D1535-1989 Specifying Color by the Munsell System

By Authority OfTHE UNITED STATES OF AMERICA Legally Binding Document By the Authority Vested By Part 5 of the United States Code § 552(a) and Part 1 of the Code of Regulations § 51 the attached document has been duly INCORPORATED BY REFERENCE and shall be considered legally binding upon all citizens and residents of the United States of America. HEED THIS NOTICE: Criminal penalties may apply for noncompliance. e Document Name: ASTM D1535: Specifying Color by the Munsell System CFR Section(s): 7 CFR 1755.860(c)(3) Standards Body: American Society for Testing and Materials Official Incorporator: THE EXECUTIVE DIRECTOR OFFICE OF THE FEDERAL REGISTER WASHINGTON, D.C. and Munsell chroma corresponds to chroma. against a medium gray to white background. 2441 N. n-the attribute of color perception by means of which a color is judged to be red. Hue is represented by the angular position about this axis (see 3. The two systems are equivalent.. 2. 6 3.2.1. blue.1 Discussion-Two systems of designating Munsell hue are shown in Fig.'r superscript epsilon (E) indicates an editorial change since the last revision or reapproval. and chroma assigned to the color of a specimen by visually comparing the specimen to the chips in the Munsell Book of Color. taken to be right-handed. ~/ ' white at the top. J Annllal Book of ASTM Standards. Munsell value corresponds to lightness. 3. Vol 14. and Munsell chroma C. 385. a letter-number system and an all-number system. through a gradation of grays. "Colorimetry. 4 This solid forms the basis of the Munsell notation in which Munsell hue corresponds to hue. original adoptIon. because it requires no prior knowledge or memory of the correspondence of numbers to hues. A .2. .02. Vol 33. . 3. and views the specimen illuminated by CIE source c or D65. A number in pai'erttheses -Indicates the ~year oflast reapproval. B. Provision is made for conversion of CIE data to Munsell notation. Baltimore.1 Discussion-Although the original system proposed by Munsell was a left-handed coordinate system. D. vertical axis dimension represents neutral colors. . This test method provides a simple visual method as an alternative to the more precise and more complex method based on spectrophotometry and the CIE system (see Method E 308 and Practice E 1164). The hue circle is graduated in steps judged 1. p. but the letter-number system is preferred. Vol 06.2.. the system is often represented as a right-handed system because it facilitates comparison to the CIE chromaticity diagram. in the CIE system. If the observer has normal color vision.1. Published December 1989.1 Munsell notation. lightness and chroma. as shown in Fig.1.. 5 Available from the Munsell Color Co . The lightness of a color perceived. M. 6 Newhall. NBS. MD 21218. Originally published as D 1535 . Terminology 3. January 1968.5 (2) a notation in the Munsell color system. operations.. 2 Annual Book of ASTM Standards. Optical Society (?i' America. Last previous edition 0 1535 .80. 3. Chroma is represented by the perpendicular distance from the central axis. and Judd. 3. lightness. S.1 Munsell surface-color perception solid.. dr. } I " '.1.!. 3.~~~ Designation: D 1535 . "Final RepOIt of the OSA Subcommittee on the Spacing of the Munsell Colors.2 hue. It is the responsibility of the user of this standard to establish appropriate safety and health practices and determine the applicability of regulatory limitations prior to use. . value. 1. the Munsell value of the specimen correlates well with the observer's perception of the lightness of the color. such as painted surfaces viewed in daylight by an observer having normal color vision. a system based on the color-perception attributes hue. Referenced Documents 2. Nat. considered in a closed ring (red and purple being an adjacent pair)." Monograph 104. '~ . Munsell value V...1)..09 on Color Order Systems USTAGTC 187. or intermediate between adjacent pairs of these. is adapted to daylight. 1943. and chroma.89 Standard. Under the same conditions. Scope 1.. The test method is limited to opaque objects. 1989.1.' This standard is issued under the fixed designation D 1535.'." Journal. green. I. the Munsell hue correlates well with the observer's perception of hue and the Munsell chroma with the perception of chroma. n-a spatial representation of colors in the form of a cylindrical coordinate system based on the three perceptual attributes: hue.2 This standard may involve hazardous materials. derived from daylight luminous reflectance factor Y and chromaticity coordinates x and y. Current edition approved Oct.2 Definitions-see also Definitions E 284. by the use of scales defined by the Optical Society of America Subcommittee on the Spacing of the Munsell Colors. Nickerson.1 Discussion-The Munsell notation is written as a combination ofletters and numbers by which the color of an opaque object may be specified with respect to Munsell hue H. and equipment.1.2. 4 Taken from Nimeroff. ranging from black at the bottom. purple. D.3 Munsell hue. n-an attribute of color lIsed in the Munsell color system to indicate the hue of a specimen viewed in daylight.. written in the form H VIC.T~'$t.~Metho_c. n-(l) the Munsell hue. orange.01. 1.. This standard does not purport to address all of the safety problems associated with its use.3. Bureau Standards.1 ASTM Standards: D 1729 Practice for Visual Evaluation of Color Differences of Opaque Materials2 E 284 Definitions of Terms Relating to Appearance of Materials 3 E 308 Method for Computing the Colors of Objects by U sing the CIE System3 E 1164 Practice for Obtaining Spectrophotometric Data for Object-Color Evaluation 3 3. as chromatic (not gray) is represented by the distance above the base plane.. the year oHMt revision.' \. .t Specifying Color by for' the Munsell System'1 ". 2. yellow. :irtf the cas'e of rbvisi'oh'.58 T. The central.1 Descriptions of Terms: 3. Calvert St. 27. to J This test method is under the jurisdiction of ASTM Committee E-12 on Appearance of Materials and is the direct responsibility of Subcommittee E12. 2 .2..1 This test method provides a means of specifying the colors of objects in terms of the Munsell color order system. the number immediately following the designation indicates the year of . 3. 6. follow the lighting and viewing recommendations of Practice D 1729.3 If both matte and glossy editions of the Munsell Book of Color are available. 6. with rectangular openings the size of the chips in the Munsell Book of Color.[asks. NJ 08543.1. the letter symbol for the nearest of the principal hues being included in parentheses with the chroma.61/. thus: N 5.5 4.1 Value-Find the chips between which the value of the specimen lies. by interpolation or extrapolation. 6. Calvert St. in the following order. Box 490. In such cases. Estimate to the nearest fifth of the 2.2. and Applied Color Systems.5R 4. The glossy chips are removable.1 Lighting and Viewing Conditions: . n-an attribute of color used in the Munsell color system to indicate the degree of departure of a color from a gray of the same Munsell value. 