Cornell University Library The original of tiiis book is in tine Cornell University Library. There are no known copyright restrictions in the United States on the use of the text. http://www.archive.org/details/cu31924004616094 TABLES EARTHWORK COMPUTATION BY C. F. ALLEN, M. Am. Soc. C. E. Associate Pbofbssob of Railroad Engineering, Massachusetts Institute of Technology oXKo BOSTON PUBLISHED BY THE AUTHOR 1893 Copyright, 1893, By C. F. Allbn. STottoooti ^tcms : J. S. Gushing & Co. — Berwick & Smith. Boston, IVIass., U.S.A. PEEFACE. The computation of earthwork without diagrams or tables is extremely laborious and unsatisfactory. Many engineers favor the use of diagrams, and if these be made upon cross-section paper and on a reasonably large scale, results may be taken off to the nearest yard with great rapidity. Others prefer tables, which have some advantages over diagrams. They are more portable, allow of greater precision, and do not call for the exercise of judgment in estimating fractions of a space. For those engineers who for any reason pre- fer tables to diagrams, this book has been prepared. Table I. is adapted for rapid computation for sections of any base or slope, and for irregular as well as for regular sections. By the use of Table II., results are readily obtained that are correct by the Prismoidal Formula. In Table III., provision is made for very rapidly taking out quantities for level sections when the center heights alone are given; in making preliminary estimates there is need of such a table, and a limited number of the most common bases and slopes are provided for in Table III. Care has been taken to make the tables strictly accurate, and no errors are known to exist. If any shall be discovered, it is requested that a memorandum be sent to the author, so that later editions may be corrected. 3 USE OF THE TABLES. In calculating earthwork, the volume, using the method of " Averag- ing End Areas," is found by Table I. When the volume by the "Prismoidal Formula" is required, the volume is first calculated by Averaging End Areas, using Table I., a correction is then applied, and the result obtained is strictly correct by the Prismoidal Formula. This "Prismoidal Correction" is taken from Table II. For preliminary estimates, the volume of level sections is often required. A few selected tables have been prepared which it is hoped may prove of some value for this purpose. These are given in Table III. Many engineers will prefer to take out quantities no closer than to the nearest yard. By these tables, quantities may be taken out to the nearest tenth of a yard for any desired width up to 100 feet. TABLE I. Triangular Prisms. Quantities in cu. yds. for 50 ft. in length. Averaging End Areas. In any full section of earthwork having parallel end faces 100 ft. apart, let Aa = area of face at Station Ai = area of face at Station 1 Fioo = volume for a full section of 100 ft. Then by the method of "Averaging End Areas," Faoo = ^^±^xl00 = 50^ + 50^1 in cu. ft. = l^^o + It A in cu. yds. or Fioo is equal to the sum of two prisms each 50 ft. in length, one of area A^ and the other of area A-^. 6 TABLES FOB EABTHWOBK COMPUTATION. When the end area is in the form of a triangle of base 6 and alti- tude a, the formula becomes K,oo-^x~ + 2^x— cu.yds. = If X Mo + If X 6iai cu. yds. Using any given values of b and a, Table I. gives a corresponding value of U X 6a (or for a triangular prism 60 ft. in length), and this we may call S. Then Vioo=So + S, When the section of earthwork is of length I less than 100 ft., F, J_ 'lOO {S, + S,) Regular " Three Level Sections " of earthwork may be quickly cal- culated by Table I. In Fig. 2, let ABODE represent a regular cross^section, and b = base of roadbed = AB S = rate of slope = ^ ^ CM USE OF THE TABLES. 7 c = center height =DG cZ; _ ( distances out from center to ) _ EL d, \ side slope stakes ) ~ BO g = altitude of grade triangle = GH Then Area, ABODE = Area, E HOD -AieaABH A = (c + g) ^' - f s =n{o + g){d^ + d;)-i^bg Vm = So + Si The value of ff (c + g) (cZ, + d,) can be taken directly from Table I., and the value of ^ bg can also be taken from Table I. Table I., in fact, gives values for ^ of any two quantities to be multiplied together. For a series^ of regular "Three Level Sections," gi is a constant and = — ; in that case f^ bg is also a constant, and need be computed ^ s » from Table I. but once. Example 1. Using the common form of notes where /*, and h, represent side heights. Sta. c~ K + 80 28.6 +12.4 + 11.5 26.2 + 10.8 1 25.3 +10.2 + 9.7 23.8 +9.2 19.9 + 6.2 17.5 +6.6 +50 Base of cutting = 20 ft. ; slope, 1^ to 1 ^ = ^=6.7 TABLES FOB EARTHWORK COMPUTATION. Station Cq + ^ = 6.2 + 6.7 = 12.9 d,+ d, = 19.9 + 17.5 = 37.4 Under heights 12. 9 find 3 = 35.83 7 = 83.61 4 = 47.78 30. 7. .4 = 358.3 = 83.6 = 4.8 g= 6.7 37.4 = 446.7 b = 20.0 Under heights 6.7 find 20.0 = 124.1 So = 322.6 Station 1. c,+g =16.4 d, + d, = 49.1 under 16.4 find 40. 9. .1 = 607.4 = 136.7 = 1.5 less grade triangle 745.6 124.1 Si So = 621.5 = 322.6 Fi«, = 944.1 Station 1 + 80. 18.2 54.8 842.6 67.4 13.5 923.5 124.1 I 80 100 100 Si+m s, = 0.8 = 799.4 = 621.5 1420.9 1136.72 \- Fioo ;>? 944.1 Veo 1136.7 «,' Total from Sta to 1 + 80 = 2080.8 cu. yds. USE OF THE TABLES. 9 TABLE II. Frismoidal Correction. Quantities in cu. yds. for a 100 ft. section. Eesults strictly correct by the Prismoidal rormula can be most easily reached by first calculating by Averaging End Areas and then applying the Prismoidal Correction. In Fig. 2, in addition to data previously given, let G = prismoidal correction I) = di + d, c„ = center height at station Ci = center height at station 1 M= area of middle section Vp = volume by prismoidal formula Ve = volume by averaging end areas Then for a section 100 ft. long F„ - n = C = ^ (A - A) (Co - cO cu. yds., and for a section of length I When a section of earthwork has triangular ends, using the nota- tion of Fig. 1, I .y . X^) Q\ 2 2 2 J 12 C = F, - F; = — ( ao&o + afii - Oo&i- tti&o) C'=^(&„-&i)(a„-ai) 10 TABLES FOR EARTHWORK COMPUTATION. Let the end section in Eegular Three Level Sections be shown in Fig. 3. Fig. 3 The solid may then be divided into three parts, represented by EGA, COB, and EGCD. The solid EGA has bases equal at the ends, being one-half the width of road-bed. For the solid EGA then C = 0. For the solid CGB also C = 0. The Prismoidal Correction for the entire solid will be the same as for EGCD. The area EGCD is composed of two triangles of common base c and altitudes c?, and d„ and di + d^=.D\ therefore 0= ^(Do-D,){co-c,) = ^-^ (-Do — Di) (co — Ci) in cu. yds. for 100 ft. in length. Table II. gives values of — — (Do — A) (co — c{), or more properly gives values of ~— - of any two quantities to be multiplied together. USE OF THE TABLES. 