Abstract
No abstract available.
Full Article | PDF ArticleMore Like This
B. W. Bartlett
J. Opt. Soc. Am. 16(6) 409-418 (1928)
W. H. Crew and L. H. Dawson
J. Opt. Soc. Am. 17(4) 261-270 (1928)
W. F. G. Swann
J. Opt. Soc. Am. 17(3) 163-197 (1928)
F. Paschen
F. Paschen
Physikalisch-Technische Reichsanstalt, Charlottenburg, Germany
No abstract available.
Full Article | PDF ArticleB. W. Bartlett
J. Opt. Soc. Am. 16(6) 409-418 (1928)
W. H. Crew and L. H. Dawson
J. Opt. Soc. Am. 17(4) 261-270 (1928)
W. F. G. Swann
J. Opt. Soc. Am. 17(3) 163-197 (1928)
Joseph Valasek
J. Opt. Soc. Am. 17(2) 102-106 (1928)
William F. Meggers and Bourdon F. Scribner
J. Opt. Soc. Am. 17(2) 83-90 (1928)
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m | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | ||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
a | |||||||||||||||||||||||||
+0.00 | 109737.1 | 27434.28 | 12193.01 | 6858.57 | 4389.48 | 3048.25 | 2239.53 | 1714.64 | 1354.78 | 1097.37 | 906.92 | 762.06 | 649.33 | ||||||||||||
Δ | 82302.82 | 15241.27 | 5334.44 | 2469.09 | 1341.23 | 808.72 | 524.89 | 359.86 | 257.41 | 190.45 | 144.86 | 112.73 | |||||||||||||
| |||||||||||||||||||||||||
+0.05 | 99534.78 | 26112.34 | 11796.52 | 6690.27 | 4302.99 | 2998.08 | 2207.88 | 1693.41 | 1339.85 | 1086.48 | 898.73 | 755.75 | 644.37 | ||||||||||||
Δ | 73422.44 | 14315.82 | 5106.25 | 2387.28 | 1304.91 | 790.20 | 514.47 | 353.56 | 253.37 | 187.75 | 142.98 | 111.38 | |||||||||||||
| |||||||||||||||||||||||||
+0.10 | 90691.82 | 24883.70 | 11419.05 | 6528.08 | 4219.04 | 2949.13 | 2176.89 | 1672.57 | 1325.17 | 1075.75 | 890.65 | 749.52 | 639.46 | ||||||||||||
Δ | 65808.12 | 13464.65 | 4890.97 | 2309.04 | 1269.91 | 772.24 | 504.32 | 347.40 | 249.42 | 185.10 | 141.13 | 110.06 | |||||||||||||
| |||||||||||||||||||||||||
+0.15 | 82977.04 | 23739.77 | 11059.42 | 6371.73 | 4137.51 | 2901.37 | 2146.55 | 1652.11 | 1310.72 | 1065.18 | 882.68 | 743.36 | 634.60 | ||||||||||||
Δ | 59237.27 | 12680.35 | 4687.69 | 2234.22 | 1236.14 | 754.82 | 494.44 | 341.39 | 245.54 | 182.50 | 139.32 | 108.76 | |||||||||||||
| |||||||||||||||||||||||||
+0.20 | 76206.33 | 22672.95 | 10716.51 | 6220.92 | 4058.33 | 2854.76 | 2116.84 | 1632.02 | 1296.52 | 1054.76 | 874.82 | 737.28 | 629.80 | ||||||||||||
Δ | 53533.38 | 11956.44 | 4495.59 | 2162.59 | 1203.57 | 737.92 | 484.82 | 335.50 | 241.76 | 179.94 | 137.54 | 107.48 | |||||||||||||
| |||||||||||||||||||||||||
+0.25 | 70231.75 | 21676.47 | 10389.31 | 6075.41 | 3981.39 | 2809.27 | 2087.75 | 1612.30 | 1282.54 | 1044.49 | 867.06 | 731.28 | 625.06 | ||||||||||||
Δ | 48555.28 | 11287.16 | 4313.90 | 2094.02 | 1172.12 | 721.52 | 475.45 | 329.76 | 238.05 | 177.43 | 135.78 | 106.22 | |||||||||||||
| |||||||||||||||||||||||||
+0.30 | 64933.18 | 20744.26 | 10076.87 | 5934.94 | 3906.63 | 2764.86 | 2059.24 | 1592.93 | 1268.78 | 1034.38 | 859.40 | 725.34 | 620.37 | ||||||||||||
Δ | 44188.92 | 10667.39 | 4141.93 | 2028.31 | 1141.77 | 705.62 | 466.31 | 324.15 | 234.40 | 174.98 | 134.06 | 104.97 | |||||||||||||
| |||||||||||||||||||||||||
+0.35 | 60212.39 | 19870.91 | 9778.31 | 5799.29 | 3833.95 | 2721.48 | 2031.32 | 1573.91 | 1255.25 | 1024.41 | 851.85 | 719.48 | 615.73 | ||||||||||||
Δ | 40341.48 | 10092.60 | 3979.02 | 1965.34 | 1112.47 | 690.16 | 457.41 | 318.66 | 230.84 | 172.56 | 132.37 | 103.75 | |||||||||||||
| |||||||||||||||||||||||||
+0.40 | 55988.32 | 19051.58 | 9492.83 | 5668.24 | 3763.28 | 2679.13 | 2003.96 | 1555.23 | 1241.93 | 1014.58 | 844.39 | 713.69 | 611.14 | ||||||||||||
Δ | 36936.74 | 9558.75 | 3824.59 | 1904.96 | 1084.15 | 675.17 | 448.73 | 313.30 | 227.35 | 170.19 | 130.70 | 102.55 | |||||||||||||
| |||||||||||||||||||||||||
+0.45 | 52193.63 | 18281.90 | 9219.67 | 5541.58 | 3694.54 | 2637.75 | 1977.16 | 1536.88 | 1228.82 | 1004.90 | 837.03 | 707.97 | 606.61 | ||||||||||||
Δ | 33911.73 | 9062.23 | 3678.09 | 1847.04 | 1056.79 | 660.59 | 440.28 | 308.06 | 223.92 | 167.87 | 129.06 | 101.36 | |||||||||||||
| |||||||||||||||||||||||||
+0.50 | 48772.04 | 17557.94 | 8958.13 | 5419.12 | 3627.67 | 2597.33 | 1950.88 | 1518.85 | 1215.92 | 995.35 | 829.77 | 702.32 | 602.12 | ||||||||||||
Δ | 31214.10 | 8599.81 | 3539.01 | 1791.45 | 1030.34 | 646.45 | 432.03 | 302.93 | 220.57 | 165.58 | 127.45 | 100.20 | |||||||||||||
| |||||||||||||||||||||||||
+0.55 | 45676.21 | 16876.14 | 8707.56 | 5300.67 | 3562.60 | 2557.83 | 1925.13 | 1501.14 | 1203.22 | 985.94 | 822.60 | 696.73 | 597.69 | ||||||||||||
Δ | 28800.07 | 8168.58 | 3406.89 | 1738.07 | 1004.77 | 632.70 | 423.99 | 297.92 | 217.28 | 163.34 | 125.87 | 99.04 | |||||||||||||
| |||||||||||||||||||||||||
+0.60 | 42866.05 | 16233.30 | 8467.37 | 5186.06 | 3499.27 | 2519.22 | 1899.88 | 1483.74 | 1190.72 | 976.66 | 815.53 | 691.21 | 593.30 | ||||||||||||
Δ | 26632.75 | 7765.93 | 3281.31 | 1686.79 | 980.05 | 619.34 | 416.14 | 293.02 | 214.06 | 161.13 | 124.32 | 97.91 | |||||||||||||
| |||||||||||||||||||||||||
+0.65 | 40307.47 | 15626.50 | 8236.97 | 5075.13 | 3437.61 | 2481.48 | 1875.13 | 1466.63 | 1178.42 | 967.51 | 808.54 | 685.76 | 588.96 | ||||||||||||
Δ | 24680.97 | 7389.53 | 3161.84 | 1637.52 | 956.13 | 606.35 | 408.50 | 288.21 | 210.91 | 158.97 | 122.78 | 96.80 | |||||||||||||
| |||||||||||||||||||||||||
+0.70 | 37971.32 | 15053.10 | 8015.86 | 4967.73 | 3377.57 | 2444.58 | 1850.85 | 1449.82 | 1166.30 | 958.49 | 801.64 | 680.37 | 584.67 | ||||||||||||
Δ | 22918.22 | 7037.24 | 3048.13 | 1590.16 | 932.99 | 593.73 | 401.03 | 283.52 | 207.81 | 156.85 | 121.27 | 95.70 | |||||||||||||
| |||||||||||||||||||||||||
+0.75 | 35832.53 | 14510.69 | 7803.53 | 4863.69 | 3319.08 | 2408.50 | 1827.05 | 1433.30 | 1154.37 | 949.59 | 794.84 | 675.05 | 580.43 | ||||||||||||
Δ | 21321.84 | 6707.16 | 2939.84 | 1544.61 | 910.58 | 581.45 | 393.75 | 278.93 | 204.78 | 154.75 | 119.79 | 94.62 | |||||||||||||
| |||||||||||||||||||||||||
+0.80 | 33869.48 | 13997.08 | 7599.52 | 4762.89 | 3262.10 | 2373.21 | 1803.70 | 1417.06 | 1142.62 | 940.82 | 788.12 | 669.78 | 576.23 | ||||||||||||
Δ | 19872.40 | 6397.56 | 2836.63 | 1500.79 | 888.89 | 569.51 | 386.64 | 274.44 | 201.80 | 152.70 | 118.34 | 93.55 | |||||||||||||
| |||||||||||||||||||||||||
+0.85 | 32063.44 | 13510.26 | 7403.42 | 4665.20 | 3206.58 | 2338.69 | 1780.80 | 1401.09 | 1131.05 | 932.17 | 781.48 | 664.58 | 572.08 | ||||||||||||
Δ | 18553.18 | 6106.84 | 2738.22 | 1458.62 | 867.89 | 557.89 | 379.71 | 270.04 | 198.88 | 150.69 | 116.90 | 92.50 | |||||||||||||
| |||||||||||||||||||||||||
+0.90 | 30398.09 | 13048.41 | 7214.80 | 4570.47 | 3152.46 | 2304.92 | 1758.33 | 1385.39 | 1119.65 | 923.63 | 774.93 | 659.44 | 567.97 | ||||||||||||
Δ | 17349.68 | 5833.61 | 2644.33 | 1418.01 | 847.54 | 546.59 | 372.94 | 265.74 | 196.02 | 148.70 | 115.49 | 91.47 | |||||||||||||
| |||||||||||||||||||||||||
+0.95 | 28859.20 | 12609.84 | 7033.30 | 4478.61 | 3099.70 | 2271.87 | 1736.28 | 1369.96 | 1108.43 | 915.22 | 768.45 | 654.36 | 563.90 | ||||||||||||
Δ | 16249.36 | 5576.54 | 2554.69 | 1378.91 | 827.83 | 535.59 | 366.32 | 261.53 | 193.21 | 146.77 | 114.09 | 90.46 | |||||||||||||
| |||||||||||||||||||||||||
+ 1.00 | 27434.28 | 12193.01 | 6858.57 | 4389.48 | 3048.25 | 2239.53 | 1714.65 | 1354.78 | 1097.37 | 906.92 | 762.06 | 649.33 | 559.88 | ||||||||||||
Δ | 15241.27 | 5334.44 | 2469.09 | 1341.23 | 808.72 | 524.88 | 359.87 | 257.41 | 190.45 | 144.86 | 112.73 | 89.45 | |||||||||||||
| |||||||||||||||||||||||||
m+a = | 0.95 | 0.90 | 0.85 | 0.80 | 0.75 | 0.70 | 0.65 | 0.60 | 0.50 | ||||||||||||||||
121592.4 | 135477.9 | 151885.3 | 171464.2 | 195088.2 | 223953.4 | 259732.8 | 304825.9 | 438948.4 |
