Verse 1 Versed Area of Area of Versed Area of Versed Area of Versed Aren of Segment. Sine. Segment. Sine. Segment. Sine. Segment. 216 20908 265 25201314 29192 363 32793 412 35882 217 20998 266 25285 315 29270 364 32862 413 35939 218 21088 267 25370 316 29347 365 32931 414 35995 219 21178 268 25454 317 29425 366 32999 415 36051 220 21268 269 25539 31829502 367 33067 416 36107 221 21357 270 25623 319 29579 368 33135 417 36162 222 21447 271 25707 320 29656 369 33202 418 36217 223 21536 272 25791 321 29733 370 33270419 36272 224 21626273 25875 322 29809 371 33337 420 36326 225 21715 274 25959 323 29886 226 21805 275 26042 324 29962 227 21894 276 26126 325 30038 228 21983 277 26209 326 30114 372 33404 421 36380 373 33470 422 36434 374 374 33537 423 36487 375 33603 424 36541 2 26624 331 30491 380 33931 429 36801 233 22426 282 234 22515 283 26706 332 30566 381 33996 430 36853 235 22603 28 284 26788 333 30641 382 34060 431 36904 236 22691 285 26871 334 30715 383 34125 432 36954 237 22780 286 26953 335 30789 384 34189 433 37004 238 22868 287 27035 336 30864 385 34253 434 37054 239-22955 288 27117 337 30937 386 34317 435 37104 240 23043 289 27198 338 31011 387 34380 436 37153 241 -23131 290 27280 339 31085 388 34443 437 37201 242 -23218 291 27361 340 31158 389 34506 438 3725 .243 -23306 292 27442 341 31231 390 34569 439 37298 244 4 -23393 293 27523 342 31305 391 34631 440 37346 245 23480 294 27604 343 31377 392 34694 441 37393 246 2356 568 295 -27685 344 31450 393 34756 442 37440 247 2365 655296 27766 345 31523 394 34817 443 37486 248 23741 1 297 -27846 346 31595 395 34879 444 37533 347 31667 396 34940 445 37578 348 31739 397 35001 446 37624 349 31811 398 35061447 37669 350 31882 399 35122 448 37713 351 31953 400 35182 449 37758 250 23915 299 28007 249 23828 298-27927 300-28087 301-28167 25124001 252 24088 253 24174 302-28247 254 24260 303 28326 352 32024 401 35242 450 37801 255 24346 304 28406 353 32095 402 35301 451 37845 256 24432 305 28485 354 32166 403 35361 452 37888 257 24518 306 28564 355 32237 404 35420 453 37930 258 24604 307 28643 356 32307 405 35479 454 37972 259 24690 308 28722-357 32377 406 35537455 38014 260 24775 309-28801 358 32447 407 35595 456 38055 26124860 310 28879 359 32517 408 35653 457 38096 |262 24946 311 28958 360 32586 409 35711 458 38136 263 25021 312 29036 361 32655 410 35768 459 38176 264.25116313 29114362-32725411 35825460 38216 Versed Area of Versed Sine. Segment. Area of Versed Area of Versed Area of Segment. Sine. Segment. 461 38255 469 38549 477 38808 462 38293 470 38583 478 38837 463 38331 471 38617 479 38866 464 38369 472 38650 480 38895 Versed Area of 49339120 487 39073 495 39222 48839095 496 39236 Rule 1.-When the zone is less than a semicircle, divide the height by the longest chord, and seek the quotient in the column of versed sines. Take out the corresponding area, in the next column on the right hand, and multiply it by the square of the longest chord; the product will be the area of the zone. Example. Required the area of a zone, whose longest chord is 50, and height 15. 15-50300; and 300, as per table, =28087. Hence, 28087×502=702·19, the area of the zone. Rule 2.