the raising cam at the white feed so that the long latches are cleared there also. Then all of the needles knit alter- nate black and white courses, which terminate the black stripe. That is, the vertical effect produced by the long-latch needles may be stopped by raising them enough to clear theu* latches; and it may be started again by depressing the raising cam. Or the raising cam at the black feed might be depressed so that the long latches would be held there, in which case the pattern would be a white block of double length stitches, four wales in width, and still in the field of alternate black and white course^. Summary — Long and Short Latches With a machine having two feeds of different colors and needles with long and short latches, a vertical stripe on the long- latch needles may be : (1) Made by not clearing the long latches at the feed whose color is to be hidden. (2) Terminated by clearing the long latches at that feed. (3) Reversed in color by not clearing the long latches at the other feed. From No. 2 it is evident that both raising cams may be raised BO that all of the needles knit plain fabric as though their latches were just aUke. It also follows that one raising cam may be lowered so that all of the needles tuck at that feed (whether long latches are used or not), in which case all must knit at the other feed in order to clear the stitches; the result of which is that the color which is cleared conceals the other color throughout, and makes what is called the a ccord i on s titch when a dial is used and all the dial needles knit. One peculiarity should be noticed in reversing the color of the stripe by causing the long-latch needles to tuck at the reverse feed. Suppose the cams are reversed simultaneously (1) just after the long-latch needles have tucked and (2) just after they have cleared. In either case, since the cams are reversed, the 158 The Science of Knitting needles with long latches must repeat at the next feed what they did at the last, i.e., in the first case must make a second tuck, or in the second case must clear a second time. In other words, it is impossible to make the change without knitting half a course at the new feed just as it was knit at the preceding feed, whether that was tucked or cleared. If, rather than to change the color of the stripe by a reversal of the cams, it is changed by a reversal of the yarns, as with automatic stripers, the half course of extra tucks or extra plain stitches will not have to be made. Now go back to the imaginary two-feed machine with the four needles with long latches tucking at the white feed, thus knitting a black stripe, and the short-latch needles knitting an alternate black and white course field. Suppose that the lengths of the latches were instantly transposed, i.e., that the long latches became short, and vice versa. The stripe would then become alternate black and white courses, and the field would become black, i.e., the whole pattern would be exactly reversed, which was impossible before when only the stripe could be changed by making use of the difference in the lengths of the latches. This complete reversal can be obtained in practice by the second method, that is by making the travel of some of the needles different from others with the use of a double cam race. There is the additional advantage that the alternate black and white field may be eliminated, when a dial is used, by tucking and clearing at alternate feeds instead of at one feed, so that the stripe may be black and the field white or vice versa. Otherwise, the same conditions hold as for long and short latches. (1) The color fed where a latch is not cleared is hidden, (2) A latch not cleared at one feed must clear at another. (3) A vertical stripe on certain needles may be made, re- versed, or terminated, respectively, by not clearing their latches at one feed, by -not clearing at the other feed, by clearing at both feeds. (4) If the pattern is reversed by a reversal of the cams, the needles with tucks add a tuck at the next feed and the needles which have just cleared, clear again at the next feed. (5) A reversal of pattern by reversal of the yarn does not in- troduce the extra tucks or the extra plain stitches. (6) Plain rib may be made by clearing all needles at both feeds or accordion (with use of a dial with all dial needles knitting), by clearing all needles at either feed and tucking at the other feed. Velocity of Yarn and Needles 159 Diametral r.p.m., and Feet and Yards of Yarn Used per Minute per Feed by the Latch-needle Rib Machine Dia. r.p.m. Needle velocity per minute Yarn velocity per min- ute (4 inches of needles to 1 foot of yarn) Difference be- tween velocity of yarn and needles, feet per minute Feet Yards Feet Yards 100 26.2 8.7 78.5 26,2 52.36 120 31.4 10.5 94.3 31.4 62.83 140 36.7 12.2 110.0 36.7 73.30 160 41.9 14.0 126.0 41.9 83.80 180 47.1 15.7 141.0 47 1 94.25 200 52.4 17.5 157.0 52.4 104.70 220 57.6 19.2 173.0 57.6 115.20 240 62.8 20.9 189.0 62.8 125.70 260 68.1 22.7 204.0 68.1 136.10 280 73.3 24.4 220.0 73.3 146.60 300 78.6 26.2 236.0 78 6 157.10 320 83.8 27.8 251,0 83.8 167 .'50 340 89.0 29.7 267.0 89.0 178 00 360 94.2 31.4 283.0 94.2 188.50 380 99.5 33.2 298.0 99.5 199.00 400 105.0 35.0 314.0 105.0 209.40 420 110.0 36.7 330.0 110.0 219.90 440 115.0 38.3 346.0 115.0 230.40 460 120,0 ~ 40.0 361.0 120.0 240.90 480 126.0 42.0 377.0 126.0 251.30 500 131.0 43.7 393.0 131.0 261.80 520 136.0 45.3 408.0 136.0 272.30 540 141.0 47.0 424.0 141.0 282.70 560 147.0 49.0 440.0 147,0 293.20 580 152.0 50.6 456.0 152,0 303.70 600 157.0 52.4 471.0 157,0 314.20 620 162.0 54.0 487.0 162,0 324.60 640 168.0 56.0 503.0 168,0 335.10 660 173.0 57.7 518.0 173.0 345.60 680 178.0 59.4 534.0 178.0 356.10 700 183.0 61.0 550.0 183.0 366.50 720 188.0 62.6 565.0 188,0 377.00 740 194.0 64.7 581.0 194,0 387.50 760 199.0 66.4 597.0 199.0 397.90 800 209.0 69.7 628.0 209.0 418.90 820 215.0 71,7 644.0 215.0 429.40 840 220.0 73.4 660.0 220.0 439.80 860 225.0 75.0 675.0 225.0 450.30 880 230.0 76.7 691.0 230.0 460.80 900 235.0 78.4 707.0 235.0 471.20 The average yarn velocity of circular loop-wheel knitting machinery is 86 per cent of the above for the same needle velocity. 160 The Science of Knitting NAMES OF CAMS Cams are divided into two general classes: namely, working cams, which transmit the work of forming the stitch^ or of simi- lar operations; and guard cams, which keep the needles from traveling too far after leaving a working cam. In other words, the guard cams are those which combine with the working cams to close the cam races and so keep the needle butts in a restricted path. The usual working cams are the stitch cam, which propels the needle when it is drawing the stitch; the landing cam, which projects the needle slightly immediately after the stitch is drawn; and the raising cam, which projects the needle preparatory to drawing the stitch, and which generally contains two rises, one to open the latch and hold it open until the yarn carrier is reached, and the other to clear the latch where the yarn carrier will keep it from closing before the yarn gets under the hook. A switch cam is one which changes the path of the needle butts, much as a railroad switch changes the path of the train. Switch cams are generally a combination of working and guard cam, since it is desirable to control the travel of the butt especially in high- speed machines. There are exceptions to this, as in some auto- matic hosiery machines, in which guard cams are seldom used, since the friction of the needle in its slot and in the work is suffi- cient to keep it from traveling too far. Switch cams are of two general kinds, sliding and swinging, or wing cams. ADJUSTING IN GENERAL Remember that screws, etc., have to be proportioned according to their uses and that consequently the force applied to them should be limited according to their size. Use screw-drivers of the proper width and ground like screw-drivers instead of like chisels. Use wrenches with straight parallel jaws. Use judg- ment in forcing screws, especially hardened ones, since they are not easily removed if the heads are broken. Always make a definite adjustment, such as a quarter turn, a half division, etc., and remember just what it was, so that it can be halved or doubled or retracted entirely according to the indications of the results. The habit of making only definite adjustments is especially desirable with knitting machinery in which the different parts are frequently duplicated many times, as in the feeds, of which 8, 12, 16, etc., may be used. Putting Needles into Ribber 161 Make only one independent adjustment at a time. For instance, if the cylinder-stitch cam is elevated, which shortens the stitch, the dial stitch which is dependent on it may break unless the dial-stitch cam is brought outward. But do not bring out the dial-stitch cam and depress the dial at the same time, since if the result is unsatisfactory, it is difficult to tell which of the two changes should be rectified. A now engineer in a promi- nent knitting mill adjusted the whole engine in one evening and the mill had to close for three days while a crew from the shop lined it up again. Tighten screws and nuts after temporary adjustment, since if something slips, more time may be lost in repairing damage than in loosening the screws or nuts for final adjustment. After adjustment of any automatic change mechanism, turn the machine through the change by hand, since for many such adjustments there are positive limits which appear only during operation and if they are exceeded with the power on, damage is almost inevitable. When dissembling any part of the machine, notice the order in which it comes apart, for use in reversing that order in re- assembling. Corresponding parts are frequently marked to correspond, with numbers or prick punch marks. These should be followed carefully in reassembling. This is especially impor- tant in replacing the cross bar. PUTTING NEEDLES INTO RIBBER Nothing but the needles manipulates the yarn during the formation of the stitch, so it is essential that the needles be good. An absolutely perfect machine will not produce good re- sults with poor needles; and since the needles are more readily changed than the machine, it is always well to look first to the needles in case of trouble. It is best to look the needles over before putting them in the machine, for even if imperfect needles are the only ones available, knowledge of their characteristics will help to locate trouble if any develops. The slot for removal and replacement of cylinder needles is in the back cam casing, closed by a swing cover to keep dirt out of the cam race. To remove a needle, swing back the cover and bring the slot opposite the needle to be removed. With a needle held in one hand hook the head of the needle to be removed and draw it up until the butt is near the spring-band, draw the 162 The Science of Knitting spring-band out with a coarse needle held in the other hand, and continue drawing the needle upward and out of the slot. Hold the new needle near the head, start the shank in the slot, pulling out the spring-band as before to clear the way for the butt, and press the needle down until it strikes the cam. The slot for removal and replacement of dial needles is under and behind the oil hole in the cap. With a needle held in the hand, hook the head of the dial needle and draw it out. About four needles may be removed through this slot without change in the position of the machine. If it is desired to remove sev- eral needles at one place, a convenient way to move the cap the right distance is to count four needles passed by the heel of the yarn carrier. This relieves the operator from stooping to look under the cap. Do not leave a needle part way in the slot. Put it all of the way in or take it out entirely, since if left otherwise, the power may be thrown on and the machine damaged. Do not turn the machine during removal or insertion of a nee- dle, as the needle may catch and necessitate the undesirabilit}'^ of turning the machine backward. Make sure that the needles do not bind, especially when inserting a number. Just how snugly they may fit has to be learned by experience. As a rule they may be tighter in a ribber than in a body machine, since resistance in a ribber can be more readily detected through the hand wheel. If the dial needles are snug, it is well to try each needle head first in its slot as the needle is likely to be widest through the rivet and binding in that location is not readily detected other- wise. Do not wedge the slots apart until every other means to loosen the needle has been tried. The slots are cut with greater ac- curacy than can be obtained by manipulation, so as often as one is forced it follows that the original accuracy is proportionately impaired. If a needle sticks, it may be due to variation in the needle, in which case try another one and keep on until one is found which will fit; or the slot may contain some dirt which needs to be cleaned out, or may have a bur at its end, which bur should be removed. If the needles fit tightly, it is well to oil them freely and run the machine without the work on it until they slide easily in the slots. It is always advisable to do this after the insertion of a Yarn for Latch-needle Rib Machine 163 new set of needles, since hooking on the cloth with a snug set of needles is not an easy operation, and if a load-up does occur, damage is very likely to result, since the double resistance is apt to be so great that an occasional butt will shear off rather than drive. A muffled thump is indication that a butt has caught seriously or has been cut off. In the latter case the dial should be raised or the cam casings should be removed, according to the location of the broken needle, and all broken parts should be found and pieced together to make sure that every piece is removed. When the cap is raised, the needles will remain in their proper position for replacement of the cap, but in removal of the cam casings, care should be taken either to leave the butts as they were in the cam race or to rearrange them so before replace- ment of the segments of the casing, otherwise the segments will not go down into place. The casing segments of a machine with many automatic changes are a little puzzling to replace until some familiarity with them is obtained, but they should never be forced. Careful examination will show how the needles should be arranged to permit replacement. Yarn for Latch-needle Rib Machine 1 2 3 4 5 6 7 Cut (Cut)2 (Cut)2 4 (Cut)2 5 (Cut)2 6 (Cut)2 7 (Cut)2 8 3 9 2.3 1.8 1.5 1.3 1.1 4 16 4.0 3.2 2.7 2.3 2.0 5 25 6.3 5.0 4.2 3.6 3.1 6 36 9.0 7.2 6.0 5.1 4.5 7 49 12.3 9.8 8.2 7.0 6.1 8 64 16.0 12.8' 10.8 9.1 8.0 9 81 20.3 16.2 13.5 11.6 10.1 10 100 25.0 20.0 16.7 14.3 12.5 11 121 30.3 26.2 20.2 17.3 15.1 12 144 36.0 28.8 24.0 20.6 18.0 13 169 42.3 33.8 28.2 24.2 21.2 14 196 49.0 39.2 32.7 28.0 24.5 Column 5 shows the cotton number of yarn generally used for the corresponding cut, column 1. Columns 3 and 4 show yarn numbers lighter than usual and 164 The Science of Knitting columns 6 and 7 yarn numbers heavier than usual. The numbers shown in column 7 are considered the heavy limit for single thread on the ordinary latch-needle rib machine. However, multiple-thread combinations with a somewhat heavier equiva- lent may be used. HOOKING FABRIC ON RIBBER It is assumed that the machine is a single feeder properly adjusted and ready to run, except that the cloth is not on the needles. See that all the latches are open. Unless there is room enough between the cylinder and dial to reach a needle down through, elevate the dial to provide suf- ficient room. Take a piece of fabric from a machine of about the same size, but loosely knit from soft yarn, trim square the end which will not ravel, pass it up through the cylinder, catch the edge with a needle in the hand, draw it up and hook it on the nearest cylinder needles. If the fabric used is too fine, or the stitch is too tight, the loops will not pass over the heads of the needles, or will break in so doing, which affords an insecure hold to start with. If the yarn of which the fabric is made is too strong, it will not break as it should when it gets caught under a hook, so that a severe pull, which may cause a butt to catch, is put on the needle. The best place to start hooking-on is right behind the feed, where the needles are drawn back to clear the stitch, but in some cases there is sufficient room between the two sets of needles at other places around the cylinder. If the cylinder is too small to admit the hand conveniently, the fabric may be pushed up on the end of a screw driver until a small section is- caught, and then the fabric must be drawn gently downward. With the dogless device the inside of the cylinder is per- fectly free from obstructions, but on other machines the fabric must be worked between the dogs sometime during the hooking- on, depending on the place where the operation is started. The amount of fabric hooked-on should be the least that will give a secure hold. If too much is hooked-on, the surplus should be trimmed off with shears, as otherwise it is likely to clog the needles before it gets down between them. Hooking Fabric on Ribber 165 After the first section of the edge of the fabric is hooked, turn the machine ahead sHghtly, reach down with the hook, catch a following portion of the edge and hook it on, continuing thus until the cylinder needles begin to withdraw through the fabric. Thi'ead the yarn through the stop motion, through the hole in the top of the stud, or through the guide in the dogless attach- ment, if one is used, and finally through the yarn carrier and under the hooks of the cylinder needles, making sure that the hooks catch it, or else the fabric will clear and leave a place that will have to be patched afterward. The yarn used at the start should be strong and rather light and the stitch should not be tight, otherwise it will break or fail to clear readily. After the fabric starts into the feed, keep it pulled down enough to make sure that the cylinder latches will clear it going up and that it will pull clear of the needles as they draw all the way back, yet not enough to break the stitches. It is well to notice the feed frequently, as it is important to form the stitches properly or they may all break away, and necessitate an entirely new start. Continue the hooking-on as before, taking care not to hook on double thickness and not to catch the opposite side of the cloth, as double thickness will break or clog the needles, and catching the opposite side will leave insufficient cloth to go around and will not provide uniform tension, which is needed to begin with. When the starting place is reached, lap the fabric over itself two or thi'ee needles to make sure of a secure hold all around. If the fabric fails to go around, or is doubled, or for any reason promises to clog the needles, it is better to break the yarn out and clear the needles by a revolution of the machine with tension on the cloth, since it is better to make a new start than to bruise and bend the needles by a bad start. Sometimes the fabric may catch on the end of the center stem and seem to be short on that account. It may be fre^ by the hand reached up through the cylinder. If the yarn breaks in drawing over the dial needle, the dial may be too high, in which case lower it, with caution not to get it so low as to obstruct raw edges of the fabric, or a possible load-up, which is likely to occur right after hooking on. Watch the dial needles ahead of the feed and open any latches which may have closed. 166 The Science of Knitting If the hooking-on seems fairly secure, start the cloth in the take-up. But if it is not secure, it is well to use hand tension a little longer, since if the stitches start to break, the hand can let up quickly, whereas the take-up may pull the fabric entirely free before the tension can be released. It is well to have the cloth in the take-up before the power is put on, since the take-up pull is much more dependable than the hand pull. After the power is put on, watch all around the needle line for loose yam and if any appears that does not quickly knit down, stop the machine, or the needles will become clogged, in which case hooks and latches get bent, latches get bruised by the carrier and butts get cut off. Pull the loose yarn clear of the needles, taking care not to injure the latter, and hook a small piece of cloth on the bare needles and keep hand tension on it until the hole mends ; or if the space is not large, take out the dial needles there, in which case the cylinder needles will generally pick up, after which the dial needles may be replaced and the rib knitting will start at once. For multiple-feed machines the operation is substantially the same, except that each feed must be threaded just before the fabric comes to it and all of the feeds should be watched to make sure that they are clearing the stitch properly until the raw edges are down out of the way, after which there is not much danger of trouble. RIBBER TAKE-UP The take-up is driven by a cotton band which may be adjusted when unhooked by twisting or untwisting according as it is to be tightened or loosened. The stop-off chain connects the take-up with the knock-off handle, and when properly adjusted releases the power if the band becomes too loose or comes off. It does not release the power if the pulley, miter gears or collars become loosened, so they should be tightened occasionally. The sheave-wheel shaft, worm, and miter gears should be kept well oiled, but the take-up rolls should not be oiled more than is necessary or the oil will run along them upon the fabric. The lightest tension is obtained when the weight hanger-rod is at its greatest extension back of the take-up and all the weights are on it. Moving the rod inward and removing the weights increase the tension, after which further increase is made by Locating Sources of Trouble in Rib Knitting 167 reversal of the head of the rod to the front of the machine, addi- tion of weights and increase in its adjustment outward. To start the cloth between the rolls lift the worm to the top of its shaft and give it a partial turn which will keep it out of mesh. See that the fabric is not twisted; after which place the end between the rolls, turning the latter with the fingers until the end comes through on the lower side, then pull it up through the opening in the leg base, and keep pulling until the take-up stops rising. Give the worm a turn, so that it will drop into mesh, and release the fabric, replacing the end through the opening in the leg base. To remove the cloth, take hold of it below the take-up and draw it up through the opening in the leg base until the take-up is lifted. This raises the worm to the top of its shaft. Keep the tension on the cloth and give the worm a part turn to hold it up out of mesh. The cloth may then be withdrawn from between the rolls and the take-up is ready to restart. j LOCATING SOURCES OF TROUBLE IN RIB KNITTING One of the most frequent troubles is a vertical streak caused by a particular needle. If it is caused by a closed latch, a glance at the needles above the location of the streak will generally show it. If it is not found in this way, take out a dial needle where the trouble seems to be and run the fabric down below the head base. If the streak has continued, count the number of wales between it and the intentional drop-stitch streak, which is the number of cylinder needles between the removed dial needle and the defective needle. If the streak is intermittent, as is frequently the case with drop stitches, put the head of a needle, back down- ward, in the intentional drop-stitch streak and follow down until opposite the last defect; there count the number of needles be- tween the two streaks and locate the defective needle as before. If the trouble manifests itself in horizontal lines, i.e., along a particular course instead of a particular wale, the cause is at a feed instead of at a needle. Mark the yarn at any convenient feed with a black oil spot, run the spot below the head base and count the courses between the marked course and the one showing the defect. This number is the number of feeds between that at which the mark was made and the defective one. If the de- fective course is below the marked course, then the defective feed is ahead of the marked feed. 168 The Science of Knitting STITCH ADJUSTMENT The stitch is important, not only because it is the essential factor next to the diameter of the yarn which decides the struc- tm-al characteristics of the fabric, but because correct stitch ad- justment is necessary for good results in the operation of the machine. By stitch is meant the length of yarn in the loop. It is necessary to distinguish stitch as applied to the loop from stitches per foot of yarn. When the stitches per foot are in- creased, the stitch or individual loop is shortened and vice versa. The stitch is determined first by the size of the yarn and there- after by the requirements of weight, appearance, and feel of the fabric. To lengthen the stitch, that is, to increase the yarn in each stitch, is to lengthen the loop, and to make the fabric loose or sleazy, if the original stitch was normal; and to shorten the stitch, that is, to decrease the yarn in each stitch, is to shorten the loop, and to make the fabric heavy or boardy. In regard to the running of the machine, too tight a stitch will tuck and load up, whereas too loose a stitch will drop off the needles or pull twits apart. The commonest and easiest way of counting the stitch is to count the number of courses with a stitch glass. The counting should be done off the machine to eliminate as much as possi- ble the disturbance due to the pull of the take-up, and when a close count is desired, it should always be counted in the same location around the cloth and away from the dog streaks. Count- ing by courses is a good way when the length of the fabric is important, as is the case generally with pattern fabric. It also eliminates differences due to such yarn characteristics as twist and harshness. But it is not reliable when the weight of the fabric is important. The most direct method to adjust the stitch is by the number of stitches per foot of yarn. Get the stitches per foot by marking on the yarn two oil spots a foot apart, running them into the machine and counting the number of cylinder needles between the spots, remembering that a space also is to be counted at one end just as in counting a screw thread. Frequently, it is possible to find on the stop motion convenient measuring dis- tances which are more than a foot in length and, consequently afford a more accurate result. For scientific purposes one whole turn of the cylinder is taken in order to eliminate the effect of Stitch Adjustment 169 untrueness in the cyhnder and dial, but for commercial purposes one foot is generally a sufficient length. The stitches per foot of yarn are desirable for solution of the weight of the fabric per unit of area, square yard or square foot, for solution of the pounds production, and many other useful details. To start the machine the first care should be to have the stitch sufficiently loose so that the machine will start well. After that it may be adjusted according to the requirements, whatever they may be, such as weight per yard, weight per dozen, ap- pearance, or feel. These adjustments are generally made to a known number of courses or stitches per foot, or by trial, but the rules given elsewhere provide a much more comprehensive method. There are three places in which the stitch may be adjusted. They are : 1. Cylinder stitch cam. 2. Dial stitch cam. i 3. Dial. The extent and frequency with which any one should be used depend on various considerations among which the follow- ing are important: The dial cannot go lower than the position which surely lets the fabric (bunches included) pass between it and the cylinder. The height to which it may go is greater than the stitch will require. The cylinder stitch must be long enough to enable the loop to clear the needles without tucking or breaking, and should not be so long as to pull the yarn apart at twits. The range of ad- justment provided in the machine is greater than that gener- ally allowed by the yarn. The dial stitch must be long enough to clear itself surely, but is limited by the length of yarn between the dial needles and cylinder needles. In fact the dial cam stitch adjustment is the most limited one of the three; moreover, it can be no longer than is allowed by the cylinder stitch. So as a rule, the dial stitch is set to clear as surely as possible and close itself as much as possible without unduly straining the yarn. After that the changes are generally made on the cylinder or dial or both, ex- cept that to shorten much on the cylinder requires reduction in the dial stitch. To lengthen on the cylinder or to change the 170 The Science of Knitting position of the dial up or down does not necessitate a change in the dial cam. Moreover, the cylinder cam does not need to be adjusted for change in the elevation of the dial. Summary The cylinder stitch cam must be set to draw enough yarn for both the cylinder and dial stitch. The dial stitch cam must be set to draw enough to clear the old stitch surely, but not enough to break the new loop. The dial must be far enough away from the cylinder to let the fabric pass through, but may be adjusted farther without necessitating change in either the cylinder or dial cams, until the yarn begins to break or unhook from the cylinder needles, but this is not likely to occur until the fabric is too loose to be useful. The cylinder stitch is adjusted by means of what is called the index eccentric in the cam casing below the place where the cylinder needles draw the yarn down to form the loop. When the screw slot is horizontal and in its highest position, the cam is at its lowest position. Half a turn in either direction gives the entire range of adjustment. The change of adjustment is greatest when the slot is vertical and reduces to zero when the slot becomes horizontal. The dial stitch is adjusted by means of an eccentric like the one in the cam casing on top of the dial cap right after the feed, or by a headless screw in the edge of the dial cap in the same location. Turn the screw clockwise to lengthen the dial stitch. The dial adjustment is effected by means of the nut at the top of the dial stud. The machines with dogs have the nut threaded on the stud so a right-hand turn of the nut elevates the dial, and a left- hand turn depresses it. The stud binding screw must be loosened before each adjustment and tightened after it. When lowering the dial, push the stud down into position after unscrewing the nut, as it will not always drop with its own weight. The dogless machines have capstan nuts threaded on a washer instead of on the stud, so they are turned to the right to depress and to the left to elevate. Use a stiff rod that fits the holes well in order not to bruise them by the slipping out of a scant or flexible wire. Stud binding screws are not used with the dogless attachment, but it is generally necessary to push the stud down after the nut is turned to depress. Rib Knitting 171 ADJUSTING THE YARN CARRIER The adjustment of the carrier involves four considerations: 1. The heel of the carrier must come as near as possible to the closing cylinder latches without touching them. 2. The bottom of the carrier must come as near as possible to the dial needles without touching them. 3. The inside of the carrier must come as near as possible to the hooks of the cylinder needles without touching them, unless knots catch between the carrier and the cheek of the needle, in which case the carrier may be moved out a little, provided the hooks surely catch the yarn. 4. The toe of the carrier should be adjusted outward to the position in which it does the least damage to the latches, a posi- tion variously estimated from i to j inch away from the needles depending on the shape and size of the carrier. When the carrier is so adjusted, the hooks of the cylinder needles should not be uncovered, cylinder latches should not close inside of the carrier or catch in the yarn hole, and dial latches should not close under the carrier or before the yarn is under the latch. If these troubles occur, then the shape of the carrier or the loca.tion of the hole should be changed to overcome them. Judgment should be used in the second adjustment, especially with machines having dial wing cams, since the height of the dial needles changes according to whether the latches are open or shut, whether the needles are in or out, whether the cloth is on or off, and whether the stitch is loose or tight either owing to adjustment or to a load-up. The carrier should be adjusted to clear the needles under all these conditions. RIB KNITTING Trouble, Cause and Remedy; especially for Ribbers It is assumed that the machines are not in bad order either from excessive use or misuse, and that they are equipped with stop motions. If the machines are in bad order, trouble may arise from so many sources that it is cheaper to have them re- paired than to search in books for remedies. If stop motions are not used, the yam and winding should be first class. These sub- jects are not treated here, since they have been considered in other books. 