a/m | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | |||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
.00 | 438948.40 | 109737.12 | 48772.04 | 27434.28 | 17557.92 | 12193.00 | 8958.12 | 6858.56 | 5419.12 | 4389.48 | 3627.68 | 3048.24 | 2597.32 | 2239.52 | |||||||||||||
329211.28 | 60965.08 | 21337.76 | 9876.36 | 5364.92 | 3234.88 | 2099.56 | 1439.44 | 1029.64 | 761.80 | 579.44 | 450.92 | 357.80 | |||||||||||||||
| |||||||||||||||||||||||||||
.05 | 398139.12 | 104449.36 | 47186.08 | 26761.08 | 17211.96 | 11992.32 | 8831.52 | 6773.64 | 5359.40 | 4345.92 | 3594.92 | 3023.00 | 2577.48 | 2223.70 | |||||||||||||
293689.76 | 57263.28 | 20425.00 | 9549.12 | 5219.64 | 3160.80 | 2057.88 | 1414.24 | 1013.48 | 751.00 | 571.92 | 445.52 | 353.78 | |||||||||||||||
| |||||||||||||||||||||||||||
.10 | 362767.28 | 99534.80 | 45676.20 | 26112.32 | 16876.16 | 11796.52 | 8707.56 | 6690.28 | 5300.68 | 4303 | 3562.60 | 2998.08 | 2557.84 | 2207.88 | |||||||||||||
263232.48 | 53858.60 | 19563.88 | 9236.16 | 5079.64 | 3088.96 | 2017.28 | 1389.60 | 997.68 | 740.40 | 564.52 | 440.24 | 349.96 | |||||||||||||||
| |||||||||||||||||||||||||||
.15 | 331908.16 | 94959.08 | 44237.68 | 25486.92 | 16550.04 | 11605.48 | 8586.20 | 6608.44 | 5242.88 | 4260.72 | 3530.72 | 2973.44 | 2538.40 | 2192.39 | |||||||||||||
236949.08 | 50721.40 | 18750.76 | 8936.88 | 4944.56 | 3019.28 | 1977.76 | 1365.56 | 982.16 | 730.00 | 557.28 | 435.04 | 346.01 | |||||||||||||||
| |||||||||||||||||||||||||||
.20 | 304825.32 | 90691.80 | 42866.04 | 24883.68 | 16233.32 | 11419.04 | 8467.36 | 6528.08 | 5186.08 | 4219.04 | 3499.28 | 2949.12 | 2519.20 | 2176.89 | |||||||||||||
214133.52 | 47825.76 | 17982.36 | 8650.36 | 4814.28 | 2951.68 | 1939.28 | 1342.00 | 967.04 | 719.76 | 550.16 | 429.92 | 342.31 | |||||||||||||||
| |||||||||||||||||||||||||||
.25 | 280927.00 | 86705.88 | 41557.24 | 24301.64 | 15925.56 | 11237.08 | 8351.00 | 6449.20 | 5130.16 | 4177.96 | 3468.24 | 2925.12 | 2500.24 | 2161.72 | |||||||||||||
194221.12 | 45148.64 | 17255.60 | 8376.08 | 4688.48 | 2886.08 | 1901.80 | 1319.04 | 952.20 | 709.72 | 543.12 | 424.88 | 338.52 | |||||||||||||||
| |||||||||||||||||||||||||||
.30 | 259732.72 | 82977.04 | 40307.48 | 23739.76 | 15626.52 | 11059.44 | 8236.96 | 6371.72 | 5075.12 | 4137.52 | 3437.60 | 2901.36 | 2481.48 | 2146.55 | |||||||||||||
176755.68 | 42669.56 | 16567.72 | 8113.24 | 4567.08 | 2822.48 | 1865.24 | 1296.60 | 937.60 | 699.92 | 536.24 | 419.88 | 334.93 | |||||||||||||||
| |||||||||||||||||||||||||||
.35 | 240849.56 | 79483.64 | 39113.24 | 23197.16 | 15335.80 | 10885.92 | 8125.28 | 6295.64 | 5021.00 | 4097.64 | 3407.40 | 2877.92 | 2462.92 | 2131.7 | |||||||||||||
161365.92 | 40370.40 | 15916.08 | 7861.36 | 4449.88 | 2760.64 | 1829.64 | 1274.64 | 923.36 | 690.24 | 529.48 | 415.00 | 331.22 | |||||||||||||||
| |||||||||||||||||||||||||||
.40 | 223953.28 | 76206.32 | 37971.32 | 22672.96 | 15053.12 | 10716.52 | 8015.84 | 6220.92 | 4967.72 | 4058.32 | 3377.56 | 2854.76 | 2444.56 | 2116.84 | |||||||||||||
147746.96 | 38235.00 | 15298.36 | 7619.84 | 4336.60 | 2700.68 | 1794.92 | 1253.2 | 909.40 | 680.76 | 522.80 | 410.20 | 327.72 | |||||||||||||||
| |||||||||||||||||||||||||||
.45 | 208774.52 | 73127.60 | 36878.68 | 22166.32 | 14778.16 | 10551.00 | 7908.64 | 6147.52 | 4915.28 | 4019.6 | 3348.12 | 2831.88 | 2426.44 | 2102.3 | |||||||||||||
135646.92 | 36248.92 | 14712.36 | 7388.16 | 4227.16 | 2642.36 | 1761.12 | 1232.24 | 895.68 | 671.48 | 516.24 | 405.44 | 324.14 | |||||||||||||||
| |||||||||||||||||||||||||||
.50 | 195088.16 | 70231.76 | 35832.52 | 21676.48 | 14510.68 | 10389.32 | 7803.52 | 6075.40 | 4863.68 | 3981.4 | 3319.08 | 2809.28 | 2408.48 | 2087.75 | |||||||||||||
124856.40 | 34399.24 | 14156.04 | 7165.80 | 4121.36 | 2585.80 | 1728.12 | 1211.72 | 882.28 | 662.32 | 509.80 | 400.80 | 320.73 | |||||||||||||||
| |||||||||||||||||||||||||||
.55 | 182704.84 | 67504.56 | 34830.24 | 21202.68 | 14250.40 | 10231.32 | 7700.52 | 6004.56 | 4812.88 | 3943.76 | 3290.40 | 2786.92 | 2390.76 | 2073.5 | |||||||||||||
115200.28 | 32674.32 | 13627.56 | 6952.28 | 4019.08 | 2530.80 | 1695.96 | 1191.68 | 869.12 | 653.36 | 503.48 | 396.16 | 317.26 | |||||||||||||||
| |||||||||||||||||||||||||||
.60 | 171464.20 | 64933.20 | 33869.48 | 20744.24 | 13997.08 | 10076.88 | 7599.52 | 5934.96 | 4762.88 | 3906.64 | 3262.12 | 2764.84 | 2373.20 | 2059.24 | |||||||||||||
106531.00 | 31063.72 | 13125.24 | 6747.16 | 3920.36 | 2477.36 | 1664.56 | 1172.08 | 856.24 | 644.52 | 497.28 | 391.64 | 313.96 | |||||||||||||||
| |||||||||||||||||||||||||||
.65 | 161229.88 | 62506.00 | 32947.88 | 20300.52 | 13750.44 | 9925.92 | 7500.52 | 5866.52 | 4713.68 | 3870.04 | 3234.16 | 2743.04 | 2355.84 | 2045.28 | |||||||||||||
98723.88 | 29558.12 | 12647.36 | 6550.08 | 3824.52 | 2425.40 | 1634.00 | 1152.84 | 843.64 | 635.88 | 491.12 | 387.20 | 310.56 | |||||||||||||||
| |||||||||||||||||||||||||||
.70 | 151885.28 | 60212.40 | 32063.44 | 19870.92 | 13510.28 | 9778.32 | 7403.40 | 5799.28 | 4665.20 | 3833.96 | 3206.56 | 2721.48 | 2338.68 | 2031.32 | |||||||||||||
91672.88 | 28148.96 | 12192.52 | 6360.64 | 3731.96 | 2374.92 | 1604.12 | 1134.08 | 831.24 | 627.40 | 485.08 | 382.80 | 307.36 | |||||||||||||||
| |||||||||||||||||||||||||||
.75 | 143330.12 | 58042.76 | 31214.12 | 19454.76 | 13276.32 | 9634.00 | 7308.20 | 5733.20 | 4617.48 | 3798.36 | 3179.36 | 2700.20 | 2321.72 | 2017.64 | |||||||||||||
85287.36 | 26828.64 | 11759.36 | 6178.44 | 3642.32 | 2325.80 | 1575.00 | 1115.72 | 819.12 | 619.00 | 479.16 | 378.48 | 304.08 | |||||||||||||||
| |||||||||||||||||||||||||||
.80 | 135477.92 | 55988.32 | 30398.08 | 19051.56 | 13048.40 | 9492.84 | 7214.80 | 5668.24 | 4570.48 | 3763.28 | 3152.48 | 2679.12 | 2304.92 | 2003.96 | |||||||||||||
79489.60 | 25590.24 | 11346.52 | 6003.16 | 3555.56 | 2278.04 | 1546.56 | 1097.76 | 807.20 | 610.80 | 473.36 | 374.20 | 300.96 | |||||||||||||||
| |||||||||||||||||||||||||||
.85 | 128253.76 | 54041.04 | 29613.68 | 18660.80 | 12826.32 | 9354.76 | 7123.20 | 5604.36 | 4524.20 | 3728.68 | 3125.92 | 2658.32 | 2288.32 | 1990.51 | |||||||||||||
74212.72 | 24427.36 | 10952.88 | 5834.48 | 3471.56 | 2231.56 | 1518.84 | 1080.16 | 795.52 | 602.76 | 467.60 | 370.00 | 297.81 | |||||||||||||||
| |||||||||||||||||||||||||||
.90 | 121592.36 | 52193.64 | 28859.20 | 18281.88 | 12609.84 | 9219.68 | 7033.32 | 5541.56 | 4478.60 | 3694.52 | 3099.72 | 2637.76 | 2271.88 | 1977.16 | |||||||||||||
69398.72 | 23334.44 | 10577.32 | 5672.04 | 3390.16 | 2186.36 | 1491.76 | 1062.96 | 784.08 | 594.80 | 461.96 | 365.88 | 294.70 | |||||||||||||||
| |||||||||||||||||||||||||||
.95 | 115436.80 | 50439.36 | 28133.20 | 17914.44 | 12398.80 | 9087.48 | 6945.12 | 5479.84 | 4433.72 | 3660.88 | 3073.80 | 2617.44 | 2255.60 | 1964.02 | |||||||||||||
64997.44 | 22306.16 | 10218.76 | 5515.64 | 3311.32 | 2142.36 | 1465.28 | 1046.12 | 772.84 | 587.08 | 456.36 | 361.84 | 291.58 | |||||||||||||||
| |||||||||||||||||||||||||||
1.00 | 109737.12 | 48772.04 | 27434.28 | 17557.92 | 12193.00 | 8958.12 | 6858.56 | 5419.12 | 4389.48 | 3627.68 | 3048.24 | 2597.32 | 2239.52 | 1950.88 | |||||||||||||
60965.08 | 21337.76 | 9876.36 | 5364.92 | 3234.88 | 2099.56 | 1439.48 | 1029.64 | 761.80 | 579.44 | 450.92 | 357.8 | 288.64 |
a/m | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | ||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
.00 | 987633.90 | 246908.52 | 109737.09 | 61727.13 | 39505.32 | 27434.25 | 20155.77 | 15431.76 | 12193.02 | 9876.33 | 8162.28 | 6858.54 | 5843.97 | ||||||||||||
