TABLE OF CUBIC YARDS IN LENGTHS OF 100 FEET. ADAPTED ESPECIALLY TO THE CALCULATION OF EAETH WOKK BY THE METHOD OF ATEKAGING E>'D AREAS. Contents of Column "A" are for the integers in column headed "Area, Square Feet." Contents of Column "B" are for the same integers plus 0.5 square foot. Contents for lengths greater or less than 100 are obtained by simple proportion, thus : 125 sq. ft. for length of 20 &.=j%%=\ of 463.0 cu. yds.; the contents for 125 sq. ft.=92.6 cu. yds. COPYRIGHT 1885 BY S. B. FISHER. Contppts, Coutents, Contents, Coiitfiiis, Contents, Ch. Yds. I II. 1 Us. Cn. Yd^. *■ ^ Cn. Yds. «3 £ i. Cn. Yds. A. B. ^ qO A. B. (Ml A. B. A. B. A. B. 1.8 100 370.4 372.2 200 740.7 742.6 300 1111,1 1113.0 400 1481.5 1483 3 1 3.7 5.6 1 374.1 375.9 1 744.4 746.3 1 1114.8 1 116 7 1 1485.2 1487.0 2 7 4. 2 377.8 379.6 2 748.1 750 0 2 1118.5 1120.4 2 1488.9 1490.7 3 11.1 13.0 3 381.5 383.3 3 751.9 753.7 3 1122.2 1124.1 3 1492.6 1494 4 4 14.8 16.7 4 385.2 387.0 4 755.6 757.4 4 1 125. li 1 127 8 4 1496.3 1498.1 5 18.5 5 388.9 .390.7 5 759.3 761.1 6 1129.(; 1131.5 6 1500.0 1501.8 6 22.2 24.1 6 392.6 394,4 6 763 0 761.8 6 1133.3 1 135.2 6 1503 7 1505.0 7 2.S.C 27.8 7 396 3 39S.1 7 766 7 768.5 7 1137.1 1138.9 7 1507.4 1509.3 8 29.6 31.5 8 400 0 401.8 8 770.4 772 2 8 1140.7 1142. 1 8 1511 1 1513.0 9 33.5 35.2 9 403.7 405.6 9 774.1 775.9 9 1144.4 1146.3 9 1514.8 1516.7 10 37. C 38.9 110 407.4 409.3 2K' 777.8 779.6 310 1148 1 1 150.11 41i. 185.3.7 1857.4 1861.1 1864.8 1 868.5 5 1870.4 1872.2 6 1874.1 1877.8 1881.5 1885.2 1888.9 1892.6 1896.3 1900.0 1903.7 1907.4 1911.1 1914.8 1918.5 1922.2 1925,9 1929.6 1933.3 3 1937.0 1940.7 1944.4 1948.1 1951.9 1955.6 1959.3 1963.0 1966.7 1970.4 1974.1 1977.8 1981.5 B. 1875.9 1879.6 1883.3 1887.0 1890 7 1894.4 1898.1 1901.8 1905.6 1909.3 1913.0 1916.7 1920.1 1924.1 1927.8 1931.5 1935.2 1938.9 1942.6 1946.3 1950.0 1953.7 1957.4 1961.1 1904.8 1968.5 1972.2 1975.9 1979.6 1983 3 1985.2 1987.0 1988.9 199 1996.3 2000.0 2001.8 2003.7 2 2007.4 2009 ■■ 2011.1 2014.8 2010.7 5 2018.6 "6 2022.2 7 2025.9 8 2029.6 2020.4 2024.1 2027.8 2031.5 2033.3 2035.2 550 2037.0 2038,9 1 2040.7 2 2041.4 2046.3 2050.0 2053. ■2057.4 3 2048.1 4 2051.9 b 20.55.6 6 2059.3 2061 1 7 2003.0 2064 8 5 2000.7 2068.5 9 2070.4 2072.2 56 0 2074.1 1990.7 1994.1 1998.1 2005.0 2013.0 2042.6 2075.9 570 1 2 3 1 2077.8 2079.6 2 2081 5 2083.3 3 2085.2 2087.0 4 2088 9 2090.7 6 2092.6 2094.4 6 2090.3 2098.1 7 2100.0 2101.8 8 2103.7 210.5.0 9 2107.4 2111.1 2118.5 2122-2 4 2125.9 6 2133.3 7 2137.0 2138.9 8 2140.7 9 580 2148.1 590 ] 600 2109.3 2113.0 2114.8 2110.7 2120.4 2124.1 2127.8 2129.6 2131.5 2144 4 2135. 2142.0 2146.3 21.50.0 2151.9 2153.7 2165.6 2157.4 2159.3 2161.1 2163.0 2161.3 5 2106 7 G 2170.4 7 2174.1 8 2177.8 9 2181.5 2168.5 2172.2 2175,9 2179 0 2183.3 185.2 2187.0 2190.7 2188.9 2 2192.6 2194.4 3 2196.3 2198.1 4 2200.0 2201.8 6 2203.7 2205.6 6 2207.4 2209.3 7 2211 1 2213.0 8 2214.8 2216.7 9 2218.5 2220.4 2222.2 2224.1 Contents, Cn. Yds. A. 2224 1 2227.8 2-231.5 2235.2 2233.9 2212.0 2216.3 2250.0 2253 7 22.57.4 2261.1 2264.S 2268.5 2272.2 2275.9 2279.0 2283 3 600 2222.2 112225.9 2j22-29.0 32233.3 412237.0 512240.7 62244.4 7 2248.1 8 2251.9 9 2-255.6 6 10,2259.3 1' 2263 0 2'2206.7 3 2270.4 4 2274.1 5 2277.8 6 2281.5 7|2285 2|2287.0 8 2288 9 2290.7 9 2292.6 2294,4 620 2-296.3 2298.1 1 2300.0 2301.8 2 2303.7 2305,6 3 2307.4 2309.3 4 2311.1 2313.0 5 2314 8 2316,7 6 2318 5'2320.4 7 2322.2' 2324.1 8 2325 9 2327.8 9 2329.6 '233 1.5 630 2333.3 23.35.2 1 2337.0 233S.9 2 2340.7:2312.6 3 2344,4 2346.3 4 2348.1 23-50.0 5 2351.9 2353.7 6 2355-6 2357.4 7 2359.3 2301.1 8 2303.0 2304.8 9 2366.7 2368.5 640 2370.4 2372.2 1 2374.1 2375.9 2 2377.8 2379.0 3 2331.5 2383,3 ■^4 2385.2 2387.0 5 2388.9 2390.7 6 2392.6 2394.4 7 2390.3 239-i.l 8 2400.0 2401.8 9 2403.7 2105.6 650 2407.4 2409.3 1 2411.1 2413.0 2 2414.8 2416,7 3 2418.5 2420.4 4 2422 2 2424 1 5'2425.9|2427 8 6 2429.6,2431.5 7j2433 3 2435.2 8, 2437.0 '2438 9 9 2440.7 1 24 42.0 660 -2444 4 2440.3 l'2448 1 2450.0 2 2151,9 2453,7 3 2456.6 2457.4 4 2459.3 2461.1 5 '2163.0 2464.8 6 2466.7 2468 5 7 2470.4 2472 2 8'2474.1 2475.9 9 2477.8 2479.ii 670 2481.5124X3.3 1 2485.2'2487.0 2 2483.9 '2490.7 3 2192.6'2494.4 4 2 496.3:2498.1 5 2500.0 2501.8 2505.6 2509.3 2513.0 2516.7 2520.4 l'2522.2j2524.1 2 2525.9'2527.8 3 2529.; '263 1.5 412533.3 2535.2 6 2537.0! 25.-i8.9 6 7 8 Comenls, Cu. Yds. A. 503.7 7 2507.4 8 2511.1 9 2514.8 680 2518.5 2540 7 2542.0 2544.4 2516.3 2548 1 2560.0 „ 2551.9 2553.7 69 0 25.55.6'2557.4 25.59.3|2561.1 2503.0 2504.8 2566.7 2568.5 2570,4,2572.2 2574.1 2575.9 2577.8 2579.6 2581.5 2583.3 2585.2:2587.0 2588.9 2590.7 70 0 2592.6 2594.4 2 3 4 5 6 7 S 9 710 1 2 3 7 8 9 720 1 2 3 4 7 8 9 730 6 7 9 r4o 1 2 1 2 3 4 £ 6 7 8 9 76(» 1 700 2-592.6 2594.4 1 2-596.3,2598.1 2600,0 2601.8 2603.7 [2605.6 •2607.4:2609.3 2611.1,2613.0 ■2614.8 2616.7 2618.5 2620,4 8 2622,2 2624.1 2625 9 2627.x 2629 6 2'i31.5 2633 3 2635 2037.0 2638.9 2640.7 2642.6 4 2644,4 2646.3 2648.1 2050.0 G 2651.9 2653.7 2655.6 2657.4 2659.3 2661.1 9 2663.0 2664.8 2066.7 2068.-' 2670.''j2H72.2 2G74.1 267-").9 2677.8 2679.6 _ 2681.5 2633.3 5 2685.2 2087,0 6 2088.9 2690.7 2692.6 2694.4 8 2696,3 2698.1 2700.0-2701.8 2703.7 2705.6 1 '2707.4 2709.3 212711.1 2713.0 3I2714.8 2716.7 4 2718.5 2720.4 5 2722 2 2724.1 2725-9 2727.8 2729.0 2731.5 2733.3 2735.2 ■2737.0 2738.9 2740.7 2742.0 2744.4 2746.3 _ -2748.1 2750.0 3 2751.9 2753.7 4 2756.6 2767.4 2759.3 2701.1 ■2703.0 2704.8 27O6.7I2768.6 2770.4'2772.2 2774.l|2775.9 75 0 2777.8'2779.6 2781.52783.3 2785.2 2787.0 2788.912790.7 792.6'2794.4 . 2796.3 2798.1 6 2800.0 2S01.8 2803.7 12805.6 2807.42809.3 2811.12813.0 2814.8 2816.7 2318.5 2820.4 _ 2822.2 2824.1 3 -2826.9 2827.8 _ -2829 6 2831.5 5 2833.3 -2835.2 6 2837.0 2838 9 7 2840 7 2842.6 8 2844,4 2846.3 9 2848.1 2850.0 7 70' 285 1.9 -2853.7 1 2855.6 '2857.4 2 2869 3 2801.1 3 2863.0 2864.8 4 -2866.7 2868.5 6 2870.4 2872 2 G 2874.1 2876.9 7 2877.8 2879.6 8 -2881.5 2883.3 9 2885.2 2887.0 780 2888.9 2890.7 1 2892.6 -2894.4 2 2896.3 2898.1 3 2900.0 2901.8 4 2903.7 2905.0 6 2907.4 2909 3 6 2911.1 2913 0 7 2914.8 2916.7 8 2918.5 -2920.4 9 2922.2 2924.1 790 29-25.9 2927.8 1 2929.6 2931.5 2 2933.3 2935.2 3 2937.0 2938 9 4 2940.7 2942.6 6 2944.4 2946.3 6 2948.1 2950.0 7 2951.9 2953.7 8 2955.6 2957.4 9 29.59.3 2961.1 800 2963.0 2964.8 1 2 3 4 i 6 7 8 9 82(1 1 2 3 4 5 G 7 8 86 Contents, Cm. Yds. s^i, A. B. 800 2963.0 2964,8 1 2066.7 2968 5 2 2970.4 2972.2 3 -2974.1 2975,9 4 -2977.8 2979.6 5 -2981 5 2983.3 G 2985.2 2987.0 -2988.9 2990.7 8 -2992,6 2994.4 , •29%.3 2998.1 810 3000.0 3001 8 3003.7 3005.6 3007.4 3009.3 3011.1 3013 0 3014.8 3016.7 3018.5 3020.4 6 3022.2 3024.1 3025.9 3027.8 8 3029.6 3031.5 3033.3 3035.2 3037.0 3038.9 3040.7 3042.6 3044.4 3046.3 3048.1 3050.0 3051.9 3053.7 3055.0 3057.4 3059.3 3001.1 3003.0 3004.8 3066 7 3068.5 9 3070.4 3072.2 83 0 3074.1 3075.9 3077.8 3079.6 3081.63083.3 3085.2'3087.0 30:i8.9'3090.7 3092.6 3094.4 3096.3 3098.1 3100.0 3101.8 8 3103.7 3105.0 84(J 1 8 3140. 9 3144.4 85 0 3148.1 3109.3 3113.0 3110.7 3120.4 31-24.1 9 3107.4 3111.1 3114.8 2 3118.5 3 3122.2 4 3125.9 3127.8 5 31-29.6 3131.5 6 3133 3 3135.2 7 3137.0 3138.9 3142,6 3140.3 3150.0 1 3151.9 3153.7 2 3165.0 3157.4 3 3159.3 3101.1 4 3103.0 3164.8 6 3166.7 3168.5 6 3170.4 3172.2 7 3174.1 3176.9 8 3177.8 3179.0 93181.631833 3185.2 3187.0 1 3188,9 3190.7 2 3192.6 3194.4 3 3196.3 3'98.1 4 3200.0 3201.8 6 3203.7 3205.6 6 3207.4 3209.3 7 3211.l'3213.0 8 3214.8|3216 7 9 3218.5 3-220.4 870 322-2.2 3-224.1 1 3225,9 3-2-27.8 2 32.9,6 3-231.5 3 3233.3 3235.2 4 3237.0 3238,9 6 3240 7 3-242.6 6 3244.4 3246.3 7 3248.1 3-250.0 8 3251.9 3253.7 9 3-255.6 3257.4 88 0 3259.3 3261.1 1 3263.0 3264.8 2 3266.7 3268.5 8 3270.4 3272.2 4^3274. 1 3275.9 6 13-277.8 3279.6 6 3281.5 3283.3 7 3285.2 3-287.0 8 3288.9 3290.7 9 329-2.6 3294,4 890 3296.3 3-298.1 3300.0 3301.8 3303.7 3305.6 3 3307.4 3309.3 3311.1 3313.0 3314.8 3816.7 .3318.5 3320.4 7 33-2-2.2 3324.1 8 33z5.9 3327.8 9 3329.6 3331.6 900 3333.3 3335.2 ] 2 3 4 5 6 7 8 9 910 1 2 3 4 5 6 7 8 9 920 1 2 Contents, Cn. Yds. 900 3333.3 3335,2 3337.0 3338.9 3340.7 3342.6 3344.4 3346.3 3348.1 .33.50,0 3351.9 33.53.7 3355.6 3357.4 3359.3 3361.1 3363.0 3364.8 9 3366.7 3368.5 3370 4 3372.2 3374.1 '3375.9 3377.8'3379.6 3381.5 3383.3 3385.2 33x7.0 3383.9 3390.7 6 3392.6 3394.4 3396.3 3398.1 3400.0 3401.8 9 3403 7 3405.6 .3407.4 3409.8 3411.1 3413.0 3414.8 3416.7 313418 5 3420.4 4 ;3422.2 34'24.1 5 3425.9 3427.8 6 3429.6 343 i .5 7 3433.3 3435.2 8 3437.0 3438.9 9 3440.7 3442.6 93 0 3 444.4 3446.3 1 3448.1 3450.0 2 3451.9 3453.7 3 3455.6 3457.4 4 3459.3 3401.1 6 3463.013404.8 6 3460.7 3468.5 7,3470.4,3472.2, 8 3474.1 3475.9 9 3477.8 3479.0 940 3481.6 3483.3 1|3485.2'3 187.0 2 3488.9 3490.7 3 3492.03494 4 4 3490.3 3498.1 5j3500.0'3501.8 6 3503.7 3505.6 7 13507.4 3509.3 8 3511.r3513.0 9 3514,8 3510.7 950 3518.6 3520.4 1 3522.23524.1 3525.9|3527.8 3 3529.0 3531.5 43533.3 3-535.2 6 3537.0 3.5,38-9 6 3540.7 3542.6 7 3544.4 3546-3 8 3548.1 3550.0 9,3551.9 3553,7 960 35-55.6 3557.4 1'3559.3 3561 1 2'3563.0 3.564 8 3 3560.7 ,3568.5 4 3570.4 3572 2 6 3574.1 3575 9 6 3577.8 3579.0 7 3581.5 3.583.3 8 3585.2 3587.0 9 3-588.9 3590.7 970 359-2.6 3.594.4 1 3596.3 3698.1 2 3000.0 3601.8 8 3603.7 3005.6 4 3607.4 3609.3 5 3611.1 3613.0 6 3614.8 3010.7 7 3618.5 3020.4 8 3622.2 3624. 1 9 3625.9 3627.8 980 36-29.0 3631.5 1 3633.3 3035.2 2 3637.0 3638.9 8 3640.7 3642 6 4 3044.4 3()40 3 6 3648.1 3650.0 6 3651.9 3053.7 7 3065.0 3057.4 8 3059.3 3601.1 9 3603.0 3664.8 990 3666.7 3668.5 1 3670.4 367-2.2 2 3674.1 3675.9 3 3677.8 3679.6 4 3681.5 3683 3 6 3685.2 3687.0 6 3688.9 3690.7 7 3692.6 3694.4 8 3696.3 3698.1 9 3700.0 3701.8 1000 3703.71 \ RATIOS OF CORRECTION FOR AVERAGE EB^D AREA CALCULATIONS. WIDTH OF UOAI) UEO. AiTa of Sdi n Knd. 1.25 2 2.5 H i^'ht III Siii 'il KikI, I lia io i>r I V.ml Ai'cns. 1:1 1:1. -2 1:1.4 1:1. (i 1:1. S 1:2 1:2.5 1::{ U-.l.o 1:1 1:4.5 1:5 1: ..5 1:(> 1:(!.5 1:7 1:7.5 1:S 1:^5 1:I> 1::».5 1:10 S«*i-t<011 Vill i ills I II a 1 SI' es. .001 .UU2 .007 .012 .019 .0.",3 .Oio .056 .01)7 .076 .()S5 .O'j:^ .100 .107 .113 .119 .124 .l--'8 .133 .13S .142 1 1 1 Slope. (Mil oo;; 006' iilO OH 023 1132 1:1 001' .004 .007 .012 .018 .032 .043 (111 .O'lo 050 .060 057 065 071 077 083 ,075 .083 .091! .098' 105 089j.ll0 094 .115' lOol.ll'O 1 06 111 117 123 .125'. .130. .134 . .138. 1J:1 .001 .004 .OON .012 .0 .033 .044 ,056 .067 .076 .084 .092 .100 .106 .111 .116 .122 .127 132 1 36 140 2-12 2.25 to 100 14 100 1—5 Slope. 6.04 5.2 4.74 Slope. 16 18 100 74 4.81 4.41 Slope. 1-1 4 • ^ 001 002 .001 006 'Jo9 016 023 .030 .ii3S ,043 049 ,0.55 060 1)65 O70 075 079 084 OSS 092 097 1:1 .001 .004 .006 010 .014 ;026 037 .047 .057 ,066 .074 ,081 ,088 ,094 ,100 105 110 115 120 125, 130 1.1:1 .001 ,004 ,007 ,011 ,015 ,027 040 051 ,061 070 07 S 084 09, 099 105 110 115 120 125 130 135 i-.l .001 .002 .003 .005 .006 012 ,019 .026 .033 .039 .044 .050 .055 1:1 .001 .003 .006 .010 .014 .001 .003 .006 .010 .014 .024.021 037 047 056 065 035 045 054 062 .0701.07 0771.030 084. OSS 060 .090' 095 065^.095 .101 069.100i.105 073, .106'. Ill ,077 111 0821,116 086. 121 090'.126: .116 .121 .125 .130 J:l .001 .002 .003 .005 .010 .016 1:1 .001 .003 .006 .010 .014 .024 .033 .022 .042 .029 .051 .035 .040 .046 001 003 006 010 .014 025 035 .047 .054 .059 .062 .066 .070 .073 .078 .051 .079 .085 .056 .085 .091 .060 .0911.097 ,004.09'i'.102 ,068 .101 .107 .072 .106 .112 076 .1111.117 086 .116'. 121 084 .120 .126 100 •5.14 4.45 4.13 4.72 4.14 3.88 4.33 3.87 3.644.00 3.62 3.4; Slope. 1-1 4.1 1:1 1J:1 .001 .002 ,003 ,005 010 ,014 ,020 025 031 036 042 047 051 055 058 062 065 069 072 .001 .003 .006 .009 .013 .022 .031 .039 .048 ,055 003 070 .076 .082 .088 .093 .098 .102 .106 111 0751.116 .001 .003 .006 .009 .013 .021 .034 ,044 ,052 ,060 ,068 ,075 082 ,088 093 098 103 108 113 117 122 20 100 Slope. 1.1 4.1 001 .002 003 005 .010 .014 .019 .02* .028 .033 .037 .041 .045 .049 .053 056 1 .0(iO| .063: ,066j .069! .001 .001 .003 .003 .005 .005 .008 .009 .012.013 .020 .023 .028 .033 .037 .042 045 .050 .053 .058 060,.066 .066. 073 .072 .079 .078 .085 .083 .090 .088 .095 .093 .100 .097 .104 .102 .109 ,106 .113 .111'. 118 100 24 100 Slope. Slope. 1:1 U:l '.001 0011.003 002'.005 003 .007 OO5LOI] 009 .019 ,014 ,019 ,022 026 030 034 037 041 044 047 050 054 057 060 063 -026 .034 .042 .049 .056 .062 .06,> .074 079 .084 .089 .094 .098 .103 .107 .001 .003 .005 .00,s .013 .021 .030 0!9 .047 .055 .062 069 .075 .081 .086 .091 .095 .100 ,105 .110 .114 1-1 4.1 001 .002 .ro3 .005 ,010 ,013 ,017 021 024 ,028 ,031 034 037 .040 043 047 050 .053 056 059 U:l .001 .003 .005 00- 012 020 02« 1:1 .001 .003 .005 .007 .010 .017 .025 .0321.036 .045 .052 .059 .066 .07 .077 .082 .0s7 .092 .097 .lol .lOi- ,110 .039 .046 .053 .059 .064 .070 .075 .080 ,084 OSS .093 .098 ,102 2G 28 100 100 30 100 !.71 3.43 3.2413.47 3.20 3.07 3.24 3.20 2.91 Slope. l-.l 001 .002 ,003 005 ,008 012 016 0i9 022 025 ()28 031 034 037 040 043 046 048 051 1:1 .001 .002 .004 .O0( 009 016 .023 .030 .037 .044 .050 055 .060 065 .070 075 080 084 088 .093 ••54 .097 U:] .001 .003 .005 .008 .011 019 .027 .034 .042 05(1 057 063 0(i9 075 .OKO 085 0s9 094 098 .10-.' 107 Slope. J:l' 1:1 1J:1 .001 .001 .002 .002 .001 .005 .006.007 .009 .010 .015 .018 .022 .025 .029 .033 .035 .040 .041 .04S .018 .054 .053 .060 001 001 ,002 003 ,006 010 013 016 019 022 025 027 030 033 036 OSS 041 044 046 049 .058 .063 06 .06fi 072 ,077 .O72L082 .076 ,086 .080.091 .084 .09 ") .088 ,100 .092 .104 Slope. 4 ,001 001 ,002 O03 005 008 Oil 014 .016 .019 021 I 1:1 1!:1 .001 .001 .002 .(J0-' .004 .005 .006 .007 .008 .010 .014.017 021 .024 .027 .('32 .034 .030 .040 04(; 045 .052 .050 .058 024 .0.55 064 .|'26 .0(30 .0(;9 029 .064 .074 031 .068 079 .034 .072 .084 036 .076 ,0.-<8 039 .(/79 .092 041 .083 .09() 044 087 .100 ll:i1ioof Ktnl Areas. 1:1 1:1.2 1:1.4 1:1. « 1:1. i» 1:2 1:2.5 l::j l::j.5 1:4 1:4.5 1:.> i:"-.o l:e deviations will usually counterbalance one another. If the work is of a peculiar nature, so the general cases here w,>rked out will not apply, cor- rections applying to it can be worked out and entered in one of the blank columns. To apply the table of corrections, we divide one area of cross section by its neiglibor, and take from the table its cor- responding ratio or percentage of correc- tion and multiply the contents by it, writing the result in the column headed " Correction" The special case, when one end is zero, or ends at grade, is not provided fi)r in table of corrections. For this case the correction is, the slope area multiplied by one sixth the length. F(;r the road bed area being the base of a wedge, the solidity is one-half base multi- plied by altitude; but the slope areas being bases of pyramids, the solidity is one-third base multiplied by altitude. One half which is used, less one-third, wdiich should be used, equals the correction, cue- sixth. This correction, as well as all others, is to be deducted from contents in main column. Estimated Q,nantities in Grading. STA- No. AHKA OF CROSS -VX. ION IN S({U»1£K ^T. KxcaT.it ion. - Em. 1 i iiieiit 11 118 'iiV) 120 121 123 50 mt com ....I 18. 16 50158 53105 ....()3(.)163325 50 638 2635 85417j297 ,...!ll02434S5 ends 20 cat! 40 Cut com men cesos no; 31 80103 ....'334280 35700 277 5.55 .5074315 12250870156 209 ..821 50534 Hlj cut 70 84 tlO 1*^7 ends AVERACE AREA. Excavation. !iiec'ces 30 560 555 314 3147 .394 .... 634 ....527. 2(;3 55 It coimen'ces 15i 72 ■im 517" 521 J 806.1 845,? 