11 Example 2. In Example 1, A - i»i = 37.4 - 49.1 = - 11.7 Co - Ci = 6.2 - 9.7 = - 3.5 Under I>„ - Di = 11.7 find 3. =10.8 From Example 1, So = 322.6 Si = 621.5 V, = 944.1 less C= 12.6 .5= 1.8 C=12.6 Fy = 931.5 from Station to 1 A-A+8o = -5.7 1.8 Ci— Ci+8o = -1.8 1.4 0=3.2 Si = 621.5 -S,.«,= 799.4 1420.9 C = 3.2 = 1417.7 — = 0.8 100 Fp = 1134.16 from Station 1 to 1 + 80 Caution. When Co — Cj and Do — A are both positive or both negative, the correction must be subtracted. When Co — Ci and Do — A are one positive and one negative, the correction must be added. (These cases are comparatively rare.) When the section is less than 100 ft. long, the correction as taken from the table should be applied before multiplying by - — , and V, = ^^(So + Si-C). The Prismoidal Correction in the form given is properly applied only when both ends of the section of Earthwork are Kegular Three Level Sections, both having the same base. The Prismoidal Correc- tion need not be applied when its value is small. Experience will dictate when its application is desirable. 12 TABLES FOB EABTHWOBK COMPUTATION. Irregular Sections. Table I. An " Irregular Section " can be divided into triangular parts as in the figure, where AB is the base and DG the centre height. Let hi and d, be the height and distance out at L ; h„ and d„ be the height and distance out at M; and others with similar notation. ^^'- 2 Sl = UKiAG-d^) A hM-0) S2 = MM» As- 2 Ss = Mc(d, + etc. Si = MM,, 85 = UKid.-dJ Se = -UK{d„-GB) S=Si + S2,+ S3 + S4 + S5 + Sb due attention being given to the minus sign in Sg. For successive sections of earthwork It will be obse'rved that in the calculations indicated above, pairs of triangles are used whenever two adjacent triangles have as a base a common height, as A, in 2, c in 3, 7i„ in 4, etc. It should be noticed that the calculation of " Irregular Sections " is very laborious in rough country. This application of the tables will result in great saving of time and should be thoroughly understood. USE OF THE TABLES. 13 Example 3. Sta. + 60 15.2 + 5.2 8.7 + 7.6 + 4.9 7.9 + 5.3 11.5 + 9.1 18.6 + 8.6 14.8 + 4.8 + 3.6 10.0 + 5.7 14.5 + 4.5 Base 20 feet. Slope 1 1 to 1. Station 0. si = If X 4.8 X 10.0 S2 = ff X 3.6 X (14.8 + 10.0) 24.8 S3 = If X 5.7 X (14.5 - 0) 66.7 13.3 2.7 82.7 52.8 21.1 2.6 44.4 82.7 76.5 ^^^^^^^^T^^^slX ^0 = 203.6 station + 60. si = |f X 6.2 X (10.0 -8.7) 1.3 4.8 1.4 6.2 s, = |fx 7.6 X (15.2-0) 70.4 35.2 1.4 107.0 ss = |f x4.9x(8.7 + 7.9) 16.6 45.4 27.2 2.7 75.3 s,= |f X 5.3 X (11.5-0) 49.1 4.9 M 56.5 s, = |o X 9.1 X (18.6 -7.9) 10.7 84.3 5.9 90.2 336.2 14 TABLES FOB EARTH WOBK COMPUTATION. s„ = -fjx 8.6 X (11.5-10.0) 1.5 335.2 8.0 4.0 12.0 'S'o+60 = 323.2 So = 203.6 526.8 I 100 = 0.6 = 316.08 By drawing figures of the sections shown in the notes it will at first be easier to follow the explanation given. With some experience the sketch will be found unnecessary. Alternative Method of Dividing the Irregular Section. A L G The area may be divided into trapezoids ' 2 A,- (d,-0)(h, + c) 2 «3= MW-0)(A, + c) S4= IKc^^-oxc + zo S6= md.-d„)(K + h,) S=Si + .% + Ss + Si + S,+ So + Sj due attention being paid to the minus signs whenever they occur. USE OF THE TABLES. 15 It is evident that this method involves a greater number of compu- tations than that previously given. It may to some seem clearer in principle, although that previously given is quite simple when once mastered. With "Irregular Sections" the Prismoidal Correction cannot be accurately and conveniently applied, and most commonly no attempt is made to use it in actual practice for such sections. The Prismoidal Correction may be obtained approximately in many cases, by calcu- lating it for Regular Three Level Sections having the same center heights Co and Cj, and the same side heights h^^, h^i, and /t,,, Jin, and dis- tances out do,., do« and dy^, d^, as the given sections ; that is, by neglect- ing the intermediate heights for calculating the Prismoidal Correction. Alternative Method for " Three Level Sections." Table I. Pier. 7 _*o • Using the same notation as previously in Fig. 2, h ■,Uh+K) A = ■ + c(d,-|-d,) S = f^l(K + K)+f^cid, + d^) For a single computation this is as simple and rapid as the method previously given. For a series of Regular Three Level Sections it is less rapid than that previously given. When the cuts or fills are large, this method will be preferred by some engineers. 16 TABLES FOR EABTHWORK COMPUTATION. TABLE III. Level Sections. Quantities in cu. yds. for 50 ft. in length. For calculating volumes of " Level Sections " Fioo = 50^o + 50A Fioo= So + Si Values of S are taken directly from Table III., as shown below. Example 4. Sta. Center hts. 2 - -3.9 + 40 - -6.7 1 - -4.3 - -1.8 16 ft. ; slope, 1^ to 1. L8 ^0 = 62.3 4.3 Vm' ^1 = 178.8 = 241.1 4.3 ■Si = 178.8 6.7 Sl+40 = 323.2 502.0 F« 0.4 200.8 6.7 Si+m = 323.2 3.9 s. = 167.8 481.0 0.6 288.6 241.1 200.8 288.6 Total, 730.5 TABLES. 18 TABLE I. TRIANGULAR PRISMS. Quantities in cu. yds. for 50 ft. in length. Width. 1 2 3 4 5 6 7 8 9 Width. Height. Height. O.I .09 .19 .28 •37 .46 .56 .65 -74 •83 0.1 .2 ■'i •37 .56 •74 •93 I. II 1.30 1.48 1.67 .2 •3 .28 .56 •83 I. II 1^39 1.67 1-94 2.2;2 2.50 •3 ■4 •37 •74 I. II 1.48 1.85 2.22 2-59 2.96 3-33 •4 •5 .46 •93 1-39 1.8s 2.31 2.78 3-24 3-7° 4.17 •5 .6 .56 I. II 1.67 2.22 2.78 3^33 3-89 4.44 5.00 .6 •7 .65 1.30 1.94 2.59 3^24 3^89 4-54 5.19 5-83 •7 .8 •74 1.48 2.22 2.96 3^70 4.44 5.19 5-93 6.67 .8 •9 •83 1.67 2.50 3^33 4.17 5.00 5-83 6.67 7-50 •9 I.O •93 ..85 2.78 3-7° 4^63 5^56 6.48 7.41 8.33 1.0 .1 1.02 2.04 3.06 4.07 5.09 6.11 7^i3 8.15 9.17 .1 .2 I. II 2.22 3^33 4.44 5^56 6.67 7.78 8.89 10.00 .2 •3 1. 