334 



THE CIVIL ENGINEER AND ARCHITECTS JOURNAL. 



[Nov. 



The elements for calculating the corrections to cubic quantity which have 

 been previously employed, require that the corrections to widths, due to 

 the inclination of the ground surface, should be determined ; that is, that 

 the values of a-, x , z, and :', should be known j and this process may 

 appear to involve as much trouble when preparing a preliminary estimate 

 for ordinary parliamentary purposes, as when the position of the line is 

 absolutely final; and when the more careful and accurate calculations are 

 undertaken. They would appear, in fact, to require that the field-work 

 should embrace every level and measurement necessary for setting out the 

 earthwork on the gidnnd. It is desirable, therefore, to present a form of 

 calculation which should dispense with so much detail, and which should 

 at the same time enable us to make an estimate that cannot be attacked 

 before a committee of tlie House of Commons for insufficiency, on the 

 score of a neglect to take into account the addition to be made to (juantities 

 derived from the central heiglits, on the supposition that the ground in 

 cross section does not diller materially from a horizontal plane ; an addi- 

 tion which is due to the fact that this supposition cannot be maintained in 

 a mountainous or rough country, such as occurred on the various lines 

 projected through Wales in the session of 1845-0. 



Under such circumstances, after the usual deposit of the plans and sec- 

 tions have been made, in accordance with the standing orders, it should be 

 included amongst the various additional particulars sought by the engineer 

 preparatory to his estimate, to obtain a number of cross sections, over the 

 length of each projected cutting or embankment, sufficient for determining 

 the increase in earthwork which may arise from a material inclination of 

 the ground to the horizon. And, noir, the first formula (A) is, on the 

 whole, the most concise in application. Such cross sections can do no 

 more than exhibit the roie at which the ground inclines; in other words, 

 to what extent it falls or rises in any given horizontal distance, as of 100 

 feet, or 1000 feel, &c. 



Table for Corrections to Widths of Railways, Sfc, due to Sidelong Ground. 

 i 2 3 4 5 G 7 8 9" 



