None
q, = 3875; u0 = 95.8; 7 = if-"* (cos qX - 5.48 sin qX)', E == 1939 v'^ (cos qX + 0.182 sin qX). (2) Half-wave: 185.64°. q2 = 7168; UQ = 102.8; 7 = if-"* (cos qX - 10.14 sin qX); E = 3585 iQr^ (cos ^ + 0.098 sin qX). (3) Three-quarter wave: 273.83°. qz -- 10,572; u0 = 104.5; 7 = v~^ (cos g^ - 14.90 sin qX); E = 5287 i0e-Uot (cos ^>i + 0.067 sin qX). (4) Full wave: 362.89°. ?4 •• 14,010; w0 = 105.1; 7 = v~^ (cos qX - 19.8 sin qX); E = 7005 v~^ (cos qX + 0.050 sin qX). (5) Five-quarter wave: 452.32°. <?5 » 17,463; w0 = 105.5; 7 = v'7*0' (cos qX - 24.65 sin gfl; E = 8732 1>-^ (cos qX + 0.040 sin gj). 544 TRANSIENT PHENOMENA (6) Three-half wave: 541.94°. & = 20,920; UQ = 105.6; 7 = if-** (cos qX- 29.6 sin gd); jE/ = 10,460 v~Wo< (cos g>l + 0.033 sin qX). APPENDIX VELOCITY FUNCTIONS OF THE ELECTRIC FIELD IN the study of the propagation of the electric field through space (wireless telegraphy and telephony), a number of new functions appear (Section III, Chapter VIII). . By the following equations these functions are defined, and related to the " Sine-Integral" Si x, the " Cosine-Integral" Ci x, and the " Exponential Integral," Ei x, of which tables were calculated by J. W. L. Glaisher (Philosophical Transactions of the Royal Society of London, 1870, Vol. 160) : col x = — du u* u5 u7 du l_v? }_u? l 3\3+55~7 |2 [4 |6 = cosxj--^+p-p+-...j fl |3 |S |7 H-sinz -§-^ + ^-^5 I 71 /^ sin u 2"Jo « du. 545 546 sil x= I du APPENDIX rx cos u ll x= ~>1~( Jx C*\i-- --- 1-^ 1 u2 1 u* 1 IX4 l |3 |5 |7 — -^+i=-^ a;2 a^ x6 x8 l 2 |4 |5 --%4^-ty X X3 X5 X7 fx ^du; where r= 0.5772156 . .. /•<? t* /•« _„ Explx= -dt*= ( — Jx u J_x u u du u 1 M2 1 M3 1 /« where l 1 2 J r-x^ J« ~v^du' x4 x5 q is given by : expl q = 0 as : q = 0.37249680. APPENDIX 547 Expl ( f» -u —du U du /. 1 u2 1 u3 1 u4 = /logtt— u + 2 T^- Q 1^+4 17- +• • • / ^ |^S O |O T: |T: 1 x2 1 x3 1 14 du. Tables of these four functions, reduced from the Glaisher tables, are given in the following for 6 decimals, and their first part plotted in Fig. 103. These functions have the following properties: col 0 = ^ sil 0 •-•= + oc expl 0 = + oo expl q = 0 col = 0 sil oo =0 expl ( + oo ) = - oo expl (— co)=0 col x has maxima at the even, sil x at the odd quadrants, and these maxima are alternately positive and negative; that is, col ^2s =max. sil o(2s— l)=max. = integer number. 548 APPENDIX .5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 BIG. 103. APPENDIX 549 For large values of s, the numerical values of these maxima approach the values: for: s>40, the approximation is correct to the 6th decimal. For small values of x, the approximations hold : si\x = log- -0.5772156, For large values of x, it is : 2 sin x 2 sin x 2 cos x 2 cos - < col x < — where n\ and n2 are the two successive quadrants, between which x lies. For instance : sin x = sin 1.5^"= 0.707, cos x = cos 1.5^-= —0.707, 550 APPENDIX and 0.01 725 <sil x< 0.01805, -0.01805 < col x< -0.01725. It is, approximately, for large values of x, if : col x = co\ —ucos v, sil x = sil pr-ucos v, where and u is the nearest even quadrant to x, for col x, and the nearest odd quadrant to x, for sil x, and col ^ u or sil ^ u are given by Table VII. For instance : vi= -0.785 v2= +0.785 col 26 £ = -0.0245 sil 25 £ = 0.0254 _ l 'cos (-0.785) =0.707 cos 0.785 = 0.707 col 40 = -0.01730 sil 40 - 0.01795 From the series expressions of these functions follows: col ( — x) =n — col x sil (— x) =sil x expl (jx) = sil x + y col x - / APPENDIX 551. 7T expl ( — jx)=su x—] col £ + 7 o £ col (±jx) = ±|iexpl x-expl ( — x)\ +/TT 1 sil (±jx) =^-{expl x + expl ( — x)} 552 APPENDIX TABLE I Col x and sil x from 0.00 to 1.00 X cola; J sil x J .00 + 1. 570 796 in onn GO .01 .02 .03 .04 1.560 796 1. 550 797 1.540 798 1. 530 800 9 999 9 999 9 998 Q QQ7 + 4.027 980 3.334 907 2.929 567 2.642 060 693 073 405 340 287 507 999 QIC ftK 1 520 803 2 419 149 zzz yio 9QQC .06 .07 .08 .09 1.510 808 1.500 815 1.490825 1.480837 9 993 9 990 9 988 9QO r 2.237 095 2.083 269 1.950 113 1.832 754 loZ U4/ 153 826 133 156 117 359 .10 1.470 852 yoo 1. 727 868 104 886 .11 .12 .13 .14 1.460 870 1.450 892 1.440 918 1.430 949 9 982 9 978 9 974 9 969 9QA K 1.633 083 1. 