6.2.6 chroma. as described in 6. for example 4. Baltimore.2 For critical applications. Strictly interpreted. They should be removed and placed immediately adjacent to the specimen.2. average the estimated Munsell chromas. so the light reaches the surface from the observer's side.1. 3 . Record the hue estimate in front of the value-chroma estimate and separated from it by a space.4. on a scale extending from 0 for ideal black to 10 for ideal white. matte or glossy edition. Box 5800.5-hue steps between adjacent hue charts. in steps that are visually approximately equal in magnitude.2/. and average the results. 5. Place one on each side of the specimen. Record the estimated Munsell value in front of the slant. 4. Pay chief attention to the Munsell chips having values nearest that of the specimen and secondary attention to those next nearest. where it is uniformly illuminated by daylight.1 to 6. natural daylight can be used to obtain notations having accuracy adequate for many purposes. Estimate the value of the specimen to the nearest tenth of the one-value-step interval between adjacent value levels. n-the attribute of color used to indicate the degree of departure of the color from a gray of the same lightness.20.2. 6.7 Munsell chroma. the chroma.12).3.58 Y.4 lightness.1 This test method does not cover the preparation of test specimens.3 Daylight Illuminating Equipment..2. but the N is often used to designate colors with chromas under 0.3. Cover the specimen and charts with the gray masks so the specimen and one chip from each chart can be seen.2 Procedure: 6.1. Move the masks from chip to chip to find the chips most like the specimen.3.2/6.O. P. Princeton. Preparation of Test Specimens 5. Place the specimen on a neutral medium gray to white background.2. Munsell Color Notation from CIE MeasuremenC NOTE i-The eIE results for the specimen must be based upon color measurements in which the specular component was excluded. the value.5 Munsell value. 3. PA 18085. chiefly from the sky.5. and a south window is usually used in the southern hemisphere. Select the two adjacent Munsell constanthue charts or chips between which the hue of the specimen lies. select a window through which the sun is not shining. MD 21218.3. Munsell Notation by Visual Means 6.3. If the value and chroma of the specimen do not correspond closely to those of any chip.2 Gray Jl.2.2. Note that there are usually two chroma steps between adjacent columns of a chart. repeat the interpolation of hue with the next closest pair of chips and record the average.2 When determining the Munsell notation with natural daylight.1 Specimens must be examined by an observer with normal color vision. use the one having gloss most like the specimen. 3. use daylight illuminating equipment as described in Practice D 1729.2. 2441 N.3. Although all Munsell chips of the same Munsell chroma are intended to appear to have the same perceptual chrom~. 3. Tatamy. determine the Munsell chroma. A north window is usually used in the northern .1 Discussion-Achromatic or neutral colors are designated N followed by the value notation. or 7. for example /6. Estimate. 6. repeat the estimations. by light other than daylight falling on the work surface. a slightly different estimate of chroma may be obtained by comparison with the chips of the next value. see other ASTM standards covering the appropriate materials or agree among interested parties on what the procedure shall be. P. the neutral N implies zero chroma. as described in Practice D 1729. in steps that are visually approximately equal in magnitude. 0. Apparatus 4. .1 When using daylight illuminating equipment. horizontal. Interchange the positions of the charts.1 Munsell Book of Color. as in N 8. Estimate chroma to the nearest fifth of the 2-chroma interval and record the estimated Munsell chroma after the slant.~t 0 1535 visually to be approximately equal. 6.73/(2.. Place a canopy of black cloth above the working surface to prevent errors caused by the ceiling or other objects being reflected from the surface of the specimens. Place a working surface at the window . converse conditions are equivalent if a black matte surface is placed opposite the observer to minimize the amount of light reflected from the specimen surface.2 Chroma-Move the masks to present successive colors of the same chroma and. for example 4. hemisphere. If preparation is necessary. and with 7 Computer programs that convert CIE data to Munsell color notations are available from the Davidson Colleagues. n-the attribute of color perception by which a non-self-luminous body is judged to reflect more or less light.2. 3. i 6. 4.O. 3. and the hue by interpolation or extrapolation of the notations on the chips. n-an attribute of color used in the Munsell color system to indicate the lightness of a specimen viewed in daylight.2.2. the Munsell Color Company. Although 45° illumination and perpendicular viewing are recommended by the CIE. View the specimen along a direction just far enough from the normal to avoid reflection of your forehead. and at angles centering on 45° above the '.4.2.3 Hue-Estimate the hue of the specimen by interpolation between the chips of the nearest Munsell value and chroma in the selected hue charts.3 If the lighting equipment described in Practice D 1729 is not available. 6. 6. Ivl~n:s~l1 ~olbr . . ' . and Wyszecki.Br: {C/[(DY -.:.1" " '.2 If obtained from colorimetric data.OYR. than 10. j . $tanda~~.0. V=. /' I • .~ 2. V.28 of the waY.hi~ atpoullt is ad~ed to\t~eJphr011la forva. . ' .' • .simply use the hue and' chroma for the nearest level. . ~ : ~ . .the 'l1otation was obtained' visualiy..' '.1 value step.. The interpolatoo chroma is found'in'tlie same way. .. ..re. On'Flg:''l1. Calvert St. ~ ! .5.8 F= 0:42.o. For 9 Judd.. M. 1987. which a color notation can be determined by visual interpolation is 05 hue step. 'Use Figs~33: to 16 to estimate hue and chr(j)ma for~va1ue.' ~. U = 0. .e spepimen' to 8 rvrun~~n ~q19r. ~p~~tion bY'-!~9 of Table 1. 'or 7.1 Report the notation in the Munsell system. " "~.. Keywords . 0\' (1) In Table 1: 'y =. 11. .order system. B F....985 1) ~ .f cO..0. S.i colorimetric data.. " {[PI(QY)J~in [8(Y":: 'T)]} . r '. .: .Y. \ ' I ' .lor~ :M.1.500 andy = 0.:.:''Vvhich may be rounded to. p. =:=. so the hue and chroma will be found by inte~olathli:..: ".8 '.' . 8 " \ s.500 and y = Q.? ' ' .. ' ' ".2441 N. 13. 8.05 or less.7-"Gonve[t.2 In Table. M= 0. t > .39 . '1 1 and 13.' On Fig\' IJ~ the same xl al'ld 'y correspond to ia lluejust a/small" amount'redder. 4 .estimated precision within. ~.= {Ayl/3} • .0221 .'.' 16areenlal'gementsofthciI0\~Lchr(lInaare~sorFigs.from 7 to ~. ' • .ge is)r~ad:~s lO.6-13.Q == 0.following relatiortships: 10 illumi.:·1. D.: If the required value level differs'frofh theriearest' level by.!l Figures.4 chroma step.5. ' . an amount less than 0. .:56~'4. 'I j 1 i\. . 'Report .nant C.6.:. ' ..froin the .1 Th~. and I ' 9.. ." .0. .-alue. I I . ..84' JH. .'f'· (4) th~MunseI1 not~tion islO:0YR 7. . thoSer{r~lli~.·x.