20 2.41 3.61 4.81 6.02 7.22 8.43 9^63 10.83 •3 ■4 1.30 2.59 3-89 5.19 6.48 7.78 9.07 io^37 11.67 •4 ■5 1-39 2.78 4.17 S-S6 6.94 8^33 9.72 11.11 12.50 •5 .6 1.48 2.96 4,44 5^93 7.41 8.89 io^37 11.85 13^33 .6 ■7 1-57 3-15 4.72 6.30 7.87 9.44 11.02 12.59 14.17 -7 .8 1.67 3-33 5.00 6.67 8.33 10.00 11.67 13-33 15.00 .8 ■9 1.76 3-52 S.28 7.04 8.80 10.56 12.31 14.07 15-83 •9 2.0 1.85 3-7° 5-56 7.41 9.26 II. II 12.96 14.81 16.67 2.0 .1 1-94 3-89 5-83 7.78 9.72 11.67 13.61 'S-56 17.50 .1 .2 2.04 4.07 6.11 8.1S 10.19 12.22 14.26 16.30 18.33 .2 •3 2.13 4.26 6-39 8.52 10.65 12.78 14.91 17.04 19.17 .3 •4 2.22 4.44 6.67 8.89 II. II 13^33 15.56 17.78 20.00 -4 •5 2.31 4-63 6.94 9.26 "•57 13.89 16.20 18.52 20.83 -5 .6 2.41 4.81 7.22 9^63 12.04 14.44 16.85 19.26 21.67 .6 •7 2.50 5.00 7.50 10.00 12.50 15.00 17.50 20.00 22.50 .7 .8 2.59 S^i9 vl 10.37 12.96 i5^56 18.15 20.74 23^33 .8 •9 2.69 5-37 8.06 10.74 13^43 16.11 18.80 21.48 24.17 -9 3-0 2.78 5-56 8.33 II. II 13.89 16.67 19.44 22.22 25.00 3-0 .1 2.87 S-74 8.61 11.48 14-35 17.22 20.09 22.96 25.83 .1 .2 2.96 S-93 8.89 11.85 14.81 17.78 20.74 23.70 26.67 .2 •3 3.06 6.11 9.17 12.22 15.28 18.33 21.39 24.44 27.50 •3 ■4 3-iS 6.30 9-44 12.59 15^74 18.89 22.04 25.19 28.33 '4 •5 3-24 6.48 9.72 12.96 16.20 19.44 22.69 25-93 29.17 -5 .6 3-33 6.67 10.00 i3^33 16.67 20.00 23^33 26.67 30.00 .6 •7 3-43 6.85 10.28 i3^70 i7^'3 20.56 23.98 27.41 30-83 ■7 .8 3-52 7.04 10.56 14.07 17^59 21. II 24.63 28.15 31-67 .8 •9 3-6i 7.22 10.83 14.44 18.06 21.67 25.28 28.89 32.50 •9 4.0 3-7° 7.41 II. II 14.81 18.52 22.22 25-93 29.63 33-33 4.0 .1 3.80 7-59 "•39 15.19 18.98 22.78 26.57 30^37 34-17 .1 .2 3-89 7.78 11.67 i5^S6 19.44 23-33 27.22 31. II 35.00 .2 ■3 3-98 7.96 11.94 i5^93 19.91 23.89 27.87 3i^85 35-83 .3 •4 4.07 8.1S 12.22 16.30 20.37 24.44 28.52 32^59 36.67 •4 •5 4.17 8-33 12.50 16.67 20.83 25.00 29.17 33^33 37-50 •5 .6 4.26 8.52 12.78 17.04 21.30 25.56 29.81 34-07 38-33 .6 ■7 4-35 8.70 13.06 17.41 21.76 26.11 30.46 34.81 39-17 .7 .8 4.44 8.89 i3'33 17.78 22.22 26.67 31.11 35-56 40.00 .8 •9 4-54 9.07 13.61 18.15 22.69 27.22 31-76 36-30 40.83 -9 5.0 4-63 9.26 13.89 18.52 23^ 2.72 4.07 5-43 6.79 8.1S 9.51 10.86 12.22 •4 •5 1-39 2.78 4.17 5^56 6.94 8.33 9.72 II. II 12.50 •5 .6 1.42 2.84 4.26 5.68 7.10 8.52 9.94 11.36 12.78 .6 ■7 1.45 2.90 4-35 5^80 7.25 8.70 10.15 11.60 13.06 •7 .8 1.48 2.96 4.44 5^93 7.41 8.89 10^37 11.85 i3^33 .8 •9 '•5i 3.02 4^54 6.05 7.56 9.07 10.59 12.10 13.61 •9 5-0 '•54 3^09 4-(>3 6.17 7.72 9.26 10.80 12.35 13.89 5-0 1 2 3 4 5 6 7 8 9 v.- 3.24 (Do-A)(Co-C,) TABLE II. PRISMOIDAL CORRECTION. 29 Quantities in cu. yds. for a section 100 ft. in length. Co-Ci 1 2 3 4 5 6 7 8 9 Co-C. Do-D, Do-Di 5-1 1-57 3-15 4.72 6.30 7.87 9-44 11.02 12.59 14.17 5-1 .2 i.6o 3.21 4.81 6.42 8.02 9-63 11.23 12.84 14.44 .Z ■3 1.64 3-27 4.91 6.54 8.18 9.81 11-45 13-09 14.72 •3 •4 1.67 3-33 5.00 6.67 8.33 10.00 11-67 13-33 15.00 •4 •5 1.70 3-40 5.09 6.79 8.49 10.19 11.88 13-58 15-28 •5 .6 1-73 346 5.19 6.91 8.64 «°-37 12.10 13-83 15-56 .6 •7 1.76 3-52 S.28 7.04 8.80 10.56 12.31 14.07 15-83 ■7 .8 1.79 3-58 S-37 7.16 8.95 10.74 12.53 14.32 16. II -8 •9 1.82 3-64 5.46 7.28 9.10 10.93 12-75 14-57 16.39 -9 6.0 1.8s 3-7° S-56 7.41 9.26 II. II 12.96 14.81 16.67 e-o .1 1.88 3-77 S-6S 7-53 9.41 11.30 13.18 15.06 16.94 -I .2 1.91 3-83 5-74 7-65 9-57 n.48 13.40 15-31 17.22 -2 •3 1.94 3.89 5-83 7.78 9-72 11.67 13.61 15.56 17.50 -3 •4 1.98 3-95 5-93 7.90 9.88 11.85 13-83 15.80 '2-7! •4 •S 2.01 4.01 6.02 8.02 10.03 12.04 14.04 16.05 18.06 -5 .6 2.04 4.07 6.H 8.1S 10.19 12.22 14.26 16.30 18.33 -6 •7 2.07 4.14 6.20 8.27 10.34 12.41 14.48 16.54 18.61 •7 .8 2.IO 4.20 6.30 8.40 10.49 12.59 14.69 16.79 18.89 .8 •9 2.13 4.26 6-39 8.52 10.65 12.78 14-91 17.04 19.17 -9 7.0 2.16 4-32 6.48 8.64 10.80 12.96 15.12 17.28 19.44 7-0 .1 2.19 4-38 6.57 8.77 10.96 13-15 15-34 17-53 19.72 • 1 ■2 2.22 4.44 6.67 8.89 II. II 13-33 15.56 17.78 20.00 .Z •3 2.25 4.51 6.76 9.01 11.27 13-52 15-77 18.02 20.28 -3 ■4 2.28 4-57 6.85 9.14 11.42 13-70 15-99 18.27 20.56 -4 •5 2.31 4-63 6.94 9.26 11.57 13.89 16.20 18.52 20.83 •5 .6 2-35 4.69 7.04 9-38 11-73 14.07 16.42 18.77 21.11 .6 •7 2.38 4-75 7-13 9.51 11.88 14.26 16.64 19.01 21.39 ■7 .8 2.41 4.81 7.22 9-63 12.04 14.44 16.85 19.26 21.67 .8 •9 2.44 4.88 7-31 9-75 12.19 14.63 17.07 19.51 21.94 -9 8.0 2.47 4.94 7.41 9.88 12-35 14.81 17.28 19-75 22.22 8.0 .1 2.50 5.00 7-So 10.00 12.50 15.00 17.50 20.00 22.50 .1 .z 2-53 5.06 7-59 10.12 12.65 15.19 17.72 20.25 22.78 .2 •3 2.56 S.12 7.69 10.25 12.81 '5-37 17-93 20.49 23.06 -3 •4 2-59 5-19 7.78 10-37 12.96 15.56 18.15 20.74 2333 -4 ■5 2.62 5-25 7.87 10.49 13.12 15-74 18.36 20.99 23.61 -5 .6 2.65 S-3I 7.96 10.62 13-27 15-93 18.58 21.23 23-89 -6 •7 2.69 5-37 8.06 10.74 13-43 16. II 18.80 21.48 24.17 •7 .8 2.72 5-43 8.1S 10.86 13-58 16.30 19.01 21-73 24.44 -8 •9 2.7s 5-49 8.24 10.99 13-73 16.48 19.23 21.98 24.72 -9 g.o 2.78 S.56 8-33 II. II 13.89 16.67 19.44 22.22 25.00 9.0 .1 2.81 S.62 8.43 11.23 14.04 16.85 19.66 22.47 25.28 .1 .^ 2.84 5.68 8.52 11.36 14.20 17.04 19.88 22.72 25.56 .2 •3 2.87 5-74 8.61 11.48 14-35 17.22 20.09 22.96 25.83 -3 •4 2.90 5.80 8.70 11.60 14.51 17-41 20.31 23.21 26.11 -4 ■5 ■ 2-93 5.86 8.80 "•73 14.66 17-59 20.52 23.46 26.39 -5 .6 2.96 5-93 8.89 11.85 14.81 17.78 20.74 23.70 26.67 .6 •7 2.99 5-99 8.98 11.98 14.97 17.96 20.96 23-95 26.94 •7 .8 3.02 6.05 9.07 12.10 15-12 18.15 21.17 24.20 27.22 .8 ■9 3.06 6.11 9.17 12.22 15-28 18-33 21.39 24.44 27-50 -9 lo.o 3-09 6.17 9.26 12-35 15-43 18.52 21.60 24.69 27.78 lO.O 1 2 3 4 5 6 7 8 9 v,-v^=c= 3.24 (X>„-A)(Co-c,) 30 TABLE II. PRISMOIDAL CORRECTION. Quantities in cu. yds. for a section 100 ft. in length. Co-Ci 1 3 3 4 5 6 7 8 9 Co-Ci Do-Di Do-Di lO.I 3.12 6.23 9-3S 12.47 15-59 18.70 21.82 24.94 28.06 lO.t .2 3-15 6.30 944 12.59 15-74 18.89 22.04 25.19 28.33 .2 •3 3.18 6.36 9-54 12.72 15.90 19.07 22.25 25.43 28.61 .3 •4 3.21 6.42 9-63 12.84 16.05 19.26 22.47 25.68 28.89 .4 ■5 3-24 6.48 9.72 12.96 16.20 19.44 22.69 25-93 29.17 .5 .6 3-27 6.54 9.81 13.09 16.36 19.63 22.90 26.17 29.44 .6 •7 3-30 6.60 9.91 13.21 16.51 19.81 23.12 26.42 29.72 .7 .8 3-33 6.67 10.00 13-33 16.67 20.00 23-33 26.67 30.00 .8 ■9 3-36 6.73 10.09 13.46 16.82 20.19 23-55 26.91 30.28 •9 II.O 340 6.79 10.19 13-58 16.98 20.37 23-77 27.16 30.56 II.O .1 3-43 6.85 10.28 13-70 i7-«3 20.56 23.98 27.41 30.83 .1 .z 346 6.91 10-37 13-83 17.28 20.74 24.20 27.65 31.11 .2 ■3 349 6.98 10.46 13-95 17.44 20.93 24.41 27.90 31-39 .3 •4 3-52 7.04 10.56 14.07 17-59 21. II 24.63 28.15 31-67 -4 ■5 3-SS 7.10 10.65 14.20 17-75 21.30 24.85 28.40 31-94 -5 .6 3-58 7.16 10.74 14.32 17.90 21.48 25.06 28.64 32-22 .6 •7 3-6i 7.22 10.83 14.44 18.06 21.67 25.28 28.89 32.50 .7 .8 3-64 7.28 10.93 14-57 18.21 21.85 25-49 29.14 32.78 .8 •9 3-67 7-35 11.02 14.69 18.36 22.04 25.71 29.38 33-06 .9 12.0 3-70 7.41 II. II 14.81 18.52 22.22 25-93 29.63 33-33 12.0 .1 3-73 747 11.20 14-94 18.67 22.41 26.14 29.88 33-61 .1 .2 3-77 7-S3 11.30 15.06 18.83 22.59 26.36 30.12 33-89 .2 •3 3.80 7-59 u-39 15.19 18.98 22.78 26.57 30.37 34-17 .3 •4 3-83 7.6s 11.48 15-31 19.14 22.96 26.79 30.62 34-44 •4 •5 3.86 7.72 "•57 '5-43 19.29 23-'5 27.01 30.86 34-72 .5 .6 3-89 7.78 11.67 ■5-56 19.44 23-33 27.22 31." 