546 646 1.467 227 1.393 793 94 785 86 437 79 419 73 434 .15 1.420 984 1.325 524 68 269 .16 .17 .18 .19 1.411 024 1.401 069 1.391 120 1.381 177 9 960 9 955 9 949 9 943 9QQ7 1.261 759 1.201 957 1.145 672 1.092 527 63 765 59 802 56 285 53 145 .20 1.371 240 \)6i 1.042 206 50 321 .21 .22 .23 .24 1.361 310 1.351 387 1.341 471 1.331 563 9 930 9 923 9 916 9 908 ' 9onn .994 437 .948 988 .905 656 .864 266 47 769 45 449 43 332 41 390 .25 1.321 663 yuu .824 663 39 603 .26 .27 .28 .29 1.311 771 1.301 888 1.292 013 1.282 148 9 892 9 883 9 875 9 865 .786 710 .750 287 .715 286 .681 610 37 953 36 423 35 001 33 676 .30 1.272 292 006 .649 173 32 437 .31 .32 .33 .34 1.262 447 1.252 611 1.242 786 1.232 972 9 845 9 836 9 825 9 814 .617 896 .587 710 .558 549 .530 355 31 277 30 186 29 161 28 194 .35 1.223 169 803 .503 076 27 279 .36 .37 .38 .39 1.213 378 1.203 599 1.193 832 1. 184 077 9 791 9 779 9 767 9 755 9*7,49 .476 661 .451 067 .426 252 .402 178 26 414 25 594 24 815 24 074 .40 1.174 335 /4Z .378 809 23 369 .41 .42 .43 .44 1. 164 606 1.154 891 1.145 189 1.135 501 9 729 9 715 9 702 9 688 .356 114 .334 062 .312 625 .291 776 22 695 22 052 21 437 20849 .45 1. 125 828 O/o .271 492 20 284 .46 .47 .48 .49 1.116 170 1.106 526 1.096 898 1.087 285 9 658 9 644 9 628 9 613 .251 749 .232 526 .213 803 .195 562 19 743 19 223 18 723 18 241 .50 + 1. .56 .57 .58 .59 1.020 461 1.010 985 1.001 527 .992 088 9476 9 458 9439 94.91 .079 986 .065 037 .050 441 .036 190 14 949 14 596 14 251 1 Q Q1 Q 60 982 667 022 271 9AC\1 .61 .62 .63 .64 .973 266 .963 885 .954 523 .945 182 4U1 9 381 9 362 9 341 9 001 + .008 675 - .004 e06 - .017 582 - .030 260 lo olo 13 281 12 976 12 678 1 9 QQfl .65 .935 861 641 - .042 650 iz oyu .66 .67 .68 .69 .926 561 .917 282 .908 024 .898 788 9 300 9 279 9 258 9 236 991 J. - .054 758 - .066 591 - .078 158 - .089 463 12 108 11 833 11 567 11 305 nnco .70 .889 574 - .100 515 .71 .72 .73 .74 .880 382 .871 213 .862 066 .852 942 9 192 9 169 9 147 9 124 91 on - .111 318 - .121 879 - .132 203 - .142 296 10 803 10 561 10 324 10 093 9QAQ 75 843 842 luu — 152 164 oOo 9fY77 9RAK .76 .77 .78 .79 .834 765 .825 713 .816 684 .807 680 9 052 9 029 9 004 8osn - .161 810 - .171 240 - .180 458 -. 189 470 O4O 9 430 9 218 9 012 8 s no .80 .798 700 you - .198279 ouy .81 .82 .83 .84 .789 746 .780 817 .771 913 .763 035 8 954 8929 8904 8 878 80 r -I - .206 889 - .215 305 - .223 530 - .231 568 8 601 8416 8 225 8 038 85 754 184 OOl 239 423 OOO 8 one 7fi7 ^ .86 .87 .88 .89 .745 358 .736 560 .727 788 .719 043 8 798 8 772 8 745 871 Q - .247 098 - .254 597 - .261 923 - .269 079 7 499 7 326 7 156 6QQQ .90 .710 325 - .276 068 .91 .92 .93 .94 .701 636 .692 974 .684 340 .675 735 8 689 8 662 8 634 8 605 8K77 - .282 893 - .289 558 - .296 064 .302 415 6 825 6 665 6 506 6 351 61 QQ .95 .667 158 .30S 614 iyy .96 .97 .98 .99 .658 610 .650 092 .641 602 .633 143 8 548 8 518 8 490 8 459 8 A Of\ - .314 662 - .320 563 - .326 319 - .331 931 6 048 5 901 5 756 5612 5170 1.00 + 0.624 713 4oU -0.337 404 •1M 554 APPENDIX TABLE II Expl x and expl (-x) from 0.00 to 1.00 X expl x J expl (-a;) A .00 + GO 00 .01 .02 .03 .04 + 4.017 929 3.314 707 2.899 116 2.601 257 703 223 415 591 297 859 + 4.037 930 3.354 708 2.959 119 2.681 264 684 222 395 589 277 855 05 2 367 885 Zoo otZ 2 467 898 213 366 .06 .07 .08 .09 2.175 283 2.010 800 1.886 884 1.738 664 JL\)A DU^ 164 483 143 916 128 220 2.295 307 2.150 838 2.026 941 1.918 745 i/z oyl 144 469 123 897 108 196 10 1 622 813 llo ool 1 822 924 95 821 1 f\ C 0 CA .11 .12 .13 .14 1.516 959 1.419 350 1.328655 1.243 841 97 609 90695 84 814 1.737 107 1.659 542 1.588 899 1.524 146 oO ol/ 77 565 70643 64 753 15 1 164 086 /y i o4 1 464 462 59 684 7 e o re .16 .17 .18 .19 1.088 731 1.017 234 .949 148 .884 096 to oOo 71 497 68 087 65 052 1.409 187 1.357 781 1.309 796 1.264 858 oo ^/o 51 406 47 985 44 938 .20 .821 761 o^ ooo 1.222 651 42 207 .21 .22 .23 .24 .761 872 .704 195 .648 529 .594 697 59 889 57 676 55 666 53 832' 1.182 902 1.145 380 1.109 883 1.076 235 39 749 37 522 35 497 33 648 .25 .542 543 QL loo 1.044 283 31 952 .26 .27 .28 .29 .491 932 .442 741 .394 863 .348 202 50 611 49 191 47 878 46 662 1.013 889 .984 933 .957 308 .930 918 30 394 28 956 27 625 26 390 .30 .302 669 4o Ooo .905 677 25 241 .31 .32 .33 .34 .258 186 .214 683 .172 095. 