67 7 r! 267 34 108 212 280 270 121. 170 27 8 i 217 156.', 171,5 130 36i 15 67^ 215,! 426 560.1 540 ■2i-l\ 280 557^ 434. 26 1.^ 232 201 73.', Em- h. cu. yds. and f lund the error less than one third of one per cent. What appeared to be a section which would show great error on account of crossing several short ravines and gullies, con- taining some 85.000 cu. yds., was less than onedialf of one per cent, out of the way. In earthwork there are only two sides of the prismoid perfect planes, and these two are the theoretical ])lanes of the cross section. The surface of the ground is never a perfect plane. The rod, in taking points usually siok< a little in the grounil, the slopes are not trimmed exact- ly, nor the grade made perf< ct. If there is any difierence between the true so'idity and that obtained by the method here presented, it is the conviction of the writer that it would be easier and chea[)- er f >r the engineer to shovel it than to calculate it. The method of calculation for earth- work should be direct and simple, so it can be used safely by assistants not speci- ally skilled in intricate calculations. It is better for the engineer to spend much of his time in the field, minutely observ- ing ;xnd closely measuring the work, than to spend it mainly in the office, basing refiued computations on erroneous or careless measurements. The errors in measurement will usually be greater than the errors of calcuhition, by averaging end ;irea.s without correction. — Publislied by— JOHN WILEY & SONS, ^eieiitific*Ir*«l>li»lier^ 15 Astor Place. NEW YORK CITY. The New and Complete Catalogue .^OF_THE PUBT^ICATIONS OF ,rOH]\WIL.EY & SOIVS, IS Astor Place, New "York, CONTAININO Scientific and other Text Books FOR COLLEfiES, INDtlSTRIAL SCHOOtS k TBEOLOGICAL SEMINARIES, with niftiiy valuable practic.,il works for ARCHiTECTS, ENGINEERS, MECHANICS, ETC. INCI-FDING -WORKS ON Ap'ricnltiire, As,-. Astrondmy, Book-keeping-, Clu'iiiistry, Drinvitit! and Piuntinj;-, Ent>-ineering-, isictiilliii-fiy, ^liiclniiei-y, Jleclianics, Jlineral- ugy, ISeamanshiii. Steam Enfiine, Venti- lation, Etc., Etc., and for THEOI-OGICAL SEMINARIES, Hebre-w and Greek Bibles, Testaments, Le.xicons, Grammars, Heading- Books and Concordances. also a full list of their editions of JOHN RUSKIN'S WORKS. ^y^ll be sent free by mail to anyone ordering it. TABLE OF CUBIC YARDS IN LENGTHS OF 100 FEET. ADAPTED ESPECIALLY TO THE CALCULATION OF EARTH WORK BY THE METHOD OF AVERAGING END AREAS. Contents of Column "A" are for the integers in column headed "Area, Square Feet." Contentsi of Column " B " are for tlie same integers plus 0.5 square foot. Contents for lengths greater or less than 100 are obtained by simple proportion, thus : 125 sq. ft. for length of 20 ft.=i%=5 of 463.0 cu. yds; the contents for 125 sq. ft.=92.6 cu. yds. COPYRIGHT IS8S BY S. B. FISHER. Contf-pts, Couteiits, Cuiiteiiis, 1 at itt Cu. Yds. U i. 7 A 385 2 387.0 4 755.6 757.4 e O 18.0 20.4 O 388.9 390.7 5 759.3 761.1 o 22.2 24.1 a o 39i.6 394.4 6 763 0 764.8 7 2,s 9 97 K 396 3 393.1 7 766 7 768.5 c r* 29.6 31.5 g 400.0 401.8 8 770.4 772 2 o 33 3 35.2 9 403.7 405.6 9 774 1 775.9 1 i\ lU 37.0 38.9 110 407.4 409.3 21<» 777.8 779.6 1 J 40.7 42.6 411.1 413.0 1 781.5 783.3 a 44.4 46.3 2 414.8 416.7 2 735-2 787.0 Q 48.1 50 0 9 o 418 5 420.4 3 788-9 790.7 A 51.9 53-7 4 422 2 421.1 4 792.6 794.4 K o 55.6 57.4 425.9 427.8 5 796-3 798.1 a o 59.3 61.1 429 6 431.5 G 800.0 801.8 i 63.0 64 8 7 • 433 3 435.2 7 803.7 805.6 fi o 66.7 68.5 g 437.0 438 9 g 807.4 809.3 Ik «F 70.4 72 2 9 440 7 442.6 9 811.1 813.0 74.1 75.9 120 414.4 416.3 220 814.8 8167 1 X 77.8 79.6 ] 448 1 4-50.0 1 818.5 820-4 O u a 81.5 83.3 2 451.9 453.7 2 822 2 824 1 85.2 87.0 3 455.6 457.4 3 825,9 827-8 A * 88.9 90.7 A 459 3 461.1 4 829.6 831-5 w 92 6 94.4 463.0 464-8 f. 833.3 835.2 n 96.3 98.1 (} 466.7 468.5 G 837.0 838.9 i loo 0 1018 7 470.4 472.2 7 840.7 842.6 c o 103.7 105.6 g 474.1 475.9 8 844.4 8463 9 107.4 109.3 9 477.8 479.6 9 843-1 850-0 30 HLl 113.0 130 481.5 4833 230 851-9 853-7 \ 1 14.8 116.: 1 485.2 437.0 1 85-5.6 857-4 2 120.4 2 488.9 490 7 2 8.59.3 861.1 122.2 124.1 3 492.6 494.4 8 863.0 864.8 4 125.9 127.8 4 496.3 493.1 4 8637 863 5 5 129'6 131.5 5 500.0 501.8 5 870 4 872 2 133.3 135.2 0 503.7 505.6 G 874.1 875-9 l37!o 133 9 7 507.4 5(19.3 7 877.8 879-6 g 140.7 142.6 g 511.1 513.0 8 881.5 833.3 9 144.4 143.3 9 514.8 516.7 9 835.2 887-0 40 143 1 150.0 14o 518.5 520.4 240 883 9 8907 1 151.9 153.7 1 522 2 524.1 1 802-6 89 1.4 2 1 5o.6 157^4 2 525.9 527.8 2 803.3 893.1 3 loois 161.1 3 529.6 531.5 8 900 0 901.8 4 103 0 164.8 4 533.3 535.2 4 903-7 91 '5.6 1637 163.5 5 537 0 533.9 5 937.4 909.3 170.4 172.2 540.7 542.6 G 911.1 913.0 7 g I74!l 175.9 7 544.4 546.3 7 914.8 916.7 177.8 179.6 g 543.1 550.0 g 918.5 920.4 9 13L5 183 3 9 531.9 553.7 9 922 2 924.1 50 135.2 187.0 15o 555.6 557.4 250 92) 9 927.8 ] 138.9 1907 \ 559 3 531.1 1 920.6 931.5 2 ll)2'6 191.4 2 563.0 534.8 2 933.3 935.2 3 193.3 193.1 3 566 7 563.5 3 937.0 933.9 4 200.0 201^8 4 570.4 572 2 4 94).7 942.6 5 203.7 205.6 5 574.1 575.9 5 914-4 946-3 c 2J7!4 209^3 ({ 577.8 579.6 G 918.1 950.0 2! 1.1 213.0 581.5 683.3 7 951-9 953.7 g 214!8 2167 g 585.2 587.0 8 955 6 9-57,4 9 218.5 220.4 9 538.9 590.7 9 959.3 961.1 GO 222 2 224.1 160 592 6 594 4 260 933-0 964.8 1 225 9 227.8 ] 596 3 598.1 1 9307 968.5 2 229.6 231.5 2 600.0 601.8 2 970 4 972.2 3 233.3 235.2 3 603 7 605 6 3 974.1 975.9 4 237.0 238^9 4 007.4 609.3 4 977.8 979.6 5 210 7 242.6 5 611.1 613.0 5 931.5 983.3 244.4 246.3 614.8 616.7 6 985.2 987.0 7 248.1 250.0 7 618.5 020.4 7 988 9 990.7 g 251.9 253.7 g 622.2 624 I 8 992-6 994-4 9 2'>5.6 257.4 9 625 9 627.8 9 996-3 998 1 70 259.3 231.1 17u 629.6 631.5 27it 1000-0 1001.8 1 2')3 0 264.8 1 633.3 635.2 1 10037 1005.6 2 2G6 7 263.5 5; 637.0 638.9 2 1007 4 1009.3 270.4 272.2 3 640 7 642.6 3 1011.1 1013-0 4 274.1 275.9 4 644 4 640.3 4 1014-8 10167 5 277.8 279.6 5 648 1 650.0 ft 1018-5 1020.4 ( 281.5 283.3 (; 651 9 653. 6 1022.2 1024.1 7 285.2 237.0 7 655 6 657.4 7 1025.9 1027.8 g 288.9 290.7 g 6')9.3 661 1 8 1029.6 1031.5 <) 2926 294.4 9 663 0 664.8 9 10-33.3 103.5.2 g(l 296 S 298.1 180 636.7 608.5 280 1037.0 1038.9 1 300.(: 301.8 ) 670.4 672.2 1 1040.7 1042.6 2 3i)3.'7 30)!6 2 674 1 675.9 2 1044.4 1046 3 g 307.4 309.3 3 677.8 679.6 3 1048.1 1050-0 4 311.1 313.0 4 631 5 683.3 4 1051.9 1053.7 h 314.8 3167 5 6852 687.0 6 1055.6 1057.4 G 318.5 320.4 6 688.9 690.7 6 1059 3 1061.1 7 322.2 324 1 7 692.6 694.4 7 1063-0 1064.8 8 325.9 327.8 8 696.3 698.1 8 1066 7 1068.5 9 329,6 331.5 9 700.0 701.8 9 1070.4 1072.2 90 333.3 335.2 190 703.7 705.6 29i( 1074.1 1075.9 1 337. u 338.9 1 707.4 709.3 1,1077.8 1079.6 2 340.7 342.6 2 711.1 713-0 2 1081-5 1083.3 3 344.4 346.3 8 714.8 716.7 3 1085.2 1087.0 4 318 1 350.0 4 718.5 "^20.4 4 1088.9 1090.7 o 351.9 353.7 722.2 724.1 5 1092-6 1094.4 6 3-)5.6 357,4 6 725.9 727.8 G 1096.3 1098.1 7 359.3 361.1 7 729 6 731.5 7 1100.0 1101.8 8 363.0 364.8 8 733 3 735.2 8 1103.7 1105.6 9 366.7 368.5 9 737.0 738-9 9 1107.4 1109.3 IOC S70.4 372.2 200 740.7 742.6 300 1111.1 1113.0 300 1 2 3 4 6 6 7 8 9 310 1 2 3 4 5 Coiiti'iiis, Cu. Yd.s. A. 1111.1 1113.0 1114.8 1 1167 9 320 ] 2 3 4 6 6 7 8 9 380 1 2 3 4 5 G 7 8 9 340 I 1118.5 1122.2 112-5.9 1129.6 113.3.3 1137.0 1140.7 1144.4 11481 1151.9 1155 6 1159 3 1163.0 1166.7 1170.4 1174.1 1177.8 1181.5 1185-2 1188 9 1192-6 1196.3 1200 0 1203.7 1207.4 1211.1 1214.8 1218 5 1222.2 1225 9 1229-6 1233-3 1237-0 12407 1244.4 1248 1 1251.9 1255-6 1259-3 1120-4 1124.1 1127S 1131.5 113-5.2 1133.9 1142-'! 1146-3 11.50-(i 1 153 7 1157.4 1161.1 1164.8 1168-5 1172.2 1175 9 1179.6 11833 1187.0 11907 11944 1198.1 1201.8 1205.6 1209.3 1213.0 1216.7 1220.4 1224.1 1227.8 1231.5 1235.2 1238.0 1242.6 1216.3 12-50 0 1253-7 1257.4 1261-1 ( ontents, Cm.. Yds. 1233.0 1264 8 1266.7 1270.4 4' 1274.1 1 2 3 4 5 6 7 8 9 360 1 2 3 4 5 6 7 8 9 370 1 2 8 6 7 8 9 380 1 2 3 4 5 G 7 8 9 390 1 2 3 4 5 G 7 8 9 1277.8 1231.5 1235.2 1283.9 1.92-6 1296.3 1300.0 13037 1307-4 1311.1 1314-8 1318-5 1322 2 1325-9 1329.6 13333 1337.0 1340.7 1344.4 1348.1 1351.9 135-5-6 1359-3 1363-0 1366.7 1370.4 1374.1 1377.8 1381-5 1385.2 1388.9 1392.6 268 1272.- 1275.9 1279 6 1233.3 1287.0 1290- 7 1291- 4 1298.1 1301.8 1305.6 1309-3 1313-0 13167 1320.4 1324.1 1.327-8 1331 5 1335-2 1338-9 1342-6 1346 3 1350-0 1353.7 1357.4 1361 1 1364.8 1368.5 1372-2 1375.9 1379.6 1383-3 1387.0 1390-7 1394.4 400 1 2 8 4 ft G 1 8 9 41(1 1 2 3 4 ft ' 6 7 8 9 42|-2444 4 2446.3 1 2448 1 '24.50.0 2 2151,9 24,537 3 24-35.6 2457-4 4 2459-3 2461-1 6'2463.0 2464-8 6'24667l2468 5 7'2470.4'2472 2 8'2474.1 2475-0 9'2477.8 2479.6 670'2181.5l24-<3.3 l'248.5.2'2487.0 2 •2433.9 '24907 3 2492.6'2494.4 4 2496.3 2498.1 5 2500.0 2-301.8 6 2503.7 2505.0 7 2507.4 2509.3 8 2511.1 2.313.0 9 2314.8 2616.7 680:2518.5 2520.4 12.322.2 2524.1 2 2325.9 25:^7.8 3 2329 ; 2531.5 4;233.3.3 2535.2 ft 2537.0 2-538.0 6 2540 7 2542 6 7 2644.4,2546.3 8 2.548 1 2.360.0 9 2351.9 2.353.7 690 '2 335.6 2-357.4 1 2.339.3 2561.1 2|2563-0 2-564.8 3 2566,7 2-368.5 2-570,4 2372.2 2574.1 '2.375.9 2.377.8 2.579-6 2581.5 2583-3 2.585.2 2587-0 2388.9 2690.7 2592.6 2594.4 4 ft 6 7 8 9 700 Conents, Cu. Yds. 730 2592.6 2.594.4 1 2506.32598-1 2600,0;2601-8 260371260.5-6 •2607.4 2609.3 •2611.lj2613.0 -26 14.8 1 26 16.7 2618.5 26-20,4 2622.22624.1 ■2623.9|26'27.,H •26-29 6 2331.5 2633 3 2635 2 8 9 710 1 2 8 ft 6 7 8 9 720 ] 2 3 2637.0 •26107 4 '2644.4 •2648-1 2638.0 2642.6 '2646.3 26.50.O 2651 9,26.53.7 2G55.6i26.57.4 26.59.3 2661.1 2663.0 2664.8 2666.7 2670.'* '2674.1 2668.5 '237'2.2 2673.9 2677.8 2679.6 '2633.3 2687.0 7 9 40 1 2 3 4 ft G 7 8 9 750 1 2 8 4 I G 7 8 9 760 1 2 3 4 5 6 7 800 1 2 8 4 ft 6 7 8 9 810 ] 2 8 4 I •2701.8 ■2705.0 707.4 2709.3 [ 2713.0 •2724.1 2727.8 2731.5 ■2735.2 273S.0 '2742.6 •2746.3 2750.0 2763.7 4'2681.5 ft 1 2685.2 6 2688.9 2690 7 '2602.6 2694.4 Sl2696,3 '2698-1 9 2700-0 730-2703 1 2-2711.1 3'2714.8 27167 4 '2718.6 2720.4 2722 2 6 -2725-0 '2720.6 2733.3 2737.0 2740.7 44.4 2748.1 2761.9 •27.35.6|27.57.4 2759.32761.1 2763.0 '2764.8 2766.712768.5 •2770.4''2772.2 '2774.l!2775.9 2777.8 '2779.0 2781.5 2783.3 2785.2 2787.0 2788.9, '2790.7 792.6''2794.4 •2796.3 2798.1 2800.0 2301.8 2803.7 2805.6 2307.4 2809.3 2811.1 2813.0 2814.8 '28167 '2318.6 '2820 4 2322.2 28'24.1 •28'25.9 2827.8 2829 6 2831.5 2833.3 2835.2 2837.0 2838 9 . '2840 7 2842.(> 8 -2844 4 2846.3 9-2848.1 28.5O.0 7 70' 235 1.9 •28.537 l'2S-35.6 '28-37.4 2 '23.39 3 2861.1 3 2863.0 2864.3 4 -2866-7 2868.5 ft '2870-4 2872 2 6 '2874-1 2875-9 7 2877-8 2879-6 8 -2881.5 2883-3 9 2885.2 2887.0 780 '2888.9 2890.7 1 2392.6 '2894.4 2 2806.3 2898.1 3 2900-0 2901.8 4 2903.7 2905.6 5 2907.4 2909 6 2911.1 '2913 0 7 2914.8 2916 H '2918.5 2920.4 9 2022.2 '2924.1 790 '20'2.3-9 2927.8 1 2929-6 2931-5 2 '2933.3 2935.2 3 2937-0 2938 9 4 2940.7 '2942.6 5 2944.4 2946,3 6 2943.1 2960.0 7 2951.9 2953,7 8 '29.36.6 2967.4 9 29.30,3 2961.1 800 2963.0 2964,8 t 8 9 820 1 2 3 4 ft G 7 8 9 880 1 2 3 4 ft 6 7 8 Contents, j I Contents, Cu. Yds. I Cii. Yds. A. B. 2963.0 2934.8 2966,7 2968 5 ;970.4 2972.2 2074.1 2976.9 •2977,8 2979.6 2931 6 '2983.3 2985.2 2987.0 •2988.9 2990.7 •2992.6 2994,4 2996.3 •2998.1 .3000.0 3001 8 3003.7 3005.6 ;007,4 3009.3 3011.1 3013 0 3014.8 3016.7 3018.5 3020,4 6 3022.2 3024.1 .3025,9 3027.8 3029.6 3031.5 3033.3 3035.2 3037.0 3038.9 3J40.7 3042.3 3044 4 3046.3 3018.1 30-30.0 3051-9 30.53-7 30-35.6 30-57.4 30.39.3 3061.1 3063.0 3064.8 3066 7 3068.5 3070.4 3072.2 3074.1 3075.9 3077.8 3079.6 3081.6 3083.3 3035.2 3037.0 30:!8.9 3090.7 3092.63094.4 3096.3 3098.1 3100.0 3101.8 31037 3105.0 840 1 9 3107.4 3111.1 3114.S 2 3118.5 3122-2 3126.9 31'29.6 850 1 2 86 11093 3113.0 31167 3120.4 124.1 3127.8 3131, 3133 3 3135 2 3137.0 8 3140.7 9 3144.4 3148.1 3151.9 _ 315.3.6 3167.4 3 3159.3 3161.1 3163.0 3164.8 3166.7 3174.1 3138.0 3142.0 3146.3 3160.0 31.53.7 3168.5 3170.4 3172.2 3176.0 3177.8 3179.6 3181.531833 3187,0 3190,7 3185.2 3188.9 319'2.6'3194.4 3 3196.3 3'08.1 4 3-200.0 3201.8 ft 3'203,7 3^206.6 6 3^207 .4 3^209.3 7 3211.1 3213.0 8 3214.8 3216 7 9 3218 5 3^2^20.4 870 3222.2 3224.1 1 32^25.9 3-227.8 2 32.9.6:3231.5 3 3233.3 3235.2 4 3237.0 '3 238 0 ft 3240 713242.6 G 3244.4 3246.3 3260.0 3253 3257.4 3^248.1 8 3251.9 9 3^255.6 880 3-2.5a.3 3261.1 1 3263.0 3264.8 2 3266,7 3^268.5 8 3270.4 3^272,2 8 9 890 1 4 3274.1 6L3^277.8 6.3'28l.5 7 3'285.2 3238.9 3-292,6 3296,3 3300.0. 330 1..S 2 3303.; 8 3307.4 3309.3 4 3311.1 3314.8 3316. 3318.6 3322.2 33-Z5.9 3327.8 3329.6 900 3333.3 3335.2 3'276.0 3279.6 3-283.3 3287.0 .3200.7 3204 4 3-298.1 3305.6 .3313.0 3320.4 3.324.1 900 1 4 ft G 7 8 9 910 1 2 3 4 ft G 7 8 9 3331.5 33.3.3.3 3335 2 3337.0 3338-9 3340-7 3342.6 3344.4 3346.3 3348.1 3350.0 3351.9 33.337 3355.6 3357.4 33.59.3 3361.1 3333.0 3364.8 3366.7 3368.5 3370 4 3372.2 3374.1 3375.9 3377.8 3379.6 8381.5 3383.3 333.3.2 33>7.0 3388.9 3390.7 3392.6 3394 4 3396.3 3398.1 3100.0 3401.8 34037 3405 6 920 3407.4 3409.3 l;3411-l 34130 2 3414.8 .3416-7 3 3418 6 3420.4 4 .34-22.2 34-24.1 6 3425.9 34-27.8 G 3429.6 343 1 .5 7 3433 3 3435.2 8 3437.0 3438.9 9 3440.7 3442.6 98 0 3 444.4 3446.3 1 3448.1 3450.0 2 3451.9 34-53.7 3 3455.6 3457.4 4 34.59.3 3461.1 ft 3163.0 3464-8 G34667|3468.5 7,3470.4,3472.2, 8 3474.1 3475.9 9|3477.8 3479.6 940 3481.5'3483.3 l'348.3.2'3 187.0 2 3483.9 34907 3 349'2-6'3494 4 4 3406.3 3408.1 5,3.300-0'3-501-8 6 3503-713505-6 7 ;.3507.4 3.509.3 8 3511.1 3513.0 9 3514.8 35167 950'3518.5'3520.4 l:35'22.2'3524.1 3.5'2.5.9|3527.8 3 3529.6 3331.5 4 3.333.3 333.3.2 ft 3.337.0 3.538.9 613540.7 3.342-6 713644.4 3.346.3 813648.1 36,50.0 9 3561.9 3.3537 960 35.35.6 3,=i57.4 1 3,5.59,3 3561 1 2 3563.0 3,564 8 3 3566,7 .3568.5 4 3570.4 3.572 I 5 3574.1 3575 9 6 3577.8 3,579.6 7 3.581.6 3.383.3 8 3585.2 3587.0 9 3.388.9 3590,7 970 3.59-2.6 3,394.4 1 3.396,3 3598.1 2 3600.0 3601.8 8 3603.7 3605,6 4 3607.4 3609,3 ft 3611.1 3613.0 6 3614.8 3616,7 7 3618.5 3620.4 8 3622.2 3624.1 9 36-25,9 36-27,8 980 36'>9.6 3631,5 1 3633,3 3635.2 2 3637.0 3638.9 3 3640.7 3642 6 4 3644.4 3646 3 ft 3648.1 3650.0 G 3651.9 3653.7 7 36.3-5.6 3657.4 8 36,39.3 3661.1 9 3663.o!3664.8 990 3666.713668.5 1 3670.4 3672.2 2 3674.1 3675.9 3 3677.8 3679,6 4 3681.5 3683 3 ft 3685.2'3687,0 6 3688.9 3600.7 7 .3692.6 3694.4 8 3696.3 3698.1 9 3700.0 3701.8 100 0 3703.71 RATIOS OF CORRECTION FOR AVERACE END AREA CALCULATIONS. WIDTH OF UUAO liEU. Arpa of l.'J5 2 2.5 I H i^'ht ur I Sill 'it KikI. Ita io nt y.nil Areas. 1:1 1:1.2 1:1.4 1:1. n 1:1.8 1:2 1:2.5 1::J i-.i.r, 1:1 1:1:..> J:') 1 :-).■> l:(t 1 :(!..-, 1:7 1:7.5 1:S l:s.5 l:i» 1:;).5 1:10 Vurj iii^' • II a, 1 Si I'K. .001 .002 .007 .012 .019 .OXi .015 .050 .0(i7 .076 .0S5 .09.3 .100 .107 .113 .119 .124 .128 .133 .13S .142 1 1 1 Slope. 1:1 1J:1 001 001 oo:i .004 001) .007 illO 014 023 032 041 050 057 065 07 077 083 089 094 100 106 111 117 123 .012 .018 .032 .043 .0i5 .066 .075 .083 .0911 .0981 .105 .110 .115| .120 .1251 .130' .134i .138' .001 .004 .008 .01 .022 .033 .044 ,056 .06 .076 .084 .092 .100 .106 ,111 .116 .122 ,127 132 136 140 2—12 2.25 to 100 14 100 Slope. Slope. 16 18 100 6.04 5.2 4.745,74 4.81 4.415.14 4.45 4.13 4.72 4.14 3.884.33 3.87 3.644.00 8.62 3.43 Slope. 001 002 004 006 009 016 023 030 .1138 ,043 ,049 ,055 060 (165 070 075 079 084 088 092 097: 1:1 .001 .004 .006 010 .014 ;026 037 .047 .057 .066 ,074 .081 .088 .094 .100 ,105 110 115 120 125; 130 1^:1 .001 .004 .007 .011 .015 .027 .040 .051 .061 .070 .078 .084 ,093 .099 ,105 110 ,115 120 12" 130 135 1:1 1:1 1^:1 .001 .001 .001 .002. (i(t;; .003 003 .006 .005 1 .006 012 .019 .026 .033 .039 .044 .050 .055 .010 .006 .010 .014 .014 .024.026 .035 .037 .045 .054 062 .070 .077 .084'.0S8 060 .09o[ 095 ,065 .095 . 