35.00 .6 ■7 3-92 7.84 11.76 15.68 19.60 23.52 27.44 3'.36 35.28 .7 .8 3-95 7.90 11.85 15.80 '9-75 23.70 27.65 31.60 35-56 .8 ■9 3-98 7.96 11.94 15-93 19.91 23.89 27.87 31.85 35.83 .9 13.0 4.01 8.02 12.04 16.05 20.06 24.07 28.09 32.10 36-11 13.0 .1 4.04 8.09 12.13 16.17 20.22 24.26 28.30 32-35 36-39 .1 .2 4.07 8.15 12.22 16.30 20.37 24.44 28.52 32.59 36-67 .2 •3 4.11 8.21 12.31 16.42 20.52 24.63 28.73 32.84 36-94 .3 ■4 4.14 8.27 12.41 16.54 20.68 24.81 28.95 33.09 37.22 ■4 •5 4.17 8.33 12.50 16.67 20.83 25.00 29.17 33.33 37-50 .5 .6 4.20 8.40 12.59 16.79 20.99 25.19 29.38 33-58 37-78 .e •7 4-23 8.46 12.69 16.91 21.14 25-37 29.60 33-83 38.06 .7 .8 4.26 8.52 12.78 17.04 21.30 25.56 ^29.81 34-07 38.33 .8 •9 4.29 8.58 12.87 17.16 21.45 25-74 30.03 34-32 38.61 ■9 14.0 4-32 8.64 12.96 17.28 21.60 25-93 30.25 34-57 38.89 14.0 .1 4-35 8.70 13.06 17.41 21.76 26.11 30.46 34-81 39-17 .1 .2 4-38 fP 13-15 17-53 21.91 26.30 30.68 35.06 39.44 .2 •3 4.41 8.83 13-24 17.65 22.07 26.48 30.90 35-31 39.72 .3 •4 4.44 8.89 13-33 17.78 22.22 26.67 31-11 35-56 40.00 .4 •5 4.48 8.95 13-43 17.90 22.38 26.85 31.33 35.80 40.28 -5 .5 4.51 9.01 13-52 18.02 22.53 27.04 31-54 36.05 40.56 .6 •7 4-54 9.07 13.61 18.15 22.69 27.22 31.76 36.30 40.83 .7 .8 4-57 9.14 13-70 18.27 22.84 27.41 31.98 36.54 41. 1 1 .8 •9 4.60 9.20 13-80 18.40 22.99 27-59 32.19 36.79 41.39 -9 15-0 150 4-63 9.26 13.89 18.52 23-15 27.78 32.41 37-04 41.67 1 2 3 4 5 6 7 8 9 V,-Vp=C = 3.24 (A-A)(co-c,) TABLE II. PRISMOIDAL CORRECTION. 31 Quantities in cu. yds. for a section 100 ft. in length. Co-Ci 1 2 3 4 5 6 7 8 9 c„-c. Do-Di 151 4.66 9-32 13.98 18.64 23.30 27.96 32.62 37-28 41.94 Do-Di .2 .2 4.69 9-38 14.07 18.77 23.46 28.15 32.84 37-53 42.22 ■3 4.72 9.44 14-17 18.89 23.61 28.33 33-06 37-78 42.50 .3 •4 4-75 9-Si 14.26 19.01 23-77 28.52 33-27 38.02 42.78 -4 •5 4.78 9-S7 14-35 19.14 23.92 28.70 33-49 38.27 43.06 -5 .6 4.81 9-63 14.44 19.26 24.07 28.89 33.70 38.52 43-33 .6 ■7 4.8s 9.69 14.54 19.38 24.23 29.07 33-92 38-77 43-61 •7 .8 4.88 9-75 14.63 19-51 24.38 29.26 34-14 39.01 43-89 .8 •9 4.91 9.81 14.72 19.63 24-54 29.44 34-35 39.26 44-17 .9 iS.o 4-94 9.88 14.81 19-75 24.69 29-63 34-57 39.51 44.44 le.o .1 4-97 9.94 14.91 19.88 24.85 29.81 34-78 39.75 44.72 .X .2 5.00 10.00 15.00 20.00 25.00 30.00 35.00 40.00 45.00 .2 •3 S-03 10.06 15.09 20.12 25-15 30.19 35.22 40.25 45.28 •3 •4 5.06 10.12 i5>9 20.25 25-31 30-37 35-43 40.49 45.56 .4 •5 5-09 10.19 15.28 20.37 25.46 30.56 35-65 40.74 45.83 .5 .6 5.12 10.25 15-37 20.49 25.62 30.74 35-86 40.99 46.11 .6 ■7 S-'S 10.31 15.46 20.62 25-77 30.93 36.08 41.23 46.39 .7 .8 S-I9 IO-37 15-56 20.74 25-93 31-11 36-30 41.48 46.67 .8 ■9 5.22 10.43 15-65 20.86 26.08 31-30 36-51 41.73 46.94 -9 17.0 5-25 10.49 15-74 20.99 26.23 31.48 36-73 41.98 47.22 17.0 .1 5.28 10.56 15-83 21. II 26.39 31-67 36-94 42.22 47.50 .1 .2 5-31 10.62 15-93 21.23 26.54 31-85 37-16 42.47 47-78 .2 •3 S-34 10.68 16.02 21.36 26.70 32.04 37-38 42.72 48.06 •3 •4 5-37 10.74 16.11 21.48 26.85 32.22 37-59 42.96 48.33 .4 ■5 5-4° 10.80 16.20 21.60 27.01 32.41 37-81 43.21 48.61 .5 .6 5-43 10.86 16.30 21-73 27.16 32-59 38.02 43-46 48.89 .6 •7 5-46 10.93 16.39 21.85 27-31 32-78 38.24 43-70 49-17 .7 .8 5-49 10.99 16.48 21.98 27.47 32.96 38.46 43-95 49-44 .8 •9 S-S? 11.05 16.57 22.10 27.62 33-15 38.67 44.20 49-72 .9 18.0 5-56 II. II 16.67 22.22 27-78 33-33 38.89 44-44 50.00 18.0 .1 5-59 II. 17 16.76 22-35 27-93 33-52 39-10 44.69 50.28 .1 .2 5.62 11.23 16.85 22.47 28.09 33-70 39-32 44.94 50.56 .2 •3 s-^s 11.30 16.94 22.59 28.24 33-89 39-54 45.19 50.83 ■3 ■4 5.68 11.36 17.04 22.72 28.40 34-07 39-75 45-43 51-11 .4 •5 S-7I 11.42 17-13 22.84 28-55 34.26 39-97 45.68 51-39 ■5 .6 5-74 11.48 17.22 22.96 28.70 34-44 40.19 45-93 51-67 .6 •7 S-77 11-54 17-31 23.09 28.86 34-63 40.40 46-17 51-94 ■7 .8 5.80 11.60 17.41 23.21 29.01 34.81 40.62 46.42 52.22 .8 •9 s-!l 11.67 17-50 23-33 29.17 35.00 40-83 46.67 52.50 .9 ig.o S-86 11-73 17-59 23.46 29.32 35-19 41.05 46.91 52-78 ig.o .1 5-9° 11.79 17.69 23-58 29.48 35-37 41.27 47-16 53.06 .1 .2 S-93 11.85 17.78 23.70 29.63 35-56 41.48 47-41 53-33 .2 •3 5-96 II. 91 17.87 23-83 29.78 35-74 41.70 47.65 53-61 .3 ■4 5-99 11.98 17.96 23-95 29.94 35-93 41.91 47.90 53-89 -4 •5 6.02 12.04 18.06 24.07 30.09 36-11 42.13 48.15 54-17 -5 .6 6.05 12.10 18.15 24.20 30.25 36-30 42.35 48.40 54-44 .6 •7 6.08 12.16 18.24 24.32 30.40 36.48 42.56 48.64 54-72 -7 .8 6.11 12.22 18-33 24.44 30.56 36.67 42.78 48.89 55-00 .8 •9 6.14 12.28 18.43 24.57 30-71 36-85 42.99 49.14 55.28 -9 20.0 6.17 12-35 18.52 24.69 30.86 37-04 43-21 49-38 55.56 20.0 1 2 3 4 5 6 7 8 9 Ve-V i=C = - ^(^« -A)(cc -c,) 32 TABLE II. PRISMOIDAL CORRECTION. •Quantities in cu. yds. for a section 100 ft. in length. Co-Ci 1 2 3 4 5 6 7 8 9 Co-C, Do-Di Do-Di 20.1 6.20 12.41 18-61 24.81 31.02 37-22 43-43 49.63 55-83 20.1 .2 6.23 12.47 18.70 24-94 31-17 37-41 43-64 49.88 56.11 .2 •3 6.27 12-53 18.80 25.06 31-33 37-59 43.86 50.12 56-39 -3 •4 6.30 12.59 18.89 25.19 31.48 37-78 44.07 50-37 56.67 •4 •5 6-33 12.65 18.98 25-3I 31-64 37-96 44.29 50.62 56.94 •5 .6 6.36 12.72 19-07 25-43 31-79 38.15 44.51 50.86 57.22 .6 •7 6.39 12.78 19-17 25.56 31-94 38-33 44.72 51.11 57-50 •7 .8 6.42 12.84 19.26 25.68 32.10 38-52 44.94 51-36 57-78 .8 •9 6.4s 12.90 19-35 25.80 32-25 38.70 45-15 51.60 58.06 -9 2I.O 6.48 12.96 19.44 25-93 32.41 38.89 45.37 51-85 58.33 21.0 .1 6.51 13.02 '9-54 26.05 32.56 39-07 45-59 52.10 58.61 .1 .■/. 