Methods for the Measurement of Certain Character Properties of Raw Cotton

TECHNICAL BULLETIN NO. 545 JANUARY 1937

METHODS FOR THE MEASUREMENT OF CERTAIN CHARACTER PROPERTIES OF RAW COTTON

HOWARD B. RICHARDSON Associate Cotton Technologist T. L. W. BAILEY, JR. Assistant Cotton Technologist and CARL M. CONRAD Cotton Technologist Bureau of Agricultural Economics

For sale by the Superintendent of Documents, Washington, D. C; --_ - Price IS < FOR INSERTION IN TECHNICAL BULLETIN NO. 545: ■ AlETHODS FOR TEE MEASUREMENT OF CERTAIN CHARACTER PROPERTIES OF RAif/ COTTON

(Published by the U. S. Départirent of AgricultiJire)

CORRECTION SHEET

Page 56, par. 3, transpose to end of preceding section« Page 60, first line under new section, after thickness read "to" for "the". Page 74, last par., line 6, read minus sign before parenthesis of middle term. Page 75, line 3, read "16" in place of "17"; table 19, last colijimn, read exponent 2 outside of parenthesis at head of column; first line below table, read "16, p, 47" for "17," p. 50",- in formula at bottom, of page, enclose in parentheses quantity under radical after p^ and follow by exponent 2. ^' TECHNICAL BULLETIN NO. 545 JANUARY 1937

UNITED STATES DEPARTMENT OF AGRICULTURE WASHINGTON, D. C.

METHODS FOR THE MEASUREMENT OF CERTAIN CHARACTER PROPERTIES OF RAW COTTON^

By HOWARD B. RICHAEIXSON, associate cotton technologist ; T. L. W. BAILEY, Jr., assistant cotton technologist; and CARL M. CONRAD, cotton technologist, Bureau of Agricultural Economics

CONTENTS Page Pag(] Introduction 1 Estimation of fiber—Continued. Determination of the strength of raw-cotton Previous methods for determining fiber fibers by the improved Chandler bundle fineness _-_ 36 method 3 Choice of a basic method 39 Methods of measuring strength of raw Special features of the improved method.. 43 cotton 4 The standardized technique 45 Summary 53 Advantages of the Chandler bundle Improvements in the Clegg method for deter- method 6 mination of "immaturity count" as a Technique of the modified Chandler measure of fiber maturity in raw cotton 54 method 6 Previous methods of measuring fiber ma- Experimental basis of the modified Chan- turity 55 dler method 17 Determination of the fiber immaturity Precision of results 31 count 57 Precision of immaturity counts 64 Practical application of the method 33 Summary 65 Summary 34 General summary 67 Estimation of fiber fineness in raw cotton Literature cited 68 with special reference to improvements in Appendix 72 the method of determining weight per unit Derivation of the formula for error of of length _. 35 mean weight per inch ..- 74

INTRODUCTION It is generally recognized that the "character" properties of raw cotton are, as a whole, very important in determining the properties of yarns and fabrics. Character properties mean those properties of the cotton fiber, other than length, which in various combinations give to the cotton classer impressions as to the body, strength, uniformity, silkiness, etc., of the cotton. Although the importance of the character properties as a whol© is generally recognized, the exact number and nature of the individual properties that comprise character and the relative importance of each are still obscure. The obscurity is due to a scarcity of exact data which would make it possible to recognize the effects of different

1 These studies are a part of the program of work of the Cotton Utility and Standards Kese3,rch Section under the leadership of Robert W, Webb, 1 2 TECHNICAL BULLETIN 5 45, U. S. DEPT. OF AGRICULTURE properties and to unravel their interrelationships. The science of cotton-fiber technology is scarcely more than 15 years old. Even 3^et desired yarn properties are obtained principally by empirical methods, by trial and error. To some extent the long and intimate experience of many spinners has led to a certain degree of success in predicting the yarn and fabric properties obtainable from a given raw cotton. But spinners of long experience frequently are mistaken in these judgments. What are needed are more exact methods for measurement and expression whereby certain predictions of yarn properties can always be made on the basis of the known properties of raw cotton. Character is especially important in cottons that are to serve special uses, as in fine yarns, tire cords, and fabrics; fabrics for airplane wings, fuselages, parachutes, and balloons; belts, conveyors, ropes, sewing thread, and typewriter ribbons; and bags for agricultural products. Very definite manufacturing and test specifications are imposed in regard to most of these products, and these specifications can be met only by certain carefully selected cottons. The properties of the raw cotton are nothing more than the summated individual and interacting properties of the individual fibers. Because of the smallness of the fiber and of its great variability within a given sample and from sample to sample, the accurate measurement and expression of composite fiber properties have proved to be extremely tedious and difficult. A full knowledge of the relation between fiber properties and yarn properties must await practicable methods of measuring and expressing each. Because of the time required to obtain reliable averages of most of the fiber properties, compromises have usually been made between reliability and expediency. Although a host of investigators have given much thought to methods of reducing the time required to measure the different properties of a sample of cotton, at the same time securing reasonable accuracy, the methods available at present are not only slow but are comparatively inexact. Until reasonably accurate methods are available, little progress can be expected in determining what fiber properties are important for yarn and fabric quality, and what are their individual and combined effects. Kecently, methods for the measurement of three of the character properties now generally recognized ^ have been the subject of special study in the technological laboratories of the Bureau of Agricultural Economics. These concern the measurement of raw-cotton strength, fineness, and maturity. In each case, a critical review of the literature dealing with methods for measuring the property in question has been provided as a background for understanding the present recommended procedures. The detailed technique for measuring these fiber properties and expressing the results have been worked out in such a way as to provide not only the required specifications, but also the necessary detailed information for those who desire to use them. Some success has been attained in reducing the time require- ments per test but it is believed the principal advantages of the proposed methods will lie in their improved accuracy.

2 CONRAD C M and WEBB, R. W. THE PROBLEM OF CHARACTP^R STANDARDIZATION IN AMERICAN RAW' COTTON, U. S. Dept. Agr., Bur. Agr. Econ. 1935. [Mimeographed.] MEASUREMENT OF CHARACTER PROPERTIES OF COTTON 3

DETERMINATION OF THE STRENGTH OF RAW COTTON FIBERS BY THE IMPROVED CHANDLER BUNDLE METHOD ^ Among the character properties, probably none is more important than strength. Strength is an important element of quality in all yarns and fabrics but it is especially important in many products intended to be used for special purposes, including such mechanical fabrics as belts, conveyors, bags for agricultural and commercial products, sewing threads, ropes, and tire cords and fabrics, and such special fabrics as those for airplane wings, fuselages, parachutes, balloons, and fine goods. The quantities of cotton and the values of the manufactured fabrics used annually in the tire industry alone, are shown in table 1, the figures being taken from recent volumes of the biennial census of manufactures (66),'^

TABLE 1.—Quantity of raw cotton used in the United States hy the tire industry and value of manufactured fahr íes during different years

Value of Eaw Raw Value of Year cotton manufac- manufac- tured fab- Year cotton used 1 used 1 tured fabrics rics

500-pound 500-pound bales Dollars bales Dollars 1919 371, 979 175, 688,152 1927 464, 360 80,974,199 1921___. 226, 464 101, 652, 434 1929 589, 420 111,720,812 1923 569, 709 106, 079, 633 1931 323, 295 41, 249,898 1925 445, 518 105, 625, 894

^J' 9,^lculated from total pounds of tire fabric produced in the United States as reported by the Bureau of the Census (66), allowing 15 percent for tare and loss in manufacture.

So important is strength in many of these products that purchases are made on strict specifications. Such strength specifications are ordinarily met through careful selection of the raw cotton. If a mill finds that the yarns are falling below specifications for strength, it is considered to be a matter of great concern. Ordinarily the mill begins to use cotton having a longer staple, and not infrequently it experiments with cotton from other growth areas or of different varieties or blends until a stock with a satisfactory strength is located. Strength is one of the most elusive properties of raw cotton from the standpoint of commercial classification. Although the cotton classer frequently forms an opinion as to the strength, experimentation has shown that such opinions are little related to actual fiber strength or to yarn strength. Balls (^) is convinced that "grader's 'strength' and 'breaking strain' are utterly disconnected." According to Balls, the classer ascertains the uniformity of strength of the fibers rather than the actual strength and is largely influenced by the slipperiness of the fiber. Because of the cotton classer's limited ability to recognize cotton that will give strong yarns, it is a rather general practice for manufacturers of mechanical fabrics, such as tire cords, to make spinning

3 By HOWARD B. RICHARDSON and CARL M. CONRAD. The authors express appreciation for assistance given by Irven Naimaii, formerly of the Bureau of Agricultural Economics m certain phases of this study. x^vuuuiux»», * Italic numbers in parentheses refer to Literature Cited, p. G8. 4 TECHNICAL BULLÈTIH 54 5, Ü. S. DÉPT. OF AGRlCULTUBE

tests each new season on small batches of cotton from different sources before they buy any considerable quantity. Even when expedited, such tests require appreciable time and are expensive. The delay itself m frequently costly. If purchases of the raw cotton are dekyed pending the completion of the tests, an option may have to be taken on the cotton in order to hold it. Otherwise, a supply of the cotton must be bought outright. In the former case, the cotton may prove disappointing and the cost of the option may be forfeited. In the latter case, the mill may find itself with a large quantity of unsuitable cotton on hand, which must be sold, perhaps at a loss. Evidently, some method for determining the strength of raw cotton is sorely needed so that the yarn strength may be predicted without spinning tests. Such a method is also needed by the cotton breeder or grower who cannot always supply sufficient quantity of lint for spinning tests, nor generally afford to run a spinning test on each variety he wishes to study.'

METHODS OF MEASURING STRENGTH OF RAW COTTON No lengthy discussion of the literature dealing with tests of tensile strength in cotton will be attempted here. A convenient summary of the work up to 1923 is given by Peirce (SS), and a somewhat later summary of the work on cotton hairs is given by Roehrich {59). The methods discussed divide themselves logically into two groups, one embracing those used in testing individual fibers and the other embracing those used in testing bundles of fibers. With reference to testing the strength of single fibers, several methods have been employed, and there are variations of each. These have been discussed and the results from several instruments compared by ISTavkal and Sen (SO). Turner (61) has made an extensive inquiry into the relation of fiber strength to yarn strength, and Turner and Venkataraman (63) have attempted to evaluate the effect of hair strength on yarn strength when a number of other properties are held constant. They found a partial correlation coefficient between hair strength and highest standard warp count of +0.1030 for the first series of 95 samples and -0.0707 for the second series of 45 samples of Indian cottons. These results do not lend much encour- agement to the use of the expression, "mean fiber strength", the measurement of which is too time-consuming and tedious anyway to be of much practical value for commercial purposes. The bundle method of determining the strength of raw cotton has resulted from a desire to overcome the variations and limitations which exist in single-fiber methods. George Butterworth, of the Bureau of Agricultural Economics, was one of the first (about 1922) to experiment with such a method. He combed and straightened a tuft of fibers by culling the fibers through the combs of a Baer sorter, and then weighed out 1 mg of the straightened fibers. He attached the ends of the resulting bundles in a special twist counter and introduced several turns to bind the fibers together compactly. He then fastened the bundles in special jaws and broke them in a single-strand yarn tester of 4 to 10 pounds capacity. One objection to Butterworth's method is that 1-mg samples of fibers from cottons of different staple length do not give comparable MEASUREMEÎi^T OF CHARACTER PROPERTIES OF COTTÔH 5

results, for the test involves a changing total cross-sectional area of hbers depending on their mean length. Therefore, this method cannot give comparable results except in those cases in which the length of staple is the same. ^ At about the time that Butterworth was experimenting with the strength of bundles of twisted fibers, Walen (69) was studying bundles of straightened fibers. He developed a method which may be described briefly, as follows: A bundle of cotton fibers is "pulled" m much the same way as a cotton classer makes his "pull" for determining staple length. All fibers shorter than seven-eighths of an inch are brushed or combed out with a toothbrush. The bundle is cut to a length of seven-eighths of an inch and is adjusted to weigh 0.004 g by removal of fibers from the side. The ends are then glued with collodion. The finished bundles are conditioned for 2 hours and are broken m a testing machine of the conventional balance type having a capacity of 10 pounds. The results are expressed in terms of an equivalent weight of 20s yarn. Walen's method is defective in that it requires all fibers shorter than seven-eighths of an inch to be combed out, so this method would not give comparable results with cottons of different staple lengths. If all the fibers below seven-eighths of an inch were combed out of the long staples, they would constitute only a small percentage of all the fibers, whereas removal of these fibers from the short staples would separate from 50 to 90 percent of the total. Then it is questionable whether only fibers longer than seven-eighths of an inch would be representative of the entire sample, and also whether in Walen's method of gluing the fiber ends, all the fibers in the bundle would be equally taut when placed in the jaws of the testing* apparatus. ^ In 1923 Chandler ' began a study of the problem. After studyino- the methods then m use for evaluating strength of raw cotton he developed, while in the Bureau of Agricultural Economics, a new method based on the strength of a wrapped bundle of combed fibers In connection with the wrapping, he obtained at the same time a measure of the cross-sectional area of the bundle and was enabled to express the results in terms of the tensile strength per square inch Alter some experimentation, he concluded that the strength, S, of raw cotton m pounds per square inch of cellulose could be determined by multiplying the machine breaking strength, B, of these bundles by the factor 20/0% with 0 the average length of thread per revolution of the bundle, thus, JS=20B/C'K The constant, 20, is derived from the product of 47r ((7y4^=cross- sectional area of the bundle) and a condensation factor—the latter being the ratio of the theoretical weight of a three-eighths-inch section cut from the bundle (assuming a density of 1.5 for cellulose) to the actual weight of this section. Several subsequent attempts have been made in this laboratory to develop methods for ascertaining the strength of raw cotton. One method involved the preparation of an artificial yarn by means of a miniature drawing frame and a twist counter, but because of the

5 CHANDLER, E E. A NEW METHOD FOR DETERMINING THE STRENGTH OF COTTON TT S Dept. Agr., Bur. Agr. Econ. 16 pp. 1926. [Mimeographed.] ^OIIXJN. U. h. 6 TECHNICAL BULLETIN 5 4 5, U. S. DEPT. OE AGRICULTURE time consumed in making a yarn of sufficiently uniform size and the inconsistency in results caused by variations in straightening and combing the fibers, discarding the neps, and rejecting the short fibers, the preliminary results did not seem very i .omismg. Moreover, an artificial yarn would seem to obscure the individual factors ot the raw cotton that inñuence the strength of yarns, and differences m strength of any two samples of artificial yarn may not be due to differences in strength of raw cotton alone but to differences m other characteristics such as length of staple, fineness, and maturity.

ADVANTAGES OF THE CHANDLER BUNDLE METHOD The Chandler method possesses an important advantage over other methods, in that it expresses the results in terms of strength per unit of cross-sectional area. Failure to take into account the effect ot cross-sectional areas of the fibers is probably the principal explana- tion of the failure of single-fiber strength measurements to be indicative of yarn strength. As can be seen by a little reflection, a yarn of a given size contains in its cross section some unknown average number of fibers of measurable mean strength. Assuming that no slippage of fibers occurs in the breaking of a yarn, it is evident that the strength of the yarn would be the smallest summation of fiber strengths per yarn cross section in the length interval of yarn tested. It is evident that the mean strength of the fibers taken alone is no criterion for the yarn strength but must be used in conjunction Avith the mean area of cross section of the fiber. In other words, it is the ratio of mean fiber strength to mean fiber cross-sectional area (the latter is proportional to fiber weight per inch) rather than mean fiber strength alone, that should be used in predicting yarn strength. But the determination of cross-sectional areas of fibers is almost impossible of attainment, since it varies along the individual fibers, and its measurement after breakage is difficult. On the other hand, the Chandler bundle method, when carefully controlled, involves a principle of integration of fiber cross-sectional areas and fiber strength m such a way as to indicate effectually the strength per unit of cross- sectional area and, other things being equal, gives a measure of the strength that under ideal conditions should be realized in a yarn of given size. Notwithstanding the advantages there are several sources ot error in the method as published by Chandler in his preliminary report.^' Some of these have been studied, and methods for their elimination or control are indicated in this bulletin. Furthermore, obtaining the final expression of strength has been considerably facilitated here by the use of tables, so that a minimum of calculation is necessary. It is believed that the method has now been improved sufficiently to be fairly reliable and that its adoption for the measurement of cotton- fiber strength would be of considerable benefit to those cotton breeders and consumers for whom strength of product is of major importance.

TECHNIQUE OF THE MODIFIED CHANDLER METHOD The operations of sampling, combing, wrapping, and breaking, herein described, should be performed under standard conditions of

« CHANDLER, E. E. See footnote 5. MEASUREMENT OF CHARACTER PROPERTIES OF COTTON 7

the atmosphere, namely, 65 percent relative humidity and 70° F temperature, after not less than 2 hours of initial exposure to these conditions. Additional periods of at least 2 hours of exposure to standard conditions should be allowed between combing and wrapping and between wrapping and breaking the bundles. A tolerance ot 3 percent m relative humidity and 5° in temperature above or below the fixed values may be permitted.

SAMPLING

The procedure according to the modified Chandler method begins with the preparation of the bundle of fibers from the original sample ' o± cotton Imt. Ordinarily the strength observations from 10 success- tul breaks are averaged. (It is desirable to prepare a few extra bundles to allow for shppages and unsatisfactory breaks.) For each bundle a small handful of cotton lint is taken from the sample gripped by both hands, pulled apart, and superimposed with the broken edges together. Then three to four pinches are withdrawn from the broken edge. These pinches (fig. 1, A) should yield a finished bundle (fig. l^F) having a circumference of approximately 0.125 inch and withm the range 0.115 to 0.135 inch. The size of the bundle can be readily controlled by weighing one or two unwrapped bundles (ng- Ij B) on a sensitive microbalance, wrapping them, and calculating the weight of bundle necessary to give a corrected circumference ot 0.125 inch A change of 1 mg in the weight of the bundle causes a change of about 0.003 inch in the circumference. The required weight of the bundle varies chiefly with the length of staple of the cotton. With a little experience it is not difficult to keep the bundles withm the required range. A convenient balance for use is the torsion type shown in figure 2.

COMBING That the strength of the bundle may truly represent the strength of the fibers, it is necessary that the fibers be carefully straightened and paralleled. Two combs are used—a coarse one for the preliminary process and a fine one for completing the paralleling and straightening. For the coarse comb, a weaver's pickout comb can be adapted by breaking out alternate teeth and mounting it in a convenient position. Any comb approximately 2.5 inches wide with needles 0.025 inch in diameter at the base, 0.5 inch long, and 16 to the inch, will serve the purpose. The fine comb should be 2.0 inches wide with needles that are 0.015 inch in diameter at the base, 0.5 inch long, and 48 to the inch. The combing action is begun by grasping the tuft almost at the center and repeatedly drawing the outer edge of the tuft of fibers through the coarse comb, gradually advancing the action toward the center of the tuft (fig. 2). After one end of the tuft has been drawn 15 times through the coarse comb to attain rough parallelization, the tuft IS reversed, the combed end is grasped approximately one-eighth inch from the center, and the other end is combed 15 times. If the

^ The method of selecting these original samples from the gin box, from the various types of bales, or from mill products will depend on the purpose for which the stSdy^s intended and on the quantity of cotton available. ^ 8 ÏEOHKICAL BUia.y.TIJüT 0 4 5, U. S. DEBT. OT" AGRICULTURE

^ . ^. :4_

\ \E •S-jf V ( / 1

^ C a

FIGURE 1.—Details of the preparation and wrapping of Cliandler bundles : A, Small tuft of raw cotton ; B, combed bundle ; (7, transfer jaws ; D, combed bundle in transfer clamp ; E, combed bundles in transfer clamp with thread attached : F, the completed bundle with, cgptgr inflicatg^ by blaclj ipark, ready for breaking ; G, a bundle successfully MEASUREMENT OF CHARACTER PROPERTIES OF COTTON tuft is properly grasped, approxiin'ately one-eighth of an inch of the bundle will be combed tiom both directions. The combings are discarded. The roughly prepared bundle is now more completely combedj by drawing each end through the fine comb 20 times. These operations remove practically all the loose fibers, neps, pieces of leaf, and like materials. At this stage the size of the bundle is adjusted by sep- arating as many fibers from the side as is necessary to give a final

FiQDBB 2.—Torsion balance and technique of combing used in the preparation of Chandler bundles. circumference within the range 0.115 to 0.135 inch. The operation is completed by drawing each end of the bundle 15 times through the fine comb, to finish aiming the fibers. Before wrapping, the combed bundles (fig. 1 B) should be exposed to standard atmospheric conditions for at least 2 hours. 10 TKCilWICAIj BULLETIN 545, U. S. DEPT. OP AGBIOULTURll

WB-^PPIKQ After the fombed biindlon hnvp been air conditioned, tliej; are wrapped in preparation for breaking. Wrapping is accomplished

FifiUEE 3.—Wrapping device used for wrapping Chandler bundles. by a special wrapping device (fig. 3) jjrovided with a finely graduated inch scale. The bundle is inserted in a special clamp (fig. 1, 6*, />, E) MEASUREMENT OF CHAKACTEll PKOPERTIES OF COTTOK H

furnished with the instrument and is centered by pulling it to one side and then back to the center to remove kinks or any slight twist that may be present in the bundle. About 30 inches of no. 20 sewing thread is cut and the ends are tied, with ordinary loop knots, to oppo*^ site ends of the bundle close to the sides of the clamp. Free ends of thread are cut short and then pressed into the end of the bundle to facilitate manipulation. The bundle is now transferred to the wrapping device by means of the clamp, the clamp (with bundle) being placed between the two jaws and held m place with one hand while the bundle is clamped into the wrapping jaws with the other hand. The bundle is stretched lengthwise by gently lowering a 10-pound weight that is hooked to the cord extending from the left-hand wrapping jaw around a pulley, rhe suspended weight should come within a distance of about one- half inch of the table upon which the instrument rests. The bundle clamp IS now removed and a 4-pound weight is hung in the loop of the wrapping thread. The handle of the wrapping device is next turned clockwise about a dozen turns with the right hand, the two threads being held slightly apart with the fingers of the left hand so they will pack closely against previous turns during successive turns of the bundle. The handle is stopped at a definite position by means of an index on its shoulder, and the fingers are temporarily removed from the threads while the initial reading of the position of the 4-pound weight on the scale is made and recorded on a special form (fig. 4) The wrapping IS continued exactly 10 revolutions; of the handle, the threads being held apart slightly as before. The hand is removed, and the ñnal reading on the scale is taken and recorded. An attempt is made to obtain the readings very near the center of the bundle. The wrapping IS now continued, but after the threads meet at the center and start back toward their original position, they are no longer spread with the fingers. Just after the threads start back, wrapping is temporarily halted and a pencil mark is made at the center of the bundle to indicate the' proper position for subsequently attaching the breaking jaws 1^ mally, wrapping is continued until the threads meet the sides of the wrapping jaws The 4-pound and 10-pound weights are taken olt 1 he thread that supported the 4-i)ound weight is cut at the bottom of the loop and each end is tied with a loop knot around the bundle to prevent unwinding. The bundle is taken out of the wrapping jaws and pinned or clamped beside its scale readings (fio- 4) Ihe two. scale readings, when properly calibrated, furnish^ measure of the circumference of the bundle and consequently permit the calculation of its cross-sectional area. Calibration of the scale is accomplished by wrapping wires of known circumference, as de- sciTbed later. Under the conditions of the tests described in this bulletin It was found necessary to subtract 0.023 inch from the mean scale reading per revolution The necessity for this correction is due to the fact that the thread length per revolution of the bundle corresponds to the length at the center of the thread and is greater than the circumference of the bundle by ir times two half diameters of the wrapped thread, . 12 TECHNICAL BULLETIN 545, U. S. DEPT. OF AGRICULTURE

Difficulty is sometimes experienced in wrapping cottons that are shorter in staple than fifteen-sixteenth of an inch. It is generally possible to make bundles from cottons not much shorter than fifteen- sixteenth-inch staple by making three or four turns of the wrapping thread on the bundle while holding the latter taut with the hand (instead of using the 10-pound weight), then suspending the 4-pound

ï'oriD No. '¿0 ORIGINA. L DATA FOR COTTON FIBER STRENGTH BY I MFBOVSD CU ANDLi» BUNDLE METHOD

-?/y^ Project A Sam pie

Problem r Pro blem Title

Observed Observed Observed Observed circum- machine Obs. Scale circum- Machine Obs. Scale ference, break. No. reading ference, break, No. reading, pounds inches inches pounds inches inches

9-vr /o/ 11 1 Z99 ¿>./y^

9.^Y 12 2 r/r .yy¿ /oz r.¿s- 3 . /y^ 9r 13 /.26-

9.5-0 4 .yv¿ /o^ 14 s-.oy

5 /.¿r ./S-o //z 15 ¿.^7 r.rá 6 ./yj- /oz 16 7V/ r.j/ 7 ./y¿ /oz 17

8 .^*/V /oz 18

r.// • yyj /oo 19 9 á.¿y 9.vs^ ./yd /o^ 20 10 7-99

, Hv J>^B.7P. Broken hv Mé.2^ Combed by j Wrappe S/:i^/3V Dat. ^A3/3y Date //3y Date.

