The stroboscopic velocity equation is v8 = (A - n/m’B)Do , where n/m is a fraction at lowest terms. Since there are as many stroboscopic velocity curves as there are different values of n/m this fraction may be referred to as the  stroboscopic parameter

Dodd, L. E.

English

University of Northern Iowa

Proceedings of the Iowa Academy of Science Volume 27 Annual Issue Article 35 1920 A Table of the Total Number of Stroboscopic Velocity Curves for Any of the Natural Numbers from 1 to 500 Inclusive Taken as a Limiting Value of n and m L. E. Dodd Bureau of Standards Copyright ©1920 Iowa Academy of Science, Inc. Follow this and additional works at: https://scholarworks.uni.edu/pias Recommended Citation Dodd, L. E. (1920) "A Table of the Total Number of Stroboscopic Velocity Curves for Any of the Natural Numbers from 1 to 500 Inclusive Taken as a Limiting Value of n and m," Proceedings of the Iowa Academy of Science, 27(1), 219-222. Available at: https://scholarworks.uni.edu/pias/vol27/iss1/35 This Research is brought to you for free and open access by the Iowa Academy of Science at UNI ScholarWorks. It has been accepted for inclusion in Proceedings of the Iowa Academy of Science by an authorized editor of UNI ScholarWorks. For more information, please contact scholarworks@uni.edu. A TABLE OF THE TOT AL NUMBER OF STROBOSCOP-IC VELOCITY CURVES FOR ANY OF THE :'-JAT-URAL NUMBERS FROM 1 TO 500 INCLUSIVE TAKEN AS A LIMITI:'-JG VALUE OF n AND m L. E. DODD The stroboscopic velocity equation 1 is v8 = (A - n/m"B)D0 , where n/m is a fraction at lowest terms. Since there are as many stroboscopic velocity curves as there are different values of 11/111 this fraction may be referred to as the "stroboscopic parameter." A question of importance in the study of stroboscopy is, what is the total number of stroboscopic velocity curves for all possible values of the stroboscopic parameter up to and including a given limit determined by the condition, n not greater than m not greater than p, where p is the limiting natural number. This total number, Q, of the stroboscopic velocity curves for each of the values of p from l to 500 inclusive has been calculated, and the Q values are given in the appended table. TABLE p I Q i> I Q __ P I Q 1 1 61 I 2323 121 I 8991 2 3 62 2383 122 9111 3 7 63 I 2455 123 9271 4 11 64 2519 124 9391 5 19 65 2615 125 9591 6 23 66 2655 126 9663 7 35 67 2787 127 9915 8 43 68 2851 128 10043 9 55 69 I 2939 129 10211 10 63 70 2987 130 10307 11 83 71 I 3127 Bl 10567 12 91 72 3175 132 10647 13 115 73 3319 133 10863 14 127 74 I 3391 134 10995 15 143 75 I 3471 135 11139 16 159 76 I 3543 136 I 11267 17 191 77 3663 137 11539 18 I 203 78 3711 138 11627 1 See Proceedings Iowa Academy of Science, vol. 24, 1917, p. 221. 1Dodd: A Table of the Total Number of Stroboscopic Velocity Curves for APublished by UNI ScholarWorks, 1920220 IOWA ACADEMY OF SCIENCE VoL. XXVII, 1920 TABLE - Continued p I Q p I Q p I Q 19 239 79 I 3867 139 I mm 20 255 80 3931 140 I 11999 21 279 81 4039 141 I 12183 22 299 82 4119 i42 I 12323 23 343 83 4283 143 12563 24 359 84 4331 144 12659 25 399 85 4459 145 12883 26 423 86 4543 146 13027 27 459 87 4655 147 13195 28 483 88 4735 148 13339 29 539 89 4911 149 13635 30 555 90 4959 !50 13715 31 615 91 5103 151 14015 32 647 92 5191 152 14159 33 687 93 5311 153 14351 34 719 94 5403 154 14471 35 767 95 5547 155 14711 36 791 % I 5611 156 14807 37 863 97 5803 157 15119 38 899 98 5887 l.'8 15275 39 947 99 6007 159 15483 40 979 100 6087 160 15611 41 1059 101 6287 161 15875 42 1083 102 6351 162 15983 43 1167 103 6555 163 16307 44 1207 104 6651 164 16467 45 1255 105 6747 165 16627 46 1299 106 6851 166 16791 47 1391 107 7063 167 17123 48 1423 J08 . 