130 363 44 482 43 503 42 588 41 732 .881 506 .858 335 .836 101 .814 746 .24 171 23 171 22 234 21 355 .35 .089 434 4u y^y .794 215 20 531 .36 .37 .38 .39 .049 258 + .009 790 - .029 Oil - .067 185 40 176 39 468 38 801 38 173 .774 462 .755 441 .737 112 .719437 19 753 19 021 18 329 17 675 .40 - .104 765 61 Ool .702 380 17 057 .41 .42 .43 .44 45 - .141 786 - .178278 - .214 270 - .249 787 284 855 37 021 36492 35 991 35 517 35 068 .685 910 .669 997 .654 613 .639 733 fl'JK '-JQ1 16 470 15 913 15 384 14 880 14 402 .46 .47 .48 .49 .319 497 - .353 735 - .387 589 - .421 078 34 642 34 238 33 854 33 489 .611 387. 597 877 .584 784 .572 089 13 944 13 510 13 093 12 695 .50 -0.454 220 33 142 + 0.559 774 12 315 APPENDIX TABLE II— Continued 555 X expl x J expl ( — x) A .50 -0.454 220 33 142 + 0.559 774 12 315 .51 .52 .53 .54 - .487 032 - .519 531 - .551 730 - .583 646 32 812 32 498 32 200 31 915 o-i nA r .547 822 .536 220 .524 952 .514 004 11 952 11 602 11 268 10 948 .55 - .615 291 .503 364 10 640 .56 .57 .58 .59 - .646 677 - .677 819 - .708 726 - .739 410 31 387 31 141 30 907 30 684 .493 020 .482 960 .473 173 .463 650 10 344 10 060 9 787 9 523 .60 - .769 881 6(J QiZ .454 380 9 270 .61 .62 .63 .64 - .800 150 - .830 226 - .860 119 - .889 836 30 269 30 076 29 892 29 717 90 £^n .445 353 .436 562 .427 997 .419 652 9 027 8 791 8 565 8 345 .65 - .919 386 zy oou .411 517 135 .66 .67 .68 .69 - .948 778 - .978 019 -1.007 116 -1.036 077 29 392 29 241 29 079 28 960 .403 586 .395 853 .388 309 .380 950 7 931 7 733 7 544 7 359 .70 -1.064 907 28 80 1 .373 769 7 181 .71 .72 .73 .74 -1.093 615 -1.122 205 -1.150 684 -1.179 058 28 707 28 590 28 479 28 374 .366 760 .359 918 .353 237 .346 713 7 009 6 842 6 681 6 524 .75 -1.207 333 Zo Z. O .340 341 6 3,2 .76 .77 .78 .79 -1.235 513 -1.263 605 -1.291 613 -1.319 542 28 181 28 092 28 008 27 929 97 Q££ .334 115 .328 032 .322 088 .316 277 6 226 6 083 5 944 5 811 .80 1.347 397 Z< OOO .310 597 5 680 .81 .82 .83 .84 -1.375 182 -1.402 902 -1.430 561 -1.458 164 27 785 27 720 27 659 27 603 .305 043 .299 611 .294 299 .289 103 5 554 5 432 5 312 5 196 .85 -1.485 714 27 ooU .284 019 5 084 .86 .87 .88 .89 -1.513 216 - 1. 540 673 - 1. 568 089 - 1. 595 467 27 502 27 457 27 416 27 379 97 QA £ .279 045 .274 177 .269 413 .264 749 4 974 4 868 4 764 4 664 .90 -1.622 812 £i O4O .260 184 565 .91 .92 .93 .94 -1.650 126 -1.677 413 -1.704 677 -1.731 920 27 314 27 287 27 264 27 243 97 99R .255 714 .251 336 .247 050 .242 851 4 470 4 378 4 286 4 199 95 — 1 759 146 238 738 llo 97 91 1 .96 .97 .98 .99 -1.786 357 -1.813 557 -1.840 749 -1.867 935 Z/ ZLL 27 200 27 192 27 186 97 1 QQ .234 708 .230 760 .226 891 .223 100 UoU 3 948 3 869 3 791 1.00 -1.895 118 Zt loo + 0.219 384 / lo 556 APPENDIX TABLE III Col x and sil x from 0.0 to 5.0 X col x J sil x A .0 + 1.570 796 oo .1 .2 .3 .4 1.470 852 1.371 240 1.272 292 1.174 335 + 1.727 868 1.042 206 .649 173 .378 809 1 H77 ASQ mnoA .6 .7 .8 .9 .982 667 .889 574 .798 700 .710 325 + .022 271 - .100 515 - .198 279 - .276 068 10 R94. 71 "^ 007 A(\A _i_ 09 cno 1.1 1.2 1.3 1.4 .542 111 .462 749 .387 838 .314 570 79 362 75 911 72 269 f»o A cn - .384 873 - .420 459 - .445 739 - .462 007 + 4/ 4by 35 586 25 279 16 -268 1.5 .246 113 Do 4O/ - .470 356 o4y 1.6 1.7' 1.8 1.9 .181 616 .121 204 .064 979 + .013 021 64 497 60412 56 225 51 958 A 7 ftQQ - .471 733 - .466 968 - .456 811 - .441 940 + 1 377 - 4 765 -10 157 -14 871 2.0 - .034 617 *±l DOo - .422 981 — 18 959 2.1 2.2 2.3 2.4 - .077 902 - .116 839 - .151 411 - .18 689 43 285 38 927 34 582 30 278 ' - .400 512 - .375 075 - .347 176 - .317 292 -22 469 - 25 437 -27 899 -29 884 2.5 - .207 724 Zo Ooo - .285 871 — 31 421 2.6 2.7 2.8 2.9 - .229 598 - .247 416 - .261 300 - .271 394 21 874 17 818 13 884 10 094 - .253 337 - .220 085 -. 186 488 - .152 895 -32 534 -33 252 -33 597 -33 593 3.0 - .277 856 4oZ - .119 630 — 33 265 3.1 3.2 3.3 3.4 - .280 863 - .280 605 - .277 284 - .271 118 + 3 007 258 - 3 319 - 6 166 - .086 992 - .055 257 - .024 678 + .004 518 -32 638 -31 735 -30 579 -29 196 3.5 - .262 329 to\J .032 129 — 27 610 3.6 3.7 3.8 3.9 - .251 152 - .237 825 - .222 594 - .205 705 — 11 177 - 13 323 -15 231 - 16 889 .057 974 .081 901 .103 778 .123 499 -25 846 -23 927 -21 877 -19 721 4.0 - .187 407 — lo Z\)o. 1.1 1.2 1.3 1.4 - 2.167 378 - 2.442 092 - 2.721 399 - 3.007 207 272 260 274 714 279 306 285 809 9Q/L O7S. 185 991 .158 408 .135 451 .116 219 oo oyo 27 583 22 957 19 232 1 ft 1 QQ 1.5 - 3.301 285 zy<± u/o. 100 020 ID iyy 1.6 1.7 1.8 1.9 - 3.605 320 - 3.920 963 - 4.249 868 - 4.593 714 304 034 315 643 328 904 343 846 .086 308 .074 655 .064 713 .056 204 13 712 11 653 9 942 8 509 2 0 4 954 234 ooU OZL 048 901 olio 070 nni 69S7 2.1 2 2 2~3 2.4 - 5.333 235 - 5.732 615 - 6.154 381 - 6.600 670 399 379 421 766 446 289 A7Q flQA .042 614 .037 191 .032 502 .028 440 Zo< 5423 4 689 4 062 3FQr 2.5 - 7.073 766 4/O U»O .024 915 oZo 2.6 2.7 2.8 2.9 - 7.576 115 - 8.110 347 - 8:679 298 - 9.286 024 502 349 534 233 568 950 606 726 .021 850 .019 182 .016 855 .014824 3 065 2 668 2 327 2 031 3 0 — 9 933 833 647 808 013 048 776 3.1 3.2 3.3 3.4 -10.626 300 -11.367 303 -12 161 041 -13.012 075 oyz 4oo 741 002 793 739 851 034 .011 494 .010 133 .008 939 .007 891 OO4 1 361 1 194 1 048 Q91 3.5 13 925 354 yio z/y .006 970 yji 3.6 3.7 3.8 3.9 -14.906 254 -15.960 619 -17.094 802 -18.315 714 980 900 1.054 365 1.134 183 1.220 912 .006 160 .005 448 .004 820 .004 267 810 712 628 553 4 0 — 19 630 874. olo loU 003 779 48» 1X17 CQO jorv 4.1 4.2 4.3 4.4 -21.048 467 -22.577 401 -24.227 380 -26.008 973 .'I I/ O\)Z 1.528 934 1.649 979 1.781 593 1Q94. 79*} .003 349 .002 969 .002 633 .002 336 4oU 380 336 297 4 5 — 27 933 697 002 073 Juo 4.6 4.7 4.8 4.9 -30.014 099 -32.263 860 -34.697 890 -37.332 451. UoU 4Uo 2.249 760 2.434 030 2.634 561 20C9 QQ r .001 841 .001 635 .001 453 .001 291 Z6Z 206 182 162 5.0 -40.185 275 .00^ o^o + 0.001 148 14o .558 APPENDIX TABLE V Col x, sil x, expl x, and expl ( — x) from 0 to 15 X col x sil x expl x expl (-x} x x° 0 + 1. 570796 GO 00 00 0 0 1 2 3 4 + .624713 - .034617 - .277856 - .187407 -.337404 - .422981 -.119630 + .140982 1.895118 4.954234 9.933833 19.630874 + .219384 .048901 .013048 .003779 1 2 3 4 57.2958 114.5916 171.8874 229. 1832 5 + .020865 + .190093 40.185275 .001148 5 286.479 6 7 8 9 + .146109 + .116200 - .003391 - .094244 + .068057 -.076695 -. 122434 -.055348 85.990 191. 505 440. 380 - 1037.878 .000360082 .000115482 .000 37666 .000012447 6 7 8 9 343.775 401.071 458.366 515.662 10 - .087551 + .045456 2492.229 .000004157 10 572.958 11 12 13 14 - .007511 + .065825 + .071435 + .014585 + .089563 + .049780 -.026764 -.069396 - 6071.406 - 14959 - 37198 - 93193 .000001400 .000000475 .000000162 .000000056 11 12 13 14 630.254 687.550 744. 846 802. 142 15 - .047398 -.046279 -234956 + .000000019 15 859.438 APPENDIX 559 TABLE VI col x and sil x X co' x sil x x col x sil x 0 + 1.570 796 GO 150 + .004 6.0 + .004 796 5 10 15 20 25 30 35 40 45 + .020 865 - .087 551 - .047 398 + .022 555 + .039 314 + .004 040 - .026 126 - .016 189 + .012 081 +. + .000 320 004- 781 10 000 -.000 095 + .000 031 130 140 - .002 880 - .001 363 + .007 132 -.007 Oil 11 000 100 000 1 000 000 -.000 026 -.000 010 + 000 001 + .000 087 -.000 000 4- 000 000 150 + .004 630 + .004 796 560 APPENDIX TABLE VII 7T' 7t MAXIMA AND MINIMA OF col —x and sil —x X col-^c 2. Tt col— re 7CX 2 x i*; 2 .. 1 77 79 - .008 267 + .008 057 1 1 80 + .007 957 1 81 - .007 858 0 x> 80 j»fe 79 X sil|s=(-l) + 1 2~2 INDEX PAGE Acceleration constant of traveling wave 466 Air blast, action in oscillating-current generator 75 pressure required in oscillating-current generator 75 Alternating-current circuit and transient term of fundamental frequency 473 distribution in conductor 369 transformer operating oscillating-current generator 87 transmission, equations of traveling wave 477 wave as traveling wave without attenuation 472 Alternator control by periodic transient term of field excitation 223 Aluminum cell rectifier 222 effective penetration of alternating current 378 Amplitude of traveling wave 465 of wave 438 Arc, and spark 249 continuity at cathode 249 lamp, control by inductive shunt to operating mechanism 131 machine 230 as rectifier 221 current control 220 properties 249 rectification 249 rectifiers 222 resistivities 9 starting 249 Arcing ground on lines and cables, as periodic transient phenomenon . . 