101 069'.100|.105 073 .106 .111 .047 .05H .0(;, .071' .030 077 082 111 .116 .116 .121 086 .121 .125 090. 1261. 130, i:l .001 .002 .003 .005 .010 .016 .022 1:1 .001 .003 .006 .010 .014 .024 .033 .042 .029 .051 .035!.059 .040 .066 .0461.073 .051 .079 .056 .085 .060 .091 .064 .09'i .068 .072 .076 086 .084 .101 106 ml 116 120' .001 ,003 ,006 010 ,014 025 ,035 047 054 062 070 078 085 091 097 102 107 112 117 121 126' 100 Slope. ,001 ,002 ,003 005 010 014 020 025 0311 1:11^:1 .001 .003 .006 .009 .013 .022 .031 .039 .048' 055 036' .063 042 .070 047 051 055 058 062 065 069 072 075 .071 .08-. .088 .093 .098 .102 .106 111 .116 .001 .003 .006 .009 .013 .021 .034 .014 .052 .000 .068 .075 .082 .0,s,s .093 .098 .103, .108 ,113 ,117 122 20 100 100 24 100 Slope. hi 001 002 ,003 )05 .010 .014 .019 .023' .028 .033 .037 .041 .045 .049 .053 ,056 .060| .063 .066 .069' 1:11^:1 .001 .001 .003 .003 .005 .005 .008 .009 .012.013 .020 .023 .028 .033 .037 .042 .045 .050 .053 .058 060.066 .066 073 .072 .079 .078 .085 .083 .090 .088 .095 .093 .100 .097 .104 .102 .109 .106 .113 111 .118 Slope. Slope. i:l 1:1 Looi'.ool 001!.003i.003 002.005 003 .007 005|.011 0o9i.019 014' 026, .019 .022 ,026 ,030 034 ,037 041 044 047 050 054 ,057 060 063 .005 .008 .013 .021 .030 .034' 0 !9 .042 .049 .056 .062 .06S .074 079 .084 .OS!) .094 .098 .103 .107 .047 .055 .062 .069 .075 .081 .080 .091 .095 .100 .105 .110 .114 4.1 001 002 ro3 .005' .010 .013 .017 j 0211 ()24 .028 .031 .034 037 040 043 047 050 053 056 059 1:1 .001 ,003 ,005 ,007 ,010 ,017 ,025 ,032^ ,039 046 053 ,059 064 070 075 080 084 088 093 098 102 1J:1 .001 .003 .005 .00, ,012 ,020 028 036 ,045 ,052 059 ,066 ,07 1' 077 082 0S7 092' 097 lol lOi 26 28 100 100 30 100 3.71 3.43 3.24I3.47 3.20 3.07 3.24 3.20 2.91 Slope. 001 .002 ,003 005 ,008 ,012 016 019 022 025 028 031 034 037 010 043 046 048 051 i-A 1:1 .001 .002 .004 .006 009 016 .023 .030 037 ,044 .050 .055 .060 065 .070 075 080 084 .088 .093 054 .097 .001 .003 O05 .008 .011 019 .02' .034 ,042 ,050 ,057 063 069 075 080: 085^ 089 094 098 102 107 Slope. i:l 1:1 15:1 .001 .001 .002 .002 .001 .005 .006 .007 .009 .010 .015 .018 .022 .025 .029 .033 .03k.040 .04r.018 .018 .054 .053 .060 001 001 .002 003 .006 010 013 016 019 022 025 027 030 033 036 OSS 041 044 046 049 .058 .063 067 .066 072 .077 .072L082 .076'. 086 .080.091 .084 .095 .088 ,100 .092 .104 Slope. i-A .001 .001 .002 .')03 .005 .008 .011 .014 .016 .019 .021 I 1:1 l',:l 001 .001 002 .002 .004 .005 006 .00 .008.010 014'.017 021 '.024 027 .032 034 .039 .040 .046 045 .052 .050 .0-58 024 .0.55 .064, .026 .060 .0(!9 029 .064 .074 031 .068 079 .034 .072 .084 .036 .076 .088 .039 .079 .092 041 .083 .096 044 .087 .100 liiitio of ElMl Arras. 1:1 1:1.2 1:1.4 1.6 1.8 1: I: 1:2 1:2.5 I::l 1:3.5 1:4 1.4.5 1:5 I 1:5.5 1:6 1:6.5 1:7 1:7.5 1:8 1:!) I:!).5 On Estimating Earthwork. The accompanying table is designed to facilitate the computation of earthwork after the areas of the cross sections have been obtained. The areas may be ob- tained by calculation from the field notes ; or the cross sections may be plotted and the areas obtained by the planimeter. I'he former method is short and easy in a level country, but where the surface of the ground is broken and irregular the latter method is to be preferred. Plotting the cross s ections also makes a complete record of the work, with its classification at every point, and allows revision and deviation within the limits to which the section is taken, by siiii[)ly indicating the position of the centre line. Usua'ly it will be found easiest to plot the rods from a line assumed as the height of in- strument ; but when the work is extend- ed so as to involve several heights of itistrument in the same section, or when the work is to be used for a great Lumber of calculations fir successive estimates, it will be found cheapest to work from elevations. A c>nvtnient form for the estimate sheets is here shown. In the two first columns are entered the stations and ploj>es at which the cross sections are taken. The column headed ''Length in Feet " is filled up by subtracting the numbers in these two first columns. The columns headed " Area uf Gross iSedion " are filitil up with areas obtained either from calculation or I'rom measurement by the planimeter. In the columns head- en, and red ink in writing quan- tities in embankment. The calculation of earthwork by the method of averaging end areas is not theoretically correct, excepting in the two special cases : one when the end areas are equal, and the other when the prismold has two of its longitudinal bounding planes parallel. As that por- tion of every roadway prisraoid, which lies between the vertical planes passing through the edges of the roadbed is practically included in the latter condi- tion, it follows that the variation from the true contents, obtained from averag- ing end areas, lies outside the central roadbed prism, and we may consider it as dependent on the four following factors : 1st. The ratio of the end areas of the prismoid. 2nd. The width of the roadbed. 3rd. The degree of the slope. 4th. The heighth of the section. This variation has been investigated with the result shown in the table called " Mutios of Correction for Average End Area Calculations." The manner of pro- ceeding was briefly thus : With the data shown in the heads of the columns in the table, and in the left hand column, the true contents of the prisms by the prisrnoidal formula were found, as well as the contents, by averaging end areas. The ratio of variation in many par- ticular cases being thus found, the curve of variation for each class was formed by measuring the ratios of end areas on the axis of abscissas, and the per- centages of variation on the axis of ordin- ates. Some maxima and minima of these curves were also traced, which seemed to differ, in extreme cases, 10 per cent, or so from the mean given in the table. It is believed these deviations will usually counterbalance one another. If the work is of a peculiar nature, so the general cases here worked out will not apply, cor- rections applying to it can be worked out and entered in one of the blank columns. To apply the table of corrections, we divide one area of cross section by its neighbor, and take from the table its cor- responding ratio or percentage of correc- tion and multiply the contents by it, writing the result in the column headed " Correction." The special case, when one end is zero, or ends at grade, is not provided for in table of correcticms. For this case the correction is, the slope area multiplied by one sixth the length. For the road bed area being the base of a wedge, the solidity is one-half base nuilti- plied byaltitude; but the slope areas being bases of pyramids, the solidity is one-third base multiplied by altitude. One half which is used, less one-third, which should be used, equals the correction, one- sixth. This correction, as well as all others, is to be deducted from contents in main column. Estimited Quantities in Grading. STA- TIOSS No. AUEA OF ( KOSS ^KC• ION IN S({U XUK IT. Cxciiv.itioii. 117 118 119 506382635: 85;417|297 120 121 125 123 50 Cut coi nen ces ....I 18 16 50158 53105. ....630163325 ....110243485 cnt ends 31 80103 ....'334280 35700 277 555 50743157 50870156 209 187 255 3147 ..'821 30534 611 m 70 84 90 mt COM men ces ends CitcoiBineii ces 68 560 555 314 AVEHAOE AREA. Excavation. 394 634 527.5 ,'263 55 105 72 218j 517 52 U ,806 i 845J 6774 267 34 108 212 280 270 121. 170 2784 217 156.1 17 U 2.32 130 36^ 15 67^ 2154 426 560J 540 242^ 280 557 1 434,! 261^ 201 m Em- b:ink nifnt Corrected Totals, CONTKNTS IN CUBIC YARDS. Escavniion. 16.7 1 162.916 729.632 1174.1 683.8 136 3 40. 11.4 63.3 161.9 670.2 400 8 2987.0 1565, 752.8 306.518 9853.7 98 14 8 63.9 200.6 394 4 362.9 150 0 90.0 1037 361.0 120 6 579 6 317.6 144.4 41.9 2945.423 9755.7|.... 2922.4;.... 5278.1 ....j 82.7..., 1/1 :s 27.8 125.0 399.1 788.9 626.5 300.0 179.6 207.4 722.7 241.3 968.5 429 6 223.3 84.4 5324.1 Em- liank- mint. 25.1 25.1 7.6 23.8 5.1 461 86.' REMARKS. The error from calculation by averag- ing end areas is not so great as appears at first sight, or as it is often represented. Taking isolated cases, where the ratio of end areas is great, it may be made to appear that the error is 10 or 15 per cent.; but taking extendeil work the whole error is trifling, the great bulk of con- secutive cross sections being nearly equal to each other, and the errors are distri- buted. The writer tested one section of 28,(;0 • cu. yds. and f lund the error less than one tiiird of one per cent. What appeared to be a section which would show great error on account of crossing several short ravines and gullies, con- taining some 85.000 cu. yds., whs less than one-half of one per cent, out of the way. In earthwork there are only two sides of the prismoid perfect planes, and these two are the theoretical planes of the cross section. The surface of the ground is never a perfect plane. The rod, in taking points usually sinks a little in the ground, the slopes are not trimmed exact- ly, nor the grade made perfict. If there is any difference between the true so'i lity and that obtained by the method here presented, it is the conviction uf the writer that it would be easier and cheap- er for the engineer to shovel it than to calculate it. The method of calculation for earth- work should be direct and simple, so it can be used «afely by assistants not speci- ally skilled in intricate calculations. It is better for the engineer to spend much of his time in the field, minutely observ- ing and closely measuring the work, than to spend it ]nainly in the office, basing refined coi;iput,iitions on erroneous or careless measurements. The errors in measurement will usually be greater than the errors of c.'ilculation, by averaging end area.s without correction. — Piililislied bv— JOHN WILEY & SONS, ^cieiitifioIPul>lislierss 15 Astor Place. NEW YORK CITY. The New and Complete Catalogue OF THE PUBMCATIOKS Or JOHJV WIL.EY & SOIVS, IS Astor Place, New York, CONTAINING Scientific and other Text Books FOK COLLEGES, INDUSTRIAL SCHOOLS & THEOLOGICAL SEMINARIES, with many valuable practical works (or ARCHiT-ECTS, ENGINEERS, MECHANICS, ETC. INCLUDING WORKS ON Ag-riculture, Assaying:, Astronomy, Book-keeping, Chemistry, Drawinfj and Paintinff, Engineering, Metallurgy, Machinery, Mechanics, Mineral- ogy, Seamanship, Steam Engine, Venti- lation, Etc., Etc., and for THEOLOGICAL. SEMINARIES, Hebrew and Greek Bibles, Testaments, Lexicons, Grammars, Heading Books and Concordances. also a full list of their editions of JOHN RUSKIN'S WORKS. Will be sentfree by mail lo anyone ordering it. cop- 3 TABLE OF CUBIC YARDS IN LENGTHS OF 100 FEET. ADAPTED ESPECIALLY TO THE CALCULATION OF EARTH WORK BY THE METHOD OF AVERAGING END AREAS. Contents of Column "A" are for the integers in column headed "Area, Square Feet." Contents of Column " B " are for the same integers plus 0.5 square foot. COPYRJQHT 1885 BY S. B. FISHER. Contents for lengths greater or less than 100 are obtained by simple proportion, thus : 125 sq. ft. for length of 20 ft.=j7j=^ of 463.0 cu. yd.s; the contents for 125 sq. ft.=92.6 cu. yds. Cont'-nts, Cu. Yds. 1 ■2 3 4 5 6 7 f> 9 10 1 2 3 4 5 6 7 8 » 20 1 2 3 4 5 6 9 30 1 2 3 4 5 6 7 8 9 40 1 2 3 4 5 6 7 8 9 50 J 2 3 4 5 C 7 8 9 CO 1 2 3 4 5 6 7 8 9 70 1 2 H 4 5 6 7 8 9 80 1 2 3 4 6 7 8 9 90 1 2 3 4 o 6 7 loci 3.7 7.4 11.1 14.8 18.5 22.2 25.9 29.« 33.3 37.0 407 44.4 48.1 51.9 55.6 59.3 63.0 66.7 70.4 74.1 77.8 81.5 85.2 8S.9 92 6 96.3 lOOO 103. 107.4 111.1 114.8 118.5 122.2 125.9 129.6 133.3 137.0 140.7 144.4 143 1 151.9 155.6 159.3 163.0 103.7 170.4 174.1 177.8 131.5 135.2 138.9 192 6 193.3 200.0 203.7 237.4 2!1.1 214.8 218.5 222 2 225.9 229.6 233.3 237.0 210 7 244.4 248.1 251.9 2-)5.6 259 3 2330 266 7 270.4 274 277.8 231.5 235.2 288.9 292 6 296 3 300.0 303.7 3(t7.4 311 ] 314.8 318.5 322.2 325.9 329 6 333.3 337.0 310 344.4 3181 351.9 3)5.6 359.3 363.0 366.7 370.4 B. 1.8 6.6 9.3 13,0 16,7 20.1 24,1 27.8 31.5 35.2 38.9 42.6 46.3 50.0 53.7 57.4 61.1 618 68.5 72 2 75.9 79.() 83.3 87.0 90 944 98.1 101 8 105.6 109.3 113.0 116 120.4 124.1 127.8 131.5 135.2 1339 142.6 143.3 150.0 153.7 157.4 101.1 101.8 103.5 172.2 175.9 179.6 183 3 187.0 190 191.4 193.1 201.8 205.0 209.3 213.0 216.7 220.4 224.1 227.8 231.5 235.2 238.9 242.6 246.3 250.0 253.7 257.4 231,1 264.8 263.5 272.2 275.V) 279,6 283.3 237.0 290.7 291.4 298,1 301.8 305.6 309.3 313.0 316.7 320.4 324 1 327.8 331.5 335.2 338.9 342.6 346.3 350.0 353.7 357,4 361.1 364.8 368.5 372.2 ] 2 3 4 5 6 7 8 9 110 1 2 3 4 5 6 7 8 9 120 1 2 3 4 6 G 7 8 9 130 1 2 3 4 h 6 7 8 9 140 1 2 3 4 5 6 7 8 9 150 1 2 3 4 5 6 7 8 9 Contents, Cn. Yds. A. B. 100 370.4 160 ] 2 3 4 5 G 7 8 9 17.. 1 t 3 4 5 0 7 8 9 180 ) 2 3 4 5 6 7 8 9 190 1 a 3 4 5 6 7 8 9 200 374.1 377.8 381.5 385 2 388.9 39i.6 396 3 4000 403.7 407.4 411.1 414.8 418 5 422 2 425.9 429,6 433 3 437.0 440 7 414.4 448 1 451.9 455,6 4-59 3 463.0 466 7 470.4 474.1 477.8 481.5 485.2 488,9 4926 436.3 500.0 503.7 507.4 511.1 514.8 518.5 522.2 525.9 529.6 533.3 537 0 540.7 544.4 543.1 551.9 555.0 559 3 503.0 566 7 570.4 574.1 577.8 531.5 585.2 538.9 592 6 596 3 600.0 603 7 607.4 611.1 614.8 618.5 622.2 625 9 629.6 633.3 637.0 640 7 644 4 048 1 651 9 655 6 659.3 663 0 666.7 670.4 674 1 077.8 681 5 6852 688.9 692.6 096.3 700.0 703.7 707.4 711.1 I 714.8 718.5 i 722 2 725.9 729 6 733 3 737.0 740.7 372.2 375.9 379.6 383.3 387.0 .390.7 394.4 39.S.1 401.8 405.6 409.3 413.0 416.7 420.4 421.1 427.8 431.5 435.2 438 9 442.6 416.3 450.0 453.7 457.4 461.1 464.8 468,5 472.2 475.9 479.6 4833 487.0 490 7 494.4 493.1 501.8 505.6 509.3 513.0 510.7 520.4 521.1 527.8 531.5 535.2 533.9 542.6 546.3 550.0 553.7 557.4 531.1 564.8 563 5 572 2 575.9 579.6 583,3 587.0 590.7 594 4 598.1 601 8 605 6 609.3 613.0 616.7 620.4 624 1 627.8 631.5 635.2 638.9 642.6 646.3 650.0 ■ 653.. , 657.4 061 1 664.8 638.5 672 2 675.9 679.6 683.3 687.0 690.7 694.4 698.1 701.8 705.6 709.3 713.0 716.7 '^20.4 724.1 727.8 731.5 735.2 738.91 Conteiiis, Cu. Yd^. A. B. 200 740 ' 749 f! 1 74,4 4 746 2 2 1 / TO, 1 7=in t\ 3 751.E 753 7 4 755 (. 5 759 ' 7fil 1 / O 1 . 1 e 733 t ICl S / ut,o 7 766 7 768.5 8 772 2 9 774. 1 775.9 2H' 777.8 779,6 1 781.5 783.3 2 735.2 787 0 3 738.1 790.7 4 792.0 794.4 5 796. t 798.1 C 80r.( 801.8 7 803.7 805.6 8 807.4 809.3 9 811.1 813,0 220 814.8 816.7 1 818.5 820.4 2 822.2 824 1 3 825.9 827.8 4 829.6 831.5 ft 833.3 835.2 G 837.0 838.9 7 840.7 842^0 8 8444 843 3 9 843.1 850.0 230 85 1 .9 853.7 1 855.6 857.4 2 859.3 861.1 8 863.0 861^8 4 833.7 863 5 5 870 4 872 2 G 874.1 875,9 7 877.8 879^6 8 881.5 883.3 9 835.2 887^0 240 883 9 890.7 1 892.3 891.4 2 893.3 893.1 3 900 0 901.8 4 903.7 9(i5!o 5 907.4 909 3 6 911.1 913^0 7 914.8 916 7 8 918.5 920.4 9 922,2 924.1 2.50 925 9 927.8 1 929.6 931.5 2 9333 935 2 3 937.0 933.9 4 940.7 942.6 5 914.1 946.3 G 918.1 950.0 7 951.9 953.7 8 955 6 957,4 9 959.3 961.1 260 933.0 964 8 1 936 7 938.5 2 970 4 972.2 3 974.1 975.9 4 977.8 979.6 5 931.5 983.3 6 985,2 987.0 7 938.9 990.7 8 992.6 994.4 9 996.3 998 1 300 1 2 3 4 6 fi 7 8 9 310 I 2 C'oiit.'iiis, Cu. Yds. 27iHooo.o 1001.8 1 1003.7 1005.6 2 1007 4 1009.3 3 1011.1 1013.0 4 1014.8 1016.7 6 1018.5 1020.4 6 1022.2 1024.1 7 1025.9 1027.8 8 1029.6 1031.5 9 1033.3 1035.2 280 l(i37.0 1038.9 1 1040.7 1042.3 2 1044.4 1046 3 3 1048,1 10.50.0 4 1051.9 1053.7 6 1055.6 1057.4 6 1059 3 1061.1 7 1063.0 1064.8 8 1066 7 1068.5 9 1070.4 1072.21 29,» 1074.1 1,1077.8 2 1081-51083.3 3,1085.2 1087.0 4 1088.91090.7 5 1092.6 G! 1096.3 711100.0 8 1103.7 1107.4 742,6|3eo|llll.l 1075.9 1079.6 4 5 (; 7 8 9 320 1 2 3 4 6 G 7 8 9 330 1 2 3 4 5 G 7 8 9 340 I 2 5 G 7 8 9 350 J 2 3 4 5 6 7 8 9 360 1 2 3 4 5 G 7 8 9 S70 1 2 3 4 1094.4 1098.1 1101.8 1105.6 1109.3 1113.0 6 7 8 9 380 1 2 3 4 5 G 7 8 9 390 1 2 3 t 1111,1 1114.8 1118.5 1122.2 1125.9 1129.6 1133.3 11370 1140.7 1144.4 1148 1 I15I.9 1155 6 1159 3 1163.0 1166.7 1170.4 1174.1 1177.8 1181.5 1185.2 1188 9 1192.6 1196.3 1200 0 1203.7 1207.4 1211.1 1214,8 1218 5 1222.2 1225 9 1229.6 1233.3 1237.0 1240.7 1244.4 1248 1 1251.9 1255.6 1259.3 1233.0 1206.7 3 1270.4 4' 1274.1 1277.8 1231.5 1285.2 1283.9 1-92.6 1296.3 1300.0 1303. 