740725.38 | 137171.43 | 48009.96 | 22221.81 | 12071.07 | 7278.48 | 4724.01 | 3238.74 | 2316.69 | 1714.05 | 1303.74 | 1014.57 | ||||||||||||||
| |||||||||||||||||||||||||
.05 | 895813.20 | 235011.06 | 106168.68 | 60212.43 | 38726.91 | 26982.72 | 19870.92 | 15240.69 | 12058.65 | 9778.32 | 8088.57 | 6801.75 | 5799.33 | ||||||||||||
660801.96 | 128842.38 | 45956.25 | 21485.52 | 11744.19 | 7111.80 | 4630.23 | 3182.04 | 2280.33 | 1689.75 | 1286.82 | 1002.42 | ||||||||||||||
| |||||||||||||||||||||||||
.10 | 816226.38 | 223953.3 | 102771.45 | 58752.72 | 37971.36 | 26542.17 | 19592.01 | 15053.13 | 11926.53 | 9681.75 | 8015.85 | 6745.68 | 5755.14 | ||||||||||||
592273.08 | 121181.85 | 44018.73 | 20781.36 | 11429.19 | 6950.16 | 4538.88 | 3126.6 | 2244.78 | 1665.90 | 1270.17 | 990.54 | ||||||||||||||
| |||||||||||||||||||||||||
.15 | 746793.36 | 213657.93 | 99534.78 | 57345.57 | 37237.59 | 26112.33 | 19318.95 | 14868.99 | 11796.48 | 9586.62 | 7944.12 | 6690.24 | 5711.40 | ||||||||||||
533135.43 | 114123.15 | 42189.21 | 20107.98 | 11125.26 | 6793.38 | 4449.96 | 3072.51 | 2209.86 | 1642.50 | 1253.88 | 978.84 | ||||||||||||||
| |||||||||||||||||||||||||
.20 | 685856.97 | 204056.55 | 96448.59 | 55988.28 | 36524.97 | 25692.84 | 19051.56 | 14688.18 | 11668.68 | 9492.84 | 7873.38 | 6635.52 | 5668.20 | ||||||||||||
481800.46 | 107607.96 | 40460.31 | 19463.31 | 10832.13 | 6641.28 | 4363.38 | 3019.50 | 2175.84 | 1619.46 | 1237.86 | 967.32 | ||||||||||||||
| |||||||||||||||||||||||||
.25 | 632085.76 | 195088.23 | 93503.79 | 54678.69 | 35832.51 | 25283.43 | 18789.75 | 14510.70 | 11542.86 | 9400.41 | 7803.54 | 6581.52 | 5625.54 | ||||||||||||
436997.52 | 101584.44 | 38825.10 | 18846.18 | 10549.08 | 6493.68 | 4279.05 | 2967.84 | 2142.45 | 1596.87 | 1222.02 | 955.98 | ||||||||||||||
| |||||||||||||||||||||||||
.30 | 584398.62 | 186698.34 | 90691.83 | 53414.46 | 35159.67 | 24883.74 | 18533.16 | 14336.37 | 11419.02 | 9309.42 | 7734.60 | 6528.06 | 5583.33 | ||||||||||||
397700.28 | 96006.51 | 37277.37 | 18254.79 | 10275.93 | 6350.58 | 4196.79 | 2917.35 | 2109.60 | 1574.82 | 1206.54 | 944.73 | ||||||||||||||
| |||||||||||||||||||||||||
.35 | 541911.51 | I78838.19 | 88004.79 | 52193.61 | 34505.55 | 24493.32 | 18281.88 | 14165.19 | 11297.25 | 9219.69 | 7666.65 | 6475.32 | 5541.57 | ||||||||||||
363073.32 | 90833.4 | 35811.18 | 17688.06 | 10012.23 | 6211.44 | 4116.69 | 2867.94 | 2077.56 | 1553.04 | 1191.33 | 933.75 | ||||||||||||||
| |||||||||||||||||||||||||
.40 | 503894.88 | 171464.22 | 85435.47 | 51014.16 | 33869.43 | 24112.17 | 18035.64 | 13997.07 | 11177.37 | 9131.22 | 7599.51 | 6423.21 | 5500.26 | ||||||||||||
332430.66 | 86028.75 | 34421.31 | 17144.73 | 9757.26 | 6076.53 | 4038.57 | 2819.70 | 2046.15 | 1531.71 | 1176.30 | 922.95 | ||||||||||||||
| |||||||||||||||||||||||||
.45 | 469742.67 | 164537.10 | 82977.03 | 49874.22 | 33250.86 | 23739.75 | 17794.44 | 13831.92 | 11059.38 | 9044.10 | 7533.27 | 6371.73 | 5459.49 | ||||||||||||
305205.57 | 81560.07 | 33102.81 | 16623.36 | 9511.11 | 5945.31 | 3962.52 | 2772.54 | 2015.28 | 1510.83 | 1161.54 | 912.24 | ||||||||||||||
| |||||||||||||||||||||||||
.50 | 438948.36 | 158021.46 | 80623.17 | 48772.08 | 32649.03 | 23375.97 | 17557.92 | 13669.65 | 10943.28 | 8958.15 | 7467.93 | 6320.88 | 5419.08 | ||||||||||||
280926.90 | 77398.29 | 31851.09 | 16123.05 | 9273.06 | 5818.05 | 3888.27 | 2726.37 | 1985.13 | 1490.22 | 1147.05 | 901.80 | ||||||||||||||
| |||||||||||||||||||||||||
.55 | 411085.89 | 151885.26 | 78368.04 | 47706.03 | 32063.40 | 23020.47 | 17326.17 | 13510.26 | 10828.98 | 8873.46 | 7403.40 | 6270.57 | 5379.21 | ||||||||||||
259200.63 | 73517.22 | 30662.01 | 15642.63 | 9042.93 | 5694.30 | 3815.91 | 2681.28 | 1955.52 | 1470.06 | 1132.83 | 891.36 | ||||||||||||||
| |||||||||||||||||||||||||
.60 | 385794.45 | 146099.7 | 76206.33 | 46674.54 | 31493.43 | 22672.98 | 17098.92 | 13353.66 | 10716.48 | 8789.94 | 7339.77 | 6220.89 | 5339.70 | ||||||||||||
239694.75 | 69893.37 | 29531.79 | 15181.11 | 8820.45 | 5574.06 | 3745.26 | 2637.18 | 1926.54 | 1450.17 | 1118.88 | 881.19 | ||||||||||||||
| |||||||||||||||||||||||||
.65 | 362767.23 | 140638.5 | 74132.73 | 45676.17 | 30938.49 | 22333.32 | 16876.17 | 13199.67 | 10605.78 | 8707.59 | 7276.86 | 6171.84 | 5300.64 | ||||||||||||
222128.73 | 66505.77 | 28456.56 | 14737.68 | 8605.17 | 5457.15 | 3676.50 | 2593.89 | 1898.19 | 1430.73 | 1105.02 | 871.20 | ||||||||||||||
| |||||||||||||||||||||||||
.70 | 341741.88 | 135477.9 | 72142.74 | 44709.57 | 30398.13 | 22001.22 | 16657.65 | 13048.38 | 10496.70 | 8626.41 | 7214.76 | 6123.33 | 5262.03 | ||||||||||||
206263.98 | 63335.16 | 27433.17 | 14311.44 | 8396.91 | 5343.57 | 3609.27 | 2551.68 | 1870.29 | 1411.65 | 1091.43 | 861.30 | ||||||||||||||
| |||||||||||||||||||||||||
.75 | 322492.77 | 130596.21 | 70231.77 | 43773.21 | 29871.72 | 21676.50 | 16443.45 | 12899.7 | 10389.33 | 8546.31 | 7153.56 | 6075.45 | 5223.87 | ||||||||||||
191896.56 | 60364.44 | 26458.56 | 13901.49 | 8195.22 | 5233.05 | 3543.75 | 2510.37 | 1843.02 | 1392.75 | 1078.11 | 851.58 | ||||||||||||||
| |||||||||||||||||||||||||
.80 | 304825.32 | 125973.72 | 68395.68 | 42866.01 | 29358.90 | 21358.89 | 16233.30 | 12753.54 | 10283.58 | 8467.38 | 7093.08 | 6028.02 | 5186.07 | ||||||||||||
178851.60 | 57578.04 | 25529.67 | 13507.11 | 8000.01 | 5125.59 | 3479.76 | 2469.96 | 1816.20 | 1374.3 | 1065.06 | 841.95 | ||||||||||||||
| |||||||||||||||||||||||||
.85 | 288570.96 | 121592.34 | 66630.78 | 41986.8 | 28859.22 | 21048.21 | 16027.20 | 12609.81 | 10179.45 | 8389.53 | 7033.32 | 5981.22 | 5148.72 | ||||||||||||
166978.62 | 54961.56 | 24643.98 | 13127.58 | 7811.01 | 5021.01 | 3417.39 | 2430.36 | 1789.92 | 1356.21 | 1052.10 | 832.5 | ||||||||||||||
| |||||||||||||||||||||||||
.90 | 273582.81 | 117435.69 | 64933.20 | 41134.23 | 28372.14 | 20744.28 | 15824.97 | 12468.51 | 10076.85 | 8312.67 | 6974.37 | 5934.96 | 5111.73 | ||||||||||||
156147.12 | 52502.49 | 23798.97 | 12762.09 | 7627.86 | 4919.31 | 3356.46 | 2391.66 | 1764.18 | 1338.3 | 1039.41 | 823.23 | ||||||||||||||
| |||||||||||||||||||||||||
.95 | 259732.80 | 1134558.56 | 63299.70 | 40307.49 | 27897.30 | 20446.83 | 15626.52 | 12329.64 | 9975.87 | 8236.98 | 6916.05 | 5889.24 | 5075.10 | ||||||||||||
146244.24 | 50188.86 | 22992.21 | 12410.19 | 7450.47 | 4820.31 | 3296.88 | 2353.77 | 1738.89 | 1320.93 | 1026.81 | 814.14 | ||||||||||||||
| |||||||||||||||||||||||||
1.00 | 246908.52 | 109737.09 | 61727.13 | 39505.32 | 27434.25 | 20155.77 | 15431.76 | 12193.02 | 9876.33 | 8162.28 | 6858.54 | 5843.97 | 5038.92 | ||||||||||||
137171.43 | 48009.96 | 22221.81 | 12071.07 | 7278.48 | 4724.01 | 3238.74 | 2316.69 | 1714.05 | 1303.74 | 1014.57 | 805.05 |
a/m | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | ||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
.00 | 1755793.6 | 438948.5 | 195088.2 | 109737.1 | 70231.7 | 48772.0 | 35832.5 | 27434.2 | 21676.5 | 17557.9 | 14510.7 | 12193.0 | 10389.3 | ||||||||||||
1316845.1 | 243860.3 | 85351.1 | 39505.4 | 21459.7 | 12939.5 | 8398.3 | 5757.7 | 4118.6 | 3047.2 | 2317.7 | 1803.7 | ||||||||||||||
| |||||||||||||||||||||||||
.05 | 1592556.5 | 417797.4 | 188744.3 | 107044.3 | 68847.8 | 47969.3 | 35326.1 | 27094.6 | 21437.6 | 17383.7 | 14379.7 | 12092.0 | 10309.9 | ||||||||||||
1174759.1 | 229053.1 | 81700.0 | 38196.5 | 20878.5 | 12643.2 | 8231.5 | 5657.0 | 4053.9 | 3004.0 | 2287.7 | 1782.1 | ||||||||||||||
| |||||||||||||||||||||||||
.10 | 1451069.1 | 398139.2 | 182704.8 | 104449.3 | 67504.6 | 47186.1 | 34830.2 | 26761.1 | 21202.7 | 17212 | 14250.4 | 11992.3 | 10231.4 | ||||||||||||