6-54 13.09 19.63 26.17 32-72 39-26 45.80 52-35 58.89 .2 •3 1|7 13-15 19-72 26.30 32-87 39.44 46.02 52.59 59-17 .3 •4 6.60 13-21 19-81 26.42 33-02 39-63 46.23 52.84 59-44 .4 •5 6.64 13-27 19.91 26.54 33-18 39-81 46.45 53-09 59.72 •5 .6 6.67 13-33 20.00 26.67 33-33 40.00 46.67 53-33 60.00 .6 •7 6.70 13-40 20.09 26.79 33-49 40.19 46.88 53.58 60.28 .7 .8 6.73 13.46 20.19 26.91 33-64 40.37 47.10 53.83 60.56 .8 •9 6.76 13-52 20.28 27.04 33-80 40.56 47.31 54-07 60.83 •9 22. 6.79 13-58 20.37 27.16 33-95 40.74 47.53 54-32 61.11 22.0 .1 6.82 13.64 20.46 27.28 34-10 40.93 47.7s 54-57 61-39 -1 .2 6.85 «3-7° 20-56 27-41 34.26 41. II 47.96 54.81 61.67 -2 •3 6.88 13-77 20.65 27-53 34-41 41.30 48.18 55.06 61-94 .3 •4 6.91 13-83 20.74 27.65 34-57 41.48 48.40 55.31 62-22 .4 •5 6.94 13.89 20.83 27.78 34-72 41.67 48.61 55.56 62.50 •5 .6 6.98 13-95 20.93 27.90 34-88 41.85 48.83 55-80 62.78 .6 •7 7.01 14.01 21.02 28.02 35-03 42.04 49.04 56-05 63.06 .7 .8 7.04 14.07 21. II 28.15 3519 42.22 49.26 56.30 63-33 .8 •9 7.07 14.14 21.20 28.27 35-34 42.41 49-48 56-54 63-61 -9 23.0 7.10 14.20 21.30 28.40 35-49 42-59 49-69 56.79 63.89 23.0 • X ''•'1 14.26 21-39 28.52 35-65 42.78 49.91 57-04 64.17 -I .•z, 7.16 14.32 21-48 28.64 35.80 42.96 50.12 57.28 64.44 .2 •3 7.19 14.38 21-57 "■W 35-96 43-15 50-34 57-53 64.72 -3 •4 7.22 14-44 21.67 28.89 36-11 43-33 50.56 57-78 65.00 -4 ■5 7-25 14-51 21.76 29.01 36-27 43-52 50.77 58-02 65.28 -S .6 7.28 '4-57 21.85 29.14 36.42 43-70 50.99 58-27 65.56 .6 •7 7-3" 14.63 21.94 29.26 36-57 43-89 51.20 58-52 65.83 .7 .8 7-35 14.69 22.04 29.38 36-73 44.07 51.42 58-77 66.11 -8 ■9 7-38 •4-75 22.13 29.51 36.88 44.26 51.64 59.01 66.39 ■9 24.0 7.41 14.81- 22.22 29.63 37-04 44-44 51-85 59.26 66.67 24.0 .1 7-44 14.88 22.31 ^9-75 37-19 44.63 52.07 59.51 66.94 .1 .2 7-47 14-94 22.41 29.88 37-35 44-81 52.28 59-75 67.22 .2 •3 7.50 15.00 22.50 30.00 37-50 45-00 52.50 60.00 67.50 .3 •4 Z1I 15.06 22.59 30-12 37-65 45.19 52.72 60.25 67.78 .4 •5 7-56 15.12 22.69 30.25 37-81 45-37 52.93 60.49 68.06 -S .6 7-59 '5-19 22.78 30.37 37-96 45-56 53.15 60.74 68.33 .6 •7 7.62 15-25 22.87 30-49 38.12 45-74 53.36 60.99 68.61 .7 .8 ^■fi^ 15-31 22.96 30.62 38.27 45-93 53-58 61.23 68.89 .8 ■9 7.69 15-37 ■ 23.06 30-74 38.43 46.11 53.80 61.48 69-17 69-44 .9 25.0 25.0 7.72 1 5 -43 23-15 30.86 38-58 46.30 54.01 61-73 1 2 3 4 5 6 7 8 9 v;-v;=c= 3.24 (,D,-D,){Co-C,) TABLE III. LEVEL SEOTIONS. Base 14 feet. Slope 1 to 1. Quantities in cu. yds. for 50 ft. in length. Center Height. .1 .2 .3 .4 .5 .6 .7 .8 .9 Center Height. .o 2.6 S-3 7-9 10.7 13-4 16.2 19.1 21.9 24.8 I 2 3 4 5 27.8 59-3 94.4 133-3 175-9 30.8 62.6 98.2 "37-4 180.4 33-8 66.0 101.9 141. 6 184.9 36.8 69.4 105.7 "45-7 189.4 39-9 72.9 109.6 149.9 194.0 43-" 76.4 1 1 3-4 154.2 198.6 46.2 79-9 ""7-3 158.4 203.3 49.4 83.5 121.3 162.8 207.9 52.7 87.1 "25.3 167.1 212.7 55-9 90.8 129.3 171.5 217.4 I 2 3 4 5 6 7 8 9 lO 222.2 272.2 325-9 3S3-3 444-4 227.1 277.4 33"-5 389-3 450.8 231.9 282.7 337-1 395-3 457-1 236.8 287.9 342.8 401.3 463- 5 241.8 293-3 348-4 407-3 469.9 246.8 298.6 354-2 4"3.4 476.4 251.8 304.0 359-9 419.6 482.9 256.8 309-4 365-7 425.7 489.4 261.9 3"4.9 37".6 431.9 496.0 267.1 320.4 377-4 438-2 502.6 6 7 8 9 10 II 13 13 14 15 509-3 577-8 650.0 725.9 805.6 5'5-9 584.8 657.4 733-7 8"3-7 522.7 59"-9 664.9 741.6 821.9 529.4 599.1 672.4 749.4 830.2 536.2 606.2 679.9 757-3 838.4 543-1 613.4 687.5 765-3 846.8 549-9 620.7 695.1 773.3 855.1 556.8 627.9 702.8 78".3 863.5 563.8 635-3 710.4 789-3 871.9 642.6 718.2 797-4 880.4 II 12 13 14 15 i6 17 i8 19 20 888.9 975-9 1066.7 1161.1 "259-3 897.4 984.8 1075.9 1 170.8 1269.3 906.0 993.8 1085.3 1 1 80.4 "279-3 914.6 1002.8 1094.6 I 190.2 1289.4 923.3 1011.8 1 104.0 1199.9 1299.6 93".9 1020.8 1113.4 1209.7 "309-7 940.7 1029.9 1 1 22.9 1219.6 i3"9-9 949.4* 1039.1 1132.4 1229.4 1330.2 958.2 1048.2 1141.9 1239.3 1340.4 967.1 "057-4 ""5"-5 "249-3 1350.8 16 "7 18 "9 20 21 22 23 24 25 1361.1 1466.7 "575-9 1688.9 1805.6 "37"-5 I477-4 1587.1 1700.4 1817.4 1381-9 1488.2 1598.2 1711.9 "829.3 "392-4 "499-1 1609.4 "723-5 "841-3 1402.9 1509.9 1620.7 "735." "853-3 1413-4 1520.8 1631.9 1746.8 1865.3 1424.0 "531-8 "643-3 1758.4 "877-3 1434.6 1542-8 1654.6 1770.2 1889.4 "445-3 "553-8 1666.0 1781.9 1901.6 "455-9 1564.8 "677.4 "793-7 "9"3.7 21 22 23 24 25 26 27 28 29 30 1925-9 2050.0 2177.8 2309.3 2444.4 1938.2 2062.6 2190.8 2322.6 2458.2 1950.4 2075-3 2203.8 2336.0 2471.9 1962.8 2087.9 2216.8 2349.4 2485-7 "975-" 2100.7 2229.9 2362.9 2499.6 1987.5 2113.4 2243.1 2376.4 25"3-4 "999-9 2126.2 2256.2 2389.9 2527-3 2012.4 2139- " 2269.4 2403.5 254"-3 2024.9 2151.9 2282.7 2417.1 2555-3 2037.4 2164.8 2295.9 2430.8 2569-3 26 27 28 29 30 31 32 33 34 35 2583-3 2725-9 2872.2 3022.2 3175-9 2597.4 2740.4 2887.1 3°37-4 3"9"-5 2611.6 2754-9 2901.9 3052-7 3207.1 2625.7 2769.4 2916.8 3067.9 3222.8 2639.9 2784.0 2931.8 3083-3 3238-4 2654.2 2798.6 2946.8 3098.6 3254-2 2668.4 2813.3 2961.8 3114.0 3269.9 2682.8 2827.9 2976.8 3"29.4 3285-7 2697.1 2842.7 2991.9 3 "44-9 330"-6 2711.5 2857.4 3007.1 3160.4 33" 7-4 31 32 33 34 35 36 37 38 39 40 3333-3 3494-4 3^59-3 3827.8 4000.0 3349-3 3510.8 3675-9 3844-8 4017.4 3365-3 3527-" 3692.7 3861.9 4034-9 3381-3 3543-5 3709-4 3879-1 4052.4 3397-3 3559-9 3726.2 3896.2 4069.9 34"3-4 3576-4 3743-1 3913-4 4087.5 3429.6 3592-9 3759-9 3930.7 4105. 1 3445-7 3609-4 3776-8 3947-9 4122.8 3461.9 3626.0 3793-8 3965-3 4140.4 3478-2 3642.6 3810.8 3982.6 4158.2 36 37 38 39 40 41 42 43 44 43 4"75-9 4355-6 4538-9 4725-9 4916.7 4"93-7 4373-7 4557-4 4744.8 4935-9 4211.6 439"-9 4576-0 4763-8 4955-3 4229.4 4410.2 4594-6 4782.8 4974-6 4247-3 4428.4 4613-3 4801.8 4994.0 4265.3 4446.8 4631.9 4820.8 50"3.4 4283-3 4465.1 4650.7 4839.9 5032.9 430"-3 4483-5 4669.4 4859.1 5052.4 43"9-3 4501.9 4688.2 4878.2 5071.9 4337-4 4520-4 4707.1 4897.4 509" -5 41 42 43 44 45 46 47 48 49 5111.1 5309-3 55"-" 5716-7 5130.8 5329-3 553"-5 5737-4 5"5o-4 5349-3 55S"-9 5758-2 5170.2 5369-4 5572-4 5779-1 5189.9 5389-6 5592-9 5799-9 5209.7 5409.7 56"3.4 5820.8 5229.6 5429.9 5634.0 5841.8 5249.4 5450-2 5654-6 5862.8 5269-3 5470-4 55Z5-3 5883.8 5289-3 5490.8 5695-9 5904.8 46 47 48 49 .1 .3 .3 .4 .5 .6 .7 .8 .9 27 S(6 + S s) 34 TABLE III. LEVEL SECTIONS. Base 14 feet. Slope H to 1. Quantities in cu. yds. for 50 ft. in length. Center Height. .1 .2 .3 .4 .5 .6 .7 .8 .9 Center Height, .0 2.6 5-3 8.0 10.8 13-7 16.6 19-5 22.5 25-6 I 28.7 31-9 35-1 38-4 41-7 4S-I 48.6 52.1 55-7 59-3 I 2 63.0 66.7 70.5 74-3 78.2 82.2 86.2 90.3 94-4 98-S 2 3 102.8 107-1 1 1 1. 