1307.4 1311.1 1314.8 1318.5 13222 1325.9 1329.6 13333 1337.0 1340.7 1344.4 1348.1 1351.9 1355.6 1,359.3 1363.0 1366.7 1370.4 1374.1 1377.8 1381.5 1385.2 1388.9 1392.6 1396.3 1398 1 1400.0 1403, 1407.4 1.411.1 1414.8 1416.7 1418.5 1422.2 1425.9 1429.6 1433.3 1437.0 1440.7 1444,4 1448.1 111.3.0 1 1167 1120.4 1124.1 1127 8 1131,5 1135.2 1138.9 1142, 1 1146,3 1150.0 1 153 7 1157.4 1161.1 1164.8 1168.5 1172.2 1175 9 1179.6 1183 3 1187,0 1190.7 11944 1198.1 1201.8 1205.0 1209.3 1213.0 1216.7 1 220.4 1224.1 1227.8 1231.5 1235,2 1238.9 1242.6 1216.3 1250 0 1253.7 1257.4 1261.1 1234 8 i 26S.."i 1272,;: 1275.9 1279 6 1233.3 1287.0 1290.7 1294.4 1298.1 1301.8 1305.6 1309.3 1313.0 1316.7 1320.4 1324.1 1327.8 13315 1335.2 1338.9 1342.6 1346 3 1350.0 1353.7 1357.4 1361 1 1364.8 1368.5 1372.2 1375.9 1379.0 1383.3 1387.0 1390.7 1394.4 400 1 2 3 4 6 G 7 8 9 410 1 2 3 4 5 ^ 6 7 8 9 42ii 1 2 3 4 5 6 I ontents, Cu. Yd«. A. B. 9 430 1 2 3 4 6 G 1401.8 1405.6 1409.3 1413.0 8 9 440 1 ,2 3 4 5 6 7 8 9 450 1 2 3 4 5 6 7 8 9 460 1 2 3 4 5 G 7 1481.5 1485.2 1488.9 1492.6 1493.3 1500.0 1503 1507.4 1511 1 1514.8 1518.5 1522 2 1525 9 1529 6 1533.3 1537.0 1540.7 1544.4 1543,1 1551.9 1555 6 1559.3 1563.0 1566.7 1570.4 1574.1 1577.8 1531.5 1585.2 1588,9 1592.6 1433 3 1487.0 1490.7 1494 4 1493.1 1501.8 1505.6 1.509.3 1513.0 1516.7 1 520.4 1524.1 1527.8 1.531.5 1535,2 1.538.9 1542.6 1546.3 1550.0 1553.7 1.557.4 1561.1 1564.8 1.568.5 1572.2 1.575.9 1579.6 1583.3 1587.0 1590.7 1594.4 9 470 1 2 3 4 5 G 7 8 9 4S0 1600.0 1603.7 1607.4 1611.1 16148 1618.5 1622.2 1625.9 1629 6 1633.3 1637.0 1010.7 1644.4 1048.1 1651.9 16.55.6 1659,3 1663.0 1666.7 1670.4 1674.1 1677.8 1681.5 1596.3 1598.1 1601.8 1605.6 1609.3 1613.0 1616.7 1620.4 1624 1 1627.8 1631.5 1635.2 1638.9 1042,6 1646.3 1650.0 1653.7 1657.4 1661.1 1664.8 1668,5 1672.2 1675.9 1679.6 1683,3 1685.2 1687,0 1688.9 1690.7 1692.6 1694,4 1696.3 1698.1 1700.0 1701.8 1703.7 1707.4 1709.3 1420 4 1424.1 1427.8 1431.5 1435.2 1438.9 1442.6 1446.3 14.50.0 1451.9 14.53.7 1455 6 1457.4 1459.3 1461.1 1463.0 1464,8 1466.7 1468.5 1470.4 1472.2 1474,1 1475.9 ., 1477.8 1479,6 400 1481.5 1483.3 1711.1 1714.8 1718.5 1722.2 1725.9 1729.6 1733.3 1737.0 1740.7 1744.4 1748.1 1751.9 175.5.6 17593 17630 1766.7 1770.4 1774.1 1777.8 1 11781.5 2!l785.2 1705.6 3,1788.9 1790.7 1792,6 1796.3 1800.0 1803.7 1807.4 1811.1 18148 1818.5 1822.2 3 1825.9 4 1829.6 5,1833.3 6:1837.0 7 1840.7 8 1844.4 9 1848.1 500.1851.9 4 5 G 7 8 9 490 1 2 1713.0 1716.7 1720.4 1724.1 1727.8 1731.5 1735-2 1738.9 1742.6 1746.3 1750.0 1753.7 1757.4 1761.1 1764.8 1768.5 1772 2 1775.9 1779.6 1783.3 1787.0 1794.4 98.1 1801.8 18056 1809.3 1813.0 1816.7 1820.4 1824.1 1827.3 1831.5 1835.2 1838.9 1842.6 1846.3 18.50.0 1853.7 9^. 500 1 2 3 4 5 6 7 8 9 510 1 2 3 4 6 6 7 8 9 520 1 2 3 4 5 6 7 8 9 Contents, Cu. Y.N. A. B. 1851.9 1855.6 1859.3 1863.0 1866 1870.4 1874.1 1877.8 1381.5 1885.2 1888.9 1892.6 1896.3 1900.0 1903.7 1907.4 1911.1 1914.8 1918.5 1922.2 1925.9 1929.6 1933.3 1937 0 1910.7 1944.4 1948.1 1951.9 1955.6 1959.3 030 1963.0 1963.7 1970.4i 1974.1 1977.8 1981.5 1985.2 8 9 540 1 2 3 4 5 18.53.7 18.57.4 1861.1 1864.,S 1 868.5 1872 1875.9 1879.3 1883.3 1887.0 1890 7 1894.4 1898.1 1901.8 190.5.0 1909.3 1913.0 1916.7 1920.1 1924,1 1927.8 1931.5 19.35,2 1938,9 1942.3 1946.3 19.50,0 1953,7 1957.4 1961.1 1961..S 196,S..-. 1972,2 1975,9 1979.6 1983 3 1987,0 1988.9 1990.7 1992,6 1994.1 1996.3 2000.0 2001.8 6 2022.2 2021.1 7 8 9 550 1 2 3 4 h 6 7 S 2003 2007.4 2011.1 2014.8 2018.5 9 560 1 2 3 4 6 7 8 9 570 1 2 3 4 5 6 7 8 9 580 1 2 2025.9 2029.6 2033.3 2037.0 2040.7 2041.4 2048, 1 2051.9 20.55.6 2059.3 1998.1 Contents, Cm. Yds. A. B. 600 2222.2 2224 1 1 '2225.9 2227.8 2 2229,6 2231.5 3 2233,3 223,5.2 4 2237.0 2233.9 2212.6 2216.3 2250.0 2253 7 5 2240.7 6 2244.4 7 2248.1 8 2251.9 9 2255.6 6 1 0,22.59.3 1 2263 0 2 2266.7 3 2270.4 4 2274.1 6 2277.8 6 2281.5 7 2-;85 2 22.57.4 2261.1 2264.S 2268.5 2272.2 2275.9 2279.6 2283.3 2287.0 Conienls, Cu. Yds. B. 7 . :)0 2592.6 2594.4 1 9 2005.6 2009 :! 5 2013.0 2016.7 2020.4 2066.7 2027.8 2031.5 2035.2 2033 9 2042.3 i046.,! 2050.0 2053. 2057.4 2061 1 2063.0 20618 2068.5 2070.4 2072.2 2074.1 2075.9 2077.82079.6 2081 512083.3 2085.2 -2087.0 2038 9 2090.7 2092 6 2094.4 6 2096.3 2098.1 100.0 2101.8 G 4 8 9 590 1 2 3 4 h G 2103.7 2107.4 2111.1 2114.8 2118.5 21222 212.5.9, 2129.6' 2133.3 2137.0 2140.7 2144 4 2105.0 2109.3 2113.0 2116.7 2120.4 2124.1 2127.,3 2131.5 2135.2 21389 2142.3 2146.;; 148.1 21.50.0 2151.9 2153.7 2155.6 2157.4 2159.3 2163.0 2161. 2166 2170.4 2174. 2177.8 2181.5 18.5.2 2161. 2168 2172 2175 2179 3 2183.3 21.37.0 8 2238 9 2290.7 9 2292.6 2294.4 620 2296,3 2298.1 1 2300.0 2301.8 2 2.303.7 2305.6 3 2307.4 2309.3 4 2311.1 2313.0 5 2314 8 2316.7 6 2318 5 2320.4 7 2322.2 2324.1 8 2325 9 2327.8 9 2329.6 '233 1.5 630 2333.3 2335.2 1 2337.0 233-1.9 2 2340.7,2342 6 3 2344.4 2343.3 4 2318.1 23.50.0 5 2351.9 2353.7 6 -2355,6 2357.4 7 2359,3 2361.1 8 2333.0 2364.8 9 2336.7 2368.5 640 2370.4 2372.2 1 2374.1 237.5.9 2 2377.8 2379.0 3 2331.5 2383 3 '"4 2385.2 2387.0 6 2388.9 2390.7 6 2392.6 2394 4 7 2396.3 2393.1 8 2400.0 2401.8 9 2403.7 2405.6 65 0 2407.4 2409.3 1 2411.1 2413,0 2 2414.8 2416 7 3 2418.5 2420.4 4 2422 2 2424 1 5 2125.9 2127 8 6 2429.6 2431.5 7 2433 3 2435,2 8 2437.0 2438 9 9!2440.7 2442.3 66«»2444 4'2446.3 1 2448 1 1 24.50.0 2 2151,9 24.5,3,7 3 245.5.6 2457.4 4 2459.3 2461.1 5'2463.0!2464.8 6'2166.7!2168 5 7'2470.4'2472 2 8 2474.1 2475.9 9'2477.8 2479,6 e70'2181.5i24s3.3 l'248.5.2'2487.0 2 2488.9'2490.7 3'2192.6'2494.4 4 2196.3 2498.1 5 2500.0 2-501.8 6 2503.712505.0 7 2,507.4: 2509..3 8 2511.1 2513,0 9 2514.8j2516,7 680 2518.5 2-520.4 3 4 5 G 7 8 9 710 1 2 3 4 5 7 8 9 720 1 2 3 2596.3 2.598.1 2600,02601.8 2303.7 ;260.5.6 2607.4 2309.3 2611.1,2613,0 •2614.8 2616.7 2618.5 2620,4 2622,2 2624,1 2625.9 2627. H 2629 6 2f>31.5 26,33 3 2635 2 2637.02638.9 2640.7 2644.4 2648.1 2642.6 2646.3 2650.0 6 2651 9 26.53. 2655.6 26.59.3 2661.1 2363.0 2664.8 2366.7 2670.^ 2374.1 2377.8 2679.6 4 2631.5 5 2685.2 6 2688.9 2690 7,2692.6 8 2696,3 2698.1 9:2700.0 7 3 0 2703. 1 '2707.4 2 2711.1 3 2714.8 7 8 9 74i) 1 2 3 4 5 6 7 8 9 750 1 2718.5 2720.4 2724.1 6 272.5.9 2727.8 2729.6 2731.5 2733.3 2735.2 2737.0 2733.9 26.57.4 2668.5 2372.2 267.'.,9 ^ .1 800 1 2 3 26S3,3 2687,0 2694.4 2701.8 2705.0 2709,3 2713 0 2716.7 2740.: 2748.1 2742,6 2744.4 2746.3 27-50.0 8 9 760 1 2188.9 2190.7 2191,4 2192.6 2196.3;2198.1 2200.0:2201 8 2203.7 1 2205. 6 2207.4 2209.3 7 2211 1 2213.0 214.8 22:6.7 9 2218.5 2220.4 600 2222.2 2224.1 1 2522.2 2524,1 2 2525,9 2-527.8 3 2529 ; 2531.5 4,2533,3 2535.2 5 2537.0 2.538.9 G 2540 7 2542 (i 7 25U.4 2516.;! 8 2543 1 2550.0 9 2.551.9 25.53.7 690 2555.6 2-557.4 1 2.559.3 2561.1 2 2-563.0 2564.8 3 2566,7 2-568.5 4 2.570,4 2-572.2 5 2.574.1 2.575.9 S 2577.8 2579.0 7 2581.5 2-583.3 8 2585.2 2587.0 9 2588.9 2590.7 700 2592.6 2594.4 2751.9 2753.7 275.5.6 2757.4 2759.3 2761.1 2763.02764.8 2766.712763.5 2770.4'2772.2 2774.1 2775.9 •2777.8 2779.6 2781.5 2783.3 278.5.2 2787.0 2788.9 2790.7 792.62794.4 2796.3 2798.1 2800.0 2-^01.8 2803.7 2805.6 2807.4 2809.3 ■2811,1 2813.0 2814.8 2816.7 2318.5 2820 4 2322.2 2824.1 3 2825.9 2827.8 •2829 6 2831.5 5 2833.3 2835.2 G 2837,0 2838 9 2840 7 2342.3 •2814,4 2846.3 9'2848.1 28.5O.0 7 70' 235 1. 9 28.53, l'23.55.6 28.57.4 2'23.59 3 286 3 2863.0 2864.3 4 2866.7 2868.5 5 2870.4 2872 2 6 2874.1 2875.9 7 2877.8 2879.6 8 2881.5 28.S3.3 9 2885.2 2887.0 780 2888.9 2890 1 2392.6 2894.4 2 2896.3 2898.1 3 2900.0 2901.8 4 29it3.7 2905.3 6 2907.4 2909 3 6 2911.1 2913 0 7 2914.8 2916,7 8 291.3.5 2920.4 9 2922.2 2924. 1 790 •29'2-5.9 2927.8 1 2929.6 2931.5 2 2933.3 2935.2 3 2937.0 2938 9 4 2940.7 2942.0 6 2944.4 2946.3 6 2943.1 2950.0 7 2951.9 2953.7 8 29-55.6 2957.4 9 2959.3 2961.1 800 2963.0 2964.8 4 5 G 7 8 9 810 J 2 3 4 {, 6 7 8 9 820 1 4 5 G 7 8 9 830 1 2 3 4 5 6 7 8 9 Contents, | Cu. Yds. I A. 840 1 3107.4 3111 3114.8 2 3118.5 3 3122.2 850 1 2963.0 2934.8 2066.7 2968 2970.4 2972 2974.1 2975 •2977.8 2979, 2931 5 2983,3 •2985,2 2987 2988.9 2990. 2992.6 2994.4 29^6.3 2998 .3000.0 3001, 3003.7 3005, 3007.4 3009, ■m\.\ 3i'13 0 ,3014.8 3016. 3018.5 3020.4 3022.2 3024, 3025.9 3027.; 3029.6 3031. 3033.3 3035 3037.0 3038. 3040.7 3042 3044 4 3043.3 3018.1 30.50, 3051.9 30.53, 3055.6 3057, 3059.3 3061, 3063.0 3064. 3066 7 3068, 3070.4 3072, 3074.1 3075. 3077.8 3079.6 3081.5 3083 ;?085.2 3037.0 30^8.9 3090 3092.6 3094.4 3096.3 3098. 3100.0 3101.8 3103.7 3105.0 3125.9 3127.8 3129.6 6 3133 3 3135,2 3137.0 3133,9 8 3140. 9 3144.4 3148.1 3151,9 3155.6 3157.4 3 3159.3 3101.1 3163.0 3164.8 6 3166.7 G 3170.4 3172.2 86 3174.1 31093 3113.0 3116 3120.4 3124.1 3131.5 3142.6 3146.3 3150.0 31.53 3168..^ 3175. 3!77.8 3179.U 3181.531833 3185.2 3187.0 3188.93190.7 3192.63194.4 3 3196.3 3' 98.1 4 3^200.0 3201.8 6 3-203.7 1 3205.(1 6 3207.4 3209.3 7 3211.1 3213.0 8 3214.8|3216 9 3218 5 3^2^20.1 870 32-22. 2' 32^24. 1 1 32-25 9,3-227.8 2 32.9.6,3231. 3 3233.3 32;i5. 4 32,37.o!3238.9 6 3240 7l321-2.( G 3244,4 3246.; 7 3'248.1 ;^250.0 8 3251 9:^253 9 3255.6 3257.4 8.80 3259.3 3261 1 3263.0 2 3266. 3 3270.4 32 4:3274.1 6 3277.8 6.3281.5 3283.3 7,3-285.2 8 '3238.9 3290 9.3292.6 89 0 3296.3 1 3300.0 3301.8 2 3303.7 3 3307.4 4 '33 11.1 6 13314.8 ;5318.6 3322.2 33^5.9 :?264.8 3233.5 3275.9 3279.6 3^287.0 3294 4 ;^'298.1 9 900 3333.3 3335.2 3305.6 .3309.3 .3313.0 3316.7 ;!;i20.4 3324.1 3327.8 3329.6 3331.5 900 J 8 4 5 6 7 8 9 910 I 7 8 9 920 Contents, Cu. Yds. 333.3.3 3335 2 3337.0 3338.9 3340.7 3342.6 3344.4 3346.3 3348.1 3350,0 :«5i. 9 3.3.53.7 ;«55.6 33.57.4 3:^59.3 3361.1 3333.0 3364,8 9 3366.7 3368.5 3370 4 3372.2 3374.1 3375.9 2 ;«77.8'3379.6 3:;«81.5 3.383,3 4 .333.5.2 33.^7.0 513388.9 3390.7 6:3392.6 3394 4 3:«6.3 3398.1 31(10.0 3401.8 3403 7 3405,6 3407.4 3409,3 1 3411.1 3413,0 2,;^414.8 3416.7 3 3418 5 3420,4 4 34^22.2 34-24.1 6 342.5.9 34-27 8 G 3429.6 3431,5 7 34.33 3 3435,2 8 3437.0 3438.9 9 3440.7 3442.6 930 3144.4 3443.3 1 3148.1 34.50.0 2 3151.9 34.53.7 3 3455.6 3457.4 4 3459.3 3461.1 5 3163.0 3464.8 6 3466.7|3468.5 7 3470.4 3472.2, 8 .3474.1 3475.9 9 ;«77.8, 3479.6 940 3131.5,3483.3 1 3485.2 3187.0 2 3488.9'3490.7 3 3492.6 3494 4 4'3493.3 3498.1 5,3.500.0 3.501.8 6.3503.713.505.6 7 ;.3507.4 3.509.3 8:3511.1 3513.0 9!3514,8'3516,7 95O3518.5'3520.4 1 3522.23524.1 •. |3525.9 ;i527.8 3 3529.6 3531.5 4 3.533.3 353.5.2 5 3,537.0 3.5.38.9 G 3510.7 3-54-2.6 7 '3541.4 3546.3 8 3548.1 3550.0 9 3-551.9 3553,7 960 3.555.6 3,^57.4 1 3.5.59.3 3.561 1 2 3563.0 3504 8 3 3.566.7 3.')68,5 4 3570.4 3572 i 5 3.574.1 3575 9 6 3577.8 3.579.6 7 3-581.6 3.583.3 8 .3.585.2 3587.0 9 3.588,9 3.590,7 970 3.592.6 3594,4 1 3596.3 3598.1 2 3600.0 3601.8 8 3603.7 3605.6 4 3607.4 3609.3 6 3611.1 3613.0 G 3614.8 3616.7 7 3618.5 3620.4 8 3622.2 3624.1 9 3625.9 3627.8 980 3629.6.3631.5 1 ,363;i3 3335 2 2 3337.0 3638.9 3;}610.7 .3612 6 4 3644.4 3(;i() 3 5 3648.1 3650.0 6 3651.9,3653.7 7 3(>55.6 3(i57,4 8 .36.59.3 3631,1 9 366:i,o ;^(;(;4.8 990 3666.7 3(!H8.5 3672.2 3675.9 1 3670.4 2 3674.1 3 3677.8 3679.6 4 3681.5|36.S3 3 5 ,3685.2!3687.0 6 3688.9 ,3690 7 7 3692.6 3694.4 8 3696.3 3698.1 9 3700.0 3701.8 100 0 3703.71 RATIOS OF CORRECTION FOR AVERACE END AREA CALCULATIONS. WIDTH OF UOAI) UKII. Area of 1.-J5 2 2.5 2 12 2.25 to 100 14 100 16 18 100 100 20 100 22 100 24 100 26 28 100 100 30 100 H ifjlit ..r 1 1 1—5 6.04 5.2 4.74 5,74 4.81 4.41-5.14 4.45 4.13 4.72 4.14 3.88 4..33 3.87 3.644.00 3.62 3.43 'i.71 3.43 3.243.47 3.20 3.07 3.24 3.20 2.91 Ua in nt Kiiil Anas, 1:1 1:1.2 1:1.4 1:1.6 1:1.8 1:2 l:2.o l:;j 1::5..> 1:1 1:4.5 1:.'» 1 :'.."> 1:6 1:6..> 1:7 1:7.5 l:s l:s.5 1:» 1:1>.5 1:10 .sertion Varj iiij; I'll a I SI -cs. Slope. }:1 .001 .002 .007 .012 .019 .033 .045 .056 .067 .076 .0S5 .093 .100 .107 .113 .119 .124 .] 28 .133 .13S .142 001 003 006 OIO 014 023 032 Oil 050 057 065 071 077 083 089 094 100 106 111 117 123 1:1 n-.i 001 .001 ,004 .004 .007 .00,s 012.01 018 .022 ,032 .033 ,043 .044 ,0i5 ,056 ,066 .067 075 .076 ,083 .084 ,0911.092 ,098 '.100 105 .106 110 .111 115! 116 120.122 125|.127 130M32 134!. 1,36 138'. 140 Slope. Slope. Slope. Slope. Slope. Slope. Slope. Slope. Slope. Slope. Ratio of Anas. 1:1 ,001 .002 .004 .006 .009 .016 .023 .030 .0,38 .043 ,049 ,055 060 065 ,070 075 079 ,084 088 092 097 1:1 ,001 ,004 ,006 010 .014 ;026 037 ,047 ,057 ,066 ,074 ,081 088 094 100 105 110 115 120 125, 130 1^:1 .001 .004 .007 .011 .015 .027 .040 .051 .061 .070 .07.S .084 ,093 ,099 ,105 110 .115 120 ,125 ,130 135 }:1 .001 .002 .003 .005 .006 012 .019 .026 .033 .039 .044 .050 .055 .060 .065' .069' .073 .077 .082 .0S6 .090 1:1 1^:1 ,001 .001 ,003 .003 006 010 .006 .010 .014.014 .024'.026 .035 .037 ,045 ,054 .04 .056 062 .065 ,070' 07 ,0771.080 084'.088 0901 095 095'.101 100|.105 106'. Ill 1111.116 116'. 121 12l|.125 126.130 .001 .002 .00:; .005 .010 .016 .022 .029 .035 .040 .046 .051 .056 .060 .064 .068 .072 .076 .086 .084 1:1 .001 .003 .006 .010 .014 ,024 .033 .042 ,051 U:l 4,1 .001 .003 ,00f .010 .014 .025 .035 .047 .054 .059 .062 .066 .070 .073 .078 .079 .085 .085 .091 ,091|.097 096'. 102 ,101 .107 106 .112 ,111|.117 116.121 120'.126 .001 .002 .003 .005 010 .014 ,020 ,025 0311 ,036 ,042 ,047 051 055 058 062 065 069 072 075 i-.m-.i hi ,001 .001 ,003 .003 ,00(i .006 .009 .00!) .013 .013 .022 .024 .031L034 .039 .044 .048i.052 .055 .063 .070 .076 .082 .088 .093 .098 .102 .106 111 .116 .060 .(i6S .075 .082 .088 .093 .098 .103 .108 113 117 .122 ,001 ,002 003 .005 010 ,014 1:1,1^:1 hi 1:1 .001 .001 .003 .003 ,005 .005 .008 .009 ,012.013 020 .023 ,028 .033 019.037 .042 .O23L045 .050 1^:1 .053 .058 060 .066 .066 073 .072 .079 .078 .085 .083 .090 ,053 .088 .095 056.093.100 .060 .097 .104 ,063 .102.109 ,066 .106 .113 ,0691.111 .118 .028 .033 .037 .041 .045 .049 001 .002 -003 .005 .009 .014 .019 ,022 ,026 ,030 ,034 ,037 041 044 047 ,050 ,054 ,057 060 063 .001 .001 .0031.003 .005 .007 .011 .019 026 .034 .042 ,049 ,05(1 ,062 ,06 s ,074 079 084 OSI) ,094 ,09S ,103 ,107 .005 .OOS .013 .021 .030 0!9 .047 .055 (HiL' 069 .075 .081 .OSO .091 .095 .100 ,105 .110 .114 1-1 4.1 1:1 .001 001 1. 003 002 .005 r03 .007 .005 '.010 010.017 013 .025, .0171.032 021 1. 039 024.046 .028 .053 ,031 .059 ,034 .064 037 .070 040 .075 043 .080 047 .084 0.50 08S 053 .093 056 .098 059 .102 U:l .001 .003 .005 .00 .012 .020 .028 .036 .045 .052 .059 .066 .07-/ .077 .082 .0>7 .092 .097 .lul .lO'v 110 1:1 001 ,002 003 005 ,008 012 016 019 022 025 028 031 034 037 040 043 046 048 051 054 1:1 ,001 .002 .004 .006 009 016 .023 .030 037 044 .050 055 .060 065 070 075 080 084 088 .