1052929.9 | 215434.4 | 78255.5 | 36944.7 | 20318.5 | 12355.9 | 8069.1 | 5558.4 | 3990.7 | 2961.6 | 2258.1 | 1760.9 | ||||||||||||||
| |||||||||||||||||||||||||
.15 | 1327632.6 | 379836.3 | 176950.7 | 101947.7 | 66200.2 | 46421.9 | 34344.8 | 26433.8 | 20971.5 | 17042.9 | 14122.9 | 11893.8 | 10153.6 | ||||||||||||
947796.3 | 202885.6 | 75003.0 | 35747.5 | 19778.3 | 12077.1 | 7911.0 | 5462.3 | 3928.6 | 2920.0 | 2229.1 | 1740.2 | ||||||||||||||
| |||||||||||||||||||||||||
.20 | 1219301.3 | 362767.2 | 171464.2 | 99534.7 | 64933.3 | 45676.2 | 33869.4 | 26112.3 | 20744.3 | 16876.2 | 13997.1 | 11796.5 | 10076.8 | ||||||||||||
1219301.3 | 362767.2 | 171464.2 | 99534.7 | 64933.3 | 45676.2 | 33869.4 | 26112.3 | 20744.3 | 16876.2 | 13997.1 | 11796.5 | ||||||||||||||
| |||||||||||||||||||||||||
.25 | 1123708.0 | 346823.5 | 166229.0 | 97206.6 | 63702.2 | 44948.3 | 33404.0 | 25796.8 | 20520.6 | 16711.8 | 13873.0 | 11700.5 | 10001.0 | ||||||||||||
776884.5 | 180594.5 | 69022.4 | 33504.4 | 18753.9 | 11544.3 | 7607.2 | 5276.2 | 3808.8 | 2838.8 | 2172.5 | 1699.5 | ||||||||||||||
| |||||||||||||||||||||||||
.30 | 1038930.9 | 331908.2 | 161229.9 | 94959.0 | 62506.1 | 44237.8 | 32947.8 | 25486.9 | 20300.5 | 16550.1 | 13750.4 | 11605.4 | 9925.9 | ||||||||||||
707022.7 | 170678.3 | 66270.9 | 32452.9 | 18268.3 | 11290.0 | 7460.9 | 5186.4 | 3750.4 | 2799.7 | 2145.0 | 1679.5 | ||||||||||||||
| |||||||||||||||||||||||||
.35 | 963398.2 | 317934.6 | 156453.0 | 92788.6 | 61343.2 | 43543.7 | 32501.1 | 25182.6 | 20084.0 | 16390.6 | 13629.6 | 11511.7 | 9851.7 | ||||||||||||
645463.6 | 161481.6 | 63664.4 | 31445.4 | 17799.5 | 11042.6 | 7318.5 | 5098.6 | 3693.4 | 2761.0 | 2117.9 | 1660.0 | ||||||||||||||
| |||||||||||||||||||||||||
.40 | 895813.1 | 304825.3 | 151885.3 | 90691.8 | 60212.5 | 42866.1 | 32063.4 | 24883.7 | 19870.9 | 16233.3 | 13510.2 | 11419.0 | 9778.2 | ||||||||||||
590987.8 | 152940.0 | 61193.5 | 30479.3 | 17346.4 | 10802.7 | 7179.7 | 5012.8 | 3637.6 | 2723.1 | 2091.2 | 1640.8 | ||||||||||||||
| |||||||||||||||||||||||||
.45 | 835098.1 | 292510.4 | 147514.7 | 88665.3 | 59112.6 | 42204.0 | 31634.6 | 24590.1 | 19661.1 | 16078.4 | 13392.5 | 11327.5 | 9705.8 | ||||||||||||
542587.7 | 144995.7 | 58849.4 | 29552.7 | 16908.6 | 10569.4 | 7044.5 | 4929.0 | 3582.7 | 2685.9 | 2065.0 | 1621.7 | ||||||||||||||
| |||||||||||||||||||||||||
.50 | 780352.6 | 280927.0 | 143330.1 | 86705.9 | 58042.7 | 41557.3 | 31214,1 | 24301.6 | 19454.7 | 15925.6 | 13276.3 | 11237.1 | 9633.9 | ||||||||||||
499425.6 | 137596.9 | 56624.2 | 28663.2 | 16485.4 | 10343.2 | 6912.5 | 4846.9 | 3529.1 | 2649.3 | 2039.2 | 1603.2 | ||||||||||||||
| |||||||||||||||||||||||||
.55 | 730819.4 | 270018.2 | 139321.0 | 84810.7 | 57001.6 | 40925.3 | 30802.1 | 24018.2 | 19251.5 | 15775.0 | 13161.6 | 11147.7 | 9563.0 | ||||||||||||
460801.2 | 130697.2 | 54510.3 | 27809.1 | 16076.3 | 10123.2 | 6783.9 | 4766.7 | 3476.5 | 2613.4 | 2013.9 | 1584.7 | ||||||||||||||
| |||||||||||||||||||||||||
.60 | 685856.8 | 259732.8 | 135477.9 | 82977.0 | 55988.3 | 40307.5 | 30398.1 | 23739.8 | 19051.5 | 15626.6 | 13048.5 | 11059.4 | 9492.8 | ||||||||||||
426124.0 | 124254.9 | 52500.9 | 26988.7 | 15680.8 | 9909.4 | 6658.3 | 4688.3 | 3424.9 | 2578.1 | 1989.1 | 1566.6 | ||||||||||||||
| |||||||||||||||||||||||||
.65 | 644919.5 | 250024 | 131791.5 | 81202.1 | 55001.8 | 39703.7 | 30002.1 | 23466.1 | 18854.7 | 15480.2 | 12936.6 | 10972.2 | 9423.4 | ||||||||||||
394895.5 | 118232.5 | 50589.4 | 26200.3 | 15298.1 | 9701.6 | 6536.0 | 4611.4 | 3374.5 | 2543.6 | 1964.4 | 1548.8 | ||||||||||||||
| |||||||||||||||||||||||||
.70 | 607541.1 | 240849.6 | 128253.8 | 79483.7 | 54041.1 | 39113.3 | 29613.6 | 23197.1 | 18660.8 | 15335.8 | 12826.2 | 10885.9 | 9354.7 | ||||||||||||
366691.5 | 112595.8 | 48770.1 | 25442.6 | 14927.8 | 9499.7 | 6416.5 | 4536.3 | 3325.0 | 2509.6 | 1940.3 | 1531.2 | ||||||||||||||
| |||||||||||||||||||||||||
.75 | 573320.5 | 232171.0 | 124856.5 | 77819.0 | 53105.3 | 38536.0 | 29232.8 | 22932.8 | 18469.9 | 15193.4 | 12717.4 | 10800.8 | 9286.9 | ||||||||||||
341149.5 | 107314.5 | 47037.5 | 24713.7 | 14569.3 | 9303.2 | 6300.0 | 4462.9 | 3276.5 | 2476.0 | 1916.6 | 1513.9 | ||||||||||||||
| |||||||||||||||||||||||||
.80 | 541911.7 | 223953.3 | 121592.3 | 76206.2 | 52193.6 | 37971.4 | 28859.2 | 22673.0 | 18281.9 | 15053.1 | 12609.9 | 10716.5 | 9219.7 | ||||||||||||
317958.4 | 102361.0 | 45386.1 | 24012.6 | 14222.2 | 9112.2 | 6186.2 | 4391.1 | 3228.8 | 2443.2 | 1893.4 | 1496.8 | ||||||||||||||
| |||||||||||||||||||||||||
.85 | 513015.0 | 216164.2 | 118454.7 | 74643.2 | 51305.3 | 37419.0 | 28492.8 | 22417.4 | 18096.8 | 14914.7 | 12503.7 | 10633.3 | 9153.3 | ||||||||||||
296850.8 | 97709.5 | 43811.5 | 23337.9 | 13886.3 | 8926.2 | 6075.4 | 4320.6 | 3182.1 | 2411.0 | 1870.4 | 1480.0 | ||||||||||||||
| |||||||||||||||||||||||||
.90 | 486369.4 | 208774.6 | 115436.8 | 73127.5 | 50439.4 | 36878.7 | 28133.3 | 22166.2 | 17914.4 | 14778.1 | 12398.9 | 10551.0 | 9087.5 | ||||||||||||
277594.8 | 93337.8 | 42309.3 | 22688.1 | 13560.7 | 8745.4 | 5967.1 | 4251.7 | 3136.3 | 2379.2 | 1847.9 | 1463.5 | ||||||||||||||
| |||||||||||||||||||||||||
.95 | 461747.2 | 201757.4 | 112532.8 | 71657.8 | 49595.2 | 36349.9 | 27780.5 | 21919.4 | 17734.9 | 14643.5 | 12295.2 | 10469.8 | 9022.4 | ||||||||||||
259989.8 | 89224.6 | 40875.0 | 22062.6 | 13245.3 | 8569.4 | 5861.1 | 4184.5 | 3091.4 | 2348.3 | 1825.4 | 1447.4 | ||||||||||||||
| |||||||||||||||||||||||||
1.00 | 438948.5 | 195088.2 | 109737.1 | 70231.7 | 48772.0 | 35832.5 | 27434.2 | 21676.5 | 17557.9 | 14510.7 | 12193.0 | 10389.3 | 8958.1 | ||||||||||||
243860.3 | 85351.1 | 39505.4 | 21459.7 | 12939.5 | 8398.3 | 5757.7 | 4118.6 | 3047.2 | 2317.7 | 1803.7 | 1431.2 |
λair | 7065.200 | 4713.143 | 4120.817 | 3867.477 | 3732.861 | 3651.981 | 3599.304 | 3562.95 | 3536.82 | 3517.327 | 3502.381 | ||||||||||||
Observed | ν | 14149.98 | 21211.34 | 24260.20 | 25849.33 | 26781.50 | 27374.61 | 27775.24 | 28058.63 | 28265.92 | 28422.56 | 28543.85 | |||||||||||
Δ | 7061.36 | 3048.86 | 1589.13 | 932.17 | 593.11 | 400.63 | 283.39 | 207.29 | 156.64 | 121.29 | |||||||||||||
Δ | 7037.24 | 3048.13 | 1590.17 | 932.98 | 593.73 | 401.03 | 283.52 | 207.81 | 156.85 | 121.27 | |||||||||||||
Table a = 0.70 | (m,a) | −15053.10 | 8015.86 | 4967.73 | 3377.56 | 2444.58 | 1850.85 | 1449.82 | 1166.30 | 958.49 | 801.64 | 680.37 | |||||||||||
m | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | ||||||||||||
2P calc | 29203.08 | 29227.2 | 29227.93 | 29226.89 | 29226.08 | 29225.46 | 29225.06 | 29224.93 | 29224.41 | 29224.2 | 29224.22 |
m (table) | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
---|---|---|---|---|---|---|---|---|---|---|---|
(m,a) | 15073.89 | 8012.53 | 4963.67 | 3374.54 | 2442.37 | 1849.26 | 1448.63 | 1165.24 | 957.95 | 801.31 | 680.02 |
*m | 2.697954 | 3.700517 | 4.701601 | 5.70217 | 6.70257 | 7.70279 | 8.70299 | 0.70375 | 10.7023 | 11.7017 | 12.7024 |
λair | 3838.29 | 3096.91 | 2851.65 | 2736.53 | 2672.43 | 2632.88 | 2606.64 | 2588.28 | 2574.93 | 2564.91 | 2557.20 | 2551.13 | |||||||||||||
Observed | ν | 26045.9 | 32280.9 | 35057.1 | 36531.8 | 37408.1 | 37970.0 | 38352.1 | 38624 2 | 38824.4 | 38976.0 | 39093.5 | 39186.5 | ||||||||||||
Δ | 6235.0 | 2776.2 | 1474.7 | 876.3 | 561.9 | 382.1 | 272.1 | 200.2 | 151.6 | 117.5 | 93.0 | ||||||||||||||
Δ | 6252.20 | 2787.42 | 1470.71 | 878.39 | 563.70 | 383.17 | 272.24 | 200.34 | 151.70 | 117.62 | 93.03 | ||||||||||||||
Table a = 0.825 | (m,a) | 13753.67 | 7501.47 | 4714.05 | 3234.34 | 2355.95 | 1792.25 | 1409.08 | 1136.84 | 936.50 | 784.80 | 667.18 | 574.15 | ||||||||||||
