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Index:Mécanique céleste Vol 4.djvu

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Title Mécanique Céleste, Volume IV.
Author Pierre-Simon Laplace
Translator Nathaniel Bowditch
Editor Nathaniel Bowditch
Year 1839
Publisher Hillard, Gray, Little, and Wilkins
Location Boston
Source djvu
Progress To be proofread
Transclusion Index not transcluded or unreviewed
Volumes Volume 1Volume 2Volume 3Volume 4
Pages (key to Page Status)
- - - - - - HalfTitle - - Plate Title 12 13 - - Plate Dedic - 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 i ii iii iv v vi vii viii ix x xi xii xiii xiv xv xvi xvii xviii xix xx xxi 22 toc toc toc toc toc toc toc toc toc toc toc toc toc toc 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 557 558 559 560 561 562 563 564 565 566 567 568 569 570 571 572 573 574 575 576 577 578 579 580 581 582 583 584 585 586 587 588 589 590 591 592 593 594 595 596 597 598 599 600 601 602 603 604 605 606 607 608 609 610 611 612 613 614 615 616 617 618 619 620 621 622 623 624 625 626 627 628 629 630 631 632 633 634 635 636 637 638 639 640 641 642 643 644 645 646 647 648 649 650 651 652 653 654 655 656 657 658 659 660 661 662 663 664 665 666 667 668 669 670 671 672 673 674 675 676 677 678 679 680 681 682 683 684 685 686 687 688 689 690 691 692 693 694 695 696 697 698 699 700 701 702 703 704 705 706 707 708 709 710 711 712 713 714 715 716 717 718 719 720 721 722 723 724 725 726 727 728 729 730 731 732 733 734 735 736 737 738 739 740 741 742 743 744 745 746 747 748 749 750 751 752 753 754 755 756 757 758 759 760 761 762 763 764 765 766 767 768 769 770 771 772 773 774 775 776 777 778 779 780 781 782 783 784 785 786 787 788 789 790 791 792 793 794 795 796 797 798 799 800 801 802 803 804 805 806 807 808 809 810 811 812 813 814 815 816 817 818 819 820 821 822 823 824 825 826 827 828 829 830 831 832 833 834 835 836 837 838 839 840 841 842 843 844 845 846 847 848 849 850 851 852 853 854 855 856 857 858 859 860 861 862 863 864 865 866 867 868 869 870 871 872 873 874 875 876 877 878 879 880 881 882 883 884 885 886 887 888 889 890 891 892 893 894 895 896 897 898 899 900 901 902 903 904 905 906 907 908 909 910 911 912 913 914 915 916 917 918 919 920 921 922 923 924 925 926 927 928 929 930 931 932 933 934 935 936 937 938 939 940 941 942 943 944 945 946 947 948 949 950 951 952 953 954 955 956 957 958 959 960 961 962 963 964 965 966 967 968 969 970 971 972 973 974 975 976 977 978 979 980 981 982 983 984 985 986 987 988 989 990 991 992 993 994 995 996 997 998 999 1000 1001 1002 1003 1004 1005 1006 1007 1008 1009 1010 1011 1012 1013 1014 1015 1016 1017 1018 - - - - - - - -

CONTENTS OF THE FOURTH VOLUME.

PARTICULAR THEORIES OF THE MOTIONS OF THE HEAVENLY BODIES.

EIGHTH BOOK.

THEORY OF THE SATELLITES OF JUPITER, SATURN, AND URANUS.

