VK 5tt AT UC-NRLF bbl CXb 13^ <2> NEW LOG AND VERSINE ALTITUDE TABLES ATTENTION! Would you ever think of going to the trouble of calculating the elements of the NAUTICAL ALMANAC, viz. declination, right ascension, equation of time, &c., by means of formulae and logarithms, when His Majesty's NAUTICAL ALMANAC Office tabulates these data every year? Certainly not. Would you ever think of working out your dead-reckoning by means of formulae and loga- rithms when the Plane Traverse Tables facili- tate the direct solution of all problems related thereto ? Not at all ! Why then go to the trouble to solve the as- tronomical triangle of position by means of complicated formulae and logarithms when we have tabulated its elements in our " Altitude and Azimuth Tables" (Spherical Traverse Tables) and have given the simplest and readiest methods for solving all problems related thereto? NEW LOG AND VERSINE ALTITUDE TABLES By LIEUTENANT R ABLER DE AQUINO BRAZILIAN NAVY [Reprinted from the author's "The 'Newest' Navigation Altitude and Azimuth Tables," 2nd edition, 1912.] 1912 LONDON J. D. POTTER Admiralty Agent for Charts 145, MINORIES, E.G. RIO DE JANEIRO D. N ORRIS Admiralty Sub- A gent for Charts 36, RUA DA ASSEMBLEA Price 2s. 6d. net M 9 NEW ALTITUDE TABLES A description of these Tables in Portuguese will be found in the Rcvista Maritima Braziltira for February, 1912, page 1335. 427358 NEW ALTITUDE TABLES HOW TO COMPUTE THE ALTITUDE OF A CELESTIAL BODY BY MEANS OF THE FOLLOWING TABLES When the Hour Angle (/) and the Declination (d) of a celestial body are given and also the Latitude (L) of the observer we may calculate very easily, very rapidly and with as great accuracy as necessary the Altitude (h) of a celestial body as follows : In the fundamental equation (1) cos (90 K) or sin ,6 = sin L sin d+cos L cos d cos / we make cos /= i 2 sin 2 - 2 and we have (2) cos (90 - h) = cos (L-d} 2 cos L cos d sin 2 - or I - cos (90 - h} i - cos (L d) + 2 cos L cos d sin 2 - If we make f- fi (3) 2 cos L cos d sin 2 - = versine 6 = 2 sin 2 - we will have finally (4) versine (90 - k) = versine (L-d) + versine Inverting equation (3), viz. : / f) 2 cos L cos d sin 2 -= 2 sin 2 - 2 2 and multiplying both members by 2 we have / fj sec L sec d cosec 2 - = cosec* - 2 2 Applying logarithms to both members and dividing by 2 we have / (5) 1/2 log sec Z+ 1/2 log sec dM-log cosec - = log cosec - Therefore by means of formulae (4) and (5) we can determine the Altitude with the aid of the following Tables. The Tables on pages 2* to 9* give us 1/2 log sec L or 1/2 log sec d. The Tables on pages 10* to 27* give us in columns marked " Hour Angle" the / f) log cosec - or log cosec - when we enter with / or 6 as arguments. In columns marked " Sum or Diff. " we find versine {L- d) and also in the same f\ columns versine 6 corresponding to the log cosec - given in columns marked " Hour Angle." The Tables on pages 28* to 36* give us log cosec - when / is comprised between 90 and 270. The Altitude corresponding to versine (90* ^) will be found from below in columns marked " Alt.," the minutes of which are to be found on the right hand side of the pages. Each versine and logarithm has been multiplied by io 6 in order to reduce it to a whole number. On this account no characteristics appear and no periods also. The numbers given correspond to six decimal places. When only five decimal place accuracy is desired drop the figure after the space or round up the fifth figure. ii* EXAMPLE I GREENWICH HOUR ANGLE WEST. The following expressions give us the value of t a . the Greenwich Hour Angle West; t a . = G. M. T. - Eq. of T. for the 4. = G. M. T. + R. A. M. S-R. A. for *, , and planets. LOCAL HOUR ANGLE WEST. Once known t a . the local hour angle west (t} is given by the expression ( when G is West and + when G is East) G standing for Longitude. When t Q . is smaller than G add 360 to t- . If t a . + G is larger than 360 drop 360 from it. EXAMPLE I. On February 21, 1910, about 8 h A.M. in Lat. by D. R. = 36* 52' N and Long, by D.R. = 86' W the Sun's true altitude was 21 7' at 2i h 6 m n 8 of the chronometer, 6 m 59 s slow of G. M. T. Required the D. R. altitude. C. = 2i h 6 m ii 8 C. C.= + 6 59 G. M. T. = 2i h 2i h 13 io 8 Eq. of T.= - 13 46 G. A. T. = 2o h 59 m 24 s or 4 = 314 51' G lv = 8 6 /=3o645' [logcosec *] 34858 L= 36 52 N [1/2 log sec L] 4845 d= io 27 S [1/2 log sec d\ 363 r\ [log cosec -] 40066 31609 [versine 0] 32205 [versine 63814 [versine (90-^)] ^ = 21 13' EXPLANATION. After applying the correction to the chronometer time and the equation of time to the G. M. T. we find the G. A. T. or / G . the Sun's Greenwich Hour Angle West t a . being G. A. T. converted into arc* The longitude by D. R. is combined with this t a ' giving us t : the local hour angle west. Thus we have t^ot> 45'. 1 This procedure, not usually followed in the text books, has the triple advantage of simpli- fying the determination of /, abolishing the argument in time in the tables and the necessity of dealing with data expressed in time and in arc after G. A. T. is converted. NEW ALTITUDE TABLES The declination of the Sun, found in the Nautical Almanac at the same time as the Eq. of T., is taken to the nearest minute of arc. It is combined with the latitude, as shown. When L and d are of the same name, both N or both S, subtract the smaller of the two from the larger. If they are of contrary names, as in our Examples, one N and the other S, add them together. We find L + d=47 19'. Entering the "Latitude or Declination" Tables with = 36 52' we find on page 5* : 4845, and with d= 10 27' we find on page 3* : 363. Entering the tables on page 20* from below 1 with /=3o6 45' in the "Hour Angle" column we find 34858, which, added to the numbers corresponding to L and d, gives us 40066. We look for this number 40066 on page 19* in the same " Hour Angle" column, and opposite it in column "Sum or Diff." we find 31609. Adding to this number 31609 the number 32205 found on page 19* corresponding to 47 19' in " Sum or Diff." column we have 63814. This number corresponds to 21 13' in the "Alt." column on page 23*. Therefore the altitude from D. R. is 21 13'. EXAMPLE II. On August 21, 1908, about ii h A.M. in Lat. by D. R. = i6 34' S. and Long, by D. R. = 38 11' W. the Sun's true altitude was 59 10' at i h i9 m 4O s of the chronometer 2 6 m $Q 8 slow of G. M. T. Required the D. R. altitude. C. = i h 19 40 s C. C.= + 26 59 G. M. T. = i h 46 m 39" Eq.ofT.= -_3 3_ G. A. T. = i h 43 m 36 s or t - 25* 54' 360 + 1 . = 385 54' G w = 38 ii '=347 43' 97067 /=347 43' L= 16 34 S 921 d= 12 10 N 493 98481 . . . 2143 L+d= 28 44' 12313 14456 ^=58 49' How TO FIND THE AZIMUTH. The Azimuth can be readily and easily found by methods explained on pages xxxvii and xxxviii of the "Altitude and Azimuth Tables." For the sake of further exercise we will find the Azimuth in one of the two examples above. Example. Given /=53 15' E, ^=10 27' S and = 36 52' N. Find the Azimuth. 