2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | ||||||||||||||
| |||||||||||||||||||||||||
23P2 | 39799.57 | 39782.37 | 39771.15 | 39766.14 | 39764.05 | 39762.25 | 39761.18 | 39761.04 | 39760.9 | 39760.8 | 39760.7 | 39760.65 | |||||||||||||
39760.5 may be taken as an asymptotic value of 23P2 for large values of m. From this value there follows for (m, D): | |||||||||||||||||||||||||
m = (m,D) | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | |||||||||||||
13714.6 | 7479.6 | 4703.4 | 3228.7 | 2352.4 | 1790.5 | 1408.4 | 1136.3 | 936.1 | 784.5 | 667.0 | 574.0 |
Values of 109737.1/(m + a)2 and the differences between m and m + 1
m | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | ||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
a | |||||||||||||||||||||||||
+0.00 | 109737.1 | 27434.28 | 12193.01 | 6858.57 | 4389.48 | 3048.25 | 2239.53 | 1714.64 | 1354.78 | 1097.37 | 906.92 | 762.06 | 649.33 | ||||||||||||
Δ | 82302.82 | 15241.27 | 5334.44 | 2469.09 | 1341.23 | 808.72 | 524.89 | 359.86 | 257.41 | 190.45 | 144.86 | 112.73 | |||||||||||||
| |||||||||||||||||||||||||
+0.05 | 99534.78 | 26112.34 | 11796.52 | 6690.27 | 4302.99 | 2998.08 | 2207.88 | 1693.41 | 1339.85 | 1086.48 | 898.73 | 755.75 | 644.37 | ||||||||||||
Δ | 73422.44 | 14315.82 | 5106.25 | 2387.28 | 1304.91 | 790.20 | 514.47 | 353.56 | 253.37 | 187.75 | 142.98 | 111.38 | |||||||||||||
| |||||||||||||||||||||||||
+0.10 | 90691.82 | 24883.70 | 11419.05 | 6528.08 | 4219.04 | 2949.13 | 2176.89 | 1672.57 | 1325.17 | 1075.75 | 890.65 | 749.52 | 639.46 | ||||||||||||
Δ | 65808.12 | 13464.65 | 4890.97 | 2309.04 | 1269.91 | 772.24 | 504.32 | 347.40 | 249.42 | 185.10 | 141.13 | 110.06 | |||||||||||||
| |||||||||||||||||||||||||
+0.15 | 82977.04 | 23739.77 | 11059.42 | 6371.73 | 4137.51 | 2901.37 | 2146.55 | 1652.11 | 1310.72 | 1065.18 | 882.68 | 743.36 | 634.60 | ||||||||||||
Δ | 59237.27 | 12680.35 | 4687.69 | 2234.22 | 1236.14 | 754.82 | 494.44 | 341.39 | 245.54 | 182.50 | 139.32 | 108.76 | |||||||||||||
| |||||||||||||||||||||||||
+0.20 | 76206.33 | 22672.95 | 10716.51 | 6220.92 | 4058.33 | 2854.76 | 2116.84 | 1632.02 | 1296.52 | 1054.76 | 874.82 | 737.28 | 629.80 | ||||||||||||
Δ | 53533.38 | 11956.44 | 4495.59 | 2162.59 | 1203.57 | 737.92 | 484.82 | 335.50 | 241.76 | 179.94 | 137.54 | 107.48 | |||||||||||||
| |||||||||||||||||||||||||
+0.25 | 70231.75 | 21676.47 | 10389.31 | 6075.41 | 3981.39 | 2809.27 | 2087.75 | 1612.30 | 1282.54 | 1044.49 | 867.06 | 731.28 | 625.06 | ||||||||||||
Δ | 48555.28 | 11287.16 | 4313.90 | 2094.02 | 1172.12 | 721.52 | 475.45 | 329.76 | 238.05 | 177.43 | 135.78 | 106.22 | |||||||||||||
| |||||||||||||||||||||||||
+0.30 | 64933.18 | 20744.26 | 10076.87 | 5934.94 | 3906.63 | 2764.86 | 2059.24 | 1592.93 | 1268.78 | 1034.38 | 859.40 | 725.34 | 620.37 | ||||||||||||
Δ | 44188.92 | 10667.39 | 4141.93 | 2028.31 | 1141.77 | 705.62 | 466.31 | 324.15 | 234.40 | 174.98 | 134.06 | 104.97 | |||||||||||||
| |||||||||||||||||||||||||
+0.35 | 60212.39 | 19870.91 | 9778.31 | 5799.29 | 3833.95 | 2721.48 | 2031.32 | 1573.91 | 1255.25 | 1024.41 | 851.85 | 719.48 | 615.73 | ||||||||||||
Δ | 40341.48 | 10092.60 | 3979.02 | 1965.34 | 1112.47 | 690.16 | 457.41 | 318.66 | 230.84 | 172.56 | 132.37 | 103.75 | |||||||||||||
| |||||||||||||||||||||||||
+0.40 | 55988.32 | 19051.58 | 9492.83 | 5668.24 | 3763.28 | 2679.13 | 2003.96 | 1555.23 | 1241.93 | 1014.58 | 844.39 | 713.69 | 611.14 | ||||||||||||
Δ | 36936.74 | 9558.75 | 3824.59 | 1904.96 | 1084.15 | 675.17 | 448.73 | 313.30 | 227.35 | 170.19 | 130.70 | 102.55 | |||||||||||||
| |||||||||||||||||||||||||
+0.45 | 52193.63 | 18281.90 | 9219.67 | 5541.58 | 3694.54 | 2637.75 | 1977.16 | 1536.88 | 1228.82 | 1004.90 | 837.03 | 707.97 | 606.61 | ||||||||||||
Δ | 33911.73 | 9062.23 | 3678.09 | 1847.04 | 1056.79 | 660.59 | 440.28 | 308.06 | 223.92 | 167.87 | 129.06 | 101.36 | |||||||||||||
| |||||||||||||||||||||||||
+0.50 | 48772.04 | 17557.94 | 8958.13 | 5419.12 | 3627.67 | 2597.33 | 1950.88 | 1518.85 | 1215.92 | 995.35 | 829.77 | 702.32 | 602.12 | ||||||||||||
Δ | 31214.10 | 8599.81 | 3539.01 | 1791.45 | 1030.34 | 646.45 | 432.03 | 302.93 | 220.57 | 165.58 | 127.45 | 100.20 | |||||||||||||
| |||||||||||||||||||||||||
+0.55 | 45676.21 | 16876.14 | 8707.56 | 5300.67 | 3562.60 | 2557.83 | 1925.13 | 1501.14 | 1203.22 | 985.94 | 822.60 | 696.73 | 597.69 | ||||||||||||
Δ | 28800.07 | 8168.58 | 3406.89 | 1738.07 | 1004.77 | 632.70 | 423.99 | 297.92 | 217.28 | 163.34 | 125.87 | 99.04 | |||||||||||||
| |||||||||||||||||||||||||
+0.60 | 42866.05 | 16233.30 | 8467.37 | 5186.06 | 3499.27 | 2519.22 | 1899.88 | 1483.74 | 1190.72 | 976.66 | 815.53 | 691.21 | 593.30 | ||||||||||||
Δ | 26632.75 | 7765.93 | 3281.31 | 1686.79 | 980.05 | 619.34 | 416.14 | 293.02 | 214.06 | 161.13 | 124.32 | 97.91 | |||||||||||||
| |||||||||||||||||||||||||
+0.65 | 40307.47 | 15626.50 | 8236.97 | 5075.13 | 3437.61 | 2481.48 | 1875.13 | 1466.63 | 1178.42 | 967.51 | 808.54 | 685.76 | 588.96 | ||||||||||||
Δ | 24680.97 | 7389.53 | 3161.84 | 1637.52 | 956.13 | 606.35 | 408.50 | 288.21 | 210.91 | 158.97 | 122.78 | 96.80 | |||||||||||||
| |||||||||||||||||||||||||
+0.70 | 37971.32 | 15053.10 | 8015.86 | 4967.73 | 3377.57 | 2444.58 | 1850.85 | 1449.82 | 1166.30 | 958.49 | 801.64 | 680.37 | 584.67 | ||||||||||||
Δ | 22918.22 | 7037.24 | 3048.13 | 1590.16 | 932.99 | 593.73 | 401.03 | 283.52 | 207.81 | 156.85 | 121.27 | 95.70 | |||||||||||||
| |||||||||||||||||||||||||
+0.75 | 35832.53 | 14510.69 | 7803.53 | 4863.69 | 3319.08 | 2408.50 | 1827.05 | 1433.30 | 1154.37 | 949.59 | 794.84 | 675.05 | 580.43 | ||||||||||||
Δ | 21321.84 | 6707.16 | 2939.84 | 1544.61 | 910.58 | 581.45 | 393.75 | 278.93 | 204.78 | 154.75 | 119.79 | 94.62 | |||||||||||||
| |||||||||||||||||||||||||
+0.80 | 33869.48 | 13997.08 | 7599.52 | 4762.89 | 3262.10 | 2373.21 | 1803.70 | 1417.06 | 1142.62 | 940.82 | 788.12 | 669.78 | 576.23 | ||||||||||||
Δ | 19872.40 | 6397.56 | 2836.63 | 1500.79 | 888.89 | 569.51 | 386.64 | 274.44 | 201.80 | 152.70 | 118.34 | 93.55 | |||||||||||||
| |||||||||||||||||||||||||
+0.85 | 32063.44 | 13510.26 | 7403.42 | 4665.20 | 3206.58 | 2338.69 | 1780.80 | 1401.09 | 1131.05 | 932.17 | 781.48 | 664.58 | 572.08 | ||||||||||||
Δ | 18553.18 | 6106.84 | 2738.22 | 1458.62 | 867.89 | 557.89 | 379.71 | 270.04 | 198.88 | 150.69 | 116.90 | 92.50 | |||||||||||||
| |||||||||||||||||||||||||
+0.90 | 30398.09 | 13048.41 | 7214.80 | 4570.47 | 3152.46 | 2304.92 | 1758.33 | 1385.39 | 1119.65 | 923.63 | 774.93 | 659.44 | 567.97 | ||||||||||||
Δ | 17349.68 | 5833.61 | 2644.33 | 1418.01 | 847.54 | 546.59 | 372.94 | 265.74 | 196.02 | 148.70 | 115.49 | 91.47 | |||||||||||||
| |||||||||||||||||||||||||
+0.95 | 28859.20 | 12609.84 | 7033.30 | 4478.61 | 3099.70 | 2271.87 | 1736.28 | 1369.96 | 1108.43 | 915.22 | 768.45 | 654.36 | 563.90 | ||||||||||||
Δ | 16249.36 | 5576.54 | 2554.69 | 1378.91 | 827.83 | 535.59 | 366.32 | 261.53 | 193.21 | 146.77 | 114.09 | 90.46 | |||||||||||||
| |||||||||||||||||||||||||
+ 1.00 | 27434.28 | 12193.01 | 6858.57 | 4389.48 | 3048.25 | 2239.53 | 1714.65 | 1354.78 | 1097.37 | 906.92 | 762.06 | 649.33 | 559.88 | ||||||||||||
Δ | 15241.27 | 5334.44 | 2469.09 | 1341.23 | 808.72 | 524.88 | 359.87 | 257.41 | 190.45 | 144.86 | 112.73 | 89.45 | |||||||||||||
| |||||||||||||||||||||||||
m+a = | 0.95 | 0.90 | 0.85 | 0.80 | 0.75 | 0.70 | 0.65 | 0.60 | 0.50 | ||||||||||||||||
121592.4 | 135477.9 | 151885.3 | 171464.2 | 195088.2 | 223953.4 | 259732.8 | 304825.9 | 438948.4 |
Values of 4-109737.1/(m + a)5 and the differences between m and m + 1.