FiC;;uiiB 4.- -Facsimile of form used for recording the scale readings and the machine breaking strength of Chandler bundles. weight, followed by the 10-pound weight. Padding the jaws with raw cotton or a thin strip of leather helps greatly and is to be recommended if trouble is experienced in wrapping. In any case, sharp edges of the jaws should be rounded off with emery cloth. Wrapping becomes increasingly difficult as the staple length decreases below fifteen-sixteenth of an inch. By decreasing the dis- MEASVKEMEWI OF CHAEACIEß PBOPEKTIES OF COTTON 13 tance between the jaws of the wrapping device, bundles irom such cottons can be wrapped easily, but it becomes very difficult or impossible to break these bundles, as their short length does not provide sufficient surface to prevent slippage in the jaws durmg the breaking, BBEAKINO AND KECOBDINO

The bundles are next placed in special jaws (fig. 5) and broken. An ordinary skein-yarn tester (fig. 6) of inclination-balance type using the 300-pound dial and a speed of the lower jaw of 12 inches per minute, may be used. The special breaking jaws are provided with a slot into which is pressed a piece of unwaxed chrome sole leather, 8 to 9 irons thick. The leather provides a gripping surface for the bundles. Before attempthig to clamp bundles in the jaws, a

FiGDKE 5.—Details of construction of brealiing Jaws and metliod of attachment to bundles : a, Long extension tester Jaw with leather in groove ; b, short extension tester Jaw assembled with bundle in place ; c, one of short tester Jaws with leather in groove ; d, rectangular clamp with setscrew for fastening bundles in tester jaws ; e, wrench for tightening setscrew. groove should be established longitudinally in the center of the leather by cutting a small slot and then impressing a wire of about one-sixteenth of an inch diameter into it. When fastening the bundle in the breaking jaws, it is convenient to have either a vise or a holder in which the connecting rods of the jaws may be held while the setscrew is being tightened. The shorter extension rod (fig. 5, &) is placed in the vise, and the bundle is clamped in the jaws with the center of the bundle, as indicated by the pencil mark previously referred to (p. 11), even with the outer end of the jaws. The jaws are tightened with a slow steady turn of the setscrew wrench. The leverage of the small wrench for tightening the jaws can be extended easily, if desired, by slipping a small piece of metal tubing about 8 inches long over it. Experience alone will determine how tight to turn the setscrew ; if it is turned too tight or is jerked, the bundle may subsequently break inside of the jaws instead of between the jaws, and if the screw is not tight enough, 14 XECHMIGAL BULLETIN 5 45, U. S. DBPT. OF AGRICULTURE the bundle will slip out of the jaws -without breaking. However, some experimentation indicates that the degree of _ tightening, in itself, does not affect the results. The short extension rod is now removed and the longer rod is placed in the vise. The shorter exten-

FiQuwj 6.^-:ï^rn-s)îein tester adapted for attachment of the special bundle jaws. sion rod containing tlie bundle is brought into ^linement so that the çn4s of the jaws are touching and the extended end of the bundle MEASUREMENT OF CHARACTER PROPERTIES OF COTTOîT 15

lies in the groove of the open jaw of the long rod (fig. 5, a). The other jaw is then fitted into place, the collar is adjusted, and the screw IS carefully turned down. The connecting rods with the bundle m their jaws are then attached in the strength tester, and tension is exerted until the bundle either breaks or slips. Care should be exer- cised to see that extension rods are in line when the load begins to be applied. If the break occurs within one of the jaws or if it is not clean and sniooth across the longitudinal center of the bundle, the result is rejected as unsatisfactory. Some cottons seem to give more trouble than others in this respect. Over a long period and with a wide range of cottons, about 70 percent of the bundles have broken successfully. Very strong cottons, especially if short in length, may give considerable trouble. Frequent replacement of the leather pad- dmg in the slot of the breaking jaws, trimming the edges of the leather that have bulged over the ends of the jaws, and using care in centering the groove, may overcome some of this difficulty. It has been noticed that unusually weak breaks in a series are frequently associated with leather pads that have become chipped or defective from use. If the groove is not properly centered, weak breaks and excessive slippages may result.

CALCULATING After 10 satisfactory bundle breaks have been made, the data for observed circumferences and machine breaks are transcribed to a second form (fig. 7) where corrections are applied. As described later, the corrected circumferences are obtained from the observed circumferences by subtracting 0.023 inch, or by the use of a prepared table (table 15, p. 72). ^ As it is practically impossible to prepare all the bundles so that they will have the same size of circumference, even if the bundles are carefully weighed, and as the size of the bundle influences the calculated strength per square inch, it is necessarv to apply a correction to the machine break of the bundle, to adjust it to that of a bundle having standard circumference (0.125 inch). This correction varies with th^ strength of the cotton, but on the average, it amounts to approximately 1 pound for each 0.001-inch deviation from Ihe standard circumference. The correction is added to the machine break when the circumference of the bundle is smaller than standard, and subtracted when it is larger. The proper corrections for deviations of circumference have been calculated for cottons of different inherent strengths and are given in table 16, p. 72. The column of the table to use in any given case can be ascertained by calculating the mean corrected circumference and the mean observed machine break of the broken bundles. If the mean of the circumferences deviates appreciably from the standard, the mean of their breaks should be corrected approximately by allowing 1 pound for each 0.001-inch deviation from standard before selecting the proper colunm. If studies of variability are desired, each indi\âd- ual break must be corrected. The strength per square inch is obtained by dividing the corrected machine break by the cross-sec- 16 TECHNICAL BULLETIN 5 4 5, U. S. DEPT. OF AGRICULTURE tional area of a bundle of standard size. The cross-sectional area may be calculated from the circumference by the formula C\_ (0.125)^ 47r~4X3.1416 which when solved reduces to 0.0012434 square inch.

Form No. 14

COTTOH FIBER STRENGTH BY IMPROVED CHANDLER BUNDLE METHOD

Project ^ _^Sanple ^^Và" Problem X. Problem Title

Circum ference. Machine t reak, Strength, 1000 lbs. Ob- In pound Der sa. in. serv Corrected Devia- tion Calculated Squared Remarles Ob- Cor- to 0.125 tion No. Observed devia- aerved rected inch cir- from from tion cumference break mean

1 o.yyr o./zr ^Û/ /o/ r/ -S' ^5"

2 .yy¿ •/■2J ^oz /ÛÔ- B-y --2 V

3 ./yo ./// 9r /o?r

7 ./yz .yyf /oz //o s-r .2 y

8 ./y^ ■ /J/ yoj. yo^ r¿ o o ./zo o 9 .yyj /OO /V H o //o 10 .;y¿ . ^23 '°7 sr -2 y 2'á/ •h9 Total /-V^^ ^-^^0 '""^^ - r v/

Mean •/V^ • ^-^^ ^^-^-^ ^á., ,

Standard deviation J.3

Standard error of mean ^■/

Standard error of mean,percent O. S'/

Tested by ^- ^ '^ .Cale, by O- '^-^ .Checked by ^ F' J^ ■

Date _Date J/Jir/jy Date 3/jo/^y

FIGURE 7.—Facsimile of form for calculating the strength and the variability of strength per square inch.

In the practical use of the method it is inconvenient and unnecessary to calculate the strength per square inch for every bundle. A table can be constructed from which the strength corresponding to various corrected machine breaks may be read off. Table 17 MEASUKEMEJSTT OF CHARACTER PROPERTIES OF COTTON 17

p. 73 is such a table covering the range of all corrected machine breaks commonly obtained. A measure of the variability of strength per square inch and the standard error of the mean are desirabfe for purposes of control and tests of significance. Provision is made for their calculation in the form ishown in figure 7. The mean of the 10 strength values expressed m units of 1,000 pounds per square inch is computed, and rounded to the nearest whole number. The error in variance due to rounding has been found to be insignificant. To avoid the necessity of having to repeat the calculations of standard deviation and standard error each time a test is completed, the calculations have been made for the range of .summated squares of deviations from the mean likely to be found in practice, and the results are recorded m table 18 (p. 73). This table gives the standard deviation of single observations and the corresponding standard error of means of 10 observations when the sum, of the squares of the deviations from the mean is known. Similar tables for other numbers of observations could be constructed.

EXPERIMENTAL BASIS OF THE MODIFIED CHANDLER METHOD An attempt has been made, thus far, to give a clear, concise de- scription of the technique of the modified Chandler method without encumbering it with the experimental details supporting the specifications. Most .of the remaining part of this section is concerned with the study of the several variables and the experimental basis lor the modified method.

EXPRESSION OF THE KEStJLTS

In the original Chandler method, strength was expressed in pounds per square inch of cellulose in a way similar to that customarily used for expressing the tensile strength of metals and other structural materials. The general formula is : rr. ., , ^1 Machine break (pounds) tensile streii£i:th= \ 5 r- ¥- r—:. : ^ Area o± cross section (square inches) but in a bundle of cotton fibers the area of cross section cannot be accurately measured because of the voids between and within the fibers. To correct for these it is necessary to multiply the right- hand expression of the equation by a correction factor which Chand- ler designated A", the formula then becoming rp -1 . ,1 Machine break TAT^í^ tensile strength^Ä^X^—-—p P—™ii--p^ ^ Area ot cros,s section C^ where B is the machine break, O is the circumference, and the area of circular cross section is

Chandler found some variability in K, depending on the tension of the wrapping thread and the moisture condition of the fibers, but he calculated for the conditions he selected a value of appro:^i- 91773°—37^ g 18 TECHNICAL BULLETIN 5 4 5, U. S. DEPT. OF AGRICULTURE matelv 1.59. Thus, he decided that a corrected and simplified formula, in which K and 47r were combined into a smgle constant and rounded thus, „^.. „ „ 1.59X4x>Cg 20X-g where S is the tensile strength and C is an uncorrected circumference expressed in inches, could be applied to bundles of raw cgtoi^ Chandler determined the value of K from the equation K^-^^W where 0 is the uncorrected circumference of the bundle as indicated bv the length of thread per revolution required to wrap the bundle, D is the density of cellulose (assumed for practical purposes to be 1.5 g. per cubic centimeter), Z is the length of a section cut from the bundle (three-eighths of an inch by specification), and W is the weight of the cut section. -j ^„j +„ The right-hand member of the equation may be considered to consist of two parts, one, -j^' giving the theoretical weight of cellulose that would completely occupy the volume of the section cut from the bundle, and the other, W the observed weight of the same section. The correction factor K thus expresses^the ratio of theoretical to actual weight of cellulose and presumably the ratio of actual to observed strength of the bundle assuming it to be pure cellulose. If the ratio is a constant, a small error in the a^umed density of pure cellulose will make little difference m the usefulness of the expression for the tensile strength of bundles of cotton fibers since the error should be the same for all samples the results of "tAÍm'ílSÍíf¿valuation of K, variations in the magnitude of any of the factors will influence the value of K and consequent^ the calculated strength per square inch of the cotton. Therefore £ oîder that the methocl may be accurate it will be necessary to choose the conditions of test so that the K component wil always be the same. Some of the chief theoretical and experimental factors affeäing K are : (1) Composition of fiber substance, (2) scale calibra- Sn of the wrapping device, (3) distance between threads at the centefoftLwSed bundle (4) size of the bundle, (5) manner and degree of combing, (6) sag of the bundle during wrapping, and (7) elongation of the thread during wrapping.

COMP08ITION OF FIBEK SUBSTANCE

In making a critical examination of the possible causes of discrepancies in the Chandler method as originally described it was found that the use of the density of pure cellulose m evaluating K and in calculating the strength per square inch, involved some serious dilti- culties. Even assuming that the density of pure eel ulose were accurately known, there remains the fact that the fiber substance is kno^vn to be subiect to fluctuations in composition and m proportion ot ash, fats waxes, nitrogenous constituents, and other substances that iire

of variable moisture content in the fibers, even under constant atmospheric conditions ^ which might influence the density of the fiber substance somewhat. In view of these considerations and of the fact that the utility of the method depends on the comparison of relative rather than upon absolute figures, it was decided that the strength could best be expressed m terms of fiber substance. Thus the use of K or any correction factor to convert to pure cellulose could be abandoned. This change resulted m a reduction of about 37 percent in the absolute figure for strength per square inch as previously calculated, but did not dimmish the comparative usefulness of the method.

SCALE CALIBRATION OF THE WRAPPING DEVICE In wrapping the bundles, the length of thread required per revolution furnishes, when properly calibrated, a measure of the circumference of the bundle and consequently a method of determining the cross-sectional area. However, the measured length of the thread required per revolution of the bundle does not in itself permit an accurate calculation of the cross-sectional area but gives too large a circumference by the amount IT times the effective diameter, d, of the thread. Chandler did not make any correction for inaccuracy m observed circumference, since the variable appeared m both the numerator and denominator of his complete formula for tensile strength, thus

in which the symbols have the same significance as above, and he considered the error tended to cancel out. It is true that when the circumference of the bundle broken is the same as that of the bundle used m the evaluation of K, any errors due to this source will cancel in the final expression of strength. However, if C^ and C^ be t\i^ observed circumferences and they are not the same, the error due to the diameter of the thread will give rise to an erroneous factor.

which is not strictly proportional to the area of cross section of the bundle. Furthermore, since in the revised method the use of the factor K was being abandoned, it was essential that the strength of the bundles be determined on the basis of their true, cross-sectional area, that is, after making subtraction for the effect of the thread on the observed circumference. The mean diameter of the wrapping thread is not readily determined by the usual method of measurement with calipers because of the irregular shape of the cross section and the flexible nature of the thread. Therefore, solution was sought in another direction. A series of wires of different diameters covering somewhat more than the range of diameters to be encountered in the bundles was

8 It has been rather well established by Urquhart and Eckersall (ff?) that the moisture content of cotton fibers exposed under constant conditions of atmospheric humid tv and temperature is dependent within limits upon the direction from which equilibrium is 20 TECHNICAL BULLETIN 54 5, IT. S. DEFT. OF AGRICULTURE obtained and measured with a micrometer.» The original measurements were carefully checked and found to be correct to the third decimal place. From the diameters, the correspondmg circumferences were calculated. Next, each wire was placed m the wrapping device and wrapped with no. 20 sewing thread m exactly the iame manner as the bundles of cotton fibers are wrapped. The mean length of thread required per revolution of the wire was ascertained 10 times for each size wire, and the results were averaged The individual means and the means for the 10 observations are shown in table 2. At the bottom of the table are shown the circumferences of the wires, calculated from their diameters. The differences, equivalent to ^ times the effective diameter of the wrapping thread, show the proper correction to apply to observed circumferences to give corrected circumferences of bundles.

TABLE 2-Jliean. length of rw. 20 sewing thread per turn required to lorap wires of différent known diameters and calculated corrections to apply to bundles of different observed circumferences

Mean length of thread required for diameters of—

Observation 0.0410 0.0472 0.0580 0.0692 0.0860 0.0265 0.0311 inch inch inch inch inch inch inch

Inch Inch Inch Inch Inch Inch Inch 0.172 0.206 0.240 0.277 1 0.104 0.120 0.153 .152 .173 .205 .240 277 2 - .100 .118 276 .104 .118 .153 .173 .206 .243 3 - .172 .206 .240 277 4 - .103 .120 .151 .118 .153 .172 .206 .241 277 .106 276 5 .104 .121 .151 .172 .207 .241 6 - .119 .152 .171 .206 .240 276 ijr _ .103 277 .103 .119 .152 .172 .205 .241 8 - - .207 .242 277 g _ .104 .119 .151 .172 .119 .152 .171 .205 .241 277 10 .105 .1191 .1520 .1720 .2059 .2409 . 2767 Mean -- - .1036 .0977 .1288 .1483 .1822 .2174 . 2532 .0832 . 0235 .0204 .0214 .0232 . 0237 .0237 .0235 1

DISTANCE BETWEEN THBEADS AT CENTER OP WRAPPED BUNDLE Chandler originally recommended that, when wrapping the bundles the wrappîng threads be permitted to approach to withm about one -fiftieth of an inch of each other before they should be caused to reverse their direction and travel in a second layer of thread away from each other. It is impossible to estimate this distance accurately wTth the eye, and the possibility existed that a variation m the distance betw^n threads at this point would cause a variation m the obïïved strength. To establish whether such variation occurred, an experiment was set up in which the threads approached withm different known distances In one case they were allowed to touch ; in a second case they approached within the distance of approximately Two threads ^anä^n a third case «f approx^n,^^^^^^^ four threads The results are shown in table 3. Ihe table snows tnat îhe strength varies with the distance between threads, being lower

»The cooperation of the American Instrument Co., Washington. D. C, in making these measurements is gratefully adinowledged. MEASUREMENT OF CHARACTER PROPERTIES OF COTTÔK 21

as the distance becomes greater. Furthermore, the standard deviations indicate that bundles in which the wrapping thread touches show the least variabihty of strength, whereas those with the greatest distance between threads show the greatest variability.

TABLE H.—Strength and standard deviation of strength of bundles having specified distance at the center between wrapping threads

Strength of bundles Strength of bundles having space of— having space of— Observation Observation No 2 4 No 2 threads 4 threads threads threads threads threads

1,000 1,000 1,000 1,000 1,000 1,000 pounds pounds pounds pounds per pounds pounds per per per per per square square square square square inch square inch inch inch inch inch 1 68 53 41 g 2 72 67 57 67 59 58 9 62 3 67 56 58 61 61 10 58 4... 73 63 55 5 70 63 46 Mean _ 68.1 60.2 53.4 67 60 49 7-I"I"___ 68 65 51 Standard deviation 3.1 4.5 6.4

In view of these facts it is evident that the easiest way to avoid variations due to variation in distance between threads is to allow the threads to come together and touch at the center. At the same time this procedure leads to greater uniformity of breaking strength tor different individual bundles. In the modified Chandler method the wrapping threads are permitted to touch at the center of the bundle. SIZEl OF THE BUNDLE

In an examination of some strength results from a single cotton calculated according to Chandler's formula, S=~, a high corre- ktion was found between strength and circumference of the bundle Ihis suggested the possibility that variation in size of bundle might be a disturbing factor in the determination of strength per square inch, buch a variation might occur if bundles of different size con- densed more or less solidly under uniform conditions of wrapping I o learn whether any relation exists between bundle size and density a scatter chart was prepared for a large number of observations of density and bundle circumference. These had previouslv been recorded for the purpose of evaluating Chandler's K The results, shown m figure 8, indicate an unmistakable relationship between the two variables. It is thus evident that the effect of bundle size must be taken into account in measuring the strength of raw cotton. ^ As the strength of bundles varies with size it is necessary to select some fixed circumference as "standard." It is desirable that the standard circumference be somewhere near the center of the range which is convenient for practicable preparation. After considering the matter from various angles, it appeared that a circumference of bundle of 0.125 inch would be most practicable as a standard of reference 22 TECHNICAL BULLETIN 5 4 5, XT. S. DEPT. 01^ AGRICULTURE

To avoid errors due to variation in size of bundle, at least two procedures are available: (1) The circumference of the bundles may be kept within a sufficiently restricted range about the standard, to reduce the error to insignificant proportions; or (2) a correction may be determined and applied to bundles the circumference of which varies

To obtain bundles of standard size, a preliminary trial is made by weifí-hing a combed bundle of the fibers and then wrapping it to determine its cross-sectional area. From the relation between the weight of the bundle and its mean circumference it is possible to calculate the correct weight of bundles to give a predetermined circumference. However, adjusting the weight of the bundle is not practicable beyond a certain point for as the size is more and more closely adjusted the time required to prepare a bundle is correspondingly increased, i hen,

1.70

1.60

1 50

1 30 0.90 .no .120 .130 .140 .150 CIRCUMFERENCES (iNCHES)

FIGURE 8.—RELATION OF SIZE OF BUNDLE TO DENSITY. Each dot represents the mean of four density and circumference determinations on eacli lot of cotton As the circumference of the bundle increases, the density attained under these conditions becomes less. too the work requires a sensitive balance, which adds to the cost of equipment. For practical purposes it has been found convenient to work within a range of circumference extending 0.010 inch on each side of the standard. With a little experience bundles can be prepared with circumferences within this range without the aid ot any special balance. . . . i v i To apply a correction for variation in size it is necessary to establish accurately the relation between bundle circumference and strength. Preliminary results indicated that the relation is somewhat curvilinear Avhen the strength is expressed in pounds per square inch, but is linear when expressed as the machine breaking strength. Furthermore, it was found that the relationship varied for cottons of different mean strength. Therefore, the corrections were finally worked out by determining on six lots of cotton of widely varying inherent strength, the relation between bundle circumference and machine breaking strength. From the results obtained it was then possible to establish corrections for bundles of varying sizes and strengths. MEASUREMEiq-T OF CHARACTER PROPERTIES OF COTTOI^ 23

The experimental work was carried out as follows : For each lot 30 or more bundles were prepared under uniform conditions with circumferences varying from about 0.100 to 0.150 inch. The corrected circumference and machine breaking strength of the bundles from the different lots are shown in table 4.