1 When t is smaller than 180 we enter the tables at the top and the body is West of the meridian ; when t is greater than 180 we enter the tables from below and the body is East of the meridian. iv* HOW TO FIND THE AZIMUTH Entering the tables with d= 10 30' and /=53 we find on page 69 : # = 52 o' and b=\j. Combining b with L we have =54 and entering the tables again with = 52 o' and C=54 we find Z=57 42'. Generally (when Z<7O) it will not be necessary to combine b and L. It is only necessary to run down column j\ corresponding to # = 52 o' until we find /fc=2i 13 and alongside the value of the altitude we would find Z= 57 42'. In the same way we would find Z=2^ 41' in the second example. NOTE. It is evident that the Hour Angle t can be found given Z, d and h by using backwards the process for finding h given Z, d and t. The author takes this opportunity to thank his good friend Lieutenant Renato Bayardino, Brazilian Navy, for his kindness in organising the " Latitude or Declination " Tables and for carefully revising with him these new Altitude Tables. Latitude or Declination 1 2 3 4 5 6 7 8 9 o o 33 '3 3 298 530 828 1193 162 5 212 4 269 o I 34 13 5 301 534 833 120 163 2 213 3 270 o i 2 o o 3 5 '37 3 4 53 9 839 120 6 164 o 214 I 271 o 2 3 36 '39 308 543 845 121 3 l6 4 8 215 o 2720 3 4 38 141 547 850 122 165 6 215 9 2730 4 1 o o 39 40 144 146 3i 8 552 557 856 862 122 6 123 3 1664 167 2 2168 2177 2740 275 1 I O I 43 148 '5 I 322 325 561 566 86 7 873 124 o 1247 l6 79 l68 7 218 6 2195 276 277 I 9 I 44 X 5 3 328 57 878 125 3 l6 95 22O 4 278 9 10 O I 45 15 5 33 2 575 884 126 o 1703 221 3 279 10 ii I 46 15 7 33 5 579 890 126 7 171 i 222 2 280 n 12 O I 48 160 33 9 584 896 1274 171 9 223 2 281 12 13 2 49 163 342 589 902 128 i 1727 224 I 282 2 13 14 2 5 165 346 593 907 1288 1735 225 o 283 2 14 15 2 5 2 168 35 598 91 3 I2 95 1743 225 9 284 2 I| 1 6 2 53 170 35 3 603 9i 9 130 i *75 i 2268 285 3 10 17 o 3 5 4 17 3 357 607 925 130 8 '75 9 2277 286 3 17 18 3 56 17 5 360 61 2 93 131 5 1767 228 6 2873 18 19 3 57 178 3 6 4 617 93 6 1322 '77 5 229 6 288 4 19 20 04 59 18 o 368 622 942 1329 1784 230 5 2894 20 21 04 60 183 372 627 948 '33 6 1792 231 4 2904 21 22 04 62 185 375 631 954 1343 180 o 2323 291 5 22 23 5 63 18 8 379 63 6 96 o 180 8 233 3 292 5 23 24 5 65 19 i 383 641 96 6 1358 181 6 2342 293 6 24 2 5 06 66 193 386 646 972 136 5 182 5 235 i 294 6 25 26 06 68 19 6 39 651 978 1372 1833 236 i 2957 20 27 07 7 199 394 65 6 984 1379 1841 2370 2967 27 28 07 7 i 20 I 398 66 i 99 138 6 1849 238 o 2978 28 29 08 7 3 20 4 402 665 996 1393 1857 2389 298 8 29 30 08 74 207 45 67 o IOO 2 140 o 1866 2398 299 9 30 31 09 76 21 4 9 675 ioo 8 1408 1874 240 8 300 9 31 32 09 78 21 2 41 3 680 101 4 141 5 1882 241 7 302 o 32 33 o 79 21 5 4i 7 68 5 IO2 O 1422 189 i 2427 33 33 34 I 8 i 21 8 42 i 69 o 102 7 1429 1899 2436 304 i 34 35 I 83 22 I 425 696 i3 3 H37 1908 244 6 3052 35 36 2 85 224 429 70 i 103 9 1444 191 6 245 5 306 2 36 37 3 8 6 227 433 70 6 104 5 1924 246 5 373 37 38 4 88 22 9 437 71 i 105 i i45 9 J 93 3 2475 3084 38 39 4 90 232 44 i 716 105 8 1466 194 i 2484 395 39 40 5 92 23 5 445 72 i 1 06 4 147 3 !95 2494 3I 5 40 41 5 94 238 449 726 107 o 148 i 1958 2503 311 6 4 1 42 6 96 24 i 453 73 i 107 6 1488 1967 2513 3127 42 43 7 98 244 457 737 108 3 1496 1975 2523 3138 43 44 8 99 247 461 742 108 9 J 5 3 1984 2532 3H9 44 45 9 IO I 250 465 747 109 5 151 o J 993 2542 315 9 4 I 46 9 103 253 470 75 3 IIO 2 151 8 200 I 2552 3!7 40 47 2 10 5 256 474 758 I.I 08 i5 2 5 2O I O 256 2 318! 