a/m | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | |||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
.00 | 438948.40 | 109737.12 | 48772.04 | 27434.28 | 17557.92 | 12193.00 | 8958.12 | 6858.56 | 5419.12 | 4389.48 | 3627.68 | 3048.24 | 2597.32 | 2239.52 | |||||||||||||
329211.28 | 60965.08 | 21337.76 | 9876.36 | 5364.92 | 3234.88 | 2099.56 | 1439.44 | 1029.64 | 761.80 | 579.44 | 450.92 | 357.80 | |||||||||||||||
| |||||||||||||||||||||||||||
.05 | 398139.12 | 104449.36 | 47186.08 | 26761.08 | 17211.96 | 11992.32 | 8831.52 | 6773.64 | 5359.40 | 4345.92 | 3594.92 | 3023.00 | 2577.48 | 2223.70 | |||||||||||||
293689.76 | 57263.28 | 20425.00 | 9549.12 | 5219.64 | 3160.80 | 2057.88 | 1414.24 | 1013.48 | 751.00 | 571.92 | 445.52 | 353.78 | |||||||||||||||
| |||||||||||||||||||||||||||
.10 | 362767.28 | 99534.80 | 45676.20 | 26112.32 | 16876.16 | 11796.52 | 8707.56 | 6690.28 | 5300.68 | 4303 | 3562.60 | 2998.08 | 2557.84 | 2207.88 | |||||||||||||
263232.48 | 53858.60 | 19563.88 | 9236.16 | 5079.64 | 3088.96 | 2017.28 | 1389.60 | 997.68 | 740.40 | 564.52 | 440.24 | 349.96 | |||||||||||||||
| |||||||||||||||||||||||||||
.15 | 331908.16 | 94959.08 | 44237.68 | 25486.92 | 16550.04 | 11605.48 | 8586.20 | 6608.44 | 5242.88 | 4260.72 | 3530.72 | 2973.44 | 2538.40 | 2192.39 | |||||||||||||
236949.08 | 50721.40 | 18750.76 | 8936.88 | 4944.56 | 3019.28 | 1977.76 | 1365.56 | 982.16 | 730.00 | 557.28 | 435.04 | 346.01 | |||||||||||||||
| |||||||||||||||||||||||||||
.20 | 304825.32 | 90691.80 | 42866.04 | 24883.68 | 16233.32 | 11419.04 | 8467.36 | 6528.08 | 5186.08 | 4219.04 | 3499.28 | 2949.12 | 2519.20 | 2176.89 | |||||||||||||
214133.52 | 47825.76 | 17982.36 | 8650.36 | 4814.28 | 2951.68 | 1939.28 | 1342.00 | 967.04 | 719.76 | 550.16 | 429.92 | 342.31 | |||||||||||||||
| |||||||||||||||||||||||||||
.25 | 280927.00 | 86705.88 | 41557.24 | 24301.64 | 15925.56 | 11237.08 | 8351.00 | 6449.20 | 5130.16 | 4177.96 | 3468.24 | 2925.12 | 2500.24 | 2161.72 | |||||||||||||
194221.12 | 45148.64 | 17255.60 | 8376.08 | 4688.48 | 2886.08 | 1901.80 | 1319.04 | 952.20 | 709.72 | 543.12 | 424.88 | 338.52 | |||||||||||||||
| |||||||||||||||||||||||||||
.30 | 259732.72 | 82977.04 | 40307.48 | 23739.76 | 15626.52 | 11059.44 | 8236.96 | 6371.72 | 5075.12 | 4137.52 | 3437.60 | 2901.36 | 2481.48 | 2146.55 | |||||||||||||
176755.68 | 42669.56 | 16567.72 | 8113.24 | 4567.08 | 2822.48 | 1865.24 | 1296.60 | 937.60 | 699.92 | 536.24 | 419.88 | 334.93 | |||||||||||||||
| |||||||||||||||||||||||||||
.35 | 240849.56 | 79483.64 | 39113.24 | 23197.16 | 15335.80 | 10885.92 | 8125.28 | 6295.64 | 5021.00 | 4097.64 | 3407.40 | 2877.92 | 2462.92 | 2131.7 | |||||||||||||
161365.92 | 40370.40 | 15916.08 | 7861.36 | 4449.88 | 2760.64 | 1829.64 | 1274.64 | 923.36 | 690.24 | 529.48 | 415.00 | 331.22 | |||||||||||||||
| |||||||||||||||||||||||||||
.40 | 223953.28 | 76206.32 | 37971.32 | 22672.96 | 15053.12 | 10716.52 | 8015.84 | 6220.92 | 4967.72 | 4058.32 | 3377.56 | 2854.76 | 2444.56 | 2116.84 | |||||||||||||
147746.96 | 38235.00 | 15298.36 | 7619.84 | 4336.60 | 2700.68 | 1794.92 | 1253.2 | 909.40 | 680.76 | 522.80 | 410.20 | 327.72 | |||||||||||||||
| |||||||||||||||||||||||||||
.45 | 208774.52 | 73127.60 | 36878.68 | 22166.32 | 14778.16 | 10551.00 | 7908.64 | 6147.52 | 4915.28 | 4019.6 | 3348.12 | 2831.88 | 2426.44 | 2102.3 | |||||||||||||
135646.92 | 36248.92 | 14712.36 | 7388.16 | 4227.16 | 2642.36 | 1761.12 | 1232.24 | 895.68 | 671.48 | 516.24 | 405.44 | 324.14 | |||||||||||||||
| |||||||||||||||||||||||||||
.50 | 195088.16 | 70231.76 | 35832.52 | 21676.48 | 14510.68 | 10389.32 | 7803.52 | 6075.40 | 4863.68 | 3981.4 | 3319.08 | 2809.28 | 2408.48 | 2087.75 | |||||||||||||
124856.40 | 34399.24 | 14156.04 | 7165.80 | 4121.36 | 2585.80 | 1728.12 | 1211.72 | 882.28 | 662.32 | 509.80 | 400.80 | 320.73 | |||||||||||||||
| |||||||||||||||||||||||||||
.55 | 182704.84 | 67504.56 | 34830.24 | 21202.68 | 14250.40 | 10231.32 | 7700.52 | 6004.56 | 4812.88 | 3943.76 | 3290.40 | 2786.92 | 2390.76 | 2073.5 | |||||||||||||
115200.28 | 32674.32 | 13627.56 | 6952.28 | 4019.08 | 2530.80 | 1695.96 | 1191.68 | 869.12 | 653.36 | 503.48 | 396.16 | 317.26 | |||||||||||||||
| |||||||||||||||||||||||||||
.60 | 171464.20 | 64933.20 | 33869.48 | 20744.24 | 13997.08 | 10076.88 | 7599.52 | 5934.96 | 4762.88 | 3906.64 | 3262.12 | 2764.84 | 2373.20 | 2059.24 | |||||||||||||
106531.00 | 31063.72 | 13125.24 | 6747.16 | 3920.36 | 2477.36 | 1664.56 | 1172.08 | 856.24 | 644.52 | 497.28 | 391.64 | 313.96 | |||||||||||||||
| |||||||||||||||||||||||||||
.65 | 161229.88 | 62506.00 | 32947.88 | 20300.52 | 13750.44 | 9925.92 | 7500.52 | 5866.52 | 4713.68 | 3870.04 | 3234.16 | 2743.04 | 2355.84 | 2045.28 | |||||||||||||
98723.88 | 29558.12 | 12647.36 | 6550.08 | 3824.52 | 2425.40 | 1634.00 | 1152.84 | 843.64 | 635.88 | 491.12 | 387.20 | 310.56 | |||||||||||||||
| |||||||||||||||||||||||||||
.70 | 151885.28 | 60212.40 | 32063.44 | 19870.92 | 13510.28 | 9778.32 | 7403.40 | 5799.28 | 4665.20 | 3833.96 | 3206.56 | 2721.48 | 2338.68 | 2031.32 | |||||||||||||
91672.88 | 28148.96 | 12192.52 | 6360.64 | 3731.96 | 2374.92 | 1604.12 | 1134.08 | 831.24 | 627.40 | 485.08 | 382.80 | 307.36 | |||||||||||||||
| |||||||||||||||||||||||||||
.75 | 143330.12 | 58042.76 | 31214.12 | 19454.76 | 13276.32 | 9634.00 | 7308.20 | 5733.20 | 4617.48 | 3798.36 | 3179.36 | 2700.20 | 2321.72 | 2017.64 | |||||||||||||
85287.36 | 26828.64 | 11759.36 | 6178.44 | 3642.32 | 2325.80 | 1575.00 | 1115.72 | 819.12 | 619.00 | 479.16 | 378.48 | 304.08 | |||||||||||||||
| |||||||||||||||||||||||||||
.80 | 135477.92 | 55988.32 | 30398.08 | 19051.56 | 13048.40 | 9492.84 | 7214.80 | 5668.24 | 4570.48 | 3763.28 | 3152.48 | 2679.12 | 2304.92 | 2003.96 | |||||||||||||
79489.60 | 25590.24 | 11346.52 | 6003.16 | 3555.56 | 2278.04 | 1546.56 | 1097.76 | 807.20 | 610.80 | 473.36 | 374.20 | 300.96 | |||||||||||||||
| |||||||||||||||||||||||||||
.85 | 128253.76 | 54041.04 | 29613.68 | 18660.80 | 12826.32 | 9354.76 | 7123.20 | 5604.36 | 4524.20 | 3728.68 | 3125.92 | 2658.32 | 2288.32 | 1990.51 | |||||||||||||
74212.72 | 24427.36 | 10952.88 | 5834.48 | 3471.56 | 2231.56 | 1518.84 | 1080.16 | 795.52 | 602.76 | 467.60 | 370.00 | 297.81 | |||||||||||||||
| |||||||||||||||||||||||||||
.90 | 121592.36 | 52193.64 | 28859.20 | 18281.88 | 12609.84 | 9219.68 | 7033.32 | 5541.56 | 4478.60 | 3694.52 | 3099.72 | 2637.76 | 2271.88 | 1977.16 | |||||||||||||
69398.72 | 23334.44 | 10577.32 | 5672.04 | 3390.16 | 2186.36 | 1491.76 | 1062.96 | 784.08 | 594.80 | 461.96 | 365.88 | 294.70 | |||||||||||||||
| |||||||||||||||||||||||||||
.95 | 115436.80 | 50439.36 | 28133.20 | 17914.44 | 12398.80 | 9087.48 | 6945.12 | 5479.84 | 4433.72 | 3660.88 | 3073.80 | 2617.44 | 2255.60 | 1964.02 | |||||||||||||
64997.44 | 22306.16 | 10218.76 | 5515.64 | 3311.32 | 2142.36 | 1465.28 | 1046.12 | 772.84 | 587.08 | 456.36 | 361.84 | 291.58 | |||||||||||||||
| |||||||||||||||||||||||||||
1.00 | 109737.12 | 48772.04 | 27434.28 | 17557.92 | 12193.00 | 8958.12 | 6858.56 | 5419.12 | 4389.48 | 3627.68 | 3048.24 | 2597.32 | 2239.52 | 1950.88 | |||||||||||||
60965.08 | 21337.76 | 9876.36 | 5364.92 | 3234.88 | 2099.56 | 1439.48 | 1029.64 | 761.80 | 579.44 | 450.92 | 357.8 | 288.64 |
Values of 9 109737./(m + a)2 and the differences between m and m + 1.