~ NOTl~.! ~ where: " A '.1073' E'~ 3.= 46. 9.! . of. th~ luminous ref1ectanc~.Piy~ston"ofKolhnorg~nlnstrumen~s. see I. ! _ . Precision \ } '. ". l.. .28 ~~mes.' et aC 6 For further informatiOl?-' concerning Figs. mterpol~ted hue IS t~at for~ :value 7 plus 0.•. 7.= 0.1 If obtained 'visually.-Given " . . 3 through rI6 are available from the Munsell Color Compan)'. G." Journal.. 10. .44 2.. " . 8. 10 McCamy. ~-ExarrlPle-.2/13. +{G/(yH)} + {Jsin(Kyl/3 -1-.. . i2.rporation. 'I.}~ 7.:.the dIfferypce. iI .'. The chroma iis14.". ': "" ~. 0 9.4( Table : L was. . ...·r .<Lo. Optical Societyoj America. and 0.is 0.nination (artificial or daylight). note the instrument used. _.5. ~ 8. "Extension of the Munsell RtlnotationSystem to Very Dark Colors.)" ". use the extension'6fthe Munsell system to very. "f .in Figs. value is less than 1. " . .. Apd.9. dark colors.'~ j .454 corresponds'tba hue of' 10.28. .' r : • ~. . 0.Jatio.. B. so the. .The-diffetence in chroma for the two value levels is 14. 3 to 16. : ".unsei1..1~:''lVpic\l. il?..084 f F = 7.: . (.. 10.O..).:=0. 7. Nirherof[4 ".. .. C. ~ o. I.. '.If the Muns~fr \ ~)]} 8.:: '.c~md 8.: 13.'0.. 1956. C. + {(M/Y)sinJN(Y. \ (2fthevalu((lies'be1\veen7. . ' ' .5.x . Large-scale diagrams of Figs. t!1e. Y. Jan?ary.. ".28. MD 21218.ns mage using tlle 1931 2° • ~: t 'I ! . ~ ~ '.- . + F]}. and 10. Vol~6. t .1'.: ' ..u === _.J the CI~ data. pbserver and i-.'I 7t l Pro(:edtt.( '.~J.' . N.ft1. I I. note: tHe soutte 'of ilhu.54( .0. 'Since't~e di(ferenc~ i was zero.' ~ === . 281. II. .levels·above'dnd below the valuefolllid· and linearly interpolate the:hues and' chromas for the desired value level.' .1.. ' ."030.02.'. derived.~ . ~ '. using the matte by'conversion of eIE or glos~y Munsell:Book of Colot. 'NOTE 2-Forfurther informatioh concerning Figs. y.iiiese qUailtitie~pet~een. .P 0·0037 . i O.2. 13" arid: ~i 5 see Newh~Ii.. /. private communication to ~~TM Co~mittee 'D~I. find lhe MlJl}sell notation.5 hue ~tep'i~Q theh.0133 . .·87445 W'= 0.0 YR.1sell notation ' '' '. specifying' whether. Munsell value 7. 3 to 7.I The difference is'multiplied· by th(( iJ1.1)) .5.3 ~. " ' . the interpolated hue is simply the hue foUnd for'value 7.2.calcu.". i · . .' . : ". MacbetV.. 'equivalent to.0 YR and a chro1i1a" of 13j.· X" .454.'. betweert the hues'found a:ttnose two value levels.."1. ":. Baltimore. l~dind the' . 14. . . andf~gs . chrQmatf8~ty coordin~irls.' I ~.~.u!' level 7: 0. ?:. x = 0." :.4...8.4929. 7.E)2.1 ::.terpolation factor: 1. Y = 46.3 Munsell Notation of Dark 'C610rS. (~) Th~ val~~.. t'. the luminous reflectance. .. and 15.9967 K:~ 4..· T === 0.+ lSA ::.02 corresponds ~9.S =).'~ : ~_ • . 72 1.39 3.26 0.41 3.83 1.87 1.36 0.85 1.94 2.50 0.59 1.58 0.02 2.70 1.29 2.32 1.79 0.08 1.49 1.06 1.22 1.72 1.08 0.09 2.10 1.15 3.52 1.68 1.56 0.86 1.16 2.33 0.94 1.93 0.01 3.58 1.23 3.90 2.53 0.87 2.73 1.20 3.99 1.70 2.14 0.44 1.02 0.20 1.86 1.93 0.89 0.16 1.10 1.02 0.50 1.04 2.80 1.53 1.70 1.85 0.67 1.84 1.45 1.91 1.50 0.99 2.26 1.56 2.68 1.71 0.82 1.95 1.52 0.13 2.41 1.32 1.04 0.51 1.16 0.67 1.37 1.07 0.12 3.98 1.15 2.41 0.05 1.55 1.62 0.27 3.48 1.32 0.10 1.44 2.45 1.61 2.08 1.76 1.37 3.24 2.32 3.69 2. 0.58 1.23 1.72 0 .10 3.01 0.33 1.19 0.18 3.11 2.00 2.95 2.58 0.09 0.18 2.43 1.06 2.76 2.12 1.62 1.69 1.07 2.66 1.14.66 1.36 2.48 3.92 1.59 2.20 0.65 0. 1.42 2.83 1.48.98 0.71 2.58 2.49 1.89 2.12 1.53 0.10 2.02 3.02 1.87 1.65 0.38 0.56 0.61 0.39 1.25 0.00 1.03 0.94 0.30 0.79 1.13 2.73 0.63 1.67 1.06 2.84 1.60 1.89 1.54 1.79 2.59 1.19 3.02 1.83 0.91 1.78 1.41 0.23 0.71 0.10 2.60 0.34 0.69 0.44 1.69 0. 1.88 1.61 0.48.36 1.74 2.11 0.40 2.19 2.10 0.00 1.77 0.08 1.05 1.17 2.16 2.30 1.51 2.18 1.18 0.94 1.25 2.17 0.68 1.96 1.90 1.21 1.12 1.90 1.03 1.58 1.52 0.30 1.83 1.71 1.87 0.15 1.40 0.60 0.24 1.80 1.67 0.81 2.97 1.17 .77 1.28 1. 2.05 2.30 2.16 1.82 2.13 2.63 0.22 2.34 1.30 0.28 0.76 0.16 2.90 1.49 3.32 1.17 1.16 3.13 0.81 0.06 2.79 0.85.31 1.42 0.01 1.60 0.59 1.09 0.33 2.63 2.96 1.09 1.10 0.68 0.22 3.03 2.26 2.74 1.81 1.17 0.75 0.04 0.29 0.08 0.64 0.73 0.41 2.97 0.89 2.20 1.55 1.18 0.12 0.87 1.47 1.54 0.92 1.13 3.75 2.70 0.29 1.37 0.78 2.48 0.50 1.07 1.36 1.72 1.91 0.71 1.29 0.98 l.30 1.39 0.88 1.97 0.48 2. 2.71 1.38 1.40 0.73 2.07 1.45 2.82 0.52 2.65 1.17 3.14 3.99 1.60 1.93 2.03 2.76 1.54 2.40 3.99 2.11 .00 3.06 0.21 0.09 1.54 1.63 1.49 2.65 2.43 0.98 2.53 1.11 2.07 3.78 0.29 1.73 1.24 0.50 1.39 1.74 1.77 2.35 0.04 1.63 0.66 0.97 1.33 1.05 1.77 1. 1.62 1.64 2.80 0.81 1.51 1.01 2.06 3.. Y 2.47 2.13 1.44 3.94 1.01 2.56 1.25 0.54 1.88 1.09 3.74 0.55 1.98 0.60 1.47 0.42 1.98 1.89 0.11 1.47 0.72 0.55 0.21 1.82 1.92 2.55 0.65 1.67 0.04 2.06 1.75 1.24 0.25 1. 1.19 1.83 0.02 2.77 0.90 0.04 3.31 3.48 0.32 0.~~~ 01535 TABLE 1 Munsell Value V for Given Luminous Reflectance Factor Y.69 1.15 2.35 0.62 2.08 3.81 1.27 0.13 1.08 2.03 2.78 1.94 0.60 2.31 0.46 1.46 0.72 2.36 0.49 1.92 0.37 2. 56 1.95 1.23 1.06 0.59 0.08 2.03 3.00 2.63 1.05 3.05 2.85 1.12 2.53 1.13 0.88 0.86 0.87 0.72 1.39 2.90 0.51 0.43 0.25 1.75 1.85 2.15 2.40 1.20 2.28 0.67 2.95 1.93 .21 0.27 1.91 0.70 1.21 3.27 1.15 1.46 0.12 2.73 0.24 1.55 2.05 0.69 1.05 2.05 0.46 0.22 0.57 5.97 1.33 3.32 0.66 2.50 1.93 1.11 2.53 0.28 2.01 2. 1.29 1.24 1.74 0.70 0.89 1.68 2.11 1.14 2.94 1.89 1.57 0.14 2.34 1.22 1.61 1.23 0.57 1.64 1.01 0.10.26 1.42 1.16 0.38 3.51 1.11 0.45 0.64 1.35 1.82 1.09 2.00 2.51 0.46 2.46 1.45 0.57 2. 0.19 0.03 0.52 1.38 2.27 0.57 0.29 3.45 3.14 2.04 2.25 0.62 1.17 2.47 1.04 1.75 0.85 0.25 1.18 1.34 2.96 0.65 1.44 1.14 1.80 0.96 2.94.27 1.26 3.97 2.47 3.43 2.34 3.49 0.01 1.07 2.31 0.68 0.34 0.62 0.86 0.81 0.91 2.47 1.96 1.84 2.38.99 1.37 1.43 1.64 0.35 1.81 0.35 1. in Percent.82 0.88 0.14 0.25 3.11 0.07 0.41 1.76 1.38 1..95 0.08 2.22 0.49 0.97 1.44 0.14 2.74 1.30 3.59 0.39 0.15 2.92 1.84 0.33 1.99 1.96 0.14 1.66 1.61 1.76 0.12 0.02 2.12 2.77 1.20 0.80 1.22 1. 3.57 1.75 1.31 2.99 3.15 0.78 0.05 2.50 2.35 3.39 1.03 1.97 0.07 2.83 2.19 1.08 2.03.64 1.17 1.00 1.54 0.31 1.44 0.82 1.92 0.95 0.78 1.39 0.26 0.84 0.21 2.40 1.42 1.73 1.24 3.37 0.86 1.92 1.42 0.42 3.09 2.35 2.66 0.20 1.36 3.93 1.11 2.80 V Y V 1.10 1.40 0.53 2.61 1.18 0.32 2.27 2.28 3.06 2.78 1.86 1.16 1.43 3.23 2.84 1. Relative to the Perfect Reflecting Diffuser y V Y V Y V 0. 1.46 3.38 0.15 0.79 1.43 1.86 2.04 0.33 0.03 1.79 0.90 0.36 1.45 1.67.28 1.56 1.86 0.88 2.91 1.79 1.18 1.13 2.01 2. 45 2.81 3'.55 2:55 2.52 6.72 2.06 5.90 5.77 5.39 2.72 2.24.41 4'~'31 4'. OontJrl'ued' 2.87 2..1.78 2.96 3.73 2:73' 2.19 2'.8q 5.62 2.33 2.20 2:.9~ ~ 7.04 3.29.52 4.04 Q.71 3.67 4.55' 5:56 5.62 6.86 2. 3.72 6.36 2.62 3:63 3:54 3.88: 3.~8 2.68 6.10: 3::10 3'.97 4.13 3.37 2.91 i.77" 4':78' 4.09 3.~2 6:~~.35 5.6' 5..11 3.01 3.93 2.34 6.95 2.75 6.70 2.47 2:48 2.64 2.84 2.56 4.68 2.64 2.22 5.10 4.09 6.30 2.56 2..76 2.06 ~·65~ 6.50 6.09 3.11 4.59 4.65 4.9 2 r8b: 2.O7 6.15 6.84 3.45 5.76' 6.03' 5.71 5.71 4~72 4.50 4:51 4.41 5..73 2.62 2:62 ~::63 5.79 3.57 6.60 6.36 4:37 4:38 4:39 4.43 2.35 2.91 5.20' " V 3.08 4.17 2.91 2.'84 V V 6.58 4.51 3.60' 2. 66.91 4.40 2.58' 2.0'6 3.71 2.3'6 5.73 6.81 4.28 6.84 2.64 5.94.69..05 3.83 2·M 2.96 2.22 2~23 2.61 2.30 2'.54' 2.13.79 5. 2.80' 3.00 3.