(i93 097 1J:1 .001 .003 .005 .008 .011 019 .02' .034 .042 .050 .057 .063 069 .075 .O.SO .085 .0M9 .091 .098 .102 .107 hV 1:1 1^1 .001 .001 .002 .002 .004 .005 .006 .007 .009 .010 .015 .018 .022 .025 .029 .033 .03"^ .040 .041 .048 .018 .054 .053 .000 hi 001 ,001 ,002 ,003 ,006 010 013 016 019 022 025 027 030 033 036 03 S 041 044 046 049 001 001 002 O03 005 008 .011 014 016 .019 021 l:l'l]:l ,058 ,063 067 .066 072 .077 .O72L082 .076'.086 .080.091 .084 .095 .088 ,100 .092 .104 .001 '.001 .002 .00-; .004 .005 .006 .00 .008 .010 .014.017 021 .024 .027 .(*32 .(•34 .03H 040 ,046 .045 .052 050 .058 024 .055 .064 I '26 .060 .069 029 .064 .074 031 .068 079 034 .072 .084 036 .076 .0S8 039 .079 .092 04 i .083 .096 044 .087 .100 1:1 1:1.2 1:1.4 1:1.6 1:1.8 1:2 1:2.5 1:;{ 1:3.5 1:4 1:4.5 1:.> 1:5.5 1:6 1:6.5 1:7 1:7.5 1:8 l:-i.5 1:!) 1:1). 5 I:m) On Estimating Earthwork, The accompanying table is designed to fiicilitate the cuinputation of earthwork after the areas of the cross sections have been obtaine(l. The areas may be ob- tained bv calculation from the field notes ; or the cross sections may be plotted and the areas obtained by the plani meter. 'J'iie firmer method is short and easy in a level country, but where the surface of the ground is broken and irregular the latter method is to be preferred. Plotting tlie cross s 'ctions also makes a complete record of the work, with its classification at every point, and allows revision atid deviation within the limits to wiiich the section is taken, by simply indicating the position of the centre line. Usua'iy it will be found easiest to plot the rods fri>m a line assumed as the height of in- strument ; but when the work is extend- ed so as to involve several heights of instrument in the same section, or when the work is to be used for a great i.i.mber of calculations tor successive estimates, it will be found cheapest to work from elevations. A convenient form for the estimate sheets is here sliown. In the two first columns are entered the stations and plus-es at which the cross sections are tiiken. The column headed "'Length in Feet" is filled up by subtracting the numbers in these two first coluinns. The columns headed " Area uf Cross /Section " are filkd up with areas obtained either from calculation or from measurement by the planimeter. In the columns head- ed "Aventcje Area" are entered one-half the sums of the areas of adjacent cross sections. If preferred the suras, in.^tead of the halt' sums, may be used, in which case the final contents will be doubled. The main columns of " Contents in Cubic yards ^' are now filled up by aid of acc(mipanying " Table of Cubic Yards in Lengths of lUO Feet." If the lengths are li'O feet the corresponding quantities are si 01 ply transferred from the table. If the distance is 50 feet, one half the quan- tity is transferred. If the distance is 25 feet, one-fourth, &c. Usually the opera- tion can be performed mentally. The table being set up before one, the arrange- ment of it is such that the eye knows just wlvere to strike for a quantity. There are no leaves to turn. Quantities can be entered as fast as one can write. Blue ink may be used in writing quantities in excavati'Mi, and red ink in writing quan- tities iu embankment. The calculation of earthwork by the metiiod of averaging end areas is not theoretically correct, excepting in the two special cases : one when the end areas are equal, and the other when the prismoid has two of its longitudinal bounding planes parallel. As that por- tion of every roadway prismoid, which lies between the vertical planes passing through the edges of the roadbed is practically included in the latter condi- tion, it follows that the variation from the true contents, obtained from averag- ing end areas, lies outride the central roadbed prism, and we may consider it as dependent on the four following factors : 1st. The ratio of the end areas of the prismoid. 2nd. The width of the roadbed. 3rd. The degree of the slope. 4th. The heighth of the section. This variation has been investigated with the result shown in the table called " Itutios of Correction for Average End Area Calculations." The manner of pro- ceeding was briefly thus : With the data shown in the heads of the columns in the table, and in the left hand column, the true contents of the prisms by the prismoidal fi)rmula were found, as well as the contents, by averaging end areas. The ratio of variation in many par- ticular cases being thus found, the curve of variation for each class was formed by measuring the ratios of end areas on the axis of abscissas, and the per- centages of variation on the axis of ordin- ates. Some maxima and miruma of these curves were also traced, which seemed to differ, in extreme cases, 10 per cent, or so from the mean given in the table. It is believed these deviations will usually counterbalance one another. If the work is of a ])eculiar nature, so the general cases here worked out will not apply, cor- rections applying to it can be worked out and entered in one of the blank columns. To apply the table of corrections, we divide one area of cross section by its neighbor, and take from the table its cor- responding ratio or percentage of correc- tion and multiply the contents by it, writing the result in the column headed " Correction." The special case, when one end is zero, or ends at grade, is not provided for in table of corrections. For this case the correction is, the slope area multiplied by one sixth the length. For the road bed area being the base of a wedge, the solidity is one-half base niulti- plied by altitude; but the slope areas being bases of pyramids, the solidity is one-third base multiplied by altitude. One half which is used, less one-third, which should be used, equals the correction, one- sixth. This correction, as well as all others, is to be deducted from contents in main column. Estimxted duantities in Grading, STA- TIO.NS No. + AUEA OF CROSS IN S({U\KK I^T. AVEKAOE AREA. Excavation, 117 118 119 120 121 122 123 50 Cut comnec'ces ....I 18 16 50158 53105. ....63o'l63325 526 595 50638 263 854171297 ....'110243485 20 Cttl 40 60 31 80103 Cut coin men ces 68 ....'334280 560 ,35700 27 •50743157 ..'821 ,30534 61| cut 70 84 1 90 mtl ends 50870156 209 1«7 ends Eni- baiik' meut 300 314 255 3147 com men ces .394 634 527.1 263.', 55' 15J 72 218^ 517 52 H m\ 845J 677 J 267" = 3 341 108 212 280 270 121^ 170 278^ 217 156.1 17U 130 36J 15 67^ 215,! 426 560^ 540 242^ 280 557 ^ 434l 26 H 232 201 73A Em- bank ment Corrected Totals, CONTENTS IN CUBIC YARDS. Kxcaralion. 16.7 1 162.916 729.632 1174.1 683.8 136 3 40.7 11.4 53.3 161.9 670, 400 S 2987.0 1565 752.8 306.518 9S53.7 98 9755.71.... 2922.4 14 8 63.9 200.6 394 4 362.9 150 0 90.0 103.7 361.0 120 6 579 6 317.6 144.4 41.9 2945.423 :z u 27.8 125.0 399.1 788.9 626.5 300.0 179.6 207.4 722, 241.3 96S.5 4296 223.3 84.4 Em liaiik- mi'Ul 25.1 25.1 7.6 23.8 .5.1 461 86.' 5278.1 82.7 UEUARKS. The error from calculation by averag- ing end areas is not so great as appears at first sight, or as it is often represented. Taking isolated cases, where the ratio of end areas is great, it may be made to appear that the error is 10 or 15 per cent.; but taking extended work the whole error is trifling, the great bulk of con- secutive cross sections being nearly equal to each other, and the errors are distri- buted. The writer tested one section of 28,(j0 > cu. yds. and f )und the error less than one third of one per cent. What appeared to be a sectitm which would show great error on account of crossing several short ravines and gullies, con- taining some 85.000 cu. yd.s., was less than one-half of one per cent, out of the way. In earthwork there are only two sides of the prismoid perfect planes, and these two are the thecjretical planes of the cross section. The surface of the ground is never a perfect plane. The rod, in taking points usually sinks a little in the ground, the slopes are not trimmed exact- ly, nor the grade made perf ct. If there is any difference between the true so'i lity and that obtained by the method here presented, it is the conviction of the writer that it would be easier and cheap- er for the engineer to shovel it than to calculate it. The method of calculation for earth- work should be direct and simple, so it can be used safely by assistants not speci- ally skilled in intricate calculations.. It is better for the engineer to spend much of his time in the field, minutely observ- ing and closely measuring the work, than to spend it mainly in the ofl!ice, basing refined computations on erroneous or careless measurenieiits. The cri-ors in measurement will usually be greater than the errors of calculation, by averaging end areas without cori'ection. — Pulili.^lied by— JOHN WILEY & SONS, Scientific? I* iil>lisliers 1.5 Astor Place. NEW YORK CITY. The New and Complete Catalogue OF THE PUBTjIOATIONS OF JOH]\ WIIiEY & 5?;OIVS, IS Astor Place, New York, CONTAINING Scientific and other Text Books FOR COILEGES, INDCSTRHL SCHOOLS k THEOLOGIC.U SEJUNARIES, with many valuable practical works for ARCHiTECTS, ENGINEERS, MECHANICS, ETC. INCLUDING WORKS ON ApTicultiirc, Assaying', Astronomy, Book-keeping-, Chemistry, Drawinfr and Paintinfr, Engineering-, Metalliirfry, Maoliinery, Jteclianics, Mineral- og-y, t^cnniaiisliip, iStram Engine, Venti- lation, Etc., Etc., and for THEOLOGICAL SEMINAKIES, Hebrew and Greek Ribles, Testaments, Le.xioons, Grammars, Heading Books and Concordances. also a full list of their editions of JOHN RUSKIN'S WORKS. Will be sent free by mail lo anyone ordering it. TABLE OF CUBIC YARDS IN LENGTHS OF 100 FEET ADAPTED ESPECIALLY TO THE CALCULATION OF EARTH WORK BY THE METHOD OF AYERAGING EXD AREAS. Contenis of Column "A" are for the integers in column headed "Area, Square Feet." Contentti of Column " B " are for the same integers plus 0.5 square foot. COPYRIGHT 1885 BY S. B. FISHER. Contents for lengths greater or less than 100 are obtained by simple proportion, thus: 125 sq. ft. for length of 20 {l.=ja%^i of 463.0 cu. yd;.; the contents for 125 sq. ft.=92.6 cu.yds. Cont'-pts, Cu. Yds. 1 2 3 4 5 6 7 S 9 10 1 2 3 4 5 6 20 30 40 B. 8 9 50 J 2 3 4 5 G 7 8 9 CO 1 2 3 4 5 C 7 8 9 70 1 2 H 4 5 6 7 8 9 80 1 2 3 4 6 6 7 8 9 90 1 2 3 4 5 6 7 8 9 10(1 3.7 7.4 II. l 14.8 18.5 22.2 2.^.9 29.»i 33.3 37.0 40.7 44.4 48.1 51.9 55.6 59.3 63.0 66.7 70.4 74.1 77.8 81.5 85.2 88.9 92 6 96.3 1000 103.7 107.4 III. l 114.8 118.r- 122.2 12.5.9 129.0 107.0 140.7 144.4 143 1 151.9 155.6 159.3 103.0 16G.7 170.4 174.1 177.8 131 135.2 13S.9 192 6 193.3 200.0 203.7 207.4 211.1 214.8 218.5 222 2 225.9 229.6 233.3 237.0 210 7 214.4 218.1 251.9 2'>5.6 2.59. 3 2il3 0 266 7 270.4 274.1 277.8 23 1. 5 285.2 288.9 292 6 296 3 300.0 3i)3.7 307.4 311.1 314.8 318.5 322.2 325.9 329.6 333.3 337.0 310.7 344.4 318 1 351.9 3")5.6 359.3 363.0 366.7 370.4 1.8 6.6 9.3 13.0 16.7 20.4 24.1 27.8 31.5 35.2 38.9 42.6 46.3 50.0 53.7 57.4 61.1 618 68.5 72 2 75.9 79.6 83.3 87.0 907 94.4 98.1 101 8 105.6 109.3 113.0 116 120.4 124.1 127.8 131 135.2 1339 142.6 1433 150.0 153.7 157.4 161.1 161.8 163.5 172.2 175,9 179.6 183 3 1S7.0 190. 191.4 19il 201.8 20 209.3 213.0 216.7 220. 221.1 227.8 231.5 235.2 238.9 242.6 246.3 250.0 253.7 257.4 261.1 264.8 26S.5 272.2 275.9 279.6 283.3 287. 0 290.7 294.4 298 301.8 305.6 309.3 313.0 316.7 32i).4 324 327.8 .331 335.2 338.9 342.6 346.3 350.0 353.7 357,4 361. 364.8 368.5 372.2 Coateiits, Cu. Yds. A. B. 100 1 2 3 4 5 6 7 8 9 110 1 2 3 4 6 7 8 9 120 1 2 3 4 6 7 8 9 130 1 2 3 4 9 140 1 2 3 4 5 6 7 8 9 loO 1 2 3 4 5 6 9 160 ] 2 3 4 5 6 7 8 9 17*. 1 S: 3 4 5 (( 7 8 i> 180 ) 2 3 4 5 6 7 8 9 190 1 2 3 4 5 6 7 8 9 200 370.4 374.1 377.8 381.5 385.2 388.9 392.6 396 3 400.0 403.7 407.4 411.1 414.8 418 5 422 2 425.9 429 6 •433 3 437.0 440 7 444.4 448 1 451.9 455 6 459 3 463.0 466 7 470.4 474.1 477.8 481.5 485.2 488.9 492.6 496.3 500.0 503.7 507.4 511.1 514.8 518.5 522 2 525.9 529.6 533.3 537 0 540.7 544.4 543.1 551.9 555.0 559 3 563.0 560 7 570.4 574.1 •577.8 581.5 585.2 538.9 592 6 5963 600.0 603 7 607.4 611.1 014.8 018.5 022.2 025 9 629.0 633.3 637.0 610 7 044 4 048.1 651.9 655 6 659.3 663 0 666.7 670.4 674 1 677.8 681 5 685.2 688.9 092.6 696.3 700.0 703.7 707.4 711.1 714.8 718.5 722 2 725.9 729 6 733 3 737.0 740.7 372.2 375.9 379.6 383.3 387.0 .390.7 394.4 39S.1 401.8 405.6 409.:h 413.0 416.7 420.4 421.1 427.8 431.5 435.2 438 9 442.0 446.3 450.0 453.7 457.4 461.1 404.8 468,5 472.2 475.9 479.6 483 3 487.0 490 7 494.4 493.1 501.8 505.0 509.3 513.0 510.7 520.4 521.1 527.8 531.5 535.2 533.9 542.6 546.3 550.0 553.7 557.4 561.1 564.8 563 5 572 2 575.9 579.6 583.3 587.0 590.7 Conteiiis, Cu. \iU. 200 1 2 3 4 5 6 7 8 9 2K' 1 2 3 4 5 0 7 8 9 220 1 2 3 4 6 7 8 9 230 1 2 3 4 a 6 7 8 9 240 1 2 3 4 5 G 7 8 9 230 1 2 3 4 5 0 7 8 9 CoiitfUis, Cu. Yds. 594 4 260 598.1 0018 005 6 609.3 613.0 016.7 620.4 6241 627.8 031.5 635.2 638.9 642.6 640.3 650.0 653.; 6>7.4 661 1 664.8 668.5 0722 675.9 679.6 683.3 687.0 690.7 694.4 698.1 701.8 705.6 709.3 713.0 716.7 '^20.4 724.1 727.8 731.5 735.2 738.9 742.6 740.7 744.4 748,1 751.9 755,0 759.3 763 0 766 7 770.4 774 1 777.8 781.5 785.2 788.9 792.6 796.3 80r.O 803.7 807.4 811.1 814.8 818.5 822,2 825,9 829.6 833.3 837.0 840.7 844.4 843.1 851.9 855.6 859.3 863.0 806.7 870 4 874.1 877.8 881.5 835.2 883 9 892.6 803.3 900 0 903.7 907.4 911.1 914.8 918.5 922 2 925 9 92D.6 935 3 937.0 94).7 914.4 948.1 951.9 955 6 959.3 903.U 966 7 970 4 974.1 977.8 931.5 985.2 988 9 992.6 996.3 27i» 1000.0 1001.8 1 1003.7 1005.6 2 1007,4 1009.3 3 1011.1 1013.0 4 1014.8 1016.7 6 1018.5 1020.4 6 1022.2 1024.1 7 1025.9 1027.8 8 1029.6 1031.5 9 1033.3 1035.2 280 1037.0 1038.9 1 1040.7 1042.3 2 1044.4 1046 3 3 1048.1 1050.0 4 1051.9 1053.7 6 1055.6 1057.4 6 1059 3 1061.1 7 1063.0 1064.8 8 1066,7 1068.5 9 1070.4 1072.2 742.6 . 7463 750 0 753.7 757.4 761.1 764,8 768.5 772 2 775.9 779.6 783.3 787.0 790.7 794.4 798.1 801.8 805.6 809.3 813.0 816.7 820.4 824,1 827.8 831.5 835.2 838.9 842.0 843 3 850.0 853.7 857.4 861.1 864.8 863 5 872 2 875.9 879.0 883.3 887.0 890.7 891.4 893.1 901.8 9(15.0 909.3 913.0 910.7 920.4 924.1 927.8 931.5 935.2 933.9 942.6 946.3 950.0 953.7 957,4 961.1 964,8 938.5 972.2 975.9 979.6 983.3 987.0 990.7 994.4 998 1 300 1 2 3 4 6 6 7 8 9 310 1 2 3 4 5 7 8 9 320 J 2 3 4 6 6 7 8 9 33) 1074.1 1,1077.8 2 1081-51083.3 4 5 6 7 8 9 300 1085.2 1 088.9 1092.6 1096.3 1100.0 1103.7 1107.4 1111.1 1075.9 1079.6 1087.0 1090.7 1094.4 1098.1 1101.8 1105.6 1109.3 1113.0 9 340 I 2 3 4' 5 6 7 8 9 350 1 2 3 4 5 6 7 8 9 360 1 2 3 4 5 6 7 8 9 370 1 2 3 4 1111,1 1114.8 1118.5 1122.2 1125.9 U-i9.6 1133.3 1137.U 1140.7 1144.4 1148 1 1151.9 1155 6 1159 3 1163.0 1166.7 1170.4 1174.1 1177.8 1181.5 1185.2 1188 9 1192.6 1196.3 1200 0 1203.7 12>I7.4 1211.1 1214.8 1218 5 1222.2 1225.9 1229.6 1233.3 1237.0 1240.7 1244.4 1248 1 1251.9 1255.6 1113.0 1 1167 1120.4 1124.1 ir/7 8 1131.5 1135.2 1138.9 1142. i 1146.3 1150. 