172 The Science of Knitting Rib Knitting Trouble Stitch dropped from one dial needle, ^ but yarn not cut Stitch dropped from one cylinder nee- , die, but yarn nof^ cut- Dial stitch dropped and yarn cut. Cause Dial latch closing under I yarn earner. Dial latch closing near heel of yarn carrier. Cylinder needles rising too soon after drawing stitch and so releasing it before the dial nee-" dies withdraw to keep the tension on it. Yarn not caught by cyl- inder needles. Yarn twisting out of cyl- inder needle hook. Dial needle in too far' when yarn is drawing, thus cutting it on sharp ^ edges of saw cut in needle. Lint or a mote clogged in s saw cut so that latch ( cuts itself out of stitch. ) Latch binding owing to needle being bent or otherwise damaged. Latch closing on one side ) of hook so letting other i side cut stitch. ) Dial needle drawing in' too far, thus cutting I stitch on edge of sinker [ or breaking it. Stitch so tight that it fails to clear and breaks i when needle comes out. i Remedy Lower carrier. Move carrier back as far as possible without in- terfering with cylinder latches as they close. Carry the yarn lower so that it prevents the closing of the latch. Adjust the cap forward so that the dial nee- dles will not come out so far, unless this in- terferes with drawing the stitch over the rivet. Grind cylinder landing cam so it raises the cylinder needles no faster than the dial needles withdraw. Adjust dial cap forward unless restricted by other requirements. Adjust guard so it will catch. Put tension on yarn. Dampen yarn. Adjust cap back so that yarn is drawn over rivet. Clean out obstruction. Replace needle. Replace needle. Adjust dial-stitch cam outward. Loosen stitch. Use lighter coarser cut. yarn or Trouble, Cause, and Remedy Rib Knitting 173 Trouble Cause Cylinder stitch I dropped and yarn" cut. Vertical line of big stitches. Vertical line or lines of dial tucks. Needles loading up all around. Latch swinging to one side and catching on dial needle thus break- ing out of the stitch. May result from saw cut being out of line with the butt, the latch being loose, the latch being bent, the needle too loose in the slot. Latch closing on yarn J carrier. Yarn cutting between ) cylinder and dial nee- ( die. ^ Stitch so long that the ) needle breaks the yarn ? in drawing it. ' Edge of spoon landing on-N hook thus preventing ! latches closing com- f pletely. J Dial latches scored by yarn carrier (on ma- chines with tucking or y welting attachment). Slack take-up. Due to (1) Insufficient weight. <{ (2) Inoperationof take up stop motion, j (3) Take-up pulley, gear, or collar loose. (4) Take-up gummed. Cloth held between dial and cylinder. | Yarn too heavy. I Stitch too tight. ' Remedy Replace needle. Adjust yarn carrier for- ward. Adjust dial so that the two sets of needles will not interfere. Use yarn suitable to the stitch, or readjust lat- ter. ) Replace needle. Raise yarn carrier so that dial needle with closed latch will pass beneath under all con- ditions, and replace damaged needles. Add front weight or ad- just take-up weight- hanger-rod outward. Take off back weight or adjust weights hanger-rod inward. Adjust stop-off chain- connecting take-up and knock-oflf handle so that power will knock off before take- up rests on leg base. Tighten loose part. Clean and oil take-up. Elevate dial. Use lighter yarn or coarser cut. Loosen stitch. 174 The Science of Knitting Rib Knitting Trouble Fabric pulling off needles. One or more cyl- /- inder s t i t c h e a I dropped in line i with dogs. L r Cut, or drop, with a seed, knot, slub,-^ or bunch in it. Press off without stop motion trip-., ping. Cause Dial needles scored all around by low carrier, and cutting stitcher Stitch far too tight. Take-up tension too se- vere. Dogs holding fabric back^ sothatcylinderstitches ! unhook from cylinder j needles. J The seed, knot, slub, or bunch. ~l Yarn parting owing to a^ pull between the nee- dles and the sweep wire. (1 ) An eye clogged with lint owing to roughness, to be- ing too long, to being too small (2) knot catching on j sharp edge of eye. | (3) knot catching be-^ tween yarn car- ] rier and cheek of ) needle. J Lint holding feeler finger. \ Stop motions improp- erly threaded. Remedy Raise carrier and replace damaged needles. Loosen stitch. Take off front weights or adjust weight-hanger- rod inward. Add back weights or ad- just weight-hanger-rod outward. Increase take-up tension. Grind landing cam down if allowable. Keep these obstructions out as much as possi- ble, by adjustment of the stop motion and by keeping the ma- chine free from collec- tions of lint. See that the freest pos- sible passage is allowed for those that do go into the machine. Knots and bunches may catch between the yarn carrier and the cheek of the cylin- der needle, or the dial needle may be out of its mid-position be- tween the cylinder needles, so that the obstruction is held be- tween cylinder and dial needle. Modify eye. Use porcelain eye. Round edge. Use porcelain eye. Move carrier out, if yarn is not likely to drop. Drill yarn hole higher. Clean stop motion regu- larly. 1 I ' ' J Use caution in threading. 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M u (ft ^ o s o t-l ^ 0) •J ■fil a a •o .2 —J g m ■•J 1 Tl frf «rt JJ •v^ Tl ^ Q B o ^ >> 0) fl Q "o 00 CO OOOOOOO^COO'-^t^^COOO COCOOTtlOOOOCOOOCOt^-^0505>— 1 t^t^C3^-*00C000rt-lr^CO «5 CO OOOOOTfiiOOOt^-^tilfSiOOO COt^(MOO(M-*C^iOCOl000005OIMI>-005CO'— icOO3l-^00M COCO»OOO^CDOCOeOO05-HOOO>OOOOOOI:^t>-l>-COO o CO CDC0CSl,-t03t^r^rtt^CDOr^C000C^ "^IMIMr^OCDOSOOOOt^t-t^COCOCO OOOOOOO'^COC^CDCOOOCOO-^ »COCOCOCO'-.eDC0CD CO coou:;cot^co'-«»*l^^ >— iCOt^OSi— l-HOO'— iOOO>OCO"5t*ioo-*a3coc**'-l03 • . ■ •■"tcc^T-irtoOiOJoooor^t^t^cococoio OO ■ • • -OOOOOt^Ol-^TjlcS-^-HOlOcOO ■ icr^coi— ii^.»0'0t:^OC0Q0C000-*<-Ht^-*C. r-C • • • •OOOOOOCOiOOOCO'-'OOCOiOCOO'M •l:^C0I>--^C.C0O5COC0i-l00CO ■ ■ ■ -COC^IrHOOSOSOOOOl^-t^COCOCOCOiCirS *(00CJC0OC005t^'^ •'*C0->!tlO0a05-HC0iCCD05>OC0 • ■ • •CSl^.-icOCOOiOO»OC^OO»OC.iC •CO-»OCO^00CD-^C— lc^)C0C0Tt<»CC0t>.t^0005O "3 Ml-* rt!w nl-* Ht Hw "!■* ril-* "IN «1^ H-* hIn «]■* hW hin «(•* C^ CO ■>*< lO CO Needles per Inch 179 Ml •C o w £ t! O « -""^ § t: 2 4) aj -C S 03 (1) H C 73 c4 i o 01 2 C0)-hOO0505000000 CO «o ' OOOOOOOOCO'-- *0t-C0Ot^00C0»-i'-i 0005-HCOt^rtCOrtt^C<50t^-«l< fOIM(M^00050000000(>-r~ 00 OOOiOMOOCOOOlCiCOO(MO-H »0»Ot^O'0i-c00»OIM eo(M^i-iooo50oooGOt^i>.t^ ■^ ■* -^»-lCS|CO.t~»00050 c . Its CSl CO ^ lO CO 180 The Science of Knitting JS o CO M u CJ Q> 03 •o J2 .9 *?. +j o ■i4 U .0 1 a 9 fil ^ « •0 a i -^ .2 "i V? 0} — • -M 2-9 hi CJ Q V S o a » Eh 00 OS oooooooec eoio-^oot^ooooo Tjtt^^iOOO'^l-- '. '. . '. '. '. . . . .ec(MM'— i'-iOO0» 02 00000000-* •«^05lM^C0C0Ot^00 0(M«C10t1<05100CO '. '. '. '. '. '. '. '. '. lTtOO^OCOCs|00 ^_ -.,-., ^ . — ^ -f ' 00 iOt^O-^Oir^OSiO^-Ht^ 50 cocoocot^cqao-^oo ^ _-,__'■ ■ OC^lTt^OOCMCO^— tl>-c005iO (N - -OOOCOCOOiCtOOC^OO-^ C0(M0qi-iOO050i0i0000 s I^r000'^OTt.(M00C0Oe0Oi0O »OCOCOl>-OOOiOOi— iCMCOCO-^^OCOt— l>-00050 C^ CO "^ lO CD Needles per Inch 181 ^ -^ j3 a> H S w t^ TJ 01 ^ ■ w C! c a >> S o o 01 c -fl s o c a; O ■ 00 CO IC "-H CJ «o • 05 po t>- e^) t^ cs • CO CO IM (M "-c 1— ( • >C J «0 .— ( ;o <— I • CO CO (M . ■ t^ <— I »o o . «0 05 Tti OO •<*< OS CO (M 0 0> 00 O t^ O CO l^ ti CO (M t>. •^ CO — ( O CO CO CJ 1— I <-l O O CO o" o -H M M cc Tf' »o «o 1^ t-' oo 05 d Needles per Inch 183 o o (A rX u oj 0) ^ •9 o ^ V •s i S s (U .Q u g 53 a> ^ « T» s_ § .2 ^-• T3 « 4> Ht H.2 a ■o .y fi a T O a 6'^ 0) « :: fi 3 00 -^ CO CO 00 ■* 00 CO CO CO CO CO o CO t>. •>*< ;;;;;;;;•;; O ■^ oi ;;;;;;;;;•. 'fcoc^ ■ co^oio ;;;;;; ci co oo ;;;•; cococi t^COOOrttO-^CiOOtO-Ht^C^OOCOOCOOiCO ^OaOt^O-^iCO^OOCt^iO^^^J^OOOt^iC^ CO'-i0050->*-000>0 s o a V a . 184 The Science of Knitting Diameter of WUdman Ribbers from Back to Back of Cylinder Needles Nominal Actual diameter Nominal Proportion of nominal diameter diameter Gauge diameter Gauge 18 24-30-36 48 18 24-30-36 48 2 1.68 1.69 1.70 2 .839 .846 .851 2i 1.93 1.94 1.95 2i .856 .863 .868 2i 2.18 2.19 2.20 2^ .871 .877 .881 2| 2.43 2.44 2.45 2f .883 .888 .892 3 2.68 2.69 2.70 3 .893 .897 .901 3i 2.93 2.94 2.95 3J .901 .905 .908 3i 3.18 3.19 3.20 3i .907 .912 .915 31 3.43 3.44 3.45 3f .914 .918 .921 4 3.68 3.69 3.70 4 .919 .923 .926 4i 3.93 3.94 3.95 4i .925 .928 .930 4^ 4.18 4.19 4.20 4i .930 .932 .934 41 4.43 4.44 4.45 41 .933 .935 .937 5 4.68 4.69 4.70 5 .936 .939 .941 5i 4.93 4.94 4.95 5^ .940 .941 .943 51 5.18 5.19 5.20 5^ .942 .944 .946 51 5.43 5.44 5.45 51 .945 .947 .948 6 5.68 5.69 5.70 6 .947 .949 .950 6i 5.93 5.94 5.95 6i .950 .951 .952 61 6.18 6.19 6.20 6^ .951 .953 .954 61 6.43 6.44 6.45 61 .952 .954 .956 Circumference of Wildman Ribbers at Back of Needles Gauge Gauge Nominal diameter Nominal diameter 18 24-30-36 48 18 24-30-36 48 2 5.273 5.317 5.349 41 13.127 13.171 13.202 2i 6.059 6.103 6.134 4f 13.913 13.957 13.988 2i 6.844 6.888 6.920 5 14.698 14.742 14.773 2f 7.630 7.674 7.706 5i 15.482 15.528 15.559 3 8.415 8.460 8.491 5^ 16.272 16.313 16.344 3i 9.200 9.244 9.276 hi 17.054 17.100 17.130 3J 9.986 10.030 10.062 6 17.841 17.883 17.915 31 10.771 10.815 10.846 6i 18.627 18.670 18.702 4 11.557 11.600 11.631 61 19.410 19.455 19.487 4i 12.341 12.386 12.417 6f 20.197 20.240 20.272 Performance of a Latch-needle Rib Body Machine 185 a o « t3 « <1> V C a IM >> •_2 •o 02 o n _^I^ ^ »iL, a> S ^ II u >, •o II TS 0) u a> a> a Q. « c3 >> It 1 2 3 O ooooor^uDOO •OOOOOCQC^OO evj_ o o_ o o e-i^ eo o «D eoiooooi-Toooo CQ CC O CO 00 M •^ -H O CO •^ !>• tflOOOOOOOO t^' o" O O O (m' 05 o o 00>COOOO«OC3l« (M* i-T o o o cT 'j' i-( O 00 ■^ «o O t^ "S «« 00000»OU300 «5 o o o o ■^ ® -> oj fli ro § C ® ti t- e H -u > > c3 oj rt 03 IS "ci C3 1 3 OQ CB > >• O .2- c8 o 3 « 186 The Science of Knitting Table of Mazimuin and Minimum Stitches Least Least number Greatest number Greatest Yarn No. of stitches number Yarn No. of stitches number V^. per foot of stitches VNo. per foot of stitches of yarn per foot of yarn per foot for stable of yarn for stable of yarn fabric fabric 5 2.2361 15.25 29.74 23 4.7958 32.70 63.79 6 2.4495 16.70 32.59 24 4.8990 33.39 65.16 7 2.6458 18.04 35.19 25 5.0000 34.09 66.50 8 2.8284 19.28 37.62 26 5.0990 34.76 67.82 9 3.0000 20.45 39.90 27 5.1962 35.46 69.12 10 3.1623 21.56 42.06 28 5.2915 36.09 70.38 11 3.3166 22.61 44.11 29 5.3852 36.72 71.62 12 3.4641 23.62 46.07 30 5.4772 37.34 72.86 13 3.6056 24.58 47.96 31 5.5678 37.96 74.06 14 3.7417 25.51 49.77 32 5.6569 38.57 75.24 15 3.8730 26.40 51.51 33 5.7446 39.16 76.41 16 4.0000 27.27 53.20 34 5.8310 39.75 77.56 17 4.1231 28.11 54.84 35 5.9161 40.34 78.69 18 4.2426 28.92 56.43 36 6.0000 40.90 79.80 19 4.3589 29.72 57.97 37 6.0828 41.47 80.90 20 4.4721 30.49 59.48 38 6.1644 41.96 81.99 21 4.5826 31.24 60.95 39 6.2450 42.58 83.06 22 4.6904 31.98 62.39 40 6.3246 43.12 84.12 One of the important things to learn about a country is its boundaries. How far can one go in that country before reaching its border? So, in knitting one of the important questions is what are the hmits? How far can one go, for instance, with the stitches per foot of yarn in either direction? This table answers that question for latch-needle rib machines, as it stands, and for flat-work machines if the stitches are for six inches of yarn. It is of course understood that these limits, and especially the loose- stitch limits, depend upon many conditions, such as opinion of what constitutes good fabric, strength of yarn, speed of machine, etc. But in "any case this table constitutes a suggestion from which the reader may make his own table to suit his particular requirements. The table is derived as follows: Least number of stitches = 6.83 VNo. Greatest number of stitches = 13.3 VNo. Yarn Counts 187 YARN COUNTS An equal weight of each of several yarns may be taken and each one may be numbered according to the length of that weight, as in the cotton count; or an equal length may be taken and each yarn may be numbered according to the weight of that length, as in the grain counts. The first, or cotton count, method is called " the length-of-a- constant-weight system" and the other, or grain, method is called "the weight-of-a-constant-length system." For brevity the first is called "the constant-weight system" and the second "the constant-length system." Both are very simple but their application is made confusing by the use of many uncommon units of measure, such as hanks, jack draws, etc., the explanation of which is of historical interest principally. Simple Units are Satisfactory. — All that it is necessary to know for practical purposes are the common equivalents of these units. Cotton Count. — Suppose the pound is taken for the unit in the constant-weight system and one pound of a certain size yarn is found to be 840 yards long. Then one pound of a yarn half as heavy would be twice 840 or 1680 yards long. These numbers 840 and 1680 might be taken as the yarn counts, but they are too big for convenient use. So a larger unit of length than the yard, namely, 840 yards, is taken as the cotton-count unit of length. Consequently the cotton count of any yarn is the number of yards in a pound divided by 840, called a hank; so the first yarn was No. 1 and the yarn half as heavy was No. 2. Evidently in this system the number increases as the yarn becomes finer. Grain Count. — Now suppose that 50 yards is taken as the unit of length in the constant-length system and grains as the unit of weight. Then a yarn of which 50 yards weigh one grain is one-grain yarn. A yarn twice as heavy weighs two grains and is called two-grain yarn. Therefore, in this system — the con- stant-length system — the number increases as the weight of the yarn increases. Transforming between Systems. — Take a round piece of elastic. It has a number in each system. Stretch the elastic to twice its length. Its number has doubled in one system and halved in the other system. That is, for change in the yarn the number multiplies as much in one system as it divides in the 188 The Science of Knitting other. Suppose the elastic is No. 1 cotton; that is, 52 grain, Cohoes. One multiphed by fifty-two equals fifty-two. After it is stretched twice its length it is No. 2 cotton and 26 grain, Cohoes. Two multiplied by twenty-six equals fifty-two, the same as before. And no matter how much the elastic is stretched, the product of its number in the two counts is fifty-two. Take the number of any yarn in any count of the constant-weight system and its number in any count of the constant-length sys- tem; multiply these two numbers together and the product will be a constant, which divided by the number of any yarn in one count will give its number in the other count. For instance, 13 cotton is 4 grain, Cohoes, 13 X 4 = 52. Then No. 10 cotton is 5.2 grain, Cohoes because 52 4- 10 = 5.2, etc. Transfonning within Systems. — Transformation between counts in either system is effected by simple proportion. For instance, the cotton count and the worsted count are both of the constant-weight system and cotton number X I = worsted number. Similarly, the Amsterdam count and the Cohoes count are both in the constant-length system, and Amsterdam num- ber X 2 = Cohoes number. On these two simple principles, division of a constant or multiplication of a ratio, depend all the yarn transformations. The table on page 194 gives the constants for practical use in transformation between systems and convenient proportions for transformation within either system. Yarn Count Definitions 840 cotton count 560 worsted count The yards in a pound 1600 is the run divided by 300 cut or lea 496 metric, strict 992 metric, modified 61 1 'Cohoes standard m Amsterdam standard The weight in grains 20 American standard of the following 50 ■ is the ■ New Hampshire standard number of yards 633.9* neat-silk denier standard 36.57 neat-silk dram standard * Some authorities differ from this number of yards. Counts Used for Different Kinds of Yarns 189 Technically, the weight in grains of < g [ jack draws is the 1 AmSrSdard [ "ut { ^ \ are used as the equivalent lengths in yards. COUNTS USED FOR DIFFERENT KINDS OF YARNS Confusion in Yam Numbering. — On page 190 is a list of the most used counts and the kinds of yarn for which they are used, but no such list is entirely dependable. For instance, 20 ramie may be metric, or metric modified, and if it is not known which, confusion is likely to result unless the individual can determine for himself. This is true of many other yarns. Consequently, any one who has to use different yarns should early form the habit of determining the number for himself instead of depend- ing on guesses. See yarn diameter, from which the cotton count can be determined. Then by simple transformations into the counts supposed to be used, the actual one will be ascertained by its substantial agreement with one of the transformed numbers. Difference, in Ply-yarn Numbering. — Another source of con- fusion is the lack of agreement in ply-yarn numbers. Thirty two-ply cotton is really 15 cotton made of two thirty yarns twisted together. Thirty two-ply spun silk is really 30 yarn composed of two threads of 60 twisted together. Therefore, for cotton, divide the nominal number by the ply to get the real number; but for silk, neglect the ply except for general informa- tion. If the distinction cannot be remembered, but some of the yarn is available, dependence should be put on actual measure- ment. Confusion between Multiple-ply and Multiple-thread Yam. — Still another source of confusion is the lack of a distinguishing indication whether yarn is two-ply or two-thread. Ply yarn is single yarn composed of finer yams twisted to- gether. Two-thread is an expression meaning that two single yarns are used as one. A two-thread fabric is generally made by running two separate threads into each feed used in making the fabric. The numerical ways of writing two-ply or two-thread 30 are 2/30, 2-30; 30/2, 30-2. In some localities one form means two-thread and the other two-ply, whereas in other localities the meaning is just the reverse. Consequently, when ^^^ The Science of Knitting such an expression gets out of its locahty, it is misunderstood. Moreover, it is so easy to forget which expression means two-ply that there seems but httle chance of agreement on a definite meamng for either form, even if a concerted effort should be made. Therefore, the only safe way apparent is to spell out two-ply or two-thread. American Count. — Used in the northeastern part of the United States and Eastern Canada for numbering yarn made in the knitting mill. Amsterdam Count. — This is merely a modification of the Cohoes count, used to obtain a more accurate weight. It is used principally through New York State for yarn made in the knit- ting mill. Cohoes Count. — Used through the eastern part of New York State for yarn made in the mill. Cotton Count. — Used almost universally for commercial cotton yarn, mcluding mercerized cotton, also used for spun silk. Cut or Lea. — Used in Great Britain for linen, ramie and fine jute, for which use it is called lea. Used for woolen yarn in Eastern Pennsylvania, where it is called cut. Metric Standard. — Sometimes used for some yarns where the metric standard is obligatory. Ramie is numbered in this standard. Metric Modified. — Used for linen and some cotton on the European Continent. New Hampshire. — Used to some extent through the New England States. Run. — Used for woolen yarns, other than worsted, in Great Britam and the United States. Silk Denier. — Used extensively for raw silk, also used for throw^n silk on the European Continent. Silk Dram. — Used for thrown silk. Worsted Count. — Used extensively in English-speaking coun- tries for worsted. EXPLANATION OF CONVENIENT EQUATIONS FOR DETERMINING THE NUMBER OF YARN IN THE CONSTANT-WEIGHT COUNTS It is generally undesirable to reel an entire hank of yarn when It IS necessary to determine the count, so it is convenient to have shorter lengths which will serve the purpose without Convenient Equations for Determining the Number of Yarn 191 necessitating reduction from the hank. The tabulation of con- venient equations shows in the first row the definition equations, except that those of the metric system are converted into yards and pounds. The second row is the same, with each term of the fraction di- vided by ten. It is evident from the fu'st equation of the second row that if 84 yards of yarn be reeled and weighed, the num- ber will be one-tenth divided by that weight. This length is long enough to give a reliable weighing, yet not long enough to be wasteful of either yarn or time. After a httle use, the decimal Convenient Equations for Determining the Number of Yam in the Constant- _ weight Counts General Equation. No. = • Weight of a constant length Cotton No. No. 1 Wt. 840 yds. .1 Wt. 84 yds. No. No. 7000 \Nt. 840 yds. 1000 Wt. 120 yds. No. 8^ X yds. weighed Wt. Worsted Wt. 560 yds. .1 Wt. 56 yds. 7000 Wt. 560 yds. 1000 80 yds. 12.5 X Yds, weighed Wt. Run Wt. 1600 yds. .1 Wt. 160 yds. 7000 Wt. 1600 yds. 1000 Wt. 228.6 4.375 X Yds. weighed Wt. Weight in pounds Weight in grains Cut No. = No. = Wt. 300 yds. ^1 Wt. 30 yds. No. = 7000 No. = Wt. 300 yds. 1000 Wt. 42.86 yds. No. = 23§X Yds, weighed Wt. Metric, modified Wt. 496 yds. .1 Wt. 49.6 yds. 7000 Wt. 496 yds. 1000 Wt. 70.86 yds. 14.11 X Yds, weighed " Wt^ Metric, strict Wt. of 992 yds. ■ 1 Wt. of 99.2 yds. 7000 Wt. 992 yds. 1000 Wt. 141.7 yds. 7.056 X Yds, weighed Wt. Weight in pounds Weight in grains 192 The Science of Knitting point may be forgotten, since it will come in the right place from habit. All of the other equations in the second row are similar to the one just explained. It is frequently customary to weigh in grains instead of pounds, so the third row gives the definition equations for use when the grain weight per hank is used. But since the hank is too long for ordinary weighing, the fourth row gives the grain weight equations with both terms divided by seven, which makes the numerator 1000, and provides a convenient length for reeling, the weight of which, divided into 1000, gives the number. The fifth row gives equations for use when it is not convenient or desirable to reel a fixed length. For the cotton count, weigh whatever length is convenient or available and divide that weight into the length in yards multiplied by 8i Proceed similarly for the other equations. SINGLE EQUIVALENT OF TWO OR MORE YARNS Let iVi and N2 be the numbers of two yarns (in the constant- weight system, i.e., cotton, worsted, run, cut, metric) whose single equivalent is desired, say Ng. By definition Ni = — :-; , weight of a constant length of Ni N2 = - . - weight of a constant length of N2' Therefore, weight of a constant length oi Ni = —-. Ni weight of a constant length oi N2 = ~ - N2 Adding, total weight of a constant length of Ni and nI ' ^i.4-l_- N,-\-N2 iVi A^2 N1N2 ' Inverting, 1 ^ NiN2 1 total weight of a constant length of Ni and A^2 Ni + N2 = Ns by definition. In other words, the produgt of two yarn numbers divided by their sum is the number of the single equivalent. From which it follows that the product of one yarn and the equivalent divided by their difference is the other yarn. Yarn Rules for Different Yarn Counts 193 Examples. — What is the single equivalent of No. 10 and No. 20? 10X20 200 . ._ -3or- = -30 = ^•^^- What yarn is required with an 18 to make 12? 18 X 12 216 18-12 6 = 36. When three or more yarns are to be reduced, combine two at a time until the single yarn is obtained. When the yarns are in the constant-length system, their numbers are simply added to obtain the number of the single equivalent. The ordinary counts in this system are Cohoes, Amsterdam, American, New Hampshire, neat silk denier, neat silk dram. Explanation of Yarn-transformation Table Page 194 The given count is at the left of the table. The required count is at the top. Divide the whole number or multiply the fraction at the in- tersection of the two counts by the number to be transformed to get the number sought. Examples. — What is No. 10 cotton in dram silk count? Find the name of the given count, cotton, on the left. Run along to the column headed silk, dram. The expression found there is 305. Since it is a whole number, divide it by the given number. 305 -7- 10 = 30.5, the dram silk number of No. 10 cotton. What is 10-grain New Hampshire in the Cohoes count? Find the name of the given count. New Hampshire, on the left. Run along to the column headed Cohoes. The expression there is 25 . . . ^^. Since it is a fraction, multiply it by the given number 10. 25 2^7: X 10 = 1.25, the Cohoes number of 10-grain New Hampshire. Yarn Rules for Different Yarn Counts Page 195 This table gives the yarn-for-cut rules transposed into the yarn counts used in America. Attention is called to the fact that the transposition is made according to the yarn numbers and not according to the diameters, although the last method is right. 194 The Science of Knitting u o ^.2 P a tn '►^ "^ 15 a> c3 cj O S Ti 0 0 CD 00 I K5 00 I C^ r-H ■^ < o o a s Yam Rules for Different Yarn Counts 195 3 CO J2 s 3 i^ll§iiggSii§isg|||§| S?5SS5^^^g^^go;5g3??^JS^??^g?§ i-li-H»-lr-(r^(M(M(M0000 0»COiOO«50iOOiCO»«0000000000 '^ ^ ^ lO o o t>: r^' ob od O)' d d -<■ c^" c.d ^' «:; o t- 00 oi S o a> « a ii5 2|5ol-5|^0 ^ I 00 I . ^- O cf • t^ 00 05 o COI>"I:^"5C00 ^501-^00050'— l'-''OCOOt^'^05»00 lCCDt^00050^Cflco-<*<'0'Ococor^oo 00 CO i/3CDI>-050'-tC^COCOTfOCOt^t^0005050 fHt— ii— 1»— lr-)»— 11— (1— (T— (1— i*— (1-Hr- (COCOI:^t^Q002OTO-H -H (M O^oc cP y t^ Csi Cv ^ ^» ^ Illustration 1. This machine is anti-clockwise since its motion is opposite to that of the hands of a clock. Clockwise motion is the same as that of the hands of a clock. (200) Figure Designing with Pattern Wheels 201 portion which left the needles last. For instance, fabric of this kind can generally be raveled only from the end which left the needles last, consequently, it is natural to keep this end up to examine a given sample. Also the figure of the design may well be regarded as being built up from below like most structures in which the first courses are at the bottom. Face of Fabric. — (2) The face of the fabric is that side towards which the new loop is drawn through the old loop. This con- vention is generally accepted, so it is repeated here as a reminder instead of an introduction. Fabric Considered to Move. — (3) The fabric is to be con- sidered the moving portion of the machine, that is, the rotor. With this agreement, it matters not whether the guide or the fabric really moves. If the fabric revolves, there can be no con- fusion. If the guide moves, the fabric is considered to move in the opposite direction, since it is only their relative motion which counts in the fabric. This will be made clear by refer- ence to Illustration 1, in which the machine is considered anti- clockwise, because the fabric moves in that direction. If, now, the fabric were kept stationary and the cam ring were moved in the opposite direction, the structure of the fabric would not be changed, therefore, this machine would still be classed as anti-clockwise. The agreement on this convention reduces the complexity of the question one-half, since it cuts in two the number of machines to be considered. Designation of Motion. — (4) Smce, when the tube of fabric is cut open, the direction of circular motion can no longer be determined, the words " right " and " left " are to be used with reference to the fabric — viewed face out, top up — instead of '' clockwise " and " anti-clockwise " to indicate the motion of knitting. The fabric from the machine in Illustration 1 is top up and face out. Therefore, the knitting motion considered with respect to the face of the cloth is right-hand. Now, consider the French circular machine shown diagrammatically in Illustration 2. The fabric revolves clockwise, runs downward, and faces inward. It is evidently right side up, but wrong side out. Consequently, from the inside, the motion of knitting is right-hand with respect to the fabric. Notice that one change of position was necessary to view the fabric correctly and that one change of the appar- ent direction of motion was necessary to obtain the correct 202 The Science of Knitting direction. Again, consider the American loop-wheel machine in Illustration 3, in which the fabric revolves anti-clockwise, runs upward and faces inward. Evidently, it is wrong side up and wrong side out, consequently two changes of position are neces- sary to give the correct view position with respect to the face of the fabric. But the first change of position reverses the ap- parent motion, and the second brings it back again where it was at first. From this comes the general rule: Rule for Motion. — To get the correct motion of knitting reverse the apparent motion of the fabric as many times as it is necessary to change position in order to view the face right side up. The knit- ter should be prepared to meet sixteen types of machine. The agreement that the fabric shall be considered the moving portion reduces the number to eight. Table 1 illustrates the eight repre- sentative types, describes the sixteen types, and shows the direc- tion of knitting motion for each one. The diagrams are drawn with the portion of the fabric on the needles larger in diameter than the first knit portion, and the latter is shown with what appears like the cutting tooth of a bit or auger. The reason for showing the tooth is that the circular machine really knits a ribbon of fabric and loops the edges of the ribbon together. This may be understood from Illustration 4 which represents an anti-clockwise multiple-feed machine in which the fabric runs downward and in which one feed is sup- plied with black yarn, while the others are supplied with white yarn. This machine knits a ribbon of fabric as many courses wide as it has feeds, which width is from black course to the next black course, and at each revolution loops the adjoining edges of that ribbon. Therefore, if the tube is cut around through one black course and then cut lengthwise along one wale to the next black course, the end of the tube will show the tooth Illustration 2. French machine. Illustration 3. American machine. Illustration 4. Ribbon structure of circular fabric. Figure Designing with Pattern Wheels 203 illustrated. The same appearance may be obtained by raveling all the threads to a certain wale. The path of this ribbon is called a helix, and the first formed portion always points in the combined direction of motion in which the fabric is formed. In this case that dii'ection is to the right and downward. If this ribbon construction of the fabric and the direction of in- clination are remembered, figure designing with pattern wheels is readily understood. Pattern Wheels for Latch-needle Machine. — Evidently, these pattern wheels do not act on a particular needle, nor do they act directly, but act through a cam on an entire set of needles, or on a fixed division of a set, as when the set of needles is operated by two independent sets of cams for making vertical stripes. On the contrary, the pattern wheel for figure designs acts directly on each individual needle of its set or division of a set, and is, theoretically, capable of making any needle oper- ate in a contrary way from any other needle. For ihstance, at one revolution it might make a given needle tuck and the next needle knit, whereas at the next revolution it might make each one do just the reverse; that is, it is capable of selecting needles, and when used in latch-needle work is actually called the selector. See " Tuck-stitch figures." In spring-needle machines it is called the presser because it presses the beards of the needles where it clears the stitches and mispresses (fails to press) where it tucks. Spring-needle Pattern Wheel. — The ordinary spring-needle presser is a bronze wheel about 3 inches in diameter with a hub in the middle for its supporting stud and 'udth two kinds of nicks around its circumference, shallow ones called prints to keep the presser traveling with the needles, and deep nicks to make the pattern effects. Material for Pattern Wheels. — The material of the presser should be durable, should cut readily, and should not roughen the needles. Bronze meets the requirements quite satisfactorily, but iron, soft brass and even fiberoid are used. The latter may be cut or filed very readily; it is quite durable and is economical, since as generally constructed the hub or bushing is removable, so that the only cost for renewal of a presser is that for a new fiberoid disc. Also with this construction several discs may be clamped together and cut at one time when duplicates are required. 