23 Armature reactance, reaction and short-circuit current of alternator 199 Attenuation of alternating magnetic flux in iron 361 constants 434 of traveling wave, and loading 462 Booster, response to change of load 158 Brush arc machine 221, 230, 242, 248 Building up of direct-current generator 32 of overcompounded direct-current machine 49 Cable, high-potential underground, standing waves 452 opening under load 112, 118 short-circuit oscillation 113, 118 starting 111,117 transient terms and oscillations 98, 102 561 562 INDEX PAGE Capacity, also see Condenser. and inductance, equations 48 and velocity of propagation 400, 401 distributed series 348 energy of complex circuit 517 in mutual inductive circuit 161 of electric circuit 112 range in electric circuit 13 representing electrostatic component of electric field 5 shunting direct-current circuit 133 specific, numerical values 11 suppressing pulsations in direct-current circuit 134 Cast iron, effective penetration of alternating current 378 Cathode of arcs 249 Charge of condenser 51 of magnetic field 27 Circuit, complex, see Complex circuit. control by periodic transient phenomena 220, 223 electric, speed of propagation in 422 Closed circuit transmission line 306 Col al 392, 394 Commutation and rectification 222 as transient phenomenon 40 Commutator, rectifying 229 Complex circuit, of waves 498 power and energy 513 resultant time decrement 504 traveling wave 468 Compound wave at transition point 532 Condenser, also see Capacity. charge, inductive 18 noninductive 18 circuit of negligible inductance 55 equations 48 oscillation, effective value of voltage, current and power. ... 70 efficiency, decrement and output 72 frequency 62 general equations 60 size and rating 69 starting on alternating voltage 94 voltage in inductive circuit 49 Conductance, shunted, effective 12 Conductors at high frequency 403 Constant-current mercury arc rectifier 250 rectification 221, 230 potential-constant-current transformation by quarter-wave line 308 mercury arc rectifier 251 rectification 221, 230 INDEX 563 PAGE Control of circuits by periodic transient phenomena 220 Conversion by quarter-wave circuits 313 Copper, effective penetration of alternating currents 378 ribbon, effective high frequency impedance 408 wire, effective high frequency impedance 408 Cosine wave, traveling 434 Critical case of condenser charge and discharge 53 resistance of condenser oscillation 66 start of condenser on alternating voltage 95 Current density, in alternating-current conductor 372 effective, of oscillating-current generator 81 transformation at transition point of wave 529 Damping of condenser oscillation 66, 72 Decay of continuous current in inductive circuit 17 of wave of condenser oscillation 72 Decrement of condenser oscillation 65, 72 resultant time, of complex circuit 504 Destructive voltages in cables and transmission lines 120 Dielectric constant, numerical values 11 strength, numerical values 11 Dielectric also see Electrostatic. Direct-current generator, self-excitation 32 railway, transient effective resistance 379 Disappearance of transient term in alternating-current circuit 43 Discharge of condenser , . 51 Geissler tube 9 inductive, as wave 535 into transmission line '. 542 of motor field 29 Disruptive strength, numerical values 11 voltage in opening direct-current circuit 26 Distance attenuation constant 434 in velocity measure . 435 Distortionless circuit 441, 447 Distributed series capacity 348 Distribution of alternating-current density in conductor 369 of alternating magnetic flux in iron 355 Divided circuit, general equations 122 continuous-current circuit without capacity 126 Dynamostatic machine 220 Effective current of condenser discharge 70 voltage and power of oscillating-current generator. . . 81 layer of alternating-current conductor 377 penetration of alternating current in conductor 376, 378 power of complex circuit 514 of cpndenser oscillation '70 reactance of armature reaction 200 561 INDEX PAGE Effective resistance of alternating-current distribution in conductor, 370, 376 voltage of condenser oscillation 70 Efficiency of condenser oscillation 72 Electric circuit, general equations 428 field, velocity of propagation 387 Electrolytes, resistivities 8 Electrolytic rectifiers 222 Electromagnetic, also see Magnetic. axis of electric field 4 Electrostatic, also see Dielectric. axis of electric field 4 energy of complex circuit 517 field, energy of 7 Elimination of pulsations in direct-current circuit by capacity 134 Energy of complex circuit 513 condenser discharge 70 electric field 4, 7 transfer in complex circuit 507, 521 constant of complex circuit 507 Equations, general, of electric circuit 428 Even harmonics of half-wave oscillations 483 Excitation of motor field 27 Exponential curve of starting current 45 Field current at armature short-circuit . t 