-When the zone is greater than a semicircle, take the height on each side of the diameter of the circle, and find, by Rule 1, their respective areas; the areas of these two portions, added together, will be the area of the zone. Example. Required the area of a zone, the diameter of the circle being 50, and the height of the zone on each side of the line which passes through the diameter of the circle 20 and 15, respectively. 20+50=400; 400, as per table, = 35182; and 35182 × 502= 879.56. 15+50=300; 300, as per table, =28087; and 28087×502= 702-19. Hence, 879-56+702-19=1581-75. TABLE Of the Proportions of the Lengths of Circular Arcs. 131 1-0452 175 1.0798 219 1 1233 132 1.0458 176 10807 220 1 1245 133 1.0465 177 10816 221 1-1256 134 1.0472 178 1.0825 222 1-1266 135 1.0479 179 1.0834 223 1-1277 136 1.0486 180 1.0843 224 1-1289 137 1.0493 181 1.0852 225 1-1300 138 1.0500 182 1.0861 226 1-1311 139 1.0508 183 1.0870 227 1 1322 140 1.0515 184 1.0880 228 1-1333 141 1.0522 185 1.0889 229 1.1344 142 1.0529 186 1.0898 230 1 1356 143 1.0537 187 1.0908231 11367 260 1-1715 304 1-2306 261 1-1728 305 1-2321 262 1-1740 263 306 1-2335 1-17 753 307 1.2349 264 1-176 766 308 1-2364 265 1-1778 *309 1-2378 266 1.1791 310 1-2393 267 1.1804 4 311 1·2407 268 1.1816 312 1-2422 269 1.1829 313 1-2436 270 1.1843 314 1-2451 271 1-1856 315 1.2 1-2465 272 1.1869 316 1-2480 273 1-1882 3 317 1-2495 274 1.1897 318 1-2510 275 1.1908 319 1-2524 353 1-3047 390 13660 426 1.4295 462 1-4965 498 1-5668 354 1-3063 391 13677 427 1-4313 463 1-4984 499 1-5688 3551-3079 392 1.3694428 1-4331 464 1-5003 500 1-5708 355 1-3095 To find the Length of an Arc of a Circle by the foregoing Table. Rule. Divide the height by the base, and the quotient will be the height of an arc, of which the base is unity. Seek in the table for a number corresponding to the quotient, and take the length of that height from the next right-hand column. Multiply the number, thus found, by the base of the arc, and the product will be the length of the arc or curve required. Example. The profiles of the intradoses of the arches of a bridge semi-ellipse; ; the span of the middle arch is 150 feet, and are each a the height 38 feet: required the length of the curve. 38-150=253, and 253, as per table=1.1628. Hence, 1-1628×150=174-4200, the length required. Height Length Height Length Height of Arc. of Arc. of Arc. of Arc. 100 1.0416 265 1-2306 101 1.0426 270 1-2371 TABLE Of the Proportions of the Lengths of Semi-elliptic Arcs Height Length Height Length 455 1.5008 640 1.7931 825 Length of Arc. 2-0971 2.1060 102 1.0436 275 1-2436 460 1-5084 645 1.8013830 103 1.0446 280 1-2501 465 1.5161650 1.8094 835 104 1.0456 285 1-2567 470 1.5238 655 1.8176 840 105 1.0466 290 1.2634 475 1.5316 660 1.8258 845 110 10516 295 1.2700 480 1.5394665 1.8340 850 115 1.0567 300 1.2767 485 1.5472 670 1-8423 855 120 1.0618 305 1.2834 490 1.5550 675 1.8505 860 125 1.0669 310 1.2901 495 1.5629 680 1.8587 865 2-1148 2-1237 2-1326 2-1416 2-1505 2-1595 2-1685 3 1775 130 1.0720 315 1.2960 500 1.5709 685 1.8670 870 2.1866 350 1.3454 535 1 6253 880 885 890 135 1.0773 320 1.3038 505 1.5785 690 1.8753 875 895 2 1956 2-2047 2 2139 2-2230 2 2322 200 1-1501 385 1.3961 570 1.6804 755 1:9845 205 1-1560 390 1.4034 575 1.6883 760 19931 210 1-1620 395 1.4107 580 1.6963 765 20016 250 1-2114 435 1.4702 620 1.7606 8052-0708 990 255 1-2177 440 1 4778 625 1-7687 810 20795 2601-2241-4451-4854-6301-7768 || 815|2-0883 1000 24231 24093 995 24194 |