4 115-8 120.3 124.8 129-3 134.0 138.6 143-4 3 4 1 48. 1 153-0 157-9 162.8 167.9 172.9 178.0 183.2 188.4 193-7 4 5 199.1 204.5 209.9 215.4 221.0 226.6 232.3 238.0 243-8 249-7 5 6 255.6 261.5 267.5 273.6 279.7 285.9 292.1 298.4 304-7 311.1 6 7 317-6 324-1 330-7 337-3 344-0 350.7 357-5 364-3 371-2 378-2 7 8 385-2 392.3 399-4 406.5 413-8 421. 1 428.4 435-8 443-3 450.8 8 9 458-3 466.0 473-6 481.4 489.1 497.0 504-9 512.8 520.9 528.9 9 lO 537-0 545-2 553-4 561-7 570.1 578-5 586.9 595-4 604.0 612.6 10 n 621.3 630.0 638.8 647-7 656.6 665.5 674.5 683-6 692.7 701.9 II 12 711. 1 720.4 729.7 739-1 748.6 758-1 767-7 777-3 787.0 796.7 12 13 806.5 816.3 826.2 836.2 846.2 856.3 866.4 876.5 886.8 897-1 13 14 907.4 917-8 928.3 938-8 949-3 960.0 970.6 981.4 992.1 1003.0 14 15 1013.9 1024.8 1035-9 1046.9 1058.0 1069.2 1080.4 1091.7 1 103. 1 1114-5 15 i6 1125.9 "37-4 I 149.0 I 160.6 1172-3 1 184.0 1 195.8 1207.7 1219.6 1231.5 16 I? 1243-5 1255.6 1267.7 1279.9 1292. 1 1304.4 1316.7 1329-1 1341.6 1354-1 17 i8 1366.7 1379-3 1392.0 1404.7 1417-5 1430-3 1443-2 1456.2 1469.2 1482.3 18 19 1495-4 1508.5 1521.8 1535-1 1548.4 1561.8 1575-3 1588.8 1602.3 1616.0 19 20 1629.6 1643.4 1657-1 1671.0 1684.9 1698.8 1712.9 1726.9 1 741.0 1755-2 20 21 1769.4 1783-7 1 798. 1 1812.5 1826.9 1841.4 1856.0 1870.6 1885.3 1900.0 21 22 19 14. 8 1929.7 1944-6 1959-5 1974-5 1989.6 2004.7 2019.9 2035.1 2050.4 22 23 2065.7 2081. 1 2096.6 2112.1 2127.7 2143-3 2159.0 2174-7 2190.5 2206.3 23 24 2222.2 2238.2 2254.2 2270.3 2286.4 2302.5 2318.8 2335-1 2351-4 2367.8 24 25 2384-3 2400.8 2417-3 2434.0 2450.6 2467.4 2484.1 2501.0 2517-9 2534-8 25 26 2551-9 2568.9 2586.0 2603.2 2620.4 2637.7 2655.1 2672.5 2689.9 2707.4 26 27 2725.0 2742.6 2760.3 2778.0 2795.8 2813.7 2831.6 2849.5 2867.5 2885.6 27 28 2903.7 2921.9 2940. 1 2958.4 2976.7 2995-1 3013-6 3032.1 3050-7 3069.3 28 29 3088.0 3106.7 3125-5 3144-3 3163-2 3182.2 3201.2 3220.3 3239-4 3258.5 29 30 3277-8 3297-1 3316-4 3335-8 3355-3 3374-8 3394-3 3414.0 3433-6 3453-4 30 31 3473-1 3493-0 3512.9 3532-8 3552-9 3572-9 3593-0 3613-2 3633-4 3653-7 31 32 3^Z4-' 3694-5 3714-9 3735-4 3756-0 3776-6 3797-3 3818.0 3838.8 3859-7 32 33 3880.6 3901.5 3922.5 3943-6 3964-7 3985-9 4007.1 4028.4 4049.7 4°7i-i 33 34 4092.6 4114.1 4135-7 4157-3 4179-0 4200.7 4222.5 4244.3 4266.2 4288.2 34 35 4310.2 4332.3 4354-4 4376-5 4398.8 4421. I 4443-4 4465.8 4488.3 4510.8 35 36 4533-3 45560 4578.6 4601.4 4624.1 4647.0 4669.9 4692.8 4715-9 4738-9 36 37 4762.0 4785.2 4808.4 4831-7 4855-1 4878-5 4901.9 4925.4 4949.0 4972-6 37 38 4996.3 5020.0 5043-8 5067-7 5091.6 5115-5 5139-5 5163.6 S187-7 5211.9 38 39 5236.1 5260.4 5284.7 5309-1 5333-6 5358-1 5382.7 5407-3 5432.0 5456-7 39 40 5481.5 5506.3 5531-2 5556.2 5581.2 5606.2 5631-4 5656.5 5681.8 5707-1 40 41 5732-4 5757-8 5783-3 5808.8 5834-3 5860.0 5885.6 5911-4 5937-1 5963-0 41 42 5988.9 6014.8 6040.9 6066.9 6093.0 6119.2 6145.4 6171.7 6198.1 6224.5 42 43 6250.9 6277.4 6304.0 6330.6 6357-3 6384.0 6410.8 6437-7 6464.6 6491-5 43 44 6518.5 6545.6 6572.7 6599-9 6627.1 6654.4 6681.7 6709.1 6736.6 6764.1 44 45 6791.7 6819.3 6847.0 6874.7 6902.5 6930-3 6958.2 6986.2 7014.2 7042.2 45 46 7070.4 7098.5 7126.8 7155-1 7183-4 7211.8 7240.3 7268.8 7297-3 7326.0 46 47 7354-6 7383-4 7412. 1 7441.0 7469-9 7498.8 7527-9 7556-9 7586.0 7615.2 47 48 7644.4 7673-7 7703-1 7732-5 7761-9 7791-4 7821.0 7850.6 7880.3 7910.0 48 49 7939-8 7969.7 7999.6 8029.5 8059.5 8089.6 8119.7 8149.9 8180.1 8210.4 49 .1 .2 .3 .4 .5 .6 .7 .8 .9 S = ^c(b + sc) TABLE III. LEVEL SEOTIONS. Base 16 feet. Slope 1 to 1. 35 Quantities in cu. yds. for 50 ft. in length. Center Height. .1 .2 ,3 .4 .5 .6 .7 .8 .9 Center Height. .0 3-0 6.0 9-1 12. 1 15-3 18.4 21.6 24.9 28.2 I 2 3 4 5 31-5 66.7 105.6 148.1 194.4 34-8 70.4 109.6 152.6 199-3 38-2 74.1 113.8 157-1 204.1 41.6 77-9 117.9 161.6 209.1 45-1 81.8 122.1 166.2 214.0 48.6 85.6 126.4 170.8 219.0 52-1 89.6 130-7 175-5 224.0 55-7 93-5 135-0 180.2 229.1 59-3 97-5 139-3 184.9 234-1 63-0 101.5 143-7 189.6 239-3 I 2 3 4 5 6 7 8 9 10 244.4 298.1 3SS-6 416.7 481-5 249.6 303-7 361-5 423.0 488.2 254-9 309-3 367-5 429-3 494.9 260.2 315-0 373-5 435-7 501.6 265-5 320.7 379-6 442.1 508.4 270.8 326.4 385-6 448.6 515-3 276.2 332-r 391.8 455-1 522.1 281.6 337-9 397-9 461.6 529-1 287.1 343-8 404.1 468.2 536.0 292.6 349-6 410.4 474-8 543-0 6 7 8 9 10 II 12 13 14 15 55°-° 622.2 698.1 777.8 861. 1 629.6 705.9 785.9 869.6 564.1 637-1 713-8 794.1 878.2 644.6 721.6 802.4 886.8 578.4 652.1 729.6 810.7 895-5 585.6 659-7 737-5 819.0 904.2 592.9 667.3 745-5 827-3 912.9 600.2 675.0 753-5 835-7 921.6 607-5 682.7 761.6 844.1 930-4 614.8 690.4 769.6 852.6 939-3 11 12 13 14 15 i6 17 i8 19 20 948.1 1038.9 II33-3 1231-5 1333-3 957-1 1048.2 1 143-0 1241-5 1343-7 966.0 1057-5 1152.7 1 25 1. 6 1 354- 1 97S-0 1066.8 1162.4 1261.6 1364.6 984.0 1076.2 1 1 72.1 1271.8 I375-I 993- > 1085.6 1181.9 1281.9 1385.6 1002. 1 1095.1 1191.8 1292.1 1396.2 1011.3 1104.6 1201.6 1302.4 1406.8 1020.4 1114.1 1211.6 1312.7 1417-5 1029.6 1123.7 1221.5 1323.0 1428.2 16 17 18 19 20 21 22 23 24 25 1438.9 1548.1 1661.1 1777.8 1898. 1 1449.6 1559-3 1672.6 1789.6 1910.4 1460.4 1570-4 1684.1 1801.6 1922.7 1471-3 1581.6 1695.7 1813.5 1935-0 1482.1 1592.9 1707-3 1825.5 1947-3 1493- 1 1604.2 1719.0 1837-5 1959-7 1504.0 1615.5 1730.7 1849.6 1972.1 1515.0 1626.8 1742.4 1861.6 1984.6 1526.0 1638.2 1 754- 1 1873-8 1997.1 1649.6 1765.9 1885.9 2009.6 21 22 23 24 25 26 27 28 29 3° 2022.2 2150.0 2281.5 2416.7 2555.6 2034.8 2163.0 2294.8 2430.4 2569.6 2047.5 2176.0 2308.2 2444.1 2583.8 2060.2 2189.1 2321.6 2457.9 2597.9 2072.9 2202. 1 2335-1 2471.8 2612.1 2085.6 2215.3 2348.6 2485.6 2626.4 2098.4 2228.4 2362.1 2499.6 2640.7 2111.3 2241.6 2375-7 2513-5 2655.0 2124.1 2254.9 2389-3 2527-5 2669.3 2137.1 2268.2 2403.0 2541-5 2683.7 26 27 28 29 30 31 32 33 34 35 2698.1 2844.4 2994.4 3148. 