lOOUO -5000 -3333 -2500 -2000 -1667 -1429 -1250 -1111 



10 -1000 •i'gOOl 8333 7G92 7143 6667 6250 5882 5556 5263 



20 -05000 4762 4545 4348 4167 4000 3846 3704 3571 3448 



30 -^3333 3226 3125 3030 2941 2857 277S 2703 2632 2564 



40 2500 2439 2381 2320 2273 2222 2174 2128 2083 2041 



50 2000 1961 1923 1887 1852 1818 1786 1754 1724 1695 



60 -^1667 1639 1613 1587 1563 1538 1515 1493 1471 1449 



70 1429 1408 1389 1370 1351 1333 1316 1299 1282 1266 



80 12a0 1235 1220 1205 1190 1176 1163 1149 1136 1124 



90 1111 1099 1087 1075 1064 1053 1042 1031 1020 1010 



100 -^1000 • 

 10 -2^19091 

 20 8333 



30 .^7692 

 40 7143 

 50 6667 



60 -5^6250 

 70 5882 

 80 5556 

 90 5263 



i!i9901 

 9009 

 8264 



7634 

 7092 

 6623 



6211 

 5848 

 5525 

 5236 



9804 

 8929 

 8197 



7576 

 7042 

 6579 



6173 

 5814 

 5495 

 5203 



9709 

 8850 

 8130 



7519 

 6993 

 6536 



6135 

 5780 

 5464 

 5181 



9615 



8772 

 8065 



7463 

 6944 

 6494 



6098 

 5747 

 5435 

 5155 



9.-)24 

 8696 

 8000 



7407 

 6897 

 C452 



6061 

 5714 

 5405 

 5128 



9434 



8621 

 7937 



7353 

 6849 

 6410 



6024 

 5682 

 5376 

 5102 



9346 

 8547 

 7874 



7299 

 6803 

 6369 



5988 

 5650 

 5348 

 5076 



9259 

 84 75 

 7813 



7246 

 6757 

 6329 



5952 

 5618 

 5319 

 5051 



9174 

 8403 



7752 



7194 

 6711 



6289 



5917 



5587 

 5291 

 5025 



200 •'i^SOOO 

 10 4762 

 20 4545 



30 -^4348 

 40 4167 

 50 4000 



60 •'1^3846 

 70 3704 

 80 3571 

 90 3448 



4975 

 4739 

 4525 



4329 

 4149 

 3984 



3831 

 3690 

 3559 

 3136 



4950 

 4717 

 4505 



4310 

 4132 

 3968 



3817 

 3676 

 3546 

 3425 



4926 

 4095 

 4484 



4292 

 4115 

 3953 



3802 

 3603 

 3534 

 3413 



4902 

 4673 

 4464 



4274 

 4098 

 3937 



3788 

 3650 

 3521 

 3401 



48 78 

 4051 

 4444 



4255 

 4082 

 3922 



3774 

 3636 

 3509 

 3390 



4854 

 4630 

 4425 



4237 

 4065 

 3906 



3759 

 3623 

 3497 

 3378 



4831 

 4608 

 4405 



4219 

 4049 

 3891 



3745 

 3610 

 3484 

 3367 



300 -^3333 

 10 3226 

 20 3125 



30 -^3030 

 40 2941 

 50 -^2857 



60 -^2778 

 70 2703 

 80 2632 

 90 2564 



3322 

 3215 

 3115 



3021 

 2933 

 2849 



2770 

 2695 

 2625 

 2558 



3311 

 3205 

 3106 



3012 

 2924 

 2841 



2762 

 2688 

 2619 

 2551 



3300 

 3195 

 3096 



3003 

 2915 

 2833 



27,55 

 2681 

 2611 

 2545 



3289 

 3185 



3086 



2994 

 2907 

 2825 



2747 

 2674 

 2604 

 2538 



3279 

 3175 

 3077 



2985 

 2899 

 2817 



2740 



2067 

 2597 

 2532 



3268 

 3165 

 3067 



2976 

 2890 

 2809 



2732 

 2660 

 2591 

 2525 



3257 

 3155 

 3058 



2967 

 2882 

 2801 



2725 

 2653 

 2584 

 2519 



4808 

 4587 

 4386 



4202 

 4032 

 3876 



3731 

 3597 

 3472 

 3356 



3247 

 3145 

 3049 



2959 

 2874 

 2793 



2717 

 2646 

 2577 

 2513 



4785 

 4566 

 4367 



4184 



4016 

 3861 



3717 

 3584 

 3400 

 3341 



3236 

 3135 

 3040 



2955 

 2866 

 2780 



2710 

 2639 

 2571 

 2501) 



Table for Corrections to Widths of Railways, ifc. — (Continued.) 