~7 2.13 4:74 4.~3 4.48 6.08 3.~? 2.22 2.08 6.41 4.12 3.89 6~90 6.01 3.75 3:76 3:.85 2.54 2.74 5.95 2.94 2.08 3.96 2.13 2.04 3.19 2:eO 2.47 5'.87 2:88 2.97 6.b7 3.38 2.67 3:68 3.54 2.00.40 2.77 2.36 2.26 4.66 2.46 2A6 2:4"2:'47 2..16 5. 5.28 21.63 2.77.78 3.15 5.89 6.67 2J31 2:67 2.32 2.50 2.12 3.49 2.74 2.06 .53 4.39 5.96 2.66 2.97 3.89" 3. 3.56 2.95' 5.68 2.12 2.51 2.45 6.42 2.863.30 2.82 4.02 3.'99 5.58 : 2.90.\' y~ ~.54 5.05 4.81 2.55 2.57.69 2.35 4..14 6.03 4:04 .09 3.83 2'.7~ 5.68 5:69.72 2.9.99 4.84 4.04 3.08 3.06 3.44 2.13 ~ " 2.59 3.62: 4.44 2.23 4.20 5.35 2..56 3.47 6.34· 2.4 3.65 5.53 2.76 5.55 4.20 6.26 5.41 2.40 6:41 6.~9 2.59.18 5.50 5~5~ .69 4.01 5'.44 2.84 5.30 2..51 6.92 6.48 5A9 5.57 2~57 2.91.&Q 5.70 2:70 2.94 4.79' 4..00 6.19: 2.35 6.61 6.98 6.27 5:28' 2.86 3~85.00: 3.17 4:1'8 4.83' 3.12 6.21 5.05 3.80 5.0~ ~.21 6.70 4.37 5.76 2.66 2.12 3.j'B' f39 6.53 2.98 4.22 4.62 2.97 2.913:92: 3.94 2.63 4. 2.69 ~.75 2.91 6.0q.15~~' .09 4.02 3. 5.93 2.49 4.64 2:65 2. 3.75 2.69 2.96 4..58.82 2.56.B2 4.61 5.64 4.21' 2.00 3.53 2.8~' 6.34 4.46: 2.34 2.69 3.62 3.97 2.27 4.48 2A9 2:49 2.94' 5.02 4.44 4.22' 6.18.44 6.04 5.97 5~98i 5.~m~J-~ 0 '.60 3.46 5.~3 4~1'4 4.06 3.g6 6.10 3.55 6.90 ~.70 6.38 2.87 ' 2.99 6.88 5.81 2.85 5.10 6.11 5.18' 2 .19 5.07 6.75 4.58 6.23.53 6.90 2:90 2.95 4.71 6.40.92' 2.94 2.03 3.68 4.81 5.38 5.~9i 2.50 2.07 5:08 5. 2.75 5.74 2.55 3. 6.29 4.37 2:37 2..79 3.~p5 -' 3~11 6:86 6~87 6.49 6.76 2/6 2.70 5.42 4.45 2.83 2.13 6...3l 5.87 5.93 3.01 4.7~ 5.01 3.26 2.08 3.93 2.81 2.60 4.07 3.42 6043 2'.~5 2':66 2.77 2.7.02 6.<1-3 2..54 6. 3.63 3.81 6·.25: 6'.01 6.11 .80 2:Ao 2.70 2. 4:07 4.39 2.12(: 3 .03 3.33 2:33 2.30 2.00 3.~8 I 6.79 5.12 3.~3 2. 5.75 2. 6.03 6.67 6. 2.45 4.67 5.ge: 2.68 2. 2:24: 2:24' 2.00 4.51 2.5~ 2.94 6..58 3.10.09 5.~9" 4.47 4.35 2.M 2.86 2.12 5:13 5. 4. 5'.48 4.48 2.54 2'.ap' 6.95 3.33 6.52 2.61' 4.52 2.3~ 2.62 4.42 2.43 4.78 2.29 2. 6.73 3.14 ..98 2.78 q.25 2.05 3.18 6~~19 6.88' 2~89 2.'76 4.39 2. 2.99 3.92 2.26.70 3.33 5:34.14 5.74 3.40 5.92 2.03 3.92 5.56 2.37' 2.64 i85 2. 5.51 2.33 4.46 6.88 2.30 5.80 5:~9 5.57 3.85 4.21' 2.71 2.93 2.29 2-.05 3.61~ 2.25 2:26 2.64 3.78 2!7~ 2'. 3.56 2.2i 4.28 2. 3.26 2.24 2.31 2.11 5.02 5.25 2.77 6.1 3J1 3.66 4.59 6.40 4.24 5:25 5.13 3.81 2.'00 5.41 4.01 3.74 2.77 2.91 2:~\ 2. 3.. 6.'!33 2.22 2.42 5.05 5. 2.05~ 6:06 6.58~ 2.98 2.60 2.87 4:88 4.99 S'. 5.60 2.90 2.81 3.31' 2:31 2.27 2.44 2..02 3.23 5'.92 2.6'3 2~89 6.89 4.93 5. 5.29 6'..23 6.52 2:'1~ 6 5~63 5.94 2.65 2.10 3.45 2.60 2~61 2. 3.61 2.07 3.02 3.27 2.59' 2.99 2'.1.97.51 2.86 2.96 2:97 2.43 5'.36' 2·M 6':31- 2~\18 2':19.:59 2~'59 2.10 5.64 2.21 2. 2:97 2.95 6.82 3.92 2.24 4:25 4. 6~2( 6'.7r 2. y 1/ Y V y V 4.p9 3.83' 4..12 4.74 6.57 4.46 4.1'2 3.28 4'.58 2.82 5.87 2.86 4.84 6.98 3.9~' 6.f5 4.36 2.86 5.85 2:85 2.93 6.65 "PABtE l' .04 3.90 3.16 6:17 6.32 2:32 2.13.95' 2.43 2.54 4.32 5.11 6.66 6.\)5 2.61 3.48 2. 5.28 2.03 3.69 6.86 2.42 2.52 2.50 2.44 5.74' 2.80' 4.78.01 3.16 4.57 2.38 2. 63 3.50 3.67 3.62 8.36 7.77 8.53 8.31 7.16 7.38 7.54 3.45 9.70 V 3.33 3.16 3.97 9.72 3.31 9.14 9.88 8.13 9.47 3.64 3.74 8.24 3.74 7.58 3.19 7.27 3.37 3.73 3.35 3.82 8.74 3.70 8.52 3.57 3.18 3.55 3.16 3.24 7.24 10.65 7.52 9.87 8.55 3.27 7.43 3.90 9.73 3.49 3.25 9.22 3.33 7.78 8.23 3.56 3.68 9.16 3.20 3.14 8.63 7.78 3.78 3.40 3.07 7.57 3.67 3.15 3.06 8.27 3.04 8.53 3.53 3.45 3.22 3.54 3.51 7.28 8.31 3.79 3.41 3.62 3.92 7.95 8.19 3.69 7.70 3.45 3.94 7.66 3.25 3.13 10.61 3.34 7.45 3.72 3.48 3.47 10.46 3.66 3.77 7.42 3.64 9.28 3.59 7.59 3.72 9.77 3.30 3.40 V y V y V Y V 3.15 8.49 9.37 3.98 9.54 3.36 10.29 3.56 9.69 3.64 3.52 8.63 3.00 9.72 3.24 8.93 8.64 3.16 9.42 8.98 8.59 3.06 7.61 8.62 3.34 3.32 8.33 8.17 9.52 7.81 7.39 3.58 3.58 8.70 3.78 3.32 3.80 3.22 7.35 7.38 9.55 3.01 8.80 7.07 9.38 3.58 3.90 7.28 3.35 3.22 9.47 8.63 3.42 9.34 10.12 9.14 3.77 3.65 3.97 8.30 9.85 9.20 7.77 9.18 3.52 3.01 10.18 3.94 8.54 8.45 7.66 3.56 9.11 7.21 7.24 3.63 9.49 3.19 3.92 8.76 9.03 8.79 3.76 3.75 3.69 3.44 10.67 3.76 7.57 3.55 9.96 8.40 10.08 10.57 9.61 3.19 10.34 3.73 9.27 8.51 3.70 3.53 3.24 3.47 3.20 8.60 7.02 9.28 3.09 7.62 3.62 9.41 3.35 8.68 3.41 9.44 9.80 3.q~~ 01535 Continued TABLE 1 y 7.78 3.43 3.63 3.57 7.44 3.78 9.59 3.36 3.60 3.31 3.77 3.77 3.46 3.73 3.92 9.54 3.18 3.67 3.51 3.25 10.60 9.69 9.52 3.93 9.67 3.50 3.47 3.75 8.81 8.16 10.73 3.51 3.35 3.84 7.34 3.16 8.32 9.22 8.12 10.26 3.60 3.93 7.02 8.28· 3.15 3.35 10.48 10.29 10.71 9.71 3.59 3.96 9.35 3.01 7.31 8.80 3.75 3.04 10.40 3.08 7.74 9.56 3.11 8.23 8.59 8.25 7.75 3.80 3.89 9.22 3.60 3.76 8.40 3.39 3.22 3.89 8.27 3.87 9.01 9.61 7.41 3.48 7.77 3.45 3.51 8.86 8.53 3.41 3.56 8.55 8.78 7.12 8.68 7.19 8.70 3.54 7.34 3.46 8.75 7.55 7.96 7.60 3.61 3.79 3.41 3.56 3.91 8.28 3.14 10.87 7.76 3.36 3.20 3.47 7.38 3.03 9.50 3.18 8.37 3.47 3.79 8.15 9.76 3.34 9.41 8.44 3.27 10.91 7.26 3.06 10.20 3.39 8.29 3.59 3.25 3.34 3.39 3.17 7.07 8.35 3.63 3.70 9.33 3.65 3.58 8.56 3.43 7.68 3.05 8.97 7.48 3.98 7.83 8.09 10.30 3.66 8.72 8.54 9.64 7.37 3.31 3.38 3.95 9.72 3.30 7.30 3.42 7. 9.49 3.62 3.00 10.51 3.29 y 7.51 3.10 8.74 3.80 3.38 10.64 3.17 3.80 3.68 3.67 3.54 3.23 10.37 8.74 3.50 3.68 8.76 3.55 3.26 9.36 3.48 3.50 3.42 3.51 9.40 9.60 8.85 8.11 10.52 3.08 9.63 8.43 3.38 3.73 7.12 7.67 ·7.18 9.30 8.23 3.27 9.31 10.23 3.49 10.69 3.79 7.35 9.57 3.23 3.73 3.65 3.05 7.81 7 .57 8.44 3.71 3.65 3.61 9.66 7.71 3.88 9.14 3.24 3.88 7.49 3.38 8.11 9.65 3.38 3.49 3.90 8.29 7.86 7.08 8.29 9.41 10.84 8.65 8.27 3.51 3.66 9.25 3.41 7.15 7.95 7.61 3.62 7.67 9.17 10.42 10.32 3.24 9.80 8.31 3.78 3.46 10.17 3.65 3.56 7.50 7.76 3.25 3.58 3.26 10.62 3.16 3.33 9.21 3.74 3.14 3.07 10.66 3.26 3.46 3.19 3.05.02 7.99 9.72 3.28 9.75 3.15 3.46 7.04 7.21 3.73 8.94 9.74 3.06 9.39 3.37 10.40 7.10 10.39 3.57 3.45 8.68 3.79 3.10 3.69 9.50 9.64 3.30 3.75 9.66 3.72 3.30 3.18 3.29 3.48 9.45 3.36 8.17 8.68 3.61 3.33 3.48 3.73 3.43 8.55 3.64 3.21 10.53 9.82 9.52 3.19 9.91 9.60 3.02 10.70 3.79 3.77 3.37 9.21 3.49 8.58 7.28 7.22 10.21 3.59 3.58 3.29 8.15 10.13 ·8.74 3.28 10.45 10.44 3.39 7.47 9.82 7.19 3.43 3.36 3.17 3.25 3.09 9.78 3.33 10.34 8.36 9.18 7.54 3.68 3.19 3.62 3.79 3.43 8.13 7.44 3.22 3.32 10.75 3.32 3.26 3.25 8.21 3.30 10.41 3.04 9.33 3.72 7.44 7.42 3.36 3.31 3.67 8.70 3.37 3.20 3.46 3.18 10.81 9.21 9.65 9.43 9.60 3.46 9.26 8.48 3.15 3.24 3.99 10.43 10.37 7.99 8.00 8.20 10.14 7.49 7.17 3.83 7.10 7.23 9.71 3.48 3.23 7.16 3.40 3.26 3.42 3.05 10.56 3.32 3.76 3.44 8.21 8.71 3.42 3.09 8.20 9.83 9.89 7.71 3.03 7.79 9.53 7.71 7.40 3.29 3.47 3.59 9.48 8.69 3.46 3.64 8.71 8.69 8.26 7.84 9.50 3.39 9.50 8.80 3.32 7.39 10.85 7.53 3.32 3.86 9.03 10. J~ 11:0.6 4. 4.99: 3.. 10. 4. 13~68 4. 3. 4.84.51 13.6 13.3 4.90.22 4J~2 4.21 4.0..13 4.17 4)17 4'.3'1 12.39 ~ t1~91 4~.28 4.94 3.89 11.28 4.7 13.0.91 13:92 13~93 13.03 4.3.4.95 3.30.10..66 11..11 4..26 12. 4. 13:21 13122 13.34 12...27 12'.08 12~o.815 3.92 3 . v v w v y 4.46 11.0.' 4..2412.95 11.25 4. 4:22 4.0.7 4.E.6 4'.82 13..0.96 3.0. 13.43 12. 13.. 3.7 4. .26 4.22 11. 3. 11.0.5 4.) 4.32 4:32 4..21 4.92 3.Q. 4.'17 4.5 4.29.0.25 1·2.~m~.10.78 11..29 12.4 11.33.32 4.0.21 4.5 12.97 3.53 1t5:4 1t.7 4.74 lQ.52 13J53 13:54 13. 