1 3305-6 2712.6 2859-3 3009.6 3163-7 3321-5 2727.1 2874.1 3024.9 3179-3 3337-5 2741.6 2889.1 3040.2 3195-0 3353-5 2756-2 2904.0 3055-5 3210.7 3369-6 2770.8 2919.0 3070.8 3226.4 3385-6 2785-5 2934.0 3242.1 3401.8 2800.2 2949.1 3101.6 3257-9 3417-9 2814.9 2964. I 3117-1 3273-8 3434-1 2829.6 2979-3 3132-6 3289.6 3450-4 31 32 33 34 35 36 37 38 39 40 3466.7 3631-5 3800.0 3972.2 4148.1 3483-0 3648.2 3817.1 3989.6 4165.9 3499-3 3664.9 3834-1 4007.1 4183.8 3515-7 3681.6 3851.3 4024.6 4201.6 3S32-I 3698.4 3868.4 4042.1 4219.6 3548.6 4059.7 4237-5 3565-1 3732-1 3902.9 4077-3 4255-5 3581.6 3749-1 3920.2 4095.0 4273-5 3598-2 3766.0 3937-5 4112.7 4291.6 3614-8 3783-0 3954-8 4130.4 4309-6 36 37 38 39 40 41 42 43 44 45 4327.8 4511.1 4698.2 4888.9 5083-3 4345-9 4529.6 4717.1 4908.2 5103.0 4364.1 4548.2 4736.0 4927.5 5122.7 4382.4 4566.8 475S-0 4946.8 5142.4 4400.7 4585.5 4774.0 4966.2 5162.2 4419.0 4604.2 4793-1 4985.7 5182.0 4437-3 4622.9 4812.2 5005-1 5201.8 4455-7 4641.6 4831-3 5024.6 5221.7 4474-1 4660.4 4850.5 5044.2 5241.6 4492.6 4679-3 4869-7 5063-7 5261.5 41 42 43 44 45 46 47 48 49 5281.5 5483-3 5688.9 5898-1 5301 -5 5503-7 5709.6 5919-3 5321.6 5524-1 5730-4 5940.4 5341-7 5544-6 5961.6 5361.8 5565." 5772-1 5982.9 5381-9 5585-6 5793-1 6004.2 5402.1 5606.2 5814.0 6025.5 5422-4 5626.8 6046.8 5442-7 5647-5 5856.0 6068.2 5463-0 5668.2 5877-1 6089.6 46 47 48 49 .1 .2 .3 .4 .5 .6 .7 .8 ,9 fif = ||c(6 + sc) 36 TABLE III. LEVEL SECTIONS. Base 16 feet. Slope 1^ to 1. Quantities in cu. yds. for 50 ft. in length. Center Height. o .1 .3 .3 .4 .5 .6 .7 .8 .9 Center Height. .0 3-0 6.0 9-1 12.3 15-5 18.8 22.1 25-5 28.9 I 2 3 4 5 32-4 70.4 II3-9 163.0 217.6 36.0 74-5 118.5 168.2 223.4 39-6 78.6 123-3 173-4 229.2 43-2 82.8 128.0 178.8 235-1 46.9 87.1 132.9 184. 1 241.0 50-7 91.4 247.0 54-5 95-8 142.7 195. 1 253.0 58-4 100.2 '47-7 200.6 259.1 62.3 104.7 152.7 206.2 265.3 66.3 109.3 "57.8 211.9 27«-5 X 2 3 4 5 6 7 8 9 lO 277.8 343-S 414.8 491.7 574-1 284.1 35°-4 422.2 499-7 582.6 290.5 357-3 429.7 507.7 591.2 296.9 364-3 437-3 515-8 599-9 303-4 371-4 444.9 524.0 608.6 310.0 378-5 452.5 532.2 617.4 316.6 385-6 460.3 540-4 626.2 323-2 392.8 468.0 548.8 635-1 329-9 400.1 475.9 557-1 644.0 336.7 407.4 483.7 565.6 653.0 6 7 8 9 10 II 12 13 14 15 662.0 755-6 854-6 959-3 1069.4 671. 1 765.2 864.8 970.0 1080.8 680.3 774-9 980.9 1092. 1 689.5 784-7 885.4 991.7 1 103.6 698.8 & 1002.7 1115.1 708.1 804.4 906.2 1013.7 1126.6 717-5 814.3 916.7 1024.7 1138.2 726.9 824.3 927-3 1035.8 1 149.9 736.4 834-4 937-9 1047.0 1161.6 746.0 844-5 948-5 1058.2 "73-4 II 12 13 14 15 i6 17 i8 19 20 1185.2 1306.5 1433-3 1565-7 1703-7 "97-1 1318.9 1446.3 1579-3 1717.8 1209.0 1331-4 1459-4 1592.9 1732.0 1221.0 1344.0 1606.5 1746.2 1233.0 1356.6 1485.6 1620.3 1760.4 1245.1 1369.2 1498.8 1634.0 1774.8 1257-3 1381.9 1512.1 1647.9 1789.1 1269.5 1394-7 1661.7 1803.6 1281.8 1407-5 1538-8 1675.7 1818.1 1294.1 1420.4 1552-2 1689.7 1832.6 16 17 18 19 20 21 22 23 24 25 1847-2 1996.3 2150.9 2311-1 2476.9 1861.9 201 1.5 2166.7 2327-4 2493-7 1876.6 2026.8 2182.5 2343-8 2510.7 1891.4 2042.1 2198.4 2360.2 2527.7 1906.2 2057-5 2214.3 2376-7 2544-7 1921. 1 2072.9 2230.3 2393-3 2561.8 1936.0 2088.4 2246.4 2409.9 2579.0 1951.0 2104.0 2262.5 2426.5 2596.2 1966.0 2119.6 2278.6 2443-3 2613.4 1981.1 2135-2 2294.8 2460.0 2630.8 21 22 23 24 25 26 27 28 29 30 2648.1 2825.0 3007.4 3195-4 3388.9 2665.6 2843.0 3026.0 3214-5 3408.5 2683.1 2861.0 3044.6 3233-6 3428.3 2700.6 2879.1 3063.2 3252-8 3448.0 2718.2 2897-3 3081.9 3272.1 3467-9 2735-9 2915.5 3100.7 3291.4 3487-7 2753-6 2933-8 3"9-5 3310-8 3507-7 2771.4 2952.1 3138-4 3330.2 3527-7 2789.2 2970.5 3157-3 3349-7 3547-7 2807.1 2988.9 3176.3 3369.3 3567.8 26 27 28 29 30 31 32 33 34 35 3588.0 3792.6 4002.8 4218.5 4439.8 3608.2 3813-4 4024.1 4240.4 4462.2 3628.4 3834-2 4045-5 4262.3 4484-7 3648.8 3855-1 4066.9 4284.3 4507-3 3669.1 3876.0 4088.4 4306.4 4529.9 3689.6 3897-0 4110.0 4328.5 4552.5 3710.1 3918.0 4131.6 4350.6 4575-3 3730-6 3939-1 4153-2 4372.8 4598.0 3751-2 3960-3 4174.9 4395-1 4620.9 3771-9 3981-5 4196.7 4417.4 4643-7 31 32 33 34 35 36 37 38 39 40 4666.7 4899.1 5137-° 5380.6 5629.6 4689.7 4922.6 5161.1 5405-2 5654-8 4712.7 4946.2 5185.3 5429-9 5680.1 4735-8 4969.9 5209-5 5454-7 5705-4 4759 -o 4993.6 5233-8 5479-5 S730-8 4782.2 5017-4 5258-1 5504-4 5756-2 4805.4 5041.2 5282.5 5529-3 5781.7 4828.8 5065.1 5306.9 5554-3 5807-3 4852.1 5089.0 5331.4 5579-4 5832-9 4875.6 5113.0 5356.0 5604.5 5858.5 36 37 38 39 40 41 42 43 44 45 5884.3 6144.4 6410.2 6681.5 6958-3 5910.0 6170.8 6437-1 6708.9 6986.3 5935-9 6197.1 6464.0 6736.4 7014.4 5961-7 6223.6 6491.0 6764.0 7042.5 5987-7 6250.1 6518.0 6791.6 7070.6 6013.7 6276.6 6545-1 6819.2 7098.8 6039.7 6303.2 6846.9 7127.1 6065.8 6329.9 6599.5 6874-7 7155-4 6092.0 6356.6 6626.8 6902.5 7183-8 6118.2 6383.4 6654.1 6930.4 7212.3 41 42 43 44 45 46 47 48 49 7240.7 7528.7 7822.2 8121.3 7269.3 7557-8 7851.9 8151.5 7297.9 7881.6 8181.8 7616.2 7911.4 8212. 1 7355-3 7645-4 7941.2 8242.5 7384.0 7674-8 7971. I 8272.9 7412.9 7704.1 8001.0 8303-4 7441-7 7733-6 8031.0 8334-0 7470.7 8061.0 8364.6 7499-7 7792.6 8091. I 8395.2 46 47 48 49 .1 .2 .3 .4 .5 .6 .7 .8 .9 S=pc(6 + sc) TABLE III. LEVEL SECTIONS. Base 20 feet. Slope 1 to 1. 37 Quantities in cu. yds. for 50 ft. in length. Center Height. .1 .2 .3 .4 .5 .6 .7 .8 .9 Center Height. .0 3-7 7-5 11-3 15-1 19.0 22.9 26.8 30.8 34-8 I 38-9 43-0 47-1 5J-3 55-5 59-7 64.0 68.3 72.7 77.1 I 2 81.5 85-9 90.4 95-0 99-6 104.2 108.8 "3-5 118.2 123.0 2 3 127.8 132.6 '37-5 142.4 147-3 152-3 157.3 162.4 167.5 172.6 3 4 177.8 183.0 188.2 193-5 198.8 204.2 209.6 215.0 220.4 225.9 4 5 231-5 237-1 242.7 248.3 254-0 259.7 265.5 271-3 277.1 283.0 5 6 288.9 294.8 300.8 306.8 312.9 319.0 325.1 331-3 337.5 343.7 6 7 350.0 356.3 362.7 369.1 375-5 381.9 388.4 395-0 401.6 408.2 7 8 414-8 421.5 428.2 435 -o 441.8 448.6 455-5 462.4 469.3 476.3 8 9 483-3 490.4 497-5 504.6 511.8 519-0 526.2 533-5 540.8 548.2 9 10 S55-6 563.0 570-4 577-9 585-5 593-1 600.7 608.3 616.0 623.7 10 II 631-5 639-3 647.1 655.0 662.9 670.8 678.8 686.8 694.9 703.0 II 12 711. 1 719-3 727.5 735-7 744.0 752.3 760.7 769.1 777.5 785.9 12 13 794-4 803.0 811.6 820.2 828.8 837-5 846.2 855.0 863.8 872.6 13 14 S81.S 890.4 899-3 908.3 917-3 926.4 935-5 944.6 953.8 963.0 14 15 972.2 981-5 990.8 1000.2 1009.6 1019.0 1028.4 1037-9 1047.5 1057.1 15 i6 1066.7 1076.3 1086.0 1095.7 1105.5 1115-3 1125.1 1135.0 1144.9 1154.8 16 17 1 164.8 1174.8 1184.9 1195.0 1205. I 1215.3 1225.5 1235-7 1246.0 1256.3 17 18 1266.7 1277. 