TABLE 4.—Machine hreaks corresponding to circumference of bundles for 6 lots of cotton of widely different strength

Lot 1 Lot 2 Lot 3 Lot 4 Lot 5 Lot 6

Observation Cir- no. Cir- Cir- Cir- Cir- Cir- cum- cum- cum- cum- Break .Break Break Break cum- cum- fer- fer- fer- fer- fer- Break Break ence ference ence ence ence ence

In. Lb. In. Lb. In. Lb. In. l-__- Lb. In. Lb. In. Lb. 0.104 96 0.099 81 0.100 79 0.100 79 0.103 2 .105 79 0.101 74 99 .102 80 .106 81 .104 79 .104 76 .104 74 3 _ .107 101 .105 84 .107 81 4 .106 80 .104 79 .104 76 .115 107 .106 85 .109 84 .106 79 .109 5 .116 81 .106 76 119 .107 93 .109 84 .109 80 .109 81 .108 80 6 .116 127 .108 86 .112 88 .110 7 85 .109 81 .109 76 .121 131 .109 85 .115 89 .111 81 .110 8 .122 81 .109 80 126 .109 91 .115 96 .112 81 .110 81 9 .125 129 .112 80 .109 94 .115 97 .113 85 .111 81 .115 81 10._ .125 138 .110 99 .117 96 .114 11 90 .114 85 .117 85 .126 129 .114 103 .117 99 .117 91 .114 12 .127 88 .119 81 130 .115 101 .117 99 .118 97 .117 85 13 .129 137 .119 85 .116 103 .121 101 .119 94 .118 88 .120 84 14 .133 149 .118 101 .123 102 .119 15 _ 96 .120 92 .123 85 .135 149 .118 104 .123 104 .121 96 .,121 16 .135 154 100 .125 90 .119 104 .128 106 .122 99 .123 102 .125 97 17 .139 154 .119 106 .130 114 .127 18_ _ 101 .133 107 .126 91 .140 157 .120 106 .131 107 .129 103 . 134 19 .141 107 .127 96 158 .123 107 .133 . 119 .129 105 .137 109 20 .147 175 .128 91 .123 115 .135 114 .131 103 .137 113 .130 101 21 .152 177 .130 115 22 .136 121 .132 110 .138 109 .133 102 .152 169 .134 130 .137 119 .132 111 .141 23 _ .154 117 .135 103 176 .139 138 .138 122 .133 107 .143 122 24 .154 185 .136 106 .142 138 .139 121 .137 116 .145 122 .138 25 .155 179 .142 104 139 .139 122 .138 119 .147 127 .138 103 26 .157 180 .145 142 .146 130 .142 27__ 121 .149 127 .138 106 .158 184 .146 141 .146 131 .143 120 .149 28 .159 131 .141 103 178 .146 145 .147 129 .146 123 .150 126 .141 113 29 .161 202 .149 146 .148 130 .147 131 .153 30 .161 127 .144 113 197 .150 147 .149 133 .147 131 .153 127 31 .163 199 .146 115 .150 139 .147 133 .146 107 32 .151 133 .149 33 130 .150 126 .158 141 .151 136 .154 120 34 .159 145 .152 35 139 .155 126 .159 151 .153 136 36 .161 148 .157 141 37 .161 150 .159 143 3S .161 150 .160 39 . 145 .162 155 .161 146 40 .165 161 .182 168

Ï or each of the lots of cotton the regression equation of machine breaking strength on bundle circumference was determined. From this equation the machine breaking strength of bundles having a circumference of 0.125 inch could be determined. Also, the regression coefficient shows the number of pounds of the breaking strength corresponding to a change of 1 inch in circumference, from which may be calculated the number of pounds breaking strength corresponding to 0.001-inch circumference. These statistics together with other information are shown in table 5. The regression lines are shown in figure 9. By reference to table 5 it will be seen that the regression coefficients of machine breaking strength on bundle circumference decrease reg- 24 TECHNICAL BULLETIN 5 4 5, U. S. DEPT. OF AGRICULTURE ularly with mean bundle strength. In other words, the regression lines converge more or less closely toward a common point, as can be seen more readily by reference to figure 9. Theoretically, the constant of the regression equation should be zero, since bundles ot zero

240

200

fßo

120

.020 .040 .060 .080 .100 .120 .140 180 .200 CIRCUMFERENCE (INCHES)

FIGURE 9.—RELATION OF MACHINE BREAK TO BUNDLE CIRCUMFERENCE. Each dot represents a machine break of a bundle having the indicated circumference^ Dots for lots 2, 3, 4, and 5 are purposely omitted to avoid confusion ^ The machine break increases with circumference in a straight-line relationship and it increases more rapidly for strong cottons than for weak ones. circumference should have zero machine breaking strength, but actually the constant is not zero but appreciably negative, probably because of the effect of bundle sag during wrapping and other factors, as discussed in a later section.

TABLE 5.—Machine breaking strength, regression coefßcients, and constants of regression equations computed from data shown in table h

Mean Mean machine Constant machine Constant breaking Regression of breaking Regression of Lot no. Lot no. strength of coeificient 2 regression strength of coeflacient 2 regression standard equation standard equation bundles i bundles i

Pounds per Pounds per Pounds inch Pounds Pounds inch Pounds 132 1, 657±52 -75 4 102 1, 207±23 -49 2 114 1, 395±38 -60 5 99 1,106±33 -39 !> 105 1, 224±25 -48 6 92 972±42 -29

1 Bundle with circumference of 0.125 inch. ^ indicated errors are standard errors. As the regression coefficients differ in magnitude, depending on the average machine breaking strength of bundles of standard size, corrections calculated on the basis of the regression coefficients must vary with the strength of the cotton. To establish a series of corrections for cottons of different mean strength, a second regression of the first regression coefficients, expressed in pounds per 0,001 inch, on machine breaking strength was calculated from the MEASUEEMENT OF CHARACTER PROPERTIES OF COTTOK 25

results on the six lots of cotton. The regression line and the individual points are shown in figure 10. The points lie nearly on a straight line. Ihe equation of the new regression line is Ä=0.01690 Bs O.oo where R is the regression coefficient corresponding: to any mean machine break of bundles of standard circumferencef and Bs IS the machine breaking strength of the bundles. Of course, the regression coefficient, R^ is also the correction in pounds to appîy to the machine breaking strengths for each 0.001-inch deviation of bundle circumierence from the standard circumference (0.125 inch^ By substituting in the equation definite values of machine breakiní¿ strength, it was possible to construct table 16 (p. 72) from which t\\Q correction to apply in any particular case can be obtained readily by preliminary calculations as previously described. 1.75 i \— R = .01690 Bs -O.SS 1.50

1.25 X- y ir. ° '00

: 2 '^ O ^ ^ Û. 0. 50

0.25

20 40 60 80 100 120 140 160 MACHINE BREAK,^5, AT STANDARD CIRCUMFERENCE. (POUNDS)

^^NV'îî^.Li^rÎ^^^"^'*^^ ^^ "^»Ê REGRESSION COEFFICIENT OF MACHINE BREAK ^Ti.^^'^^^î^^siJi^^î^^^^ ™ ^"^ ^^^"'^^ BRE/K^C?F''B1?N"¿I::L^^!í;í

4íT^^Íí^P^I*^^^^-^^ applying a correction to the machine breaks ot bundles ot varying size is shown in a series of 18 tests of 10 breaks each made on the same cotton, in which the results obtained are compared with those calculated on the basis of Chandler^s formula, S==^' The results are plotted as scatter diagrams in figure 11, using the mean strengths as ordmates and their corresponding mean sizes as abscissas. The broken line shows the regression line through the i-esults calculated from Chandler's formula, and the solid line shows the corresponding line through the results in which the machine- breaking load has been corrected for circumference of bundle. The line through the points calculated from Chandler's formula has a decided slope whereas the line for the corrected results is practically horizontal. This experiment therefore confirms the value of applying a correction to the machine-breaking load of any bundles the circumference of which differs from standard. 26 TECHNICAL BULLETIN 5 4 5, U. S. DEPT. OE AGRICULTUBE

MANNER AND D'EIGKKB OF COMBING Conceivably, tlie degree of i)arallelization of the fibers in the finished bundle could play an important part in determining the strength per square inch. To learn the inñuence of the amount of combing, bundles were prepared from the same cotton by drawing the bundles 15 30 45, 60, 90, and 180 times through a coarse comb (16 needles per inch). In each case approximately half of the combing was made from opposite ends of the bundles. The bundles were then wrapped and broken in the usual way with the results shown in table 6. A scatter diagram of the results is plotted in figure 12. It is evident that an appreciable increase in strength was brought about by increasing the number of times drawn through the comb from 15 to 30; but beyond 30, no increase in strength resulted, the

100

u. 90 Original Chandler formula ( s = -^ ) "•H^:. z S 80

I 'x r • I \y Modified Chandler method

.110 .120 J30 .140 160 .170 CIRCUMFERENCE (INCHES)

Fr,r-,,RP 1 1 —RELATION OF STRENGTH CALCULATED BY THE MODIFIED CHANDLER METHCÎD AND BY THE ORIGINAL CHANDLER METHOD TO THE CIRCUMFER- ENCE OF THE BUNDLE. Each dot represents the mean of 10 strength tests and the corresponding niean circumference The modified method gives practically the same strength fegardless of the sizlof'the bundle, whereas the original Chandler method gives significant differences with different sizes. apparent increase with the bundles combed 180 times being within the experimental error. We may thus conclude that with the comb used, a technique involving 15 or more excursions through the bundle from each end is sufficient to provide the maximum strength. On the other hand, it will be noted that with the exception ot the bundles combed 30 times, the standard deviation of individual bundle strength decreases progressively with additional combing, i o this extent, extra combing is advantageous since the lower the standard deviation, the lower the estimated standard errors of the means will be and the smaller the difference in strength between two samples that may be considered significant. -i . i In carrying out the combing operation, another worker adopted the seemingly insignificant variation in technique of gently stroking the bundle by catching hold of and releasing the free ends of.the fibers as they were being drawn through the comb. It was noticed MEASUREMENT OF CHARACTER PROPERTIES OF COTTON 27

that, on the average, the strength values he obtained on the same cottons were about 10 percent higher than those of the first operator. To learn the effect on mean bundle strength of stroking them during combing, 10 bundles each were combed with 60, 120, and 180 strokes through the coarse comb, half of the strokes being made from each end of the bundle. The results are shown in table 7, in comparison with results of bundles combed the same number of times without stroking.

• • V 80 -♦ .V — .-'T I —X"" V • •

60 •

0- 20 40 60, 80 , 100 120 140 160 180 200 NUMBER OFTIMES BUNDLE WAS DRAWN THROUGH COMB

FIGURE 12. —RELATION OF AMOUNT OF COMBING TO BUNDLE STRENGTH. Each dot represents the strength of a bundle drawn through the comb the indicated number of times. The strength of the bundles increased with increased combing up to 30 times after which only a negligible increase resulted. Table 7 shows that stroking the fibers during combing resulted in an increase in mean strength per square inch of from 5,500 to 7,700 pounds, or an increase of from 6.9 to 9.9 percent. The precise cause of this large increase in strength is unknown, but the increase has been repeatedly verified. Presumably, stroking with the fingers

TABLE 6.—Strength of bundles prepared with specified amounts of comMng

Strength of bundles when combed with the coarse comb— Observation no. 15 times 30 times 45 times 60 times 90 times 180 times

1,000 pounds 1,000 pounds 1,000 pounds 1,000 pounds 1,000 pounds 1,000 pounds per square per square per square per square per square per square inch inch inch inch inch inch 1 70 74 83 81 80 83 2 _ 70 79 81 81 79 77 3 . 75 78 70 76 76 82 4 61 80 72 80 72 84 5 73 84 80 80 79 84 6 76 80 79 72 77 80 7 76 75 80 75 80 80 8 69 76 76 75 82 73 9 80 78 76 77 76 83 10 73 80 76 79 76 75

Mean.. _ 72.3 78.4 77.3 77.6 77.7 80.1 =M.=.^. : Standard deviation 5.2 2.9 4.1 3.1 2.9 2.6 j- 28 TECHNICAL BULLETIN 5 45, U. S. DEPT. OF AGRICULTUEE not only assists in the removal of neps and trash but tends to improve the straightening and parallelization of the fibers. The mean strength increases only slightly for increasing numbers of strokes through the comb over 60, but, as before, the variability of individual breaks, as indicated by the standard deviation, was found to decrease regularly, from 3,900 to 2,200 pounds per square inch. There is thus an appreciable advantage in the more extensive combing of the bundles.

TABLE 7.—Strength of hundles combed speeified number of times, with and without stroking

Strength of bundles when combed with the coarse comb— Method of combing 60 times

1,000 pounds 1,000 pounds 1,000 pounds per square per square per square inch inch inch Without stroking 77.6 79.9 80.1 With stroking 85.3 85.4 86.9 Increase with stroking. 5.5 Percent Percent Percent Do 6.! 8.5

The foregoing studies demonstrated the possibility of variation m results due to the adoption by different operators of varying combing technique. It was thought that the type of comb and the method and degree of combing should be more completely specified. Some preliminary trials indicated that the effect of holding and stroking fibers with the fingers during combing could be largely duplicated by use of a much finer comb having instead of 16 needles per inch (coarse comb), 48 needles per inch (fine comb). Some difficulty was experienced in the first part of the combing process in using the fine comb, and it was soon determined that more practical results could be obtained by producing a rough parallelization with the coarse comb and then finishing the process with the fine comb. After the technique of combing with coarse and fine combs had been fairly well standardized, a comparative test was run in which the bundles of one series were combed 90 times (45 from each end) on the coarse comb, whereas, the bundles of another series were combed first 24 times (12 from each end) on the coarse comb, and then 66 times (33 from each end) on the fine comb in both cases without stroking. Thus, in each of the series of bundles the total times through the combs were the same. The results are brought together in table 8. This table shows that the use of the fine comb increased the mean strength per square inch from 77,700 to 85,800, an increase of 8,100 pounds. This increase amounts to over 10 percent. Moreover, the strength of the bundles combed with the fine comb compared favorably with the strength of those conibed with the coarse comb and stroked, the results for 60 and 120 times through the coarse comb (stroked) being 85,300 and 85,400 pounds, respectively, as previously shown in table 7. Not only is the mean strength higher as a result of using the fine comb, but the variability MEASUEEMENT OF CHAKACTER PROPERTIES OE COTTOÎ^ 29

in strength of individual bundles is much less, as can be seen from the standard deviations in the two cases.

TABLE 8.—Strength of hundles prepared ivitJi coarse comh alone, and with hoth coarse and fine comb

Strength of bundles Strength of bundles prepared by prepared by combing— combing—

24 times 24 times through Observation Observation through 90 times coarse coarse comb, 1 90 times through through comb, 1 coarse then then 66 times coarse comb 1 comb 1 66 times through through fine fine comb 2 comb 2

1,000 1,000 1,000 1,000 pounds pounds pounds pounds per per per per square square square square inch inch inch inch 80 87 8 82 87 2 79 87 9 76 3 85 76 88 10 76 88 4 72 84 5 79 84 77.7 85.8 6 77 85 7 80 83 2.9 1.8

1 Comb 2y2 inches wide, 16 needles per inch, needles 0.025 inch in diameter at base. 2 Comb 2 mches wide, 48 needles per inch, needles 0.015 inch in diameter at base. As a result of these experiments and of others of a similar nature, a routine practice has been adopted in the technological laboratory Bureau of Agricultural Economics of combing the bundles first on a coarse and then on a fine comb. They are drawn through the coarse comb 15 times from each end, to produce a rough alinement of the fibers, and then through the fine comb 35 times from each end. A question often raised in connection with the combing of the bundles is the extent to which this procedure disturbs the original length distribution of the fibers. To throw some light on this point, a study was made of the fiber length distribution of (1) the raw cotton, (2) the preliminary bundle after 24 strokes through the coarse comb, (3) the finished bundle after m strokes through the fine comb, and (4) the discarded fibers from the fine comb. Curves showing the cumulative weight percentage of the different lengths of the fibers have been plotted and are shown in figure 13. Examination of the different curves shows some disturbance to the length distribution of the raw cotton as a result of combing, but much less than might have been expected. The preliminary combing re- moves a portion of the short fibers, and another portion is removed by the fine comb. Of course, the purpose of the combing is so to straighten and parallel the fibers that each fiber will contribute its share to the strength of the bundle. N'aturally, short fibers that do not pass through the center of the bundle are not gripped by the thumb and forefinger during combing and are withdrawn by the combing action. But the bundle is always broken at or near its center, and most if not all the short fibers that are removed during comb- 30 TECHNICAL BULLETIN 5 4 5, U. S. DEPT. OF AGRICULTURE ino- have come from the ends of the bundles and therefore would not have contributed to the strength of the bundle had they been retained. The change in the distribution of fiber length in the bundle thereiore, does not indicate the extent of change at the center of the bundle but rather in the ends, where the short fibers are more or less completely removed. Probably at the center of the bundle, where the break is actually made, very little disturbance of the original length distribution of the raw cotton occurs.

X 20

100 10 20 30 40 50 60 70 80 90 CUMULATIVE WEIGHTS (PERCENT)

FIGURE 13 -FIBER-LENGTH DISTRIBUTION OF RAW COTTON, BUNDLES, AND COMBINGS. In preparing a Chandler bundle some disturbance to the length distribution occurs the lonler fibers being retained in the finished bundles and the shorter fibers m the comb- ingl Obviously the short fibers are largely separated from the outer ends ot the bundles. SAG OF THE BUNDLE DURING WEAPPING In wrapping, the 4-pound weight suspended in the loop of the wrapping thread causes the bundles to sag between the supporting laws There is some evidence that the amount of sag varies with the size of the bundles, being greater for those of smaller size, but this is not certain. At any rate the amount of displacement ot the indi- cator with respect to the scale of the wrapping device, which results from sag, differs in the final reading from that in the initial reading, so that the mean circumference, as measured by the difference m readings, is always too small and the bundle strength per square inch too large. Preliminary studies have indicated that the error due to bundle sag is about 6.5 percent of the bundle strength. ^ No convenient method for overcoming the discrepancies due to bundle sag has been discovered. However, the relative strength is usually all that is required, the absolute magnitude being unessen- tial. When the circumference of the bundles is kept near standard, the effect of sag will be approximately constant and can be disre- garded, considering the more serious sources of error. Moreover, the curves used for correcting machine break to standard circumference include the element of sag and thus tend further to minimize any error due to this factor. MEASUREMENT OF CHARACTER PROPERTIES OF COTTON 31

ELONGATION OF THREAD DURING WRAPPING Another slight error is caused by the time effect upon thread elongation after suspending the 4-pound weight in the loop of the wrapping thread. Ordinarily, this effect will be very small and approximately constant; but it might conceivably become significant if the operation of wrapping were interrupted for any reason between the initial and final readings or if the kind of wrapping thread should be changed between tests.

PRECISION OF RESULTS After some experience had been attained with the new technique, an experiment was performed (1) to establish the approximate order of precision obtainable with it and (2) to show, insofar as possible, whether any further sources of systematic error remained. The first purpose could be attained by calculating from a large number of observations on a single sample of cotton, the standard error of means based on 10 observations each. The second purpose could be partly realized by making the tests over a period of time during which opportunity would be afforded for sources of variability to operate if they existed. Their existence would then be disclosed by lack of homogeneity in the resulting data as shown by an analysis of variance according to Fisher's (26) procedure. For the study, a sample of comparatively strong cotton was obtained. Classification by cotton experts showed the cotton to be 1% inches in staple length and Strict Low Middling in grade. Bundles were combed, wrapped, and broken in succession until 100 satisfactory breaks had been obtained. The test extended over a period of 53 days and included bundles prepared or broken on 8 different days. The breaking strengths were calculated and the data collected in groups of 10 observations each, comparable with the number of observations previously selected on other grounds for a single test. The data, expressed in units of 1,000 pounds per square inch, are presented in table 9.

TABLE 9.—Tensile strengths in thousands of pounds per square inch of individual bundles and means of groups of 10 Chandler bundles, prepared from the same cotton and arranged in sequence according to time of breaking

Strength of bundles for— Observation— Group Group Group Group Group Group Group Group Group Group 1 2 3 4 5 6 7 8 9 10

1,000 1,000 1,000 1,000 1,000 1,000 1,000 1,000 1,000 1,000 pounds pounds pounds pounds pounds pounds pounds pounds pounds pounds per per per per per per per per per per square square squre square square square square square square square inch inch inch inch inch inch inch inch inch inch 1 _ 87 83 86 86 81 87 81 87 89 88 2 86 87 87 85 84 90 83 90 87 87 3 84 92 90 84 87 88 84 84 82 86 4 84 85 90 87 88 89 80 82 88 82 5 ■ 86 83 85 84 88 89 84 87 84 84 6 _ 84 85 86 83 85 88 84 87 89 88 7 87 87 81 87 88 84 80 86 89 85 8.. 84 85 84 82 86 88 87 88 84 84 9 88 87 82 88 86 86 88 88 88 92 10 83 90 83 80 88 87 84 88 89 81 Mean 85.3 86.4 85.4 84.6 86.1 87.6 83.5 86.7 86.9 85.7 Sum of squares !_-- 2.5 3.6 1.6 14.4 .9 32.4 52.9 8.1 12.1 .1

1 Sum of squares obtained by taking 10 times the square of the deviation of the particular group mean from 85.8, the grand mean. 32 TECHNICAL BULLETIN 5 4 5, U. S. DEPT. OF AGRICULTURE

The mean strengths based on 10 observations each seem to agree within a comparatively narrow range, namely: 83.5 to 87.6. The average of all observations was found to be 85.8. TABLE 10.—Analysis of variance of the strength of 100 Cha^idler bundles arranged in sequence with respect to time of breaking

Degrees of Sum of Mean Standard Probabil- Source of variability freedom squares square deviation ity!

Between erouDS - -- 9 128.6 14.28 3.78 About 0.03 Within groups 90 580.2 6.45 2.54 Total 99 708.8 7.16 2.68

1 Probability that differences as large as those obtained would occur in groups of 10 observations taken from a normal population. The data were then treated according to Fisher's procedure for analysis of variance, and the results shown in table 10 were obtained. A mean square of 14.28 is obtained for the variance between groups of 10 observations, whereas a mean square of 6.45 is obtained for the variance within the groups. The difference, 7.83, is appreciable, and the probability that the observations may be considered to be- long to a homogeneous population is only about 0.03. Therefore, the results, although not highly significant, are indicative of an interfering factor or factors that operated during the performance of the tests. In table 9, a line called "sum of squares" is found at the bottom. The figures in this line show the contributions from each mean to the sum of squares between groups. They total 128.6—the figure shown in the first line of table 10 under "sum of squares." It will be noted that groups 6 and 7 of table 9 make the greatest contributions to the sum of squares, the figure for group 7 alone being 52.9. Furthermore, in referring back to notes made when group 7 was being tested, it was found that a defective leather pad had been detected in one of the bundle-breaking jaws at the end of the seventh break. In table 9 it will be found that three of the first seven observations in group 7 are very low, being 81 or less. This largely accounts for the low probability figure obtained in the analysis of variance. The disturbing effect of the defective leather is further shown m table 11, which contains an analysis of the variance remaining after deducting the sums of squares arising from group 7 and making appropriate changes in the degrees of freedom. The mean square between groups is now reduced from 14.28 to 9.46, and that within groups is reduced from 6.45 to 5.71. The resulting probability, calculated by standard methods, is now found to be appreciably greater than 0.05. The remaining nine means of groups are accordingly shown to agree within the normal range of expectation, based on a homogeneous population, and to suggest that no other factors seriously disturbed the results. By reference to the fifth column of table 10, it will be seen that the standard deviation of all observations was 2.68 expressed in units of 1,000 pounds per square inch. From this, the precision of a single MEASUREMENT OF CHARACTER PROPERTIES OF COTTOIíT 33

test comprising 10 observations can be calculated and can be represented by a standard error of the mean of 0.85 ; that is (2.68/VÏÔ). The corresponding standard error of the difference would be 1.20, and a difference of approimately 3,500 i)ounds per square inch between two means could be considered significant with odds of 99 to 1. If the standard deviation shown in table 11 is used, namely 2.46, the standard error of a mean becomes 0.78, and the standard error of the difference between two means becomes 1,100 pounds per square inch. In this case, a difference between two means of about 3.2 would indicate significance with odds of 99 to 1,

TABLE 11.—Analysis of the variance remaining after group 7 of table 9 was omitted

Source of variability Degrees of Sum of Mean Standard Probabil- freedom squares square deviation ity! Between groups 8 75.7 9.46 3.08 0.05 Within groups 81 463.2 5.71 2.39 Total 89 538.9 6.05 2.46 1 Probability that differences as large as those obtained would occur in groups of 10 observations taken from a normal population.