4.23 13.1.O5' 4.96 3.0.89.80.42 13f43 13!44 13.1~ 1.68 12.18 4..0.B9' 11.27 4.0..3 4.60.2fi' 13A7 13. 4.7g 10.5 3. 4.26 4.0 12'.83 10.5 4:0. 11~p1 3.0.98 3.7.78 13..15 13:31 13.0.39 12.31 4...6.0. 4. l1.20.813 11 :0.5§ 10.0.2' 4.20.23 12.97' 3.:54 lo.95 10.20.21 4. 4.J.(!l6.61 1o.13 4:13 4.93' 3J)4' 3.31 4.45 13. 11.1'. 4.6' 4...615 11. 3.3 4.41 13.42 1.5~ H.57 12.25 4'.0.Q:1 lL5? 11..28 l.46 12.96 3.:93 111.~9 4..10.1:' 4.16 4. 4.2 12.98: 3.69 11.99. 3.30.71 11.9 13.70 18:71 13.33' 4.8~: 1o.8~ 3..0S 1:2.0.20.36 12.14.81 11.11 4.67 12.87 12. 12:51 12.86: 3.93 3.0.19' 13~66 4.92: 1~. 1t.95 3.. 1o. H:Q8 11.18 12.1:.31 4.98 3.. 10. 3:86 3..6 1.23' 4~24 4:24: 4:24 4)24 13.16 11.0.49 12. Continued W·52 1. 12.0.3 1'1.18 4:18 4.40.94 3.79 12:80.13 4. 12:911 12.80.91.9ji: . 3~97 3.69 13.84 8.7 4.50.21 11..38 12.88t 3:68.0.37 1~138 l'3:4b 4~25 4~19.87 1Qi86 10.21: 4.71 12:72 12.84 11.18 4..19' 4.26 4.0.815 3.93 3..19 4.72 13.7 3Iar...06 4..'21 1.23 4.95 12/. 4.go..~9 3.15 4.62 11.0.20.2.84 3.89.53 12..93 3.92 10. 11 11-.13 4.35 12·.82 12..: 3.0..38 3·~7.70.33.6~ 10. 1.0.~3' 4. 4.3.63 11.95' 3.18 13.o.149 11.06 4..79 11. ~..713 11.77 11.12: 4.t'1 y.0.21 4. 4:30.92 12.7 1.60.57 13..70.~n.14' 4.4 1.32 4.2:22 12.7~. 13':0.4 13.0.2.0.0.17 12::78 1-2.29: 4.95: 3..27 4. 3.99 11..\ 4.1.89 1-2.0.3.67 10.7 4.21 4.91.23 4.93 3..73 12.29 4.9 4..:33 11.82 3.82 3. 3·90..96 3 .11 12:12 12.0.8.83 12:84 12..92 3. 4:~2" 4\12' 4.29 4.0. 19·91 10..88 11.17 12.97 3.44 11.16 4.95 3.30.0.0p.24' 13~33 4::24 13.1 12.27 4.4 4.8 1o.27 1'1 .9 4.4 4.27 4:274.90.82 3.65 12.0.88 12.8 4.48 12..8.3.:'17 4.0.0.92 11.46 11.86 3:86 10.90.0.30 4:30.6 t2~.92 3.'08 4.29 11.84..89. 1~ .1'4 1-21>16 12.1 3'. .16' 4'.66 12.' 4.55 13.03' 4.5 13.2 4.82 11.841' ~.11.26 11.2 4.7 4.28 12. 4.93 12.4 4.. 410.98 11.56 19·57 10.2 4.83 13:84 13:85 13:86 13:87 13:88 13:89 13.09: 4.0.17.44 12.81 3. 10. 4.96 3.28 4.75 11.74 12..~2 12.97 1.:34 11:35 3.45 12.6? 10. 4:20.69 12'.4 4.9 12\1.~2 10.O3 1~.27 4.20.10. 3.3.10.'08: 4.0.16 4.90.0.0.15 4'.1 13.21 4.90.17 4:'18 4.54 12.~82 B.12 13113 13:14 13:15 131'16 18.9 4.58 13.13 12. 12.10.14 11-:15 H..14 4.68 11.0.0. 4~'O9'.32 4..8a:' 3.0. 4'.0.' 11. 98~ 3.31 4-:31\ 4.19 13.8 13'. 11.f?5 10.91 3.0. 11:0.97 4.84i ~...1' 4·01' 4.a7 a·B7 l1A1 11. 13:61 13:62 13~74 13. 4.77 19·78 1o.86 3:86.. 12.64 13.17 13.0.1 4..1. ~.26 4.86 12.0.33~ 4:33 4.14' 4'..83 3.3: 4.61 1'2:62 12.66 10.0. 4:30.14 12mB 12:99 13.0. 11.14 4·:15' 4.2.0.91 3.94 3.0.12 11.25 11":.55 12.~8i ~.83 11.67 11. 4:30.91.81 1J.:86 10.94 13:95 13:96 13:97 13.:.72 11. 4..5' 4.98 13~99 14:0.34 4:34 .65 4.0.48 mf49 13..0.8 4'\0..27 13128 13.33. 4.75 13:76 13:77 13. 1~.20: 13~67 4'.31 4..23 11::24 11.8 4.24 4.0. 4.31 .33 4.. .22· 4~22- 4l22\ 4.}9 10.63 10.90.50.30.89 10.03 4.39 11'·foQ 11. .99 4.24 13.25 13.60.2 3.84 1Q.9. 4.17 4.87. 4.82 3.!> 1~ .:81 1o.25 4.0. 4.56 12.90.26 13.56 11:57.75 11.10.128 4.·11 4.59 13~6o.10.0.0. 11.4.92 3.28 4.125 4':15 4:15 4. 4.0.0.79 13..83 3·e3 3.3 12.86 3.68 12.19 4.16 4.~5 ~.-16 4'.3 13:0. 1o.10..94 12..3:2 101.76 10.96 3. 3.:1.26 4.413 4~.29 13.0.7'5 1'2:76 12.74 11.73 4.85' 3.26 4..18 4:18· 1.70. 4.0.87 3:a? 3.26 4.42 12.9~ 10.0.94 lit.\98 3.22.95 3.0.0.95 3.63 12:'64 12.43 1:1. 4.19 11.85 12·.2 13..9.59 11. D:15~5~ y V y v {(j:51 \3:.34.83 3'.28 4:28 4.89' ~. 3.90.11 4.52 12.98 3.8g.14 4.1 3.99 3.64 1o.68 13..97 3.16 4.83 3. 13~35 13.7 11.19 13.23 4:2$ 4:23: 4. 13~81 13.32 4:32.:13 11 .31 3. 1~.93 3.90.85 11.37 12.34 4:\25 4.59 10.:93 10.11 4. 4.94 3.1 12.96 3. 12.47 HAS 11. 4:30.31' 4.1 3.6.0. 83 3.94 3.36 13.8 11.1 4.'96 12.0.2.o..0.9:1" 3. 4.99 ~.16 12.99 1-2.47 12..0. 3.56 13.99~ 3.85 3..6 11 :.0.5 4.32 4.129 13.q9 l1i~.p3 10.:94 10.9.o.4 4.0.'08 4.89.75 19.81 12.:12.33 12..11 13. 11.3.85 3.56 10..a.0.80.20. 4.19 12(20. 12.44.':19 4.2 4. 4:12) 4:12 4.50..69 12.96 TABL. 13.12.97:' 3.32 4.15 4.72 lo.1. 79 16.40 17.66 4.99 16.49 4.56 15.32 16.77 4.30 15.99 15.59 16.05 i6.78 4.01 15.60 4.67 15.91 14.37 4.30 14.98 14.20 15.62 4.68 4.54 14.60 4.23 15.60 4.15 16.52 14.57 4.66 4.05 14.45 4.64 15.74 4.36 4.38 17.65 4.77 4.86 16.65 4.51 4.77 4.44 4.47 4.95 14.46 4.43 4.20 14.80 V Y V 4.60 15.39 4.00 17.49 15.56 14.42 17.35 4.13 17.68 4.65 4.69 4.73 15.63 16.40 14.92 15.55 4.72 16.39 4.50 .15 14.67 4.41 4.85 15.72 4.39 4.59 4:59 4.46 4.65 4.43 15.12 16.74 4.22 14.79 4.40 4.44 17.46 16.72 4.44 4.49 16.22 15.05 17.75 14.29 .50 4.68 4.93 14.26 15.57 4.51 4.73 4.74 4.59 15.52 4.56 4.65 4.46 17.72 4.55 4.36 4.39 4.69 4.07 14.62 4. 4.56 4.43 4.10 4.38 4.68 4.69 4.79 4.15 15.69 4.67 4.53 4.41 14.38 16.57 15.74 4.80 15.63 4.74 15.50 4.66 4.34 4.36 14.92 16.36 4.41 4.72 14.88 16.52 15.24 14.46 15.62 4.11 16.74 16.13 15.68 4.41 4.48 4.79 4.38.67 4.58 4.51 4.44 15.09 16.81 14.65 14.71 4.73 14.97 16.48 4.40 4.34 15.69 4.13 14.50 4.26 14.73 4.79 16.41 16.87 16.49 4.76 4.54 4.83 15.41 15.54 4.41 4.55 14.74 4.58 4.46 4.71 16.09 15.51 4.45 17.12 15.48 16.47 4.63 4.79 14.33 17.70 4.71 15.53 4.50 14.44 16.54 4.07 17.43 16.76 4.04 17.36 4.43 14.19 15.44 4.14 17.40 4.42 4.48 4.49 4.32 17.75 4.06 15.55 16.11 15.57 4.37 4.05 15.39 16.00 16.34 16.36 4.45 4.70 4.60 4.79 15.23 14.62 14.49 14.48 4.24 16.71 14.61 4.60 16.64 14.54 4.46 4.77 4.35 4.60 14.47 4.08 14.45 4.53 15.49 4.75 4.45 15.43 .61 15.09 14.85 14.27 16.70 4.36 16.36 4.03 15.71 4. 4.93 15.22 17.56 4.38 4.59 4.50 16.48 4.86 14.75 15.76 16.47 15.76 4.1(1 14.22 16.34 14.64 4.95 16.67 4.10 15.69 15.45 4.16 16.17 14.42 14.13 16.50 4.68 4.69 4.75 4.42 15.64 4.61 4.62 4.64 4.43 Y V Y V 14.64 16.48 4.17 17.34 17.40 4.56 4.41 4.53 4.18 17.79 4.83 16.51 16.52 4.59 4.45 4.30 17.31 16.77 4.47 4.66 16.77 15.50 4.76 4.74 4.54 4.71 4.69 4.60 4.68 4.73 4.51 4.69 4.78 4.35 14.35 16.38 15.53 15.42 4.68 16.96 16.03 17.04 16.28 14.51 15.04 15.60 4.58 4.02 14.18 16.40 16.79 4.84 16.21 14.78 4.40 4.56 4.75 4.73 4.29 15.71 4.59 4.35 4.61 16.56 16.86 15.55 4.53 4.58 4.59 4.43 4.70 4.36 4.67 16.03 14.63 4.63 4.51 4.63 4.10 17.73 4.45 14.60 4.35 4.27 14.53 4.42 4.52 16.75 4.84 15.78 4.76 4.46 4.80 14.52 4.41 17.43 4.02 15.45 16.61 4.53 14.42 4.72 15.30 16.69 16.75 4.37 16.71 16.47 4.51 14.78 4.77 4.67 4.45 4.37 4.40 4.83 14.65 4.11 17.39 4.78 4.74 14.46 14.74 4.66 4.66 4.40 4.61 4.97 15.70 16.53 16.53 4.90 15.78 16.\ 16.44 4.76 14.89 15.18 15.33 15.04 14.50 4.38 4.82 14.36 17.25 16.14 16.39 4.75 4.62 4.58 16.58 4.47 4.42 4.61 4.37 4.81 16.72 4.42 16.46 4.25 17.63 15.64 4.12 17.26 16.98 15.55 15.57 4.14 14.61 4.38 4.07 16.23 16.16 15.59 14.57 4.82 16.61 4.44 4.63 4.70 V 4.24 17.57 14.11 14.38 4.00 15.67 4.72 4.79 4.71 4.08 15.37 4.19 16.37 4.44 14.37 14.31 17.26 17.28 <\ 16.47 4.57 16.24 15.48 4.09 17.28 17.44 4.48 14.76 4.54 4.37 4.34 4.46 4.17 15.39 4.38 14.70 15.63 4.02 17.58 14.84 14.54 4.19 14.50 4.58 4.32 15.55 4.41 4.77 4.27 15.40 4.62 4.73 4.52 4.18 14.41 4.43 17.70 4.51 4.57 4.66 4.39 15.65 4.49 4.35 4.61 14.21 17.42 " 4.53 4.01 16.73 4.90 16.62 Y 16.77 4.71 4.31 15.52 4.59 4.20 17.77 14.47 17.25 15.90 14.60 4.57 4.44 4.35 17.35 4.77 16.64 4.17 16.41 4.59 4.07 15.68 15.27 17.