1 1287.5 1297.9 1308.4 1319-0 1329.6 1340.2 1350.8 1361.5 18 19 1372.2 1383-0 1393-8 1404.6 "415-5 1426.4 1437-3 1448.3 1459.3 1470.4 19 20 1481-5 1492.6 1503-8 1515.0 1526.2 1537-5 1548.8 1560.2 1571.6 1583.0 20 21 1594.4 1605.9 1617.5 1629. I 1640.7 1652.3 1664.0 1675.7 1687.5 1699-3 21 22 17H.1 1723.0 1734-9 1746.8 1758.8 1770.8 1782.9 1795.0 1S07.1 1819-3 22 23 1831-5 1843-7 1856.0 1868.3 1880.7 1 893. 1 1905-5 1917.9 1930.4 1943.0 23 24 1955.6 1968.2 1980.8 1993-5 2006.2 2019.0 2031.8 2044.6 2057.5 2070.4 24 25 2083.3 2096.3 2109.3 2122.4 2135-5 2148.6 2161.8 2175.0 2188.2 2201.5 25 26 2214.8 2228.2 2241.6 2255.0 2268.4 2281.9 2295-5 2309.1 2322.7 2336-3 26 27 2350.0 2363-7 2377-5 2391-3 2405. 1 2419.0 2432-9 2446.8 2460.8 2474.8 27 28 2488.9 2503.0 2517.1 2531-3 2545- 5 2559-7 2574.0 2588.3 2602.7 2617. 1 28 29 2631.5 2645.9 2660.4 2675.0 2689.6 2704.2 2718.8 2733.5 2748.2 2763.0 29 30 2777.8 2792.6 2807.5 2822.4 2837-3 2852.3 2867.3 2882.4 2897.5 2912.6 30 31 2927.8 2943-0 2958.2 2973-5 2988.8 3004.2 3019.6 30350 3050.4 3065.9 31 32 3081.5 3097-1 3112.7 3128.3 3144.0 3159-7 3175-5 3191.3 3207.1 3223-0 32 33 3238-9 3254.8 3270.8 3286.8 3302.9 3319-0 3335- 1 3351-3 3367.5 3383-7 33 34 3400.0 3416.3 3432-7 3449-1 3465-5 3481.9 3498.4 3515.0 3531.6 3548.2 34 35 3564.8 3581-5 3598-2 3615.0 3631-8 3648.6 3665-5 3682.4 3699.3 3716.3 35 36 3733-3 3750-4 3767-S 3784.6 3801.8 3819.0 3836.2 3853.5 3870.8 3888.2 36 37 3905.6 3923.0 3940.4 3957-9 3975-5 3993-1 4010.7 4028.3 4046.0 4063.7 37 38 4081.5 4099-3 4117.1 4135-0 4152-9 4170.8 4188.8 4206.8 4224.9 4243.0 38 39 4261.1 4279-3 4297-5 4315-7 4334-0 4352-3 4370-7 4389.1 4407.5 4425.9 39 40 4444-4 4463.0 4481.6 4500.2 4518.8 4537-5 4556.2 4575.0 4593.8 4612.6 40 41 4631-5 4650.4 4669.3 4688.3 4707-3 4726.4 4745-5 4764.6 4783.8 4803.0 41 42 4822.2 4841.5 4860.8 4880.2 4899.6 4919.0 4938.4 4957.9 4977.5 4997-1 42 43 5016.7 5036-3 5056.0 5075-7 5095-5 5115-3 5135.1 5'55.o 5174.9 5194.8 43 44 5214.8 5234.8 5254-9 5275.0 5295-1 5315-3 5335-5 5355.7 537^-2 5396.3 44 45 5416.7 5437-1 5457-5 5478-0 5498-5 5519.0 5539-6 5560.2 5580.8 5601.5 45 46 5622.2 5643.0 5663-8 5684.6 5705-5 5726.4 5747-3 5768.3 5789.3 5810.4 46 47 5831-5 5852.6 5873-8 5895-0 5916.2 5937.5 5958.8 5980.2 6001.6 6023.0 47 48 6044.4 6065.9 6087.5 6109. 1 6130.7 6152.3 6174.0 6195.7 6217.5 6239.3 48 49 6261. 1 6283.0 6304.9 6326.8 6348.8 6370.8 6392.9 6415.0 6437.1 6459.3 49 .1 .2 .3 .4 .5 .6 .7 .8 .9 S=pc(6 + sc) 38 TABLE III. LEVEL SEOTIONS. Base 20 feet. Slope 1^ to 1. Quantities in cu. yds. for 50 ft. in length.. Center Height. .1 .2 .3 .4 .5 .6 .7 .8 .9 Center Height. .0 3-7 7-5 11.4 15-3 19.2 23-2 27-3 31-4 35-6 ' I 2 3 4 5 39-8 85.2 136. 1 192.6 254.6 44.1 90.0 141-5 198.5 261. 1 48-4 94.9 147.0 204.6 267.7 52.8 99.9 152.5 210.6 274.3 57-3 104.9 158.0 216.7 281.0 61.8 IIO.O 163-7 222.9 287.7 66.4 115. 1 169-3 229.1 294.5 71.0 120.2 175.1 235.4 301.4 7S-7 125-5 180.9 241.8 308.3 80.4 130.8 186.7 248.2 315-2 I 2 3 4 5 6 7 8 9 lO 322.2 395-4 474.1 648.1 329.3 403.0 482.2 567.1 657.4 336.4 410.7 490.5 666^8 343.6 418.4 498.8 584-7 676.2 350.8 426.2 507.1 593-6 685.6 358-1 434.0 602.5 695.1 365-4 441.9 524.0 611.6 704-7 372.8 449.9 620.6 714-3 380.3 457-9 541.0 629.7 724.0 387.8 466.0 549-7 638.9 733-7 6 7 8 9 10 II 12 13 14 15 743-5 844.4 950-9 1063.0 U80.6 753-4 854.8 961.9 1074.5 1192.6 763.3 865.3 972.9 1086.0 1204.7 773-2 875.8 984.0 1097.7 1216.9 783.2 886.4 995.1 1109.3 1229. 1 793-3 897-0 1006.2 1121.1 1241.4 803.4 907-7 1017.5 1132.9 1253.8 813.6 918.4 1028.8 1144.7 1266.2 823.8 929.2 1040. 1 1156.6 1278.6 834.1 940.0 1051-5 1168.5 ■1291. 1 II 12 13 14 15 i6 17 i8 19 20 1303-7 1432.4 1566.7 1706.5 1851.9 1316.3 1445.6 1580.4 1720.8 1866.7 1329.0 1458.8 1594.2 1735-1 1881.6 1341-7 1472.1 1 608.0 1749-5 1896.5 1354-S 1485.4 1621.9 1764.0 1911.6 1367-4 1498.8 1635-9 1778.5 1926.6 1380.3 1512.3 1649.9 1793.0 1941.7 1393.2 1525.8 1664.0 1807.7 1956.9 1406.2 1539.4 1678.1 1822.3 1972.1 1419.3 1553.0 1692.2 1837.1 1987.4 16 17 18 19 20 21 22 23 24 25 2002.8 2159-3 2321.3 2488.9 2662.0 2018.2 2175.2 2337-8 2506.0 2679.7 2033.6 2191.2 2354-4 2523.1 2697-3 2049. 1 2207.3 2371.0 2540.2 2715.1 2064.7 2223.4 2387-7 2557-5 2732.9 2080.3 2239.6 2404.4 2574-8 2750.7 2096.0 2255-8 2421.2 2592.1 2768.6 2111.7 2272.1 2438.0 2609.5 2786.5 2288.4 2454.9 2627.0 2804.6 2143-4 2304.8 2471.9 2644-5 2822.6 21 22 23 24 25 26 27 28 29 30 2840.7 3025.0 3214.8 3410.2 3611.1 2858.9 3043.7 3234.1 3430.0 3631.5 2877.1 3062.5 3253-4 3449-9 3652.0 2895.4 3081.4 3272.8 3469.9 3672.5 2913.8 3100.3 3292.3 3489.9 3693.0 2932.2 3119-2 3311-8 3510.0 3713-7 2950.6 3138-2 3331.4 3530.1 3734-3 2969.1 3157.3 3351.0 3550-2 3755-1 2987.7 3176-4 3370.7 3570.5 3775-9 3006.3 3195.6 3390-4 3590.8 3796.7 26 27 28 29 30 31 32 33 34 35 3817.6 4029.6 4247.2 4470.4 4699.1 3838.5 4051. I 4269.3 4493.0 4722.2 3859.6 4072.7 4291.4 4515-7 4745-5 3880.6 4094.3 4313-6 4538.4 4768.8 3901-7 4116.0 4335-8 4561.2 4792.1 3922.9 4137-7 4358.1 4584.0 4815.5 3944.1 4159.5 4380.4 4606.9 4839-0 3965-4 4181.4 4402.8 4629.9 4862.5 3986.8 4203.3 4425-3 4652.9 4886.0 4008.2 4225.2 4447-8 4676.0 4909.7 31 32 33 34 35 36 37 38 39 4° 4933-3 5173-1 5418-S 5669.4 5925-9 4957.1 5197-4 5443-4 5694.8 5951-9 4980.9 5221.8 5468.3 5720.3 5977-9 5004.7 5246.2 5493-2 5745-8 6004.0 5028.6 5270.6 5518.2 5771-4 6030.1 5052-5 5295.1 5543.3 5797.0 6056.3 5076.6 5319-7 5568.4 5822.7 6082.5 5100.6 5344-3 5593-6 5848.4 6108.8 5124.7 5369.0 5618.8 5874.2 6135.1 5148.9 5393-7 5644.1 5900.0 6161.5 36 37 38 39 40 41 42 43 44 45 6188.0 6455.6 6728.7 7007.4 7291.7 6214.5 6482.6 6756-3 7035-6 7320.4 6241.0 6509.7 6784.0 7063.8 7349-2 6267.7 6536.9 6811.7 7092. 1 7378.0 6294.3 6564.1 6839-5 7120.4 7406.9 6321.1 6591-4 6867.4 7148.8 7435-9 6347-9 6618.8 6895.3 7177-3 7464.9 6374-7 6646.2 6923.2 7205.8 7494.0 6401.6 6673.6 6951-2 7234-4 7523-1 6428.5 6701. I 6979-3 7263.0 7552.3 41 42 43 44 45 46 47 48 49 7581.5 7876.9 8177.8 8484-3 7610.8 7906.7 8208.2 8515.2 7640.1 7936.6 8238.6 8546.2 7669.5 7966.5 8269.1 8577-3 7699.0 7996.6 8299.7 8608.4 8026^6 8330.3 8639.6 7758-0 8056.7 8361.0 8670.8 7787.7 8086.9 8391-7 8702.1 7817-3 8117.1 8422.5 8733-4 7847.1 8147.4 8453-4 8764.8 46 47 48 49 .1 .2 .3 .4 .5 .6 .7 .8 .9 S = ^cCb + so)