PRACTICAL APPLICATION OF THE METHOD It is evident that a considerable portion of the uncontrolled variability present in the technique of the original Chandler method has been brought under control with corresponding increase in the meaning and reliability of results. But the results obtainable could conceivably be reproducible with a high degree of accuracy without being indicative of yarn strength. Of course, this is an old story with respect to the poor relation between mean fiber strength and mean yarn strength. During the period of study and improvement of the Chandler bundle method, a number of opportunities occurred for comparing the relationship between mean bundle strength and mean yarn strength of different cottons. The results have been most reassuring and suggest the practicability of this method when properly applied. Of course, fiber strength is not the only important fiber property that affects yarn strength; other properties, such as fiber length and fiber fineness, must always be taken into account in attempting to predict the strength for a given count of yarn. Table 12 shows in a typical way the strength of yarn and cord manufactured from three cottons of different bundle strengths. For purposes of comparison, the figures showing length and fineness of these cottons are also given.

TABLE 12.—Strength of yarns and cords manufactured from 3 cottons having the different properties indicated

Property Sample C Sample D Sample K

Upper quartile length-.-. inches m m2+ IMe- Fiber fineness 0.0001 mg per inch- 39 46 47 Strength of raw cotton -..1,000 pounds per square inch 76.2 60.8 67.5 Skem strength, 13s yarn pounds 205.5 173. 3 190.7 Skein strength, 23s yarn do 107.8 90.7 100.6 Cord strength, 13/3/31 do 14.4 13.1 13.7 Cord strength, 23/5/3 '''.'''do"" 14.8 13.0 14.8 1 Corrected to 1.28s size. 917730—37 3 34 TECHNICAL BULLETIÍ^- 5 4 5, U. S. DEPT. OF AGRICULTURE

The length of the fibers in the three cottons differed by about one- sixteenth of an inch, but the samples differ considerably in fiber fineness, the fibers of samples D and K being about the same and coarser than those of sample C. It is possible that the greater fineness of sample C may be responsible for its greater bundle strength as well as its relatively high skein and cord strength. Comparing the bundle, skein, and cord strengths of the three samples, they are found to vary in the same direction with respect to each other. The results of the experiment just described are more striking than are those usually observed. These cottons differed greatly both in raw cotton strength and in capacity to give yarns of good strength. However, even with cottons of less contrast, the bundle-strength test usually has indicated the order of arrangement with respect to yarn strength. When the test has failed to accomplish this, it has usually been possible to discover some large difference in other fiber properties, such as length or fineness, which accounted for the failure.

SUMMARY It is evident that the Chandler bundle method for determining the strength of cotton fibers, as originally described, contained several sources of error. These have been studied and to a large extent either eliminated or controlled. The more salient points may be summarized as follows : (1) For reasons given, it has seemed desirable to abandon the use of Chandler's factor, K, for converting the strength to that for pure cellulose. The revised method gives the strength per square inch of bundles of fibers prepared and wrapped under carefully specified conditions. (2) By proper calibration, the area of bundle cross section is determined, and the error due to the effect of the diameter of the wrapping thread upon the calculation is eliminated. (3) To eliminate errors in strength due to variability in distance between wrapping threads at the center of the bundle, the threads are now allowed to come together and touch. With this change, the constant conditions of tension during wrapping result in uniform conditions of thread contact at the center. (4) The size of the bundle is an important variable influencing the strength expressed in pounds per square inch. This effect was found to be associated with varying density of bundles of different size. To overcome variability in results due to this factor, the bundles are now all made with circumferences within the range 0.115 to 0.135 inches; and then a correction is applied to the machine break for variations of circumference from 0.125 inch. The details for applying the correction are given. (5) The method of combing and treating the fibers during combing was found to have an important bearing on the strength of the bundles. The conditions of combing have been carefully specified in the revised method. (6) The sag of the bundles during wrapping and the possibility of variations in elongation of the wrapping thread are recognized as sources of variability. The former is not conveniently eliminated but should not lead to any appreciable error, since the same error entered MEASUREMENT OF CHARACTER PROPERTIES OF COTTON 35

into the data for correction to specified size. The latter source of variability will ordinarily be immaterial. The revised method of test is described in detail, and tables are given for determining under the specified conditions of test (1) the corrected bundle circumference from the observed circumference (2) corrections in machine breaking strength for deviations of corrected circumference from standard bundle circumference, (3) the strength per square inch from corrected machine breaking strength and (4) the standard deviation and standard error of means of 10 observations from the sum of the variance.

ESTIMATION OF FIBER FINENESS IN RAW COTTON WITH SPECIAL REFERENCE TO IMPROVEMENTS IN THE METHOD OF DETERMIN- ING WEIGHT PER UNIT OF LENGTH'"

Fineness of fiber is considered to be important in cotton because it has been found to be a significant factor in other textile fibers and as a result of limited experimentation with cotton. Its importance has been recognized in the silk and artificial-silk industries, and in the wool industry it is the chief criterion of quality standardization and constitutes the basis of the official grades for wool {ß^). Owing to the high correlation between fineness and length of fiber which appears to exist rather generally in cotton, the element of fineness has been utilized indirectly and in part unknowingly in the selection of raw cotton for special uses. The relationship appears to be tairly close, yet it is uncertain just what role each of the two elements, length and fineness, plays in the final product, and until accurate methods for the measurement of each are available progress cannot be expected in an understanding of the influence of these properties on manufacturing behavior and quality of product. Although the degree of maturity (wall thickness) is one of the tactors that determine cross-sectional area, it also has some effects upon fiber, yarn, and fabric quality which are independent of this area {5^). Because of its high cellulose content, the average area of cross section m cotton fibers must be almost exactly proportional to the weight, per unit of length and thus it determines the number of fiber's to be found in the cross section of a given count of yarn. As will be seen in the review of the literature, fineness has been given different nieanings by different workers. Most of the defini- tions can be classified into two groups, those dealing with an imaginary "fiber diameter" which it is sought to approximate by measurement of one or more of the real dimensions of the fiber, and those seeking to determine the cross-sectional area of the fiber wall—usually by means of measurement of weight per unit of length. In this bulletin the authors have adopted the average cross-sectional area of a cotton fiber or of a sample of cotton fibers as the most practical measure of fiber fineness since it can be determined accurately from the average fiber weight per unit of length. As defined above, fineness of cotton fibers may be considered to vary according to two principal causes, (1) original diameter, and

lOBy T. D. W. BAILEY JR., and CARL M. CONRAD. The authors are indebted to Edward W S Calkins, junior cotton technologist, for assistance with the work o^this method • microgra^hr^ Pearson, assistant cotton technologist, for assistance with thf photo- 36 TECHNICAL BULLETIN 5 45, U. S. DEFT. OF AGRICULTURE

(2) degree of wall thickening. Average fiber diameter is a genetical or hereditary quality, associated with variety and species. On the other hand, the degree of wall thickening probably depends on environmental factors which encourage or inhibit growth. Balls (3) states that a particular cotton fiber reaches its maximum diameter very early in its development, and that subsequent wall thickening comes through secondary deposits of cellulose on the inside. The wide variation that exists in the fineness of cotton fibers is perhaps not generally realized, and its importance is realized even less. Not only are there wide differences in size of mature cotton fibers in different growths (pi. 1), but there are also large differences within a single growth (pi. 2). It is recognized that fine yarns require long staples. However, there is a high correlation between fiber length and fineness, and there are indications that this require- ment for fine yarns is to a considerable extent a matter of fineness as well as of extra fiber length (65, p,21). Furthermore, the manu- facturer who wants to increase the strength of his yarn often resorts to longer staples and in so doing generally obtains finer fibers. When long-fibered cottons are cut to simulate short-staple cottons, and are spun into yarns, the strength of these yarns is by no means reduced to that of yarns spun from cottons naturally of correspondingly short staples. . . ,.1 ' ^ • P The improved method for determining fiber weight per unit ot length as an expression of cotton-fiber fineness, here described, is not necessarily recommended as a routine procedure for testing raw cotton used in all kinds of manufacture. It is too slow for such a purpose. Eather, it is recommended for use by manufacturers who must meet detailed and severe specifications, as for instance, manufacturers of balloon fabrics, airplane-wing fabrics, and tire and other mechanical fabrics ; and by investigators who seek to establish the relation between fiber fineness on the one hand and properties of the manufactured products on the other. The special merit of the method lies in the precision which the writers believe it possesses.

PREVIOUS METHODS FOR DETERMINING FIBER FINENESS Various methods for determining fiber fineness have -previously been developed. Among the more important are methods based upon (1) measurement of ribbon width, (2) direct measurement of area of cross section, (3) mean diameter from diffractive properties, (4) use of yarn count, and (5) weight per unit of length.

MEASUREMENT OF KIHBON WIDTH

Early measurements of fineness were based upon microscopic determinations of so-called diameter or ribbon width of a representative number of fibers. Among the first to report diameter measurements of cotton fibers was Leigh {U) ; but he did not describe the technique he employed. In 1881 Bowman {10) measured the diameter of cotton fibers, making use of a parallel wire eyepiece micrometer. For determining fiber diameter. Balls {3 p. 186) describes a more rapid method than by means of the eyepiece micrometer. A camera lucida is attached to a microscope so that the fiber image is seen at a known magnification on a piece of paper. The two edges of each fiber image Technical Bulletin 545, U. S, Department of Agriculture PLATE 1

Untreated cotton fibers of difíerent growths representing a range in fineness. Specimen A represents a very coarse fiber of the variety Garo Hill, staple length about five-eighths of an inch; C represents a fine fiber from sea-island cotton, staple length IH inches; and B is a fiber from American upland cotton, staple length 1% inches, representing fineness intermediate between A and C. X 475. ? ¥ m-à

% rí,

¡I m¡m -a Mature cotton fibers showing different degrees of über flreness in American upland cotton. X 3Q0.

PI MEASUREMENT OF CHARACTER PROPERTIES OF COTTON 37

are indicated by marks on the paper and the distance between these iriarks IS subsequently measured. By averaging a sufficient number ot such measurements he obtained a mean diameter of the fiber Bergen {9) reports a method of measuring the projected image of wool fibers with a wedge rule. Pope (Ô7) in a study of fiber diameter measured the ribbon width, W, and thickness, T, to obtain a "mean ribbon width*', —^—, an expression previously used by Barritt (5). Calvert and Harland (W) suggested that the reliability of diameter measurements could be greatly increased by mercerization of the fibers before measurement. They concluded that the measurements of the mercerized fibers were not subject to the serious errors usually accom- panying nbbon-width determinations. In summarizing the application of this method to the measurement of fineness they state that measurements of diameter and length will accurately gíade a commercial cotton and the former alone is probably sufficient except when dealing with Sea Island and Egyptian." Calvert and Summers (IS) made an exhaustive study of the relationship of the mercerized diameter to the ribbon width of the untreated fiber through the stages of mercerization washing, and drying, and found that the ratio of the average dried mercerized diameter to the average ribbon width was approximately 0.8 to 1. They also showed that the maximum swelling in caustic soda brings the fiber almost exactly to the diameter it had m the boll before collapse, and that this diameter is about 1 3 times the ribbon width. Barritt (S) employed approximately the same technique as a means of checking his mean ribbon-width measurements.

DIBBOT MEASUREMENT OF AREA OP CEOSS SBOTION

Peirce (65) describes a method based on the area of cross section in w;hich fiber cross sections are cut and their outlines traced with the aid ot a camera lucida. The cross-sectional areas are obtained with the aid of a planimeter or by cutting out the fiber outlines and weighing the pieces of paper. The disadvantage of cutting cross sections for measurement of fineness is due to the difficulty of preparing the slide without distorting the fibers. Clegg and Harland (^7) who used a method similar to that described by Peirce state that, the results are probably fairly accurate for comparative purposes, but it must not be supposed that they represent the actual areas of cross sections Zee • an unknown amount of expansion takes place when a section of a hair is cut. .^CLLIUH UL a Johnson (SS) originated a simple method of cutting cross sections ot rayon filaments by drawing them through a hole in a piece of metal and cutting them flush with the top surface by the use of a razor blade. Schwartz (ßO) improved Johnson's method by the use of a thinner disk and drew the fibers through by the use of a looped thread or wire, cutting the fibers off flush with both surfaces. Viviani (68) Herzog (SS) and Bauer (8) applied a similar principle, drawing the fibers through a hole m a cork and slicing the cork and fibers together Barthélémy (7) drew his fibers into a slit in the side of the cork to ^Inl ^«"blmg, and Niblack (51) used a slit in heavy paper. Hardy (Jy) used a slit m a metal disk, in which the fibers were compressed 38 TECHNICAL BULLETIN 5 4 5, U. S. DBPT. OF AGEICULTUEE

by a sliding key or plunger. He cut the fibers flush with both sides of the disk by the use of a razor blade, and measured the fineness of wool by counting the number of fibers in a given area. These methods seem equally applicable to cotton fibers. • • xi c Hardy (30) describes a rapid method for determining the fineness of wool and there appears to be no reason why this niethod should not be applied to the measurement of cotton fibers. A thread or tutt of fibers IS placed in a slot of known size and a knife is brought down to cut part way through the thread, leaving a small portion uncut. Since the knife is made always to stop the same distance from the bottom of the slot, the number of fibers remaining uncut will be an expression of the fineness of the fibers. MuUer {P) has developed an instrument based on a similar principle, for measuring the fineness, and indirectly the length, of wool or cotton fibers. Kusebauch (P) has modified this method to determine fineness by measuring the thickness of a bundle of 100 fibers. Fedorow CM) combined his measurement for ribbon width and cell-wall development into a single expression representing the area of cross section and thus expressed fineness as a function ot both.

MEAN DIAMEflEE FROM DÜTÍBAOTIVE PEOPEBTIBS The use of diffraction methods for the measurement of average fibL diameter has been reported by Young {71 p ^4^) Ewles W, McNicholas and Curtis (46), and Matthew (^7), These methods depend upon the principle of the optical gratmg in which the fibers form the parallel lines. Such a system of parallel Imes produces diffraction bands the distance between which depends upon the number of lines per inch. The fiber diameter determines the gratmg number and consequently the distance between bands, and by proper calibration of the instrument it can be made to read directly the mean diameter of the fibers and may give some measure of the variability in diameter (IS).

USB OF TAEN COUNT

Methods involving the extension of the idea of yarn size or fineness count to fiber size or fineness have been used by f number ot fnTestÎgaTors-Hermann and Herzog (SS) Johannsen (38), Lipow- skv (J), Oxley and Peirce [62), Koehrich {S9), and others. They have be¿n developed principally in connection with yarns but through variations have been applied to bundles of parallel cotton fibers as well. One form of the expression {3i, pp. m, 291), known as the metric fineness number is

in which Nr. is the metric fineness number of the fibers, ^ is the average number of fibers per yarn cross section and L and ^ are the length and weight respectively of the piece of yarn used The units for Z and G may be either meters and grams or millimeters and milli'n-ams, respectively. It is seen that this expression differs from the ¿etric expression for yarn number only m containing the variable A. The same equation in which, however, L and 6- are ex- MEASUREMENT OF CHARACTER PROPERTIES OF COTTON 39

pressed in hanks and pounds gives the English fiber fineness number Ne, The method consists in counting the number of fibers in a cross section either by prying them apart with needles under a lens or low magnification of a microscope {JfS)^ or by cutting sections from the yarn, mounting in gelatin, and observing under the microscope according to the Herzog {SJ^, p. 230) procedure. The average number of fibers in the yarn cross section must be obtained from a number of individual observations and is then multiplied by either the metric or English number for yarn fineness. The fiber metric number is determined and used by Koehrich {69) in obtaining his "coefficient of maturation." The formula for the English fiber fineness number was used by Oxley and Peirce {62) except that they solved for the weight in pounds per yard of fiber. This latter expression corresponds to the weight per unit of length except for the units of measurement and the method of arriving at the final result.

WEIGHT PER UNIT OF LENGTH Probably the first to study fiber weight per unit length as an index of fiber fineness was Balls {S, pp, 186-188), He cut a bundle of fibers to a length of 1 cm, weighed the cut portion, counted the number of fibers, and obtained, by division the mean fiber weight per centimeter. This method, often referred to as the cutting method because it involves cutting a section from the center of a bundle of parallel fibers, was adopted with modification by Clegg and Harland {16), Burd {11), Morton {1^8), Eoehrich {69), and Clegg {15). A variation of the cutting method is described by Krauter (4^). He clamped a known number of fibers between two glass plates of a known width and burned off the protruding fiber ends with a small pointed flame. He then removed and weighed the remaining portions of fibers. The Indian Central Cotton Committee, according to Ahmad {2) has completely abandoned the use of cut sections for estimating the fiber weight per unit of length. Instead, 28 to 40 small tufts weighing approximately 0.5 mg each and comprising 100 to 150 fibers each, are taken from the original sample and accurately weighed on a quartz microbalance. The fibers in each bunch are then counted and the average weight per fiber is calculated. From the mean length per fiber, determined separately, the mean fiber weight per inch IS calculated. CHOICE OF A BASIC METHOD Each of the methods referred to above has some disadvantage which makes its use more or less difficult or tedious, or its result unreliable. The measurement of ribbon width requires microscopic measurements of individual fibers which are tedious and time- consuming. Besides, the continual and exacting use of the microscope tends to cause severe eye strain. Then, too, measurements of ribbon width can never give a reliable expression proportional either to the original fiber diameter or to the area ot fiber cross section, since the ribbon width varies between 1 11 T{^ (=1.57) times the circular diameter, depending on the fiber wall-thickness. The area of cross section on the other hand is directly 40 TECHNICAL BULLETIN 545, U. S. DEPT. OF AGRICULTURE

proportional to the square of the difference between circular fiber diameter and circular lumen diameter. Barritt {6) attempted to minimize this discrepancy by obtaining a "mean ribbon width , ^2 ' ^^ ^^î^^ ^ ^^ ^^® ^^^^^ ^^^ ^ *^® thickness of the collapsed fiber. But frequently this procedure must be inexact, for often the ribbon is folded or irregular. Calvert and Summers (lo) partly overcame this discrepancy between ribbon width and diameter by their mercerization procedure but introduced other uncertainties, including the uncertainty that the constancy of swelling of different fibers IS always the same, and their method was still tedious, and exacting on the eyes. . The direct measurement of the area of cross section has much to commend it from the theoretical standpoint, since the results so obtained ought to be directly related to yarn size. Actually, however, technical difficulties largely offset the theoretical advantages of the ribbon-width method. The cross-sectional area of cotton fibers varies greatly from base to tip, and sectioning in such a way as to obtain a representative series of cross sections from a sample offers many problems. Unlike the measurement of ribbon width which may be made rapidly at a number of points along a single fiber, the cross- sectional area can be measured only at one point at a time. Then, too, the work of tracing a sufficient number of fiber outlines and measuring their area is much greater than is that of obtaining the ribbon- width measurements. Finally, it has been argued that the cross-sec^ tional areas of the fiber sections may be distorted during cutting and that an unknown expansion occurs which may not be equal for all fibers. One objection to the use of the diffraction method is that cotton fibers do not have circular cross sections. A second is that the ribbon widths and thicknesses alternate along the fibers and thus cause lack of definition in the diffraction bands. This lack of definition cannot be readily distinguished from that arising from variations in mean diameter of different fibers. Third, the small number of fibers that can be accommodated in a single measurement, with the instruments thus far designed, makes it difficult to obtain a representative sample. Finally the method can give only a "mean diameter" comparable to Barritt's "mean ribbon width" and subject to the same inaccuracies as exist in that expression. Mercerization of the fibers before examination might remove some of these difficulties. The yarn-count method, when applied to yarns, doubtless gives a satisfactory expression for fiber fineness, but is not very applicable to small tufts of cotton prepared artificially, because of the impracti- cability of determining the true count. The weight-per-unit-length method, as used by most previous investigators, is subject to one or more of several sources of inaccuracy. These are due principally to the fact that sections cut from the centers of fibers do not give an accurate measure of the average fiber fineness as it exists in a yarn. This follows from at least three causes: (1) That fiber sections of equal length give equal importance to fibers of all lengths, whereas in a yarn, a fiber influences the fineness in proportion to its length; (2) that the fineness of the midportion of a fiber bears a variable relation to the fineness of the entire fiber ; and MEASUREMENT OE CHARACTER PROPERTIES OF COTTON 41