204 The Science of Knitting "o d t3 T) 73 "^ o d d d d 1-S Z C3 > d ^ d ^ .2 -^ 1^ § « i? d .2 ^ cS 2 V $ d o -tJ r? £•0 02 ui > 2 b © >i *O.S 1 3 •g ^ 1 ° ^ d ^ .2 §i « .0 •r3 Vj -« 2 V .2 i"o ■ 1 -^ n - d J ^ o3 < m 02 < m m 5 [^ ^^ ^ ^^^ ) u 1 ,M^\ I \ M \ f^^^^ a \ \ u r ^1::==/ \i^ \ 1 ^ r / ^ ne ot three positions on any machine. Representing Presser by a Paper Ring. - It is evident that he directions of motion of the inside presser and the outside resser are opposite. It is also evident thkt the vertical presser lay be considered to revolve like the inside presser or the outside resser according to whether its outside face or inside face is aken as the top. It is shown farther on that a paper pattern lay be formed m a circle to represent the circumference of the resser. Then exact comparison may be made between the actual resser and the circular pattern, with the circular pattern held I the position of the presser and with the operating side of the attern considered the same as that of the presser. 210 The Science of Knitting Printing Presser with Needles. — When it is inconvenient to have pressers cut by machine, the following method is sometimes used. The presser blank is turned to the calculated .size, orj slightly over that size, and then run on the knitting machme with j moderate pressure against the shanks of the needles, where they are stiff. The presser becomes marked by the needles according to the needle spacing. These marks are counted and there should be as many as there are needles in the pattern, or in a multiple of it. If there are too many prints in the presser, it is turned down slightly and reprinted until it contains just the right number. Then the prints which are to skip needles are made deep enough and wide enough to skip with the use of a file or a hack saw or both. Since designs with tuck stitches are the commonest, the dis- cussion is continued with respect to tuck work; but the principles apply to practically all circular pattern devices. Presser Like a Wheel Printing a Ribbon. — From the fact that the presser operates directly on the needles it may be considered to operate directly on the fabric ; and since the fabric travels in a hel- ical path, the presser may be considered to be a printing wheel beneath which the ribbon of fabric runs and receives the pattern impression. The subject will be treated in accordance with these considerations, starting with a single pattern wheel. Suppose that the circumference of the pattern wheel divides a whole number of times — that is, divides integrally — into the circumference of the fabric. Then whatever impressions are on the presser will fall in line with the wales and so make what are called vertical stripes. Now, the pattern on the presser is not changeable without recut- ting the presser, so the pattern is considered to be fixed. Causes of Changes in the Figures. — The different figures in the fabric which may be obtained from any pattern are caused by change in the number of needles, or by change in the direction of motion of the machine. Evidently, change in the direction of motion of the machine changes the end of the pattern which comes on the fabric first and change in the number of needles tips the stripes out of their vertical position. The essential part of figure designing consists of the few simple principles which con- nect these changes of needles and of motion with the resulting changes, in the vertical stri])es. Definition of Pattern. — In order to avoid confusion it is I necessary to understand clearly what each term means and to Figure Designing with Pattern Wheels 211 restrict its use to that particular meaning. One of the obstacles heretofore in the way of a clear description of the principles of figure designing has been the lack of such understanding. For instance, it has been customary to use the term pattern to desig- nate both the impressions on the circumference of the presser and the figures in the fabric obtainable with it. But since there may be at least as many of these figures as the number of needles in one circumference of a non-repeating presser, it is evidently necessary to distinguish between the arrangement of impressions on the presser, which is fixed, and the result in the fabric, which Illustration 6. A single tuck stitch viewed from the back of the fabric. A is the held loop, B is the tuck loop. is variable. Therefore, it is advisable to restrict the term pattern to the impressions around the circumference of the presser and to its duplication along the ribbon of fabric. Moreover, some pressers 'are sufficiently large to contain the pattern more than once, so the actual pattern is any successive portion of the circumference of the presser or of the ribbon of fabric which does not repeat itself. Tuck Stitch. — Illustration 6 shows a tuck stitch viewed from the back of the fabric. It is seen to consist of a V-shaped loop 212 The Science of Knitting with the point upward and a long loop from the next lower course, through both of which a loop from the next higher course is drawn. The term tuck stitch is also used to indicate either the inverted V-shaped loop or the long loop. In order to avoid confusion it | seems advisable to restrict the term tuck stitch to the combina- tion just described, to call the inverted V-shaped loop the tuck loop and to call the long loop the held loop. This agrees well with the conventions and the facts, since the inverted V-shaped loop is produced at what is called the tuck feed and since the long loop is held over a course before it is cleared. Illustration 7 shows a double-tuck stitch viewed from the back of the fabric. In this there are two tuck loops and the held loop Illustration 7. A double tuck stitch viewed from the back of the fabric. A ia the held loop. B is the first tuck loop. C is the second tuck loop. is carried over two courses before it is cleared. When the tuck stitch contains more than one tuck loop, these are numbered in the order of their formation, so in Illustration 7 the longest tuck loop is No. 1 and the shortest one is No. 2. The longest loop of all remains the held loop. Illustration 8 shows four adjoining tucks in the same course viewed from the back of the fabric. Each held loop is like the one in the single tuck, but the tuck loop appears as a long loose thread on the back of the fabric. Before the stitches are further discussed, it should be stated that these sketches are diagrammatic and that the actual stitches would not always be recognized from sketches of this kind. Indeed, one of the remarkable things about tuck-stitch combina- Figure Designing with Pattern Wheels 213 tions is how different they look from what is expected. This introduces one of the principal characteristics of tuck stitches, the distortion which they produce in the fabric. Illustration 8. Back view of four successive single tucks in the same course. A, A, A, A are the held loops. B is the floated loop resulting from the four tuck loops. Fabric Distortion due to Tuck Stitches In plain fabric one of the requirements for good fabric is to have the stitches all alike. But consideration of Illustration 6, single tuck, shows that if the yarn is fed uniformly, the tuck loop will be too long and the held loop will be too short . Consequently tuck stitches pucker the fabric in the locality of the tucks. The general effect is to shorten the fabric along the wales and widen it along the courses. For this reason smaller-size cylinders are needed for tuck work than for plain work. The extent of the change depends largely on the proportion of tuck stitches to plain stitches. Some designs contain so few tucks that the widen- ing is inappreciable. It is evident that the held loop has a tendency to steal some yarn from its adjoining loops in the same course; and, although it is not so evident, still it is just as true, that the tuck loop has a 214 The Science of Knitting tendency to lend some yarn to the adjoining loops in its course. Therefore, as a general rule, loops next to held loops in the same course are short, and loops next to tuck loops in the same course are long. But it must be remembered that a series of tucks close together may produce a different effect than that produced by one isolated tuck stitch. Indeed, the variations due to stitch •' distortion alone are too numerous to classify. Tuck-stitch Limits Necessary to clear Held Loops. — It was shown that the tuck stitch involves the drawing of a loop through the tuck loop and the held loop. In other words, unless the tuck loop and held loop are cleared, there can be no tuck stitch. This is true prac- tically as well as theoretically, since the needle must be cleared or else it or the loops on it must break. Consequently, the strength of the yarn is a factor which determines how many tuck loops may be carried on one needle. The strength of the needle is generally sufficient, provided the burden of loops can be thoroughly cleared within reasonable time, but it is difficult to clear many loops at a time, and failure to clear them allows so many loops to accumulate on the needle that their combined strength ultimately bends or breaks it. From five to seven tucks on the needle, according to the yarn and the machine, is con- sidered the practical limit. The number of adjoining tucks along a course is limited in a different way. Consideration of Illustration 8 shows the tuck loop to be a long loose loop on the back of the fabric. In reality, the loop is longer than it is shown, for two reasons : one is that the fabric generally narrows on leaving the needles, which makes the loop longer by comparison; and the other is that there was as much yarn supplied to this loop as to the four stitches which it crosses. The result is that the back of the fabric is not only unsightly, but these loops catch and tear in use, which makes the fabric less durable than it would be otherwise. Six adjoining tucks along a course is considered the practical limit. The Tuck Loop is kept out of the Face of the Fabric Examination of any of Illustrations 6, 7 and 8 shows that the tuck loop is kept on the back of the fabric. This is not of much importance when the yarn is all of the same color, but when Figure Designing with Pattern Wheels 215 different colored threads are used, it affords an opportunity for keeping the tucked color out of the face at intervals. This in- troduces the customary arrangement of feeds. We have to start with: a tuck must be cleared; the number of adjoining tucks both horizontally and vertically is limited; and two differ- ent colors are generally used. If it were not for the first two con- ditions, the idea would at once suggest itself to use two colors Illustration 9. Face view of a white block in a mixed field. The floated threads are seen behind the white held loops. of marked contrast, say black and white, and to reverse them alternately from face to back. This would make, say, a black figure on a white field, which constitutes a distinct design. But since the number of successive tucks in either direction is ad- visably not over six, the greatest extent of the figure or of any part of the field would be six stitches in height and in width, and even that size is accompanied with much puckering. The other alternative is to keep the first color in the face, to keep the second color in the face part of the time, — when it combines with the first color to make a mixed field, — and to throw the second color to the back during the rest of the time in order to leave the 216 The Science of Knitting first color entirely in the face for a short interval to form the small solid figure. Illustration 9 shows the face of a piece of fabric made in this way. The black thread is thrown back out of the mixed field in order to leave the white exclusively on the face to form the rectangular figure. The equipment necessary to produce this is one tuck pressure alternating with a plain presser, which is the combination used in most figure designing when colors are used and even when they are not. Evidently this requires an even number of feeds, 2, 4, 6, 8, etc. To reverse the colors at the feeds reverses the color of the figure but leaves the field unchanged, since both threads combine to form the field. Relation of Pattern Wheel and Yam. — Since one color re- mains in the face all of the time, the plain presser operates im- mediately after that color is fed, as it does with plain fabric. Consequently, the tuck presser operates on the needles im- mediately after the feeding of the yarn which is sometimes thrown on the back of the fabric. The use of colors is not necessary, since the contrast between the tuck and the plain stitches shows the design clearly enough for most purposes and sometimes more pleasingly than with the assistance of colors. The effect produced in the fabric by the pattern is probably best called the design. The design, like the pattern, is that portion of the fabric which entirely repeats itself. It follows then that there are no fractional designs. The design is composed of two parts, the figure, and its back- ground, the field. The main technical feature of figure design is the controlled disposition of the tucks in the field, which control embraces the size of the figure and of the field, the shape and position of the figure, and its relation to the top of the fabric. Almost any knitter can make a design by filing nicks in a presser and putting it on the machine, just as almost any cook can make a cake by mixing flour, sugar, eggs and baking powder and putting the mixture in the oven. But it takes a fairly good knitter to nick the presser so as to obtain the exact design de- sired, just as it takes a fairly good cook to mix batter which will turn out a predetermined kind of cake. Learning to Design. — The object of this discussion is to en- able the knitter to know how to nick the presser in order to have the design come out just as he desires, instead of upside Figure Designing with Pattern Wheels 217 down, backward or entirely different from that which he had planned. It is exact knowledge such as this which the knitter needs, and it cannot be obtained without a certain amount of mental effort. However, if that effort is well directed, the sub- ject should be learned readily and retained permanently. Both of these objects may be accomplished by learning first how to work out the principles; second, by learning the principles; and last, by learning the application of them ; and then remembering these divisions in the same order. The application of the prin- ciples involves the most details and so is easily forgotten; more- over, even when remembered, the necessity for use may be on some unfamiliar type of machine, so the principles themselves will be needed in order to work out the application. Conse- quently, the principles are the essentials, but disuse may cause even them to be forgotten. However, if the method of deriv- ing the principles is remembered, then whenever any question regarding figure design arises, the knitter can without books or assistance start right at the bottom and derive not only the principles but the application of them to any machine. The subject is developed in line with the above suggestions, by estab- lishing unmistakable terms, by using the analogy of the printing wheel on the ribbon, and by gradually introducing the varia- tions which may be produced with the fixed pattern. The size of the design is measured in stitches, since this unit has a fixed connection with the needles, whereas any other unit has not. Consider that from a piece of fabric knit with two feeds — one, tuck, and the other, plain — the following pattern is ob- tained by copying a tuck course until repetition of the pattern begins : oooooooooooooxoxoxoxoooxoxoxoxoooooooxoxoooooooxox The ciphers represent plain stitches and the cross-marks indi- cate, tuck stitches, showing altogether fifty needles in the pat- tern. It is desired to know what designs are possible with this pattern. Winding Strip Pattern to Make the Design. — If the above- mentioned pattern is repeated several times on a long strip of paper equally divided in spaces corresponding to needles, and then this piece of paper is wound helically to form a tube, the cross marks will show different figures according to the diameter 218 The Science of Knitting of the tube, among which figures will be those shown in Illus- \ trations 10, 11, 12, 13, 14. But it is somewhat difficult to ar- ' range and hold such a long strip, so a substitute may be made for No. 10, say, by copying the 50-needle pattern on cross-section paper so that the same needles fall in the same vertical lines, as Models of tubular pattern fabrics. The designs are such as are obtainable with the pattern shown in 20 by change in the number of needles and the direction of motion of the machine. The results could be duplicated practi- cally with a two-feed machine, one feed having a tuck presser cut like one row of 20 and the other feed having a plain presser. The models are not shown for Nos. 25 to 30 inclusive. No. 10. Vertical stripes caused by the use of a number of needles equal to a multiple of the pattern. The fabric motion is right-hand. No. 20 is the development of No. 10, and would be unchanged for left-hand motion. No. 11. Inclined stripes caused by the use of slight overlap (needles one less than a multiple of the pattern). The motion is right-hand. No. 21 is the development. No. 12. Stripes inclined diagonally in two directions, caused by the use of overlap of half a pattern division (needles five less than a multiple of the pat- tern). The motion is right-hand. No. 22 is the development. No. 13. Inclined figure caused by the use of a number of needles nearly one pattern division less than a multiple of the pattern (needles nine less — the division is ten). No. 23 is the development. No. 14. Vertical figure caused by the use of a number of needles one divi- sion less than a multiple of pattern (needles ten less). The motion is right- hand. No. 24 is the development. Notice that the front of the pattern, indicated by the double tuck, is uppermost. in Illustration 20. If this is cut out and the ends are curved to meet, the stripes will be just like those in Illustration 10. Evi- dently, there are 50 needles in the circumference the same as in the pattern. From this comes the conclusion that when the number of needles in the cylinder is the same as the number in the pattern the design consists of vertical stripes. Now it is evident that two strips just like Illustration 20 might be pieced end to end, or three or any number, and still the design would be vertical stripes, from which comes the conclusion that when Figure Designing with Pattern Wheels 219 the pattern divides the needles integrally the design consists of ver~ tical repetitions of the elements of the pattern. Development. — When a tubular figure is cut lengthwise and spread out, it is called the development of the original figure Consequently, Illustration 20 is the development of Illustration 10, also 21 is the development of 11 and so on, each development No. 20. No. 22. Development of No. 10. No. 21. Development of No. 11 Development of No. 12. No. 23. Development of No. 13. INo. 24. Development of No. 14. )eing designated by the number which is ten greater than that )f the figure. Decreasing the Number of Needles in the Cylinder. — Con- idermg Illustration 21 the observer will notice that it is made by epeatmg the pattern over itself, but that each repetition start- tig from the lower right corner is one needle to the left of 220 The Science of Knitting that above it, so that the ends have a step-hke appearance. If the piece of paper is cut out and the ends are matched so that the double courses marked A, B, C, D meet, then development 21 will be like tube 11, but the distance around the tube will be only 49 needles, which is one less than the number in the pattern. Evidently, the vertical stripes are tipped with the bottoms to the right, in which direction the fabric is supposed to be moving, since the double course marked is free, as if the yarn were raveled to that point. If other pieces like 21 but with 50 needles were put end to end with 21, and formed into a tube with cor- responding terminal courses meeting as they do in Illustration 21, then the number of needles might be 99, 149, 199, etc., always 1 less than a whole number of patterns, and the inclina- tion would be the same as in 21, which shows that when the number of needles is one less than an exact multiple of the pattern, the upper end of the vertical stripes falls back from the direction of motion of the fabric. That is, the front part of the pattern falls back over the front part of the pattern previously knit, or overlaps it. Development 22 has five needles less than the pattern, and it will be noticed that the inclination has gone so far that the stripes begin to mix. Development 23 has 9 needles less than the pattern and it is evident that a figure is beginning to form from the gathering together of one element from each stripe with the front of the pattern uppermost. Condition for Desired Design. — Development 24 has 10 needles less than the pattern and shows the figure completely formed. In this the pattern may be read horizontally to the left along the courses, or vertically down the wales. This is the result generally sought in figure designing — that is, one in which the pattern or horizontal portion is repeated vertically in the figure. To obtain this, the pattern is divided into sec- tions of equal length, and the impressions in each section, or division, are arranged with some sort of symmetry about the middle of the division. It will be noticed that division 5 is blank. This is to make a break in the vertical effect, which would otherwise still be a vertical stripe (although an irregular one) since it is made up of portions of each division of the pattern. Reversing Motion. — Now consider the machine to contain 50, or 100, or 150 needles makiag vertical stripes, except that Figure Designing with Pattern Wheels 221 it turns in the opposite direction so that the fabric moves to the left side instead of to the right. Note, however, that since it is agreed to call the part of the pattern which first makes its im- pression the front, the beginning of the pattern is now on the left instead of on the right. In other words, when the motion IS reversed, the front of the pattern is also reversed. Evidently with the number of needles just given the effect in the fabric will be vertical Imes as before, so that Illustration 20 will still represent the development. For one needle taken out, the development is like that in Illustration 25, and for 10 needles taken out, the development is like that m Illustration 26. From Illustrations 24 and 26 it follows as it did for motion in the opposite du-ection that when the number of needles in the cylmder fails to divide by the number in the pattern by one division of the pattern, then the divisions of the pattern arrange themselves vertically with the front of the division at the top. Therefore, one rule holds for each direction of motion. Increasing the Number of Needles in the Cylinder. - When the total number of needles m the cylinder is one division of the pattern more than a whole number of patterns, the result for right-hand motion is shown by Illustration 27, and for left- hand motion, by Illustration 28, both of which show that the tront of the pattern is at the bottom of the figure. From the preceding comes the general fundamental rule of figure designmg. The divisions of the pattern arrange themselves vertically ^th the front [^^Z^^ ^vhen the needles in the cylinder are one division (^""^t') ^,^hole number of patterns. Needle Changes of More than One Division. — So far the change m the total number of needles in the cylinder has not been more than one section - that is, 10 needles -from an 3qual division by the pattern. If the change extends beyond me division of needles, the figure inclines and reforms into two igures when the discrepancy from an equal division by the )attern is two divisions, as it is seen for right-hand motion in llustration 29 for needles two divisions less than one pattern ■nd m Illustration 30 for needles two divisions more than one lattern. fft^«. M J""! - -- s z.l _. _-g: _g " " :g=^=gi=? _g < i S 'i -,- S ,"? „" ' g g :!:i ■&?tSJ^ -S-^ s s .: i <-^T'Z'' :: 3 "g g ■J-g-R S g -g_i^g 8 : :: g s i ""8 s > g g"S " _« g ; " g g g'g ^ -S-g__ ^g g : i g:: _g~^ :?.. :: o No. 25. Development of a model such as No. 11 would be with left-hand motion. Comparison with 21 shows that reversal of tiie motion reverses the initial inclination of the stripes. No. 26. Development of a model such as No. 14 would be with left-hand motion. Comparison with 14 and 24 shows that reversal of the direction of motion inverts the figure abolit a horizontal axis in its plane. No. 27. Development of a model such as No. 14 would be for needles one division more than a multiple of the pattern and for right-hand motion. No. 28. Same as No. 27, but for left-hand motion. Comparisons of 24 with 28 and of 26 with 27 show that reversal of both the lap and the direction of motion leaves the figure undisturbed. No. 29. Development obtained by the use of a number of needles two divisions less than a multiple of the pattern and right-hand motion. Notice the division of the pattern into two figures instead of one. No. 30. Development obtained by the use of a number of needles two divisions more than a multiple of the pattern and right-hand motion. Notice the division of the pattern into two figures instead of one. (222) Figure Designing with Pattern Wheels 223 Advantages of Paper Strip Method. — The above method of connecting the pattern and the design should be remembered, for It affords a convenient way of working from the design right back to the tube of fabric with the direction of motion and needle relation clearly shown. Indeed, this method is preferable to working exclusively on the machine, smce machines are re- stricted to a narrow range of variation, whereas this paper method IS subject to all of the variations possible; moreover, it is graphical, even to the dupHcation of an equivalent tube, and best of aU, it proves what will be obtained, whereas the ordinary method' of drawmg the figure in a rectangle is not susceptible of proof that the result in the fabric will be as it appears m the plan. The variations due to more extensive overlap may also be shown by this method, but they are more readily shown by the followmg one which is substantially an abbreviation of the one just given, and is advantageous in that it is much quicker, and does not require cross-section paper. It does not, however, show the slight variations obtainable by a change of needles between whole divisions of the pattern. Numerical Method For convenience consider a pattern having five divisions of ten needles each, just such as has been used. The width of the pat- tern may be any number of feeds. Number these divisions 1, 2 3, 4, 5, beginning with the one which first makes its impression' Suppose that the machine has ten needles, which is one division. Then the first division will just finish the first revolution, the sec- ond division will just finish the second revolution, etc.^ so that if the fabric is cut lengthwise between the first and the tenth needle, it will show the pattern in the numerical order of its divisions with number one at the bottom: Illustration 32. Now, consider that the machine has 20 needles, which is two divisions. Then the first revolution will take the first two divi- sions, the second revolution wiU take the thu-d and fourth divi- sions, and the third revolution will take the last division and the first one over again in order to fill up. Consequently, when the tube is cut open and flattened out, the different divisions will appear on it as in Illustration 33. It is evident that four straight Imes will not bound this design, but that six are required. The reason for this is clearly that the number of divisions in the pattern is not evenly divisible by two, the num- 224 The Science of Knitting ber of divisions of lap. In each of these cases, and in those that immediately follow, the flattened piece of fabric is a develop- ment of the tube, with the division following a wale, instead of following the end of the pattern as it is shown in Illustra- tions 21 to 24. It is noticeable that when there is one division of needles there is only one design of one figure; but when there are two divisions, there are two designs each composed of two figures. Now consider the machine to contain three divisions of needles, that is, 30. The fabric appears like Illustration 34'. Evidently, there are three different designs, each composed of three groups of figures. For four divisions of needles there are really four different designs, as Illustration 35 indicates; but they all look like Il- lustration 32, except that now division 1 is at the top instead of at the bottom. Of course, when the machine contains five divisions of needles, the fabric shows vertical stripes corresponding to each section as Illustration 20 shows. For six divisions of needles. Illustration 36, the fabric shows just what it did for one division. This may be seen by a com- parison of 36 and 32 which are put close together for the purpose. Range of Designs. — Moreover, it will be found that all of the vertical figures obtainable with any number of needles are shown by the changes between one division and the total num- ber of divisions in the pattern. Of course, the inclination of the stripes is not shown within that range, since all of the stripes do not appear until the number of needles in the cylinder is equal to the number of needles in the pattern. But one more division is enough to give all of the inclinations of the stripes. Moreover, a conglomeration is obtainable with a number of needles less than One division. So, in general, all obtainable de- signs including all elements of the pattern are embraced by a range of needles from zero to one division more than the length of the pattern. Real and Apparent Design. — Before going farther with the above understanding of the word design, it is necessary to dis- tinguish the real frond the apparent design. Take Illustration 33 for instance. It shows two designs, each with two figures, of which one is the reverse of the other. Now refer to 37 which is the same as 33, except that the piece of fabric is larger, and affords a more comprehensive view of the designs. Reading Figure Designing with Pattern Wheels 225 32. Numerical Diagrams For explanation see Numerical ^Method, page 223. Arrangement of pat- tern divisions in the fabric when the number of needles is just one pattern division. 4 3 2 1 5 4 3 2 1 5 4 3 2 1 4 3 2 1 5 4 3 9 1 4 3 2 1 5 4 3 2 1 a 4 3 2 1 f) 4 3 1 5 1 4 3 2 1 5 1 4 1 3 2 1 36. Ditto six pattern di- visions. 5 4 3 2 1 5 4 3 2 1 33. Arrangement of pat- tern divisions when the number of nee- dles in the cylinder is two pattern di- visions. 3 2 1 4 3 J 1 5 4 3 2 1 ; 5 4 3 2 1 5 4 3 2 1 5 4 3 2 1 5 4 3 2 1 5 4 3 2 1 5 4 3 1 5 4 3 2 1 T 4 3 2 1 5 4 3 2 1 5 4 3 2 1 37. Ditto seven pat- tern divisions. 5 4 1 3 2 1 1 5 4 1 3 1 2 JJ5 3 1 2 4 1 34. Arrangement of pat- tern divisions when the number of nee- dles in the cylinder is three pattern di- visions. 2 1 5 4 1 3 2 1 5 4 3 2 1 5 4 3 2 1 5 4 3 2 1 5 4 3 2 1 5 4 3 2 1 5 4 1 3 2 1 5 4 3 2 1 5 4 3 2 1 5 4 3 2 1 ^574 3 2 1 3 5 2 4 1 3 2 1 5 1 4 3 5 2 4 1 38. Ditto eight pat- tern divisions. 5 14 13 12 1 2 3 15 4 3 4 5 2 3 4 1 2 3 5 1 2 4 5 1 3 4 5 1| 5 1 4 1 3 1 2 5 1 5. Tl 1| 5 i 4 3 1 2-| 1 [T 4 5 1 3 4 5 2 3 4 1 2 3 5 2 4 5 1 3 4 5 2 3 4 1 2 3 30. Ditto nine 4 1 3 1 2 1 1 pattern di- visions. Ditto four pattern di- 2 1 5 4 3 9 1 [5 4 visions. 3 2 n~i 5 4 3 2 "rj5 4 3 1 2 rr, 5 4 3 2 n" Illustrations 32 to 39, inclusive. 