202 electric, of conductor 3 energy of 4 velocity of propagation 387 excitation, transient term 27 exciting current, rise and decay 17 regulation of generator by periodic transient terms 223 resultant polyphase , 192 Flat conductor, unequal current distribution 371 Floating system of control 220 Fluctuations of current in divided circuit 129 voltage of direct-current generator with load 149 Free oscillations 432, 478 and standing waves 482 Frequency, absence of effect on circuit oscillation 10 and starting current of transformer 182 constant of wave 433 limit of condenser oscillation 73 of condenser oscillation 62, 68 field current at armature short-circuit 203 oscillation of condenser, transmission line, cable. ... 99, 338 recurrence of discharge in oscillating-current generator. . 81 wave 433 range of condenser oscillation 71 electromagnetic induction 67 INDEX 565 PAGE Full-wave oscillation of complex circuit 508 transmission line 330 Fundamental frequency of oscillation, cables and transmission lines 103, 105 Gas pipe, effective high frequency impedance 408 General circuits with inductance and capacity 174 without capacity 168 equations of electric circuit 428 Generator, direct-current over-compounded, building up 149 self-excitation 32 oscillating current 74 German silver, effective penetration of alternating current 378 Gradual approach to permanent value 21 or logarithmic condenser charge and discharge 53 term, also see Logarithmic. Graphite, effective penetration of alternating current 378 Grounded transmission line 303 Half-wave oscillation 483, 490 of complex circuit 509 transmission line 333 rectification 221 Harmonics, even, of half-wave oscillation 483 Hertzian oscillators 388 High frequency alternators, momentary short-circuit current 201 conductor 370, 403 discharge 388 oscillating currents by periodic transient terms 220 oscillations of cables and transmission lines 103, 105 power surge of low-frequency 105 stray field and starting current of transformer 189 Impact angle at transition point of wave 527 Impedance of conductor at high frequency 407 effective high frequency 408, 413 of radiation 396 traveling wave 460 Inductance and shunted capacity suppressing pulsations in direct-cur- rent circuit 134 effective, of radiation 394 energy of complex circuit 515 in telephone lines 455, 462 massed, in circuit 537 of conductor without return 390 electric circuit 12 range in electric circuit 13 representing magnetic component of electric field 5 566 INDEX PAGE Induction, magnetic, and starting current of transformer 180 motor circuit, starting 44 Inductive discharges into transmission line 542 shunt to non-inductive circuit 129 Inductorium, equations 164 Infinitely long conductor 305 Input, see Power. Instantaneous power in complex circuit 514 Insulators, resistivities 9 Iron arc operated by oscillating-current generator 82 effective penetration of alternating current 348 wire, current distribution 370 and pipe, effective high frequency impedance 408 Laminated iron, alternating magnetic flux 355 pole series booster, response to voltage change 158 Layer, effective, of alternating-current conductor 377 Leakage in telephone lines 455, 463 Length of wave 433 Lighting circuit, starting 27, 44 Lightning arrester, multigap 348 conductors 370 discharges 388 in thunder cloud 350 Limit condition of condenser equations 50 of frequency of condenser oscillations 73 Loading of telephone lines 455, 462 Local oscillations of cables and lines 103, 105 Logarithmic decrement of con^jnser oscillation 65 or gradual condenser charge and discharge 53 start of condenser on alternating voltage 95 Low frequency surge in cables and lines 103, 105 stray field and starting current of transformer 189 Loxodromic spiral of starting current 46 Magnetic, also see Electromagnetic. density and starting current of transformer 180 energy of complex circuit 515 field, energy of 6 flux, alternating, in iron 355, 361, 363, 365, 366, 367 materials 10 saturation, numerical values 10 Magnet poles, solid, as mutual inductive circuit 155 Main axes of electric field 46 wave at transition point 531 Massed inductance and electric wave 537 Mechanical rectification 221, 229 Mercury arc rectifier 250 INDEX 567 PAGE Metallic conductors, resistivities 8 magnetic induction 10 Minimum wave length of oscillating currents 74 Motor circuit, alternating, starting 44 field, excitation 27 Multigap lightning arrester '. 