(3) that the proportion of fibers shorter than the selected length of cut section is appreciable and variable with type of cotton, manner of ginning, and length of staple. The fact that fibers of difierent length have different weights per unit of length and therefore that the results for any length should be given importance in proportion to their length seems to have been overlooked until Turner (62) began a comparison of the results obtained from whole fibers and from cut sections. lyengar and Turner (37) then made a more complete investigation of the two methods and summarized their findings in the statement: "It cannot be ac- cepted as universally true that the fiber weight per unit length is the same for different lengths of fiber for a given cotton." Kesults obtained in the technological laboratory of the Bureau have thoroughly confirmed the normal occurrence of widely divergent weights per unit of length in the different fiber lengths in a sample. Since the differences are frequently large, it is important to weight the figures for weight per inch in each length group by the length of that group, and this is not possible when the cutting method is used. A second source of error resulting from the use of the central sections of fibers was first pointed out by Turner (6^). It is that the fineness of the midportion of a fiber bears a variable relation to the fineness of the whole fiber. In the three cottons that Turner tested, he obtained a lower weight per inch when the whole fiber was used than when it was calculated from the sections, although in one case the difference was slight. To check his observations he cut fibers into several sections and weighed the sections separately. The results showed the tip or apex portion of the fibers to be the lightest and the portion just below the center of the fiber to be the heaviest. His conclusions were further confirmed by Ahmad (^) who compared the results obtained by the cutting and whole-fiber methods on 21 standard Indian cottons for the season 1929-30. He reported that in every case the whole-fiber method gave lower figures for the weight per unit length than the cutting method, the differences ranging from 3.3 to 26.5 percent, with an average at 11.5 percent. The fact that the weight per unit length by the cutting method gave higher values than were obtained by the whole-fiber method was not important in itself, but the fact that the differences varied so widely makes the cutting method entirely unreliable. Still a further source of inaccuracy in the weight per unit length obtained by the cutting method is the variable proportion of fibers omitted from the cut section. The fiber length of any sample of cotton varies greatly ; for example, fibers from a sample classed as having a staple length of 1 inch maj^ have fibers with a maximum length of ly^ inches or more and a minimum of one-sixteenth of an inch or less. If a section of given length is cut from all the fibers, either the length of such a section must be adapted to the shortest fiber length, or the shorter fibers must be excluded from the determination. In the first case, the sections w^ould have to be so short that an enormous number would have to be counted to provide a weighable quantity and any method that might be developed would be laborious and im- practicable. In the actual use of this method the sections have usually been 1 cm lone; and most workers have tried to remove the shorter fibers 42 TECHNICAL BULLETIN 54 5, U. S. DEPT. OE AGRICULTURE by combing or sorting. In the longer staples this might exclude 7 to 8 percent of the weight of the sample, and in some of the shorter staples, 15 percent or more might be excluded. Thus, in the practical use of the cutting method, not only is a considerable portion of the fibers excluded from the determination but the quantity so excluded is variable from sample to sample and from staple to staple. Since the shorter fibers ordinarily have a considerably greater weight per inch than the longer ones, the mean fiber weight per inch for the cotton is lowered to a variable degree by their exclusion. Furthermore, the short fibers cannot be completely removed from the sample by combing or even by length sorting, and some fibers that are actually shorter than the cut length are included in the cut section. Their inclusion tends further to lower the mean fiber weight per inch found by this method. If it were not for the fact that some of these inaccuracies are compensating, discrepancies between observations obtained with the cutting and whole-fiber methods would be much greater than they actually are. Of the various methods that have been proposed, the weight-per- unit-of-length method has some especially desirable features. The weight per unit of length of a cotton fiber provides an extraordinarily good measure of the average area of cross section of that fiber, since every portion of the length contributes to the results. Since the composition of cotton lint varies so little and the density is known approximately, the actual average area of the cross section may be calculated with considerable precision if desired. The area, so calculated, is not subject to the various sources of inaccuracy arising from a limited number of measurements along the fiber, to irregu- larities of form of the fiber cross section, or variations in the relation between ribbon width and theoretical diameter of the fiber. Also the estimated area of cross section obtained in this way is not subject to the criticism of distortion during sectioning, which has been urged against the areas of cross section obtained by direct microscopic measurement. Perhaps a still more important feature of the weight-per-unit- length method is that it provides a measure of fiber fineness readily comparable with yarn count or fineness. If the average weight per inch is known for the fibers that go into a yarn, the average number of fibers per cross section for a yarn of any given count can be readily calculated. In fact, with a knowledge of the fiber weight per inch the "fiber count" can be readily calculated and expressed, if desired. Not one of the other measures previously discussed, such as ribbon width, mean ribbon width, mean diameter, or mean area of crosr section, provides a figure so readily interpreted in terms of yarn fineness. This is a matter of considerable importance if the relations of fiber properties to yarn properties are to be unraveled. The final conclusion then, as to the superiority of the weight-per- unit-of-length method, depends on whether the errors inherent in the older cutting technique can be successfully overcome, and whether the resulting technique is unduly tedious. In the first instance it has been found practicable to supplant the cutting technique completely by the use of whole fibers, a procedure which was adopted in the technological laboratory from the beginning. In the second MEASUREMENT OF CHARACTER PROPERTIES OF COTTON 43 instance the resulting method is not believed to be more tedious, if as much so, as the other methods involving individual fiber measurements.

SPECIAL FEATURES OF THE IMPROVED METHOD The improved technique for determination of fiber weight per unit of length combines the following important features : (1) Use of entire fibers instead of cut sections. (2) Systematic sampling from all groups of fiber lengths within the sample. (3) Accurate weighting of the fiber weight per inch in each length group by the relative length of fiber in that group, to obtain an expression representative of the raw cotton and comparable to the distribution of fiber fineness in a yarn. (4) Contribution of an additional criterion of fiber quality, namely, a measure of variability of fiber fineness in the different length groups. In using entire fibers instead of sections, it is necessary to know the average length and average weight per fiber. Ahmad (2) accomplished this by obtaining the average fiber length with either a Balls or a Baer sorter, and the average weight per fiber by carefully weighing 28 to 40 small tufts and then counting the number of fibers in them. By using the small tufts he overcame the tendency to select the longer fibers for weighing—a tendency inherent in the technique Avhen fibers are selected individually. He also obtained a systematic sampling from all length grouj)s represented in his tufts and eventu- ally obtained an expression properly weighted for fiber length and for the variability of fineness in the different length groups. The influence of method of sampling and size of sample in the determination of fiber properties has been discussed in considerable detail by Koshal and Turner {40^ ^l). Although the method worked out at the technological laboratory of the Indian Central Cotton Committee for determination of weight per unit of length, is undoubtedly the best suggested thus far, it is believed that a still further improvement can be achieved by selecting groups of fibers from the fiber-length array for weighing. It is believed that this procedure provides a better sampling technique in that a much larger tuft can be used for sorting and the tendency for similar fibers to remain associated can be more thoroughly overcome. This follows because the tufts of similar fibers can be dissolved or separated more readily in the sorter than in any other way, and the different types of fibers can be more intimately mixed. Furthermore preparation for sorting has involved a preliminary mixing in which some 64 to 96 tufts are finally represented in the length arrays and the resulting length groups can be used for the weight determination with only slight additional labor. The length array has a second advantage over the individual- tuft method, as a basis of sampling, in that it permits an expression for the variability of fiber fineness in the different length groups. This may be a matter of considerable interest since it has been observed, both by lyengar and Turner (37), and by the writers, that different cottons differ markedly in this respect. Instead of attempted random sampling, systematic sampling from each length group of the length array provides a basis from which the original random distribution of fiber fineness can be reproduced 44 TECHNICAL BULLETIN 54 5, U. S. DEPT. OF AGRICULTURE mathematically. This is accomplished by multiplying the fiber weight per inch for each length group by the calculated total fiber length for that group, accumulating the products, and dividing by the calculated total length of fiber for the sample. Mathematical reproduction of the original distribution of fiber fineness can be accomplished through the following considerations: Let W be the weight of any group of known length, Z, taken from the fiber length array, and F^ the mean weight per fiber determined experimentally in the same group. Then the number of fibers, N, in that length group will be ^^ s and the total length of fiber in the length group will be

Also, the weight per inch, /, of the fibers in this length group will be

These relations will hold for each length group in the length array of the sample. To find the mean weight per inch, /, for the sample it is necessary to multiply the individual values of / for each length group by the total length of fiber in that group, summate over all groups, and divide the sum by the total length of fibers of all the OToups, thus

LW F But LN =—pr-and I =-j] therefore ^LW F = ^F LXW

This last equation is equivalent to the statement that the mean fiber weight per inch for the sample is equal to the sum of the weights of the different length groups divided by the sum of the lengths of fiber in them. From the foregoing it is evident that three sets of observations must be obtained for each length group—^the length, the weight per fiber, and the weight of the group. From these, all other necessary computations can be made. The length and weight of the length groups are obtained in connection with the determination of the fiber length of the sample so that the only new observations required for determining the fiber weight per inch, are the weights of a representative number of fibers from each length group to provide a representative weight per fiber for the group. From the work of other investigators, particularly Clegg and Harland (Í7), Clegg (^5), and Ahmad (â), it is certain that two samples of 100 fibers each taken from each length group will furnish a sufficiently reliable sample for all practicable purposes for the weight per fiber of that group. The standardized procedure, as described immediately below, is designed to be carried out in connection with an analysis of fiber MBAtíUHEMEÍÍT OF OHARAOTBR PROPBETIKB OF COTTON 4S length on a sorter of tlie comb-bank type. The operations require an air-conditioned room in whioh the relative humidity and temperature can be controlled. If such a room is not available approximate corrections might be made by means QÎ a table constructed according to the scheme shown by Ahmad (^). The entire series of laboratory operations for a sample can be carried ont by one worker in 7 to 10 hours, depending on the staple length of the cotton and assuming tliat the length arrays have previously been completed. With the aid of a calculating machine or slide rule, the calculations can be completed in about 1 hour. THE STANDARDIZED TECHNIQUE

ATMOSPHERIC CONDITIONS The same conditions used in the other fiber tests are employed for this determination—65 percent relative humidity and 70° F. A toler-

^5WI^^^^^^^^^ ^^^^^^^Bl^^^

FlGUKE 14.—Part of the laboratory and apparatus used for the determination of fiber weight per inch in the Bureau of Agricultural Economics. ance of 3 percent in relative humidity and 5° in temperature above or below the fixed value is permitted. The samples should be exposed to the prescribed conditions for at least 2 hours before they are weighed. Although probably only the weighing needs to be done under controlled conditions, it has been found convenient in this laboratory to perform all the operations connected with this determination in the same room. These involve sampling, sorting, measuring, two operations of weighing—one before and one after extracting—and counting out the fibers (fig. 14)." SAMPLING

As this method of measuring fineness is based on whole-fiber weight per inch, it is convenient to have the fibers of nearly the same length segregated ; therefore, the fiber-length array is used as the foundation 46 TECHNICAL BULLETIN 545, TJ. S. DEPT. or AGKICULTUKE for sampling. The general procedure for sorting as described by Webb {70) is followed, with the exception of the method of sampling and the length interval used in measuring. Briefly the revised method of preparing the small sample from which the length array is to be made consists in the taking of 32 pinches of cotton from different parts of the original sample. Each of the 32 pinches is divided into two parts by pulling apart lengthwise, and one portion is discarded. The remaining parts are combined in pairs and are mixed by lapping between the fingers. The resulting 16 pinches are again divided and half of each is discarded. This process of combining, mixing, and dividing is continued until finally only two portions remain, which are combined and lapped several times. From this final tuft approximately 75 ing are sejjarated for one of the length arrays.

FioL'EE 15.—Method of sampling from the lensth arrays for the determination of mean fiber weisht per inch. After the fibers are placed on velvet-covered boards they are grouped in intervals of one-eighth of an inch. All the fibers of the same length group are picked up together and are weighed on a delicate balance, and the weights are recorded on a standard form that has been developed in connection with the length measurement. After the weighing, the groups are wrapped in small papers, arc labeled with the correct group length, and are placed in storage or used immediately as the occasion demands. The same procedure is followed for the one or more other arrays on the same cotton and the results are averaged for the final determination. In preparation for the fiber-weight determination the papers are opened and the fibers of the same length group from the two or more arrays are combined (fig. 15). The groups are thoroughly mixed by lapping and, beginning with the longest group, or the MEASUREMENT OF CHARACTEK PROPERTIES OF COTTON 47

second longest if the first is too small to yield 200 fibers, a pinch of at least 200 fibers is laid out parallel on a board covered with black velvet. With tweezers, two sets of 100 fibers each are counted out and are wrapped m separate small pieces of paper. This process IS repeated for each length group of the array with the exception o± the two shortest, which are too short to be handled readily and rarely make up an appreciable portion of the total weight of the arrays. WEIGHING THE GROUPS OF 100 FIBERS It is convenient to carry out the operation of weighing the groups of 100 fibers separately from that of extracting and counting them. Iheretore, when a sufficient number of samples has been prepared the bundles of 100 fibers each are weighed. A sensitive torsion balance (capacity 3 mg) is used and the weights of the groups are determined and recorded on a standard form (fig. 16). The duplicate

Jarm Uo. 18 "MHIAIT WSIOHT P^R TWCH ATO VARIABILITY Project 3,Z _ Problem Ho. ^ _ Problem Title S/,J^ f^f^r^2£ Z^r,^ _Samóle Ko. oj^rr Weight ffel^t of 100 length No. of n-/ln. Deviation fibers extracted, xogfl. of array 1/16 fibera Relative 10-'* mes. from grotipo» inches lOOff (N) Length assumed (LM) (LNd2) Ayerage (r) (L) (LW) mean (d) Ul _J2_

Js-áv =fe ^/^^ ^L^Z£- ::;^ ■yr ¿090 /r.oy .^2/_ 3-iyá ^^"9 mzi ^^^^

L¿2^ Classera' Length üxtracted feiííied -Z^ f.oo ^>y

FiGUKB 16.—Facsimile' Of form used for recording the weights of the fibers and computing the mean fiber weight per inch and other statistics. determinations on the two sets of fibers from each length group are recorded m columns a and l on lines numbered to correspond to the length of the group. In column W is recorded the sum of the weights m milligrams of the two or more groups from the separate length arrays. Ordinarily this already has been added and is merely transcribed from the average sheet of the length computation. This constitutes all the original data for this determination and the remaining figures are obtained by computation. At the upper part of the sheet spaces are provided for the proper identification ot the sample. There is provision in the lower part for the initials of the worker and the date of performance of each operation, feimilar provision is made on the length sheet for the operations in connection with the sorting:. 48 TECHNICAL BULLETIIs^ 5 4 5, U. S. DEPT. OF AGRICULTURE

COMPUTATIONS The individual weights as shown by an example (fig. 16) are seen to vary somewhat between the duplicate weighings. An average of the two weighings is calculated and recorded in column F. In making this calculation the values are rounded to two digits by dropping or raising a 5 in the third decimal plac^ according as the preceding digit is even or odd, respectively. ^ The length in one-sixteenth of an inch is shown m column L. For convenience of reference in calculation, this column is located near the center of the sheet. Column 7y^ contains the computation of number of fibers m each length group tested and is obtained, as indicated at the top, by dividing the weight of the length group by the mean weight per fib^r for that group, both expressed in milligrams, that is,

F F 100 The total length of fiber in each length group is computed by multiplying the number of fibers in that group by the length of the group. This is recorded in column LN, Since only relative length is required here, it is unnecessary to express this in inches ; it is expressed for convenience in one-sixteenth units with the dropping of three digits. The reduction of digits at this point greatly simplifies the subsequent calculations and does not significantly affect the accuracy. If only the mean fiber weight per inch for a sample is to be calculated the remaining columns of the sheet are not required. The weight in milligrams of all the length groups used in the determination is obtained and divided by the total length in inches, which is obtained from the total relative length by dividing by 16 and mov- ing the decimal point three places to the left. The division by 16 compensates for the units of measure employed and the trans- position of the decimal compensates for the three digits dropped in lecording the relative length. Column / of the sheet contains the weight per inch for each length group. These figures are required for plotting and for calculating the variability. The values are obtained as indicated at the top of the column by dividing the weight per fiber,- F/lOO, by L/16, the length in inches : F_ 100^ 16i^ ^"L^ lOOL 16 The values are recorded in units of 0.0001 mg to simplify the computation and to avoid the unnecessary recording of ciphers. When the weight per inch for each length group has been found, it is possible by inspection to determine approximately the- mean value for all of the length groups, that is, for the sample. The use of an assumed mean adds greatly to the simplicity of computation. In the example cited in figure 16, it appears that the mean weight per inch for the sample will be approximately 51. A further simpli- MEASUREMEÎsTT OF CHARACTER PROPERTIES OF COTTOISi 49

fication is accomplished whenever an assumed mean can be selected, which occurs several times in the column. As will be seen immediately, the difference between any figure and an assumed mean which IS identical gives a zero deviation and eliminates further computations in the corresponding rows. Using 51 as an assumed mean, the deviations are determined by subtracting this value from each of those m column / and recording the difference in column ¿, care being taken to record the proper sign. The product of the deviation and the relative length (column LN) are recorded in column LNd. The sum of the latter column, due regard being given to sign, divided by the total relative length provides the correction for the assumed mean. The data shown in the LNd^ or final column are obtained by multiplication of the values in the two preceding columns labeled í¿ and LNd^ respectively. In this column all signs become positive. The sum of the items in this column divided by the total relative length, ^LN^ and corrected by subtraction of the square of the value used m correcting the mean gives the variance of the weight per mch for the length groups throughout the array, that is, the sample. i3y extracting the square root, the standard deviation is obtained. Space IS provided at the bottom of the sheet for final calculations and other information needed in .connection with the determination. The first line at the lower left-hand part of the page provides for recording the staple length as determined by the cotton classer, the second for recording the upper quartile length as determined by laboratory measurements. These two figures are of value for indi- cating whether the mean fiber weight per inch is high or low for the particular staple and fiber length. The third line provides for recording the assumed mean and the fourth line for applying the correction. The fifth line shows the corrected mean which may be converted to milligrams if desired by dividing the final figure by 10,000. The first line in the lower .central portion of the sheet shows the quotient obtained by dividing the sum of column LNd ^ by the summation of relative length of fiber. This is corrected for an assumed mean by subtracting the square of the correction factor used for obtaining the true mean weight per inch. The standard deviation IS then found by extracting the square root. If the mean has been expressed m milligrams this should be converted to milligrams in the same way. The coefficient of variability is found by dividing the standard deviation by the mean fiber weight per inch and multiplying by 100, and is recorded on the fifth line. The figures show the uniformity or lack of uniformity of the fineness in fibers of different length groups. A low .coefficient of variability means that the fibers m the array are of approximately the same fineness, regardless of length. ^

GRAPHICAL PRESENTATION OF THE RESULTS

In addition to expressing fineness and its variability statistically, the results may be shown graphically. Figure 17 shows the relation between weight per inch and length, in two American upland cottons. 91773°—37 4 50 TECHNICAL BULLETIN 5 4 5, IT. S. DEPT. OE AGBICULTURE

The Ordinate shows the weight per inch in units of ten-thousandths milligrams and the abscissa shows the midpoint values of the fiber- length groups. The units of the abscissa begin at the right-hand side in order to conform to the cumulative weight-length curve m which it has become generally customary to show the long fibers at the left-hand side of the array. In this figure the unweighted relationship between weight per inch and fiber length for cotton B appears to be almost a horizontal line. However, m the case ot cotton A the slope of the curve is rather steep. Cotton A contains some fibers as fine as found in cotton B but most of them are coarse. The mean weight per inch for cotton A calculated without weighting from all the length groups from five to twenty-one sixteenths inclusive is 69, while for cotton B the mean calculated m the same way from length groups five to twenty-three sixteenths inclusive is 53. The difference in fiber-fineness characteristics of these two cottons is evidently large.

120

100

3 80

ü 20

21 19 17 15 13 11 LENGTH (1/16 INCHES) FIGURE 17—THE VARIATION OF FIBER WEIGHT PER INCH WITH LENGTH FOR COTTONS A AND B. The unweighted relationship between weight per inch and fiber length for ^-otton B appears to be almost a horizontal line. In the case ot cotton A the slope ot the curve is rather steep. The graphical presentation just described considers equal quantities of each fiber-length group. It indicates variation but does not give an idea of the relative proportion of the fibers with any given degree of fineness. The latter may be brought out more clearly by plotting the weight per inch against the cumulative percentages of the different lengths. This may be, done in different ways. The fiber weight per inch may be plotted against the cumulative percentage by relative length, by weight, or by number of fibers. These cumulative percentages may all be calculated from the data contained on the form shown in figure 16. The cumulative percentage for relative length is calculated from the LN column by first expressing the length in each length group as a percentage of the total and then summating and recording the percentages cumulatively. The cumulative percentages by weight and by number can be ob- MEASUREMEîNTT OF CHARACTER PROPERTIES or COTTON 51

tained, if desired, in an identical way, using the data in the W and N columns respectively. The fiber weights per inch for the two cottons used in figure 17 have been plotted in figure 18 against the cumulative percentage of relative length. The midpoint length of the fibers in one-sixteenth inches is indicated in each case by figures at the proper points on the curves. ^ These could be indicated in actual inches if desired. These curves, in contrast to those of figure 17, show in each case that a comparatively large proportion of the fibers have a weight per inch withm a restricted range and that a considerable number of the shorter length groups, where the greater part of the variability occurs, contain a relatively small proportion of the total length of fibers. The mean weight per inch for cotton A may be calculated to be 61 while the corresponding figure for cotton B comes to 52. The mean fiber weight per inch without weighting (fig. 17) was 69 and 53, respectively, and evidently overemphasized the difference in fineness between the two samples.

Î20

en 100

o 80

IK '3 40 -Cotton B (Mean 52) LENGTH IN 1/16 INCHES

-20 30 40 50 60 70 80 90 100 CUMULATIVE PERCENT OF RELATIVE LENGTH FIGURE 18.--THE VARIATION OF FIBER WEIGHT PER INCH WITH CUMULATIVE PERCENT OF RELATIVE LENGTH FOR COTTONS A AND B. ^«-^"^^ These curves show in each case that a comparatively large proportion of the fibers have fpXT^* P^'' mch.within a restricted range and that several of the coarse short- length groups contain a relatively small proportion of the total length of fibers. By comparison of the curves in figures 17 and 18 it is evident that, where the weight per inch does not vary greatly from length to length, no great difference in form or average level of curve results from weighting; but where the weight per inch differs greatly in the different length groups, weighting causes a much larger change in curves. Thus the mean of cotton B (nearly horizontal curve when unweighted) changed only one unit when weighted whereas that of cotton A (steep curve when unweighted) changed 8 units. Accord- ingly, the benefits of weighting the values for fiber weight per inch m the different length groups and plotting the figures cumulatively, are most pronounced in those cases in which the individual values differ most. 52 TECHNICAL BULLETIN 5 4 5, U. S. DEPT. OF AGRICULTURE

In plotting the relation between fiber weight per inch and cumulative percentages it is undoubtedly best to use the cumulative percentage by relative length. Of the three cumulative percentages that might be used, this most accurately represents the distribution of fiber fineness in the yarn cross section. Because of the rather close relationship between length and weight of the fibers, however, the cumulative percentage by weight may be used in place of the cumulative percentage by relative length in many cases where only an approximate representation is desired. The use of the cumulative percentage by weight has one special advantage in that it is usually calculated in connection with the length analysis and in such case can be taken directly from the sheet used in that analysis without requiring further calculation. It should be pointed out that the cumulative percentage by weight calculated from the length array is not quite comparable with the corresponding percentage calculated from the sheet shown in figure 16. The discrepancy is due to the fact that a small portion of the fibers in the two shortest and usually the longest length groups of the length array are not used in the fineness determination and the cumulative percentages calculated from the two sets of data will not be quite identical. Therefore, whichever basis is chosen for calculation should be adhered to for all comparisons. The cumulative percentage of fibers by number is of little or no value as a basis for showing the relative''proportion of different degrees of fineness in the different length groups. Unlike the cumulative percentage based on either relative length or weight it gives no consideration to variation in length of the fibers and consequently places entirely too much importance on the fineness of the shorter fibers and not enough importance on the fineness of the longer fibers. Furthermore, unlike the cumulative percentage by weight the cumulative percentage by relative number is not regularly calculated in connection with any other routine test and w^ould have to be especially calculated if used.*^ The more exact cumulative percentage by relative length can be calculated just as rapidly and has much greater meaning for interpretation of yarn properties.