226 The Science of Knitting the numbers upward in vertical columns, one sees that the group- ing 24135 constantly repeats itself over the whole extent of the fabric. Consequently, this apparent design fills the condition for a design, namely, that it is an effect which entirely repeats itself. In short, as far as appearances are concerned, there is but one single figure design for each case in which the number of needles is a multiple of the pattern division. Illustration 38 shows this for Illustration 34, as does 39 for 35. Key to Illustrations ii to 28, Inclusive Overlap. Needle remain- der less than a whole number of patterns. Right-hand Motion Left-hand Motion Underlap, Remainder more than a whole number of patterns. Illustrations 11,12,13,14, 21,22,23,24 Illustration 27 Illustrations 25,26 Illustration 28 The direction of motion and lap is shown on the upper and left margins of the table. The diagram in the right corner of the squares is recognized as the diagram produced by the given pattern. The position of the diagram is for lap of one division according to the direction of lap and the direction of motion given. The diagram in the left corner of the squares shows how the vertical Unes start to incHne when a shght change in the direction of lap IS made from an equal division of cyHnder needles by the pattern. It is evident that whereas a change of either direction of lap or direction of motion reverses the position of the design about a horizontal axis, the change of both together leaves the design undisturbed. Figure Designing with Paticern Wheels 227 Inclination of Designs. — It is evident, however, that the relative arrangement of these apparent designs is different for each change of needles amounting to a pattern division. For one division, or six divisions, or eleven divisions, etc., each, the design rises to the right above the preceding one by the width of the pattern (for right-hand motion of the fabric). But when the number of needles is two divisions, seven divisions, twelve divisions, etc., the direction of inclination is the opposite and the second rises two widths above the first, and so on. Illustrations from 36 to 39 inclusive show the relative arrange- ments of the apparent designs for five section patterns. It is unnecessary to try to remember these relations, or even the groupings. But it is advisable to remember the method, for then all of this information may be quickly obtained when needed, and without the necessity of sketching the actual design. This method affords a convenient way of telling what the design will be for a lap of any number of divisions. , It will be recalled that the width of the strip pattern may be any number of feeds. But a certain length was taken, namely five divisions of 10 needles each, which length has not changed. Therefore, if one tuck feed is used, the design will be five tuck courses high; if two feeds are used, the design will be ten tuck courses high; and in general the height of the design in tuck courses will be the number of tuck feeds multiplied by the number of divisions. Design Calculations The mathematical part of figure designing is the big stumbling block to learning how to design from books. However, the cal- culations in connection with figure designing are very simple, as the following explanation will show. There are four points to consider, namely: The number of needles in the cylinder. The width of the design (horizontally). The length of the pattern. The height of the design. Evidently, the easiest way to consider them is one at a time. The number of needles in the cylinder. A change in this number of one or two per cent is allowable in leaded spring-needle ma- chines; but other machines are changeable only by the substi- 228 The Science of Knitting tution of a new cylinder, which is expensive and troublesome. Consequently, it is generally necessary to adapt the design to the number of needles in the machine, and it is advisable to do so even in the case of leaded-needle machines, since changing to a certain number of needles and retaining that number is some- what troublesome. Many users of knitting machinery facilitate the manufacture of pattern fabric by having their machines made originally with a suitable number of needles in each cylinder. (It will be shown later what numbers are suitable.) Since, then, the number of needles in the cylinder is sometimes practically unchangeable, and at others changeable only inconveniently, this number is the basis of the calculations. Therefore, given designs should be modified accordingly, or new designs should be made accordingly. The numbers of needles in different cylinders are generally known to the man who makes or modi- fies the design, or may be procured from the manufacturers of the machines if the machines are not where the needles may be counted. This book gives the numbers of needles for some types of machine. Illustration 40 will help the balance of the explanation. Dia- gram A 1 shows a developed needle line — that is, the circular needle line cut open and spread out straight. It might con- tain any number of needles, but here for convenience it con- tains 65, each one represented by a vertical space. The Width of the Design. — This must divide into the num- ber of needles in the cylinder, that is, into 65 in this case. If the number of needles in the cylinder is not divisible, that is, if the number is a prime number, then vertical figures cannot be made. Diagonal effects may be produced, but they are not considered in this discussion. Therefore, if the number of cylinder needles is not divisible, the cylinder is not usable for this kind of designing. But in this case the number is divisible, since 65 may be divided by 5 and by 13. These are the only widths of pattern usable, since they are the only divisors of the number of needles. For illustration select 5, since the paper is laid off in groups of five. Then 5 is the pattern division, since it not only has to divide into the number of needles but also into the pattern, as will be shown later. Moreover, it is more convenient to continue the discussion with divisions as the measure, instead of needles, just as it is more convenient to dis- cuss fortunes in thousands of dollars instead of dollars or cents, Figure Designing with Pattern Wheels 229 both of which are such small units that the figures would be cumbersome. There are 13 divisions in the cylinder, since 5 divides into 65 thirteen times. The Length of the Pattern. — Now it has been repeatedly- shown that the pattern must not divide evenly into the number rrr^ . X Ijl ' 'i 1 - ii 3 ^" : :i£_'^" i): 31" iS tf A:' '- - -~ g - T" ^ 1 1 ^^ 1 j^^ • - - -D >. r*i 1 ' ' Tir. - 1 1 ' i i ■ 1 M ■ 1 : 1 do \i/Z -|_ -1- _j_ .... 1 1 ..---.^-.. ...._._...-.-.-.--.-. LL Illustration 40. Al represents a developed needle line containing 65 needles. The other strips show the total pattern lengths and divisions usable with 65 needles. Bl, B2, B3 are for underlap. CI, C2 are for overlap. of needles by one division. Therefore, the pattern must divide into 12 divisions, or into 14 divisions, which numbers are one less and one more than the number of divisions in the cylinder. Diagrams 51, 52 and 53 contain 12 divisions, and diagrams CI and C2 contain 14 divisions. The principal use of these diagrams is to make clear this step of the calculations, which is the con- fusing one to the student. It should be thoroughly understood, that the number of needles is not changed by one division. These lengths 5 and C are taken merely for the purpose of de- termining what length of pattern is permissible. The reason for taking them is at once apparent ; for, evidently, if the pattern 2^^ The Science of Knitting divides these lengths without a remainder, then it must divide the number of needles with a remainder of just one division, or one design width, which is the condition to be met. The B diagrams show that the usual patterns for underlap may be 2, 3 or 4 divisions in length. The C diagrams show that the usable patterns for overlap may be 2 or 7 divisions in length. The inversion of the design caused by change from overlap to underlap is shown by Illustrations 24 and 27, and is stated in the general rule for tuck figure design. This inver- sion of the design is one of the considerations in the selection of the lap. The Height of the Design. — This is the other consideration in the choice of the lap. It is expressed in courses and equals the number of divisions of the pattern multiplied by the number of feeds. The diagrams show a range of patterns having 2, 3, 4 and 7 divisions. Suppose four feeds are to be used. Then the height of the design in courses may be either 8, 12, 16 or 28. This is all there is to customary pattern calculations, when the work is based on the number of needles in the cylinder. Copying or modifying a given design is one of the most im- portant parts of the subject, and it may be explained by follow- ing through all of the processes. First, however, it is advisable to understand clearly the conventional method of sketching designs. Representing Tuck Stitches. — It is customary to lay out designs on cross-section paper, so that horizontal rows represent courses and vertical rows represent wales. When the squares contain no crosses, the diagram represents plain fabric. Then the individual squares represent loops of plain fabric. They are frequently considered to represent stitches, but since a stitch is a combination of at least two loops, this practice causes con- fusion when it is necessary to reconcile the diagram with the fabric which it represents. It should be thoroughly understood, therefore, that before any crosses are made on the diagram the squares represent loops of plain fabric, and when a cross is put in a square it means that what would have been a loop of plain fabric is changed to a tuck portion of pattern fabric. This cross does not make the diagram look like the fabric which it repre- sents, for several reasons. The tuck loop remains on the back of the fabric, whereas the face is viewed. The loop which does appear on the face is the held loop which belongs in the next Figure Designing with Pattern Wheels 231 square below if single tuck, and in the second square below if double tuck. The cross would seem to indicate that the loop in that position is more prominent than the others, just as the conventional sketches of tuck stitches do, but in reality the loops alongside of the marked one are frequently larger. And finally, the stresses caused by the tucking pull the wales and courses out of the positions which they would occupy in plain fabric. Consequently, the only way for the novice to see the diagram in the fabric is to see a tuck loop represented by the cross, in the place of a corresponding plain loop of plain fa,bric. At first it may be necessary to turn the fabric over in order to make sure that the tuck loop is there. Inspection against the light frequently shows the tuck loop like a broad arrow head pointing upward. The student should learn to look at fabric in many different positions and in many different lights, for it takes thorough acquaintance to prepare one for understanding the puzzling combinations which are possible. ) Showing Plain and Tuck Courses in Diagram. — It is custom- ary to omit the plain courses from the diagrams, for several good reasons, such as to save time and space, and probably best of all to contract the diagram vertically by omission of the plain courses so that it is nearly proportional to the result in the fabric, which is reduced vertically by the narrowness of the courses with respect to the wales, and by the shortening and widening caused by the tucking. But in spite of these reasons it seems better, especially for the beginner, to show all courses in the diagram, because the true structural representation is more desirable than the exact appearance of the design; and because the method should not be restricted to a plain presser for every second feed, but should accommodate any combination of feeds, so that the knitter may not only be able to make novel designs but may be encouraged to do so. Accordingly, the diagrams used in this book show all courses, but it is to be understood that the design will appear in the fabric relatively shorter (vertically) than it is in the diagram. This distortion of the diagram may be obviated by using paper ruled with spaces about twice as wide as they are high. Design Should not Begin and End with the Same Kind of Course. — A consideration which really belongs to the question of the number of needles is of so much importance that it is mentioned here also. Since the feeds are generally used in 232 The Science of Knitting pairs, the height of the diagram must be an even number of courses; and since a tuck feed is followed by a plain feed, every diagram must begin with a tuck course and end with a plain course or vice versa. This arrangement of the feeds in pairs re- lieves the designer from remembering that the ending and be- ginning of the diagram must be with a different kind of presser in order to prevent the meeting of courses of the same kind Illustration 41. where the designs join. But it is advisable to bear this in mind when every other feed is not plain, or else double tucks may occur unintentionally at the joining of the designs. Illustration 41 shows the face of a small piece of flat under- wear fabric knit with a tuck figure design. The portion which came last from the needles is at the top. Since this is a small piece of fabric, it is impossible to trace the pattern along the courses far enough to copy all of it; and since the shape is not tubular, it is impossible to determine the number of feeds by raveling the threads to one wale and count- ing them. Analyzing Samples. — There are three ways in which this design may be duplicated. One way is to ravel as many courses as the design has courses, and to mark on cross-section paper Figure Designing with Pattern Wheels 233 each tuck stitch in the order in which it occurs. Another way, is to sketch out on cross-section paper a similar design of appar- ently the same width and height. The third, and probably most used method, is a combination of the two just mentioned, consisting of some raveling and counting assisted by judicious estimating. The advantages of the third method are that it saves time, saves fabric — since frequently only a small piece is available, and often the preservation of that is desirable — and further- more, it saves eye strain, since a stitch-by-stitch analysis is try- ing, especially if the fabric is fine. So this method will be used for illustration. At first it is desirable to disburden the mind of thought of the direction of motion, the number of feeds, and everything but the determin- ation of the dimensions of the design. The other details will introduce themselves in time for their consideration. Recalling that most designs are made by arranging the pkttern or the number of needles in the cylinder so that the ends of the pattern lap one division over or under, which makes the divisions read vertically in the same order in which they read horizontally in the pattern, we may assume that this design was made in that way. Then the boundary of the design will be four sided. The first step is to determine its width and height. Determining the Width of the Design. — Consider the width first. It is evident that one vertical stripe is the duplicate of the others. Therefore, the w^idth equals the number of wales from a point in one stripe to the corresponding point in the next stripe. The surest way to obtain this width is to ravel the rough top edge of the fabric — the bottom will not ravel — until it is sufficiently smooth and clear of lint to ravel freely all the way across. During this raveling it will be found that a plain feed followed a tuck feed in regular succession, conse- quently, the number of feeds must be even, that is 2, 4, 6, 8 etc. This information is needed for future reference. When the edge ravels freely, one course should be raveled slowly enough to count the wales from, say, the right side of one stripe to the right side of the next one. Provision should be made to guard against counting too far, since the tendency is to count from one tuck to the duplicate tuck inclusive, whereas if counting is started with one tuck it should extend to the dupli- cate tuck but should not include it. 234 The Science of Knitting Marking the Limiting Stitches. — When it is difficult to dis- tinguish the beginning and the ending of the count, the wales may be selected before the counting is begun, and marked down their centers with a pen. Indeed, one of the fundamental qualifications for design analysis is efficiency. It is not un- usual to see a sample of fabric raveled nearly away before the observer has learned anything definite about it. In order to avoid such mistakes, it is advisable to form the habit of making every move show for something. Starting and stopping places may be marked with a little ink in the loop of the selected stitches; or a pin may be put through each selected loop, and then the counting may be done between the pins on the sides where the heads are not, since the heads prevent counting close to the shank of the pin. During the raveling to ascertain the arrangement of the tucks, a starting wale should be selected, and marked with ink, and then the tucks should be recorded on cross-section paper in the order in which they occm*. An at- tempt to remember the tuck arrangement is almost sure to re- sult in confusion unless the observer is quite familiar with the work. The width of the sample in question is found, by counting, to be 30 wales. Determining the Height of the Design. — The height of the design is the number of courses from any point in a square to the corresponding point in the next square above or below. The starting and stopping points are sometimes not readily de- termined, since counting in the figured portion is confusing. To overcome this difficulty, it is sometimes permissible to cut from one side of the pattern a narrow strip of fabric, say five or six wales in width. Ravel this from a selected point in one square to the corresponding point in the next square below, counting the threads as they are raveled and keeping them to- gether for checking the count after the raveling is finished. The height of this design is found to be 24 courses. If the count had come out an odd number, it would obviously have been wrong, since it is known that an even number of feeds was used. Two limitations of the number of feeds are now known, namely, that the number is even and that the number must divide evenly into 24, since each feed must make its impression in the design as many times as there are divisions in the pattern. Figure Designing with Pattern Wheels 235 From this it is easy to make a table of the possible combinations of numbers of feeds and divisions of pattern, since the only fabric conditions are that the number of feeds be even and that the product of feeds and fabric divisions in the pattern be equal to 2 Table Feeds Divisions Courses in design 2 X 12 4X6 6X4 24 8X3 12 X 2 24 X 1 This table gives all the possible combinations of feeds, from which selection may be made according to convenience and to the facilities available, since any of these combinations will make the design. In other words, a design may generally be duplicated without duplication of the particular equipment with which it was produced. But it is frequently desirable to know how many feeds were actually used to produce the design in question. This is learned for one division lap by counting the difference in elevation in courses of two adjoining designs, as is seen by reference to Illustrations 36 and 39. Raveling from the top of one square to the top of the corre- sponding one in the next design shows a difference of 4 courses, consequently, four feeds were used to make the sample in ques- tion. Of course, if the pattern lap is more than one section, then the difference in the height of two adjoining designs would be a multiple of the number of feeds as in Illustrations 37 and 38, but that case is not the usual one so it is not considered here. The Structure and Dimensions of the Figures. — The next step is the determination of the dimensions and structure of the figures. The raveling so far has shown that only single tucks are used, both vertically and horizontally, and that these are Illustration 42. Diagram of the design shown in Illustration 41. 236 The Science of Knitting arranged diagonally with respect to each other. Moreover, close inspection, taken in consideration with the symmetrical arrangement of the figures and some stitch comiting, shows the design to be as in Illustration 42, Knitting Motion. — Since the direction of motion is not in- dicated by the sample, this also may be a matter of choice just as the number of feeds, if the inversion of the figure as in Illus- tration 26 compared with 24 is not objectionable. Table 1, on page 204, classifying machines by fabric motion facilitates adapting the motion to any particular type of machine. Sup- pose that the third type from the top of the table is selected, since this is a representative American type. Then, as the table shows, the fabric motion is right-hand. Consequently, the design illustrated in the sketch is to be produced in the fabric by motion toward the right. Table 2, on page 235, of feeds and corresponding pattern sec- tions shows a practical range of 4, 6 or 8 feeds, but inasmuch as the sample was apparently made with 4 feeds, the discussion may well be carried out with that number. Then according to the table, the number of divisions in the pattern must be six, which is also the number of divisions in the diagram. Direction of Lap. — The next consideration is whether the lap is to be over or under. Evidently, if the pattern overlaps, the number of cylinder needles is one division less than a whole number of patterns, and if the pattern underlaps, the number of cylinder needles is one division over a whole number of pat- terns. That is, if the lap is under, the remainder is over, and vice versa. If this is not perfectly clear, one can make it so by forming a closed circle of a paper pattern with end margins, and then underlapping or overlapping the ends of the pattern. The sample was evidently made with underlap, so the needle remainder was one division over an integral number of patterns. The following table gives the numbers of cylinder needles for producing this design with either overlap or underlap. The second number of the bracketed pair is for underlap and should be used for strict duplication of the design. Referring to the diagram of the design. Illustration 42, and remembering that the motion of knitting is right-hand, the observer sees that the lower right corner of the design will be knit first. The rule is: The divisions of the pattern arrange Figure Designing with Pattern Wheels 237 Table 3 (1) (2) (3) (4) Number of Number of pat- terns multiplied by the number of Number of divisions in Number of needles in patterns divisions in one pattern (1) X6 cylinder, (2)±1 cylinder, (3) X 30 1 30 1 » \ 5 7 150 210 2 n 1 11 13 330 390 3 >s { 17 19 510 570 4 - 1 23 25 690 750 5 30 { 29 31 , 870 930 6 36 { 35 37 1050 1110 themselves vertically with the front ( , , ) when the \ flown ward/ needles in the cylinder are one division ( ) a whole number \ over / of patterns. In order to avoid confusion this rule may be stated in terms of the lap for this case as follows: The divisions of the pattern arrange themselves vertically with the front ( ^P^'^^ ] \ downward/ Therefore, for underlap the divisions of the pattern will repeat themselves vertically with the first one at the bottom. Consequently the design may be numbered upward on the right side, 1, 2, 3, 4, 5, 6, as it is showTi, according to the six equal divisions of four feeds each, ar- ranged in pairs with one tuck presser followed by a plain presser. Inversion of Figures. — It is interesting to note in this con- nection that when the figures are symmetrical with respect to a horizontal axis, it generally matters little whether the lap is over or under. This design has figures which are symmetrical 1 under J 238 The Science of Knitting with respect to a horizontal axis, that is, these figures may be turned upside down without changing their appearance. Change in the direction of the lap inverts the design and changes the arrangement of the duplicate designs with respect to each other, as a comparison of Illustrations 36 and 39 shows; but this change in relation of the designs is much less noticeable than 6 5 4 3 2 I 6 X X X ^ X X X ><^ X X X X X X X X X X X X X X X X X X X X X ■" X — X k X X X X X X X X X r X X X X X X X X X X X ^ >^ X X X X X X X X X xj X X X X X X X X X r — — -^ p r— r— — _ p^ r— 1 X X r X X Illustration 43. Strip pattern copied from Illustration 42. the inversion of an unsymmetrical design, such as Illustration 24. Consequently, many designers use figures which may be inverted and pay no attention to the direction of the lap, since by neglecting it they double the available numbers of cylinder needles. These divisions may be copied from Illustration 42 from left to right in the reverse of their numerical order on a strip of paper as shown in Illustration 43. Figure Designing with Pattern Wheels 239 Proving the Pattern. — It is advisable to leave a margin at the top of the strip pattern, for this not only allows the num- bering of the divisions without confusion of the numbers with the tuck crosses, but it provides a margin for coiling the strip in order to prove the accuracy of the design and its transference to the strip. Table 3, page 237, shows that the design is obtain- able with 30 needles, so if this strip is coiled in a helix, so that the first needle of the pattern comes under the 31st needle, and so on to the end, the resulting tube will show the design just as it is in the diagram, provided the work has been properly done. It should be noted that this amounts to bringing division 2 over division 1, and that it is for underlap, w^hich results from a number of needles one division more than an integral number of patterns. On the contrary, if the design needs overlap, which results from a number of needles one division less than an integral number of patterns, then division 6 must be brought over division 1 in order to prove the pattern by coiling it. This necessitates a much longer strip in order to show the whole design in the re- sulting tube. , After the strip pattern is proved, the next question is how to transfer it to the presser so that the design will not be reversed or inverted. Forming the Presser from the Pattern. — Bring the ends of the strip together as in Illustration 44. This represents the edge of a printing wheel which will make the required design, for it is the right length, 180 needles, and it contains all of the required impressions in their proper order. But this wheel would have to run on the back of the fabric and print through to the face in order to make the design just as the sketch shows it. Some types of machine have the pressers placed so that this analogy holds. In this type the fabric runs downward, faces outward, revolves anti-clockwise and has the presser inside of the needle line. Consequently, for this type of machine Illustration 44 show^s just how the pattern is to be put on the pressers, of which there are two, the first for the lower line of tucks and the second for the upper line of tucks. The first is to make the lowest course in the design; moreover the relative position of the pressers with respect to the needles which they press is to be just as it is shown in the strip pattern. However, the most used types of machine are not like the type just described, for not the front but the back of the presser 240 The Science of Knitting Illustration 44. Model presser formed from the pattern in Illustration 43 for duplication of the design in Illustration 41 for right-hand motion of fabric and front side of presser acting. Illustration 45. The same pattern as that in Illustration 44, but adapted by reversal to type 7 machine, Table 1, page 205. Figure Designing with Pattern Wheels 241 operates to make the design. How can the pattern be adapted to them without the mistake of turning it end for end, or up- side down? Adapting the Pattern to Different Presser Positions. — Illus- tration 45 shows the strip pattern with its ends joined to form a circle, except that this time the strip is inside out. It is still right side up as it was at first. The pattern has been traced through on the back with the strip held against a window pane and the tuck crosses duplicated with a pencil on the back. The observer sees now by regarding the inside of the strip, that if this presser operates with the back side moving toward the right, the effect in the fabric will be just the same as before when the strip was right side out and the front side acted toward the right. Consequently, the pencil markings on the outside of the circular strip show how the pattern should be put on the presser when the back side operates on the needles. As it was explained, there are two pressers, the pattern for each is on its respective tuck line, and the lower one knits first. The circumference called for by the paper strip is 180 needles, but it may be 360, or any other multiple of 180, provided the pattern is duplicated all around the edge of the presser. Suppose that the number of needles in the available cylinder- is 957. This number is not suitable for a design 30 needles in width, since it is not in Table 3, page 237. Consequently, it is necessary to find what widths are possible with this number of cylinder needles, in order to modify the design to correspond to 957 needles and still to use four feeds. To begin with, the width of the design must divide into the cylinder needles, so it is necessary to find what numbers will divide 957. This is simply factoring, which may be set down as follows: 3957 111319 29 Evidently, 3, 11, 29, 33 (3 X 11) and 87 (3 X 29) are the low numbers which will divide 957, and the two numbers nearest to 30, the width of the sample, are 29 and 33. Try 29, since it is the nearer to 30 — so near that if it is usable, the design may be adapted to it by the omission of one wale from the field between the two squares. The way to try the number is to see if its pattern divisions are 242 The Science of Knitting suitable. Six would be preferable, since the height of the design should be left as it is, if the width is not to be changed more than one needle, which is practically no change so far as appearance is concerned. The width 29 is contained in 957 thirty-three times; that is, the number of cylinder divisions is 33. But the pattern itself must divide into the needles with a remainder of one division over or under, so to find the possible pattern lengths, factor 32 and 34 = (33 ± 1). 