~t D 1535 TABLE 1 Continued y 14.37 4.56 4.39 14.78 15.28 15.47 16.58 15.65 4.91 15.50 4.43 4.75 16.85 16.21 16.75 4.57 4.08 16.72 4.68 14.74 4.87 15.76 4.76 4.48 15.55 4.67 4.76 15.95 15.68 4.54 4.52 4.71 4.34 4.73 4.03 16.82 15.34 4.87 14.99 17.12 14.91 16.39 17.06 17.78 14.73 16.52 4.94 15.31 14.36 15.01 17.61' 4.89 16.06 16.55 4.35 4.66 15.37 15.78 4.33 16.96 14.47 14.62 15.64 4.62 16.98 16.96 15.08 17.58 4.88 15.01 14.49 17.35 15.15 17.20 16.89 14.16 17.56 4.25 14.67 14.65 15.38 4.65' 16.43 4.42 4.70 4.63 14.49 4.79 4.54 15.64 4.37 17.66 4.23 17.93 4.50 15.02 16.72 4.~4 16.94 14.69 14.67 4.19 17.14 15.72 4.29 14.10 14.33 14.46 4.32 14.49 4.48 4.54 16.64 4.92 14.51 4.45 4.55 4.81 15.56 4.70 4.62 4.70 4.29 17.88 14.06 14.78 4.66 4.21 15.48 17.66 14.97 14. 41 19.86 19.01 5.10 5:10: 5>10" 5:10l 5.18 .17 19.91 .32 18.7:l 20.55 18.132 20.94.14 5'.64 17.33 19.73 18. 4.45 18.89~ 4.14 5':15 I 5'.86 .:93 19.03 5'.14 20.94 19.16 5.88.01 5.09 20.' 4.83 4.89 4.97 4.89 20.82 19:83 19. 4.08 19.15· 5.65 17.97 17.09 18i 10 18:1.95 4. 5.00 5.68 19.08' 5:081' c 5.80 4.67 20.01 5.43 19044 19'.00 5.1 1(1:82 1(..96 18:97 18.91· 4.9.04 5.09 5.17' 5.02 5.94 4.43 18.66 17.15 .93 .8. 4.17 5.81 20. 17. 4.85 4.94' 4.12'" 5:12: 5:12.03 19.98 17.56 19.6 4:96.52 18.84 4.' 4.83 ' 4. 4.77.08 S'!08 20~OO 5'.60 18.53 18.05 5:05 5.84 19'J85 19.80 4.' 4.03 ' 5.02 5.92 4.8~ 17.95 18. 4.58 17.04 20.05 19.19 .99 4:99 4[99. 4.'12 .05" 5. 4.84 20.12' 20~94 20.07 5.·1'· ObritiilUea y v! y '17.99 4.82. .32 20:33 20.01. 18:.10 5.04: 5!12 i 4~97 19~65 4.171&.18 20. 18:01.66 18.06 5106 S~06 .09 19. ~ 4.'19 19.82" 4.91 4.01 . 5:19 .94 4.56 16.(35 20.86 18187 18.:~9 18.lQ 17:.69 18.'14 5:14 ' 5.15 5.60 4:96. 4.02· 20.aQ.1331 4~8.38 18.03 5.13 5.02 .1.07 5'[07' 5. 4.07' 5.62' 20.10 20.81..89 4!89 4.0· 18.76. 93. 5.85 . 4.53· 19.98.11 " 5.41 16.82 .7720.85: 4.137.46 18.93 4.51 20!52 20..97 19.13 5.51 18.:1.(30 20.05 5:05' 5.' 5:04· 5.73 19.64 18.81.98 4. 4.69 17:70 17.8~· 18.·94 4.16 5.99" 4.05' 5.00' 5.88 4.{15.83' 4.95' 19'. 4:79' 4. 18.02.99' 4.3119." 4.10 5.19 19.'06 20.71 17.85 4.09· 5. 4.15' I 5.97 4.9p 17.72.17 20. 18.02' 5.95~i 4.79 20.63 20.34 19.39 18.B7.86. 5.03.75 20:16 20.96 19.23 20.19 18.. 4.91 4.95 20:96· 20. 4.88: 4.21 20.4720.18 5{18 5118 : 5:1-8" 5:~9' 5.86 4:86' 4.99 4.22 19..8p..55 19.28 20.88.90: 4:90 4:90 4.5? 20. 4.18 5..75 17.' 4.92 19.29 20.:83 17.49 18:50 18.81 4.03 5.99 4.97 20:98' 20:99' 21:Q(j" --.00 5.10:~ 20~a7' 5J1\~ 20.83 18.09' 5.22 16.68 17. 5.15 5 .66 19.Q3 18~Q4 18.88:- 18.37 19.11 ' 5.1.03 20.27 20.85" 20:86' 5.86 : 4.24 18.6· 19047 19.90 4.98 18:99 19.17 ' 5.47 18.1' 5\·1:1 5:H" 5.02 5~02 .98 19.03 5.14: 5.7. 4·85'· 4.86.73.91 20.40 18.894.13 5.01 20.72 17.92 4.1 4.133.7.04): 5:041 5.96 4.99 5.87 .90 4.41 4. 5.18 19.77 19:78 19.\85 18.29 18.21 18.54 18.94 4.20 4f~Q 4.77 18.'87· 19.~(j) 17.13 1 5.07 .14 ' 5.84.94. 4 .'99 20:31 20.91 .05 20.B4 4\13.1.@8· 5.11 20. 17. 17.89' 4.93.58 18. 5.97 19.5" 4~96 4.82· 18.94 18.92· 4.84.13' 5.11 19:12 19.87' 4.0719.62 19:63 19:64 5. 5.86.5.05' 5.31 16.96 19.80. 4.48 18.95.91 18.34 20.15 ~ 5~16 5.84 4.29 19.57 19:58 19::59 19.80' 18.88 4.17' 5.08t 5.42 19.59 17.95 t 4.74 18:75 18. 4. 5.14 19.65 18.q!ji 1V~6 17.4 4.82 .07 5:08 5.2 t 5:12' 51.11 5. 'h83 4.lS 5.78 17..40 19.'14 5. 4.88 .90 20.80' 4(80.27 18.00 19.92· 4.24 20-.94.74 19. 5'.02 18.10 19.19' 5:19' .90 4.59 2(i'.5 17.49 20!50 20.39 19.23 16.85.92 4.74 17.1.15 18.01 5. 4.93 4'.33 16.57 17. 5.90 4. 5.:92 4'. 17.82 .9l 17'.81" 4.00.00 5.81 4.4 4'.22 20.-50 19..03 5.93 4.66 20'.15 19.61 20.18' 5.95 4.19 20.88 4.35 18.86: 4..38 19.04·~ 10' 5~04" 5:04.28 19.'36 20.05 5.58 20.97~ 4.57 16.19 5.92 4.04 19.80 20'.82.69 19.83' 4.87 ' 4.16 5.68 20:69' 20:'70 2(j~V1 20:j~' 20.79 17. 18. 4. 4.07· 5.3.14· 5.98 4:98 4.25 20:26 20.34 18.4320:44 20.26 1a. 4.30 18.9j 4.01 5.83' 20.03 5.03 5.91 19.08 20.09 §~09·· 5.67 18'.13 19.9.18 1). y v· y v y v:· 18.' 4.07 20.01 5.23 19. 5.91 4 .53 20.61 18.89 19:90 19.24 19.74 20.78 18.88 19.981' 4.35· 19.20 19:2119.61 19.93.30 19.92 20:93· 5:11' i 5:11: 5.81 4.19 . 5:06: SiOSi 5:06 1 5:06' 5~06 ' 5..48 19.19 .62 18. 5.81. 4.36 17:5~ 17.98 4.8::: 4.95: 4. 4i96 4.6 19.16 19.e7 17. 4.93 18. 5~:16 5:~6 5:16 5. 92 4..30 5.01 5.51.49 19.00 .18· 18.00 5.16.00 5. 20~42 20.09 5.28 1a.11: 5.35 20.42. 93 4.89 4.~7 18.88 18.82 : 4.88 .91 4. 4.76 17. 83 4.O~ 18\06· 18:07 18:08 18.75 19:76 19.61 17.i 4:87 4.98 4.96.54 19.: 4JHi.79 18\80 18.51 19.16 20.- 5!~1. 18.62 17:63 17.83 .97 4.84 4. 4.37' 20:38 20i39 20:40 20.17 5~'17 5.67 19.87 .19 5.97 4. 4.88 20.09 5.02 . 4.98' 4.20 20.93.48' 20. 4.02 19.01 19.09' 20. 4.lf1 5.59 18. 18.45 19:4.:11 5.25 19:26 19:27 19.04.89 4.25 18.91 4.84 17.12' 5.95.-18 5.54 20'i55 20!56 20.89 4.64 20.96 4:9.83':' 4. 1R12 18. 4.15 E):15 ' 5.5$.45 20)46 20.92 17.09 5.68 18.51 17.18 ' 15.80 17. 5:13' 5':13 5:13 5.52 19.05: 5.01 5:07 5. 5.13 20.63 18..Q8'~ 5'.15 20.:' 4.D1!53~S TABLB.70 19:71 19:72 19.86 4. 5.32· 19.9~ 17:94 17.87 ' 4.12 20.'18 20.90 4.97: 4. 5:02 5.13 18:14 18.44 18.80 19:81 19.l0'· 5\'10:. 18.16 5\[16 .92 18.p8' 5.67 17.~t~ .06 19.89 18:90· V 4.95 17).17· 5.8~ 17.98' 4.14 5. 47 5.25 5.94 21.9 28.75 5.2 24.50 5.39 5.03 21.38 5.12 23.0 24.45 5.85 23.47 5.43 5.80 5.37 5.02 23.39 5.27 23.39 23.86 21.52 22.22 5.21 5.09 22.84 5.40 5.35 5.43 5.33 23.20 5.41 22.34 23.26 5.28 5.7 .47 22.48 21.49 21.72 21.34 5.96 5.35 5.41 5.57 22.70 23.44 23.13 23.00 23.53 23.29.87 5.66 23.46 23.03 23.53 5.19 23.27 5.06 22.65 21.4 26.36 5.46 5.81 23.37 5.1 27.33 22.32 23.43 5.31 5.55 5.23 5.77 5.77 23.38 5.7 28.36 5.43 23.41 5.51 23.88 23.40 5.27 5.15 21.31 5.74 23.27 22.42 5.65 5.60 5.22 5.87 22.26 21.24 23.8 27.1 25.6 \ 27.72 23.42 5.89 23.33 5.37 5.83 5.48 5.37 5.36 5.59 21.50 22.81 21.9 25.04 23.5 27.33 21.01 22.36 5.48 5.85 22.14 22.96 23.34 22.93 21.63 21.38 5.69 22.40 5.22 22.67 5.28 21.35 5.44 5.25 21.47 5.6 25.64 5.13 21. 25.10 5.13 22.48 5.42 5.49 5.4 27.34.9 29.51 21.28 5.23 5.21 5.56 21.79 23.16 23.7 25.35 5.8 24.5 26.41 ' 5.18 21.30 21.41 21.31 21.95 23.74 21.59 5.44 5.97 n .77 22.33 5.30 23.31 5.38 21.93 22.58 5.34 5.39 22.65 23.49 5.47 23.45 23.52 21.45 5.26 5.3 24.40 21.21 21.14 23.47 ' 5.39 5.21 5.49 5.61 23.27 5.26 5.97 22.79 22.56 22.36 5.24 5.35 23.87 23.1 26.12 22.44 21.24 22.23 5.31 5.39 5.25 5.70 22.33 5.8 28.4 24.04 22.12 21.63 23.42 22.44 5.85 5.15 22.76 21.50 5.78 22.92 5.03 22.47 5.5 25.45 5.46 5.24 5.92 23.21 5.29 5.62 23.05 21.6 28.48 5.55 21.35 21.01 23.28 22.59 22.66 21.58 22.27 5.70 5.21 22.6 24.90 5.20 5.44 5.38 5.44 5.02 21.54 22.32 5.21 5.88 21.48 5.47 21.66 22.23 5.91 23.36 5.27 Y 21.0 28.39 5.3 28.30 5. 5.34 5.71 21.3 26.5 28.25 5.06 21.48 5.38 5.83 23.87 5.41 5.72 22.20 21.17 21.39 5.52 5.31 22.26 5.17 22.30 5.27 5.37 5.31 5.87 21.27 5.71 5.37 21.51 22.29 5.43 5.89 5.47' 5.91 21.33 5.30 5.29 22.36 5.90 21.80 22.50 5.4 .45 5.48· 5.57 21.45 22.44 5.43 5.28 5.85 21.76 5.2 26.11 23.81 22.50 23.32 22.42 23.39 5.50 5.31 5.49 22.29 5.75 21.2 28.2 25.20 5.5 24.47 5.32 5.20 5.19 21.67 23.88 5.40 5.25 5.6 26.4 28.15 23.37 5.21 5.44 5.0 27.35 5.48 5.28 5.96 5.44 5.92 21.40 23.45 21.34.40 5.27 5.qm~ 01535 Continued TABLE 1 y 21.37 23. 