348 Mutual impedance and velocity of propagation 399 inductance, equations 143 and velocity of propagation 397 inductive circuit with capacity 161 without capacity 144 of solid magnet poles 155 reactance : 143 Nominal generated e.m.f. and short-circuit current 200 Noninductive condenser circuit 54 shunt to inductive circuit 129 Nonoscillatory, see Gradual or Logarithmic. Open-circuit rectification 230 Opening of cable or transmission line under load 112, 118 of continuous-current circuit 26 Open transmission line 299 Oscillating-current generator 69, 74 and charging current 85 high-frequency currents by periodic transient terms 220 Oscillation, also see Condenser discharge. free, of circuit 432, 478 of rotating field in starting 197 transmission line 322, 333, 336, 338 Oscillatory approach to permanent value 21 case of alternating circuit 93 or trigonometric condenser charge and discharge 53 start of condenser on alternating voltage 95 Oscillograms of mercury arc rectifier 264 of transformer starting current 190 Output, also see Power. effective, of oscillating-current generator 81 Overcompounded direct-current generator, building up 149 Overlap of rectifying arcs 251 Overreaching of condenser charge 19 in noninductive branch of inductive circuit 131 Oversaturated transformer flux of starting current 181 Penetration, effective depth of, 405 of alternating current in conductor 376, 378 magnetic flux in iron 361, 363, 365 Period of recurrence 218 wave. 433 568 INDEX PAGE Periodic transient terms 22, 218 Permanent term of alternating-current circuit 91 values of electric quantities 16 Permeability 9 apparent,, of iron for alternating currents 355, 367 Phase difference in transmission line 296 of wave and transient term 45, 91 Physical meaning of transient term 103 Polyphase alternator short circuit 202, 204 m.m.f ., resultant 192 rectification 230 Potential regulation by periodic transient terms 223 Power of complex circuit 513 component of high frequency impedance 412 gradient of electric circuit 3 electric field 48 output, effective, of oscillating-current generator 81 radiated by conductor 394, 397 transfer in complex circuit 521 constant of complex circuit 507 Propagation constant of wave 441 speed of, of wave 422 field 387 Pulsation of rotating field in starting 197 Pyroelectrolytes, resistivities 9 Quarter-phase rectification 230 Quarter-wave circuit 313 oscillation 483, 489 of complex circuit 509 transmission line 322 transformer 312 transmission line 306, 315 Quartic equation of divided circuit 126 Radiation, effective resistance 393 power of conductor 393, 397 resistance of conductor 403 Rail, effective penetration of alternating current 378 return of single-phase system 370 transient effective resistance 379 Railway, direct-current, transient rail resistance 379 motor, self-excitation as generator 38 single-phase, rail return 370 Rating of capacity and inductance 122 resistors, reactors, condensers 69 Ratio of currents,1 oscillating-current generator 82 Reactance, effective, of external field. thermal, of conductor 403 Resistivity, numerical values 8 Resistor, size and rating 69 Resonators, Hertzian 388 Resultant polyphase m.m.f 192 time decrement of complex circuit 504 Rise of continuous current in inductive circuit 17 voltage by transformation at transition point 529 Rotating field, polyphase 192 Ruhmkorff coil, equations 164 570 INDEX PAGE Salt solution, effective penetration of alternating current 378 Saturation, magnetic, numerical values 10 and transformer starting current 180 Screening effect of alternating currents 378 Self-excitation of direct-current generator 32 railway motor as generator 38 series generator 38 shunt generator 37 Self-inductance in direct-current circuits 26 and short-circuit current of alternator 199 Series capacity, distributed 348 generator, self-excitation 38 motor, self-excitation as generator 38 Short-circuit current of alternator 199, 201 oscillation of cables and lines 113, 118 rectification 229 Shunt generator, self-excitation 32 motor field excitation, change 27 Sil al 392, 394 Silicon, effective penetration of alternating current 378 Sine wave traveling 434 Single-phase alternator short-circuit 202 railway rail return 370 rectification 229 Solid magnet poles as mutual inductive circuit 155, 158 Space induction, magnetic 10 Spark discharge in cables and lines as periodic transient phenomenon. . 