7135 168 17219 49 1507 109 7351 169 17531 50 1547 110 7431 170 17659 51 1611 111 7575 171 17875 52 1659 il2 7671 172 18043 53 1763 113 7895 173 18387 54 1799 114 7%7 174 18499 55 1879 115 8143 175 18739 56 1927 116 8255 176 18899 57 II 1999 117 8399 177 I 19131 58 2055 118 8515 178 19307 59 2171 119 I 8707 179 19663 60 I 2203 i20 8771 180 I 19759 181 20119 241 35567 301 I 55299 182 I 20263 242 35787 302 55599 183 20503 243 36111 303 I 55999 184 20679 244 36351 304 56287 185 20967 245 I 36687 305 I 56767 186 21087 246 I 36847 306 I 56959 187 21407 247 I 37279 307 I 57571 188 21591 248 I 37519 308 I 57811 189 I 21807 249 37847 309 I 58219 l CXl 21951 250 I 38047 310 I 58459 191 22331 251 I 38547 311 I 59079 192 22459 252 I 38691 312 I 59271 193 22843 253 I 39131 313 I 59895 194 23035 254 39383 314 I 60207 195 I 23227 255 39639 315 60495 196 23395 256 39895 316 I 60807 197 23787 257 40407 317 I 61439 2Proceedings of the Iowa Academy of Science, Vol. 27 [1920], No. 1, Art. 35https://scholarworks.uni.edu/pias/vol27/iss1/35STROBOSCOPIC VELOCITY CURVES 221 TABLE-Continued p Q p Q p Q 198 23907 258 40575- 318 61647 199 24303 259 41007 319 62207 200 24463 260 41199 320 62463 201 24727 .261 41535 321 62887 202 24927 262 41795 322 63151 203 25263 263 42319 323 63727 204 25391 264 42479 324 63943 205 25711 265 42895 325 64423 206 25915 266 43112 326 64747 207 26179 267 43463 327 65179 208 26371 268 43727 328 65499 209 26731 269 44263 329 66051 210 26827 270 44407 330 66211 211 27247 271 44947 331 66871 212 27455 272 45203 332 67199 213 20503 273 45491 333 67631 214 27947 274 45763 334 67963 215 28283 275 46163 335 68491 216 28427 276 46339 336 68683 217 28787 277 46891 337 69355 218 29003 278 47168 338 69667 219 29291 279 47527 339 70115 220 29451 280 47719 340 70371 221 29835 281 48279 341 70071 222 29979 282 48463 342 71187 223 30423 283 4<X>27 343 71775 224 30615 284 49307 344 72111 225 30855 285 49595 345 72463 226 31079 286 49835 346 72807 227 31531 287 50315 347 73499 228 31675 288 50507 348 73723 229 32131 289 51051 349 74419 230 32307 290 51275 350 74659 231 32547 291 51659 351 75091 232 32771 292 51947 352 75411 233 33235 293 52531 353 76115 234 33379 294 52699 354 76347 235 33747 295 53163 355 76907 236 33979 296 53451 356 77259 237 34291 297 53811 357 77643 238 34483 298 54107 358 77999 239 34959 299 54635, 359 78715 240 35087 300 54795 360 7f§.)()7 361 79591 408 101283 455 126143 362 79951 409 102099 456 126431 363 80391 410 102419 457 127343 364 80679 411 102963 458 127799 365 81255 412 103371 459 128375 366 81495 413 104067 460 128727 367 82227 414 104331 461 129647 368 82589 415 104987 462 130887 369 83059 416 105371 463 130811 370 83347 417 105923 464 131259 371 83971 418 106283 465 131739 372 84211 419 107119 466 132203 373 84955 420 107311 467 133135 374 85275 421 108151 468 133423 375 85675 422 108571 469 134215 376 86043 423 109123 470 134583 3Dodd: A Table of the Total Number of Stroboscopic Velocity Curves for APublished by UNI ScholarWorks, 1920222 IOWA ACADEMY OF SCIENCE Vor,. xxvrr, 1920 TABLE - Continued p I Q 377 I 86715 378 86931 379 87687 380 I 87975 381 I 88479 382 88859 383 89623 384 89879 385 90359 386 90743. 387 91247 388 91631 389 I 92407 390 92599 391 93303 392 I 93639 393 I 94159 394 I 94551 395 95175 396 95415 397 96207 398 96603 399 I 97035 400 97355 401 I 98155 402 98419 403 I 99139 404 99539 405 I 99971 406 100307 407 101027 BUREAU OF STANDARDS, vVAsmNcToN, D. c. p I Q 424 I 109539 425 110179 426 I 110459 427 111179 428 I 111603 429 112083 430 112419 431 113279 432 113567 433 114431 434 114791 435 115239 436 115671 437 116463 438 116751 439 117627 440 117947 441 118451 442 118835 443 119719 444 I 120007 445 I 120711 446 121155 447 121747 448 122131 449 123027 450 123267 451 124067 452 124515 453 125115 454 I 125567 --··-p I Q 471 135207 472 135671 473 136511 474 136823 475 I 137543 476 I 137927 477 I 138551 478 I 139027 479 I 139983 480 I 140239 481 I 141103 482 I 141583 483 I 142111 484 I 142551 485 I 143319 486 143643 487 I 144615 488 I 145095 489 145743 490 146079 491 I 147059 492 I 147379 493 I 148275 494 I 148707 495 I 149187 496 149667 497 I 150507 498 I 150835 499 151831 500 152231 I 4Proceedings of the Iowa Academy of Science, Vol. 27 [1920], No. 1, Art. 35https://scholarworks.uni.edu/pias/vol27/iss1/35

A Table of the Total Number of Stroboscopic Velocity Curves for Any of the Natural Numbers from 1 to 500 Inclusive Taken as a Limiting Value of n and m

https://scholarworks.uni.edu/cgi/viewcontent.cgi?article=6298&context=pias

A Table of the Total Number of Stroboscopic Velocity Curves for Any of the Natural Numbers from 1 to 500 Inclusive Taken as a Limiting Value of n and m

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