PEEClSIOiN OF THE! KESUT.TS ' It is shown in the appendix (p. 74) that the error, E^ of the mean fiber w^eight per inch can be determined approximately according to the formula lYLNdV E= XLN where LN is the number of inches of fiber in any length group, F is the mean weight per fiber in any group, and d is the deviation of a single determination of F from' the mean of two determinations. Presumably, the fluctuations in F are caused principally by variations in the mean length and the mean fineness of 100 fibers selected from length groups of the same length designation. Preliminary results have indicated that, on the average, standard errors do not MEASUBEMENT OF CHAKACTER PKOPEKTIES OE COïïOî^ 53

exceed 2 to 3 percent of the sample mean, and are frequently much less (table 19, p. 75). It is of interest to find that for a given set of conditions the value of d tends to be a constant for all length groups. This was shown by a tabulation of the frequencies of deviations of mean weight per fiber for each length group in 84 arrays (table 20, p. 76). This is probably due to the fact that the interval of length between groups is the same for all lengths of fiber and that the deviations are caused principally by variations in the average length of fibers in groups of the same indicated length but from different arrays. Where the error in weight per fiber is constant for the different length groups, the expression for error in mean weight per inch for the samples may be altered to

E~- Jd\i:\ F ) XLN

SUMMARY Limited evidence indicates that from the standpoint of spinning quality, fineness as a character element of cotton fiber is of considerable importance. Moreover, it is an element that has been found to vary greatly from cotton to cotton, from length to length of fiber m the same cotton, and from fiber to fiber of the same length. A thorough survey of the literature and a critical examination of the methods that have been used previously for measurement of fiber fineness indicate that all these methods have disadvantages that limit their accuracy or usefulness. It is believed that weight per unit of length is the most practical expression for fiber fineness. But the common method of determining it by the cutting of sections from the midportions of fibers is subject to serious inaccuracies, the causes of which are here pointed out. Some of the limitations of other methods for determining fiber fineness are overcome in the method described for cotton in this bulletin. Among the more important features of this method are: (1) Use of whole fibers as they occur in the sample instead of sections cut from the fibers, (2) systematic sampling throughout the length array rather than dependence upon an attempted random selection from the sample, and (3) weighting of the mean weight per inch for every length group according to relative length of fiber in that group to give results comparable to the distribution of fiber fineness in yarn cross sections. The proposed method of determining fineness on the basis of fiber weight per inch is described in detail. A standard form is suggested for recording the original and derived data. Some methods of presenting the results graphically are shown. A special treatment is described for determining the standard error of the mean fiber weight per inch for the sample. Eesults reproducible with a standard error of only 2 to 3 percent of the mean have been obtained with the proposed method and it seems probable that the degree of accuracy can be further improved. 54 TECHNICAL BULLETIN 5 4 5, U. S. DEPT. OF AGRICULTUEE

IMPROVEMENTS IN THE CLEGG METHOD FOR DETERMINATION OF "IMMATURITY COUNT" AS A MEASURE OF FIBER MATURITY IN RAW COTTON" Maturity is perhaps best defined by a brief consideration of the process of growth of the cotton hair. As discussed by Farr {23) the hair is formed by the outward extension of a single cell from the epidermis of the seed, this extension beginning some time between the day of ñowering and the next 10 or 12 days. .Balls (^, pp. 7,5-7^), Hawkins and Serviss {32), and others have found that the full cell diameter is attained almost at once but that its length continues to increase until about the twenty-fifth day. Up to this point the outer wall of the fiber is extremely thin and delicate. Now, during an additional period of 20 to 25 days the cell wall thickens by the deposition of successive layers of cellulose on the inside, so that the "mature" fiber, after it dries out and collapses, is a ñattened, twisted tube, the wall thickness of which may be from one-fifth to one-third of its diameter. If for any reason the boll opens prematurely or the growth of a fiber is interrupted during this thickening period, a thin-walled tube results which may rightly be called an "immature" or thin-walled fiber, since it was not allowed to complete its normal development. Fiber maturity appears to be important from a number of stand- points. Undoubtedly the flexibility or rigidity of the fiber depends to a considerable extent on the degree of wall development. The wall development influences the external shape of the fiber—whether flat and ribbonlike, folded, convoluted, or irregular. Also, as pointed out by Preston {58), the degree of secondary wall development influences the luster of the raw cotton, the more mature fibers having the greater luster. Not only is raw cotton with a high percentage of thin-walled or immature fibers a potential source of neps, as discussed by Pearson {5If), but also in an attempt to remove them a certain quantity of good fiber is removed, thus increasing the waste and the cost of the finished product. Immature fibers are familiar to finishers and dyers, who recognize in them one of their most difficult problems. Neppy^ yarns give neppy fabrics and the defects may become even more noticeable upon dyeing because of the large proportion of immature fibers in the neps and because these do not dye so deeply as do mature fibers. Likewise fabrics containing portions of filling from different cottons of different degrees of fiber maturity may show pronounced bar effects and streaks in color after dyeing. Wall thickness or maturity is intimately related to fineness of fiber as measured by the weight per unit of length. As pointed out by Clegg {15), as well as others, the original cell diameter for a given type of cotton varies within comparatively narrow limits. However, the wall thickness may vary Avithin extreme limits (pi. 3) thus giving rise to wide limits of weight per unit of length. The weight per unit of length reflects variations in the area of cross section of the fiber, whether due to variations in diameter of the original cell, or to variations in the degree of secondary thickening. However, the weight per

11 See footnote 10. "5 Variations in maturity of fibers from American upland cotton. X 300. r m MEASUREMENT OE CHARACTER PROPERTIES OF COTTON 55

unit of fiber length does not in itself indicate whether the fiber is of large diameter and thin-walled or of small diameter and thicker availed. ITius, in a consideration of the fineness of fiber in a sample of cotton lint it is desirable to have an expression of the maturity in order to determine the qualitative nature of the fiber fineness. Although the effects of maturity of fiber have been recognized in a general way almost no exact information exists concerning such problems as the relations and relative importance of fiber maturity to yarn and fabric quality ; the maximum proportion of immature fibers that may be safely countenanced in products intended for a given purpose ; the effect of the early processes prior to spinning on the proportion of immature fibers in the material ; and the relation of the proportion of immature fibers in a sample to the cotton classer's perception and judgment of the cotton. The answer to the above and other related questions depends on reliable methods of determining and expressing maturity. It is very simple to measure the wall thickness of a single fiber in a number of places along the length and obtain a measure of the wall thickness or relative maturity of that fiber. It is quite a different problem to measure the wall thickness of a sufficient number of fibers in an 80-bale mix, each bale of which may contain between 50 and 80 billion fibers, grouped in various ways as a result of association on the seed, of the variation on different seeds from different bolls and different posi- tions in the boll, of soil differences and even, perhaps, of climatic differences. It is the relative smallness of the fiber and the great variability both within its length and from fiber to fiber that brings complexity into this problem.

PREVIOUS METHODS OF MEASURING FIBER MATURITY As a background for the proposed method and as an aid in evaluating its merits a brief review and criticism of various otlier methods that have been used or proposed for measuring and expressing fiber maturity are discussed. Among the methods suggested may be mentioned those based on (1) a fiber-wall thickness, (2) ratio of ribbon width to ribbon thickness, (3) ratio of average actual to average potential area of cross section, and (4) physical appearance of the fibers after mercerization. In addition to these methods several other principles which, if properly applied, might prove useful in the measurement of maturity, have been suggestei Determination of maturity through direct measurement of the fiber walls is very slow and tedious. Presumably most measurements reported in the literature have been made in this way. Hawkins and Serviss {S2) apparently made direct measurements although the details of their method are not given. Balls (^, p. 65) describes an improved method based on direct measurement. The fibers are not mounted in water since, because of the difference in refractive index between water and the fiber, that mounting makes ih^ walls appear nearly double in size. Instead they are mounted in a liquid of nearly the same refractive index as the fiber, and only one of the doubly refracted rays is used. The ribbon width and the width of the central canal are measured and their difference is divided by 2 to give the wall thickness. 56 TECHNICAL BULLETIN 5 4 5, U. S. DEPT. OF AGRICULTUEE

The use of the ratio of ribbon width to ribbon thickness as a measure of wall development was mentioned by Adderley (i) in connection with his studies of luster. Pope (S7) used this dimensional ratio as a measure of fiber maturity. Several investigators have devised measures of maturity based on area of fiber cross section. Probably the most interesting is the method developed by Eoehrich {S9) who calculates what he calls a "coefficient de maturation." This may be expressed algebraically by the formula loos; where O is the coefficient of maturity, S is the cross-sectional area of the fiber wall and S' is the area of a circle constructed from the calculated diameter of the fiber. The cross-sectional area S in square microns is found by dividing the weight W in milligrams, of 10 m of the fiber (based on sections from the center of a fiber bundle) by 1.5, the density of cellulose, and multiplying by 100 thus ^_ lOOTF

S^ is found from the mercerized diameter of 100 cotton fibers, convoluted and flattened fibers being neglected, and expressed in terms of the original untreated fibers with the aid of the appropriate factor as given by Calvert and Summers (IS). Therefore, theoretically the coefficient of maturity expressed the quantity of cellulose in the fiber as a percentage of the quantity which a circle of the same diameter would contain if completely filled. It is the purpose of this part of this bulletin to describe an improved method for determining and expressing fiber maturity in raw cotton. Although the proposed method utilizes the mercerization principle first proposed by Clegg (Í4, IS) it differs from the Clegg method in several important features. As a result of these changes, it is believed that the precision of the proposed method is considerably better than that of the Clegg procedure. A method similar to the one developed by Eoehrich has been described by Fedorov (25) in which the degree of filling is expressed by a numerical coefficient. Clegg and Harland (17) also carried out a measurement similar to the one described by Eoehrich but calculated the percentage of pore space instead of the, degree of filling. Still another method which may prove useful in the measurement of fiber maturity depends on the nature of the interference colors resulting with polarized light. Herzog (34) has discussed the usefulness of this method although he uses it principally for qualitative purposes. Pattee {5S) has developed a quantitative method based on this principle and considers his "maturity rating", so obtained, to be a valuable adjunct to cotton classers and buyers. Whether or not variations in micellar orientation, as discussed by Farr and Clark (^4), seriously interfere with the accuracy of this method is a matter yet to be established. Clegg (14) was probably the first to study mercerized fibers as a means of determining fiber maturity. This method is much more rapid than the other methods described and depends on the ratio of MEASUREMENT OF CHARACTER PROPERTIES OF COTTOIS^ 57

wall thickness to original fiber diameter. However, this ratio is materially altered by the mercerizing- process, which causes the walls to swell without affecting the diameter proportionately. Clegg examined fibers under the microscope in 18-percent caustic soda solution, and classified them into three groups according to the degree of wall thickening—"normal," "thin-walled," and "dead" fibers. She expressed the proportion of normal and dead fiber as percentages, the "immaturity count" ; the percentages of thin-walled fibers could then be obtained by subtracting the sum of the first two from the total or 100 percent. Clegg {15) also distinguished a fourth group of "abnormally thickened" fibers which on treatment with alkali burst their cuticle and in this condition readily absorbed Congo red and other dyes. Hawkins {31) used essentially the method described by Clegg in correlating fiber maturity with seed development, environmental conditions, and time of picking, but he recorded only the percentages of immature fibers. Several workers have discussed still other fiber properties that might be used as a measure of fiber maturity. One of these Adder- ley's (i) discovery of the relation between maturity and luster. Foster {27) says luster is improved by any process that tends to reduce the minimum diameter or number of convolutions and especially one that makes the ratio of the diameters approach unity. These studies suggest that luster might provide a basis for the rapid measurement of maturity in cotton fibers, provided the conditions can be properly controlled. Theories and methods of measuring luster are discussed by Preston {58) and by Pelton {56). According to Crookes {IS), M. Daniel Koechlin-Schouch, as early as 1848, called attention to the production of light spots in dyed cotton goods by the occurrence of hairs which resist the dye and remain white. He suggested that unripe cotton might be a possible cause. Crum {19^ 20^ 21) found the undyed portions of the cloth to consist of remarkably thin flattened and transparent fibers, of greater ribbon width than normal fibers. Later studies by Haller {28) and Herzog {SJ^) supported his conclusions. Clegg and Har- land {16) studied thin-walled fibers in relation to neps and to various dyeing problems. An investigation dealing with thin-walled fibers and their influence in formation of neps and other imperfections in cotton were reported by Pearson (54). A review of all these studies seems to suggest that an index of maturity might be obtained by dyeing samples of cotton and measuring the amount of dye absorp- tion with a colorimeter or by chemical means.

DETERMINATION OF THE FIBER IMMATURITY COUNT It is apparent from the foregoing review that most, if not all, of the methods that have been used by previous investigators for measurement of maturity are slow and tedious. The method developed by Clegg (Í5), based on qualitative differences in appearance of fibers after mercerization, is probably the least tedious of the methods reviewed, with the possible exception of the interference color method, the accuracy of which is not yet established. The method herein described differs from the Clegg method (1) in the method of securing a representative sample of fibers, (2) in classify- 58 TECHNICAL BULLETIN 5 4 5, U. S. DEPT. OF AGRICULTURE ing the fibers entirely on the basis of ratio of wall thickness to lumen width rather than on external appearance, convolutions, etc., (3) in the accurate definition or specification of "immature fibers," (4) in the method of computing the results, and (5) in the method of expressing the immaturity count. The determination of percentage of fiber-wall types is subject to one of the same difficulties of sampling as that described in connection with the determination of weight per inch, that is, the natural tendency to select the longer fibers for observation. Since percentage of immature fibers is connnonly associated with length to a greater or less degree, it seems desirable to overcome this effect as much as possible by taking fibers from all groups of the length array, instead of from five length groups selected arbitrarily as^ in the Clegg procedure. By using all length groups and knowing the relative quantities of each, it is possible to reconstruct the true distribution of fiber-wall types in the sample and in this way obtain an absolute rather than a comparative figure. In other words, practically the same result is obtained as would be obtained by a thoroughly random selection of the fibers from the sample, if that could be realized. At the same time, the systematic sampling from the length array makes possible a more thorough mixing of the fibers than can be attained by sampling from the unsorted sample, as is sometimes done. In samples of ginned lint, immature fibers tend to remain associated in the same tufts that were pulled by a single saw tooth from dis- eased, aborted, or otherwise poorly developed seeds or motes. These similar fibers remain associated together in tufts throughout the clean- ing and baling processes and consequently are still associated w^hen small pinches are taken to make a composite sample for an immaturity count. In the making of length arrays, an extensive and systematic sampling process is necessary. This may involve as many as 96 small tufts taken from various parts of the original sample which are combined in pairs successively halved, and thus gradually reduced to 3, which are then sorted separately. Still more important, the sorting process itself affords an unusual opportunity for mixing. In the routine process adopted, the fibers are three times separated on the basis of length into thin layers and are twice recombined in a bundle. Since in the sorting process the fibers are removed almost singly, there is a real advantage in definitely overcoming a large part of the association. As will be shown below^, tufts of the same length group from the three separate arrays are finally combined and mixed. Thus, in the proposed method, not only all length groups are represented, but thorough mixing helps to overcome the association of fiber types that undoubtedly exists in the original lint sample. In the Clegg method an incomplete correlation between presence or absence of convolutions in the fibers after mercerization and degree of wall thickening is made the basis of a system of classification to indicate the general fiber maturity of the sample. Obviously, to the extent that the correlation is not perfect the method fails to give a satisfactory measure of the relative wall thickness. Numerous observations have indicated that the correlation is not so good as might be desired. It is believed, therefore, that the accuracy can be materially improved and without much loss of rapidity, by classifying MEASUREMENT OF CHARACTEK PROPERTIES OF OOTTOK 59

directly on the basis of ratio of wall thickness to lumen width rather than on the basis of associated external appearances. Although Clegg (iJ, f, TJ¡7) mentions such a ratio, it is evident from the emphasis which she places on external appearance of the fibers that she depends largely on the latter for purposes of classification. In the Clegg method a "dead" fiber is defined as one that is highly convoluted after treatment with 18-percent sodium hydroxide solution and a "thin-walled" fiber is one wdiich still retains some convolutions after treatment. No means is suggested for deciding how many convolutions in a given length are required before the fiber is to be considered "highly convoluted" or how fibers wîth "some convolutions" are to be exactly recognized in practice. Experience shows that while in general there are qualitative differences in appearance of fibers such as "rodlike", "having some convolutions" and "highly convoluted", nevertheless, the graduation is continuous and intermediate types are generally present. Furthermore, it has been observed that different technicians have much difficulty in obtaining agreement in results, due no doubt to differences in their mental pic- tures of fiber types. To do away with this vagueness in definition it has been decided to define thin-walled fibers in terms of dimensional relation of the wall and lumen so that any technician can easily adjust his own classification in terms of a fixed ratio, easily ascertained. Computation in the proposed method differs from that in the Clegg procedure. In the Clegg procedure, the different counts obtained from the five places scattered "down the diagram", are averaged to give an arithmetic mean. In the method herein proposed, the counts in each length group are averaged and weighted according to the relative number of fibers in that group. Consequently, the average figure finally obtained for the sample takes into account the relative importance of each portion of the length array. It is believed this procedure is very desirable since the variability of immaturity count with length has not been observed to be a straight-line function but is much augmented in certain lengths, especially at the shorter end of the array. In an effort to simplify the expression for immaturity it was thought advantageous to classify the fibers into two distinct groups, that is, those of normal wall-thickness classed as "thick-walled", and those with subnormal wall thickness classed as "thin-walled." In order that a more definite criterion may be used to differentiate between the fibers of the two groups, certain definite limits have been set for each catagory. For instance, in the improved procedure fibers after treatment with 18-percent caustic soda, with a wall thickness equal to one-half the lumen wîdth are classified as thick-walled fibers, those with a wâll thickness of less than one-half the lumen width are classified as thin-walled fibers. All fibers that are not readily distinguished as to the proper class to be assigned are measured by the aid of a filar micrometer. This procedure provides a more uniform classification. Finally, in the Clegg expression for immaturity count, a duplex figure is used. Thus, such a figure as 65-15 indicates 65 percent normal and 15 percent dead hairs. The two figures add to 80 percent, leaving by calculation 20 percent thin-walled hairs. Such a 60 TECHNICAL BULLETIN 5 4 5, U. S. DEPT. OF AGRICULTURE system of expression is cumbersome, combining as it does comple- mentary parts of the same idea, that is, mature-immature. In the revised method herein described, only two groups of wall thickness are considered, thin and thick. Since the sum of the two must always add to 100 percent either group might serve equally well as a measure of maturity. But because of the special interest in the percentage of thin-walled or immature fibers as an indication not only of the potentiality of the cotton to form both neps and excess waste, but of other manufacturing difficulties as well, it is believed it will be advantageous to use the percentage of thin-walled fibers as the measure of maturity. Thus the "immaturity count" would be simply the weighted average percentage of thin-walled fibers in the entire sample.

GENEItAL PBINCIPLEI OF THE PROPOSED MEil'HOD In using the ratio of wall thickness the lumen w^idth as a measure of wall development the proposed method is independent of the original or growing diameter of the fiber (that is, of an ideal diameter of a circle calculated from the perimeter). This is an advantage in that maturity may be evaluated independently of fiber fineness. It is not certain how completely this holds when convolutions are used as a basis of classification. Since the fibers are more readily visible when mounted in liquid than when mounted dry and since swelling increases the wall thickness thus making it more readily nieasured and compared, it is desirable to continue to use the mercerizing procedure first introduced by Clegg. Furthermore, the examination of mercerized fibers makes it possible to relate (approximately) the results obtained by the proposed technique to results obtained by the original Clegg method. In choosing a ratio of wall thickness to lumen width attention should be given to practicability as well as precision. It should be possible to recognize the class of most fibers without actual measurement. However, it should be possible to determine accurately the class of any doubtful fiber by measurement if necessary. If many fibers must be measured speed of observation is greatly reduced and practicability of the method is limited. Probably the easiest ratio to judge would be that in which the lumen is equal to the wall thickness. The next most practicable ratio would be one in^ which the lumen is twice the wall thickness. Successively large ratios must be more and more difficult to differentiate without actual measurement. As a result of a rather extensive survey it was found that a ratio of lumen width to wall thickness of 2:1 was most practicable. A ratio of 1:1 placed too large a proportion of the fibers in the thin- walled class and consequently extended the thin-walled group too far into the normal or average range. Even the 2:1 ratio gave a group of thin-walled fibers which includes both the "thin-walled" and "dead" of Clegg's classification (pi. 4). However, a ratio of 3:1 was already somewhat difficult to judge and too frequent recourse would have to be made to the micrometer. It was therefore decided to adopt for routine work the ratio of 2:1 and to consider all fibers with ratios larger than this as thin-walled, or immature fibers and all others normal, or thick-walled fibers. This ratio is effectively equivalent to a ratio of ribbon width to wall thickness of 4:1. Technical Bulletin 545. U. S. Department of Agriculture PLATE 4

^ B C

G n c7 K

Coarse and fine fibers before and after treatment with 18 percent sodium hydroxide solution. Fibers A, B, and Carefromaeoarse American upland cotton while D, E, and i^ are from a fine American upland cotton. Fibers G, H, I, J, K, and L are the same fibers as those directly above, but after treatment with sodium hydroxide solution. Fibers A, G, D, and J would be normal according to Clegg's designation and thick-walled according to the classification adopted in this bulletin. Fibers B, H, E, and ii would be thin-walled and C, 7, F, and L dead, according to Clegg's system but all are tbin-walled according to the definition adopted in this bulletin. X 220. MBASÜßEMENT OF OHAEAOïKK PRÓPEKÍIÉS ÓF COTTON ßl

SAMPLING In sampling for the counting of fiber-wall types almost exactly the same procedure is followed as in sampling for the weight-per-inch determination described for fineness (pp. 45-4T). Whenever both fineness and maturity determinations are to be made, the same set of 100 fibers employed for weighing may be used for the maturity determination, although this increases the time of mounting somewhat.