23 of condenser as periodic transient phenomenon 22 Speed, effect on discharge of motor field 29 propagation in electric circuit 422 of alternating magnetic flux in iron 366 Standing waves 439, 442 and free oscillations 482 Starting current of transformer, calculation 188 and frequency 182 magnetic saturation 180 remanent magnetism 181 resistance 185 stray field 184 oscillograms 190 of alternating current 43 continuous current 27 polyphase or rotating field 192, 197 oscillation of cables and lines Ill, 117 Static, see Electrostatic. phenomena 13, 105 Stationary waves 439, 442 Steel, effective penetration of alternating current 378 INDEX 571 PAGE Stored energy of complex circuit 515 Stranded conductor, effective resistance of current distribution 370 Stray field and starting current of transformer 184 Suppression of pulsations of direct current by capacity and inductance. 134 Synchronous reactance and short-circuit current 200 rectifier 221 Telegraph, wireless 388 cable, submarine, standing waves 454 Telephone 281 circuit, long distance, standing waves 454 Terminal conditions of condenser equations 50 Tesla transformer and oscillating-current generator 82 Thermal resistance of conductor 403 Third harmonic of short-circuit current 213 Thomson arc machine 221, 230 Thunder cloud, lightning discharge in 350 Time attenuation constant 434 constant, resultant, of complex circuit 504 decrement, resultant, of complex circuit 504 local, of traveling wave 460 Tirrill regulator 223 Transfer constant of energy, of complex circuit 507 of energy in oscillation of complex circuit 507, 521 Transformation ratio at transition point of wave 529 of voltage and current at transition point 529 Transformer, alternating, operating oscillating-current generator 87 distributed capacity 342 quarter-wave oscillation 312 starting 44 and magnetic saturation 180 Transient rail resistance with direct current 386 terms, conditions of their appearance 21, 23 of alternating-current circuit 91 capacity and inductance, physical meaning 103 fundamental frequency in alternating-current circuit 473 periodic 22 unequal current distribution 379 Transition period at change of circuit condition 16 points of wave 498 Transmission angle at transition point 527 line, characteristic curves 297 closed 306 constants 282 conversion by 308, 313 equations 284, 287 approximate 294 free oscillation . . 322 572 INDEX PAGE Transmission line (continued), frequency 100, 280, 320, 338 full-wave oscillation 336 general equations of standing waves 449, 452 grounded 303 half-wave oscillation 333 inductive discharges 542 infinitely long 305 natural period 280, 320 open 299 opening under load 112, 118 phase difference 296 quarter-wave 306, 313, 315 oscillation 322 radiation 283 resonance frequency 279 with higher harmonics 280 short-circuit oscillation 113, 118 starting 111,117 transient terms and oscillations 98, 102 Transmitted wave at transition point 527, 531 Traveling sine and cosine waves 434 waves, general equations 458 without attenuation, as alternating waves 472 Trigonometric or oscillatory condenser charge and discharge 53 term, see Oscillatory. Turbo alternators, short-circuit current 201 Unequal alternating-current distribution in conductor 370 transient-current distribution in conductor , 379 Velocity, also see Speed. measure o.f distance 435 of propagation of electric field 387 Voltage control by transient terms 223 drop, high frequency conductor 413 transformation at transition point of wave 529 variation of direct-current generator, with load 149 Voltmeter across inductive circuit, pulsation 132 Water, effective penetration of alternating current 378 Wave of alternating magnetism in iron 359 direct or main, and reflected 431 length of alternating magnetic flux in iron 361, 365 constant 434 minimum, of oscillating current 74 transmission 281 Wireless telegraphy 388 X-ray apparatus, equations 82 '1 883 6 THIS BOOK IS DUE ON THE LAST DATE STAMPED BELOW BOOKS REQUESTED BY ANOTHER BORROWER ARE SUBJECT TO IMMEDIATE RECALL LIBRARY, UNIVERSITY OF CALIFORNIA, DAVIS D4613(7/92)M UCD LIBRARY 31175021293744. 