Object of this theory [6019] 1

CHAPTER I. EQUATIONS OF THE MOTIONS OF THE SATELLITES OF JUPITER 1

The reciprocal action of the satellites, the sun's attraction, and the oblateness of the spheroid of Jupiter, arc noticed [6020—6077] § 1, 2

CHAPTER II. ON THE INEQAULITIES OF THE MOTIONS OF JUPITER'S SATELLITES, WHICH ARE INDEPENDENT OF THE EXCENTRICITIES AND INCLINATIONS OF THEIR ORBITS 17

Development of the equations of the motions of these satellites. Analytical expressions of the perturbations of their radii vectores and of their longitudes. The sun*s action produces an inequality analogous to the variation in the lunar theory [6078–6125] § 3

Investigation of the terms of these expressions which can acquire considerable values by the divisors introduced by integration; these divisors being very small, in consequence of the nearly commensurable ratios of the mean motions of the three inner satellites. Necessity of retaining, in these small divisors, the terms depending on the product of the constant part of the disturbing force by the variation of the radius vector, this product having a sensible influence upon their values [6125′–6171] § 4

Effect of terms of this kind on the times of the eclipses of the three inner satellites. All the inequalities produced by such terms depend upon the same angle, having a common period of 437days,650. This result is conformable to observation [6173–6193] §5

CHAPTER III. ON THE INEallALmES OF THE MOTIONS OP THE SATELLITES DEPENDING ON THB BXCBfTRICITIES OF THE ORBITS « 38

Expression of the different equations of the centre of the satellites, and of the motions of their [6194–6244″] § 6

Investigation of the terms which can become sensible by the effect of small divisors, introduced by integration, although they may be multiplied by the excentricitics, which are very small [6245–6270] § 7

The sun's action produces also in the motion of the satellites some sensible inequalities, depending on the excentricities. Expression of these inequalities. That which affects the longitude is composed of two parts analogous to the evection and to the annual equation in the lunar theory [6271–6294] § 8

CHAPTER IV. ON THE INEQUALITIES OF THE SATELLITES IN LATITUDE 62

Analytical expressions of the latitude of a satellite and of the motion of its nodes [6295–6336] § 9

The part of this expression which depends on the displacements of the equator and of the orbit of Jupiter, represents the latitude which each satellite would have, if it should move in an intermediate plane which passes between the equator and orbit of Jupiter, through their common intersection. This effect is analogous to that which the earth produces upon the moon, as we have seen in [5352, &c.], but it is much more sensible. Determination of its value [6337–6431]; § 10

Investigation of the terms which acquire very small divisors by integration in the expression of the latitude, in consequence of the nearly commensurable values of the mean motions of the three inner satellites. Estimates of their values [6432–6486] § 11

CHAPTER V. INEQUALITIES DEPENDING ON THE SQUARES AND PRODUCTS OF THE EXCENTRICITIES AND INCLINATIONS OF THE ORBITS 102

Calculation of these inequalities. It is sufficient to notice those only which have a long period [6487–6524] § 12

The terms which become the most important in the secular equations of the satellites, are those which depend on the secular variations of the equator and of the orbit of Jupiter, and on the motion of the nodes of the fourth satellite. They are analogous to those which produce the moon's secular equation, and the equation of the moon's motion depending on the longitude of its nodes. Calculation of these terms [6525–6555'] § 13

CHAPTER VI. ON THE INEQUALITIES DEPENDING ON T[IE SQUARE OF THE DISTURBING FORCE. 126

The most remarkable of these inequalities has already been discussed under its general form, in Book II. [1214' — 1242y]. It depends on the circumstance, that, at the origin of the motion, the mean longitude of the first satellite, minus three times that of the second, plus twice that of the third, was very nearly equal to the semi-circumference π ; and subsequently, by means of the mutual action of the three bodies upon each other, it became accurately equal to π. Development of the theory of these motions by a different method from that which is used in [1214', &c.]. From this it follows, as in [1242v], that the mean motions of the three inner satellites are subjected to a species of libration, and it is of importance for astronomers to investigate and determine the limits of this libration by observations. Hitherto it has appeared to be insensible. From this it follows that the relation which now exists between the mean motions of the three inner satellites, will continue unchanged to future ages. Moreover, the two inequalities of the first satellite, arising from the attractions of the second and third

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