1409.3 1413.0 1416.7 1420 4 1424.1 1427.8 1431.5 1435.2 1438.9 1442.6 1446.3 1450.0 1451.9' 1453.7 1455 6 1457.4 1459.3 1461.1 1463.0 1464,8 1466.7 1468.5 1470.4 1472.2 1474.1 1475.9 1477.8 1479.0 2 3 4 5 * 6 7 8 9 42<* 1 2 3 4 5 6 7 8 9 430 1 2 3 4 J> 6 9 440 1 ,2 3 400 1481.5 1483.3 1481.5 1485.2 1488.9 1492.6 1496.3 1500.0 1503 7 1507.4 1511 1 1514.8 1518.5 1522 2 1525 9 1529 6 1533.3 1537.0 1540.7 1544.4 1543.1 1.551.9 1.555 6 1559.3 1563.0 1.506.7 1570.4 1574.1 1577.8 1581.5 1585.2 1588.9 1592.6 1596.3 1600.0 1603.7 1607.4 1611.1 16148 1618.5 1622.2 1625.9 1629 6 16.33.3 1637.0 1040.7 4' 1644.4 6 1648.1 6 7 8 9 450 1 2 3 4 5 6 1651.9 1655.6 1659.3 1663.0 1666.7 1670.4 1674.1 1677.8 1681.5 9 4Go 1 2 3 4 5 6 7 8 9 470 1 2 3 4 5 6 7 8 9 4S0 1 2 3 4 5 6 7 8 9 490 1 2 3 1483 3 1487.0 1490.7 1494 4 1493.1 1501.8 1505.6 1509.3 1513.0 1516.7 1520.4 1524.1 1.527.8 1.531.5 1535.2 1,538.9 1542.6 1546.3 1550.0 1553.7 1557.4 1.561.1 1.564.8 1568.5 1572.2 1575.9 1579.6 1583.3 1587.0 1590.7 1594.4 1598.1 1601.8 1605.6 1609.3 1613.0 1616.7 1620.4 1624 1 1627.8 1631.5 1635.2 1638.9 1642.6 1646.3 1650.0 1653.7 1657.4 1661.1 1664.8 1668.5 1672.2 1675.9 1079.6 1683.3 1685.2 1687.0 1688.9 1692.6 1696.3 1700.0 1701.8 1703.7 1707.4 1709.3 1711.1 1714.8 1722.2 1729.6 1733.3 1737.0 1740.7 1744.4 1748.1 1751.9 1755.6 1759 3 1690.7 1694 4 1698.1 1705.6 1713.0 1716.7 1718.5 1720.4 1724.1 1725.9 1727.8 1731.5 1735-2 1738.9 1742.6 1746.3 1750.0 1753.7 1757.4 1761.1 17630 1764.8 1766.7 1770.4 1774.1 1777.8 1781.5 1785.2 1792,6 1796.3 1800.0 1803.7 1807.4 1811.1 1814 8 1818.5 1822.2 1825.9 4 1829.6 5 1833 3 6 1837.0 7 1840.7 8-1844.4 9 1848.1 600,1851.9 1768.5 1772 2 1775.9 1779,6 1783.3 1787.0 1788.9 1790.7 1794.4 1798.1 1801.8 1805,0 1809.3 1813.0 1816.7 1820.4 1824.1 1827.S 1831.5 1835.2 1838.9 1842.6 1846.3 1850.0 1853.7 Contonts, Cu. Y>U. 500 1 2 3 4 5 6 7 8 9 510 1 2 3 4 b 6 7 8 9 520 1 2 3 4 5 6 7 8 9 530 1 2 3 4 r, 6 7 8 9 ilO 1 2 3 4 1851.9 1855.6 1859.3 1863.0 1866 7 1870.4 1874.1 1877.8 1381.5 1885.2 1888-9 1892.6 1896.3 1900 0 1903.7 1907.4 1911.1 1914.8 1918.5 1922 2 1925,9 1929.6 1933.3 1937 0 1940.7 1944.4 1948.1 1951.9 1955.6 1959.3 1963.0 1963.7 1970.4 1974.1 1977.8 1981.5 18-53.7 1857.4 1861.1 1864.8 868.5 1872.-' 1875.9 1879.6 1883.3 1887.0 1890 7 1894.4 1898.1 1901.8 1905.6 1909.3 1913.0 1916.7 1920.4 1924.1 1927.8 1931.5 1935.2 1938.9 1942.6 1946.3 19.=v0.0 1953.7 1957.4 1961.1 1964.8 1968..^ 1972.2 1975.9 1979.6 1983 3 Contents, Cu. Yds. B. GOO 22-22.2 2224 1 l!2-22").9!2227.8 2 2J-29.6j2231.5 3 2233 3 2235.2 Conpnts, Cu. Yds. A. 2-233.9 2242.6 22 16.3 2250.0 2253 7 22.57.4 2-261.1 2264.S 2-268.5 2-272.2 2275.9 2279.3 2-283.3 2287.0 1985.2 1987.0 1988.9 1990.7 1992.6 1994.1 1996.3 -2000.0 2003.7 2007.4 2011.1 2014.8 2013.5 2022.2 2025.9 2027.8 550 1 2 3 4 b 6 7 8 9 56(» 1 2 3 4 6 6 2029.6 1033.3 •2037.0 2040.7 2044.4 2048.1 2051.9 2055.6 -2059.3 2061 1 •2063.0 2066.712068.5 ■2070.4 2072.2 2074.1 2075.9 2077.8 2079.6 2081 5 2083.H 2085.22087.0 2088 9 2090.7 •2092 6-2094.4 2096.3 2098.1 2100.0 2101.8 9 570 1 2 3 4 b 6 7 8 9 580 1 2 3 4 6 G 9 590 J 2 3 4 b G 7 600 1993.1 2001.8 2005.0 2009,:: 2013.0 2016.7 2020.4 •2024.1 2031,5 2035.2 2033 9 2042.6 2046...! 2050.0 2U53.7 2057.4 2064 8 4 2237.0 5 2240.7 6 2244.4 712-248.1 8'2251.9 9 2255.6 610,2259.3 1 2263 0 2 2266.7 3 2-270.4 4 -2274.1 6 -2-277.8 6-2281.5 7!2i85 2, 8 -2238 9 2290.7 9 '2292.6 2294.4 620 2-296.3 -2-298.1 1 2300.0 2301.8 2 2303.7 2305,0 3 2307.4-2309.3 4 2311.l|23I3.0 6 2314 8 2316 7 6-2318 5 2320.4 7 232-2.2 2324.1 8 2325 9 2327.8 9 23-29.6 '233 1.5] 630 2333.3 23.35.2 1 2337.0 233 -t.9 2-2340.7,2342 0 3 2344.4 2343.3 4-2348.1 23.50.0 6 '2.351.9 2353.7 6 2355,6 '2357.4 7 2359.3 2361.1 8 2363.0 2364.8 9 2366.7 '2368.5 640 '2370.4 '2372.2 1 2374.1 2375.9 2 '2377.8 2379.6 3 2331.5 2383.3 "■4 2.335.2 2387.0 5 '2388.9 2390.7 6 2392.6 2394.4 7 '2396.3 2393.1 8 2400.0 2401.8 9 2403.7 2405.0 650 2407.4 2409.3 1 2411.1 2413.0 2 '2414.8'2416 7 3 '2418.5 24-20.4 4 2422 2 24-24 1 6 2425.9 21-27 8 6 '2429.6 '243 1.5 7 2433 3 2435.2 8 2437.0,2438 9 9'-2440.7|'244'2.6 660 2444 4 2446.3 7 .)0 2502.6 259 1.4 1 -i.V.tC,.:; '259S.I 2, '2000,0 -2001.8 3|'2603.7i2605.0 4' -2607. 4 '2309.3 6;-2611.l|'2613.0 6 7 8 9 710 1 2 3 2103.7 2107.4 2111.1 2114.8 2118.5 2122 2 4 2125.9 2129.6' 133.3 2137.0 21407 144 4 2148.1 210.5.6 2109.3 2113.0 21167 2120.4 21-24.1 2127. H 2131.5 2135.2 2138.9 2142.6 2146.3 2150.0 2450.0 2453,7 1 '2448 1 2 2451,9 3 2455.6 2457.4 4 '2459.3 2461.1 6 2463.0''2464.8 6 2466.7^2468 '2472 2 2475.9 2479.6 7, '2470.4 8 2474.1 9 2477.8 670 2181.5!'24s3.3 1 '2485.2 '2487.11 2 -24.S3.9 -2490.7 3 2492.6 -2494.4 4 2 496.3 2498.1 6 2500.0 2501.8 G 2503.7 7 2507.4 8 2511.1 1505.6 :509.3 2.513.0 2151.9 2153 2155.0 2157.4 21.59.3 2163.0 2166 7 2170.4 2174.1 8 2177.8 2181.5 2185.2 2188.9 2192.6 2196.3 2198 -2200.0 2201 8 2203.7 2205.6 2207.4'2209.3 2211 1 2213.0 •2214.8 2216.7 9-2218.6 2220.4 2222.2 2224.1 2161.1 216 1..-^ 2168.5 217-2.2 2175 9 2179 0 2183.3 2187.0 2190.7 2194.4 9 2514.8 2516.7 68 0 2518.5 2520.4 1-2.522. 2 '2-524.1 2 2-525.9'25:i7.8 3 '2-529 ; '-2-531.-'i 4:253 {.3 253-5.2 6 2537.0: -25,-i8.9 -2-540 7 i 2-542 0 •2.544.4 2546.3 '2.548 l''2550.0 2-551.9 '2553.7 C90 2555.6 '2-557.4 1 2 S 4 6 C 7 8 9 700 '25-59.3 2531.1 '2563.0 2564.8 -2-566,7,2-568.5 2-570.4 2572.2 '2-574.1 '2575.9 -2577.8''2579.0 2581.5 2583.3 2585.2 2587.0 2588.9 '2590.7 1592.6 2594.4 •2614.8 '2616 '2618.5''26'20,4 2322 2 2024,1 •.!625 1) '26'27.« '2629 6I2H31.5 '26.33 3:'2635 2 2637.0 '2638.9 '2642.6 2646.3 2650.O '2640.7 4 2644.4 6 '2648.1 6 '2651 9 26.53 7 2655.6|'26.57.4 8 26.59.3 '2661.1 9 2663.0 2664.8 2638.5 '2rt72.2 267-'..9 720 '2336.7 1 '2670.4 2 2374.1 3 2677.8 2679.6 4'2681.5 '2633.3 6l'2685.2 2687,0 6 2688.9 2690.7 7|269'2.6 2694.4 8 '2690,3 2698.1 9,2700.0 73O|'2703.7 1 2707.4 2:'2711.1 3 2714.8 2716.7 4 6 6 7 8 9 740 1 o 2718.5 2722 2 272-5.9 2729.6 2701.8 2705.0 2709.3 2713,0 20.4 2724.1 '2727.8 '2731.5 800 1 2 3 4 6 6 7 8 9 810 1 2 3 4 i 6 7 8 9 820 1 2 3 4 6 G 7 8 9 830 1 2 3 2733.3 2735.2 '2737.0 2738.9 740, 1744.4 :743.1 '2751.9 2742.0 2740.3 27-50.0 •2753.7 4 2755!6''2757.4 9 750 1 2 3 4 -2759.3 2761.1 -2763.0|2764.8 -2766.712768.5 -2770.4'2772.2 •2774.112775.9 '2777.8 '2779.6 -2781.5 2783.3 '278-5.2 2787.0 2788.9''2790.7 792.6 2794.4 •2796.3 2798.1 2800.0 2-sOl. 8 •2803.7 2805.0 2807.4 2809.3 2811.1 '2813.0 761» 2814.8 2816.7 '2818.5 2820 4 '2822 2 2824.1 2825.9 28'27.8 2829 6 '2831.5 2833.3 2835. ■2837.0 2838 9 '2840 7 2842.6 •2844 4 '2846.3 9''2848.1 2.3-50.0 7 70' 235 1.9 28-53.7 1' 23-55.6 '28-57.4 2 2S-59 3'2861 3 2863.0 '2864.8 4 2866.T '2868 6 2870.4 2872 2 6 '2874.1 -2875.9 7 2877.8 •2879.( 8 '2881.5 '28.83 9 288-5.2 '2887.0 780 '288.8.9 '2890,7 1 2392.6 '2894.4 2 2896.3 2898. 3 '2900.0 2901.8 4 29113.7 2905.(i 6 2907.4 2909 3 6 2911.1 2913 0 7 2914.8 2916 8 2918.6 2920.4 9 2922.2 2924. 1 790 29'25.9 2927.8 1 '29-29.6 2931.5 2 '2933.3 '2935.2 3 2937.0 '2938 9 4 2940.7 2942.0 6 2944.4 2946.3 6 2943.1 2950.0 7 2951.9 295,3.7 8 29-55.6 2957.4 9 29-59.3 2961.1 800 2963.0 2964.8 Contents, Cu. Yds. B. 2903.0 -2964.8 2060.7 2968 5 2970.4 2972,2 -2974.1 2975.9 ■2977.8 2979.6 •2981 5 2983.3 2985.2 29.S7.0 ■2988.9 2990.7 2992.6 2994.4 •29^6.3 2998.1 3000.0 3001,8 3003.7 3005.6 3007.4 3009.3 3011.1 3i'13 0 3014.8 3016.7 3018.5 3020.4 30^22.2 30-24.1 3025.9 3027.8 30-29.6 3031.5 3033.3 3035.2 3037.0 3038.9 3040.7 3042.6 3044 4 3046.3 3048.1 30-50.0 3051.9 3053 30-55.0 30-57.4 3059.3 3061.1 ,3063.0 3064.8 3066 7 3068.5 3070.4 307-2.2 3074.1 3075.9 3077.8 3079.6 3081.5 3083.3 3085.2 3087.0 900 1 840 1 2 30 38.9 3090.' 3092.6 3091.4 3096.3 3098.1 3100.0 3101.8 8 3103.7 3105.0 9 3107.4 3111.1 3114.8 3118.5 850 1 2 3 4 6 6 7 8 3 3122.2 31-25.9 3129.6 3109,3 ;113.0 ;ll6.7 3120.4 3124.1 3127.8 3131.; 6 3133 3 3135.2 3137.0 8 3140.7 9 3144.4 3148.1 3151.9 3153. 3155.6 31.57.4 '3159.3 3161.1 .'3163.0 3164.8 3166.7 86 3170.4 3172 3174.1 3177.8 3179.6 9 3181.5 3183 3 133,9 3142.6 3146.3 31.50.0 3168..' 3175.0 3187.0 3185.', 3188 9 3190 319'2.6'3194.4 3 3196.3'3'98.1 4.3-200.0 3-201.8 6 3-203.7 1 3-20-5.6 6 3207.4 3209.3 7 3211.1 3213.0 8 3214.8|3216 7 9 3218 5,32-20.1 8 70 32-22.2 .3224. 1 1 3-225,9,3-227.8 2 32.9 6 3231.5 3 3-233.3 4 3237.0 6 3240 7 6 3244.4 7 3-248.1 8 3'25l.9 9 3255.6 32-57.4 88 0 32-59.3 3'261.1 1 3-263.0 2 3266.7 3 3270.4 413274.1 3235.-. 3238 9 324-2.6 3246.3 3^250.0 3253 3-264.8 3-268.5 3-27-2.2 3-275.9 6 3'277.8 3279.6 6 3'28l.5 3'283.3 7 3285.2 8 9 890 1 2 3292.6 3296.3 3303.7 3 3307.4 4 3311.1 6 3314.8 3322. 33z5.9 33-29.6 3331.5 900 3333.3 3335.2 3287.0 3288.9 3290.7 3294 4 3298.1 3300.0 3301.8 3305.6 3309.3 ,3313.0 3816.7 331.8.6 3320.4 3324.1 3327.8 Contents, Cu. Yds. 3333.3 3.335,2 3337.0 3338.9 3340.7 3342.6 3344.4 3346.3 3.348.1 3350.0 3351.9 3353.7 3355.6 3357.4 3359.3 3361.1 8:3363.0 3364.8 9 3366.7 3368.5 910 1 o 4 6 6 7 8 9 920 3370 4 3372.2 3374.1 13375.9 3377.8 3379.6 3 3381.5 3383.3 338.5.2 33>7.0 3388.9 3390.7 3392.6 3394 4 3396.3 3398.1 34()0.0 3401.8 3403.7 3405,6 3407.4 3409.3 1 3411.1 3413,0 2 3414.8 3416.7 3 3418 6 3420.4 4 34'22.2 34-24.1 5 34-2.5.9 3427.8 G 34-29.6 3431.5 7 3433 3 3436.2 8 3437.0 3438.9 9 3440.7 3442.6 930 3444.4 3446.3 1 3448.1 3450.0 2 3451.9 3453.7 3 3465.6 3457.4 4 3459.3 3461.1 5 3463.0'3464.8 6 3466.7 3468.5 7^3470.4 3472.2 8 3474.1 3475.9 9 3477.8 3479.6 94 0 3481.5 3483.3 1 '3435.2 3187.0 2'3488.9:3490.7 33492.6,34944 4|3496.3 3498.1 5j3-500.0'3501.8 6 3503.7 13.505.6 7 , .3507.4 3509.3 8 3511.1 3613.0 9 3514 8,3516.7 950 3518,5 3520.4 1I3522.2'3524.1 3525.9'.3527.8 3 3.529.6'3.531-5 4 3533.3 3535.2 6 3-537.0 3-538.9 6'3540.7 3-54-2.6 7|3544,4 3546.3 8 3548.1 3650.0 9 3551.9 3:^.53.7 900 35.55.6 3.^.57.4 1 3.5.59.3 3561 1 2 3563.0 3564 8 3 3566.7 3668.5 4 3570.4 3672 2 6 3574.1 3575 9 6 3577.8 3579.6 7 3-581.5 3.583.3 8 3585.2 3587.0 9 3-588.9 3.590,7 970 359-2.6 3594,4 1 ;5596.3 3598.1 2 3600.0 3601.8 8 3603.7 3605.6 4 3607.4 3609.3 6 3611.1 3613.0 6 3614.8 3616.7 7 3618.5 3620.4 8 3622.2 3624.1 9 3625.9 36-27.8 980.36-29.6 3631.5 1 3633.3 3635 2 2 3637.0 3638.9 3 3640.7 3612 6 4 3644.4 3646 3 6 3648.1 3650.0 6 3061.9,3663.7 7 3665.6 3667.4 8 36-59.3 '366 1.1 9 3603,0 -MCA S 990 .3666.7 3668.5 1 3670.4 367-2.2 2 3674.1 3675.9 3 .3677.8 3679.6 4 3681.5 3683 3 5 .3685.2 3687.0 6 36.88.9 3690,7 7 3692.6 3694.4 8 3696.3 3698.1 9 3700,0 3701.8 100 0 3703.71 1 RATIOS OF CORRECTION FOR AVERAGE END AREA CALCULATIONS. WiniH OF Kt*A)> ItEU. 2-12 16 18 20 22 24 20 28 30 Area of 11 Kn'l 1.-25 2 2.5 2.25 to 100 100 100 H i^Ut »r Siii^il Kiiil. ; Ifa io or Arciis. 1:1 1:1.2 1:1,4 1:1.0 1:I.S 1:2 1:2.5 1 ::{..> 1:1 1:4.5 J:'. !:"».■> 1:0 1:0.5 1:7 1:7.5 l:s 1:S.5 1:1> 1:0.5 1:10 >f(tlOII Viirj in:; I'll a I SI OS. .001 .002 .007 .012 .019 .o:w .045 .056 .0117 .070 .0,S5 .O'j:? .100 .107 .11.3 .119 .124 .128 .133 .13S .112 1 1 1 1—5 Slope. Slope. 6.04 5.2 4.74 "1.74 4.81 4.41 Slope. Slope. 1-1 4.1 ,001 003 001 ,010 014 ,023 ,032 041 050 057 ,065 071 077 0«3 089 094 100 106 111 117 123 1:1 U:l }:1 001 .001 ,004 .004 .007 .OOS 012 .01- ,018 .0-.'2 ,032 .033 .043 .044 ,0-)5 ,056 .066 .067 075 .076 .083 .084 ,0911.092 ,098 .100 105 .106 110.111 1151,116 l'-'0.122 125i.l27 130 .132 134 .136 138. 140 001 002 .004 .006 .009 .016 .023 .030 .1 '38 .043 .049 .055 ,060 065 ,070 ,075 079 ,084 08 S 092 097, 1:1 .001 .004 .006 010 .014 ;026 037 .047 .057 ,066 ,074 ,081 088 094 100 105 110 115 120 125 130 .001 .004 .007 .011 .015 .027 .040 051 .061 070 ,078 ,084 093 099 105 110 115 120 125 130 135 .001 .002 .003 .005 .000 012 .019 .026 .033 .039 .044 .050 .055 .060 .065 .069 073 .077 082 086 .090' 1:1 n-.i ,001 .001 ,003 .003 ,006 010 .006 .010 014 .014 ,024.026 ,035 .037 045 054 .047 .056 062 .065 ,070' 07 ,077|.O80 084:. 088 090: 095 095. 101 1001.105 106.111 1111.116 116'. 121 12Lj.l25 126. 130 J:l .001 .002 .003 .005 .010 .016 .022 .029 .035 .040 .046: .051 .056 060 064 .068 .072 .070 086 .084 m 001 .003 006 010 .014 025 .035 .04 .054 1:1 .001 .003 .006 .010 .014 ,024 ,033 ,042 ,051 ,059 .062 ,066 .070 ,073 .078 ,079 .085 ,085 .091 0911.097 09'i'.102 ,101 .107 106 .112 1111.117 116 .121 120.126 100 100 100 100 100 100 100 5.14 4.45 4.1.' 4.72 4.14 3.884.33 3.87 3.644.00 3,62 3,4 Slope. Slope. Slope. .71 3.43 3,24:3.47 3.20 3.07 3.24 3.20 2.91 Slope. Slope. J:l .001 .002 ,003 ,005 010 014 020 025 031 030 .001 1.001 .003 ,003 .000 .006 .009 .009 ,013.013 .022 .024 .031. 034 .039 .044 .048 '.052 i-.l 055 003 042 .070 047 051 055 058 .062 .005 .009 072 .076 .082 .088 .093 .098 .102 .106 111 .0751.110 .000 .008 .075 .082 .088 .093 .098 .103 .108 .113 .117 .122 .001 .002 003 .005 ,(»10 .014 .019 l:l'li-l i:l 1:1 li:l .001 .001 ,003 .003 .005 .005 .008 .009 .012 .013 .020 .023 .028 .033 037 .042 .023 .045 .050 .028 .0.53 .058 ,033 060.060 .037 .041 .045 .006 073 .072 .079 .078 .085 .049!. 083 .090 .053'.088 .095 .0561.093 .100 .0601,097 .104 .063'. 102 .109 ,0061,100 .113 .009! Ill .118 Lool! ,0011.003: ,002'.005 003 .007 005 '.Oil 0091.019 014! 026 .034 .042 ,049 .056 .062 .00 s .074 079 .084 .089 .094 .098 .103 .107 ,019 022 026 030^ 034 037 041 044 047 050 054 057 060 063 001 003 .005 .008 .013 .021 .030 0!9 .047 .055 -062 009 .075 .081 .086 .091 .095 .100 .105 .110 .114 1:1 1:1 001 002 .ro3 005 .010 .013 017 021 024 .028 .031 .034 037 040 043 047 050 ,053 ,056 059 .001 .003 .005 .007 .010 .017 .025 1^1 .001 .003 ,005 00,- 012 .020 028 hi .032.036 .039 .045 .046 .053 .059 ,064 ,070 ,075 ,080 ,084 088 ,093 ,098 ,102 .052 .059 .066 .07-/ .077 .082 .0S7 .092 .097 .101 .10' .110 001 ,002 003 00.51 ,008 012 010 019 022 025 028 031 034 037 040 043 040 048 051 I '54 1:1 001 002 004 006 009 016 .023 03(1 037 044 .050 055 060 065 .070 075 080 084 .088 093 097 U:l ,001 ,003 ,005 ,008 Oil 019 ,027 034 042 050 057 063 069 075 080 085 089 094 098 10-J 107 Slope. Slope. i-.r 1:1 1^:1 .001 .001 .002 ,002 .004 .00 .000.00 .009 .010 .015 .018 .022 .025 .029 .033 .03) .040 .041 .048 .018 .054 .053 .000 001 001 002 003 ,000 010 013 010 019 022 025 027 030 033 036 03 S 041 044 040 049 001 .001 ,002 ,003 ,005 008 Oil 014 016 .019 021 I 1:1 1]:1 .058 .063 06 00(5 072 .077 .072'.082 .076 .086 .080.091 .084 .095 .088 ,100 .092 .104 .001 .001 .002 .00--' .004 .005 .006 .00' .008 .010 .014.017 .021 .024 027 .< 32 .034 ,039 .040 (I4() 045 .052 050 .058 024 .055 .064 .1126 ,060 .009 ,029 .004 ,074 031 .008 ,079 .034 .072 .084 030 .076 .088 .039 ,079 .092 041 .083 .096 044 .087 .100 liatioof A reas. 1:1 4:1.2 1:1.4 1:1.0 1:1.8 1:2 I l::{ f 1:8.5 1:4 I 1:4.5 1:., I i:"i.5 1:0 1:0.5 1:7 1:7.5 1:8 l:-i.5 1:!) l:!».o On Estimating Earthwork. The accompanying table is designed to facilitate the computation of earthwork after the areas of the cross sections have been obtained. The areas may be ob- tained bv calculation from the field notes ; or the cross sections may be plotted and tlie areas ol)taiiif'd by the plani meter. The foruier method is short and easy in a level country, but where the surface of the ground is liroken and irregular the latter method is to be preferred. Plotting the cross sections also makes a complete record of the work, wdlh its classification at every point, and allows revision and deviation within the limits to which the section is taken, by simply indicating the position of the centre line. Usua'iy it will be found easiest to plot the rods from a line assumed as the height of in- strument; but when the work is extend- ed so as to involve several heights of instrument in the same section, or when the work is to be used for a great i.umber of calculations for successive estimates, it w'll be found cheajjest to woik from elevations. A c 'nvtnient form for the estimate sheets is here shown. In the two first columns arc^ entered the stations and plu&>es at which the cross sections are taken. The column headed " Length hi Feel" is filled up by s-ubtracting the nu(ubers in these two first columns. The Columns headeiponding quantities are simply transferred from the table. If the distance is 50 feet, one half the quan- tity is transferred. If the distance is 25 feet, one-fourth, &c. Usually the opera- ti( n can be performed mentally. The tal)le being set u[) before one, the arrange- ment of it is such that the eye knows just wiiere to strike for a quantity. There are no leaves to turn. Quantities can be entered as fast as one can write. Blue ink may be used in writing quantities in excavati'^u, and red ink in writing quan- tities in e[nbankmeut. The calculation of earthwork by the method of averaging end areas is not theoretically correct, excepting ia the two special cases : one when the end areas are equal, and the other when the prismoid has two of its longitudinal bounding planes parallel. As that por- tion of every roadway prismoid, which lies between the vertical planes passing through the edges of the roadbed is practically included in the latter condi- tion, it follows that the variation from the true contents, obtained from averag- ing end areas, lies outside the central roadbed prism, and we may consider it as dependent on the four following factors : 1st. The ratio of the end areas of the prismoid. 