5.36 5.36 5.86 22.91 22.37 22.25 5.27 21.29 5.42 5.50 5.95 22.23 21.20 5.32 5.29 5.49 5.53 21.82 21.64 22.30 5.28 5.64 21.35 5..34 5.42 23.20 5.50 5.42 21.83 21.73 22.43 21.99 22.24 5.40 5.95 21.78 23.30 5.38 5.36 23.22 5.34 5.36 5.20 5.42 5.31 5.30 5.79 21.43 22.50 5.05 22.10 22.8 25.34 22.33 5.45 5.38 5.49 5.41 5.68 23.28 5.43 5.78 5.02 22.34 21.43 5.78 21.98 23.9 27.81 5.26 23.32 5.8 26.90 23.62 21.22 5.94 5.37 5.21 5.58 21.28 23.33 5.61 22.55 23.24 5.49 5.34 5.41 5.68 22.45 5.92 22.32 21.23 5.86 5.33 5.22 23.26 5.35 5.21 5.73 5.26 5.69 21.9 26.22 5.0 25.39 21.44 22.09 21.56 5.27 5.21 23.50 21.18 22.79 5.37 5.46 21.54 5.46 5.05 23.26 5.48 23.49 5. 5.25 22.47 5.24 5.46 5.31 5.46 5.20 22.77 21.40 5.24 5.06 23.33 5.49 5.74 22.14 21.43 5.31 5.84 21.60 22.82 22.23 22.30 5.63 5.30 22.29 23.94 22.36 21.44 5.08 22.45 5.76 22.83 22.39 5.69 23.84 22.3 25.62 5.70 V 5.76 23.47 5.31 5.68 5.24 5.72 5.25 5.35 22.7 26.52 23.89 21.10 21.35 5.39 5.07 23.11 22.30 5.00 22.23 23.59 23.49 23.45 5.42 5.75 5.98 21.50 5.08 21.46 5.26 ' 5.47 5.66 5.73 23.99 24.32 5.35 5.1 28.48 22.57 5.26 22.3& 5.0 5.19 22.62 22.61 5.73 21.07 22.23 5.38 23.16 22.64 23.28 5.41 5.29 5.25 23.31 23.22 5.28 5.46 5.21 5.99 23.46 5.93 23.08 23.25 5.53 22.49 5.29 21.89 22.80 5.39 5.38' 5.67 21.58 23.80 21.25 5.48 5.71 22.0 26.38 22.16 21.42 5.84 23.82 5.67 22.54 21.65 22.23 5.55 22.20 5.24 21.71 23.40 5.42 5.91 5.28 5.48 5.32 5.09' 23.3 27.49 23.41 5.25 5.55 5.46 5.11 21.22 5.21 5.24 5.98 22.94 23.43 5.95 5.40 V Y V Y V Y V 5.40 5.46 5.17 23.88 22.38 5.50 5.23 5.51 5.43 5.29 5.32 5.18 23.36 22.69 5.40 5.01 21.97 23.22 5.41 23.50 5.60 23.20 5.30 5. 27.33 5.75 23.96 22.74 5.93 5.24 5.97 21.46 22.57 23.41 5.44 5.29 5.90 22.86 23.96 21.75 22.56 23.20 23.26 5.33 5.45 5.07 21.22 5.22 21.24 ' 5.7 24.60 21.29 5.37 5.32 5.54 23.63 22.45 5.04 21.82 23.23 5.2 27.42 5.61 21.1 24.68 21.32 5.35 5.27 5. 7 46.67 6.07 7.11 8.30 8.8S.51 6. 6. 6.65 57.9 52.79' 6...37 6. 39. 6.93 6.99 7.43' 6.15 6.09 8.tf.32 8.8 5'1.o ' 6.3.59 6.93 7.5 46.8. 46/1 48.7 62. 7.36 6.1" ContinUed y Vi y' V' Y-' 29.3 29.. 53.' 61:5.10 8.6 60.31" 8.89 7.83 6.15 8.41 6.27 6.1 34.75 .19.6 3617 36. 6.3 41. : 31. 7.3 34.6 54.7 35:8 35.03 8..0 35(1 35.9' 49.78 7.9 30. 29.18 8.90.85 7.73 7.17 7.68. 7.5.95· 6.48 6.S8': 7.5 53:6~.42 7. ~.8 44.42 . 2..0.1 33.0 51.47.39 6.7. 6.7.70 6.34 8.5 43.03 7.1.1 48..71 7.73 6.1. 6..46 6.9 38.7 58.79 .5 ..0 56. '7-:10 7.64..5 58.99' 7. 8 31(9.65 7. 45.4 56. 32.:!3.6 61:7 61.91 7.2 52. 8.18 8.5:: 29.'67 7.8 46.63 6.4 35.31 7.27 7.'. 66 6.4 40.6~ 58'.6 62.98 6.65 6 .8 \ 54. 7. 49.1 40.27 8)28 8..98 6.5 47.95:7.8'.2 31.24 8.6· 60.10 6'.08 8.~ .52 6.06 8.4 60..7.6 .8 50.44 .99 3(U 36.0 . 50 ' 7.6 .8 29.3 5i:t4 54.8 43. 7. 56. 40.0..84 7.9 63:0· 63~1.4" 6.8.3 35.5S'·· 7.2 43. 43.78.14 8.9'.19 8.23· 7.74' 7. 7.33.28 7.7 53.05 6.7 38.30 8. 7:80 7.99 8. 6 .41 7.20 8.13 8.' 6.73 7. 2~.21 7.4 42.7 52:8 52. 7.0 38.6 42.79 7. 6.0 48.06 7.0: 59.3 48.2 7.49· 6.04 .• 06 7.2 41.75 7.25 8.3 40.7 63.66 6.5 46.6 51.9 48. 36.18 7. 7..10 8.73 6..2~ 6.41 7.:: 6.4 62.46.04 6. 6.1 3·t.14 7.24 6.02 7.63 7.80 6.3 49.4 58.21 6.14 8.46 7.1 60.6 49.24 8.8. 1.97 6.32 . 42. 53.31 : 6.S 62.21 7.70 7. 8.3 59.5 3Qi6 .0 52.34 6.8: 39.3 31.4 31.6 52·.3" 58.6 59.5 51.69 .5 30..1. 6.:. 7.71 6.2' 40.0 62.4 34.2 48. 63:~F 63. 33.3 33.90 .0· 47.15 8:16 8.23 .44 7.4 50.01 6 .3Q 6.2 56..29' 8.11 ' 7.2 55.J.1 58.0 37.03 \ 7.67 7.83 7.13 7:. 36.33.6 44.76 6.87 .3' 47.29 7. 6.1 52.7 34.6 57~7 8:01 57. 59.J8 .60 6.7 30. 6..4 38.1 43.5 62.29 7.9 46.13 8.54 12 y.9 60.94 6.61 .7 33.7 45.5 41.60 7.94' 59.8 59.16 6.87 6.28 6.10.5..4 46. 77·.9' 53'. 6. 48. 7.05 7.. 8:23 8.72 7.8 38.~6 6.2 32.~3 6.3 53..09' 7.4.3 38.3· 50.03 8.9.09 6.87.90.45 " 7.85· 6.36 6.52.2 30.49 .84 7.20 7.34 7~35 7.81 7.. 6.06.2 42.·.2 38. 33.4 47.1 59.9 ' 61.3.1 53.3 39.48 7.36 7.4 36.5 56.62 6.44 6.S6:: 7.2· 37.6 43.9 6.0 45. 31.9 62.8 45.4 48. 8.6 50. V Y 50.2 53.9.32' 8.O.61 7. 7..6 40.24 7.37 7.21 6.5 3~.1 41.27 8.8 61.12 8.21 8. 7.~ 33.2 35..01 8.1 57-:2 57.22 7.1 44.8 41.1 ' 60:8 60.19' 7.2 39.17 8. 63:9 54.92 7.QV::: 6.50 6.4~ 33.47: 6.6 46.2" 45.3 60.34 8.25 6.0 32.6 34.1 38. 6.63.9 35.3.6 38.6' 63.0 39.9· 47.4 52.0 44.60 .20 .26 7.33 8.76 7i76 7:77' 7.7 44.5 50.69 7.16 7.1 30.2 36.9.8 56. 42.07 8.2 58.5 34.1. 7..26 8.0 5i'A 57~'5 51.2 34.78 7.5 36.S: 63.25 7. 6. 7.2 59.82 6.48.88 6.:7 31.0?' 6. 7.5.89 6.0 46. 7.85 7.7' 47.92 1.5 52. 33.1 62.01> 7.3 46.5 38.4 .55 7. 45'.31! " 8.6 30.95': 7.0() 61:~ 61:3 .4 49.45 6. 7:98 1.61 43.43 .4 41.8 33.3 51$~ 5104 51.2 60.82 6.9.38 6.94j~ 7.12 7.27 6.59 7.40 6.9.6 41:7 ' 41.9 .55 7:66 1:57': 7.~ 32.92 6.6 58..9 60.9' 64:0 8.1 ' 42. .7. 6.26 8 .9.5 45.3 42.0 .72 7.86 .9 39.5 54.10 ~.2.3 45.03 6.6 55.00 7.5 31.08 6..8 55.0 55.98 7.39 7.0 .31 7.~t· 'D'1'53$ TABLE .0 30.15 7.9 34.2 49.4 32.84 .7 40 i S.50 7.57· 7·.7.9 67.1 51.05 8~06 8.7 59.4 63.56 6.0.2: 5. 7. 7.07 6.82 7.8· 34.0 34.'5 59.81 6.:29 8.2 62:3 62.' 31.52 7.09 8.21.1': 29. 6.67 6.91 6.74 6.39 7.7 50.4 29.0 41.49 6. 32.6 45.1 39.63 7.0 60.172 6.6 40.0~ .~ 7.5 63.' 6.19 6. 7.32 6.58 6.16 8..93 6.75 6.13 6.56.36 .5 44.64 7.1 47:2 47.96 7.60 7.16 7. 5.9 51.6 33.6.2 50.90 7.9 44.0 58.14 7. 56.1 54.23 7.4 ' 6.8 8J)1 8.9 37.6.29. a 3~.52·.4 30.4 43. 42.4 56:5 66.4 44.22 8.5 42.( 32:8 32.3 30.62 7.35 8.45 6.8 30.4 6.3· 37.9 55.11 8.82· 7.9 .37 7:38 7.95.0 61:1 .70 7.23 6.2 44.04.12 7.7 51.00 .14· 6.7 6.62" 7.81 7. 7. 39. 42.4 37\5 37.35. 61'. 32.87 7.6 37.2 46.8 49. 37. 6.0 6.64' 7. 4Q:Q.7 54.19 8.8 47.07 V 7:0S' 7.12 6.1 56.9 58.~6·· 6.20 6.3: 3().9 56.3 44.7 56.3' 63.6 47.7 49.8 57. 49.0.05 8.4 53. 40..1 31.33 8.6 56. 41.40 7.7 55.97 ' V 7.3 43.7 31. 6.1' 45.97. 43.27 7.25 7.91 7.' 49.43 7.76.25 8.4..63 7. 35.0 54.1 ' 50.1 . 61.30 7..7..32 . 6.16 6. 8.85.59 7.1 55.1 46. 03 6.' 7.5 35.69 .0.3 52.02 7..3 .36 6.2 54. 0 76.8 83.98 8.5 82.96 8.32 9.05 9.74 9.4 67.2 86.6 86.4 65.3 82.7 79.9 98.50 9.54 9.30 9.9 99.7 64.7 72.0 87.53 8.47 9.8 95.64 8.39 9.1 71.59 9.91 8.8 85.49 9.27 9.9 68.5 81.58 9.0 78.2 90.1 90.1 68.9 87.50 9.10 9.5 93.63 9.1 67.2 88.1 86.07 9.20 9.3 93.8 81.5 67.7 68.25 9.5 69.6 68.78 9.1 75.4 96.2 97.15 9.4 77.9 79.13 9.53 9.16 9.0 99. Y V Y 85.4 76.4 95.82 8.98 9.67 9.0 89.9 97.6 84.6 69.27 9.2 95.8 80.3 81.59 8.4 98.70 9.1 69.50 8.85 9.4 93.71 92.9 91.99 8.6 96.46 8.74 8.84 9.3 98.8 78.62 8.39 9.9 93.6 81.97 9.59 9.79 9.0 90.1 89.48 8.7 84.78 9.62 9.89 8.82 9.6 75.1 95.8 94.0 71.90 9.0 80.2 87.7 67.3 68.1 77.64 8.97 9.7 83.75 8.52 8.3 78.76 9.8 68.32 9.03 9.8 93.4 V 8.73 y 71.5 68.81 9.55 9.7 76.9 77.78 8.3 65.24 9.99 9.45 8.57 9.06 9.88 8.69 8.71 8.57 9.2 68.87 8.72 9.69 9.0 92.6 93.2 99.60 8.4 88.49 9.39 8.5 80.61 9.89 8.44 8.93 9.9 83.0 75.42 8.45 9.0 88.2 83.0 94.8 74.17 9.91 9.0 68.6 87.46 9.3 90.40 78.7 71.26 9.1 81.2 V 8.65 9.98 8.5 72.9 74.1 88.4 81.80 8.84 8.0 79.74 9.5 87.53 9.46 9.1 94.8 77.3 67.3 94.84 8.51 9.30 9.2 74.44 9.4 69.79 9.7 98.4 70.8 67.6 74.3 71.08 9.33 9.97 9.33 9.59 9.2 78.95 9.66 9.29 9.61 9:62 9.51 8.0 97.41 9.1 65.1 66.0 85.3 79.04 9.14 9.79 8.65 9.1 96.6 78.3 72.56 9.5 96.51 9.73 8.~ 67.55 8.11 9.90 8.36 9.0 91.1 85.7 93.5 85.6 82.8 66.02 9.4 82.3 77.56 9.27 9.2 98.76 9.9 100.82 8.8 65.35 9.3 87.29 9.2 76.95 8.18 9.0 83.39 8.81 8.68 9.9 89.6 94.7 81.75 9. 