MOUNTING, TBEATING, AND COUNTING THE WALL TYPES For observation of the fibers an ordinary student model microscope with square stage of corrosion-resisting material serves well. It

PiGUBE IB,—Apparatus and technique for determining flber-wall types. should be provided with double or triple revolving nosepiece and coarse and fine adjustment of the body tube. The underside of the stage should be equipped with an iris diaphragm and a stationary ring carrying a substage condenser and diaphragm. The use of the double-diaphragm system makes possible the best control of scattered light rays which impair the definition of the image. The microscope should be equipped with a graduated mechanical stage, a 10- and 45-diameter objective and a filar micrometer eyepiece of about 10 diameters. A magnification of about 400 diameters is used in the examinations. Illumination should be provided by means of a good microscope lamp with adjustable condenser. The use of a euscope in connection with the microscope (fig. 19) decreases eye fatigue and greatly adds to the convenience of the operator. Thin tufts of more than 100 fibers from the various length groups are straightened and paralleled, placed on a 2- by 3-inch glass slide, 62 TECHNICAL BULLETIN 5 4 5, V, S. DEPT. OF AGRICULTURE covered with a cover slip, and flooded with an 18-percent solution of sodium hydroxide. The slide is then placed on the mechanical stage of the microscope and brought into focus. The treatment causes the walls to swell almost immediately and it is not necessary to delay the operation of counting. Beginning at one end of the slide and with the aid of the mechanical stage, the operator moves the central portion of the fibers successively into view. Frequent adjustment of the focus may be necessary. In the case of each fiber he decides whether the wall thickness is more or less than one-half the lumen width. These decisions may be somewhat slow and frequent measurements may have to be made at first, but they soon become relatively easy and can be made without appreciable hesitation. Doubtful cases are measured in each instance. As each fiber passes its classification is recorded with the aid of a novel

Form So. 81 FIBER I^aiATURITV COUNT -- ÜLAM PERCENT AND VARIABIUTY

Project ^^ Problen J- probier» Title .S.,^r,.nr. ¿'.,r.n,no ^"»Pl* N»' ^^^'-'^^

j*tt«r Id#ntiflcatioD

1 ifffi-i-iiritY Counts Length 1; Rel. Average 1/16 m. No. Immatur- ity (d) (fd) (ni«) (•) (b) (L) Counts Assianed ¡¿ean ^^ co yo o/ 41 39 Correction (cH_J/. (e) -*"/' .. 87 Mean ^¿ 39 Jy -J^ 86 iTm 33 ^^¿ 31 Cr^r^ of Variation , ^JT/j^ 29 27 Classer'e Ungth ¿2¿ 25 Upper Quartile Length -^ ^^■■~' ^¿ -¿y -2J>""/ ? 23 // -y ,, 21 3¿ -'V Fibers Observed by (f VC— /J- 19 .rr ^f o //ry /o 17 /y /o - y -^9¿

^J 15 ¿/ /y Û — — raiA,.i«t.*d hv V Q /3 'J 13 y-i /3 -/ - y¿ V->- /:Lg' /y 11 3-Z /¿ -¿ ¿y // m,»«v..a hv ^A/ yP v?y ¿o ¿ :ioy /^^y J.Í /¡r 9 Jjoy J.3 J.C 7 3á ¿í ? -? tr jj / jj. ^f ag- 6 ¿7 J» /y 9Jr 8 1 ^OfJL /»¿/o Tot*l. vré

FIGURE 20.—Facsimile of standard form used for recording the original percentages of fiber-wall types and the results of statistical calculation. counting device (fig. 19). This consists of one or two counters held in an upright position by a special clamp, so as to be conveniently operated by the left hand of the observer. The thin-walled fibers are recorded on one counter and the total fibers observed on the other. The operator may simply count the total number of fibers observed while recording the thin-walled fibers on one counter. As the individual counts are obtained they are recorded on the proper line of a standard form (fig. 20). Two counts are made on each length group.

COMPUTATIONS For the purpose of calculating immaturity count for a sample of cotton a procedure somewhat similar to that used for the determination of weight per inch for the sample is followed. The principal divergence consists in using the relative number of fibers in each MEASUREMENT OF CHARACTER PROPERTIES OF COTTOIi 63

length group instead of the relative length to weight the immaturity count for that length. This divergence is desirable in view oiE the fact that the percentage of wall types ordinarily does not vary so greatly for the different length groups as does the fiber weight per inch and it is much simpler to maintain the significance and meaning of the final expressions by considering them as being merely representative fiber "wall-type counts" for a cotton. The standard form (fig. 20) used for recording the original data is used also for recording the calculated statistics for the sample including the mean immaturity count, the standard error of the immaturity count mean, the standard deviation of the immaturity count in different length groups, and the coefficient of variability of immaturity count in the different length groups. Spaces are provided at the top of the sheet for the identification of the sample and for information needed for purposes of filing. On the left-hand portion of the sheet are recorded in duplicate the original immaturity counts for each length group. In the third column ,^ Z, are printed the midpoints of the length groups. Next to the right of this column is recorded the relative number of fibers, f, to be used with each length group. The relative number is, of course, the weight of the length group from the length-array data divided by the weight per fiber (obtained from the fiber-weight-per- inch determination) and rounded off to the desired number of digits. Little error can result in the final calculations if only two digits are retained here. Although the relative number of fibers is indicated for frequency, no great error would be introduced by use of the weight-percentage frequency from the length array, which would be available from the length-array data without requiring the determination of fiber fineness. However, if the weight-percentage frequency is used in one case it should be used in all cases to permit comparisons of different samples. Next to the right of the frequency column the average immaturity count for each length group is recorded. Still further to the riglit columns are provided for calculation of means and standard deviations for the sample (fig. 20). The d column is provided for recording the deviations of immaturity counts in different length groups from an assumed sample mean. The use of an assumed mean simplifies the calculations considerably and lessens the chances for error. The fd and fd^ columns provide for recording of the necessary products which must be totaled and divided by the total of the / column to give the means. The totals are recorded at the bottom of the columns, but the means are recorded in special spaces to the right of the sheet. At the top right-hand portion of the sheet the assumed mean immaturity count is recorded. Next to this on the same line is recorded the mean variance calculated from the assumed mean immaturity count. The latter is obtained from the total in the fd^ column by division by the total in the / column. Both of these means must be corrected to the true observed mean. The corrections are indicated on the second line. The o correction is obtained by division of the total in the fd column by the total in the / column. The c^ correction is simply the square of the c correction. The third line gives the true observed mean immaturity count and variance respectively. The 64 TECHNICAL BULLETIN 5 4 5, U. S. DEPT. OF AGRICULTURE mean is used to represent the sample while from the variance may be calculated an approximate standard error of the mean, the standard deviation of the observed distribution and the coefficient of variation of immaturity count in different lengths. Two figures of special interest in connection with any sample, namely, staple length and upper quartile length (length at the 25- percent point in the length-cumulative weight percent distribution curve beginning with the longest fibers), are recorded in the lower right side of the sheets. Also spaces are provided for recording the initials of the fiber technician and calculator and the dates of observation and computation. As a whole, the sheet provides a concise record of all the essential data for each test. The original data for the relative number of fibers may be consulted on the sheets giving the fiber weight per inch if desired. PRECISION OF IMMATURITY COUNTS Theoretically with the arrangement described and with the specification of thin-walled fibers, an observer should be able to place almost every fiber in its proper category. Such ability nevertheless would be limited by the variation of wall and lumen dimensions at different points along the fiber, diffraction effects, improper focus, and the sensitivity of the measuring equipment. Only a small proportion of the fibers should be of doubtful classification. In order to determine how well an observer can repeat his readings, 50 fibers were cemented to each of two slides, covered with cover slips, and treated with 18-percent sodium hydroxide solution. The 100 fibers were then observed in rotation 10 successive times and the number of immature fibers recorded. This was done for each of three samples. The results are shown in table 13.

TABLE 13.- -Vaviations in the immaturity count in 10 successive examinations of the same 100 ßbers from each of S samples ^ of cotton

Sample Sample Sample Examination no. Sample Sample Sample Examination no. 1 2 3 1 2 3

Percent Percent Percent Percent Percent Percent 1 34 31 36 8 30 29 29 2 36 35 31 9 30 29 34 3 27 34 34 10 - 26 29 30 27 30 36 5 26 29 33 Mean 29.0 30.2 32.8 24 28 33 7 30 28 32 Standard deviation ±3.6 ±2.3 ±2.2

1 Samples 1 and 2 were from the same cotton. By reference to table 13, it is seen that even w^hen examining repeatedly the same set of fibers, the number placed in the thin- walled or immature class differs considerably. The standard deviation varies from 2.2 to 3.6 for the three samples. It is quite probable that these differences were due partly to viewing the fibers at different focal levels in successive observations and possibly at different parts of the fibers since the slides were removed from the stage between each examination. It was also desirable to determine the effect on the precision, of examining successive sets of 100 fibers each drawn from the same MEASUREMEJSTT OF CHARACTER PROPERTIES OF COTTOî^ 65

supply of cotton. The total error here should include not only the errors of observation but also those of sampling. For such dis- contnmous distributions, the theoretical samplino; error E may be written ^ E=^n'p{l—p) where n is the number counted and p is the proportion of the total which falls in one of the classes. For the study, successive groups of 100 fibers each were drawn from the same supply and observed. The percentage of thin-walled fibers was recorded for each group and the results were combined mto three sets of 10 counts each, or a total of 3,000 fibers. The results, together with the means and standard deviations of the three successive sets, are presented in table 14.

TABO^ 14.—Variations in the immaturity count in successive groups of 100 fibers each drawn from the same sample of cotton

Count no. Set 1 Set 2 Set 3 Count no. Set 1 Set 2 Set 3

Percent Percent Percent 1 Percent Percent Percent 29 33 40 8 41 41 34 2 46 37 38 9 3 37 34 46 40 37 10 45 39 33 4 29 31 37 .5 33 39 45 37.7 35.7 37.1 6-. 40 31 40 7 31 32 32 Standard deviation ±6.5 dz3.7 ±3.7

Mean and standard deviation of series 36.8±4.99.

An examination of table 14 shows that the variation in the immaturity count for successive groups of fibers from the same cotton IS greater than the variation when the same fibers are repeatedly examined (table 13). Thus, the standard deviation ranged from ±3.7 m two of the sets to ±6.5 in the most variable set. In the latter, most of the variability is due to two low counts. The standard deviation of the count for the entire series of 3,000 fibers is 4.99. The standard deviation calculated on the basis of the above formula would be ±4.82 for an immaturity count of 36.8 (average for the series). The standard error for the entire 30 counts is 4.99/ v'30 which IS 0.91. Since in an ordinary test at least 10 different length groups are examined, the standard error for a sample on the above basis would be approximately 4.99/ VIO or ±1.6.

GRAPHICAL PRESENTATION OF THE RESULTS

When several cottons are to be compared closely the wall types should be grouped into only two components, as for instance immature and mature and only one of the components should be plotted. In this way several curves may be shown on the same chart (fig 91)* Other forms of presenting the data graphically doubtless can be developed that will be suitable for particular comparisons.

SUMMARY Maturity as an element of character in raw cotton is known to have an important bearing on spinning behavior and yarn and fabric 91773°—P>7——5 66 TECHNICAL BULLETIN 54 5, U. S. DEPT. OF AGRICULTURE quality. But its importance has not been thoroughly analyzed and many relationships between fiber-wall development and yarn and fabric properties remain to be determined. Before these relationships can be disclosed, it is necessary to develop precise methods for the measurement of the properties in question. The method described in this bulletin is based principally on the mercerization method first reported by Clegg. It diifers from that method in that (1) a more thoroughly mixed representative sample is obtained for study, (2) the fibers are classified entirely on the basis of ratio of wall thickness to lumen width rather than on external appearance, convolutions, etc., (3) the immature class of fibers is more

100

90 100 10 20 30 40 50 60 70 CUMULATIVE NUMBER (PERCENT)

FIGURE 21 —VARIATION OF PERCENTAGE OF THIN-WALLED FIBERS WITH PER- CENT CUMULATIVE NUMBER OF FIBERS FOR THREE COTTONS. There is a relatively high percentage of thin-walled fibers in all length groups for cotton no 114 There is a trend toward increasing percentage of thm-walled fibers as the fiber length becomes shorter. (Figures under the points represent mean fiber length in sixteenths inches.) precisely specified, (4) the immaturity count is weighted in terms of the relative proportion of the different length groups, and (5) the immaturity count is expressed by a single figure instead of two figures. Details of the revised technique and necessary apparatus are given. Sampling is the same as for the fineness determination. Two sets of 100 fibers each from each length group are mercerized on a slide and examined at a magnificaticm of about 400 diameters. Fibers whose ratio of lumen width to wall thickness is greater than 2:1 are considered to be immature or thin-walled. Others are considered to be normal or thick-walled. The results are recorded on a convenient form and the details of a suitable statistical treatment are described. Some preliminary studies of the precision of the revised method indicate that this is affected by the technique of observation but dei^ends largely on sampling variations. MEASUREMENT ÜE CHAllACTER PllOPEllTIES OF COTTOii 67

GENERAL SUMMARY In studying the relationship of cotton-fiber properties to yarn and fabric quality it is highly essential to have reliable methods for the measurement of the physical characteristics of the fibers if the greatest progress is to be made. Methods that have been devised previously for measuring the so-called "character" properties are not only generally laborious but as a rule comparatively inaccurate. This bulletin describes detailed improvements in methods for three of the character properties—fiber strength, fineness, and maturity. Eeviews of the pertinent literature have been included in each case as a background for understanding the importance of the principles, and as a basis for adopting the improved procedures. The merits and demerits of some of the various procedures previously in use have been pointed out. The Chandler bundle method for determining strength has been carefully studied and the technique has been more completely specified. Variables that are now controlled or corrected for are distance between threads at the center of the bundle, size of bundle, manner and amount of combing, and elongation of wrapping thread during wrapping of the bundle. The effect of sag of the bundle during wrapping is recognized and approximately evaluated. The feature of calculating the strength to an imaginary rod of pure cellulose has been abandoned and the results are now calculated to the area of the bundle cross section as determined by wrapping. Improvements in the weight-per-unit-length method for estimating fiber fineness for a sample of cotton lint include the use of entire fibers instead of cut sections, systematic sampling from all groups of fiber length in the sample, accurate weighting of the fineness in each length group in proportion to the fraction which that group contributes to the whole, and provision for obtaining a useful measure of variation of fiber fineness in the sample. Improvements in the Clegg method for estimating fiber maturity in a sample of cotton lint include a more extensive and adequate sampling process, sampling from all the principal length groups of the length array, classification of fiber-wall types into two groups depending on ratio of lum-en width to wall thickness, weighting of the percentage of immature fibers of each group according to the fraction which that group contributes to the whole sample, and in simplification of the expression for maturity into a single figure— the immaturity count. It is believed that in each case the methods described constitute a material improvement in accuracy and consequently provide more reliable data for use in studies of the interrelations of fiber, yarn, and fabric properties. LITERATURE CITED

(1) ADDERLEY, A. O., . . X ^ HT 1924 THE PHYSICIAL CAUSES OF LUSTHE IN COTTON. Shirley IllSt. MCIH. 3: 105-116. Also in Jour. Textile Inst. 15 : T195^T206, illus. (2) AHMAD, N. ^ ,. 1932 TECHNOLOGICAL REPORTS ON STANDARD INDIAN COTTONS, 1932. InÜiail Cent. Cotton Com., Technol. Lab., Technol. Bull., Ser. A, 21, 100 pp., illus. (3) BALLS, W. L. ^^_ ... 1915. THE DE\^ELOPMENT AND PROPERTIES OF RAW COTTON. ¿Zl pp., liiUS. London. (4) 1928. STUDIES OF QUALITY IN COTTON. 376 pp„ iHus. Londou. (5) BARRITT, N. W. A A 1 1929. SOME PROPERTIES OF THE OEILL-WALL OF COTTON HAIRS. Ann. Appl. Biol. 16: 438-443, illus. (ß) 1930 THE DETERMINATION OF FINENESS OF EGYPTIAN COTTON AND ITS RELA- TION TO QUALITY. Empire Cotton Growing Rev. 7: 19-29, iJlus. (7) BARTHELEMY, H. L. x^ 4- -i ^o Q1« 1930. SCHNELLVERFAHREN FÜR FASERQUERSCHNITTE. KunStseidC 1¿ '. dib- 317, illus. (8) BAUE», F. 1929. EIN lEITRAG ZUR SCHNELLMETHODE ZUR HERSTELLUNG VON FASERQUER- scHNiTTEN. Kuustseide 11: 307, illus. (9) BERGEN, W. V. ^^ ^.. , 1932 MEASUREMENT OF FIBER WIDTHS BY THE WEDGE METHOD. MellmUd Textile Monthly 4: 182-184, 238-240, 428-431, 486-487, illus. (10) BOWMAN, F. H. ^ ^^ 1881 THE STRUCTURE OF THE COTTON FIBKE IN ITS RELATION TO TECHNICAL APPLICATIONS. Ed. 2, 211 pp., illus. Manchester. (11) BURD, L. H. ^ . r>. ^^ ri * 1924 FURTHER USES OF THE BALLS SLEDGE SORTER. Empire CottOU (jrrOW" ing Rev. 1: 290-298. (12) CALVEET, M. A., and HARLAND, S. C. 1924. THE MEASUREABLE CHARACTERS OF RAW COTTON. III.—AN APPROXI- MATION OF THE ORIGINAL CELL DIAMETER. JoUr. Textile lUSt. 15: T8^T9. (13) and SUMMERS, F. 1925 THE SWELLING OF RAW COTTON DURING MERCERISATION WITHOUT TENSION. Shirley Inst. Mem. 4: 49-84, illus. Also Jour. Textile Inst. 16: T233-T268. (14) CLEGG, G. G. ^ . ^ ri -P r>. 4- 1930 iMMxVTURiTY OF COTTON. Empire Cotton Growing Corp., Cont. c.otton Growing Prol)lems. Rept. and Summary Proc. 1930: 13-17. (25) 1932 THE STAPLING OF COTTONS. LABORATORY METHODS IN USB AT THE SHIRLEY INSTITUTE, 1031. Jour. Textile Inst. 23: T35-To4, illus. (Iß) and HARLAND, S. C. 19'^3 NEPS IN COTTON FABRICS AND THEIR RESISTANCE TO DYEING AND PRINTING. Shirley Inst. Mem. 2: 97-104, illus. Also Jour. Tex- tile Inst. 14: T125^132, illus. (17) and HARLAND, S. C. 1923 THE MEASURABLE CHARACTERS OF RAW COTTON. I. THE DETERMINA- TION OF AREA OF CROSS SECTION AND HAIR WEIGHT PER CENTIMETRE. Jour. Textile Inst. 14 : T489-T49:>. (18) CROOKES, W. _OA ,,^ 1874, A PRACTICAL HANDBOOK OF DYEING ANP CALICO PRINTING, 7oO pp., illus,. London, 68 MEASUREMENT OF CHARACTEE PROPERTIES OF COTTON 69

(19) CRUM, W. 1844. ON THE MANNER IN WHICH COTTON UNITES WITH COLOURING MATTER. Phil. Soc. Glasgow Proc. (1841-44) 1: 98-104, illus. (20) 1855. ON A PECULIAR FIBRE OF COTTON WHICH IS INCAPABLE OF BEING DYED. Phil. Soc. Glasgow Proc. (1848-55) 3: 61-64. (21) 1863. ON THE MANNER, IN WHICH COTTON UNITES WITH COLOURING MATTER. Jour. Chem. Soc. [London] (n. s. 1) (16: 1-17, 404-414, illus. (22) EwLEs, J. 1928. A SIMPLE OPTICAL METHOD FOR DETERMINING RAPIDLY THE MEAN DIAMETERS OF A NUMBER, OF FIBRES. Jour. Textile Sci. 2: 101-102, illus. (23) FARR, W. K. 1931. COTTON-FIBERS. I. ORIGIN AND EARLY STAGES OF FJLONGATION. CON- trib. Boyce Thompson Inst. 3: 441-458, illus. (24) and CLARK, G. L. 1932. COTTON FIBERS. II. STRUCTURAL FEATURES OF THE WALL SUGGE^STED BY X-RAY DIFFRACTION ANALYSES AND OBSERVATIONS IN ORDINARY AND PLANE-pO'LARizED LIGHT. Coutrib. Boyce Thompsou Inst. 4: 273-295, illus. (25) FEDOROV, V. S. 1930. CONCERNING THE RIPENESS, FINENESS AND STRENGTH OF THE COTTON FIBER. 39 pp., illus. Tashkent, Izdatel'stov Nikhi. [In Rus- sian. English summary.] (26) FISHER, R. A. 1932. STATISTICAL METHODS FOR RESEARCH WORKER.S. Ed. 4, 307 pp., illus. Edinburgh and London. (27) FOSTER,, G. A. R. 1926. THE REFLECTION OF LIGHT FROM TEXTILE MATEaiiALs AND THE PHYSI- CAL CAUSES OF THEIR LUSTRE. Shirly Inst. Mem. 5: 1-5. (28) H ALLER, R. 1908. BEITRÄGE ZUR KENNTNIS DER ''TOTEN BAUMWOLLE." Chem. Ztg. 321 838-839. (29) HARDY, J. I. 1933. NEW DEVICE FOR DETERMINING WOOL FINENESS. Textile Research 3: 189-193. (30) 1933. DETERMINATION OF FIBRE FINENESS. A RAPID METHOD USING A NEW CROSS-SECTIONING DEiviCE. Textile Research 3: 381-387. (31) HAWKINS, R. S. 1931. METHOD OF ESTIMATING COTTON FIBER MATURITY. Jour. Agr. Re- search 43: 733-742, illus. (32) and SERVISS, G. H. 1930. DEIVELOPMENT OF COTTON FIBERS IN THE PIMA AND ACALA VARIETIES. Jour. Agr. Research 40: 1017-1029, illus. (33) HEERMANN, P., and HERZOG, A. 1931. MIKROSKOPISCHE UND MECHANISCH-TECHNISCHE TEXT1LUNTP:RSUCH- UNGEN. Ed. 3, 451 pp., illus. Berlin. (33) HERZOG, A. 1914. MIKROSKOPISCHE STUDIEN ÜBER BAUMWOLLE. Chem. Ztg. 38 I [10891-1091, [1096]-1100, illus. (35) 1930. EIN ALLGEMEIN ANWENDBARES SCHNELLVERFAHREN ZUR HERSTELLP^N VON FASERQUERSCHNITTEN. KuUStSCide 12 ! 92-96, illUS. (36) HOLM AN, S. W. 1897. DISCUSSION OF THE PRECISION OF MEASUREMENTS ; WITH EXAMPLES TAKEN FROM PHYSICS AND ELECTRICAL ENGINEERING. Ed. 2, 176 pp. New York. (37) IYENGAR, R. L. N., and TURNER, A. J. 1930, THE WEIGHT PER INCH OF FIBRES OF DIFFERENT LENGTHS, AND THE NUMBERS OF FIBRES OF DIFFERENT LENGTHS PER SEED, FOR EACH OF THE STANDARD INDIAN COTTONS. Indian Cent. Cotton Com, Techno!, Lab., Technol. Bull. Ser. B, 7, 24 pp., illus. 70 TECHNICAL BULLP^TIN 5 4 5, U. S. DEPT. OE AGRICULTUBE