2nd. The width of the roadbed. 3rd. The degree of the slope. 4th. The heighth of the section. This variation has been investigated with the result shown in the table called "Ratios of Correction for Average Fad Area Calculations." The manner of pro- ceeding was briefly thus : With the data shown in the heads of the columns in the table, and in the left hand column, the true contents of the prisms by the prismoidal formula were found, as well as the contents, by averaging end areas. The ratio of variation in many par- ticular cases being thus found, the curve of variation for each class was formed by measuri.ig the ratios of end areas on the axis of abscissas, and the per- centages of variation on the axis of ordiu- ates. Some maxima and minima of these curves were also traced, which seemed to differ, in extreme cases, 10 per cent, or so from the mean given in the table. It is believed these deviations will usually counterbalance one another. If the work is of a peculiar nature, so the general cases here worked out will not api)ly, cor- rections applying to it can be worked out and entered in one of the blank columns. To apply the table of corrections, we divide one area of cross section by its neighbor, and take from the table its cor- responding ratio or percentage of correc- tion and nmltiply the contents by it, writing the result in the column headed " Correction." The special case, when one end is zero, or ends at grade, is not provided for in table of corrections. For this case the correction is, the slope area multiplied by one sixth the length. For the road bed area being the base of a wedge, the solidity is one-half base multi- plied by altitude; but the slope areas being bases of pyramids, the solidity is one-third base multiplied by altitude. One half which is used, less one-third, which should be use(j, equals the correction, one- sixth. This correction, as well as all others, is to be deducted from contents in main column. Estimited Quantities in Grading. STA- TIONS, No. AKEA OF ( KOSS >K(; ION IN S({U U£K •■T. KxciiTiition. ■r j^' bitiik- ~ r meiit 117 .50 rnt'coiTences II8....I 18, .501.58! 53105 119, .50 638203 854171297 120 121 122 123 .030163.325 526 , _ . 595 ..'110243485 2(.) cm 40 cm 00 31 80,103 ends cm com men ces08 .3,34 280.500 3570(127 .50 743157 50870 1,56 ..'821 30534 Oil i:m 70, 84 to int commences 314 209 187 2-55 73147 ends AVERAGE AREA. ExcaTation. 394 -..034 ....527 A -1263'. 55' 15j 72 218^ 517 521.', 806,1 845J 677^ 267 341 108 212 280 270 12K 170 278i 217 1.56 J 171^232 130 36^ 15 67.^ 215i 426 500^ 540 242^ 280 5.572 434i 201.1 201 73,! Eni- b:ink mtnt Corrected Totals, CONTtNTS IN CUBIC YARDS. ExcaTation. 16.7 102.910 729.632 1174.1 083.8 136 3 40. 11.4 53.3 101.9 670.213 400 8 2987.0 1565,7 752,8 306.518 9853.7 98 9755.71.... 14 S 63.9 200.0 394 4 302.9 150 0 90.0 1037 301.0 120 6 679 0 317.0 144.4 41.9 2945.423 2922.4!..., 27.8 125.0 399.1 788.9 62(3.5 300.0 179.0 207.4 722,7 241.3 908.5 429,6 223.3 84.4 Em- l»aiik, mciil. 25. 1 25,1 7.0 23.8 .5.1 .53211 40j_8(); 627S.I ....j 82.: REMARKS. The error from calculation by averag- ing end areas is not so great as appears at first sight, or as it is often represented. Taking isolated cases, where the ratio of end areas is great, it may be made to appear that the error is 10 or 15 per cent.; but taking extended work the whole error is trifling, the great bulk of con- secutive cross sections being nearly equal to each other, and the errors are distri- buted. The writer tested one section of 28,00 > cu. yds. and found the error less than one tiiird of one per cent. What appeared to be a section which would show great error on account of crossing several short ravines and gullies, con- taining some 85,000 cu. ydn., was less than one-half of one per cent, out of the way. In earthwork there are only two sides of the prismoid perfect planes, and these two are the theoretical planes of the cross section. The surface of the ground is never a perfect plane. The rod, in taking points usually sinks a little in the ground, the slopes are not trimmed exact- ly, nor the grade made perf ct. If there is any difference between the true so'i.lity and that obtained by the method here pKesented, it is the conviction wf the writer that it would he easier and cheap- er' for the engineer to shuvel it than to calculate it. The method of calculation for earth- work should be direct and simple, so it can be used «afely by assistants not speci- ally skilled in intricate calculations It is better for the enQ:ineer to spend much of his time in the field, minutely observ- ing and closely measuring the work, than to spend it mainly in the office, basing refined computations on erroneous or careless nie;isnrements. The errors in measurement will usually be greater than the errors of calculation, by averaging end areas without cori-ection. —Published bv — JOHN WILEY "& SONS, $^cieiitifioJPiil>lisliers 15 Astor Place. NEW YORK CITY. The New and Complete Catalogue OF THE PUBI>ICATI0NS OP JOHN WIL.EY 4& HOIVS, 15 Astor Place, New "York, CONTAINING Scientific and other Text Books FOR COLLEGES, IKDCSTRIAL SCBOOLS & THEOLOGICAL SEMINARIES, with many valuable practical works for ARCHITECTS, ENGINEERS, MECHANICS, ETC. INCLUDING WORKS ON Agriculture, Assajnnfr, Astronomy, Book-keeping, Chemistry, Driiwinfr and Painting-, Engineering-, Metalliii'g-y, Macliiner.y, Mechanics, Mineral- ogj'. Seamanship, Steam Eng-ine, Venti- lation, Etc., Etc., and for THEOLOGLCAl- SEMINAHIES, Hebrew and Greek Bibles, Testaments, Le.xicons, Grammiu-s, Heading Books and Concordances. also a full list of their editions of JOHN RUSKIN'S WORKS. Will be sentfree by mail to anyone ordering it. 1 TABLE OF CUBIC YARDS IN LENGTHS OF 100 FEET. ADAPTED ESPECIALLY TO THE CALCULATION OF EARTH WORK BY THE METHOD OF ATERAGING END AREAS. Contents of Column "A" are for the integers in column headed "Area, Square Feet." Contents of Column " B " are for the same integers plus 0.5 square foot. Contents for lengths greater or less than 100 are obtained by simple proportion, thus: 125 sq. ft. for length of 20 ft.=x%=i of 463.0 cu. yd.-.; the contents for 125 sq. ft.=92.6 cu. yds. COPYRIGHT 1885 BY S. B. FISHER. Area, Sq. n,. Contfpts, Cii. Yds. Contents, Cn. Yds. Area, Sq. Ft. Contents, Cii. Yd^. 1 Coiit<-iiis, Cii. Yds. ( ontents, Cu. Yds. Contents, Cii. YiN. A A.. A £i.. T5 A A ■R A ■R A ■R 1.8 1 AA 370.4 372.2 200 740.7 742.6 1111,1 1113.0 1481.5 1483 3 1851,9 1853.7 1 J 3.7 6.6 1 J 374.1 375.9 1 744.4 7463 \ 1114.8 1 1167 1 X 1485.2 1487.0 1 1856.6 1857.4 o 7.4 9.3 £i 377.8 379.6 2 748.1 750 0 2 1118.5 1120.4 o 1488.9 1490.7 2 1859.3 1861.1 3 11.1 130 9 O 381.5 383.3 3 751.9 753.7 3 1122.2 1124.1 3 149i.6 1494 4 g o 1863.0 1864.8 \ 14.8 16.7 A 4 385.2 387.0 4 755.6 757.4 4 1125.9 ll:i7,H 4 1496.3 1493.1 4 1866 7 1 868.5 18.0 20.4 » 388 9 .390.7 5 759.3 761.1 5 1129.6 1131.5 R w 1500.0 1501.8 5 1870.4 1872.2 ( 22.2 24.1 O 39i.6 394.4 G 763 ( 761.8 113.3.3 1135.2 <: \r 1503 7 150.5.6 (] 1874,1 1875.9 2^.9 27.8 i 396 3 39.S.1 7 706 7 768.5 7 1137,0 1133.9 7 1507.4 1509.3 7 1877.8 1879.6 2!9.b 31.5 400.0 401.8 8 770.4 772 2 % 1140.7 1142. i 1511 1 1513.0 1381.5 18833 {] 33.3 35,2 tf 403.7 405.6 9 774.1 775.9 9 1144.4 1146.3 9 1514.S 1516.7 9 1885.2 1887.0 1(1 37.0 38.9 1 1 A 407.4 409.;^ 210 777.8 779.6 310 11481 1150.(1 41(1 1518.5 1520,4 510 1888.9 1890 7 ] 407 42.6 1 411.1 413.0 1 781.5 783.3 1151.9 1 153 7 J 1522 2 1524.1 1 1892.6 1891.4 2 44.4 46.3 a 414.8 416.7 2 785.2 787.0 2 1155 6 1157.4 2 1525 9 1.527.8 2 1896,3 1898.1 g 48.1 50.0 Q O 418 5 420.4 3 788.9 790.7 3 1159 3 1161.1 3 1529 6 1531,6 1900,0 1901.8 \ 51.9 63.7 A 'k 422 2 424.1 4 792.6 794.4 4 1163.0 1164.8 4 1533,3 1535.2 4 1 903.7 1905.6 5 55.6 57.4 *> 425.9 427.8 6 796.3 793.1 5 1166.7 1168.5 5 1637.0 1538.9 5 1907.4 1909.3 c 59.3 61.1 o 429 6 431.5 6 8or.o 801.8 G 1170.4 1172.2 1540.7 1542.6 ( 1911.1 1913.0 7 63.0 618 i 133 3 435.2 7 803.7 805.6 7 il74.1 1175 9 7 1544.4 1546.3 1914.8 1916.7 s C6.7 68.5 Q o 437.0 438 9 8 807.4 809.3 8 1177.8 1179,6 1543.1 1550.0 1918,5 1920.4 <) 70.4 722 <) 440 7 442.6 9 811.1 813.0 9 1181.5 11833 9 1551.9 1553.7 5) 19222 1924.1 20 74.1 75.9 120 414.4 446.3 220 814.8 816.7 320 1185.2 1187,0 42o 1555 6 1557,4 520 1925.9 1927.8 1 77.8 79.6 1 448 1 450.0 1 818.5 820.4 ] 1188 9 1190.7 1 1559.3 1561,1 1 1929.6 1931.5 2 81.5 83.3 a £i 451.9 453.7 2 822 2 824.1 2 1192.6 11944 2 1563.0 1564,8 2 1933.3 1935.2 3 85.2 87.0 •> o 45.).6 457.4 3 825.9 827.8 3 1196.3 1198.1 3 1566.7 1568,5 1937 0 1933,9 4 88.9 90.7 A *± 459 3 461.1 4 829.6 831.5 4 1200 0 1201.8 4 1570.4 1572.2 4 1940.7 1942.6 5 92 6 94.4 K O 463.0 464.8 833.3 835.2 1203.7 1205.6 5 1574,1 1575.9 1944,4 1946.3 G 96.3 98.1 a M 466 7 468.5 6 837.0 838.9 G 12'J7.4 1209.3 G 1577.8 1579.6 G 1948.1 19-50.0 7 lOOO 101,8 i 470.4 472.2 7 840.7 842.6 7 1211.1 1213.0 7 1581.5 1583.3 1951.9 19537 8 103.7 105.6 474.1 475.9 8 844.4 846 3 8 1214.8 1216.7 % 1585.2 1687.0 1955.6 19-57.4 9 107.4 109.3 <) 477.8 479.0 9 843.1 850.0 9 1218 5 1220.4 9 1688.9 1590.7 9 1959.3 1961.1 30 Ul.l 113.0 130 481.5 483.3 230 851.9 853.7 330 1222.2 1224.1 430 1592.6 1594.4 530 1963.0 196 1.8 1 114.8 116.: 1 485.2 487.0 1 855.6 857.4 1 1225,9 1227.8 1 1596.3 1698.1 ] 1963.7 1968.-5 2 118..^ 120.4 2 488.9 490 7 2 859.3 861.1 2 1229.6 1231.5 2 1600.0 1601.8 2 1970.4 1972 2 3 122.2 124.1 3 492.6 491.4 8 863.0 864.8 3 1233.3 1235,2 3 1603.7 1605.6 3 1974.1 1975.9 4 125.9 127.8 4. 496.3 493.1 4 838.7 863 5 4 1237.0 1238.9 4 1607.4 1609.3 4 1977.8 1979.6 5 129.0 131.5 600.0 501.8 5 870 4 872 2 5 1240.7 1242.0 5 1611.1 1613.0 I. 1931.5 1983 3 6 1.13.3 135.2 g 503.7 505.6 G 874.1 875.9 G 1244.4 1246.3 G 1614,8 1616.7 G 1985.2 1987,0 7 137.0 133.9 7 ff 507.4 509.3 7 877.8 879.6 7 1248 1 1250 0 r 1618.5 1620,4 1988.9 1990.7 8 140.7 142.6 & o 511.1 51.3.0 8 881.5 833.3 8 1251.9 1253.7 8 1622.2 1624 1 g 1992.6 1994.1 9 144.4 143 3 9 514.8 516.7 9 835.2 887.0 9 1255.6 12-57 .4 9 1025.9 1627,8 9 1996.3 1903.1 40 143 1 150.0 140 518.5 520.4 240 883 9 890.7 340 1259.3 1261.1 440 1629 6 1631.5 540 2000.0 2001.8 1 151.9 153.7 1 522 2 524.1 1 892.6 894.4 I 1233.0 1264 8 1 1633.3 1635.2 \ 2003.7 2005,0 2 155.6 157.4 2 525.9 527.8 2 803.3 893.1 2 1266.7 i268.:i , 2 1637.0 1638.9 2 2007.4 2009 3 159.3 101.1 3 529.0 531.6 900 0 931.8 3 1270.4 1272.- ' 8 1640.7 1642,6 3 2011.1 2013.0 4 1G3.0 161.8 4 533.3 535.2 903.7 9' 15.6 4' 1274.1 127.5.9 4 1644.4 1646.3 4 2014.8 2016.7 5 1G3.7 163.5 537 0 533.9 5 907.4 909.3 5 1277.8 1279 6 5 1643.1 1650.0 5 2018.5 2020.4 G 170.4 )72.2 g 540.7 542.6 6 911.1 913.0 6 1231.5 12,3.3 G 1651.9 1053.7 G 2022,2 2024.1 7 174.1 175.9 7 1 544.4 546.3 7 914.8 916.7 7 1285.2 1287.0 7 1656.6 1657.4 2025.9 2027..S 8 177.8 179.G fi o 543.1 550.0 8 918.5 920.4 8 1233.9 1290.7 8 1659.3 1661.1 g 2029.6 2031,5 9 131.5 183 3 9 531.9 553.7 9 9222 924.1 9 1-92.6 1294.4 9 1663.0 1664.8 9 2033,3 2035.2 50 135.2 187.0 15o 555.6 557.4 230 92)9 927.8 a 350 1290.3 1298.1 450 1666.7 1668,5 550 2037.0 203 S 9 1 153.9 190.7 1 559 3 531.1 1 920.6 931.5 1 1300.0 1301.8 1 1670.4 1672,2 2040.7 2042.6 2 102 6 191.4 o 563.0 564.8 2 933.3 935.2 2 1303.7 1305.6 2 1674.1 1675.9 2 2041.4 2046.3 3 193.3 1911 Q o 506 7 563 5 3 937.0 9319 3 1307.4 1309.3 3 1677.8 1679.6 3 J048,l 2050,0 4 200.0 201.8 4. 570.4 572 2 4 940.7 942.0 4 1311.1 1313.0 4 1631.5 1683.3 4 2051.9 2053.7 6 203.7 205.6 K 574.1 575.9 5 914.4 946.3 5 1314.8 1316.7 1685.2 1687.0 5 20.55.6 20.57.4 G 217.4 209.3 a 577.8 579.6 6 918.1 950.0 G 1318.5 1320.4 G 1688.9 1690.7 2059.3 2001 1 7 2!l.l 213.0 581.5 583,3 7 951.9 953.7 7 1322 2 1324.1 7 1692.6 16944 2063.0 2064 8 8 211.8 216.7 c o 585.2 587.0 8 955 6 957,4 8 1325.9 1327.8 g 1696.3 1698.1 2066.7 2008.5 9 218.5 220.1 9 538.9 590.7 9 959.3 961.1 9 1329.6 1331 5 9 1700.0 1701.8 9 2070.4 2072.2 60 222 2 221.1 160 592 6 594 4 260 933.0 964 8 360 13333 1335.2 4 Co 1703.7 1706.6 560 2074.1 2075.9 1 22.1.9 227.8 } 596.3 598.1 1 936 7 938.5 1 1337.0 1338.9 1 X 1707.4 1709.3 ] 2077.812079,6 2 229.6 231.5 2 600.0 6018 i 970 4 972.2 2 1340.7 1342.6 2 1711.1 1713.0 2 2081 5 2083.3 3 233.3 235.2 }{ 603 7 005 6 974.1 975.9 3 1344.4 1346 3 a o 1714.8 1716.7 Q o •2085.212087.0 4 237.0 238.9 4 607.4 609.3 4 977.8 979.6 4 1348.1 1350.0 4. 1718.5 1720.4 4 2088 9 2090.7 5 2 to 7 242.6 5 611.1 613.0 5 9S1.5 983.3 5 1351.9 1363.7 1722.2 1724.1 K w 2092 6 2094.4 6 244.4 246.3 614.8 616.7 G 985.2 987.0 G 1355.6 1367.4 a 1725.9 1727,8 2096.3 2098.1 7 218.1 250.0 7 618.5 620.4 7 938 9 990.7 7 1359.3 1361 1 7 • 1729.6 1731.5 7 2100.0 2101,8 8 251 9 253.7 g 622.2 624.1 8 992.6 994.4 8 1363.0 1364.8 c 1733,3 1735-2 8 2103.7 2105.6 9 2->5.6 257.4 <> 625 9 627.8 o! 996.3 998 1 9 1366.7 1368.5 9 1737.0 1738.9 9 2107.4 2109.3 70 259 3 231.1 17*» 629.6 631.5 27.» 1000.0 1001.8 370 1370.4 1372.2 470 1740.7 1742.6 570 2111.1 211.3.0 1 2t'.3 0 264.8 \ 633.3 635.2 1 1003.7 1005.6 1 1374.1 1375.9 1 1744.4 1746.3 1 2114.8 2116.7 2 236.7 263.5 037.0 638.9 2 1007 4 1009.3 2 1377.8 1379.6 2 1748.1 1750.0 2 2118.5 2120.4 H 270.4 272.2 Q o 640 7 642.6 i 3 1011. 1 1013.0 3 1381.5 1383.3 3 1751.9 1763.7 3 2122 2 2124.1 4 274.1 275.'^ 4. 644 4 646.3 4 1014.8 1016.7 4 1385,2 1387.0 4 1755.6 1757.4 4 212.5.9 2127.H 6 277.8 279.6 K 648 1 650.0 ' 5 1018.5 1020.4 1388.9 1390.7 5 1759 3 1761.1 6 2129.6 2131.5 6 281.5 283.3 051 9 653./ 1 G 1022.2 1024.1 6 1392.6 1394.4 G 17630 1764.8 6 21,33.3 21.35,2 7 235.2 237.0 7 655 6 6'>7.4 i 7 1025.9 1027.8 7 1396.3 1398 1 7 1766.7 1768.5 7 2137.0 21389 8 238.9 290.7 e 6>9.3 661 1; 8 1029.6 1031.5 8 1400.0 1401.8 8 1770.4 1772 2 S 2140-7 21 42.6 9 292 6 294.4 <^ 663 0 634 8; 9 1033.3 1035.2 9 1403.7 1405.(i 9 1774.1 1775.9 9 2144 4 2146.3 80 296 3 298.1 isi) 666.7 668.5 280 1037.0 1038.9 380 1407.4 1409.3 4S0 1777.8 1779.6 580 2148.1 21.50.0 1 300.0 301.8 ] 670.4 672 2; 1 1040.7 1042.'v 1 1.411.1 1413.0 1 1781.5 1783.3 1 2151.9 2153.7 2 3i)3.7 305.6 o it 674 1 675.9 ' 2 1044.4 1046 3 2 1414.8 1416.7 2 1785.2 1787.0 2155.6 21.57.1 3 307.4 309.3 a o 677.8 679.6 ; 3 1048.1 1050.0 3 1418.5 1420 4 3 1788.9 1790.7 i 2159.3 2161,1 4 311.1 313.0 4. 631 5 633.3 4 1051.9 1053.7 4 1422.2 1424.1 447926 1794.1 4 2163.0 2161..-; f. 314.8 316.7 5 685.2 687.0 6 1055.6 1057.4 5 1425.9 1427.8 6! 1796.3 1798.1 h 2166 7 2168,5 6 318.5 320.4 6 688.9 690.7 6 1059 3 1061.1 6 1429.6 1431.5 6 1800,0 1801.8 C 2170.4 2172,2 7 322.2 324 1 7 692.6 694.4 7 1063.0 1064.8 7 1433.3 1435.2 7 1803.7 18056 7 2174.1 2175.9 8 325.9 327.8 8 696.3 698.1 8 1066.7 1068.5 8 1437.0 1438.9 8 1807.4 1809.3 8 2177,8 2179 6 9 329.6 331.5 9 700.0 701.8 9 1070.4 1072.2 9 1440.7 1442.6 9 1811.1 1813,0 9 2181.5 2183,:! 