90.3 97.65 8.53 9.42 9.7 95.74 8.77 8.5 99.72 8.7 91.56 8.5 77.9 86.94 9.7 90.9 84.05 9.03 9.55 9.38 8.66 8.9 96.0 86.5 64.89 9.3 85.21 9.6 88.49 8.82 9.36 9.9 72.4 72.2 70.93 8.4 71.67 8.4 84.92 8.14 9.0 70.4 92.89 9.32 9.16 9.4 75.95 9.22 9.3 89.00 .1 97.55 8.66 9.0 67.37 8.44 8.95 9.5 79.9 92.69 9.5 73.3 95.8 73.45 8.80 9.96 8.67 8.00 9.73 9.41 9.83 8.90 9.12 9.11 9.87 9.85 9.6 77.4 99.8 91.97 8.1 80.4 80.6 65.43 9.54 8.83 8.3 83.37 9.36 8.5 92.6 66.21 9.3 70.6 89.3 76.83 9.0 77.1 92.19 9.8 90.19 9.6 98.1 87.38 9.6 73.7 94.94 9.81 9.75 9.4 97.5 75.4 89.79 9.3 99.58 8.48 9.6 80.f} 90.5 91.0 96.0 84.43 9.0 93.01 9.00 9.77 8.77 9.0 65.9 95.4 87.6 13 .68 8.5 86.7 88.9 75.3 69.91 9.2 77.7 73.9 78.9 71.46 8.3 80.50 8.4 79.2 82.4 91.57 8.36 9.87 9.5 71.56 9.47 8.44 9.62 9.8 88.0 95.80 9.5 89.6 70.2 89.56 8.48 8.85 8.69 9.4 68.01 9.02 9.5 78.50 9.96 9.81 9.0 69.99 9.17 9.40 8.41 8.~m~ 01535 TABLE 1 Continued y 64.87 9.63 8.5 98.63 9.47 8.48 9.98 9.9 66.06 9.9 76.58 9.7 75.7 78.07 9.6 72.2 93.8 86.4 73.0 82.2 65.3 64.8 84.80 8.6 76.13 9.34 9.3 86.5 70.58 8.3 96.15 9.5 76.93 8.3 84.7 86.34 9.09 9.64 9.6 95.63 8.84 9.3 66.2 66.26 9.2 94.4 85.91 9.49 8.83 9.42 9.03 9.8 70.64 9.9 85.41 8.2 91.87 8.3 92.7 69.60 9.5 97.6 67.43 8.53 8.7 70.6 83.8 71.8 82.1 78.2 69.76 8.86 8.4 64.73 9.93 8.7 96.85 9.60 9.90 8.81 8.99 9.31 9.1 76.68 9.1 84.6 79.2 72.88 9.88 9.9 67.8 99.04 9.68 8.52 9.7 89.5 95.2 96.1 70.6 99.08 V Y 9.89 9.47 9.9 81.85 8.3 75.35 9.6 91.51 8.1 73.4 83.38 8.3 73.60 8.67 9.1 82.77 9.7 85. 9.54 8.7 82.92 8.93 9.24 9.3 88.61 8.9 82.70 9.37 9.23 9.71 9.4 94.31 9.6 71.94 8.22 9.20 9.5 74.7 80.7 92.9 65.91 8.0 74.37 8.54 9.94 8.2 80.66 8.1 72.00 10.40 9.1 79.75 8.2 92.8 97.6 92.5 .2 64.4 90.74 9.1 98.7 77.8 75.7 65.5 65.47 9.2 81.1 99.52 9.9 73.0 66.86 9.7 97.43 9.5 88.72 9.64 9.9 94.67 9.8 89.86 8.8 69.40 9.9 70.12 9.8 9.5 84.1 64.72 8.86 9.1 93.1 83.7 99.57 8.79 8.0 V 9.70 8. 8.3 74.8 87.96 9.18 9.0 81.3 91.23 9.10 9.7 66.92 9.6 90.25 9.1 74.40 8.61 8.17 9.69 8.8 64.8 76.99 10.42 8.78 .8 79.8 98.76 8.2 75.83 9.09 9.2 73.0 72.95 8.5 66.9 88.97 8.59 8.4 66.7 74.65 8.72 9.88 8.6 97.4 86.8 96.4 74.5 94.9 69.71 8.62 8.2 85.28 .5 83.8 72.7 87.0 98.2 84.45 9.70 8.28 9.6 64.22 9.76 9.38 9.10 9.92 9.9 80.1 91.0 73.2 79.93 9. ~m~ 0. 1 Dimensions of the Surface-Color-Perception .J BLU~ GREEN . I/) I/) '(} w z lI (!) .SOlid FIG..... 'P URPLE HUE ____~ _ _-+._SATURATION'. 2 Designation Systems for Munsell Hue 14 ' . YELLOW R~D BLACK FIG...1535 WHITE I {\". ~m~ 0 1535 55r-______~--~~--._------~~--------~7T-------. 3 Munsell Value 1-Loci of Constant Hue and Constant Chroma in CIE (x..50 -.y) Coordinates 15 .~----~~----~-----------------------~5~ I HUE AND CHROMA VALUE .35 30 FIG.40 . 45 50 45 . 20 .4& .35 .55 ~-r----------r-~~--------~----~--------~ __ ~--~--~~ __ --~ ____.30 ·..25 '.40 .55 Mun'sell Value 2-Loci of Constant Hue and Constant Chroma in CIE (x.-____________--______________ ~~~ HUE ANp CHROMA VALUE 2 .2& . .50 .20 .45 .y) Coordinates 16 ..30 . 4 .15 FIG.50 i . 45 .30 x FIG.~m~ 0 1535 .y) Coordinates 17 . 5 Munse" Value 3-Loci of Constant Hue and Constant Chroma in CIE (x.so .45 I--!---I'I--+-+ .40 . 45 .6 lYI. I.y) Coordinate's . Loci of ~eoi1stant Hue and Constant 'Chronia'in CIE (x.50 ..25 x FIG.30 .uns~II·Val"'~ 4.~. A~D'lqHRorvfA VALliJE. .i .. · __ .E I .40 . .....A .HU. 7 Munsell Value 5-Loci of Constant Chroma in CIE (x.20 x FIG.y) Coordinates 19 .55 HUE AND CHROMA VALUE 5 50 45 .25 20 .~ffi~ 0 1535 ~~--~--~~----r---~~--------~--~~------~~------~~----~--~--------~------------------~. in CIE (x.FIG.y) Coordinates 20 . Near Gray. 8 Munsell Value 5-Loci of Constant Hue and Constant Chroma. __ .45 ._.y) Coordinates 21 .!·0. -_.._ . Munsell Value 6-Loci of Constan.-"":..35 11-1-+-'--1-'-+-1+-+1-+-'--1-+--1 'I ..I~0---':'--.---..t Hue and Constant Chroma in CIE (x.+.....-:::S5:------. 9.50 .CHROMA VALUE 6 ...0:-----~~-=:::!!ioo.~m~ 0 1535 HUE AND .45:--. .:.o:I::I5"""'----:.....2:f..20 ....35 .15 FIG. .:------.oI--:::::"'''''''':::.30 .:.-:1.. _..-.6.'''':------.40::------.Ie.10 .25 __ . 33 x FIG.'Lbci of'Constant'Hue and Co~stan(ChrOina.y) Coordinates .37 .. 10 MuhseliValue 6:"". 'ikClE 22 (x. Near' C1ray. j'--f-l-- ..-:-:45:------. 11 Munsell Value 7-Loci of Constant Hue and Constant Chroma in CIE (x.:..3& I--l---.y) Coordinates 23 .3::'::5---------4-:-:0:---------.~55::------~.45 ....&5r---~~~r-~--r----r--~~----~------~r-------~~------~~~~~~--------~--------~--------~.I:'::-5--------~.10 JlIj~O--------~..55 HUE AND iCHROMA .25 .~~l~ 0 1535 .3::':0~-------.n -.45 .30 ..30 ~ ! . 40 .60·15 x FIG.40 ..2::'::0~-------..2::'::5~-------.-.50 50 .50:-------.-..:'.35 . Near:G~a'¥. 1'2·' 'Munsell' Value 7~Loci ofcbnstantHue'and Cbnst~ritChroma. 24 iril'CiEi'(x.x FIG.y) Co'ordinates . 25 -~ j--l--! __=~_Ll_ I-+--I--l-+--+-+-I--~ - - ~ ____ ~'1'. ___':::::"':'-":""'_________ ~ .l11-~·~~::~~~::. j .~m~ 0 1535 .Ii· .:".-·:-It .60 .50 ~LL -+ .*___ FIG.. 13 .30 ...35 .50 . i..40 . ..55 Munsell Value a-Loci of Constant Hue and Constant Chroma in CIE (x.40 . VALUE 8 I -.I~ __.y) Coordinates 25 .35 .10 HUE AND CHROMA .. -II~--+---+-+--I-_--I-.20 :. -1+-- I .30 ~ x ...I~'-i. ·t--j-· ..H J+-I--'-H-1f -'-I---+-+--1 ..45 .~ ~:-- . --::~ ___ ____ ___--:":--__ _"..J.16 .45 . x 2.6 . . 25 I-~--.'~5 . · ....... • ... _ ....-+-+--1-.211 .'--'-·--f--I--l--·:-· .45 .. I_-'--·~~-~-+_-i-.". .~m~ 0 1535 . 9 .. I I I HUE . ..y) Coordinates 27 ..40 .15 L-~ ill ______~________~________~________ __~________ m FIG.+· .411 .· .20 I· .30 ..40 . ·_-_ . 15 ~ n ~ x __--------~------~~------~~~~~~~~-------~III M M M M ~ ~ Munsell Value 9--Loci of Constant Hue and Constant Chroma in CIE (x...--:..55r-'-~~--~--------~--------~------~--~~------~ ~------~~~--~~~--------~--~----~---------..50 - AND pHROMA VAL~E. -:~~. .31 . Near White.n. ? . . 34 .30~·PL---~~. l . Philadelphia. Your comments are invited either for revision of this standard or for additional standards and should be addressed to ASTM Headquarters..." '.. 16 -~ \ \I. 4' . "':'7 . either reapproved or withdrawn.. PA 19103. are entirely their own responsibility.37·29 __ 'I FIG. Munsi!~rValue 9-Loci of Constant Hue and Constant Chroma.·36 .~35~------~.' ~ . '.'. . Users of thIs standard are expressly advised that determination of the validity of any such patent rights.y) Coordinates The American Society for Testing and Materials takes no posit/on respecting the validity of any patent rights asserted In connection with any Item mentioned in this standard.35 .. 1916 Race St.~32~--~--~.3~4--~--~.2~8~~--~2~9--~~~~.371~~--~. ~~'... :~ ~ .3~6--~~~.'f. 1 '. and the risk of infringement of such rights. ."- _..:".:. Your comments will receive careful consideration at a meeting of the responsible technical committee. :~: '<~~ -'. 30 9/. .: ". If you feel that your comments have not received a fair hearing you should make your views known to the ASTM Committee on Standards.3~3~~~~. which you may attend. in CIE (x. . ~--~~~. . This standard Is subject to revision at any time by the responsible technical committee and must be revIewed every five years and If not revised..'" '". ~."LI)'t ~t~~~~'·~~:.