(38) JOHANNSEN, O. 1911. ÜBER DEN EINFLUSS DER FASERZAHL AUF DIE GESPINSTFMNHEIT ODER NUMMER. Leipziger Monatschr. Textilindus. 26: 7-10, 109^112. (39) JOHNSON, A. K. 1928. IDENTIFYING RAYONS AS TO GROUP, TYPE, AND MAKER. . . In RayOll Year Book, 1928-29 ed., pp. 92-100, illus. New York. (40) KosHAL, R. S., and TURNER, A. J. 1930. STUDIES IN THE SAMPLING OF COTTON FOR THE DETERMINATION OF FIBRE-PROPERTIES. PART I. INTRODUCTORY AND EXPERIMENTAL. PART II. FREQUENCY CURVES FOR VARIOUS FIBRE-PROPERTIES. In- dian Cent. Cotton Com. Technol. Lab., Technol. Bull. Ser. B, C, 46 pp., illus. (41) and TURNER, A. J. 1930. STUDIES IN THE SAMPLING OF COTTON FOR THE DETERMINATION OF FIBRE-PROPERTIES. PART III. THE SIZE AND RELIABILITY OF A SATISFACTORY SAMPLE. Indian Cent. Cotton Com. Technol. Lab., Technol. Bull. Ser. B, 10, 39 pp., illus. (42) KRAUTER, G. 1932. HILFSMITTEL ZUR BESTIMMUNG DER FEINHEIT VON EINZELFASERN. Leipziger Monatschr. Textilindus. 47: 215-216, illus. (43) KtJvSEBAUCH, K. 1931. NEUE METHODE ZUR WOLLFEINHEITS-BZW. VTOLLDICKENBESTIMMUNG, SOWIE ZUR GÜTEBEURTEILUNG NACH FASERLÄNGE UND DICKE. Melliand Textilber. 12: 21-23, 97-100, illus. (44) LEIGH, E. 1873. THE SCIENCE OF MODERN COTTON SPINNING. ED. 2, V. 2, üLUS., London. (45) LiPOWSKY. 1933. FASERFEINHEITSBESTTMMUNG UND VERSUCHE ÜBER DEN EINFLUSS DER VERARBEITUNG AUF DIE FEINHEIT DER BAUM WOLLFASER. Spinner u. Weber 51 (7) : 1-4. (46) McNicHOLAs, H. J., and CURTIS, H. J. 1931. MEASUREMENT OF FIBERS BY THE DIFFRACTION METHOD. Bur. Stand- ards Jour. Research 6: 717-734, illus. (47) MATTHEW, J. A. 1932. MEASUREMENT OF FIBRE AND YARN DIAMETERS BY DIFFEACTTON METHOD. Jour. Textile Inst. 23 : T55-T70, illus. (48) MORTON, W. E. 1926. THE IMPOŒITANCE OF HAIR WEIGHT PER CENTIMETRE AS A MEASURABLE CHARACTEK OF COTTON AND SOME INDICATIONS OF ITS PRACTICAL UTILITY. Shirley Inst. Mem. 5: 177-192, illus. (49) MÜLLER, E. 1923. EIN NEUER STAPLEMESSER. Leipziger Monatschr. Textilindus. 38 : 151-152. (50) NAVKAL, H., and SEN, K. R. 1930. A COMPARISON OF SOME METHODS OF TESTING THE BREAKING STRENGTH OF SINGLE COTTON FIBRES. Indian Cent. Cotton Com. Technol. Lab., Technol. Bull. Ser. B, 5, 10 pp., illus. (51) NiBLACK, K. G. 1930. MAKING RAYON CROSS SECTIONS IN THREE MINUTES. Textile World 78: (1997), illus. (52) OxLEY, A. E., and PEIRCE, F. T. 1922. SOME PHYSICAL QUANTITIES OF MULE YARNS. Shirley lust. Mem. 1: 101-117, illus. (53) PATTEE, C. L. 1934. THE COTTON ClASSER, FINDS A VALUABLE TOOL IN THE POLARIZING MICROSCOPE. Textile World 84: 2012-2013, illus. (54) PEARSON, N. L. 1&'_.3. NEPS AND SIMILAR IMPERFECTIONS IN COTTON. U. S. Dcpt. Agr. Tech. Bull. 396, 19 pp., illus. (55) PEIRCE, F. T. 1923. THE MECHANICAL TESTING OF COTTON MATERIALS. A—THE MEASURE- MENT» OF THE MECHANICAL PROPERTIES OF COTTON MATERIALS. A SUMMARY OF THE LITERATURE. Shirley Inst, Mcm, 2: 100^130, Also Jcur. Textile Inst. 14 : T161-T182, MEASUREMENT OF CHARACTER PROPERTIES OF COTTOiii 71

(56) PELTON, M. D. 1929-30. THE LUSTRE OF TEXTILE FIBEES AND A METHOD OF MEASUBLîMBNT. Optical Soc, London, Trans. 31: 184-200. (57) POPE, O. A. 1931. THE DETEEMINATION OF SAMPLE SIZE FOR DIAMETER MEASUREMENTS IN COTTON FIBER STUDIES. JouF. Agi". Research 43: 957-984, illus. (58) PRESTON, J. M. 1931. THEORIES OF LUSTRE. Jour. Soc. Dyers and Colourists 47: 136-143. (59) ROEHRIOH, O. 1928. METHODE D'APPRECIATION SCIENTIFIQUE ET' PRATIQUE DES QUALITÉS TEXTILES D'UN COTON BRUT. 59 pp., illus. Paris. (60) SCHWARZ, E. R. 1930. DON'T BE AFRAID OF THE MICROSCOPE. ARTICLE VIII. PREPARING CKOss-SECTioNS OF TEXTiLEis. Textile World 77: 320^323, 359, illus. (61) TURNER, A. J. 1928. THE FOUNDATIONS OF YARN-STRENGTH AND YARN EXTENSION. PART 1. THE GENERAL PROBLEM. PART 2. THE RELATION OF YARN-STRENGTH TO FIBRE-STRENGTH. Indian Cent. Cotton Com. Technol. Lab., Technol. Ser. 7, Bull. 12, 29 pp., illus. (62) 1929. GINNING PERCENTAGE AND LINT INDEX OF COTTON IN RELATION TO THE NUMBER OF COTTON FIBRES PER SEED, THE EFFECT OF ENVIRONMENT ON GINNING PERCENTAGE AND THE DETERMINATION OF UNIT FIBRE- WEIGHT. Indian Cent. Cotton Com. Technol. Lab., Technol. Ser. 13, Bull. 18, 41 pp., illus. (63) and VENKATARAMAN, V. 1933. THE FOUNDATIONS OF YARN-STRENGTH AND YARN EXTENSION. PART V. THE PREDICTION OF THE SPINNING VALUE OF A COTTON FROM ITS riBRErPROPERTiES. Indian Cent. Cotton Com., Technol. Lab., Technol. Bull. Ser. B, 17, 48 pp., illus. (64) UNITED STATES DEPARTMENT OF AGRICULTURE, BUREAU OF AGRICULTURAL ECONOMIOS. 1932. OFFICIAL STANDARDS OF THE UNITED STATES FOR GRADES OF WOOL AND WOOL TOP, AND RULES AND REGULATIONS FOR DISTRIBUTION OF PRAC- TICAL FORMS OF WOOL AND WOOL TOP STANDARDS UNDER WOOL STANDARDS ACT OF MAY 17, 192 8. U. S. Dopt. Agr., Bur. Agr. Econ., Serv. and Régulât. Announc. 135, 5 pp. (65) 1934. REPORT OF THE OHIEF OF THE BUREAU OF AGRICULTURAL ECONOMICS, 1934. 29 pp. (66) UNITED STATES DEPARTMENT OF COMMERCE, BUREAU OF THE CENSUS. 1922-. BIENNIAL CENSUS OF MANUFACTURES. Issued every two years, commencing with 1st report for 1921. (67) UROUHART, A= R,, and BCKERSALL, N. 1930. THE MOISTURE RELATIONS OF COTTON. VH. A STUDY OF HYSTERESIS Shirley Inst. Mem. 9: 123-134, illus. (68) ViviANi, E. 1929. SCHNELLMETHODE ZUR HERSTELLUNG VON FASERQUBRSCHNITTEN Kunstseide 11: 111-112, illus. (69) WALEN, E. D. 1922. THE STRENGTH OF COTTON . . . Textile World, 62: 2017, 2019 2021 2023, illus. (70) WEBB, R, W. 1932. THE SUTER-WEBB COTTON FIBER DUPLEX SORTER AND THE RESULTING METHOD OF LENGTH-VARIABILITY MEASUREMENTS. Amer. SoC. for Testing Materials, Proc, v. 32, PI. 2, pp. 764-771, illus. (71) YOUNG, T. 1855. MiscET.LANEOUs WORKS. V. 2, illus. Loudou. APPENDIX

TABLE 15.- -Corrccted circumferences corresponding to observed circumferences mithin recommended range

Observed Corrected Observed Corrected Observed Corrected Observed Corrected circum- circum- circum- circum- circum- circum- circum- circum- ference ference ference ference ference ference ference ference

Inch Inch Inch Inch Inch Inch Inch Inch 0.138 0.115 0.144 0.121 0.149 0.126 0.154 0.131 .139 .116 .145 .122 .150 .127 .155 .132 140 .117 .146 .123 .151 .128 .156 .133 .141 .118 .147 .124 .152 .129 .157 .134 .142 .119 .148 .125 .153 .130 .158 .135 .143 .120

TABLE 16.—Corrections applicable to machine breaks for cottons having different mean corrected ynachine breaks'" and circumferences deviating from standard circumference '^ ^

Corrections applicable to cottons having average corrected machine break of— Deviation of circumference from standard (inches) 60 65 70 75 80 85 90 95 100 105 110 115 120 125 130 lbs. lbs. lbs. lbs. lbs. lbs. lbs. lbs. lbs. lbs. lbs. lbs. lbs. lbs. lbs.

Lbs. Lbs. Lbs. Lbs. Lbs. Lbs. Lbs. Lbs. Lbs. Lbs. Lbs. Lbs. Lbs. Lbs. Lbs. 0 1 1 1 1 1 1 1 1 1 1 1 1 2 2 0001 3 3 0 002 - - - 1 1 1 1 2 2 2 2 2 2 3 3 3 1 2 2 2 2 2 3 3 3 4 4 4 4 5 5 0 003 5 6 6 6 7 0 004 - - - 2 2 3 3 3 4 4 4 5 5 2 3 3 4 4 4 5 5 6 6 7 7 7 8 8 0005 9 9 10 0 006 - -- 3 3 4 4 5 5 6 6 7 7 8 8 3 4 4 5 6 6 7 7 8 9 9 10 10 11 12 0007 12 13 0 008 - --- - 4 4 5 6 6 7 8 8 9 10 10 11 12 4 5 6 6 7 8 9 9 10 11 12 13 13 14 15 0 009 - - 14 16 16 0 010 5 5 6 7 8 9 10 11 11 12 13 15

1 The mean corrected machine break is obtained by a first approximation, by allowing Ipound for each 0.001 inch deviation of the mean circumference from standard circumference (0.125 inch). This determines * 2®Bund1es^smSler^han standard circumference require that the corrections be added: those larger than standard reauire that the corrections be subtracted. _ . , . , ^^ . ^, tÄcorrSns are calculated by means of the formula i2=0.01690 5,-0.55 m which^. is the mean machine break for bundles of standard circumference and R is the correction for each 0.001 inch deviation of circumference from standard. 72 MEASUEEMENT OF CHARACTER PROPERTIES OF COTTON 73

TAJBJLB 17.—Strength in pounds per square inch corresponding to the machine l)reaking strength of bundles of 0.125 inch standard circumference

Machine Strength Machine Strength Machine Strength Machine break break break break Strength

1,000 1,000 1,000 1,000 Pounds pounds Pounds pounds Pounds pounds Pounds pounds 30 24 60 48 90 72 120 97 31 25 61 49 91 73 121 97 32 26 62 50 92 74 122 98 33 27 63 51 93 75 123 99 34 27 64 51 94 76 124 100 35 28 65 52 95 76 125 101 36 29 66 53 96 77 126 101 37 30 67 54 97 78 127 102 38 31 68 55 98 79 128 103 39 31 69 55 99 80 129 104 40 32 70 56 100 80 130 105 41 33 71 57 101 81 131 105 42 34 72 58 102 82 132 106 43 35 73 59 103 83 133 107 44 35 74 60 104 84 134 108 45 36 75 60 105 84 135 109 46 37 76 61 106 85 136 109 47 38 77 62 107 86 137 110 48 39 78 63 108 87 138 111 49 39 79 64 109 88 139 112 50 40 80 64 110 88 140 113 51 41 81 65 111 89 141 113 52 42 82 66 112 90 142 114 53 43 83 67 113 91 143 115 54 43 84 68 114 92 144 116 55 44 85 68 115 92 145 117 56 45 86 69 116 93 146 117 57 46 87 70 117 94 147 118 58 47 88 71 118 95 148 119 59 47 89 72 119 96 149 120

TABI.B 18.—Standard deviations and standard errors of means of 10 observations corresponding to sum of squares of deviations from the mean ^

Sd2

1 0.3 0.1 31 1.9 0 6 61 2.6 0.8 91 3.2 1.0 2 .5 .1 32 1.9 6 62 2.6 .8 92 3.2 1.0 3 .6 .2 33 1.9 6 63 2.6 .8 93 3.2 1.0 4 . 7 .2 34 1.9 0 64 2.7 .8 94 3.2 1.0 5 .7 .2 35 2.0 6 65 2.7 .8 95 3.2 1.0 6 .8 .3 36 2.0 6 66 2.7 .9 96 3.3 1.0 7 .9 .3 37 2.0 6 67 2.7 .9 97 3.3 1.0 8 .9 .3 38 2. 1 6 68 2.7 .9 98 3.3 1.0 9 1.0 .3 39 2. 1 7 69 2.8 .9 99 3.3 10 1.1 .3 40 2. 1 7 70 2.8 .9 100-___ 3.3 11 1.1 .3 41 2. 1 7 71 2.8 .9 10]_^_ 3.3 12 1.2 .4 42 2.2 7 72 2.8 .9 102____ 3.4 13 1.2 .4 43 2.2 7 73 2.8 .9 103^___ 3.4 14 1.2 .4 44 2.2 7 74 2.9 .9 104 3.4 15 1.3 .4 45 2.2 7 75 2.9 .9 105 _ _ 3.4 16 1.3 .4 46 2.3 7 76 2.9 .9 106-.___ 3.4 17 1.4 .4 47 2.3 7 77 2.9 .9 107____ 3.4 J8 1.4 .4 48 2.3 7 78 2.9 .9 108 3.5 19 1.5 . 5 49 2.3 7 79 3.0 .9 109.___ 3.5 20 1.5 . r 50 2.4 7 80 3.0 .9 110__._ 3.5 21 1.5 .5 51 2.4 8 8! 3.0 .9 1]1___ 3.5 22 1.6 .5 52 2.4 8 82 3.0 1.0 112 3.5 23 1.6 .5 53 2.4 8 83 3.0 1.0 113____ 3.5 24 1.6 .5 54 2.4 8 84 3.1 1.0 114____ 3.6 1.1 25 1.7 .5 55 2.5 8 85 3.1 1.0 115 3.6 26 1.7 .5 56 2.5 8 86 3.1 1.0 116__.._ 3.6 27 1.7 .5 57 2.5 8 87 3.1 1.0 117_-_- 3.6 28 1.8 .6 58 2.5 8 88 3.1 1.0 118____ 3.6 29 1.8 .6 59 2.6 8 89 3.1 1.0 119 3.6 30 1.8 .6 60 2.6 8 90 3.2 1.0 120____ 3.7 1.2

1 s ¿2=sum of squares of deviations from mean; ir=standard deviation= Vs d2/(n^) = V^ rfV9; e=standard eTTOT=

DERIVATION OF THE FORMULA FOR ERROR OF MEAN WEIGHT PER INCH The approximate standard error of the mean fiber weight per inch for a sample of cotton may be calculated from the variations of the weight per fiber in the different length groups of the array. Let the standard deviations of the weight per fiber in each length group be calculated in the usual manner by the formula

where d is the deviation of the observations from their common mean. Then if the standard deviations depend on duplicate determinations the standard error, (3, of the weight per fiber is expressed by the formula

e=~^/N~^| i^.=J- NiN-1)'^..^^~ .. =d It was shown on page 44 that the mean weight per inch, /, for the sample could be obtained by means of the formula

where W is the weight in any length group, and L is the length and F the weight per fiber iN^^Jin the same group. By consideration of the right-hand expression it is seen that errors in / may be due to errors in each W, L, or F. But L is the midpoint length for any length group and any errors in mean length of the fibers as well as variations in mean fineness will be expressed in variations of F. Errors in W probably may be considered negligible in comparison to errors in F. Therefore we may compute the error in / as being due to errors in the determination of F, and as affecting the expression L2V ( ~~p~ ) of the denominator which is, in effect, the total length of the fibers.

Bv application of methods for determining the precision of indirect measurements {'36, p. 59) it is seen that a fractional error y^. m if can be determined from the fractional error in 7:LN^~^jj^ of the denominator where

As an example of the method of applying the formula to specific cases it will be appropriate here to calculate the standard error of the mean fiber weight per 'inch from the data, shown in figure 17. Part of the data shown in that figure is recorded in table 19^—the individual and average weight of the fibers and the figures occurring in the LN column. In transcribing the weights of the fibers it is advantageous to move the decimal two places to the right giving the weight per fiber in units of 10-* mg.

TABLE 19.—Calculation of standard error (E) of mean fiher weight per inch

Weight per fiber 10-* mg Relative length a b Average Deviation (LN) m (F) (d)

68 07 68 0.5 36 0.1 66 67 66 0.5 75 .3 61 59 60 1.0 110 3.4 53 55 54 1.0 127 5.5 48 49 48 0.5 91 .9 42 44 43 1.0 55 1.6 36 38 37 1.0 36 1.0 32 _ 32 32 .0 31 .0 25 26 26 0.5 25 .2 17 19 18 1.0 34 3.6 Total r)20 16.6

7=52X10-^ mg per inch (see fig. 17, p. 50). ^ 52xVl6-6 620—=0-34X10-4 mg per inch. 0.34X100 ^ „^ — 52 =0.66 percent.

The deviations, d, of the weight per fiber must be calculated. Theoretically this is done by subtracting the average figure from either of the individual determinations. But the averages are rounded figures so that, practically, the deviations are found by taking one-half of the difference between the individual fiber weights and recording without regard to sign. The final column is obtained by performing the indicated arithmetic, namely, by multiplying the figures in the LN column by those of the d column dividing by the average (rounded) fiber weights and squaring the quotient. These operations are conveniently performed on a calculating machine with the aid of a table of squares, or in the absence of a machine with the aid of a table of logarithms. The LN and final columns are added and the final computations performed as shown below the table. The mean fiber weight per inch found previously is 52X10"* mg. The standard error is seen to be 0.34X10"* mg or 0.66 percent of the mean. It appears from a considerable group of data that the deviations in weight per fiber are practically constant for the different length groups. This is shown by table 20, in which are tabulated the frequencies of deviations of duplicate determinations of weight per fiber from their common mean for various le-inch length groups. The data were collected from determinations made on alternate sixteenth-inch groups of 84 individual fiber-length arrays, and with a balance of insufiicient sensitivity. Thus, the data are not applicable to any other set of conditions but probably indicate the nature of the deviations in duplicate determinations of fiber weight. If in any series of measurements the deviations of F are found to be constant for the different length groups we may remove d from beneath the radical with a corresponding simplification of the equation, thus— LN Id E= XLN~ 76 TECHNICAL BULLETIN 54 5, U. S. DEPT. OP AGRICULTURE

TABLE 20.—Frequency of deviations from the mean of fiber weight and mean standard deviation and mean standard error for different sixteenth-inch length groups of the cotton flher length array

Devia- Sixteenth-inch groups tions (d) from means two 4 6 8 10 12 14 16 18 20 22 24 26 28 30 3? Total (0.0001 mg)

0 20 J4 14 16 22 16 16 16 14 6 10 2 6 0 0 172 0.5 18 18 12 12 24 12 28 14 14 12 24 12 2 2 208 1.0 12 30 12 16 20 24 28 24 24 20 10 14 "'io 4 248 1.5 24 24 22 18 16 32 14 26 32 14 6 6 4 238 2.0 16 20 12 34 18 16 10 8 16 8 12 8 " "2 2 182 2 5 16 26 16 14 8 12 22 16 12 8 10 2 2 164 3 0 16 4 6 12 16 6 10 10 6 4 10 2 4 106 3.5 10 2 20 14 6 10 10 12 4 4 2 2 96 4 0 10 10 4 8 10 6 10 6 8 2 2 76 4 5 4 ""'io 8 10 6 6 2 6 6 58 5 0 6 6 12 10 14 4 10 2 2 2 74 5 5 2 2 2 2 - 2 2 14 60 2 2 10 2 2 2 24 6 5 4 2 2 4 2 — - 6 20 7 0 4 2 2 8 2 18 7 5 2 2 2 2 2 10 8 0 2 4 6 8 5 2 2 9 0 2 2 4 8 9 5 2 2 4 10.0 10.5 11 0 2 2 11.5 12 0 12.5 2 2 2 6 13 0 2 2 TotaL-- 158 168 168 168 166 168 168 152 140 94 84 58 30 14 2 1,738 Sfd 340 3'/0 481 411 366 428 369 337 274 194 135 135 56 25 1 3,922 Mean d-.- 2.15 2.20 2.86 2.45 2.55 2.20 2.22 1.96 2.06 1.61 2.33 1.87 1.79 1.79 0.5 2.26 2fd^ 1,160 1, 418 2,171. 5 1, 636. 5 1,412 1,914 1, 434. 5 1, 341. 5 956 644 5,425 715.5 173 71.5 .5 15, 591 d2 7.34 8.44 12.93 9.74 8.51 11.39 8.54 8.83 6.83 6.85 6.46 12.34 5.77 5.11 .25 8.97 Meano--. _ 2.71 2.91 3.60 3.12 2.92 3.37 2.92 2.97 2.61 2.62 2.54 3.51 2.40 2.26 .5 2.99 Mean EF- 2.71 2.91 3.60 3.12 2.92 3.37 2.92 2.97 2.61 2.62 2.54 3.51 2.40 2.26 0.5 2.99 ORGANIZATION OF THE UNITED STATES DEPARTMENT OF AGRICULTURE WHEN THIS PUBLICATION WAS LAST PRINTED

Secretary of Agriculture HENRY A. WALLACE. Under Secretary REXFORD G. Tue,WELL. Assistant Secretary M. L. WILSON. Director of Extension Work C. W. WARBURTON. Director of Finance W. A. JUMP. Director of Information M. S. EISENHOWER. Director of Personnel W. W. STOCKBERGER. Director of Research JAMES T. JARDINE. Solicitor MASTíN G. WHITE. Agricultural Adjustment Administration H. R. TOLLEY, Administrator. Bureau of Agricultural Economics A. G. BLACK, Chief. Bureau of Agricultural Engineering S. H. MCCRORY, Chief. Bureau of Animal Industry JOHN R. MOHLER, Chief. Bureau of Biological Survey IRA N. GABRIELSON, Chief. Bureau of Chemistry and Soils HENRY G. KNIGHT, Chief. Commodity Exchange Administration J. W. T. DUVEL, Chief. Bureau of Dairy Industry O. E. REED, Chief. Bureau of Entomology and Plant Quarantine. LEE A. STRONG, Chief. Office of Experiment Stations JAMES T. JARDINE, Chief. Food and Drug Administration WALTER G. CAMPBELL, Chief. Forest Service FERDINAND A. SILCOX, Chief. Bureau of Home Economics LOUISE STANLEY, Chief. Library CLARIBEL R. BARNETT, Librarian. Bureau of Plant Industry FREDERICK D. RICHEY, Chief. Bureau of Public Roads THOMAS H. MACDONALD, Chief. Soil Conservation Service H. H. BENNETT, Chief. Weather Bureau WILLIS R. GREGG, Chief.

This bulletin is a contribution from

Bureau of Agricultural Economics A. G. BLACK, Chief. Division of Cotton Marketing CARL H. ROBINSON, Principal Marketing Specialist in Charge. 77

U. S. GOVERNMENT PRINTING OFFICE: 1937