2 2 2 2 Evidently, 2, 4, 8, 16, 17 are available factors, and the nearest number of divisions for the pattern is 8, which multiplied by the number of feeds, 4, equals 32 instead of the 24 courses desired. The field could be made higher by eight courses, but the squares could not be enlarged proportionately, since the design has been narrowed by one needle. Consequently, this solution is not so satisfactory as it should be. Generally Advisable to Reduce the Extent of the Design. — However, the 33-needle design width is still available for in- vestigation, since the sample design might be widened so much without objection. This width divides into 957 twenty-nine times, so 29 is the number of cylinder divisions. The pattern must divide into one more or one less divisions, so factor 28 and 30 equal to (29 =b 1) to find the possible pattern divisions 32 2|34 16 17 8 4 2 2 28 2 30 2 14 3 15 7 5 Evidently, the number of pattern divisions may be 2, 3, 4, 5, 6, 7. This is a happy solution, for the height of the design may be left as it is by the use of 6 divisions in the pattern, or may be increased by four courses to correspond roughly to the increase in width due to the use of 33 needles instead of 30. As far as the appearance of the design is concerned it will probably be satis- factory to use the original number of divisions in the pattern, namely, 6. However, there are practical considerations which Figure Designing with Pattern Wheels 243 sometimes make it advisable to reduce the design whenever modification is necessary. One consideration is that it is fre- quently desirable to recut the original pressers, which may be done if the length of the pattern is reduced, for the old cuts may be turned off and the new ones may then be made on the same pressers. This is especially desirable where the mill is isolated from the knitting machine shop, or when it is inconvenient to wait to get the pressers recut to order. Adapting a Design to a Range of Cylinder Sizes. — So far the discussion has been carried on principally with one machine in view. But designs for underwear should be adaptable to the range of sizes used in underwear manufacture, including the sizes from which sleeves and drawers are cut, since all parts of the suit should match. This involves making one design adapt- able to different numbers of feeds as well as to different numbers of needles, since the numbers of feeds decrease, as well as the numbers of needles, with decrease in the diameter of the machine. However, the feeds do not change by rule, whereas the needles do. Knowledge of the particular machine in question is gen- erally required in order to plan for the numbers of feeds. But evidently the numbers of needles should change according to the difference in the diameters of the machines. Difference in Standards. — An inch difference in diameter corresponds to 3.14 inches difference in circumference. Ac- cordingly, if the machines are 10 cut, the difference between sizes is 31 or 32 needles. Moreover, since the diameters are generally even inches, the numbers of needles in the cylinders should be multiples of 31.4; that is, a one-inch cylinder should have 31 or 32 needles; a two-inch machine should have 62, 63 or 64 needles, etc. Consequently, for 10 cut, as a general rule, 31 or 32 might be adopted as a convenient design width. There are local qualifications to be looked for, such as difference be- tween the nominal diameter and the actual diameter. For in- stance, in America two types of spring-needle loop- wheel machines will be unchanged. (4) the weight per square yard. J Notice that the stitch is kept at the same number of needles per foot of yarn, since it is assumed that the cut is too coarse, so the cut is to be conformed to the stitch instead of vice versa. Then, as far as the fabric is Concerned, the only change neces- sary is to readjust the machine sizes to the width of the fabric. This is readily done. The main considerations are the adapta- bility of the cut to the same yarn. When the cut is made finer, the needles are generally decreased in size and, consequently, in strength; moreover, the clearance for the yarn in and between the needles is decreased, so there is the double objection that the yarn is more likely to load up and that the needles are more readily damaged. Consequently, the advisability of change in the cut resolves itself into retention of the gain due to increased production greater than the loss due to increased needle breakage and consequent stoppage. Evidently, the gain due to increased production increases much slower than the loss due to crowd- ing the cut, since this involves not only lost time but damaged needles and damaged fabric. Therefore, the cut should not be made finer, unless it is evident that the original cut is coarse for the yarn. Whether this is so may be determined by the rules Economics of Knitting 257 and tables given elsewhere, or preferably in the mill itself if several different cuts or different yarn numbers are used. Suppose the mill runs successfully under the same conditions; (a) 7 cut with 10 yarn, and (b) 10 cut with 16 yarn. Also suppose the question arises whether the 7-cut machine may advantageously be made finer. From the preceding it is evident that to make it finer without change in other conditions will increase the production, which is advantageous, but will the increased waste and needle breakage counterbalance it? Now the yarn is proportional to the square of the cut for similar conditions. Conversely, the cut is proportional to the square root of the yarn. cutg _ Vyarria ^^^6 Vyarn& , ^ VySbTUa CUta = CUtb ' vyarru, CUta = 10^^= Vl6 = iov/!2 V 16 16 = 10 VO.625 = 10 X 0.79 = 7.9, say 8. Therefore, the 7-cut machine may be changed to 8 cut with the result that the new production will be to the old as 8: 7 = f = 1.143, or 14.3 per cent gain, and with the expectancy of its running as well as the 10-cut machine. If the result had come out less than 7, it would have indi- cated that 7 cut was already too fine, in which case those ma- chines should be watched for waste, and if it were high, then a change to a coarser cut would be advisable, provided that the loss from reduced production would not be more than the gain from reduced waste. Yarn Number So far, only the factors of the equation above the line have been considered. It will be noticed that none of them affects the weight per square yard of the fabric. On the contrary, both 258 The Science of Knitting of the factors below the Hne do affect the fabric in this regard. Obviously, if the yarn is made heavier, i.e., if the number is re- duced, the production in pounds will be increased. The ques- tions which arise regarding such a change are similar to those regarding increase in the cut, except that weight, as well as size, readjustment must be considered. If increased weight per yard is not permissible, then the yarn cannot be changed without a corresponding change in the stitch. Suppose that the fabric may be heavier, there will still be doubt about the advisability of making it so, for if the goods are sold by the dozen and no advance in price is obtained for more weight, it would be foolish to give away some extra weight per dozen just to reduce the knitting cost per pound. But for the sake of argument it may be assumed that heavier weight goods may be marketed at sufficient advance to pay for the extra weight per square yard, as may be the case when the fabric is sold in the roll. Then, of course, whatever reduction may be made in the cost per pound of knitting is gain. So the disadvantages of decreasing the yarn number should be considered, and if they do not out- weigh the advantages, the change should be made. Since the yarn is proportional to the square of the cut, the yarn to be used may be determined just as the cut was de- termined. For simplicity, the same conditions are assumed as when the cut was considered, except that now the correct yarn number is desired instead of the correct cut. The mill is sup- posed to be running successfully under similar conditions: (a) 7 cut with 10 yarn, and (6) 10 cut with 16 yarn. The question is whether coarser yarn may be used on 7 cut and, if so, what number will correspond to 16 yarn on 10 cut. yaruq ^ cutg- yarub cutb^ * cut 2 yarua = yaruft X -^ CUtft^ 4Q = 1^^x10 = 7.84, say 8. Economics of Knitting 259 This will change the production as 1/8 : 1/10, or as Y = 1-25, i.e., 25 per cent gain. It will increase the weight per yard in the same proportion. The width of the fabric will be changed inversely as the square roots of the yarn numbers, i.e., as 1 1 VTo /- — The courses per inch will be increased to the same extent. Stitches The last means to increase the production is to lengthen the stitch, i.e., to decrease the stitches in one foot of yarn. This makes the fabric lighter, since the courses per inch decrease more rapidly than the stitches do. Suppose that the cut is 7 and that the stitches per foot of yarn are 28. A change to 25 stitches per foot changes the A ^- 1 1 28 production ^s^^ : 23 = 25 "" ' °^* ^^ P^^ ^^^* Sain. The width of the fabric is not changed. - The running of the machine is generally benefited, since a loose stitch favors good running. Of course, if the fabric is made unstable by loosening the stitch, then this means of in-~ creasing the production is not permissible. Conclusion It should be evident from the f oregomg that economical com- bmations of all of the conditions mentioned are not likely to happen. Indeed it is singular that the combinations which do happen are sufficiently economical to be profitable. But if profit can be made by unscientific methods, then careful in- vestigation ought to pay a good return. One of the first things to do is to calculate the theoretical pro- duction of each machine. The production tables and rules aheady given afford facihties for such calculations according to whatever conditions have to be met. In general, however, a convenient rule is: Production, in pounds per day of ten hours, equals d ia. in inches X r.p.m. X feeds X cylinder needles per inch (cut) 1.333 X cotton number of yarn X stitches per foot of yarn 260 The Science of Knitting Now for each machine everything in this equation is generally- constant except the yarn nifmber. Substitute in the equation everything except the yarn number, thereby getting a constant which divided by the yarn number at any time that it is con- venient gives the production of that machine without the trouble which the whole calculation would involve. For instance, sup- pose the mill contains among others a machine of the follow- ing details, dia. 18 inches; r.p.m., 52; feeds, 12; cut, 8; stitches per foot of yarn, 30. The first four numbers multiplied to- gether give 898,560, which divided by 30 X 1.333 (= 40) gives 2246.4, the number which divided by the cotton yarn number gives the production for ten hours continuous running. Con- sequently, if No. 10 yarn is used, the theoretical production is 224.6 lbs. The actual production may be compared with this to obtain the lost time. If the actual production is 180 lbs., 44 6 the hours lost were 10 X ^^ . ^ = 2 nearly. It is not right to charge all of this lost time to the operator, because the machine must stop for ends, as a preceding explanation shows. Just what this stoppage is, should be determined by actual count of the stops on one machine, especially if the production drops down. Suppose this twelve-feed machine stops for ends six times an hour. Assume that the operator averages one minute lost time in getting the machine in operation. Then the machine is stopped sixty minutes of the day, or 10 per cent. Since there are 12 ends, the stoppage chargeable to an end is 10 -^ 12 = 0.833 per cent. Therefore, a ten-feed machine will lose 8.33 per cent. Consequently, it would be unfair to expect a man operating machines with 10 feeds to obtain twice the production of one operating an equal number of 5-feed machines. To keep track of the production in this way is to do very much to keep it up; for if the operator knows that his lost time is checked, he will be careful to get to the machines quickly to restart them. If two machines are stopped at a time he will start first the one with the most feeds; and if the yarn comes bad, he will report it quickly rather than accept unjust blame. Moreover, observa- tions of this kind afford a reliable foundation for a merit system of remuneration which will be quickly satisfactory to all con- cerned, instead of one which will necessitate a probationary period of readjustment with consequent discouragement and dis- satisfaction. Economics of Knitting 261 Change of Yarn with Corresponding Change of Stitch One of the commonest considerations is that of the adapta- bihty of the yarn for the cut. This is discussed in the preceding pages for stitch constant, but not for change of stitch, which however is the most frequent combination in which it is met. For instance, a manufacturer buys at bargain price some sHghtly used machines which are one or two needles per inch coarser than he is using. After he has had them for a time he wonders if they are as much of a bargain as they had seemed as far as production in pounds is concerned. How is he to satisfy him- self? This can be done by analysis of the question or by mathe- matics. The analysis is as follows: Since the cut is coarse for the yarn, the question is the same as that in which the yarn is fine for the cut, so the latter should be considered, since it is simpler. Suppose that a certain cut with a certain yarn gives the highest knitting economy. Now suppose that finer yarn is used. What is the result as 'far as production is concerned? Since the yarn is finer, the production (without change of stitch) is changed in inverse proportion to the yarn number. That is, if the change is from No. 10 to No. 20, the production is changed to one-half of what it for- merly was, according to the explanation given elsewhere in the^ book. But fabric made under such conditions would be sleazy, and so probably unsalable. Consequently, the stitches per foot must be increased in order to make satisfactory fabric. Now it has already been shown that it is customary to increase the stitches per foot just as the diameter of the yarn is decreased. But if the stitches per- foot are increased, then the length of yarn fed in a given time is proportionately less, consequently, the production is still further decreased. Just how much the two changes affect the production is best shown mathematically. The production of a rib knitting machine for 7.5 hours is equal to dia. in inches X feeds X r.p.m. X cut number of yarn X cylinder stitches per foot of yarn * No quantity above the line is to be changed, but both quanti- ties below the line are to be increased, therefore, the relative production before and after the change is represented by the expression 1 No. X stitches 262 The Science of Knitting But the stitches are proportional to the VNo. as reference to the rules for regular fabrics shows. Consequently, the produc- tion is proportional to 1 No. X VNa " But this is a rather inconvenient form for the practical man. It is made more understandable and usable by a reduction to terms of the yarn diameter. The No. is proportional to — dia.2 and the VNo. is proportional to ^r~ . Therefore, the pro- duction is proportional to dia.^ Take the illustration already given of the change from No. 10 yarn to No. 20. Their respective diameters and cubes are shown in the following table. Number Diameter Diameter^ 10 20 15.06 10.65 342 121 (The decimal points have been moved to corresponding con- venient places in order to avoid confusion in pointing-off, which is permissible, since only relative values are desired, instead of absolute values.) It is evident that the production with No. 10 yarn is nearly three times that with No. 20 yarn. Of course, the supposed change of yarn is greater. than any which is apt to occur in practice, but the prmciple is true regardless of the extent of the change. Accordingly, it is advisable to consider before the use of yarn too fine for the cut, or what is the same thing, cut too coarse for the yarn, for such use very seriously reduces the production. This reduction, by increasing the pro- duction cost, increases the final cost, unless compensation is made by changes in other cost factors, such as increase in speed, reduc- tion in waste, etc. The above discussion makes clear many questions which are generally misunderstood. For illustration, the manufacture of fine flat balbriggan in America is conducted on two different principles: light yarn with a tight stitch, and heavy yarn with a loose stitch. The light-yarn-tight-stitch method gives such a Minimum Weight per Square Yard 263 comparatively small production that repeated efiforts have been made to account for it by the speed and feeds, but the disparity there is insufficient without the above-mentioned difference due to the yarn and the stitch. The rate of production of machines using jack sinkers, and, consequently, having a relatively low needle speed, has gener- ally been based on the speed and feeds without considering the important compensation which they have in the increase of pro- duction due to the use of heavy yarn, which use is made possible by the jack sinker. Finally, and generally, the fact that the production in pounds is proportional to the cube of the diameter of the yarn is useful for the selection of machines for special purposes. A machine having loop wheels with fixed blades is especially adapted to knit light yarn, whereas a jack-sinker machine is especially fitted to knit heavy yarn. It is as uneconomical to use a jack-sinker machine for very light yarn as it is to use a loop- wheel machine for very heavy yarn, since the former cannot give a reasonable production and the latter will give unreason- able trouble. MINIMUM WEIGHT PER SQUARE YARD, YARN-DIAM-- ETER CONSTANT. — DEMONSTRATION Illustration 1 shows four stitches of plain knit fabric with four wales per inch and one course per inch, as seen with a stitch glass having an opening one inch by one inch. The following is evident: There are eight threads crossing the opening. The average distance between the threads is one yarn diam- eter. (This is shown by the dotted circles of the same diameter as the yarn and midway between the ends of the loop.) Now, as the courses per inch decrease, these threads will approach the parallel position, becoming exactly parallel when the courses become zero; but their distance apart will not be changed, since by supposition the yarn diameter is constant. Then a square inch of fabric will be made up* of threads an inch long, and the number of these threads will be equal to half the diameters per inch. These relations are true no matter what units be taken, so the weight per square yard will be the weight of as many threads one yard long as half 264 The Science of Knitting the number of diameters per yard. This is for plain flat fabric. Plain ribbed fabric is the same on the back as it is on the face, so it will have twice as many threads. Therefore, the minimum weight of ribbed fabric with a given diameter of yarn is the weight of as inany yards of that yarn as there are diameters per yard. Or, 36 Minimum weight 1 t^t • i. r per square yird = Weight of one ^ of plain rib fabric J ^^^^ ^^ ^^^^ dia. of yarn, m mches Illustration 1. Very loose stitches, flat fabric. What is the minimum weight in pounds per square yard of plain rib fabric made of No. 23 yarn? 23X'840 ^mO = -^^^2' ^^'^^"- Brief Chronological List of Important Knitting Inventions 265 2 J . a' a a a a' •p-i '-H >-H c3 CI s ^ cS cj ^^ so u -:! ^ i S3 TJ 7^ ~ +J "xj 41 a> » a> 5 m i -a § . ^ ^ ^ s s a c3 c3 C3 o < 03 73 o O .« a o o go a c ~ a . a "2 ~ S S ^' « i )b • a - o V V c 3 ■ o o be tc to • 013 1 n a Pi :] , • c s • a a a a a ■ « d _o c > a 1 c 3 3 „ 3 T r, - - . ^' -u 1— 1 (, fc. t, ^ TO _. « « « a ^ 1 5P 1 3 a 3) "m : o .S £ . S • a -tf c3 I- o • o ° i; c3 <:; : H-i ;z; fiH Ah H si 4) 41 0) g S tH 'S '33 'S "S ^ I C 5 H 3 a 1 »r K ^ a ; ) g o 1 a > a a a -0 a a u -G c3 -a t- o -a a j5 "-5 cj ij a 2 ^ -fa 2 1 C r^ 4. a c •c ■* c a i : • ; : 'o 4) fc, to u O 41 o f c . c . 4 . a .■ e : S . c ra 4) 03 o a o O g o a a fix §> O > h3 ^ "-5 . ^H ffi^ . < eg Q o rt Q ,:^ ^5 f^ § s h 2; HH- cd u 'Eib CT! oc '^ t^ 05 »c C3 00 CO -H t^ t^ 05 CO to CO o c3 S2 IC CD cc > «D t— OO OO 05 O T»< -*■<*< -^ »o lO CO Q •i; t^ r^ t^ t^ t^ t^ t^ t^ OO 00 00 00 00 OO 00 00 g ^ , U 03 !§ a. 4) 'G a a n o s 73 .S 4) J3 a i;a ; S ^ : mS • .2 M ■ _2 a c c 6 ." 6 ■ a 6 a la 3 -a •at^ : ^•g : a> 03 a ■ : S S J ® -a J c mJJ a a 1— 1 s § : • 2-3 2 S J -s =5 ^ S a '-3 '3 • 6 c ^ ^ on S : .5 a a " • o D. 4) . ;; CO -lis 3 aj ^ a 4> 03 "^ a S " 4) '^ 4) -S M 5 " • J a -5 -^ • 3 c O 1 O a a o D fecrai2:uo>> o =3 ^ -a .fa .b; o o 3-S- fa ^^ 1^ a cS -fa c3 03 266 The Science of Knitting THEORY OF KNIT FABRICS The primary object of this book is to supply useful informa- tion for practical knitters. There were two courses open for the accomplishment of that end. One was to collect, edit and print tables and rules from whatever source available. The other course was to endeavor to find the fundamental laws of knitting, to derive comprehensive tables from them, and to put the laws in such simple form that the practical knitter would have available, reliable foundation knowledge of his occupation, which would not only increase his usefulness but would enable him to derive rules and "tables which would be generally useful, instead of being restricted to the practice of a single mill as is most of the present information. The latter course was se- lected, so the task involved not only the computation of original tables and the writing of what was supposed to be desirable explanatory matter, but the more difficult task of the discovery and the proof of the fundamental laws of a big industry in which so few were known that the industry was considered prac- tically lawless. Only the simplest of this research work is thus far included in the book since there is insufficient demand for the remainder to warrant its publication. This limited demand for theoretical matter is not the fault of the individual knitter, but of the industry as a whole. Even at the present time a good laiitting education is attained only by practical applica- tion so continuous that general education must be curtailed. One of the causes of this is the lack of technical knowledge of the very kind which this book is designed to supply; which lack, in turn, is due to the absence of exact experimental knowledge. Knitting, especially in America, is probably unique as an im- mense industry without technical literature, without experiment stations, without standards, and possibly not without schools, but certainly without scholars, for the schools have little to teach except that which can be obtained almost as well in prac- tice. They should have what cannot be obtained in practice, that is, the foundation principles. Engineering in all of its branches, astronomy, agriculture, medicine — practically all im- portant divisions of human endeavor — are pushed along by investigations, by schools, by colleges, by associations, and even by the government. But the knitting industry, instead of hav- ing all this assistance, seems to lack even the realization of needing it. Theory of Knit Fabrics 267 In view of the above-mentioned attitude of knitters regarding the sUght value of theory, it was concluded not to devote any space to it, but this seemed unfair to the few whose attitude is just the reverse, and more than that it seemed unwise, since it would leave ground for the supposition that the theory is not founded in fact, whereas it is really the expression of demon- strated facts. So it was decided to outline the theory. How- ever, the explanation is made as brief as possible, and in order to secure brevity no attempt is made to popularize the language for those who are not used to elementary experimental science. The laws are the result of measurements of some 200 samples of rib fabric made in the search for the laws out of single-mule- spun carded cotton yarn, which measurements were interpreted in the light of extensive experience with flat knit fabrics and memorandums of that experience. It is not supposed that all of the laws are final. Indeed those under Case 2 are only par- tially determined, owing to the lack of sufficient experimental data to warrant definite determination; and it is likely that further investigation will show minor variations in some of those already accepted as practically final. However, no law has been used which did not appear to be as reliable in practice as the average law used as a basis of calculation in every-day affairs. It would be highly desirable to give the percentage of error in these laws. So would it be desirable, and even more so, to give the constants for use with wool, worsted, two-thread work, etc., but this data cannot be derived readily within rea- sonable time from private experiments. A fair idea of the varia- tion to be expected may be obtained from the tabulation of the dimensions of regular fabrics. Let any one interested com- pare the dimensions given, with those of a few pieces of fabric which meet the conditions of yarn and stitch. The proportional variation of the actual dimensions from the theoretical, will be a good criterion for the variation. It should be remembered that take-up pull, hygroscopic con- ditions, error in the yarn number or diameter, or in the stitches, all enter into the final error. Indeed, one cause of the lack of scientific investigation has undoubtedly been aversion to un- dertake scientific work with such unsatisfactory measures as are available in knitting, where no dimension, either of weight, diameter or length, is readily obtainable with even fair accuracy. The following explanation of the terms used is made to avoid 268 The Science of Knitting cumbering the formulas with details which may just as well be understood once for all. Stitches are the number of cylinder needles per foot of yarn. Wales are the number of wales — or ribs — per inch on one side of the fabric. Coin-ses are the number of courses per inch. Weight is the weight in pounds of a square yard of fabric. Diameter is the sensible diameter of the yarn in inches — not the diameter obtained from the specific gravity. Number is the cotton number of the yarn. The theory is developed for normal plain rib fabrics, i.e., fabrics in which each and every loop in a course is tangent to the adjacent loops in the same course, but is not tangent to loops of adjoining courses; or in popular language, fabrics which are neither sleazy nor boardy and have properly formed loops. It is evident that the equations apply also to plain flat knit- ting, and probably to other kinds of knitting. The only differ- ence is in the constants. Case 1. — Stitches constant and yarn number variable. Chart 1. wales X courses = a constant (1) width = dia. X a constant (2) > from experiment. courses = dia. X a constant (3) All these are straight-line curves. No. 1 is parallel to the axis of diameters. The others pass through the origin, but do not extend to infinity, since the stitch tightens to the breaking point within finite limits. . /o\ 1 ^ constant ... (1) ^ (3) wales = ^^r^ (4) This curve is of hyperbolic form. For dia. = 0, wales = oo , and for dia. = oo , wales = 0, theoretically only, since this is re- stricted for large diameters just as are Nos. 2 and 3. The weight per square yard is obtained by combining these equations with the weight per square yard formula which is fully explained elsewhere in the book. No explanation is required here, except that this formula is not dependent on theory but on facts, hence it may properly be used for demonstration. This formula is . , _ wales X courses ^ "~ 1.944 number X stitches Theory of Knit Fabrics 269 Relations of Rib-fabric Dimensions for Stitches per Foot of Yarn Constant (30.8) and Size of Yarn Variable. " n 1 T3 o ^ >. ?^ O :^i y >» \ t< .21 rs \ a _« h) < .i: ■Hi u |.y si o 't^ O -y. s \ ii \ ^ !:i'° V s ors \ \ 5; is \ k "o,-^ V ^s f- \ \ -r \ o \ s ] 3 N. N V, n \ N, 1 / \ s s \ l<^ \ s / V N •s \ \ \ ^ ^ ^ \ < \ N \ / N \ 2s y n .^ N s, \ a ^ s. \ ^ "3 " ^ s s \ f^ 6 \ ^ \ \ ^ k ^^ s N, \ N \ N \ ^ S \ r N N^ \ s^ N \ \ s s \ \ N \ \ \ s S M » \^ \ s x, ^ s L L -Q . -0 _J -& __, >— -fl- ^ 1 ~-i ^ >— s ss ^d »& JO ffl -H ao I- o qonj u« JO sq^puBsnoqc^ ui 'uxbA p ja^auiBiQ Chart 1. Case 1. Select the yarn diameter on the left, follow its horizontal line to the right to the curve, and then follow the vertical line to the scale at the bottom. For instance, for yarn 0.010 inches in diameter: wales X courses = 34X 10 = 340.000 courses = 13.700 wales = 25.000 width of flattened tube from 88 needles = 1.760 weight per square yard = 24.2 -h 100 = 0.242 270 The Science of Knitting c V -1 -H -H - H ■H ■H -( -1 -1 -1 ~ ■* ^ \ ! ■* J ■t* \ f -** \ J / •V 5 Tt* V '■f d \ -^ r \ / \ « / »J \ r ^ \ / J3 / / •t* / W^ / \» ^ii d / "^ c5o / i \ / / r fei; d' / f ' \ ^i^ / J i / \ tf^^^ Z^ / d ^ / b \ / / \ /J ^ \ •^ / \ ^ ^ V ^ C ^ \ ^,m - -p^ X 0^ ^ \ 3" o^V^ ->- ^ \ bo-: ^ K.^ ^ ^ 1 V ^ ^ \ •»t^ -^ J?- 3 ' \ M \ CI \ ;i! \ v '"' \ y v \ \ s \ M V \ V _ _ _ _ A i|oui UBjo sq-^puBsnoii; ui 'uiTsA JO ja^auiBiQ Chart 2. Case 3. The diagonal is the curve of the weight per square yard multiplied by 100. Select the yarn diameter on the left, follow its horizontal line to the right to the curve, and then follow the vertical line to the scale at the bottom. For instance, for yarn .010 inches in diameter: wales = 25.00 courses = 31.30 stitches per foot = 46.70 weight per sq. yd. = 38 - - 100 0.38 Theory of Knit Fabrics 271 But from No. 1 for stitches constant, wales X courses = a constant. , Therefore, I weight X number = a constant (6) But from the definition of yarn number, number = g^T^^°^ Substituting this value for number in (6) weight = dia.2 X a constant. , (7) Therefore, the weight curve is a parabola with its vertex at zero diameter. Case 2. — Diameter constant and stitches variable. No chart, since such determinations as were made can be shown readily without. Wales = a constant except for slight increase with increase of stitches. Width = a constant except for slight decrease with increase of stitches. Courses are proportional to stitches, but not directly so. Weight is proportional to stitches, but not directly so. The forms of the course and weight curves were not definitely determined. The minimum weight = wt. of 1 yard of yarn 36 dla. ' ^^ ^® 6xplamed in the demonstration given elsewhere of " minimum weight per square yard." Case 3. — Loop proportional to diameter of yarn. Chart 2. This is the general case. Fabrics under it are called regular fabrics m this book, because the rules are worked out for it quite completely. For the principles see Elements of Knitting m this book, also an article in the " Textile Manufacturers Journal," March 9, 1912, entitled Science in Knitting. No special experimental work was done in this case, since the theory 5vas regarded as sufficiently substantiated without it. wales X dia. = a constant ^g) courses X dia. = a constant * m) stitches X dia. = a constant qq) These curves are all of hyperbolic form, so for dia. = all = ». Dia. =00, all = 0. ' 272 The Science of Knitting The weight formula weight X 1.944 X number X stitches = wales X courses, with the above values and dia. instead of number substituted, becomes weight X ^^''^^' . X ^^''^^- - J— V ^Q^«^- V ^Q^^t- "^^'^^^ ^ dia.2 ^ dia. - 1.944 ^ ^diaT ^ "dkT' from which, weight = dia- X a constant (11) Consequently, the weight curve is a straight line passing through and 00 . (8) X ( 9) wales X courses X dia.^ = a constant. . (12) (10) X (10) stitches^ X dia.