90 333.3 335.2 190 703,7 1 705.6 29>» 1074.1 1076.9 390 1444.4 1446.3 490 1814 8 1816.7 590 2185.2 2187.0 1 337.0 338.9 1 707.4 709.3 lil077.8 1079.6 1 1448.1 1450.0 1 1818.5 1820.4 J 2188.9 2190.7 2 310.7 342.6 2 711.1 1 713.0 2 1081-5 1083.3 2 1451.9 1453.7 2:1822.2 1824.1 2 2192.6 2194,4 3 344.4 346.3 3 714.8 716.7 3 10S5.2 1087.0 3 1455 6 1457.4 3 1825.9 1827.8 3 2196.3 2198.1 4 318 1 350.0 4 718.5 "^20.4 4 1088.9 1090.7 4 1459.3 1461.1 4 1829.6 1831.5 4 2200.0 2201 8 5 351.9 353.7 722 2 724.1 5 1092.6 1094.4 5 1463.0 1464,8 5:i833,3 1835.2 h 2203,7 2205.6 6 3-)5.6 357,4 6 725.9 727.8 611096.3 1098.1 G 1466.7 1468.5 6,1837.0 1838.9 6 2207,4 2209.3 7 3)9.3 361.1 7 729 6 731.5 711100.0 1101.8 7 1470.4 1472.2 7 1840.7 1842,6 7 2211 1 2213.0 8 363.0 364.8 8 733 3 735.2 8 1103.7 1105.6 8 1474,1 1475.9 8 1844.4 1846.3 8 2214.8 22:6.7 9 loci 366.7 368.5 9 737.0 738.9 9 1107.4 1109.3 9 1477.8 1479.6 9 1848.1 1850.0 9 2218.5 2220.4 370.4 372.2 200 740,7 742.6 3eo|iiii.i 1113.0 400 1481.5 1483.3 500,1851.9 1853,7 6OOI2222.2.2224.I Contents, _^ ^ Cu. Yds. 3.1; 1 B. \^f. 2242.6 2246.3 2250,0 2253 7 22-57.4 2261,1 2264.S 2268.5 2272.2 2275.9 2279.6 2283 3 2287,0 600 2222.2 2224 1 1 [2225.9 2227.8 2 2229,6 2-231.-5 3'2233 3 22.35.2 4'2237,0 223S,9 5'2240.7 62244.4 712248.1 8 2251.9 9 2255.6 610 22-59,3 1 2263 0 2 2266.7 3 2270.4 4 2274.1 5 2277.8 G 2281.5 712^85 2 8 2238 9 '2290. 9 2292.6 2294,4 620 2296,3 2298.1 1 2300.0 2301.8 2 2303.7 2305,6 3 2307.4 2309.:'. 4 2311.1 2313.0 6 2314 8 2316,7 6 2318 5 2320.4 7 2322.2 '2324.1 8 2325 9 2327.8 9 23-29.6 '2331..'; 03 0 23;}3.3 2.335.2 1 2337.0 233 -i.O 2 2340.7 1 2342 6 3 2344 4 2346.3 4 2348.1 23.50.0 5 2351.9 23-53 6-2355 6 2357.4 7 2359,3 2361.1 8 2363.0 2364.8 9 2366.7 2368.5 640 2370,4 2372.2 1 2374.1 2.375.9 2 2377.8 2379.6 3 2331.5 2383 3 "4 2:?35.2 2387.0 6 2388.9 2390.7 6 2392.6 2394 4 7 2396.3 23911 8 2400.0 2401.8 9 2403.7 2405.6 650 2407.4 2409.3 1 2411.1 2413,0 2 2414.8 2416 7 3 2418,5 24-20.4 4 2422 2 2424 1 5 2425.9,2427 8 6 2429.6 2431.5 7 2433 3 2435,2 8 2437.0 2438 9 9, 2440.7 1 24 42.6 660 -2444 4 2446.3 Conients, Co. Yds. B. 2450.0 2453,7 1 2448 1 2 2151,9 3 2455.6 2457,4 4 2459,3 2461.1 5'2463.0 2464.8 G'2466.7 2468 5 7 2470.4 24721 8 2474.1 2475.9 9!2477.8 2 479.6 6 7 0 2 481.5j24S3.3 1 2485.2 2487,0 2 2433.9 2490.7 3 2492.6'2494.4 4 2496.3 2498.1 5 2-500.0 2-501.8 G 2503.712605.6 7 2507.4 2509.3 8 2511.l|25l3.0 9 2514.8 2516,7 680,2518.5 2520.4 1 2-522.2 2524.1 2 2525.9 2527.8 3 2^29 ; 2531.-5 4 253 { 3 2-53.5.2 6 '2537.0 25.-t8.!) 6 2-540 7 2-542 6 2544.4 2546.:! 2.348 1' 2-550.0 9 2-551.9 2-5.53.7 69 0 25.55.6 2-5.57.4 9 700 25-59.3 2561.1 2563.0 2564.8 2566,712568.5 2570.4 2-572.2 2-574.1 '2576.9 2577.8 2579.6 2581.5 2583.3 8 2585,2 2587.0 588.9 2590.7 2592.6 2594.4 7 ->0 -2592.6 2.594.4 1 12-596.3 2-598.1 2 2600,0 2601.8 3 2603.7i2605,6 4 2607.4 2609.3 6 -2611.112613.0 G -2614.8 2616.7 7 2618.5 2620,4 8 2622,2 2624,1 9 2625,9!2627.--< 710 2629 6f2ri31.5 1 26.33 3^2635 2 2 2637.0 2638.9 3 2640.7 2642,6 4 2614.4 2646.3 6 1 26 48.1 26.50.0 6 2651 9 26.53.7 7 2655.6|2657.4 8 26-59.3 2661.1 9l2'i63.0 2664,8 720,2366.7 1 2670.'',, 2|2374.1 3 2677.8 4 2631.5 51268-5.2 268/, 6 2688.9 2690 7 2692.6 2694.4 8i2696,3 2698.1 2668 2ii72.2 267-5,9 2679.() 2653,3 9 2700.0 73O'2703.7 1 2707.4 2709,3 2713,0 2701.8 2705.6 9 r4f) 1 2!2711,1 3 2714.8 2716 2718.5j2720.4 2722 2 2724.1 272-5.9 2727,8 2729.6 2731.5 2733.3 2737.0 2740.7 2744.4 2743.1 3 2751.9 5 6 7 8 9 750 1 2 3 4 8 9 76<» 1 2 3 4 5 G 7 2735.2 2733.9 ,2742,6 2746,3 2750.0 2753.7 4'27.55.6'2757.4 2759.3 2761.1 2763.0;2764.8 -2766.712763.5 2770.4'2772.2 2774.l|2775.9 •2777.8 2779.0 2781.5 2783.3 2785.2 2787.0 2788.9 2790.7 7920 2794.4 2796.3 2798.1 2300.0 2^>01.8 2803.7 2805.6 -2807.4 2809,3 2811.1 2813.0 2814.8 2816.7 2318.5 2820 4 •2322,2 2324,1 28-25,9 2827.8 •28*29 6 2.331.5 2333.3 2835.2 2837,0 2838 9 2840 7 2842,6 8 •2844,4 2846.3 9 2848.1 28.50.0 770'2851.9 28.53.7 1 '23-55.6 28-57.4 2 •2359 3 2861.1 3 2863.0 2864.8 4 2866.7 2868.5 6 2870.4 2872 2 6 2874,1 2875.9 7 2877.8 2879.0 8 2881.5 28H3.:! 9 2385,2 2887.0 780 2.SS8.9 2890 7 1 2392.6 2894.4 2 2896.3 2898.1 3 2900.0 2901.8 4 29' 13.7 290.5.6 6 2907.4 2909 :! 6 2911.1 2913 0 7 2914.8 2916,7 8 2918.5 2920.4 9 2922,2 2924,1 790 2925.9 2927.8 1 2929,6 2931.5 2 29;i3.3 2935.2 3 2937.0 2938 9 4 2940.7 2942,6 6 2944.4 2946,3 G 2943.1 2950.0 7 2951.9 2953.7 8 2955.6 2967,4 9 2959.3 2901.1 800 2963,0 2964.8 800 1 2 3 4 5 6 7 8 9 810 1 2 3 4 I C 7 8 9 82(1 1 2 3 4 5 G 7 8 9 830 1 2 3 4 5 G 7 8 9 84o 1 2 850 1 2 3 Contents, Cu. Yds. A. 2963.0 -2964.8 2966.7 2968 5 2970.4 2972,2 ■2974.1 2975 9 •2977.8 2979,6 •2981 5 2983,3 2985.2 2987.0 •2988.9 2990.7 2992.6 2994.4 29^6.3 -2998,1 .3000.0 3001 8 3003.7 3005.6 3007,4 3009.3 .■Ml 1.1 3013 0 3014.8 3016.7 ,3018.5 3020.4 3022.2 3024.1 3025.9 .3027.8 3029,6 3031.5 3033.3 303-5.2 ;5037.0 3038.9 ;3040.7 3042.6 3044 4 3046.3 :3018.1 30-50,0 3051.9 3053.7 3055.6 3057.4 ,30.39.3 3061.1 3063.0 3064.8 3066 7 3068.5 3070.4 30722 .3074,1 3075.9 3077.8 3079,6 3081.5 3083.3 .3035.2 3037.0 3038.9 3090.7 3092.6 3094.4 3096.3 3098.1 3100.0 3101.8 3103.7 3105.0 3107.4 3111.1 3114.S 3118..3 3 31222 3125.9 3129.0 3133 3 3135 2 3137.0 8 3140.7 9 3144.4 3148.1 3151.9 3155.6 3159.33161.1 4 3163,0 3164.8 86 1 2 3166.7 3170.4 3172 3174.1 3'.77.8 9 3181,5 3109 3 3113.0 3116,7 3120.4 3124.1 3127.8 3131.5 3133,9 3142.0 3146.3 3150.0 31.53.7 3157.4 3168.5 3175.0 3179,6 3183 3 3185.2 3187.0 3188 9 3190, 31926 3194.4 3 3196.3 3198 4 3-200.0 3-201.,S 6 3203.7|3205.6 6 3207.4 3209.3 7 3211.1 3213.0 8 3214.8|3216 7 9 ;?218 5 3220.4 870 32-22.2 3^224. 1 1 3-2-25.9 3-227.8 2 32.9.6 3231.5 3 3233.3 3235.2 4 3237.0:3238 9 6 3240 7j32426 G 3244.4 3246,3 7 3248,1|3250.0 8 3251,9 3253,7 3257.4 9 3255.6 880 32.59,3 3261.1 890 1 2 1 3263,0 2 3266, 3 3-270.4 4'3274,1 6:3277,8 6'.328l,5 7 3-285,2 8 9 3296.3 ,3303. 3!3307.4 4 3311.1 3314.8 ;5318.5 332-2.2 33-/5.9 3329.6 900 3333.3 3335.2 3-264.8 3268.5 3272.2 3275.9 3279.(i 3283..i 3287.0 3-288.9 3290,7 3292.6 3294 4 3298.1 3300.0 330 l.K 3305.6 ;«09.3 .3313.0 3316.7 3320.4 5324.1 3327.8 3331.5 900 1 2 3 4 5 7 8 9 910 1 2 3 4 5 6 7 8 Contents, Cu. Yds. A. B. 3333.3 3335 2 3337.0 3338.9 3340.7 3342.6 3344.4 3346.3 3:548.1 33.50,0 3351.9 33.53.7 6 3355.6 33.57.4 :5359.3 3361.1 3363.0 3364,8 9 3366.7 3368,5 3370 4 337-2.2 .3374.1 3,375.9 3377.83379.6 :5381.5 3:133,3 338-5.2 33>7,0 3388.9 3390.7 3392.6 3394 4 3396.3 3398.1 3400.0 3401.8 9 3403 7 3405 6 920.3407.4 3409.3 l!3411.1 34130 2;;5414.8 3410.7 3 3418 6 3420,4 4 34-22 2 3424.1 6 342.5.9 3427,8 6 3429.6 3431,5 7 3433 3 3435.2 8 3437.0 3438.9 9 3440.7 3442.6 9 3 0 3 444.4 3446.3 1 3448.1 34,50.0 2 3451.9 3453.7 3 3455.6 34.57.4 434.59.3 3461. 1 5 3463.0'3404.8 G 3466.7 13463.5 7,3470.4,3472,2, 8|3474,1 3475,9 9 3477,8 3479,6 940 3431.5'3483.3 1 '3435.23 187.0 2 3488.9|3490.7 3 3492.6 3494 4 4 3496.3 3498.1 5,3500.0'3.501.8 G 3.503.7 3,505.6 7 :.3507.4 .3509.3 8 3511.l'3513.0 9,3514.8'3516.7 950 3518.53520.4 1|3522.2 3524.1 : 352,5.9'3527.8 3 3529.6'3.531.5 4 3-533.3 353,3.2 5 3-337.0 3-5,38.9 6;3540.7 3-542.6 7:3544,4 3546.3 8[3-548.1 35,50.0 9 3551.9 3553,7 960 3.5-55.6 3.'^57.4 1 3.559.3 3561 1 2 3.563.0 3.564 8 3 3566.7 3.')68,6 4 3570.4 3.572 2 6 3574.1 3575 9 6 3577.8 3,579.6 7 3581.5 3.583.3 8 3585.2 3587.0 9 3-588.9 3590,7 970 3.592,6 3.594.4 1 3596.3 3598.1 2 3600.0 3i;ol,8 8 3603.7 3()05.6 4 3607.4 3609.3 6 3611.1 3613.0 6 3614.8 3616.7 7 3618.5 36-20,4 8 36222 3624.1 9 36-2.5.9 ,36-27,8 980 3629.6 3631.5 1 36;}3.3 3635 2 2 3037.0 3638.9 3 3640.7 ,3642 6 4 3644.4 ,3(i4(> 3 6 3648.1 3650.0 G 3651.9,3653.7 7 ,3655.6 3657.4 8.36,59.3.3661.1 9 3663.0 :5664,8 990 3666.7 3(;68.5 1 3670.4 3672,2 2 :5674.I 3675.9 3 3677,8 3079.6 4 3681.6 3683 3 5 368.5.2I3687.O G 3688.9 36!)0,7 7 .3692.6 3694.4 8 3696.3 3698.1 9 3700.0 3701.8 100 0 3703.71 RATIOS OF CORRECTION FOR AVERACE END AREA CALCULATIONS. WIDTH OP UUAI) BED. Area of 11 I'n.l l.'J5 2 2.5 H ih-lit lit' Kiii iil Kiiil, lla io of Knil Areas. 1:1 1:1.2 1:1.4 ]:!.(> 1:1. S 1:2 1:2..> ]::S 1 ::$..> 1:1 1:4.5 !:"> ^:^.^> 1:(; 1:«..> 1:7 1:7.5 1:S l:s.5 !:!> 1:<.>.5 1:10 ^»■l•tiOIl Varj iiif; Ml a 1 Si I's. .001 .002 .007 .012 .019 .0,S3 .015 .056 .0(i7 .07(3 .OSo .093 .100 .107 .113 .119 .124 .128 .133 .13S .142 Slope. i:l 001 003 005 mo ()14 ,023 ,032 041 ,050 057 ,065 071 ,077 083 0«i» 094 100 106 111 117 123 1:1 1.5:1 001 .001 .004 .004 .007 .008 ,012 .012 ,018 .02 ,032 .033 .043 .044 ,0 "i5 ,056 ,066 .067 ,075 .076 ,083 .084 ,09lj.092 ,093'. 100 ,105 .100 110 .111 115|.116 120.122 1251.127 130 .132 134.136 138.140: 2 12 2.25 to 100 14 100 1—5 Slope. 6.04 5.2 4.74 Slope. 1-1 .001 .002 .004 .006 .009 .016 .023 .030 .038 .043 ,049 .055 ,060 065 ,070 ,075 079, ,084 088 092 097 1:1 1^:1 .001 .004 .006 010 .014 ;02fi 037 .047 ,057 ,066 ,074 ,081 088 094 100 105 110 115 120 125, 130 .001 .004 .007 .011 ,015 .027 ,040 .051 ,061 ,070 ,078 ,084 093 ,099 105 110 115 120 125 130 135 }:1 .001 .002 .003 .005 .006 012 .019 .026 .033 .039 .044 .050 .055 .060 .065 .069' .073 .077 082 086 .090. 1:1 1J:1 16 18 100 5,74 4.81 4.41 Slope. i:l ,001 .001 .003 .003 .006 .010 .014 .026 .037 .047 .056 .065 .006 .010 .014 .024 .035 .045 .054 062 .070|.07 .077|.030 .084'.088 ,09o' 095 ,095 .101 ,100 .105 ,106.111 1111.116 ,116'. 121 12l|.125 126 .130 .001 .002 .003 .005 .010 .016 .022 .029 .035 .040 .046 .051 .056 060 064 068 .072 .076 086 .084 1:1 .001 .003 .006 .010 .014 .024 .033 .042 .051 U:l 001 .003 006 010 014 025 .035 047 .054 ,059 .062 ,066 .070 ,073 .078 ,079 .085 ,085.091 ,0911.097: 09')'. 102 ,101 .107 106 .112 1111.117 116 .121 120'. 126 100 5.14 4.45 4.13 1.72 4.14 3.88 4.33 3.87 3.644.00 3.62 3.43 Slope. J:l .001 .002 ,003 ,005 010 014 020 025 031 036 042 047 051 055 058 .062: .065 069 072 075 ^Ijl^l .001 [.001 .003,-003 .006 .006 .009 '.009 .013.013 .022 .024 .0311.034 .039 .044 .0481.052 20 100 Slope. i:l 055 063 .070 .076 .082 .088 .093 .098 .102 .106 111 .116 .060 .068 .075 .082 .088 .093 .098 .103 .108 .113 .117 .122 001 .002 003 .005 010 014 019, 1:1 li:l .001 .001 .003 .003 .005 .005 .008 .009 .012.013 .020 .023 .028 .033 037 .042 ,023'.045 .050 028 .053 .058 033 060.066 .037 .041 .045 .049 .053 056 ,060 .066 .073 .072 .079 .078 .085 .083 .090 .088 .095 .093 .100 ,097 .104 063' 102.109 ,066 .106 .113 069'. 111'. 118 100 24 100 Slope. Slope. 1:1 1^:1 LOOl ,001 1.003 ,002.005 003 .007 ,005 '.Oil 009 .019 014'. 026 ,019 ,022 026 030 034 037 041 044 047 050 054 057 060 063 .034 .042 .049 .050 .002 .06,-s .074 079 .084 .089 .094 .098 .103 .107 .001 .003 .005 .008 .013 .021 .030 0!9 .047 .055 OO-J 060 .075 .081 .086 .091 .095 .100 .105 .110 .114 1-1 1:1 001 002 ro3 005 .010 .013 .017 021 .024 028 031 .034 .037 040 043 .047. 050 053 .056 059 .001 .003 .005 .007 .010 .017 .025 .032 .039 .046 .053 .059 .064 .070 .075 .080 .084 088 .093 .098 .102 .001 .003 .005 .00.- .012 .020 028 036 .045 .052 .059 .066 .07 -J .077 .082 .0S7 .092 .097 .101 .10'- .110 26 28 100 100 30 100 3.71 3.43 3.24|3.47 3.20 3.07 3.24 3.20 2.91 Slope. i:l 001 .002 ,003 005 ,008 ,012 016 019 022 025 028 031 034 037 040 043 046 048 051 054 1:1 U:! 001 002 004 006 009 016 .023 030 .037 044 .050 055 .060 .065 .070 ,075 ,080 084 .088 093 097 .001 .003 .005 .008 .011 019 .027 .034 042 .050 057 063: 069 075 .080 .085 089 094 .098 10-J 107 Slope. I I .001 .001 .002 .002 .00 i .005 .006.007 .009 .010 .015 .018 .022 .025 .029 .033 .035 .040 .041 .0+8 .018 .054 .053 .060 001 001 002 003 ,006 010 013 016 019 022 025 027 030 033 036 03-i 041 044 046 049 .058 .063 067 .072 .066 072 .077 .082 .076 .086 .080.091 .084 .095 .088 ,100 .092 .104 Slope. 001 ,001 ,002 .003 005 008 Oil 014 .016 019 021 l:l'lj:l .001 .001 .002 .002 .004 .005 006.00' .008 .010 .014'.017 .021 '.024 .027 .032 034 .039 .040 . 1:5.5 1:6 1:6.5 1:7 1:7.5 1:8 1:1.5 1:1) I:!). 5 On Estimating Earthwork. The acc(jmpanying table is designed to facilitate the cotnputatiou of earthwork after the areas of the cross sections have been obtained. The areas may be ob- tained by calculation from the field notes ; or the cross sections may be plotted and the areas obtained by the plani meter. Tlie former method is short and easy in a level country, but where the surface of the ground is broken and irregular the latter method is to be preferred. Plotting the cross sections also makes a complete record of the work, with its classification at every point, and aUows revision and deviation within the limits to which the section is taken, by sim[)iy indicating the position of the centre line. Usua'iy it will be found easiest to plot the rods I'rom a line assumed as the height of in- strument ; but when the work is extend- ed so as to involve several heights of instrument in tlie same section, or when the work is to be used for a great i. ember of calculations for successive estimates, it will be found cheapest to work from elevations. A cmvinient form for the estimate sheets is here shown. In the two first columns are entered the stations and pluf-~es at which the cross sections are tiiken. The Column headed "Length in Feet" is filled up by subtracting the numbers in these two first columns. The Columns headed " Area of Gross Section " are filhd up with areas obtained either from calculation or from measurement by the planimett^r. In the columns head- ed "Average Area" are entered one-half the sums of the areas of adjacent cross sections. If prei'erred the sums, in>tead of the half sums, may be useil, in which case the final conttnts will be doubled. The main columns of " Contents in Cubic Yards " are now filled up by aid of accompanying " Table of Cubic Yards in Lengths of 100 Feet" 'if the lengths are liiQ feet the corresponding quantities are simply transferred from the table. If the distance is 50 feet, one half the quan- tity is transferre cu. yds. and f)und the error less than one-third of one per cent. What appeared to be a sectitm which would show great error On account of crossing several short ravines and gullies, con- taining some 85.000 cu. yds., was less than one-half of one per cent, out of the way. In earthwork there are only two sides of the prismoid perfect planes, and these two are the theoretical planes of the cross section. The surface of the ground is never a perfect plane. The rod, in taking points usually sinks a little in the ground, the slopes are not trimmed exact- ly, nor the grade made perfi ct. If there is any difierence between the true so'i iity and that obtained by the method here presented, it is the conviction of the writer that it would be easier and cheap- er for the engineer to shovel it thau to calculate it. The method of calculation for earth- work should be direct and simple, so it can be used safely by assistants not speci- ally skilled in intricate calculations. It is better for the engineer to spend much of his time in the field, minutely observ- ing and closely measuring the work, than to spend it inainly in the office, basing refiued computaiions on erroneous or careless measurements. The errors in measurement will usually be greater than the errors of calculation, by averaging end areas without cori-ection. — Piiljlislied by — JOHN WILEY & SONS, Scientific.* I* ixtolisliers 1,5 Astor Place. NEW YORK CITY. 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