6 



8 



400 •'^2500 2494 2488 2481 2475 2469 2463 2457 2451 2445 



10 2439 2433 2427 2421 2115 2410 2404 2.398 2392 2387 



20 2381 2375 2370 2304 2358 2353 2347 2342 2336 2331 



30 '^2326 2320 2315 2309 2304 2299 2294 22i-8 2283 2278 



40 2273 2268 2262 2257 2252 2247 2242 2237 2232 2227 



50 2222 2217 2212 2208 2203 2198 2193 2188 2183 2179 



60 -^2174 2169 2165 2160 2155 2151 2140 2141 2137 2132 



70 2128 2123 2119 2114 2110 2105 2101 2096 2092 2088 



80 2083 2079 2075 2070 2066 2062 2058 2053 2049 2045 



90 2041 2037 2033 2028 2024 2020 2016 2012 2008 2004 



500 -^2000 1996 1992 1988 1984 1980 1976 1972 1969 1965 



10 1961 1957 1953 1949 1946 1942 1938 1934 1931 1927 



20 1923 1919 1916 1912 1908 1905 1901 1898 1894 1890 



30 -^1887 1883 1880 1876 1873 1869 1866 1862 1859 18.5S 



40 1852 1848 1845 1842 1838 1835 1832 1828 1825 1821 



50 1818 1815 1812 1808 1805 1802 1799 1795 1792 1789 



60 -^1786 1783 1779 1776 1773 1770 1767 1764 1761 17S7 



70 1754 1751 1748 1745 1742 1739 1736 1733 1730 1727 



80 1724 1721 1718 1715 1712 1709 1706 1704 1701 1698 



90 1695 1692 1689 1686 1684 1681 1678 1675 1672 1669 



600 -^^^1667 1664 1661 1658 1656 1653 1650 1647 16|5 1642 



10 1639 1637 1634 1631 1629 1626 1C23 1621 1618 1616 



20 1613 1610 1608 1605 1603 1600 1597 1595 1592 1590 



30 -^^1587 1585 1582 1580 1577 1515 1572 1570 1567 1565 



40 1563 1560 1558 1555 1553 1550 1548 1516 1543 1541 



50 1538 1536 1534 1531 1529 1527 1524 1522 1520 9517 



60 -^1515 1513 1511 1508 1506 1504 1502 1499 1497 1495 



70 1493 1490 1488 1486 1484 1481 1479 1477 1475 1473 



80 1471 1468 1466 1464 1462 1460 1458 1456 1453 1451 



90 1449 1447 1445 1443 1441 1439 1437 1435 1433 1431 



700 -^1429 

 10 1408 

 20 1389 



30 -^1^11370 

 40 1351 

 50 1333 



30 ••'^1205 

 40 1190 

 50 1176 



60 -^1163 

 70 1149 

 80 1136 

 90 1124 



1427 1425 1422 1420 1418 1416 1414 1412 1410 



1406 1404 1403 1401 1399 1397 1395 1393 1391 



1387 1385 1383 1381 1379 1377 1376 1374 1372 



1368 1366 1364 1362 1361 1359 1357 1355 1353 



1350 1348 1346 1344 1342 1340 1339 1337 1335 



1332 1330 1328 1326 1325 1323 1321 1319 1318 



1314 1312 1311 1309 1307 1305 1304 1302 1300 



1297 1295 1294 1292 1290 12S9 1287 1285 1284 



1280 1279 1277 1276 1274 1272 1271 1269 1267 



1264 1263 1261 1259 1258 1256 1255 1253 1252 



1248 1247 1245 1244 1242 1241 1239 1238 1236 



1233 1232 1230 1229 1227 1225 1224 1222 1221 



1218 1217 1215 1214 1212 1211 1209 1208 1206 



1203 1202 1200 1199 1198 1196 1195 1193 1192 



1189 1188 1186 1185 1183 1182 llSl 1179 1178 



1175 1174 1172 1171 1170 1168 1167 1166 1164 



1161 1160 1159 1157 1156 1155 1153 1152 1151 



1148 1147 1145 1144 1143 1142 1140 1139 1138 



1135 1134 1133 1131 1130 1129 1127 1126 1125 



1122 1121 1120 1119 1117 1116 1115 1114 1112 



900-^1111 1110 1109 1107 1106 1105 1104 1103 1101 1100 



10 1099 1098 1096 1095 1094 1093 1092 1091 1089 1088 



20 1087 1086 1085 1083 1082 1081 1080 1079 1078 1076 



30 -^1075 1074 1073 1072 1071 1070 1068 1067 1066 1065 



40 1064 1063 1062 1060 1059 1058 1057 1056 1055 1054 



50 1053 1052 1050 1049 1048 1047 1046 1045 1044 1043 



60 '2^1042 1041 1040 1038 1037 1036 1035 1034 1033 1032 



70 1031 1030 1029 1028 1027 1020 1025 1024 1022 1021 



80 1020 1019 1018 1017 1016 1015 1014 1013 1012 loil 



90 1010 1009 1003 IqO? 1006 1005 1004 1003 1002 lOOl 



1000 -iii^l 000^^^9990 9980 9970 9960 9950 9940 9930 9921- 99H 



lOnjiiiggoo 9891 9881 9872 9862 9852 9843 9833 9823 9814 



20 9804 9794 9785 9775 9766 9756 9747 9737 9728 9718 



30 9709 9699 9690 9681 9671 9662 9653 9643 9634 9625 



40 9615 9606 9597 9588 9579 9669 9560 9551 9542 9533 



50^2^9324 9515 9506 9197 9483 9479 9470 9461 9452 9443 