a/m | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | ||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
.00 | 987633.90 | 246908.52 | 109737.09 | 61727.13 | 39505.32 | 27434.25 | 20155.77 | 15431.76 | 12193.02 | 9876.33 | 8162.28 | 6858.54 | 5843.97 | ||||||||||||
740725.38 | 137171.43 | 48009.96 | 22221.81 | 12071.07 | 7278.48 | 4724.01 | 3238.74 | 2316.69 | 1714.05 | 1303.74 | 1014.57 | ||||||||||||||
| |||||||||||||||||||||||||
.05 | 895813.20 | 235011.06 | 106168.68 | 60212.43 | 38726.91 | 26982.72 | 19870.92 | 15240.69 | 12058.65 | 9778.32 | 8088.57 | 6801.75 | 5799.33 | ||||||||||||
660801.96 | 128842.38 | 45956.25 | 21485.52 | 11744.19 | 7111.80 | 4630.23 | 3182.04 | 2280.33 | 1689.75 | 1286.82 | 1002.42 | ||||||||||||||
| |||||||||||||||||||||||||
.10 | 816226.38 | 223953.3 | 102771.45 | 58752.72 | 37971.36 | 26542.17 | 19592.01 | 15053.13 | 11926.53 | 9681.75 | 8015.85 | 6745.68 | 5755.14 | ||||||||||||
592273.08 | 121181.85 | 44018.73 | 20781.36 | 11429.19 | 6950.16 | 4538.88 | 3126.6 | 2244.78 | 1665.90 | 1270.17 | 990.54 | ||||||||||||||
| |||||||||||||||||||||||||
.15 | 746793.36 | 213657.93 | 99534.78 | 57345.57 | 37237.59 | 26112.33 | 19318.95 | 14868.99 | 11796.48 | 9586.62 | 7944.12 | 6690.24 | 5711.40 | ||||||||||||
533135.43 | 114123.15 | 42189.21 | 20107.98 | 11125.26 | 6793.38 | 4449.96 | 3072.51 | 2209.86 | 1642.50 | 1253.88 | 978.84 | ||||||||||||||
| |||||||||||||||||||||||||
.20 | 685856.97 | 204056.55 | 96448.59 | 55988.28 | 36524.97 | 25692.84 | 19051.56 | 14688.18 | 11668.68 | 9492.84 | 7873.38 | 6635.52 | 5668.20 | ||||||||||||
481800.46 | 107607.96 | 40460.31 | 19463.31 | 10832.13 | 6641.28 | 4363.38 | 3019.50 | 2175.84 | 1619.46 | 1237.86 | 967.32 | ||||||||||||||
| |||||||||||||||||||||||||
.25 | 632085.76 | 195088.23 | 93503.79 | 54678.69 | 35832.51 | 25283.43 | 18789.75 | 14510.70 | 11542.86 | 9400.41 | 7803.54 | 6581.52 | 5625.54 | ||||||||||||
436997.52 | 101584.44 | 38825.10 | 18846.18 | 10549.08 | 6493.68 | 4279.05 | 2967.84 | 2142.45 | 1596.87 | 1222.02 | 955.98 | ||||||||||||||
| |||||||||||||||||||||||||
.30 | 584398.62 | 186698.34 | 90691.83 | 53414.46 | 35159.67 | 24883.74 | 18533.16 | 14336.37 | 11419.02 | 9309.42 | 7734.60 | 6528.06 | 5583.33 | ||||||||||||
397700.28 | 96006.51 | 37277.37 | 18254.79 | 10275.93 | 6350.58 | 4196.79 | 2917.35 | 2109.60 | 1574.82 | 1206.54 | 944.73 | ||||||||||||||
| |||||||||||||||||||||||||
.35 | 541911.51 | I78838.19 | 88004.79 | 52193.61 | 34505.55 | 24493.32 | 18281.88 | 14165.19 | 11297.25 | 9219.69 | 7666.65 | 6475.32 | 5541.57 | ||||||||||||
363073.32 | 90833.4 | 35811.18 | 17688.06 | 10012.23 | 6211.44 | 4116.69 | 2867.94 | 2077.56 | 1553.04 | 1191.33 | 933.75 | ||||||||||||||
| |||||||||||||||||||||||||
.40 | 503894.88 | 171464.22 | 85435.47 | 51014.16 | 33869.43 | 24112.17 | 18035.64 | 13997.07 | 11177.37 | 9131.22 | 7599.51 | 6423.21 | 5500.26 | ||||||||||||
332430.66 | 86028.75 | 34421.31 | 17144.73 | 9757.26 | 6076.53 | 4038.57 | 2819.70 | 2046.15 | 1531.71 | 1176.30 | 922.95 | ||||||||||||||
| |||||||||||||||||||||||||
.45 | 469742.67 | 164537.10 | 82977.03 | 49874.22 | 33250.86 | 23739.75 | 17794.44 | 13831.92 | 11059.38 | 9044.10 | 7533.27 | 6371.73 | 5459.49 | ||||||||||||
305205.57 | 81560.07 | 33102.81 | 16623.36 | 9511.11 | 5945.31 | 3962.52 | 2772.54 | 2015.28 | 1510.83 | 1161.54 | 912.24 | ||||||||||||||
| |||||||||||||||||||||||||
.50 | 438948.36 | 158021.46 | 80623.17 | 48772.08 | 32649.03 | 23375.97 | 17557.92 | 13669.65 | 10943.28 | 8958.15 | 7467.93 | 6320.88 | 5419.08 | ||||||||||||
280926.90 | 77398.29 | 31851.09 | 16123.05 | 9273.06 | 5818.05 | 3888.27 | 2726.37 | 1985.13 | 1490.22 | 1147.05 | 901.80 | ||||||||||||||
| |||||||||||||||||||||||||
.55 | 411085.89 | 151885.26 | 78368.04 | 47706.03 | 32063.40 | 23020.47 | 17326.17 | 13510.26 | 10828.98 | 8873.46 | 7403.40 | 6270.57 | 5379.21 | ||||||||||||
259200.63 | 73517.22 | 30662.01 | 15642.63 | 9042.93 | 5694.30 | 3815.91 | 2681.28 | 1955.52 | 1470.06 | 1132.83 | 891.36 | ||||||||||||||
| |||||||||||||||||||||||||
.60 | 385794.45 | 146099.7 | 76206.33 | 46674.54 | 31493.43 | 22672.98 | 17098.92 | 13353.66 | 10716.48 | 8789.94 | 7339.77 | 6220.89 | 5339.70 | ||||||||||||
239694.75 | 69893.37 | 29531.79 | 15181.11 | 8820.45 | 5574.06 | 3745.26 | 2637.18 | 1926.54 | 1450.17 | 1118.88 | 881.19 | ||||||||||||||
| |||||||||||||||||||||||||
.65 | 362767.23 | 140638.5 | 74132.73 | 45676.17 | 30938.49 | 22333.32 | 16876.17 | 13199.67 | 10605.78 | 8707.59 | 7276.86 | 6171.84 | 5300.64 | ||||||||||||
222128.73 | 66505.77 | 28456.56 | 14737.68 | 8605.17 | 5457.15 | 3676.50 | 2593.89 | 1898.19 | 1430.73 | 1105.02 | 871.20 | ||||||||||||||
| |||||||||||||||||||||||||
.70 | 341741.88 | 135477.9 | 72142.74 | 44709.57 | 30398.13 | 22001.22 | 16657.65 | 13048.38 | 10496.70 | 8626.41 | 7214.76 | 6123.33 | 5262.03 | ||||||||||||
206263.98 | 63335.16 | 27433.17 | 14311.44 | 8396.91 | 5343.57 | 3609.27 | 2551.68 | 1870.29 | 1411.65 | 1091.43 | 861.30 | ||||||||||||||
| |||||||||||||||||||||||||
.75 | 322492.77 | 130596.21 | 70231.77 | 43773.21 | 29871.72 | 21676.50 | 16443.45 | 12899.7 | 10389.33 | 8546.31 | 7153.56 | 6075.45 | 5223.87 | ||||||||||||
191896.56 | 60364.44 | 26458.56 | 13901.49 | 8195.22 | 5233.05 | 3543.75 | 2510.37 | 1843.02 | 1392.75 | 1078.11 | 851.58 | ||||||||||||||
| |||||||||||||||||||||||||
.80 | 304825.32 | 125973.72 | 68395.68 | 42866.01 | 29358.90 | 21358.89 | 16233.30 | 12753.54 | 10283.58 | 8467.38 | 7093.08 | 6028.02 | 5186.07 | ||||||||||||
178851.60 | 57578.04 | 25529.67 | 13507.11 | 8000.01 | 5125.59 | 3479.76 | 2469.96 | 1816.20 | 1374.3 | 1065.06 | 841.95 | ||||||||||||||
| |||||||||||||||||||||||||
.85 | 288570.96 | 121592.34 | 66630.78 | 41986.8 | 28859.22 | 21048.21 | 16027.20 | 12609.81 | 10179.45 | 8389.53 | 7033.32 | 5981.22 | 5148.72 | ||||||||||||
166978.62 | 54961.56 | 24643.98 | 13127.58 | 7811.01 | 5021.01 | 3417.39 | 2430.36 | 1789.92 | 1356.21 | 1052.10 | 832.5 | ||||||||||||||
| |||||||||||||||||||||||||
.90 | 273582.81 | 117435.69 | 64933.20 | 41134.23 | 28372.14 | 20744.28 | 15824.97 | 12468.51 | 10076.85 | 8312.67 | 6974.37 | 5934.96 | 5111.73 | ||||||||||||
156147.12 | 52502.49 | 23798.97 | 12762.09 | 7627.86 | 4919.31 | 3356.46 | 2391.66 | 1764.18 | 1338.3 | 1039.41 | 823.23 | ||||||||||||||
| |||||||||||||||||||||||||
.95 | 259732.80 | 1134558.56 | 63299.70 | 40307.49 | 27897.30 | 20446.83 | 15626.52 | 12329.64 | 9975.87 | 8236.98 | 6916.05 | 5889.24 | 5075.10 | ||||||||||||
146244.24 | 50188.86 | 22992.21 | 12410.19 | 7450.47 | 4820.31 | 3296.88 | 2353.77 | 1738.89 | 1320.93 | 1026.81 | 814.14 | ||||||||||||||
| |||||||||||||||||||||||||
1.00 | 246908.52 | 109737.09 | 61727.13 | 39505.32 | 27434.25 | 20155.77 | 15431.76 | 12193.02 | 9876.33 | 8162.28 | 6858.54 | 5843.97 | 5038.92 | ||||||||||||
137171.43 | 48009.96 | 22221.81 | 12071.07 | 7278.48 | 4724.01 | 3238.74 | 2316.69 | 1714.05 | 1303.74 | 1014.57 | 805.05 |
Values of 16 · 109737.1 /(m + a)2 and the differences between m and m + 1.