^ = a constant. . (13) no\ . /io\ wales X courses ^^^^ ^ ^^^^ stitches^ = ^«^«*^^^- • • (14) THEORY OF KNIT FABRICS — GENERAL CONSIDERATIONS Although the theory itself is rather technical for knitters as a rule, still the general considerations are not, and they should be read in order to obtain a better understanding of the results worked out by the theory. In the practical application of the rules and formulas the in- vestigator should consider three important questions: (1) pos- sibility of a misunderstanding of a principle; (2) possible errors due to mistakes in interpreting the experiments; (3) differences of opinion where opinion has to be used. In regard to No. 1, it is believed that no principle has been mistaken. As to No. 2, further investigation may show, for instance, that for stitches constant, the weight per square yard is not exactly inversely proportional to the yarn number. But even if it does so show, the simplicity of this rule and its practical accuracy will un- doubtedly keep if in use. However, this should not stand in the way of a more accurate rule if one is obtainable. Regarding No. 3, differences of opinion are bound to occur, for there is no accounting for tastes. But they can be reduced by an explana- tion of the considerations on which the opinions are based. Con- sequently, the following explanations are made: (cut^ yarn = — -— for rib machines, and yam = gauge^ \ ^ , , , . . — ^ — I are not supposed to be restrictive any more than to say Theory of Knit Fabrics — General Considerations 273 a man walks three miles an hour is to mean that he can neither loiter nor run. Everybody knows to the contrary, but to en- able mutual understanding it is desirable to have an agreed average standard. The same holds true for the selection of wales to courses as 1 is to 1.25, and for the selection of the speed standards. Probably before long the limits of yarn, speed, and ratio of wales to courses will be determined, and tables will be calculated for short intervals between these, so that the fabric dimensions and related values can be found for practically all conditions. But it would be a waste of time to base such elab- orate calculations on such disproportionately scant observations. It is likely that the stitches per foot used will be found to make rather tight fabric for good running conditions on some machmes. This is to be expected, since the theory is developed from consideration of the fabric rather than of the machine. Consequently, if some machine of some particular cut is un- symmetrically designed — and all machines made in a series of cuts are so, since it is impractical to make them otherwise — the formulas should not be considered erroneous for not conforming to that particular machine. Indeed, one of the big advantages of the principles of knitting is the impetus which will be given to systematic knitting machine design. For instance, the design of loop-wheel knitting machinery has been lamentably faulty" on the finer gauges, owing partially to the fact that there was not enough call for such gauges to warrant the manufacturer in going to more trouble than to put more needles in the cylinder and more blades in the burs. Consequently, the burs were inordinately big and the needles ridiculously long for the work which they had to do. Such machines will not knit according to the rule on fine gauges, which is not the fault of the rule, but of the machine, for generally what a machine does on one gauge, it should do on another. This deficiency of machines on the extreme gauges (coarse and fine) is generally true of all types. In some cases it is ap- parently unavoidable, but in many cases it could be partially remedied, at least, by designing the machine in conformity with the work which it has to do. One of the most important requisites for the practical appli- cation of the principles is the accurate determination of the yarn diameter. Evidently much work must be done in this line on every different kind of material with different twists and 274 The Science of Knitting different methods of spinning, etc. The diameter here used, namely -===. seems to be somewhat greater than it should 21 V No. be, as the fabric width given by it for flat-work circular machines indicates, namely 1.26, which is considerably higher than the 1.1 generally allowed. However, it has been considered best to give the formulas just as they work out, and not to shade them in the least, so that the user may learn just how much depend- ence he may put in them, and may make his own shading once for all. Even when excessive shading is required, the formulas are useful as a proportional guide, which is better than no guide at all. The Strength of Knit Fabrics Two factors are considered in the strength question; namely, the number of threads which sustain the stress, and the strength per thread. The number of threads crosswise of the fabric is evidently the number of courses per inch, and the number of threads length- wise of the fabric is the number of wales per inch multiplied by two or by four according to whether the fabric is flat or ribbed. The strength per thread is based on the Draper Tables of Breaking Weight of American Yarn. The values used are the New Breaking Weight of Soft Twist Yarn, according to which the tensile strength per square inch of sensible cross-sectional area of No^O is 7671 pounds, based on the diameter equal to 1 -j- 21 VNo., from which it follows that the tensile strength of the yarn is very nearly 6000 X (diameter)2, which value has been used in calculating the formulas, since the strength of yarn is approximately proportional to the square of the diameter, with variation of a greater decrease in strength than in diameter. The use of 6000 X'(diameter)2 for the strength of the yarn makes No. 4 weaker by 13 per cent than the actual tests show, and makes No. 30 stronger by 8 per cent; but these variations are probably no more than would be found in different sections of any one yarn. The following pages are copied by permission from Kent's "Mechanical Engineers' Pocket Book." Knots 275 Varieties of Knots. — A great number of knots have been devised of which a few only are illustrated, but those selected are the most frequently used. In the cut, Fig. 84, they are shown open, or before being drawn taut, in order to show the position of the parts. The names usually given to them are: ^ Bight of a rope. Simple or Overhand knot. Figure 8 knot. Double knot. Boat knot. Bowline, hrst step. Bowline, second step. Bowline completed. Square or reef knot. Sheet bend or weaver's knot. Sheet bend with a toggle. Carrick bend. Stevedore knot completed. Stevedore knot commenced. Slip knot. P- Flemish loop. Q. Chain knot with toggle. R. Half-hitch. S. Timber-hitch. T. Clove-hitch. U. Rolling-hitch. V. Timber-hitch and half-hitch. W. Blackwall-hitch. X. Fisherman's bend. Y. Round turn and half-hitch Z. AVall knot commenced. A A. Wall knot completed. BB, Wall knot crown commenced. CC. Wall knot crown completed. 276 The Science of Knitting RATIO AND PROPORTION. ♦h?t5*? ^^ *^K relation of one number to another, as obtained bv divirlinp the first number by the second. Synonymous with quotient '^'''''^'''^ Ratio of 2 to* 4, or 2 : 4 = 2/4= 1/2. Ratio of 4 to 2, or 4 : 2 = 2. of ?'tn^fi '"l/**'*-?^^ ^^^ equality of two ratios. Ratio of 2 to 4 equals ratio ^^^^^ 9' 2/4=3/6; expressed thus, 2 : 4 :: 3 : 6- read 2 is tn 4 ac % ioT,. « The first and fourth terms are called tfeextremes or oSter terms th.' second and third the means or inner terms terms, the The product of the means equals the product of the extremes: 2 : 4 : : 3 : 6; 2 X 6 = 12; 3 X 4 = 12. Hence, given the first three terms to find the fourth multinlv th« second and third terms together and divide by the first "^"^^^P^^ the 2 : 4 : : 3 : what number? Ans, ^^ ^ == 6. Algebraic expression of proportion. —a:b::c:d; ~ =-;ad 'mbc from which a = ^ : c/= - • 6= ^^ r = i^ . d a ' c ' b From the above equations may also be derived the following: b:a::d:c a + b : a : :c + d : c a + b : a - b : : c + d ; c ^ d a :c::b Id a + b : b : :c + d : d a^ -. bn • • c^ - d^ a-.b^cid a-b:b::c-d:d ^ : ^ : : '?/c ^/5 a - b : a::c - d :c Mean proportional between two given numberq let nnH o^ ,•„ v. 9 anH s T-rTfir!^ Vv, ^' - = 4 :: 4 : 8 ; 4 IS a mean proportional betwppn Mean proportional of 2 and 8 = \/2X 8 = 4. wh^eift^hreft"rmslr?^iJp,^ ""'' ^u?'""^ *^^ ^°"'*,^ ^^'^ ^^ ^ Proportion iV. f i ''"f^e terms are given. — Rule, as above, when the terms arp<5tntpH firi^®'^T^^'"''5?^°'"?5' ."multiply the second by the third and Svide hv the first. The difficulty is to state the terms in their proneroTdPr Thp term which is of the same kind as the required or fourth tSm is ma'dpTh^ given terms should be made the second teVm- otherwise rtl to Thm &Tropo"?ronns'??e°n"^Stlr " ""^' "' reduced! ^i'VloTuSo^feS! 54 : 270 ::3:x (the required number) ; x = §2<^Z2 ==15 j^en 54 . £4; -¥fc-^ trjbPt'Stfo.jf zusiVXiitTs ?^rire Ratio and Proportion Decimal Equivalents of Fractions of One Inch. 277 1-64 .015625 17-64 .265625 33-64 .515625 49-64 .765625 1-32 .03125 9-32 .28125 17-32 .53125 25-32 .78125 3-64 .046875 19-64 .296875 35-64 .546875 51-64 .796875 1-16 .0625 5-16 .3125 9-16 .5625 13-16 .8125 5-64 .078125 21-64 .328125 37-64 .578125 53-64 .828125 3-32 .09375 11-32 .34375 19-32 .59375 27-32 .84375 7-64 .109375 23-64 .359375 39-64 .609375 55-64 .859375 1-8 .125 3-8 .375 5-8 .625 7-8 .875 9-64 .140625 25-64 .390625 41-64 .640625 57-64 .890625 5-32 .15625 13-32 .40625 21-32 .65625 29-32 .90625 n-64 .171875 27-64 .421875 43-64 .671875 59-64 .921875 3-16 .1875 7-16 .4375 11-16 .6875 15-16 .9375 13-64 .203125 29-64 .453125 45-64 .703125 61-64 .953125 7-32 .21875 15-32 .46875 23-32 .71875 31-32 .96875 15-64 .234375 31-64 .484375 47-64 .734375 63-64 .984375 1-4 .25 1-3 .50 3-4 .75 1 1. Long Measure. — Measures of Length. 12 inches = 1 foot. 3 feet = 1 yard. ) 1760 yards, or 5280 feet = 1 mile. Additional measures of length in occasional use: 1000 mils = 1 inch; 4 inches = 1 hand; 9 inches = 1 span; 21/2 feet = 1 military pace; 2 yards = I fathom; 51/2 yards, or 16 1/2 feet = 1 rod (formerly also called pole or perch). Measures of Weight. — Avoirdupois, or Commercial Weight. 16 drachms, or 437.5 grains = 16 ounces, or 7000 grains = 28 pounds = 4 quarters = 20 hundred weight = 2000 p6unds = 2204.6 pounds = 1 stone = 14 pounds; 1 ounce, oz. 1 pound, lb. 1 quarter, qr. 1 hundredweight, cwt. = 112 lbs. 1 ton of 2240 lbs., gross or long ton. 1 net, or short ton. 1 metric ton. 1 quintal = 100 pounds. The drachm, quarter, hundredweight, stone, and quintal are now seldom used in the United States. Measures of Work, Power, and Duty. Work. — The sustained exertion of pressure through space. Unit of work. — One foot-pound, i.e., a pressure of one pound exerted through a space of one foot. Horse-power. --- The rate of work. Unit of horse-power = 33,000 ft.-lbs. per minute, or 550 ft.-lbs. per second = 1,980,000 ft.-lbs. per hour. Heat unit = heat required to raise 1 lb. of water 1° F. (from 39° to 40°). Horse-power expressed in heat units = ^-??S^ = 42.416 heat units per minute = 0.707 heat unit per second = 2545 heat units per hour. 1 lb. of fuel per H. P. per hour = { ^;|tg'gSt"uA^i" ^"' « * °^ ^"^^• 1,000,000 ft.-lbs. per lb. of fuel == 1.98 lbs. of fuel per H. P. per hour. Velocity.— Feet per second = ^|^ = T?X miles per hour. 3600 15 Gross tons per mile = ^~ = j-| lbs. per yard (single rail.) 278 The Science of Knitting SQUARES, CUBES, SQUARE BOOTS AND CUBE BOOTS No. Square. Cube. Sq. Root. Cube Root. No. 3.1 Square. Cube. Sq. Root. Cube Root. 0.1 .01 .001 .3162 .4642 9.61 29.791 1.761 1.458 .15 .0225 .0034 .3873 .5313 .2 10.24 32.768 1.789 1.474 .2 .04 .008 .4472 .5848 .3 10.89 35.937 1.817 1.489 .25 .0625 .0156 .500 .6300 .4 11.56 39.304 1.844 1.504 .3 .09 .027 .5477 .6694 .5 12.25 42.875 1.871 1.518 .35 .1225 .0429 .5916 .7047 .6 12.96 46.656 1.897 1.533 .4 16 .064 .6325 .7368 .7 13.69 50.653 1.924 1.547 .45 .2025 .0911 .6708 .7663 .8 14.44 54.872 1.949 1.560 .5 .25 .125 .7071 .7937 .9 15.21 59.319 1.975 1.574 .55 .3025 .1664 .7416 .8193 4. 16. 64. 2. 1.587^ .6 .36 .216 .7746 .8434 .1 16.81 68.921 2.025 1.601 .65 .4225 .2746 .8062 .8662 .2 17.64 74.088 2.049 1.613 .7 .49 .343 .8367 .8879 .3 18.49 79.507 2.074 1.626 .75 .5625 .4219 .8660 .9086 .4 19.36 85.184 2.098 1.639 .8 .64 .512 .8944 .9283 .5 20.25 91.125 2.121 1.651 .85 .7225 .6141 .9219 .9473 .6 21.16 97.336 2.145 1.663 .9 .81 .729 .9487 .9655 .7 22.09 103.823 2.168 1.075 .95 .9025 .8574 .9747 .9830 .8 23.04 110.592 2.191 1.687 1. 1. 1. 1. 1. .9 24.01 117.649 2.214 1.698 1.05 1.1025 1.158 1.025 1.016 5. 25. 125. 2.2361 1.710( 1.1 1.21 1.331 1.049 1.032 .1 26.01 132.651 2.258 1.721 1.15 1.3225 1.521 1.072 1.048 .2 27.04 140.608 2.280 1.732 1.2 1.44 1.728 1.095 1.063 .3 28.09 148.877 2.302 1.744 1.25 1.5625 1.953 1.118 1.077 .4 29.16 157.464 2.324 1.754 1.3 1.69 2.197 1.140 1.091 .5 30.25 166.375 2.345 1.765 1.35 1 .8225 2.460 1.162 1.105 .6 31.36 175.616 2.366 1.776 1.4 1.96 2.744 1.183 1.119 .7 32.49 185.193 2.387 1.786 1.45 2.1025 3.049 1.204 1.132 .8 33.64 195.112 2.408 1.797 1.5 2.25 3.375 1 .2247 1.1447 .9 34.81 205.379 2.429 1.807 1.55 2.4025 3.724 1.245 1.157 6. 36. 216. 2.4495 1.8171 1.6 2.56 4.096 1.265 1.170 .1 37.21 226.981 2.470 1.827 1.65 2.7225 4.492 1.285 1.182 .2 38.44 238.328 2.490 1.837 1.7 2.89 4.913 1.304 1.193 .3 39.69 250.047 2.510 1.847 1.75 3.0625 5.359 1.323 1.205 .4 40.96 262.144 2.530 1.857 1.8 3.24 5.832 1.342 1.216 .5 42.25 274.625 2.550 1.866 1.85 3.4225 6.332 1.360 1.228 .6 43.56 287.496 2.569 1.876 1.9 3.61 6.859 1.378 1.239 .7 44.89 300.763 2.588 1.885 1.95 3.8025 7.415 1.396 1.249 .8 46.24 314.432 2.608 1.895 2. 4. 8. 1.4142 1.2599 .9 47.61 328.509 2.627 1.904 .1 4.41 9.261 1.449 1.281 7. 49. 343. 2.6458 1.9125 .2 4.84 10.648 1.483 1.301 .1 50.41 357.911 2.665 1.922 .3 5.29 12.167 1.517 1.320 .2 51.84 373.248 2.683 1.931 .4 5.76 13.824 1.549 1.339 .3 53.29 389.017 2.702 1.940 .5 6.25 15.625 1.581 1.357 .4 54.76 405.224 2.720 1.949 .6 6.76 17.576 1.612 1.375 .5 56.25 421.875 2.739 1.957 .7 7.29 19.683 1.643 1.392 .6 57.76 438.976 2.757 1.966 .8 7.84 21.952 1.673 1.409 .7 59.29 456.533 2.775 1.975 .9 8.41 24.389 1.703 1.426 .8 60.84 474.552 2.793 1.983 3. 9. 27. 1.7321 1 .4422 .9 62.41 493.039 2.811 1.992 Squares, Cubes, Square and Cube Roots 279 No. Square Cube. Sq. Root. Cube 1 Hoot. No. Square Cube. Sq. Root. Cube Root. 8. 64. 512. 2.82841 2. 45 2025 91125 6.7082 3.5569 .1 65.61 531.441 2.846 2.008 46 2116 97336 6.7823 3.5830 .2 67.24 55I.36g 2.864 2.017 47 2209 103823 6.8557 3.6088 .3 68.89 571.787 2.881 2.025 48 2304 110592 6.9282 3.6342 .4 70.56 592.704 2.898 2.033 49 2401 1 1 7649 7. 3.6593 .5 72.25 6(4.125 2.915 2.041 50 2500 125000 7.0711 3.6840 .6 73.96 636.056 2.933 2.049 51 2601 132651 7.1414 3.7084 .7 75.69 658.503 2.950 2.057 52 2704 1 40608 7.2111 3.7325 .8 77.44 681.472 2.966 2.065 53 2809 148877 7.2801 3.7563 .9 79.21 704.969 2.983 2.072 54 2916 1 57464 7.3485 3.7798 9. 81. 729. 3. 2.0801 55 3025 166375 7.4162 3.8030 .1 82.81 753.571 3.017 2.088 56 3136 175616 7.4833 3.8259 .2 84.64 778.688 3.033 2.095 57 3249 185193 7.5498 3.8485 .3 86.49 804.357 3.050 2.103 58 3364 195112 7.6158 3.8709 .4 88.36 830.584 3.066 2.110 59 3481 205379 7.6811 3.8930 .5 90.25 857.375 3.082 2.118 60 3600 216000 7.7460 3.9149 .6 92.16 884.736 3.098 2.125 61 3721 22698 1 7.8102 3.9365 .7 94.09 912.673 3.114 2.133 62 3844 238328 7.8740 3.9579 .8 96.04 941.192 3.130 2.140 63 3969 250047 7.9373 3.9791 .9 98.01 970.299 3.146 2.147 64 4096 262 1 44 8. 4. 10 100 1000 3.1623 2.1544 65 4225 274625 8.0623 4.0207 11 121 1331 3.3166 2.2240 66 4356 287496 8.1240 4.0412 12 144 1728 3.4641 2.2894 67 4489 300763 8.1854 4.0615 13 169 2197 3.6056 2.3513 68 4624 314432 8.2462 4.0817 14 196 2744 3.7417 2.4101 69 4761 328509 8.3066 4.1016 15 225 3375 3.8730 2.4662 70 4900 343000 8.3666 4.1213 16 256 4096 4. 2.5198 71 5041 357911 8.4261 4.1408 17 289 4913 4.1231 2.5713 72 5184 373248 8.4853 4.1602 18 324 5832 4.2426 2.6207 73 5329 389017 8.5440 4. 1 793 19 361 6859 4.3589 2.6684 74 5476 405224 8.6023 4.1983 20 400 8000 4.4721 2.7144 75 5625 421875 8.6603 4.2172 21 441 9261 4.5826 2.7589 76 5776 438976 8.7178 4.2358 22 484 , 10648 4.6904 2.8020 77 5929 456533 8.7750 4.2543 23 529 12167 4.7958 2.8439 78 6084 474552 8.8318 4.2727 24 576 13824 4.8990 2.8845 79 6241 493039 8.8882 4.2908 25 625 15625 5. 2.9240 80 6400 512000 8.9443 4.3089 26 676 17576 5.0990 2.9625 81 6561 531441 9. 4.3267 27 729 19683 5.1962 3. 82 6724 551368 9.0554 4.3445 28 784 21952 5.2915 3.0366 83 6889 571787 9.1104 4.3621 29 841 24389 5.3852 3.0723 84 7056 592704 9.1652 4.3795 30 900 27000 5.4772 3.1072 85 7225 614125 9.2195 4.3968 31 961 29791 5.5678 3.1414 86 7396 636056 9.2736 4.4140 32 1024 32768 5.6569 3.1748 87 7569 658503 9.3276 4.4310 33 1089 35937 5.7446 3.2075 88 7744 681472 9.3808 4.448U 34 1156 39304 5.8310 3.2396 89 7921 704969 9.4340 4.4647 35 1225 42875 5.9161 3.2711 90 8100 729000 9.4868 4.4814 36 1296 46656 6. 3.3019 91 8281 753571 9.5394 4.4979 37 1369 50653 6.0828 3.3322 92 8464 778688 9.5917 4.5144 38 1444 54872 6.1644 3.3620 93 8649 804357 9.6437 4.5307 39 1521 59319 6.2450 3.3912 94 8836 830584 9.6954 4.5468 40 1600 64000 6.3246 3.4200 95 9025 857375 9.7468 4.5629 41 1681 68921 6 4031 3.4482 96 9216 884736 9.7980 4.5789 42 1764 74088 6.4807 3.4760 97 9409 912673 9.8489 4.5947 43 1849 79507 6.5574 3.5034 98 9604 941192 9.8995 4.6104 44 1936 85184 6.6332 3.5303 99 9801 970299 9.9499 4.6261 280 The Science of Knitting CIRCUMFERENCES AND AREAS OF CIRCLES. Diara. Circum. . 04909 .09818 .14726 .19635 . 29452 .39270 . 49087 . 58905 . 68722 . 78540 .88357 .98175 1.0799 1.1781 1.2763 1.3744 1.4726 1.5708 1.6690 1.7671 1.8653 1 . 9635 2.0617 2.1598 2.2580 2.3562 2.4544 2.5525 2.6507 2.7489 2.8471 2.9452 3.0434 3.1416 3.3379 3.5343 3.7306 3.9270 4.1233 4.3197 4.5160 4.7124 4.9087 1051 3014 4978 6941 8905 Area. 6.0868 6.2832 6.4795 6.6759 6.8722 7.0686 7.2649 .00019 .00077 .00173 .00307 . 00690 .01227 .01917 .02761 .03758 Diam, .04909 .06213 .07670 .09281 .11045 .12962 .15033 .17257 .19635 . 22 1 66 .24850 .27688 . 30680 .33824 .37122 .40574 .44179 .47937 .51849 .55914 .60132 . 64504 . 69029 .73708 .7854 .8866 .9940 .1075 .2272 .3530 .4849 .6230 .7671 .9175 .0739 .2365 4053 5802 7612 9483 1416 3410 5466 7583 9761 2000 33/8 7/16 1/2 9/16 5/8 11/16 3/4 13/16 7/8 15/16 Circum. 3. 1/16 1/8 3/16 1/4 5/16 3/8 7/16 1/2 9/16 5/8 11/16 3/4 13/16 7/8 15/16 4. 1/16 1/8 3/16 1/4 5/16 3/8 7/16 1/2 9/16 5/8 11/16 3/4 13/16 7/8 15/16 5. 1/16 1/8 3/16 1/4 5/16 3/8 7/16 1/2 9/16 ■5/8 11/16 3/4 13/16 7/8 15/16 6. 7.4613 7.6576 7.8540 8.0503 8.2467 8.4430 8.6394 8.8357 9.0321 9.2284 9.4248 9.6211 9.8175 10.014 10.210 10.407 10.603 10.799 10.996 11.192 1 1 . 388 11.585 11.781 11.977 12.174 12.370 12.566 12.763 12.959 13.155 13.352 13.548 13.744 13.941 14.137 14.334 14.530 14.726 14.923 15.119 15.315 15.512 15.708 15.904 16.101 16.297 16.493 16.690 16.886 1 7 . 082 17.279 17.475 17.671 17.868 18.064 18.261 18.457 18.653 18.850 Area. 4.4301 4.6664 4.9087 5.1572 5.4119 5.6727 5.9396 6.2126 6.4918 6,7771 7.0686 7.3662 7 . 6699 7.9798 8.2958 8.6179 8.9462 9.2806 9.6211 9.9678 10.321 10.680 1 1 . 045 11.416 1 1 . 793 12.177 12.566 12.962 13.364 13.772 14. 186 14.607 15.033 1 5 . 466 15.904 16.349 16.800 17.257 17.721 18. 190 18.665 19. 147 19.635 20.129 20.629 21.135 21.648 22.166 22.691 23.221 23.758 24.301 24.850 25 . 406 25 . 967 26.535 27.109 27 . 688 28.274 Diam, 61/8 1/4 3/8 1/2 5/8 3/4 7/8 7. 1/8 V^ 3/8 1/2 5/8 3/4 7/8 8. 1/8 1/4 3/8 1/2 5/8 3/4 7/8 9. 1/8 1/4 3/8 1/2 5/8 3/4 7/8 10. 1/8 1/4 3/8 1/2 5/8 3/4 7/8 11. 1/8 1/4 3/8 1/2 5/8 3/4 7/8 13. 1/8 1/4 3/8 1/2 5/8 3/4 7/8 13. 1/8 1/4 3/8 1/2 Circum. 19.242 19.635 20.028 20. 420 20.813 21.206 21.598 21.991 22.384 22.776 23.169 23 . 562 23.955 24.347 24.740 25. 133 25.525 25.918 26.311 26.704 27.096 27.489 27.882 28.274 28 . 667 29.060 29.452 29.845 30.238 30.631 31.023 31.416 3 1 . 809 32.201 32.594 32.987 33.379 33.772 34.165 34.558 34.950 35.343 35.736 36.128 36.521 36.914 37.306 37 . 699 38.092 38.485 38.877 39.270 39.663 40.055 40.448 40.841 41.233 41.626 42.019 42.412 Area. Circumferences and Areas of Cii'cles 281 Diam. Circura. Area. Diam.j Circum. Area. Diam.l Circum. Area. 42.804 43. 197 43.590 43 . 982 44.375 44.768 45.160 45.553 45.946 46.338 46.731 47.124 47.517 47.909 48.302 48.695 49.087 49.480 49.873 50.265 50.658 51.051 51.444 51.836 52.229 52.622 53.014 53.407 53.800 54. 192 54.585 54.978 55.371 55.763 56.156 56.549 56.941 57.334 57.727 58.119 '58.512 58.905 59.298 59.690 60.083 60.476 60.868 61.261 61.654 62 . 046 62.439 62.832 63.225 63.617 64.010 64.403 64.795 65.188 65.581 65.973 66.366 66.759 6/ . 1 52 67.544 67.937 68.330 145.80 1 48 . 49 151.20 153.94 156.70 159.48 562.30 165.13 167.99 170.87 173.78 176.7! 179.67 182.65 185.66 188.69 191.75 194.83 197.93 201.06 204.22 207.39 210.60 213.82 217.08 220.35 223.65 226.98 230.33 233.71 237.10 240.53 243.98 247.45 250.95 254.47 258.02 261.59 265. 18 268.80 272.45 276.12 279.81 283.53 287.27 291.04 294.83 298.65 302.49 306.35 310.24 314.16 318.10 322.06 326.05 330.06 334.10 338.16 342.25 346.36 350.50 354.66 358.84 363.05 367.28 371.54 317/8 22, 1/8 1/4 3/8 1/2 5/8 3/4 7/8 33. 1/8 1/4 3/8 1/2 5/8 3/4 7/8 34. 1/8 1/4 3/8 1/2 5/8 3/4 7/8 35. 1/8 1/4 3/8 1/2 5/8 3/4 7/8 36. 1/8 1/4 3/8 1/2 5/8 3/4 7/8 37. 1/8 1/4 3/8 1/2 5/8 3/4 7/8 38. 1/8 1/4 3/8 1/2 5/8 3/4 7/8 39. 1/8 1/4 3/8 1/2 5/8 3/4 7/'8 ! 30. I 68.722 69.115 69.508 69.900 70.293 70.686 71.079 71.471 71.864 72.257 72.649 73 . 042 73.435 73.827 74.220 74.613 75.006 75.398 75.791 76. 184 76.576 76.969 77.362 77.754 78. 147 78.540 78.933 79.325 79.718 80. Ill 80.503 80.896 81.289 81.681 82.074 82.467 82.860 83.252 83.645 84.038 84.430 84.823 85.216 85.608 86.001 86.394 86.786 87.179 87.572 87.965 88.357 88.750 89.143 89.535 89.928 90.321 90.713 91.106 91.499 9 1 . 892 92 . 284 92.677 93.070 93.462 93.855 94.248 375.83 380. 13 384.46 388.82 393.20 397.61 402.04 406.49 410.97 415.48 420.00 424.56 429. 13 433.74 438.36 443.01 447.69 452.39 457.11 461.86 466.64 471.44 476.26 481.11 485.98 490.87 495.79 500.74 505.71 510.71 515.72 520.77 525.84 530.93 536.05 541. 19 546.35 551.55 556.76 562.00 567.27 572.56 577.87 583.21 588.57 593.96 599.37 604.81 610.27 615.75 621.26 626.80 632.36 637.94 643.55 649. 18 654.84 660.52 666.23 671.96 677.71 683 . 49 689.30 695.13 700.98 706 . 86 301/8 1/4 3/8 V2 5/8 3/4 7/8 31. 1/8 1/4 3/8 1/2 5/8 3/4 7/8 33. 1/8 1/4 3/8 1/2 5/8 3/4 7/8 33. 1/8 1/4 3/8 1/2 5/8 3/4 7/8 34. 1/8 1/4 3/8 1/2 5/8 3/4 7/8 35. 1/8 1/4 3/8 1/2 5/8 3/4 7/'8 36. 1/8 1/4 3/8 1/2 3/4 7/8 37. 1/8 1/4 3/8 1/2 5/8 3/4 7/8 38. 1/8 1/4 I 94.640 95.033 95.426 95.819 96.211 96.604 96.997 97.389 97.782 98.175 98.567 98.960 99.353 99.746 100. 138 100.531 100.924 101.316 101.709 102. 102 102.494 102.887 103.280 103.673 104.065 104.458 104.851 105.243 105.636 106.029 106.421 106.814 107.207 107.600 107.992 108.385 108.778 109. 170 109.563 109.956 110.348 110.741 111.134 111.527 111.919 112.312 112.705 113.097 1 1 3 . 490 113.883 114.275 114.668 115.061 115.454 n 5 . 846 116.239 116.632 117.024 117.417 117.810 118.202 118.596 118.988 119.381 119.773 120. 166 712.76 718.69 724.64 730.62 736.62 742.64 748.69 754.77 760.87 766.99 773. 14 779.31 785.51 791 73 797.98 804.25 810.54 816.86 823.21 829.58 835.97 842.39 848.83 855.30 861.79 868.31 874.85 881.41 888 . 00 894 . 62 901.26 907 . 92 914.61 921.32 - 928.06 934.82 941.61 948 . 42 955.25 962.11 969.00 975.91 982 . 84 989.80 996.78 1003.8 1010.8 1017.9 1025.0 1032.1 1039.2 1046.3 1053.5 1060.7 1068.0 1075.2 1082.5 1089.8 1097.1 1104.5 1111.8 1119.2 1126.7 1134.1 1I4I.6 1149.1 282 The Science of Knitting NATURAL TRIGONOMETRICAL FUNCTIONS. • M. "o 15 30 45 15 30 45 15 30 45 15 30 45 15 30 45 15 30 45 15 30 45 15 30 45 15 30 45 15 30 45 15 30 45 15 30 45 15 30 45 15 30 45 15 30 45 Sine. .00000 .00436 .00873 .01309 01745 02181 02618 .03054 .03490 ,03926 .04362 .04798 .05234 .05669 .06105 .06540 .06976 .07411 .07846 .08281 .08716 .09150 .09585 .10019 .10453 .10887 ,11320 .11754 .12187 .12620 .13053 .13485 .13917 .14349 .14781 .15212 15643 16074 .16505 .16935 .17365 17794 18224 .18652 .19081 .19509 .19937 .20364 .20791 .21218 .21644 .22070 .22495 .22920 .23345 .23769 24192 .24615 .25038 .25460 .25882 Co- vers. Co- sine. 1 .0000 .99564 .99127 .98691 .98255 .97819 .97382 .96946 .96510 .96074 .95638 .95202 .94766 .94331 .93895 .93460 .93024 .92589 .92154 .91719 .91284 .90850 .90415 .89981 .89547 .89113 .88680 .88246 .87813 .87380 .86947 .86515 .86083 .85651 .85219 .84788 .84357 .83926 .83495 .83065 .82635 .82206 .81776 .81348 .80919 .80491 .80063 .79636 .79209 .78782 .78356 .77930 .77505 .77080 .76655 .76231 .75808 .75385 .74962 .74540 .74118 Cosec. Tang Ver. Sin. Infinite 229.18 114.59 76.397 57.299 45.840 38.202 32.746 28.654 25.471 22.926 20.843 19.107 17.639 16.380 15.290 14.336 13.494 12.745 12.076 11.474 10.929 10.433 9.9812 9.5668 9.1855 8.8337 8.5079 8.2055 7.9240 7.6613 7.4156 7.1853 6.9690 6.7655 6.5736 6.3924 6.2211 6.0589 5.9049 5.7588 5.6198 5.4874 5.3612 5.2408 5.1258 5.0158 4.9106 4.8097 4.7130 4.6202 4.5311 4.4454 4.3630 4.2837 4.2072 4. 1336 4.0625 3.9939 3.9277 3.8637 Secant. .00000 .00436 .00873 .01309 .01745 .02182 .02618 .03055 .03492 .03929 .04366 04803 05241 .05678 .06116 .06554 06993 .0743 .07870 .08309 .08749 .09189 .09629 . 1 0069 .10510 .10952 .11393 .11836 .12278 .12722 3165 .13609 14054 14499 .14945 15391 15838 16286 16734 .17183 .17633 .18083 .18534 .18986 .19438 .19891 .20345 .20800 .21256 .21712 .22169 .22628 23087 23547 24008 .24470 24933 25397 25862 .26328 26795 Co tan. Cotan Infinite 229.18 114.59 76.390 57.290 45.829 38.188 32.730 28.636 25.452 22.904 20.819 19.081 17.611 16.350 15.257 14.301 13.457 12.706 12.035 11.430 10.883 10.385 9.9310 9.5144 9.1309 8.7769 8.4490 8.1443 7.8606 7.5958 7.3479 7.1154 6.8969 6.6912 6.4971 6.3138 6.1402 5.9758 5.8197 5.6713 5.5301 5.3955 5.2672 5.1446 5.0273 4.9152 4.8077 4.7046 4.6057 4.5107 4.4194 4.3315 4.2468 4.1653 4.0867 4.0108 3.9375 3.8667 3.7983 3.7320 Se- cant. 1 .0000 1 .0000 1 .0000 1.0001 1.0001 1 .0002 1 .0003 1 .0005 1 .0006 1 .0008 1 .0009 1.0011 1.0014 1.0016 1.0019 1.0021 1 .0024 1 .0028 1.0031 1.0034 1 .0038 1 .0042 1 .0046 1 .005 1 1.0055 1 .0060 1 .0065 1.0070 1.0075 1.0081 1 .0086 1 .0092 1 .0098 1.0105 1.0111 1.0118 1.0125 1.0132 1.0139 1.0147 1.0154 1.0162 1.0170 1.0179 1.0187 1.0196 1 .0205 1.0214 1.0223 1.0233 1.0243 1.0253 1.0263 1.0273 1 .0284 1 .0295 1 .0306 1.0317 1 .0329 1.0341 1.0353 Ver. Sin. Tang. Cosec. .00000 .00001 .00004 .00009 .00015 .00024 .00034 .00047 .00061 .00077 .00095 .00115 00137 .00161 00187 .00214 ,00244 .00275 .00308 .00343 .00381 .00420 .00460 .00503 .00548 .00594 .00643 .00693 .00745 .00800 .00856 .00913 .00973 .01035 .01098 ,01164 .01231 01300 .01371 .01444 01519 .01596 .01675 .01755 .01837 .01921 .02008 .02095 .02185 .02277 .02370 .02466 .02563 .02662 02763 02866 .02970 .03077 .03185 .03295 ,03407 Cosine. Co- vers. 1 .0000 .99999 .99996 .99991 .99985 .99976 .99966 .99953 .99939 .99923 .99905 .99885 .99863 .99839 .99813 .99786 .99756 .99725 .99692 .99656 .99619 .99580 .99540 .99497 .99452 .99406 .99357 .99307 .99255 .99200 .99144 .99086 .99027 .98965 .98902 .98836 .98769 .98700 .98629 .98556 .98481 .98404 .98325 .98245 .98163 .98079 .97992 .97905 .97815 .97723 .97630 .97534 .97437 .97338 .97237 .97134 .97030 .96923 .96815 .96705 .96593 90 89 87 86 85 84 83 82 81 80 79 78 77 76 75 Sine. M. From 75° to 90° read from bottom of table upwards. Natural Trigonometrical Functions ^8S • M. Sine. Co- vers. Cosec Tang Cotan Secant Ver. Sii. Cosine. .25882 .74118 3.8637 .26795 3.7320 1.0353 .03407 .96593 75 ( 15 .26303 .73697 3.8018 .27263 3.6680 1.0365 .03521 .96479 4; 30 .26724 .73276 3.7420 .27732 3.6059 1.0377 .03637 .96363 3( 45 .27144 .72856 3.6840 .28203 3.5457 1 .0390 .03754 .96246 74 1! .27564 .72436 3.6280 .28674 3.4874 1 .0403 .03874 .96126 ( 15 .27983 .72017 3.5736 .29147 3.4308 1.0416 .03995 .96005 4; 30 .28402 .71598 3.5209 .29621 3.3759 1 .0429 .04118 .95882 3( 45 .28820 .71180 3.4699 .30096 3.3226 1 .0443 .04243 .95757 1! .29237 .70763 3.4203 .30573 3.2709 1.0457 .04370 .95630 73 C 15 .29654 .70346 3.3722 .31051 3.2205 1.0471 .04498 .95502 4f 30 .30070 .69929 3.3255 .31530 3.1716 1.0485 .04628 .95372 3( 45 .30486 .69514 3.2801 .32010 3.1240 1.0500 .04760 .95240 15 .30902 .69098 3.2361 .32492 3.0777 1.0515 .04894 .95106 73 C 15 .31316 .68684 3.1932 .32975 3.0326 1.0530 .05030 .94970 43 30 .31730 .68270 3.1515 .33459 2.9887 1.0545 .05168 .94832 3C 45 .32144 .67856 3.1110 .33945 2.9459 1 .0560 .05307 .94693 13 .32557 .67443 3.0715 .34433 2.9042 1.0576 .05448 .94552 71 C 15 .32969 .6703 I 3.0331 .34921 2.8636 1.0592 .05591 .94409 43 30 .33381 .66619 2.9957 .35412 2.8239 1.0608 .05736 .94264 3C 45 .33792 .66208 2.9593 .35904 2.7852 1 .0625 .05882 .94118 19 .34202 .65798 2.9238 .36397 2.7475 1 .0642 .0603 1 .93969 70 C 15 .34612 .65388 2.8892 .36892 2.7106 1.0659 .06181 .93819 43 30 .35021 .64979 2.8554 .37388 2.6746 1.0676 .06333 .93667 30 45 .35429 .64571 2.8225 .37887 2.6395 1 .0694 .06486 .93514 19 .35837 .64163 2.7904 .38386 2.6051 1.0711 .06642 .93358 69 Q 15 .36244 .63756 2.7591 .38888 2.5715 1.0729 .06799 .93201 43 30 .36650 .63350 2.7285 .39391 2.5386 1 .0743 .06958 .93042 30 45 .37056 .62944 2.6986 .39896 2.5065 1 .0766 .07119 .92881 15 .37461 .62539 2.6695 .40403 2.4751 1.0785 .07282 .92718 68 Q 15 .37865 .62135 2.6410 .40911 2.4443 1 .0804 .07446 .92554 45 30 .38268 .61732 2.6131 .41421 2.4142 1.0824 .07612 .92388 30 45 .38671 .61329 2.5859 .41933 2.3847 1 .0844 .07780 .92220 15 .39073 .60927 2.5593 .42447 2.3559 1 .0864 .07950 .92050 67 15 .39474 .60526 2.5333 .42963 2.3276 1 .0884 .08121 .91879 45 30 .39875 .60125 2.5078 .43481 2.2998 1 .0904 .08294 .91706 30 45 .40275 .59725 2.4829 .44001 2.2727 1 .0925 .08469 .91531 13 .40674 .59326 2.4586 .44523 2.2460 1 .0946 .08645 .91355 66 15 .41072 .58928 2.4348 .45047 2.2199 1.0968 .08824 .91176 4S 30 .41469 .58531 2.4114 .45573 2.1943 1.0989 .09004 .90996 30 45 .41866 .58134 2.3886 .46101 2.1692 1.1011 .09186 .90814 15 .42262 .57738 2.3662 .46631 2.1445 1.1034 .09369 .90631 65 15 .42657 .57343 2.3443 .47163 2.1203 1.1056 .09554 .90446 49 30 .43051 .56949 2.3228 .47697 2.0965 ?.1079 .09741 .90259 30 45 .43445 .56555 2.3018 .48234 2.0732 1.1102 .09930 .90070 15 .43837 .56163 2.2812 .48773 2.0503 1.1126 .10121 .89879 64 15 .44229 .55771 2.2610 .49314 2.0278 1.1150 .10313 .89687 45 30 .44620 .55380 2.2412 .49858 2.0057 1.1174 .10507 .89493 30 45 .45010 .54990 2.2217 .50404 1 .9840 1.1198 .10702 .89298 15 .45399 .54601 2.2027 .50952 1 .9626 1.1223 .10899 .89101 63 15 .45787 .54213 2.1840 .51503 1.9416 1.1248 .11098 88902 45 30 .46175 .53825 2.1657 .52057 1.9210 1.1274 .11299 .88701 30 45 .46561 .53439 2.1477 .52612 1 .9007 1.1300 .11501 .88499 15 .46947 .53053 2.1300 .53171 1 .8807 1.1326 .11705 .88295 63 15 .47332 .52668 2.1127 .53732 1.8611 1.1352 .11911 .88089 45 30 .47716 .52284 2.0957 .54295 1.8418 1.1379 .12118 .87882 30 45 .48099 .51901 2.0790 .54862 1 .8228 1.1406 .12327 .87673 15 .48481 .51519 2.0627 .55431 1 .8040 1.1433 .12538 .87462 61 15 .48862 .51138 2.0466 .56003 1.7856 1.1461 .12750 .87250 45 30 .49242 .50758 2.0308 .56577 1.7675 1.1490 .12964 .87036 30 45 .49622 .50378 2.0152 .57155 1.7496 1.1518 .13180 .86820 15 .50000 .50000 2.0000 .57735 1.7320 1.1547 .13397 .86603 60 Co- sine. Ver. Sin. Se- cant. Co tan. Tang. Cosec. Co- vers. Sine. o M. From 60* to 75° read from bottom of table upwards. 284 The Science of Knitting o M. Sine. Co- vers. Cosec Tang. Co tan. Secant. Ver. Sin. Cosine 80 .50000 .50000 2.0000 .57735 1.7320 1.1547 .13397 .86603 60 15 .50377 .49623 1 .9850 .58318 1.7147 1.1576 .13616 .86^84 45 30 .50754 .49246 1 .9703 .58904 1.6977 1.1606 .13837 .86163 30 45 .51129 .48871 1.9558 .59494 1 .6808 1.1636 .14059 .85941 15 81 .51504 .48496 1.9416 .60086 1 .6643 1.1666 .14283 .85717 59 G 15 .51877 .48123 1 .9276 .60681 1.6479 1.1697 .14509 .85491 45 30 .52250 .47750 1.9139 .61280 1.6319 1.1728 .14736 .85264 30 45 .52621 .47379 1 .9004 .61882 1.6160 1.1760 .14965 .85035 15 S3 .52992 .47008 1.8871 .62487 1 .6003 1.1792 .15195 .84803 58 15 .53361 .46639 1.8740 .63095 1 .5849 1.1824 .15427 .84573 45 30 .53730 .46270 1.8612 .63707 1.5697 1.1857 .15661 .84339 30 45 .54097 .45903 1 .8485 .64322 1.5547 1.1890 . 1 5896 .84104 15 33 .54464 .45536 1.8361 .64941 1.5399 1.1924 .16133 .83867 57 15 .54829 .45171 1 .8238 .65563 1.5253 1.1958 .16371 .83629 45 30 .55194 .44806 1.8118 .66188 1.5108 1.1992 .16611 .83389 30 45 .55557 .44443 1 .7999 .66818 1 .4966 1.2027 .16853 .83147 15 34 .55919 .44081 1.7883 .67451 1.4826 1 .2062 .17096 .82904 56 15 .56280 .43720 1.7768 .68087 1 .4687 1 .2098 .17341 .82659 45 30 .56641 .43359 1.7655 .68728 1.4550 1.2134 .17587 .82413 30 45 .57000 .43000 1.7544 .69372 1.4415 1.2171 .17835 .82165 15 35 .57358 .42642 1.7434 .70021 1.4281 1 .2208 .18085 .81915 55 15 .57715 .42285 1.7327 .70673 1.4150 1.2245 .18336 .81664 45 30 .58070 .41930 1.7220 .71329 1.4019 1.2283 .18588 .81412 30 45 .58425 .41575 1.7116 .71990 1.3891 1.2322 .18843 .81157 15 36 .58779 .41221 1.7013 .72654 1.3764 1.2361 .19098 .80902 54 15 .59131 .40869 1.6912 .73323 1.3638 1 .2400 .19356 .80644 45 30 .59482 .40518 1.6812 .73996 1.3514 1 .2440 .19614 .80386 30 45 .59832 .40168 1.6713 .74673 1.3392 1 .2480 .19875 .80125 15 37 .60181 .39819 1.6616 .75355 1.3270 1.2521 .20136 .79864 53 15 .60529 .39471 1.6521 .76042 1.3151 1.2563 .20400 .79600 45 30 .60876 .39124 1.6427 .76733 1.3032 1 .2605 .20665 .79335 30 45 .61222 .38778 1.6334 .77428 1.2915 1.2647 .20931 .79069 15 38 .61566 .38434 1 .6243 .78129 1.2799 1 .2690 .21199 .78801 53 15 .61909 .38091 1.6153 .78834 1 .2685 1.2734 .21468 .78532 45 30 .62251 .37749 1 .6064 .79543 1.2572 1.2778 .21739 .78261 30 45 .62592 .37408 1.5976 .80258 1 .2460 1 2822 .22012 .77988 15 89 .62932 .37068 1.5890 .80978 1.2349 1 .2868 .22285 .77715 51 15 .63271 .36729 1.5805 .81703 1.2239 1.2913 .22561 .77439 45 30 .63608 .36392 1.5721 .82434 1.2131 1 .2960 .22838 .77162 30 45 .63944 .36056 1.5639 .83169 1 .2024 1.3007 .23116 .76884 15 40 .64279 .35721 1.5557 .83910 1.1918 1.3054 .23396 .76604 50 15 .64612 .35388 1.5477 .84656 1.1812 1.3102 .23677 .76323 45 30 .64945 .35055 1.5398 .85408 1.1708 1.3151 .23959 .76041 30 45 .65276 .34724 1.5320 .86165 1.1606 1 .3200 .24244 .75756 15 41 .65606 .34394 1.5242 .86929 1.1504 1.3250 .24529 .75471 49 15 .65935 .34065 1 5166 .87698 1.1403 1.3301 .24816 .75184 45 30 .66262 .33738 1 .5092 .88472 1.1303 1.3352 .25104 .74896 30 45 .66588 .3341-2 1.5018 .89253 1.1204 1.3404 .25394 .74606 15 42 .66913 .33087 1 .4945 .90040 1.1106 1.3456 .25686 .74314 48 15 .67237 .32763 1.4873 .90834 1.1009 1.3509 .25978 .74022 45 30 .67559 .32441 1 .4802 .91633 1.0913 1.3563 .26272 .73728 30 45 .67880 .32120 1.4732 .92439 1.0818 1.3618 .26568 .73432 15 43 .68200 .31800 1 .4663 .93251 1 .0724 1.3673 .26865 .73135 47 15 .68518 .31482 1.4595 .94071 1 .0630 1.3729 .27163 .72837 45 30 .68835 .31165 1.4527 .94896 1.0538 1.3786 .27463 .72537 30 45 .69151 .30849 1.4461 .95729 1 .0446 1.3843 .27764 .72236 15 44 .69466 .30534 1.4396 .96569 1.0355 1 .3902 .28066 .71934 46 15 .69779 .30221 1.4331 .97416 1 .0265 1.3961 .28370 .71630 45 30 .70091 .29909 1.4267 .98270 1.0176 1 .4020 .28675 .71325 30 45 .70401 .29599 1 .4204 .99131 1 .0088 1.4081 .28981 .71019 15 45 70711 .29289 1.4142 1 .0000 1 .0000 1.4142 .29289 .70711 45 Cosine Ver. Sin. Se- cant. Cotan. Tang. Cosec. Co- ver.-. Sine. o M. From 45° to 60° read from bottom of table upwards. Tables of Time 285 Table of Time in Dififerent Units Counting 9 hours per day and 300 days per year Second Minute Hour Day Week Month Year 9,720,000 810,000 194,400 32,400 3,600 60 162,000 13,500 3,240 540 60 2700 225 54 9 300 25 6 50 4i 12 Month Week Day Hour Minute Table of Time in Different Units Counting 10 hours per day, and 300 days per year Second Minute Hour Day Week Month Year 10,800,000 900,000 216,000 36,000 3,600 60 180,000 15,000 3,600 600 60 3000 250* 60 10 300 25 6 50 4i 12 Month Week Day Hour Minute 286 The Science of Knitting MENSURATION PLANE SURFACES Quadrilateral. — A four-sided figure. Parallelogram. — A quadrilateral with opposite sides parallel. Varieties. — Square: four sides equal, all angles right angles. Rectangle : opposite sides equal, all angles right angles. Rhom- bus: four sides equal, opposite angles equal, angles not right angles. Rhomboid: opposite sides equal, opposite angles equal, angles not right angles. Trapezium. — A quadrilateral with unequal sides. Trapezoid. — A quadrilateral with only one pair of opposite sides parallel. Diagonal of a square = V2 X s ide^ = 1.4142 X side. Diag. of a rectangle = Vsum of squares of two adjacent sides. Area of any parallelogram = base X altitude. Area of rhombus or rhomboid = product of two adjacent sides X sine of angle included between them. Area of a trapezoid = product of half the sum of the two parallel sides by the perpendicular distance between them. To find the area of any quadrilateral figure. — Divide the quadrilateral into two triangles; the sum of the areas of the triangles is the area. Or, multiply half the product of the two diagonals by the sine of the angle at their intersection. To find the area of a quadrilateral which may be inscribed in a circle. — From half the sum of the four sides subtract each side severally; multiply the four remainders together; the square root of the product is the area. Triangle. — A three-sided plane figure. Fane^zes. — Right-angled, having one right angle; obtuse- angled, having one obtuse angle; isosceles, having two equal angles and two equal sides; equilateral, having three equal sides and equal angles. The sum of the three angles of every triangle = 180 degrees. The sum of the two acute angles of a right-angled triangle = 90 degrees. Hypothenuse o f a ri ght- angled trian gle, the side oppo site the right angle, = Vsum of the squares of the other two sides. If Plane Surfaces 287 a and b are t he tw o sides and c t he hypothenuse, c~ = «« _|_ 52. a = Vc2 - 62 = V(c + 6) (c - 6). If the two sides are equal, side = hyp -i- 1.4142; or hyp X .7071. To find the area of a triangle : Rule 1. Multiply the base by half the altitude. Rule 2. Multiply half the product of two sides by the sine of the included angle. Rule 3. From half the sum of the three sides subtract each side severally; multiply together the half sum and the three remainders, and extract the square root of the product. The area of an equilateral triangle is equal to one-fourth the square j)f one of its sides multiphed by the square root of 3 = ~J~> « bemg the side; or a^ X 0.433013. Area of a triangle given, to find base: Base = twice skea. ^ perpendicular height. Area of a triangle given, to find height: Height = twice area -7- base. Two sides and base given, to find perpendicular height (in a triangle in which both of the angles at the base are acute). Rule. —As the base is to the sum of the sides, so is the differ- ence of the sides to the difference of the divisions of the base made by drawing the perpendicular. Half this difference being added to or subtracted from half the base will give the two divisions thereof. As each side and its opposite division of the base constitutes a right-angled triangle, t he perpendic ular is ascertamedby therule: Perpendicular = Vhyp2 - base^. Areas of similar figures are to each other as the squares of theu- respective hnear dimensions. If the area of an equilateral triangle of side = 1 is 0.433013 and its height 0.86603, what is the area of a similar triangle whose height = 1"? 866032- 12 :: 0.433013 : 0.57735, Ans. Polygon. — A plane figure having three or more sides. Reg- ular or irregular, according as the sides or angles are equal or unequal. Polygons are named from the number of their sides and angles. To find the area of an irregular polygon. — Draw diagonals dividmg the polygon into triangles, and find the sum of the areas of these triangles. 288 The Science of Knitting Horse Power Transmitted by Cold-rolled Steel Shafting at Different Speeds as Prime Movers or Head Shafts Carrying Main Driving Pulley or Gear, well Supported by Bearings. Formula H.P. = d^R -^ 100. Revolutions per m nute. Revolutions per minute. Dia. 100 200 300 400 500 Dia. 100 200 300 400 500 ^ 3.4 6.7 10.1 13.5 16.9 21 24 48 72 95 119 1^ 3.8 7.6 11.4 15.2 19.0 211 25 51 76 101 127 If 4.3 8.6 12.8 17.1 21.0 3 27 54 81 108 135 IH 4.8 9.6 14.4 19.2 24.0 3| 31 61 91 122 152 If 5.4 10.7 16.1 21.0 27.0 3il 32 65 97 129 162 lit 5.9 11.9 17.8 24.0 30.0 n 34 69 103 137 172 11 6.6 13.1 19.7 26.0 33.0 H 38 77 115 154 192 \\% 7.3 14.5 22.0 29.0 36.0 3/6 41 81 122 162 203 2 8.0 16.0 24.0 32.0 40.0 3^ 43 86 128 171 214 2i's 8.8 17.6 26.0 35.0 44.0 3l«6 45 90 136 180 226 2i 9.6 19.2 29.0 38.0 48.0 3| 48 95 143 190 238 2^ 10.5 21.0 31.0 42.0 52.0 3H 50 100 150 200 251 2i 11.4 23.0 34.0 45.0 57.0 3f 55 105 158 211 264 2t\ 12.4 25.0 37.0 49.0 62.0 H 58 116 174 233 291 2| 13.4 27.0 40.0 54.0 67.0 015 61 122 183 244 305 2/b 14.5 29.0 43.0 58.0 72.0 4 64 128 192 256 320 n 15.6 31.0 47.0 62.0 78.0 4fs 74 147 221 294 367 2j% 16.8 34.0 50.0 67.0 84.0 4i 77 154 230 307 383 21 18.1 36.0 54.0 72.0 90.0 4/b 88 175 263 350 438 2H 19.4 39.0 58.0 77.0 97.0 4 91 182 273 365 456 2f 21.0 41.0 62.0 83.0 104.0 4f 107 214 322 429 537 m 22.0 44.0 67.0 89.0 111.0 5 125 250 375 500 625 For H.P. transmitted by turned steel shafts, as prime movers, etc., multiply the figures by 0.8. For shafts, as second movers or line I Cold-rolled Turned shafts, bearings 8 feet apart, multiply by } 1*43 1.11 For simply transmitting power, short countershafts, etc., bearings not over 8 feet apart, multiply by 2 2.50 The horse power is directly proportional to the number of revolutions per minute. Speed of Shafting. — Machine shops 120 to 240 Wood-working 250 to 300 Cotton and woolen mills 300 to 400 Plane Surfaces 289 Horse Power of a Leather Belt One Inch Wide. (Nagle.) Formula: H.P. = CVtw{S - 0.012 V^) -h 550. For/ = 0.40, a = 180 degrees, C = 0.715, w = 1. Laced Belts, S = 275. Riveted Belts, S = 400. >, 8 Thickness in inches = f. ii Thickness in inches = t. IS. O » •3 a 1 1 0.51 0.59 1% 0.63 0.73 1 0.84 1.05 1.18 /j I 4 ^B i 1 3..39 3.87 10 15 1.69 1.94 2.42 2.58 2.91 15 0.75 0.88 1.00 1.16 1.32 1.66 1.77 20 2.24 2.57 3.21 3.42 3.85 4.49 5.13 20 1.00 1.17 1.32 1.54 1.75 2.19 2.34 25 2.79 3.19 3.98 4.25 4.78 5.57 6.37 25 1.23 1.43 1.61 1.88 2.16 2.69 2.86 30 3.31 3.79 4.74 5.05 5.67 6.62 7.58 30 1.47 1.72 1.93 2.25 2.58 3.22 3.44 35 3.82 4.37 5.46 5.83 6.56 7.65 8.75 35 1.69 1.97 2.22 2.59 2.96 3.70 3.94 40 4.33 4.95 6.19 6.60 7.42 8.66 9.90 40 1.90 2.22 2.49 2.90 3.32 4.15 4.44 45 4.85 5.49 6.86 7.32 8.43 9.70 10.98 45 2.09 2.45 2.75 3.21 3.67 4.58 4.89 50 5.26 6.01 7.51 8.02 9.02 10.52 12.03 50 2.27 2.65 2.98 3.48 3.98 4.97 5.30 55 5.68 6.50 8.12 8.66 9.74 11.36 13.00 55 2.44 2.84 3.19 3.72 4.26 5.32 5.69 60 6.09 6.96 8.70 9.28 10.43 12.17 13.91 60 2.58 3.01 3.38 3.95 4.51 5.64 6.02 65 6.45 7.37 9.22 9.83 11.06 12.90 14.75 65 2.71 3.16 3.55 4.14 4.74 5.92 6.32 70 6.78 7.75 9.69 10.33 11.62 13.56 15.50 70 2.81 3.27 3.68 4.29 4.91 6.14 6.54 75 7.09 8.11 10.13 10.84 12.16 14.18 16.21 75 2.89 3.37 3.79 4.42 5.05 6.31 6.73 80 7.36 8.41 10.51 11.21 12.61 14.71 16.81 80 2.94 3.43 3.86 4.50 5.15 6.44 6.86 85 7.58 8.66 10.82 11.55 13.00 15.16 17.32-- 85 2.97 3.47 3.90 4.55 5.20 6.50 6.93 90 7.74 8.35 11.06 11.80 13.27 15.48 17.69 90 2.97 3.47 3.90 4.55 5.20 6.50 6.93 100 7.96 9.10 11.37 12.13 13.65 15.92 18.20 The H.P. becomes a maximum at T he H.P. becomes a maximum at 87.41 f t. per sec. =5245 ft. per min. 105. 4 ft. per £ ec. = 6324 ft. per min. In the above table the angle of subtension, a is taken at 180 degrees. Should it be I 90°[l00''|110°|l20°[130''|l40''|150°!l60°|l70°[180''|200'' Multiply above values by. I .651 .701 .751 .791 .831 .871 .91 1 .941 .971 1 1 1.05 A. F. Nagle's Formula {Trans. A. S. M. E., vol. ii, 1881, p. 91. Tables published in 1882). 'S - 0.012 F2^ ^•^• = ^^^"^1— ^50 ]' C= 1 - 10-°-oo758/a: a= degrees of belt contact; /= coefficient of friction; w= width in inches; t= thickness in inches; V = velocity in feet per second; S= stress upon belt per square inch. 290 The Science of Knitting MISCELLANEOUS NOTES ON BELTING. Formulae are useful for proportioning belts and pulleys, but they furnish no means of estimating how much power a particular belt may be transmitting at any given time, any more than the size of the engine is a measure of the load it is actually drawing, or the known strength of a horse is a measure of the load on the wagon. The only reliable means of determining the power actually transmitted is some form of dynamometer. (See Trans. A. S. M. E., vol. xii, p. 707.) If we increase the thickness, the power transmitted ought to increase in proportion; and for double belts we should have half the width required for a single belt under the same conditions. With large pulleys and moderate velocities of belt it is probable that this holds good. With small pulleys, however, when a double belt is used, there is not such perfect contact between the pulley-face and the belt, due to the rigidity of the latter, and more work is necessary to bend the belt-fibers than when a thinner and more pliable belt is used. The centrifugal force tending to throw the belt from the pulley also increases with the thickness, and for these reasons the width of a double belt required to transmit a given horse power when used with small pulleys is generally assumed not less than seven-tenths the width of a single belt to transmit the same power. (Flather on "Dyna- mometers and Measurement of Power.") F. W. Taylor, however, finds that great pliability is objection- able, and favors thick belts even for small pulleys. The power consumed in bending the belt around the pulley he considers inappreciable. According to Rankine's formula for centrifugal tension, this tension is proportional to the sectional area of the belt, and hence it does not increase with increase of thickness when the width is decreased in the same proportion, the sectional area remaining constant. Scott A. Smith {Trans. A. S. M. E., x, 765) says: The best belts are made from all oak-tanned leather, and curried with the use of cod oil and tallow, all to be of superior quality. Such belts have continued in use thirty to forty years when used as simple driving-belts, driving a proper amount of power, and having had suitable care. The flesh side should not be run to the pulley-face, for the reason that the wear from contact with the pulley should come on the grain side, as that surface of the Miscellaneous Notes on Belting 291 belt is much weaker in its tensile strength than the flesh side- also as the grain is hard it is more enduring for the wear of attrition; further, if the gram is actually worn off, then the belt may not suffer in its integrity from a ready tendency of the hard grain side to crack. The most intimate contact of a belt with a pulley comes, first m the smoothness of a pulley-face, including freedom from ridges and hollows left by turning-tools; second, in the smoothness of the surface and evenness in the texture or body of a belt- third in havmg the crown of the driving and receiving pulleys exactly ahke, — as nearly so as is practicable in a commercial sense- "^ fourth, m havmg the crown of pulleys not over i inch for a 24-inch face, that is to say, that the pulley is not to be over i inch larger in diameter m its center; fifth, in having the crown other than two planes meetmg at the center; sixth, the use of any material on or in a belt, m addition to those necessarily used in the currying process, to keep them pliable or mcrease then- tractive quality should wholly depend upon the exigencies arising in the use of belts; non-use is safer than over-use; seventh, with reference to the lacing of belts, it seems to be a good practice to cut the ends to a convex shape by using a former, so that there may be a nearly uniform stress on the lacing through the center as conr- pared with the edges. For a belt 10 inches wide, the center of each end should recede j\ inch. Lacing of Belts. - In punching a belt for lacing, use an oval punch, the longer diameter of the punch being parallel with the sides of the belt. Punch two rows of holes in each end, placed zigzag. In a 3-mch belt there should be four holes in each end — two m each row. . In a 6-inch belt, seven holes - four in the row nearest the end. A 10-in. belt should have nine holes. The edge of the holes should not come nearer than f inch from the sides nor i mch from the ends of the belt. The second row should be at least If mches from the end. On wide belts these distances should be even a little greater. Begin to lace in the center of the belt and take care to keep the ends exactly in line, and to lace both sides with equal tightness. The lacmg should not be crossed on the side of the belt that runs next the pulley. In taking up belts, observe the same rules as m putting on new ones. Setting a Belt on Quarter-twist. - A belt must run squarely on to the pulley. To connect with a belt two horizontal shafts 292 The Science of Knitting at right angles with each other, say an engine-shaft near the floor with a line attached to the ceiling, will require a quarter-turn. First, ascertain the central point on the face of each pulley at the extremity of the horizontal diameter where the belt will leave the pulley, and then set that point on the driven pulley plumb over the corresponding point on the driver. This will cause the belt to run squarely on to each pulley, and it will leave at an angle greater or less, according to the size of the pulleys and their distance from each other. In quarter-twist belts, in order that the belt may remain on the pulleys, the central plane on each pulley must pass through the point of delivery of the other pulley. This arrangement does not admit of reversed motion. To find the Length of Belt required for two given Pulleys. — When the length cannot be measured directly by a tape-line the following approximate rule may be used: Add the diameter of the two pulleys together, divide the sum by 2, and multiply the quotient by 3j, and add the product to twice the distance between the centers of the shafts. ANALOGIES BETWEEN THE FLOW OF WATER AND ELECTRICITY Water Head, difference of level, in feet. Difference of pressure, lbs. per sq. in. Resistance of pipes, apertures, etc., increases with length of pipe, with contractions, roughness, etc.; decreases with increase of sectional area. Rate of flow, as cubic ft. per second, gallons per min., etc., or volume divided by the time. In the mining re- gions sometimes expressed in "miners' inches." Electricity Volts; electro-motive force; dif- ference of potential; E. or E.M.F. Ohms, resistance, R. Increases directly as the length of the conductor or wire and in- versely as its sectional area, R (X) I -^ s. It varies with the nature of the conductor. I'Amperes: current; current strength; intensity of current ; rate of flow; 1 ampere = 1 i coulomb per second. volts , E Amperes = IR. ohms' ^ R' ^ Analogies Between the Flow of Water and Electricity 293 Water Quantity, usually measured in cubic ft. or gallons, but is also equivalent to rate of flow X time, as cu. ft. per second for so many hours. Electricity Work, or energy, measured in foot-pounds ; product of weight of falling water into height of fall; in pumping, product of quantity in cubic feet into the pressure in lbs. per square foot against which the water is pumped. Power, rate of work. Horse power = ft. -lbs. of work in 1 min. -r- 33,000. In water flowing in pipes, rate of flow in cu. ft. per second X re- sistance to the flow in lbs. per sq. ft. -^ 550. Coulomb, unit of quantity, Q, = rate of flow X time, as ampere-seconds. 1 ampere- hour = 3600 coulombs. 'Joule, volt-coulomb, W, the unit of work, = product of quantity by the electro-mo- tive force = volt-ampere- second. 1 joule = 0.7373 ■^ foot-pound. If C (amperes) = rate of flow, and E (volts) = difference of pressure between two points in a circuit, energy expended = lEt, = PRt. CWatt, unit of power, P, = volts X amperes, = current or rate of flow X difference -{ of potential. 1 watt = 0.7373 foot-pound- per sec. = 1/746 of a horse power. 294 The Science of Knitting TABLE OF ELECTRICAL HORSE-POWERS. Formula: - °^^^ X Amperes ^ ^ ^^ ^^ 1 volt ampere = .0013405 H.P. 74o Read amperes at top and volts at side or vice versa. Volts or Amperes. Is 1 10 20 30 40 60 60 70 80 90 100 110 120 1 .00134 .0134 .0268 .0402 .0536 .0670 .0804 .0938 .1072 .1206 .1341 .1475 .1609 2 .00268 .0268 .0536 .0804 .1072 .1341 .1609 .1877 .2145 .2413 .2681 .2949 .3217 3 .00402 .0402 .0804 .1206 .1609 .2011 .2413 .2815 .3217 .3619 .4022 .4424 .4826 4 .00536 .0536 .1072 .1609 .2145 .2681 .3217 3753 .4290 4826 .5362 .5898 .6434 5 .00670 .0670 .1341 .2011 .2681 .3351 .4022 .4692 .5362 .6032 .6703 .7373 •8043 6 .00804 .0804 .1609 .2413 .3217 .4022 .4826 .5630 .6434 .7239 .8043 .8847 .9652 7 .00938 .0938 .1877 .2815 .3753 .4692 .5630 .6568 .7507 .8445 .9384 1.032 1.126 8 .01072 .1072 .2145 .3217 .4290 .5362 .6434 .7507 .8579 .9652 1.072 1.180 1.287 9 .01206 .1206 .2413 .3619 .4826 .6032 .7239 .8445 .9652 1.086 1.206 1.327 1.448 10 .01341 .1341 .2681 .4022 .5362 .6703 .8043 .9383 1.072 1.206 1.341 1.475 1.609 11 .01475 .1475 .2949 .4424 .5898 .7373 .8847 1.032 1.180 1.327 1.475 1.622 1.769 12 .01609 .1609 .3217 .4826 .6434 .8043 .9652 1.126 1.287 1.448 1.609 1.769 1.930 13 .01743 .1743 .3485 .5228 .6970 .8713 1.046 1.220 1.394 1.568 1.743 1.917 2.091 14 .01877 .1877 .3753 .5630 .7507 .9384 1.126 1.314 1.501 1.689 1.877 2.064 2.252 15 .02011 .2011 .4022 .6032 .8043 1.005 1.206 1.408 1.609 1.810 2.011 2.212 2.413 16 .02145 .2145 .4290 .6434 .8579 1.072 1.287 1.501 1.716 1.930 2.145 2.359 2.574 17 .02279 .2279 .4558 .6837 .9115 1.139 1.367 1.595 1.823 2.051 2.279 2.507 2.735 18 .02413 .2413 .4826 .7239 .9652 1.206 1.448 1.689 1.930 2.172 2.413 2.654 2.895 19 .02547 .2547 .5094 .7641 1.019 1.273 1.528 1.783 2.037 2 292 2.547 2.801 3.056 20 .02681 .2681 .6362 .8043 1.072 1.340 1.609 1.877 2.145 2.413 2.681 2.949 3.217 21 .02815 .2815 .5630 .8445 1.126 1.408 1.689 1.971 2.252 2.533 2.815 3.097 3.378 22 .02949 .2949 .5898 .8847 1.180 1.475 1.769 2.064 2.359 2.654 2.949 3.244 3.539 23 .03083 .3083 .6166 .9249 1.233 1.542 1.850 2.158 2.467 2.775 3.083 3.391 3.700 24 .03217 .3217 .6434 .9652 1.287 1.609 1.930 2.252 2.574 2.895 3.217 3.539 3.861 25 .03351 .3351 .6703 1.005 1.341 1.676 2.011 2.346 2.681 3.016 3.351 3.686 4.022 26 .03485 .3485 .6971 1.046 1.394 1.743 2.091 2.440 2.788 3.137 3.485 3.834 4.182 27 .03619 .3619 .7239 1.086 1.448 1.810 2.172 2.534 2.895 3.257 3.619 3.981 4.343 28 .03753 .3753 .7507 1.126 1.501 1.877 2.252 2.627 3.003 3.378 3.753 4.129 4.504 29 .03887 .3887 .7775 1.166 1.555 1.944 2.332 2.721 3.110 3.499 3.887 4.276 4.665 30 .04022 .4022 .8043 1.206 1.609 2.011 2.413 2.815 3.217 3.619 4.022 4.424 4.826 31 .04156 .4156 .8311 1.247 1.662 2.078 2.493 2.909 3.324 3.740 4.156 4.571 4.987 32 .04290 .4290 .8579 1.287 1.716 2.145 2.574 3.003 3.432 3.861 4.290 4.719 5.148 33 .04424 .4424 .8847 1.327 1.769 2.212 2.654 3.097 3.539 3.986 4.424 4.866 5.308 34 .04558 .4558 .9115 1.367 1.823 2.279 2.735 3.190 3.646 4.102 4.558 5.013 5.469 35 .04692 .4692 .9384 1.408 1.877 2.346 2.815 3.284 3.753 4.223 4.692 5.161 5.630 40 .05362 .5362 1.072 1.609 2.145 2.681 3.217 3.753 4 290 4.826 5.363 5.898 6.434 45 .06032 .6032 1.206 1.810 2.413 3.016 3.619 4.223 4.826 5.439 6.032 6.635 7.239 fiO .06703 .6703 1.341 2.011 2.681 3.351 4.022 4.692 5.362 6.032 6.703 7.373 8.043 55 .07373 .7373 1.475 2.212 2.949 3.686 4.424 5.161 5.898 6.635 7.373 8.110 8.847 60 .08043 .8043 1.609 2.413 3.217 4.022 4.826 5.630 6.434 7.239 8.043 8.047 9.652 65 .08713 .8713 1.743 2.614 3.485 4.357 5.228 6.099 6.970 7.842 8.713 9.584 10.46 70 .09384 .9384 1.877 2.815 3.753 4.692 5.630 6.568 7.507 8.445 9.384 10.32 11.26' 75 .10054 1.005 2.011 3.016 4.021 5.027 6.032 7.037 8.043 9.048 10.05 11.06 12.06 80 .10724 1.072 2.145 3.217 4.290 5.362 6.434 7.507 8.579 9.652 10.72 11.80 12.87 85 .11394 1.139 2.279 3.418 4.558 5.697 6.836 7.976 9.115 10.26 11.39 12.53 13.67 90 .12065 1.206 2.413 3.619 4.826 6.032 7.239 8.445 9.652 10.86 12.06 13.27 14.48 95 .12735 1.273 2.547 3.820 5.094 6.367 7.641 8.914 10.18 11.46 12.73 14.01 15.28 100 .13405 1.341 2.681 4.022 5.362 6.703 8.043 9.384 10.72 12.06 13.41 14.75 16.09 200 .26810 2.681 5.362 8.043 10.72 13.41 16.09 18.77 21.45 24.13 26.81 29.49 32.17 300 .40215 4.022 8.043 12.06 16.09 20.11 24.13 28.15 32.17 36.19 40.22 44.24 48.26 400 .53620 5.362 10.72 16.09 21.45 26.81 32.17 37.53 42.90 48.26 53.62 58.98 64.34 600 .67025 6.703 13.41 20.11 26.81 33.51 40.22 46.92 .53.82 60.32 67.03 73.73 80.43 600 .80430 8.043 16.09 24.13 32.17 40.22 48.26 66.30 64.34 72.39 80.43 88.47 96.52 700 .93835 9.384 18.77 28.15 37.53 46.92 56.30 65.68 75.07 84.45 93.84 103.2 112.6 800 1.0724 10.72 21.45 32.17 42.90 53.62 64.34 75.07 85.79 96.52 107.2 118.0 128.7 900 1.2065 12.06 24.13 36.19 48.26 60.32 72.39 84.45 96.52 108.6 120.6 132.7 144.8 1.000 1.3405 13.41 26.81 40.22 53.62 67.03 80.43 93.84 107.2 120.6 134.1 147.5 160.9 2,000 2.6810 26.81 53.62 80.43 107.2 134.1 160.9 187.7 214.5 241.3 268.1 294.9 321.7 3,000 4.0215 40.22 80.43 120.6 160.9 201.1 241.3 281.5 321.7 361.9 402.2 442.4 482.6 4,000 5.3620 53.62 107.2 160.9 214.5 268.1 321.7 375.3 429.0 482.6 536.2 589.8 643.4 5,000 6.7025 67.03 134.1 201.1 268 1 335 1 402.2 469.2 536.2 603.2 670.3 737.3 804.3 6,000 8.0430 80.43 160.9 241.3 321.7 402.2 482.6 563.0 643.4 723.9 804.3 884.7 965.3 7,000 9.3835 93.84 187.7 281.5 375.3 469.2 563.0 656.8 750.7 844.5 938.4 1032 1126 8.000 10.724 107.2 214.5 321.7 429.0 536.2 643.4 7.50.7 857.9 965.2 1072 1180 1287 9,000 12.065 120.6 241.3 361.9 482.6 603.2 723.9 844.5 965.2 1086 1206 1327 1448 10,000 13.405 134.1 268.1 402.2 536.2 670.3 804.3 938.3 1072 1206 1341 1475 1609 INDEX Contents in serial order and illustrations and tables in alphabetical order are listed in front of book. This index includes topics, designated by heavy figures, illustrations and tables. A Page Abbreviations 2 Adapting, a design to a range of cylinder sizes 243 the pattern to different presser positions 241 Adjusting in general 160 Adjusting the yarn carrier j 171 Analogies between the flow of water and electricity 292 Analysis of designs (see also Design). determining, direction of lap 236 height 234 knitting motion . 236 possible number of feeds, table 235~ width 233 diagram of sample design, illustration 235 dimensions of sample design 235 marking limiting stitches 234 methods 232 numbers of needles to dupUcate sample, table 237 structure of sample 235 Areas of circles, table 280 B Backing (see Fleeced goods). Backward motion 1 Belt, leather, power transmission, table 289 Bobbin, Bobbins, delivery twists yarn 103 how wound 103 number, effect on lost time 96-255-260 winder, upright, capacity, table 115 yarn delivery, illustration 104 295 296 Index Page Boiler, floor-space allotment, table 118 discussion 120 Brief chronological list of important knitting inventions. . . 265 Bur, Burs, cast-off 147 compared with cast-off jack 99 invention, table 265 lander 146 sinker 140 two sinkers for two-thread work 99 C Calculation, Calculations (see also Example and Deri- vations), adapting a design to a given number of needles . . 241-242 design, figure 227 Cam, Cams, names 160 race, double 158 Cardigan fabric, variation from regular width 58 Carding, floor-space allotment, discussion 119 table 118 Carrier, yarn, adjusting . 171 Cast-off, bur 147 comparison of jack and rotary 99 Causes of lost time 70 Change of yarn with corresponding change of stitch 261 Circumferences of circles, table 280 of Wildman ribbers at back of needles, table 184 Clearing tucks (see Design and Pattern wheel). Clockwise motion, definition 1 Coal for knitting miUs, consumption per set 117 Coils (see also Yarn diameter). determination, illustration 13 per inch and haK-inch, table , 196 Conditions for high needle velocity 67 Cone, Cones, dehvery twists yarn 103 how wound 103 number, effect on lost time 96-255-260 winder, Nutaper, capacity, table 114 yarn dehvery, illustration 104 Constant, definition 1 Index 297 Page Convention, Conventions. constant, general 1 design 216 direction, anticlockwise 1 backward 1 clockwise 1 forward 1 left-hand 1 right-hand 1 fabric, bottom 15 ^ fiat, back 19 face 19 loop-wheel, fundamental relations, table .... 45 length 15 motion of knitting, table 204 rib, latch-needle, fundamental relations, table. ) . 36 top 15 width 15 ^ loop, bottom 15 held 212 top 15 tuck 212 machine, cut (needle spacing) 1 motion, table 204 pattern 210-211 speed for automatic ribbers 67 stitch, tuck 212 variable, general 1 Cost, floor-space maintenance 121-249 knitting machinery, per set 117 mill buildings, per set 117 Count, Counts, Constant-length system 187 constant-weight system 187 cotton 187 definitions, table 188 importance of topic 9 grain 187 importance of topic 9 transformation between systems 187 rules 193 table 194 298 Index Page Count, Counts, transformation within systems 188 used for different kinds of yarns 189 importance of topic .... 9 where used 190 Course, Courses, definition 14 first 15 length 15 number in tuck wale 156 per hour, determination 75 size, comparison 18 width 18 Courses per inch, and wales, product dependent on stitches. 29 compared with stitches per foot to describe fabric ... 70 formula, importance of 43 from other fabric dimensions, formula 93 maximum number, tables 40-48 regular fabrics, relation to wales 32 relation to wales for stitches constant and yarn variable 27 for yarn variable, illustration 28 Cube, Cubes, table 278 roots, table 278 Cut, Cuts (of machine) (see also Gauge and Needles per inch) . effect on economy 255 formula, importance of 41 latch-needle rib, relation to yarn 49 relation to yarn, illustration 50 meanings 1 measured on cam surface, table 175 on needle line, table 130 of hosiery machines and ribbers 138-129 range of fabric from 138 relation, to gauge 134 formula 124 to needle difference between machine sizes 243 to yarn for different machines, table . 53 to yarn number 23-25 to correspond to given conditions 257 Cut (of yarn) (see also Yarn and Count). conflict with machine cut 1 Index 299 D Page Definition, Definitions, anticlockwise 1 cams 160 clockwise 1 constant 1 course 14 cut (needle spacing) 124 design 216 diametral revolutions 2 field 216 figure 216 gauge (needle spacing) 2-124 table 127 gauge (needle thickness) 2 geometric terms 286 held loop 212 knitting 14 left-hand motion 1 twist 102 pattern 21 L power 277 right-hand motion 1 twist 101 stitch, stitches 15 per foot of yarn 19 rib 21 tuck loop 212 stitch 212 variable 1 wale 15 work 277 yarn counts, table 188 Derivation, Unear yards per hour, formula 75 of cut for given conditions 258 of diameter of yarn from yarn-cut-rule constant 55 of yarn number from given conditions 257 relation of cut and coils 23 of diameter of yarn to needle spacing 55 of gauge and cut 134 of yarn, diameter and cut 23 300 Index Page Derivation, relation of yarn number and cut 25 numbers for rib and flat machines 125 single equivalent of two or more yarns 1918 square yard production 78 weight-per-square-yard formula 92 width of fabric 17 yarn number for fabric as wide as straight machine. . . 63 Design, Designs (see Analysis of Designs, Pattern, Pat- tern wheel). adaptable cy Under sizes 244 adaptation of pattern to different presser positions 241 to a given number of needles 241 to a range of cyUnder sizes 243 arrangement, inclination 227 calculations 227 changing needles to clear tucks 245 size of presser to clear tucks 245 condition for 220 conversion of diagram into strip pattern, illustration . . . 238 definition 216 diagram 231 without plain pressers 246 double-cam-race pattern rules 158 effect of increasing needles 221 effect of lap of more than one division, illustrations. . . . 222 of motion and lap, table 226 of needle changes of more than one division 221 of reversal of lap, illustrations 222 of motion, illustrations 222 of reversing motion 220 exception to rule, illustrations 247-248 figure and field 216 fully formed, illustrations 218-219 inchned, illustrations 218-219 formation of strip pattern to represent pattern wheel. . . 239 general fundamental rule 221 generally reduced in modification 242 height 227-230 improper pattern wheel 245 inversion of figure 237 length of pattern 229 Index 301 Page Design, long-and-short-latch pattern rules 157 needles decreased 219 not readily changed 227 numerical method 223 illustrations 225 paper-strip method, advantages 223 pattern wheel represented by strip pattern, illustrations 240 possible numbers of feeds, table 235 of needles, table 237 proof of strip pattern 239 range 224 real and apparent 224 reversal of the color of the figure 216 rule for selection of lap 237 "sample, illustration 232 selection of lap j, 236 self-clearing pattern wheel 244 several seK-clearing pattern wheels 246 strip pattern, winding 217 stripes, incUned, illustrations 218-219 mixed, illustrations 218-219 vertical, illustrations 218-219 successive, incUnation 227 terminal courses should be different 231 Designing (see also Design, Pattern, Pattern wheel. Stitch). causes of figure changes 210 definition of pattern 210 learning 216 with pattern wheels, importance of topic 10 Determining weight per square yard by weighing 95 Diagram of design (see also Design and Pattern wheel). from a sample, illustration 235 of design without plain presser 246 representation of plain and tuck courses 231 terminal courses should be different 231 Diameter, of machine, effect on economy 252 of yarn (see Yarn). Diameters of Wildman ribbers from back to back of cyhn- der needles, table 184 Diametral revolutions and yarn velocity, table 159 constant 67 302 Index Page Diametral revolutions and yarn velocity, defined 2-66 for automatic work on ribbers 67 loop-wheel machine, formula 45 rib machine, formula 36 Difference between yarn velocity and needle velocity, table 159 Dimensions, of regular rib fabrics, illustration 270 of rib fabric, yarn variable, illustration 269 Direction, of lap (see Analysis and Design) . of motion (see Motion), of twist in fabric (see Fabric), of twist in yarn (see Yarn). Drying, floor-space allotment, table 118 discussion 120 heat requirement - 117 Duplication of a sample design (see Design). Economics of knitting 249 Electricity, and flow of water, analogies 292 power for rib-knitting machinery, table 122 for different volts and amperes, table 294 Element of fabric 14 Elements of knitting 14 Engine, floor-space allotment, table 118 Equivalent, of two or more yarns 192 of two yarns, table 198 Example, approximate cut of ribbers and footers, table .... 129 change in production produced by change of cut .... 255 cut to correspond to given conditions 257 derivation of yarn-rule constant 197 diametral revolutions 2-66-67 dram-silk number transformed to cotton 193 effect of yarn change on fabric 259 extent of yarn twist 102 loss of time per feed 255-262 per machine 260 minimum weight per square yard 264 needle difference between machine sizes 243 Index 303 Page Example, New Hampshire number transformed to Cohoes number 193 pounds production rib . • 260 presser diameter for 180 needles 206 production, hanks 69 in pounds from coils 44 pounds 69-260 square yards 78 relation of fabric dimensions, yarn variable 31 of wales and courses for yarn variable 27 of yarn numbers for rib- and fiat-work machines . 125 relative length of yarn used, same cut and needle velocity 87 single equivalent of two yarns 71-193 speed determination from diametral revolutions . . . 66-67 stitch effects on production and fabric : 259 the second of two yarns equivalent to a given single yarn 193 weight, of knit goods, yarn variable 43 per square yard, determination by weighing .... 95 yarn, number to correspond to given conditions 257 transformation, between systems 188 within systems 188 Examples solved with the aid of tables. approximate cut of ribbers and footers 128 gauge transformations 127 cut for a given weight per yard 92 production, Unear yards 68-75 loop-wheel, pounds from hanks 74 pounds, stitches regular 71 rib, pounds from hanks, stitches regular 71 pounds, stitches regular 71 rib-tops 82 square yards 68 for wales, courses and cut known . . 