a/m | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | ||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
.00 | 1755793.6 | 438948.5 | 195088.2 | 109737.1 | 70231.7 | 48772.0 | 35832.5 | 27434.2 | 21676.5 | 17557.9 | 14510.7 | 12193.0 | 10389.3 | ||||||||||||
1316845.1 | 243860.3 | 85351.1 | 39505.4 | 21459.7 | 12939.5 | 8398.3 | 5757.7 | 4118.6 | 3047.2 | 2317.7 | 1803.7 | ||||||||||||||
| |||||||||||||||||||||||||
.05 | 1592556.5 | 417797.4 | 188744.3 | 107044.3 | 68847.8 | 47969.3 | 35326.1 | 27094.6 | 21437.6 | 17383.7 | 14379.7 | 12092.0 | 10309.9 | ||||||||||||
1174759.1 | 229053.1 | 81700.0 | 38196.5 | 20878.5 | 12643.2 | 8231.5 | 5657.0 | 4053.9 | 3004.0 | 2287.7 | 1782.1 | ||||||||||||||
| |||||||||||||||||||||||||
.10 | 1451069.1 | 398139.2 | 182704.8 | 104449.3 | 67504.6 | 47186.1 | 34830.2 | 26761.1 | 21202.7 | 17212 | 14250.4 | 11992.3 | 10231.4 | ||||||||||||
1052929.9 | 215434.4 | 78255.5 | 36944.7 | 20318.5 | 12355.9 | 8069.1 | 5558.4 | 3990.7 | 2961.6 | 2258.1 | 1760.9 | ||||||||||||||
| |||||||||||||||||||||||||
.15 | 1327632.6 | 379836.3 | 176950.7 | 101947.7 | 66200.2 | 46421.9 | 34344.8 | 26433.8 | 20971.5 | 17042.9 | 14122.9 | 11893.8 | 10153.6 | ||||||||||||
947796.3 | 202885.6 | 75003.0 | 35747.5 | 19778.3 | 12077.1 | 7911.0 | 5462.3 | 3928.6 | 2920.0 | 2229.1 | 1740.2 | ||||||||||||||
| |||||||||||||||||||||||||
.20 | 1219301.3 | 362767.2 | 171464.2 | 99534.7 | 64933.3 | 45676.2 | 33869.4 | 26112.3 | 20744.3 | 16876.2 | 13997.1 | 11796.5 | 10076.8 | ||||||||||||
1219301.3 | 362767.2 | 171464.2 | 99534.7 | 64933.3 | 45676.2 | 33869.4 | 26112.3 | 20744.3 | 16876.2 | 13997.1 | 11796.5 | ||||||||||||||
| |||||||||||||||||||||||||
.25 | 1123708.0 | 346823.5 | 166229.0 | 97206.6 | 63702.2 | 44948.3 | 33404.0 | 25796.8 | 20520.6 | 16711.8 | 13873.0 | 11700.5 | 10001.0 | ||||||||||||
776884.5 | 180594.5 | 69022.4 | 33504.4 | 18753.9 | 11544.3 | 7607.2 | 5276.2 | 3808.8 | 2838.8 | 2172.5 | 1699.5 | ||||||||||||||
| |||||||||||||||||||||||||
.30 | 1038930.9 | 331908.2 | 161229.9 | 94959.0 | 62506.1 | 44237.8 | 32947.8 | 25486.9 | 20300.5 | 16550.1 | 13750.4 | 11605.4 | 9925.9 | ||||||||||||
707022.7 | 170678.3 | 66270.9 | 32452.9 | 18268.3 | 11290.0 | 7460.9 | 5186.4 | 3750.4 | 2799.7 | 2145.0 | 1679.5 | ||||||||||||||
| |||||||||||||||||||||||||
.35 | 963398.2 | 317934.6 | 156453.0 | 92788.6 | 61343.2 | 43543.7 | 32501.1 | 25182.6 | 20084.0 | 16390.6 | 13629.6 | 11511.7 | 9851.7 | ||||||||||||
645463.6 | 161481.6 | 63664.4 | 31445.4 | 17799.5 | 11042.6 | 7318.5 | 5098.6 | 3693.4 | 2761.0 | 2117.9 | 1660.0 | ||||||||||||||
| |||||||||||||||||||||||||
.40 | 895813.1 | 304825.3 | 151885.3 | 90691.8 | 60212.5 | 42866.1 | 32063.4 | 24883.7 | 19870.9 | 16233.3 | 13510.2 | 11419.0 | 9778.2 | ||||||||||||
590987.8 | 152940.0 | 61193.5 | 30479.3 | 17346.4 | 10802.7 | 7179.7 | 5012.8 | 3637.6 | 2723.1 | 2091.2 | 1640.8 | ||||||||||||||
| |||||||||||||||||||||||||
.45 | 835098.1 | 292510.4 | 147514.7 | 88665.3 | 59112.6 | 42204.0 | 31634.6 | 24590.1 | 19661.1 | 16078.4 | 13392.5 | 11327.5 | 9705.8 | ||||||||||||
542587.7 | 144995.7 | 58849.4 | 29552.7 | 16908.6 | 10569.4 | 7044.5 | 4929.0 | 3582.7 | 2685.9 | 2065.0 | 1621.7 | ||||||||||||||
| |||||||||||||||||||||||||
.50 | 780352.6 | 280927.0 | 143330.1 | 86705.9 | 58042.7 | 41557.3 | 31214,1 | 24301.6 | 19454.7 | 15925.6 | 13276.3 | 11237.1 | 9633.9 | ||||||||||||
499425.6 | 137596.9 | 56624.2 | 28663.2 | 16485.4 | 10343.2 | 6912.5 | 4846.9 | 3529.1 | 2649.3 | 2039.2 | 1603.2 | ||||||||||||||
| |||||||||||||||||||||||||
.55 | 730819.4 | 270018.2 | 139321.0 | 84810.7 | 57001.6 | 40925.3 | 30802.1 | 24018.2 | 19251.5 | 15775.0 | 13161.6 | 11147.7 | 9563.0 | ||||||||||||
460801.2 | 130697.2 | 54510.3 | 27809.1 | 16076.3 | 10123.2 | 6783.9 | 4766.7 | 3476.5 | 2613.4 | 2013.9 | 1584.7 | ||||||||||||||
| |||||||||||||||||||||||||
.60 | 685856.8 | 259732.8 | 135477.9 | 82977.0 | 55988.3 | 40307.5 | 30398.1 | 23739.8 | 19051.5 | 15626.6 | 13048.5 | 11059.4 | 9492.8 | ||||||||||||
426124.0 | 124254.9 | 52500.9 | 26988.7 | 15680.8 | 9909.4 | 6658.3 | 4688.3 | 3424.9 | 2578.1 | 1989.1 | 1566.6 | ||||||||||||||
| |||||||||||||||||||||||||
.65 | 644919.5 | 250024 | 131791.5 | 81202.1 | 55001.8 | 39703.7 | 30002.1 | 23466.1 | 18854.7 | 15480.2 | 12936.6 | 10972.2 | 9423.4 | ||||||||||||
394895.5 | 118232.5 | 50589.4 | 26200.3 | 15298.1 | 9701.6 | 6536.0 | 4611.4 | 3374.5 | 2543.6 | 1964.4 | 1548.8 | ||||||||||||||
| |||||||||||||||||||||||||
.70 | 607541.1 | 240849.6 | 128253.8 | 79483.7 | 54041.1 | 39113.3 | 29613.6 | 23197.1 | 18660.8 | 15335.8 | 12826.2 | 10885.9 | 9354.7 | ||||||||||||
366691.5 | 112595.8 | 48770.1 | 25442.6 | 14927.8 | 9499.7 | 6416.5 | 4536.3 | 3325.0 | 2509.6 | 1940.3 | 1531.2 | ||||||||||||||
| |||||||||||||||||||||||||
.75 | 573320.5 | 232171.0 | 124856.5 | 77819.0 | 53105.3 | 38536.0 | 29232.8 | 22932.8 | 18469.9 | 15193.4 | 12717.4 | 10800.8 | 9286.9 | ||||||||||||
341149.5 | 107314.5 | 47037.5 | 24713.7 | 14569.3 | 9303.2 | 6300.0 | 4462.9 | 3276.5 | 2476.0 | 1916.6 | 1513.9 | ||||||||||||||
| |||||||||||||||||||||||||
.80 | 541911.7 | 223953.3 | 121592.3 | 76206.2 | 52193.6 | 37971.4 | 28859.2 | 22673.0 | 18281.9 | 15053.1 | 12609.9 | 10716.5 | 9219.7 | ||||||||||||
317958.4 | 102361.0 | 45386.1 | 24012.6 | 14222.2 | 9112.2 | 6186.2 | 4391.1 | 3228.8 | 2443.2 | 1893.4 | 1496.8 | ||||||||||||||
| |||||||||||||||||||||||||
.85 | 513015.0 | 216164.2 | 118454.7 | 74643.2 | 51305.3 | 37419.0 | 28492.8 | 22417.4 | 18096.8 | 14914.7 | 12503.7 | 10633.3 | 9153.3 | ||||||||||||
296850.8 | 97709.5 | 43811.5 | 23337.9 | 13886.3 | 8926.2 | 6075.4 | 4320.6 | 3182.1 | 2411.0 | 1870.4 | 1480.0 | ||||||||||||||
| |||||||||||||||||||||||||
.90 | 486369.4 | 208774.6 | 115436.8 | 73127.5 | 50439.4 | 36878.7 | 28133.3 | 22166.2 | 17914.4 | 14778.1 | 12398.9 | 10551.0 | 9087.5 | ||||||||||||
277594.8 | 93337.8 | 42309.3 | 22688.1 | 13560.7 | 8745.4 | 5967.1 | 4251.7 | 3136.3 | 2379.2 | 1847.9 | 1463.5 | ||||||||||||||
| |||||||||||||||||||||||||
.95 | 461747.2 | 201757.4 | 112532.8 | 71657.8 | 49595.2 | 36349.9 | 27780.5 | 21919.4 | 17734.9 | 14643.5 | 12295.2 | 10469.8 | 9022.4 | ||||||||||||
259989.8 | 89224.6 | 40875.0 | 22062.6 | 13245.3 | 8569.4 | 5861.1 | 4184.5 | 3091.4 | 2348.3 | 1825.4 | 1447.4 | ||||||||||||||
| |||||||||||||||||||||||||
1.00 | 438948.5 | 195088.2 | 109737.1 | 70231.7 | 48772.0 | 35832.5 | 27434.2 | 21676.5 | 17557.9 | 14510.7 | 12193.0 | 10389.3 | 8958.1 | ||||||||||||
243860.3 | 85351.1 | 39505.4 | 21459.7 | 12939.5 | 8398.3 | 5757.7 | 4118.6 | 3047.2 | 2317.7 | 1803.7 | 1431.2 |
λair | 7065.200 | 4713.143 | 4120.817 | 3867.477 | 3732.861 | 3651.981 | 3599.304 | 3562.95 | 3536.82 | 3517.327 | 3502.381 | ||||||||||||
Observed | ν | 14149.98 | 21211.34 | 24260.20 | 25849.33 | 26781.50 | 27374.61 | 27775.24 | 28058.63 | 28265.92 | 28422.56 | 28543.85 | |||||||||||
Δ | 7061.36 | 3048.86 | 1589.13 | 932.17 | 593.11 | 400.63 | 283.39 | 207.29 | 156.64 | 121.29 | |||||||||||||
Δ | 7037.24 | 3048.13 | 1590.17 | 932.98 | 593.73 | 401.03 | 283.52 | 207.81 | 156.85 | 121.27 | |||||||||||||
Table a = 0.70 | (m,a) | −15053.10 | 8015.86 | 4967.73 | 3377.56 | 2444.58 | 1850.85 | 1449.82 | 1166.30 | 958.49 | 801.64 | 680.37 | |||||||||||
m | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | ||||||||||||
2P calc | 29203.08 | 29227.2 | 29227.93 | 29226.89 | 29226.08 | 29225.46 | 29225.06 | 29224.93 | 29224.41 | 29224.2 | 29224.22 |
m (table) | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
---|---|---|---|---|---|---|---|---|---|---|---|
(m,a) | 15073.89 | 8012.53 | 4963.67 | 3374.54 | 2442.37 | 1849.26 | 1448.63 | 1165.24 | 957.95 | 801.31 | 680.02 |
*m | 2.697954 | 3.700517 | 4.701601 | 5.70217 | 6.70257 | 7.70279 | 8.70299 | 0.70375 | 10.7023 | 11.7017 | 12.7024 |
λair | 3838.29 | 3096.91 | 2851.65 | 2736.53 | 2672.43 | 2632.88 | 2606.64 | 2588.28 | 2574.93 | 2564.91 | 2557.20 | 2551.13 | |||||||||||||
Observed | ν | 26045.9 | 32280.9 | 35057.1 | 36531.8 | 37408.1 | 37970.0 | 38352.1 | 38624 2 | 38824.4 | 38976.0 | 39093.5 | 39186.5 | ||||||||||||
Δ | 6235.0 | 2776.2 | 1474.7 | 876.3 | 561.9 | 382.1 | 272.1 | 200.2 | 151.6 | 117.5 | 93.0 | ||||||||||||||
Δ | 6252.20 | 2787.42 | 1470.71 | 878.39 | 563.70 | 383.17 | 272.24 | 200.34 | 151.70 | 117.62 | 93.03 | ||||||||||||||
Table a = 0.825 | (m,a) | 13753.67 | 7501.47 | 4714.05 | 3234.34 | 2355.95 | 1792.25 | 1409.08 | 1136.84 | 936.50 | 784.80 | 667.18 | 574.15 | ||||||||||||
2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | ||||||||||||||
| |||||||||||||||||||||||||
23P2 | 39799.57 | 39782.37 | 39771.15 | 39766.14 | 39764.05 | 39762.25 | 39761.18 | 39761.04 | 39760.9 | 39760.8 | 39760.7 | 39760.65 | |||||||||||||
39760.5 may be taken as an asymptotic value of 23P2 for large values of m. From this value there follows for (m, D): | |||||||||||||||||||||||||
m = (m,D) | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | |||||||||||||
13714.6 | 7479.6 | 4703.4 | 3228.7 | 2352.4 | 1790.5 | 1408.4 | 1136.3 | 936.1 | 784.5 | 667.0 | 574.0 |