80 needles, speed and yarn known 80 two-thread, two methods 71-72 weight per square yard of fiat fabric 92 Explanation of convenient equations for determining the number of yarn 190 of formulas for regular rib fabrics 36 304 Index Page Explanation of regular flat-fabric formulas 45 of yarn-transformation table 193 F Fabric, Fabrics (see also Production). as wide as machine, formulas, table 56 bottom, definition 15 changing characteristics 26 characteristics, how determined 29 circular, ribbon structure illustrated 202 determination of good fabric 26 distortion due to tuck stitches 213 first case, stitches constant, yarn variable 27 flat, back, distinguished 19 back, illustration 17 edges, curhng tendency of flat and rib 20 elasticity, flat and rib compared 20 face, distinguished 19-201 illustration 16 loop-wheel, hanks, table 74 raveling, flat and rib compared 20 regular, dimensions, table 48 fundamental formulas 45 general formulas 46-47 rule for twist 107 structure, comparison of flat and rib 19 thickness per inch, table 48 thicknesses per inch, table 48 twist caused by yarn twist 107 importance of topic 9 with self -feeding needles 101 weight per square yard, table 90 width, flat and rib compared 20 formula for weight per yard, importance 43 foundation principles 26 from different machines, width variation 58 length, defined 15 of yarn in square yard, stitches constant 31 minimum weight per square yard 363 illustration 264 Index 305 Page Fabric, motion, classified, table 204 conventions 199-201 of different yarn size but same characteristics 21 of same yarn size but different characteristics 22 open work, invention, table 265 pattern 199 production, topic 66 range from the same gauge or cut, illustrations 138 importance of topic ... 7 regular, relations, illustration 33 relation of wales and courses 32 of width and height, yam variable 30 illustration 30 relative width from different machines, rule 66 rib, dimensions, yarn variable, illustration 269 edges, curling tendency of flat and rib ] 20 elasticity, flat and rib compared 20 illustration ; 19-21 raveling, flat and rib compared 20 regular, dimensions 40 illustrations 27(L explanation of formulas 36 fundamental formulas 36 general formulas 38-39 structure, comparison of flat and rib 19 thicknesses per inch, table 36 thickness, table 40 twist, illustration 112 importance of topic 9 weight per square yard, table 90 width, flat and rib compared 20 second case, yarn constant, stitches variable 32 stitches per pound 92 per square yard, formula, derivation 89-92 tight rib illustration 21 strength 274 summary regarding twist, importance of topic 9 theory 266 importance of topic 11 third case, yarn diameter inversely proportional to stitches 32 306 Index Page Fabric, three general cases 26 top, defined 15-199 twist, illustration 107 minor causes Ill not dependent on machine motion Ill summary 113 various, width variation from rule 58 weight per square yard formula 92-93 for different yarn counts 94 stitches constant 32 width, defined 15-17 formulas, various 17 from different machines, importance of topic ... 7 table 65 topic 63 of flattened tube, table 59-62 topic 57 various formulas 18 Factors of production, general 66 linear yards 70 Feeds and pattern divisions for 24 courses, table 235 effect on economy 70-255-260 maximum number 67 number in set 116 to produce a given design, table 235 Field, of design, definition 216 Figure designing with pattern wheels 199 definition 216 dimensions 235 inversion. 237 inverted by lap and motion, table 226 structure 235 tuck, illustration 232 white block in mixed field, illustration 215 Finishing and seaming, floor-space allotment, table 118 discussion 120 required proportion of mill power, table 123 First course 15 Fleeced goods, flat, invention, table (see also Machine, loop-wheel) . . . .' 265 production, method of calculating 74 Index 307 Page Fleeced goods, flat, yarn for different gauges 138 table 139 Floor-space in knitting mills, allotment, conclusions 121 per set, explanation 119 cost of maintenance 121 table 118 Footer (see Machine, automatic hosiery). Formation of loop 15 Formula, Formulas (see also Derivations). courses, from other fabric dimensions 93 cut, relation to coils 23 to gauge 125 to needle spacing 23 diameter of yarn for fabric as wide as straight machine 63 fabric, fabrics, fiat, regular, fundamental, table 45 regular 271 rib, regular, fundamental, table 36 stitches constant and yarn variable 268 weight, minimum per square yard 264 width in various terms 17 - of flattened tube in various terms 18 production, relative for proportional change of yarn and stitch 262 rib, ten hours 259 without constants 252-261 stitches per foot from other fabric dimensions 93 rib, maximum number 186 minimum number 186 'per pound of fabric 92 per square inch, relation to yam number .... 81 per square yard of fabric 89-92 ■ wales, from other fabric dimensions 93 weight per square yard for different yarn counts .... 94 importance of topic 8 single thread 92 two-thread, different stitch ... 93 same stitch 93 width of fabric equal to machine width, table 56 winder capacity, Nutaper, table 114 upright, bobbin, table 115 308 Index Formula, yarn, diameter, from the yarn-cut rule 55 relation to cut 23 to needle spacing 23 number, relation to yarn size, illustration 24 for fabric as wide as straight machine . 63-65 for fabric width equal to machine diam- eter 64-65 from other fabric dimensions 93 relation to gauge for backing, loop-wheel 139 to latch-needle cut, illustration 50 to spring-needle gauge, illustra- tion 52 table 191 relation of number and cut 25 and diameter 25 to cut for different counts 195 to gauge for different counts 195 single equivalent of two, importance 10 of two or more 192 the second of two equivalent to a given single yarn 192 Forward motion defined 1 Functions, trigonometric, natural, table 282 G Garments, weight per dozen, stitches constant 32 Gauge (needle spacing) definitions, table 127 different standards 125 needles per inch, table 126 explanation : 2 range of fabrics from 138 relation to cut 124 to yarn for different machines, table 53 spring-needle loop-wheel, relation to yarn 52 Gauge (needle thickness) explanation 2 H Hanger friction 122 Hanks, explanation 24 production, factors 70 Index 309 Page Hanks, production, latch-needle rib, table 73 loop-wheel flat, table 74 Heat for knitting mills, cost per set 117 Height (see the subject of which the height is desired). Help, effect on economy 254 Hooking fabric on ribber 164 Horse power (see Power). I Illustrations (see the subject in this index, also separate hst at front of book). Incandescent mantle pattern 155 Inch, fractions, decimal equivalents, table 277 Inventions, knitting, important, table 265 Inventors, knitting, important, table 265 Inversion of tuck figure 237 J Jack, cast-off, comparison with rotary cast-off 99 sinker bur, inventions, table 265 sinker machine (see Machine). K Knitting and winding, floor-space allotment, table 118 definition 14 economics 249 importance of topic 11 elements, importance of topic 5 flat, trouble, cause and remedy 150 floor-space, discussion 119 inventions, brief chronological hst 265 machine, expense 250 operator, expense 251 required proportion of mill power, table 123 rib, trouble, cause and remedy 171 rules, practical variations, importance of topic 6 space, expense 249 yarn damage, expense 250 310 Index L Lander bur j^g Lap (see Pattern, Analysis and Design). Left-hand motion defined i twist, illustration (see also Fabric and Yarn) 102 explanation 2Q2 Length (see the subject of which the length is desired). Linear yard (see Yard, linear). Locating sources of trouble in rib-knitting 167 Loop, Loops, bottom n^ distortion caused by yarn twist 105 floated 213 formation 15 held, illustration 211-212-213 must be cleared 214 length, relation to stitches per foot 19 needle 15 illustration iq normal, illustration . 106 sinker 15 illustration 16 structure, influenced by yarn resilience 35 top-- • 15 tuck, is kept out of face of fabric 214 single and double, illustration 212 illustration 211 two-thread, on latch needle, illustration 100 on spring needle, illustration 97 which causes left-hand- twist fabric, illustration 106 right-hand-twist fabric, illustration ... 106 Lost time, causes of 70 effect of change in the number of feeds 255-260 in two-thread work due to the extra threads. . . 96 M Machine, Machines (see also Ribber). adjusting in general 160 automatic hosiery, convenient cut calculations 138 fabric width, proportion of diameter, table 65 Index 311 Machine, fabric width, variation from theoretical 58 yarn-cut rule, similarity to loop-wheel rule 49 table 53 yarn diameter, for fabric width equal to machine diameter 64 proportion of needle spacing, table ; . . . 56 illustration ... 57 yarn number, for fabric width equal to machine diameter 64 circular latch-needle for flat work. fabric width, proportion of machine diameter, table 65 variation from theoretical 58 production, linear yards, table 76 square yards, needles, speed and yarn known, table 81 wales and courses known, table 79 yarn-cut rule, table 53 yarn diameter for fabric width equal to machine diameter 64 proportion of needle spacing, illustration 57 table 56 number for fabric width equal to machine diameter 64 circular spring-needle loop-wheel. cast-off bur 147 diametral revolutions per minute 49 fabric, dimensions, table 48 width, variation from rule 58 fundamental formulas, regular fabric 45 gauge, table 126 general formulas, table 46-47 invention, table 265 knitting motion classified, table 204 lander bur 146 length of needle line filled by one foot of yarn ... 70 needle, needles, dimensions and data, table 149 in cylinder, table 154 ^^elocity 159 with two-thread loops, illustration 97 number in set 116 312 Index Page Machine, circular spring-needle loop-wheel, power require- ment, table 123 production, comparison with rib machines, tables 85-87-88 in hanks, table 74 linear yards, table 76 relative to latch-needle rib machine 84 square yards, needles, speed and yarn known, table 81 wales and courses known, table .... 79 proportion of yarn diameter to needle spacing, table 56 sinker bur 140 speed for balbriggan and for fleece 49 trouble, cause and remedy 150 weight of leaded needles per thousand, table .... 149 width of flattened tube of fabric, table 59 yarn-cut rule, table 53 yarn-gauge rule, table 53 yarn-gauge rule, illustration 52 table 53 yarn, for different gauges, table 129 velocity 159 circular spring-needle rib. fabric width, proportion of machine diameter, table 65 production, linear yards, table 76 square yards, for needles, speed, and yarn known, table 81 wales and courses known, table 79 yarn-cut rule, table 53 yarn, diameter, for fabric width equal to ma- chine diameter 64 proportion of needle spacing, illustration 57 of needle spacing, table 56 number, for fabric width equal to machine diameter 64 diameter, effect on economy 252 different, relative width of fabric 63 effect on economy 254 expense, knitting 250 inventions, table 265 Index 313 Page Vlachine, motion, effect on fabric twist 108-111 effect on yarn revolution in feeding Ill rib body, fabric width, variation from rule 58 performance, table 185 power 122 shop, floor-space allotment, table 118 straight jack-sinker. fabric width, proportion of diameter of machine, table * 65 invention by WiUiam Lee, table 265 method of casting-off compared with that of bur 99 needle with two-thread loops 97 production, linear yards, table 76 yarn-cut rule, table 53 yam-gauge rule, table 53 yarn, diameter, for fabric as wide as machine, rule 63 proportion of needle spacing, illustration 57 of needle spacing, table 56 number for fabric as wide as straight machine, rule 63 warp, machine, invention, table 265 - course, definition 14 which does not twist yarn, illustration 110 which twists yarn, illustration 109 Machinery, knitting mill, cost per set 117 Measures, length, weight, work, power 277 ^lensuration, plane surfaces 386 klill, Mills, knitting, buildings, cost per set 117 coal consumption 117 floor space 117 table 118 power requirements, table 122 proportionate distribution of power, table 123 water consumption 117 klinimum weight per square yard 363 ►lotion, anti-clockwise, defined •, 1 illustrated 200 backward, defined 1 clockwise, defined 1 fabric, rule , 202 forward, defined 1 314 Index Pai Motion, knitting, table 2C conventions IS illustrations 2C determination from figured fabric 23 left-hand, defined machine, effect on yarn revolution in feeding 11 on fabric twist 11 right-hand, defined winding, cone 10 bobbin 10. Mule spindles, number per set 11' N Names of cams 16( Napping, floor-space allotment, discussion 12( table 11^ Needle, Needles. allowable change in leaded-needle machines 227 cylinder, used to designate fineness of fabric or machine 21 difference in number between cylinder sizes 24c double sets 2C| gauge (spacing) different standards, table 12C in pattern to duplicate a given design 241 in Tompkins loop-wheel cylinders 154 latch, average total circular travel, table 185 vertical travel, table 185 invention, table 265 total reciprocations, table 185 with double loop, illustration 100 leaded, weight per thousand, table 149 loop, definition 15 number, changed to clear tucks 245 in cylinder, adapted to designing 244 to duplicate a sample, table 237 per inch, effect on economy 255 measured on cam surface, table 175 on needle line, table 130 of hosiery machines and ribbers 128 simple calculations, table 129 putting into ribber 161 Index 315 Page Needle, space, net, for different gauges, table 149 spacing for different gauges, table 149 proof of relation to yarn diameter 22 relation to yarn diameter 22-53 illustration 57 is elastic 23 table 56 spring, dimensions and data, table 149 with double loops, illustration 97 twist in fabric produced by self-feeding needles 101 with long and short latches 156 dumber. Numbers (see also Yarn and Count). meaning in this book 1 squares, cubes, square roots, cube roots 278 Numerical method of designing ^23 O >ffice, floor-space allotment, table 118 Operating, loop-wheel machine (see Machine, loop-wheel). ribber (see Ribber). Operative expense, knitting 251 P 'acking, floor-space allotment 118 'attern, Pattern (see also Pattern wheel and Designing). adapting to different presser positions 241 definition 210 derived from design, illustration 238 designing 199 exception to rule, illustrations 247-248 lap, effect, table 226 latch needle 153-203 length, limitations 229 strip, conversion into presser model 239 proof 239 representing pattern wheel, illustrations 240 wheel, latch-needle, selector, description 207 *attern wheel, spring needle. advantages of making in mill 206 allowance over pitch diameter 207 316 Index Pag Pattern wheel, and yarn relation 21( description 20t material 20J must count needles 20^ pitch diameter 20/ positions 20£ illustration 20t printing with needles 21C relation of diameter and cuts 206 represented by paper ring 209 by strip pattern 239 illustrations 240 self-clearing 244 several 246 diagram, illustration 246 size, changed to clear tucks 245 limitations 208 relation to number of patterns 208 special, where made 206 strip, winding 217 tip, to keep in position 207 Performance of a latch-needle rib-body machine, table 185 Picking, floor-space, relative to carding and spinning 119 allotments, comparison 119 table 118 Plating (see also Two-thread knitting) 95 Plush (see Fleeced goods). Pounds (see Production). Power, electrical, table 294 for knitting mill, cost per set 117, table 122-123 for spring-needle loop-wheel machines 123 knitting machine, invention, table. 265 proportionate distribution in a knitting mJll, table 123 required by latch-needle rib machines, table 122 by upright bobbin winder, table 122 by various machines used in knitting mills 121 transmitted by leather belt, table 289 by shafting, table 288 Practical variations from knitting rules 34 Preface iii Index 317 Presser (see also Pattern wheel). interference with lander bur I47 plain, like raising cam 207 positions, different, adaptation of pattern 241 Production, dozen pairs per hour, rib tops, table 82 factors gg hanks, how found jO loop-wheel flat fabric, table 74 rib machine, example 7I table 73 linear yards, example 75 explanation of table 74 factors 7Q table 76-77 methods of calculating, subject 68 hanks 59 importance of topic 7 pounds 69 yards, linear 68 square 68 of circular knitting machines 6^ pounds, fleeced-underwear fabric, method of calcu- lating 74 for corresponding change of yarn and stitch 261 formula, importance 43 of an average rib machine, table 185 rib fabric, explanation of general table 70 general table 72 rib machine, 7.5 hours 252-261 winder, Nutaper, table 114 upright, bobbin, table II5 relative, of different types of knitting machines 84 importance. 8 of rib and flat-work machines, tables 85-87-88 rib-tops, table 02 square yard, derivation 78 example for table for cut known 80 explanation of table for yarn, needles and speed known 80 formula, importance 45 how found 7q 318 Index Page Production, square yard, stitches constant 31 table, for cut known 79 for yarn needles and speed known. .... 81 total of an average rib machine 185 two methods for two-thread work 71-72 units 66 Proportion of needle spacing to yarn diameter, table 56 Putting needles into ribber 161 R Range of fabrics from the same gauge or cut 138 Raw stock, floor space allotment, table 118 Regular fabrics (see Fabrics). Relation, Relations, of machine gauge and cut 124 of the diameter of the yarn to the needle spacing .... 53 of rib-fabric dimensions for stitches constant, illus- tration 269 of yarn number and diameter and machine cut 24 Relative production of different types of knitting machines. 84 Revolutions (see also Diametral revolutions). per minute, effect on economy 252 Rib fabric. Rib fabrics (see also Fabric). cardigan, width variation from rule 58 elasticity, compared to flat 20 hanks production table 73 illustration of face 19 non-curHng of edges 20 pounds-production, explanation of table 70 . table 72 ravehng 20 regular, dimensions, table 40 explanation of formulas 36 fundamental formulas 36 general formulas, table 38-39 relations, regular, illustration 270 yarn variable, illustration 269 structural difference from flat fabric 19 tuck, width variation from rule 58 twist, illustration 112 importance of topic 9 Index 319 ., » . Page Lib fabric twist, summary 113 weight per square yard, explanation of table 92 table 90-91 width, compared to flat 20 of flattened tube, table 59 proportion of machine diameter, table 65 topic 57 variation from rule 5g ib stitch, dimensions (see also Stitch) 21 illustration 21 Jb tops, dozen pairs per hour, production table 82 explanation of production table 82 ibber. adjusting in general 160 the yarn carrier 171 circumferences, Wildman, at back of needles, table 184 convenient method of calculating the cut i;28 cut (see Cut). diameters, Wildman, back to back of needles, table .... 184 diametral revolutions 36-67 fabric width proportion of diameter, table 65 variation from rule 58 hooking-on fabric 164 locating sources of trouble 167 needle velocity, table I59 patterns (see Patterns). power, table 122 production, comparison with k)op-wheel machine, tables 85-87-88 hnear yards, table 76 production, relative to loop-wheel machine 84 rib-tops, table 82-83 square y^irds, needles, speed and yarn known, table 81 wales, courses and cut known, table 79 putting needles in 161 stitch adjustment 168 summary 170 take-up 166 yarn rule, table 53 cut rule, chart, explanation 49 illustration . 50 320 Index Pag Ribber yarn, diameter, for fabric width equal to machine diameter, rule 6- proportion of needle spacing, illustration 5- table 5t; number for fabric width equal to machine diameter, formula . 64 rule 6^ for different cuts, table 16c velocity, table 15^ Right-hand, applied to motion meaning ] twist (see Yarn and Fabrics). Rule, Rules (see also Formulas). adjustment of yarn carrier 171 approximate cut of ribbers and footers 128 designing, exception, illustrations 247 direction of flat fabric twist, self-feeding needles 116 of lap 237 of rib-fabric twist 113 of twist in yarn delivery 113 extent of twist in yarn delivery 113 fabric motion 202 height of design 227 length of loop next to tuck stitch 214 of yarn in square yard, stitches constant 31 machine which does not twist yarn or fabric 108 minimum weight per square yard 264 positions of yarns for plating, illustrations 97-100 pattern effects with double cam race 158 with long and short latches 157 practical variations 34 importance of topic 6 production, square yard, stitches constant 31 range of designs 224 relation of diameter of yarn to needle spacing 22 of width of rib and flat fabrics 20 of yarn-cut-rule constant and yarn diameter 55, to needle spacing 55 number and cut 26 i and diameter 25 j numbers for rib and flat machines 125 1 relative length of yarn used, different cuts 88 Index 321 Page Rule, relative length of yarn used, same cut and velocity. 87 width of fabric from different machines 66 reversal of the color of tuck figure 216 revolution of yarn in seK-feeding needles 105 single equivalent of three or more yarns 193 of two yarns 192 stitches of different characteristics 22 stitch proportions for corresponding fabrics 21-22 thickness of fabric 26 tuck presser design, fundamental 221 twist in flat fabric 108 width of flattened tube or fabric 18 of wale 26 yarn-cut, yarn-gauge, different machines, table 53 diameter for fabric as wide as straight machine ' 63 width equal to machine diameter. ... 64 for flat cotton fleeced goods 139 number for fabric as wide as straight machine 63 width equal to machine diameter 64 S Sample design (see Analysis and Design). Seaming and finishing, floor-space allotment, table 118 discussion 120 required proportion of mill power, table 123 Set, appHed to knitting miUs 116 Sewing machines, number per set 116 Shafting (see Hanger and Power). power transmission, table 288 Single equivalent of two or more yarns 193 Sinker-blade, discussion 142 I thickness, loop-wheel, table 149 Sinker bur 140 Sinker loop 15 Space allotment in knitting miUs 117 Space, between needle and blade, loop-wheel, table 149 floor, allotment in knitting mills, table 118 knitting, expense 249 floor, cost of maintenance 121 ?peed (see also Diametral-revolutions and Velocity). 322 Index Page Speed, condition for high speed 67 effect on economy 252 of shafting, table 288 Spindle, Spindles, mule, number per set IIG power per 100, table 121 winder, number per set 116 Nutaper, capacity, table 114 formulas, table 114 speed 114 upright bobbin, capacity, table 115 formulas, table 115 speed 115 Spinning, floor-space allotment, table 118 relative to picking and carding 119 Square roots, table 278 Square yard (see Yard). Squares, table 278 Standards (see Gauge, Cut, Motion, Diametral-revolutions). Stitch, Stitches. accordion, method of knitting 157-158 adjustment 168 definition 15 distortion in the formation 35 double-tuck, illustration 212 effect on economy 254 flat, plain, illustration of face 16 marking for design analysis " 234 number made by an average rib machine, table 185 per pound-, formula 92 of different characteristics 22 of same characteristics 21 per foot of yarn . and yarn diameter determine characteristics of fabric 29 constant, yarn diameter varied 27 counting, in sample 234 effect on economics 259 flat, for different yarn numbers, table 48 formula, importance of 42 from other fabric dimensions, formula 93 in the three general fabric cases 26 Index 323 Page Stitch, per foot of yarn includes stitches on cyhnder only. 21 length occupied in machines 68-70 maximum and minimum, table 186 relation to length of yarn in loop 19 to weight per yard and yarn number, table ... 90 rib, for different yarn numbers, table 40 varied, j^arn diameter constant 32 per hour, determination 78 per inch, counting 168 per needle, of an average rib machine 185 per square inch, relation to yarn number 81 for different rib-machine cuts, table 79 rib, dimensions 21 face, illustration K 21 greatest number per foot of yarn, table 186 least number per foot of yarn, table 186 side, illustration 21 ribber, adjustment 168 summary 170 short, for concealed yarn in plated work 99 twist more than long 98 single-tuck, illustration 211 structure, dependent on yarn resilience 35 tuck, adjoining in one course, illustration 213 description 211 distort fabric 213 hmits 214 representing on paper 230 Storage, finished goods, floor space discussion 120 floor-space allotment, table 118 raw stock, floor-space discussion 119 Straight machine (see Machine). Strength of knit fabrics 274 Strip pattern (see Design and Pattern). Stripes (see also Design and Pattern). inchned by lap and by motion, table 226 Suggestions for a course of reading 2 Summary regarding twist of knit fabrics 113 Suppositions of Elements of Knitting 16 324 Index Tables (see the subject in this index, also separate list at front of book). Take-up, ribber 166 Theory of knit fabrics ^66 general considerations 212 suggestions 11 Thickness of fabric, flat, table 48 rib, table 40 Thicknesses of fabric per inch, flat, table 48 rib, table 40 Thread (see Yarn). Time, lost, causes 70-255-260 in different units, tables 285 Trigonometric functions, natural, table 282 Trouble, cause and remedy, loop wheel 150 ribbers 171 in rib knitting, locating sources 167 Tuck fabric (see also Fabric), rib, width variation from theoretical 58 Tuck figure (see also Design). white block in mixed field, illustration 215 Tuck stitch (see also Stitch). figures, latch-needle 153 Twist in fabric caused by yarn twist 107 effect of machine motion 108-111 flat-fabric, made with self-feeding needles 101 rule.... 108 minor causes Ill rib 112 right-hand, illustration 107 summary, flat 116 general 113 rib 113 Twist in yarn. affected by dehvery from yarn package 103 determining extent 102 extent 102 illustration with strip of paper 102 influence of knitting machine 108 Index 325 Page Twist in yarn, left-hand 102 loop-distortion effect, illustrations 105-106 right-hand 101 Two-thread knitting. advantages 95 casting-off from spring needle 99 comparison of jack and rotary cast-offs. 99 disadvantages 96 helps to spring-needle plating 98 importance of topic 9 latch needle, illustration 100 locating causes of defects 97 plating 96 inside of rib fabric 101 silk and worsted 98 position of threads in spring needle 9^ in latch needle, illustration 100 reduction of fabric twist 113 rolUng of yarn by rotary sinker 58 separating the threads in feeding 97 short stitch for concealed yarn 99 stitches twist more than long stitches 98 spring needle, illustration 97 topic 95 tracing trouble 101 treatment of yarn 98 two holes in carrier 101 sinker burs 99 yarn difficulties 98 Types of machines (see also Machine). Cotton 24-53 Fouquet .r. . . 24-202-265 V Variable, defined 1 Variation of yarn number on rib machine 67 Velocity (see also Diametral-revolutions and Speed). difference between that of yarn and needles, table 159 high, conditions for 67 of needles in knitting machines, table 159 of yarn feeding into knitting machine, table 159 326 Index Page Vertical patterns in latch-needle knitting 155 suggestions 11 W Wale, Wales, definition 15 per inch 18 and courses, product, dependent on stitches 29 formula, importance of 43 from other fabric dimensions, formula 93 relation to courses, regular fabrics 32-36-45 for stitches constant and yarn variable 27 for yarn variable, illustration 28 size, comparison 18 width, illustration 16 in terms of yarn diameter 17 Washing, floor-space allotment, table 118 general allowance 1 19 heat requirement 117 required proportion of mill power, table 123 Water, for knitting mill, consumption 117 Weight per square yard, determined by weighing 95 formula, derivation 89 minimum 363 illustration 264 of knit goods, stitch constant 32-43 table 90-91 two yarns with dilTerent stitches, formula 93 with the same stitches, formula 93 Wheel, pattern (see Pattern). Width of fabric from different machines 63 of flattened tube of fabric for different numbers of needles and yarn 57 table 59 Willkomm, Gustav 22-26-53 Winder, capacity, Nutaper, table 114 upright bobbin, table "... 115 power, upright bobbin, tables 121-122 spindles, number per set 116 Winding and knitting, floor-space allotment, table 118 Index 327 Page Winding and knitting, floor-space discussion 119 effect on economy 253 required proportion of mill power, table 123 Y Yard, linear production, example 75 explanation of table 74 factors 70 table 76-77 square, determining weight by weighing 95 importance of topic. . . 8 minimum weight 363 importance of topic 11 of cotton rib fabric, explanation of weight, table .... 92 weight, table 90 production, derivation 78 example, wales and courses given 80 factors 70 general table 79 regular table 81 explanation 80 stitches constant 31 total of an average rib machine, table 185 weight, formula, derivation 89 flat fabric, from table 92 formula for different yarn counts 94 single-thread 92 transformations 93 two-thi"ead, different stitch 93 same stitch 93 stitch constant, proportioning 32 Yarn, Yarns, carrier, adjusting 171 conditions of feeding 104 confusion between multiple-ply and multiple-thread 189 consumption, in miles by an average rib machine, table. 185 length, relative, two machines 88 counts (see also Count, yarn) 187 count definitions, importance 9 counts used for different kinds of yarn 189 diameter 13 328 Index Page Yarn diameter and coils, table 196 stitches per foot determine characteristics of fabric 29 constant, stitches per foot varied 32 distortions 34 for fabric as wide as straight machine, rule 63 width equal to machine diameter 64 formula, importance 41 from yarn-cut rule, formula 55 rule 55 in the three general fabric cases 26 proportion of needle spacing, illustration 57 table 56 proportional to stitch dimensions in corresponding fabrics 21 relation, to cut 23 to needle spacing 22-53 illustration 57 importance of topic 7 is elastic . 23 proof 22 rule 55 table 56 relative, for flat and rib machines 125 topic, importance 5 varied, stitches per foot constant 27 difficulties, in two-thread work 98 direction of revolution not determined by machine. ... Ill effect on economy 253 exchanged at tuck and plain feeds 216 length fed in equal needle travel, formula 87 in fabrics of the same or different characteristics .... 22 in square yard, stitches constant 31 of one foot in needle, fiat and rib 70 making, required proportion of mill power 123 number, numbers, convenient equations for determining, table 191 effect on economy 257 for fabric as wide as straight machine, formula 63 rule 63 width equal to machine diameter, formula .... 64 rule 64 Index 329 Page Yarn for flat cotton fleeced goods, table 139 for latch-needle rib machines 163 illustration 50 for loop-wheel machines 129 illustration 52 formula, importance of 41 from other fabric dimensions, formula . . 93 meaning 1 one of two equivalent to a given single yarn, table .... 198 possible variation, rib machine 67 proportional to square of cut 67 relation, to cut 25 to loop-wheel-machine gauge, illustration 52 to rib-machine cut, illustration 50 to stitches per square inch, formula 81 to weight per yard and stitches, table ^0 relative, for flat and rib machines 125 rule, rules, for different machines, table 53 yarn counts, discussion 1^3 for flat cotton fleeced goods 139 for one of two yarns equivalent to a single yarn . 192 for relation to cut and gauge, importance 6 rib-cut 49 to gauge, loop-wheel 51 for single equivalent of two yarns 192 of three or more yarns 193 single equivalent, derivation of formula 192 example 71 of two yarns, table 198 to correspond to given conditions 258 transformation table, importance. . ; 10 variable, fabric relations, illustration 269 ply, numbering 189 relation to pattern wheel 216 resilience affects loop structure 35 revolved in feeding 105 shape 34 silk, plating 98 space between needle and blade, loop wheel, table 149 stitches per foot 19 strength, explanation .- 274 330 Index Page Yarn strength, fundamental formula 36-274 suppositions for mathematical discussion 16 twist due to delivery, illustration 104 makes it revolve during feeding 104 twisted by knitting machine 108 during delivery from bobbin or cone 103 velocity, less needle velocity, table 159 table 159 ways to control 98 worsted, plating 98 £lB^ 20 IS^O Wildman Mfg. Co. Circular Rib Knitting Machinery Automatic Stop Motions Electric Cloth Cutters NORRISTOWN PENNSYLVANIA U. S. AMERICA TRADE MARK