47 48 2 I 107 259 478 763 in 5 153 3 201 8 257 3192 48 49 2 2 10 9 262 482 768 I 12 I 154 202 7 2 5 8 3203 49 50 23 ii i 266 486 774 1127 1548 203 6 259 321 4 50 51 24 ii 3 26 9 49 i 779 113 4 155 6 2044 260 3225 51 52 25 ii 5 272 495 784 1140 156 3 205 3 26l 323 6 52 53 26 ii 7 27 5 499 79 1147 1571 206 2 262 o 3247 53 54 27 n 9 278 5 3 795 1154 1578 207 I 263 o 3258 54 55 2 8 12 2 282 508 80 i 116 o 158 6 208 o 264 o 3269 55 56 2 9 124 285 5 1 2 806 116 6 159 4 208 8 265 o 328 o 50 57 3 126 28 8 81 2 I1 7 3 1 60 i 2097 266 o 329 i 57 58 3 i 128 29 i 52 i 817 118 o 1 60 9 2IO 6 267 o 3302 58 59 32 130 29 5 52 5 822 118 6 161 7 211 5 268 o 33 1 3 59 60 3 3 13 3 298 828 IT 9 3 162 5 2124 269 o 3324 00 1 2 3 4 5 6 7 8 9 Latitude or Declination Latitude or Declination 10 n 12 13 14 15 JL," 16 17 18 19 332 4 4027 4798 5638 6 54 8 7528 8579 9702 1089 7 1216 5 I 333 5 43 9 481 i 5 6 5 3 6564 7545 8597 9721 1091 7 121.8 7 i 2 334 7 405 i 4825 5667 658 o 7562 861 5 974 i 1093 8 1 220 9 2 3 335 8 4064 4838 568 2 6 595 7579 8634 9760 1095 9 1223 o 3 4 3369 4076 4852 5 6 97 661 i 759 6 865 2 9779 1097 9 1225 2 4 1 3380 339 I 408 8 410 i 4865 4879 571 i 5726 6627 6643 7 61 3 7630 8670 8688 9799 981 8 1 100 1 102 12274 1229 6 I j 34 3 4 11 3 4892 574i 6659 7647 870 6 9838 1104 I 1231 8 7 g 34 1 4 412 6 4906 575 5 6675 7664 8725 9857 1106 2 12340 8 9 3425 4i3 8 491 9 577 669 o 768 i 8743 9876 1108 2 1236 2 9 10 343 7 415 o 4933 5785 670 6 7698 8761 9896 mo 3 1238 4 10 ii 3448 4 l6 3 4947 580 o 672 2 77I 6 878 o 991 6 11124 1240 6 ii 12 345 9 417 5 496 o 5814 6738 773 3 8798 993 5 1114 5 1242 8 12 13 347 I 418 8 4974 5829 6 754 775 881 6 995 5 1116 5 1245 13 14 3482 420 i 4988 5844 6770 7767 8835 9974 inS 6 12472 14 It 3493 35 5 421 3 422 6 500 i 5 01 5 5859 5874 678 6 6802 7784 7801 8853 8872 9994 looi 4 1 120 7 1122 8 12494 1251 6 11 11 35 1 7 3528 4238 425 i 5029 543 5889 594 681 9 6835 7819 7836 8890 8908 10033 1005 3 II249 1127 o 12538 1256 o 11 19 353 9 4263 55 6 59 1 9 685 i 7853 8927 1007 2 1129 o 1258 2 19 20 355 I 427 6 5070 593 4 6867 7871 8945 1009 2 1131 I 1260 4 20 21 3562 4289 5084 5949 688 3 7888 8964 IOII 2 11332 1262 6 21 22 3574 43 i 5098 5964 6899 7905 8982 1013 2 "35 3 12648 22 23 3585 431 4 511 2 5979 691 5 7923 900 i 1015 2 "374 1267 i 23 24 3597 4327 512 6 5994 693 2 7940 902 o 1017 I "395 12693 24 25 3609 4340 5'3 9 600 9 6948 7957 9038 1019 I 1141 6 1271 5 25 26 362 o 435 2 5'5 3 602 4 6964 7975 9057 1021 I "437 12737 26 27 363 2 43 6 5 5167 6039 698 o 7992 9076 1023 I 11458 1276 o 27 28 3 6 44 4378 518 i 6054 6997 801 o 994 1025 o 1148 o 1278 2 28 29 365 5 439 * 5*95 606 9 7 01 3 8027 9 11 3 1027 o 1150 i 1280 4 29 30 3667 4404 520 9 6084 7029 8045 9132 1029 o 1152 2 12827 30 31 3679 4- J. I 7 5223 609 9 7046 8062 9150 1031 o "543 12849 3 1 32 3690 442 9 5237 611 5 706 2 808 o 9169 10330 11564 1287 2 32 33 3702 4442 525 * 613 o 7078 8097 9188 10350 "585 12894 33 34 37 1 4 4455 5265 6145 795 811 5 9207 10370 1160 6 1291 6 34 35 3726 4468 528 o 616 o 7 II I 8i33 9225 1039 o 11628 1293 9 35 36 3738 448 i 5294 6176 7128 815 o 9244 1041 o 11649 1296 i 36 37 3749 4494 5308 619 i 7H4 8168 9263 1043 o 1167 o 1298 4 37 38 376 i 457 5322 620 6 716 i 8186 928 2 10450 1169 i 1300 6 38 39 3773 4520 533 6 622 2 7177 8203 9301 10470 1171 3 13029 39 40 3785 4533 535 6237 7194 822 i 9320 1049 o "734 1305 i 40 4 1 3797 4546 53 6 4 625 2 721 o 8239 9339 1051 I "75 5 !374 4 1 42 3809 455 9 5379 6268 7227 825 6 9358 1053 1 "777 13097 42 43 382 i 4572 5393 6283 7243 8274 9377 1055 1 11798 1311 9 43 44 3833 4585 5407 6298 726 o 8292 9396 1057 I 1182 o 13142 44 3 3845 3857 4599 461 2 542 i 5436 631 4 6329 7276 7293 831 o 8328 94 1 5 9434 10591 1061 2 1184 i "86 3 13165 13187 $ 47 3869 462 5 545 6345 73 10 8346 945 3 1063 2 1188 4 1321 o 47 48 388 i 4638 5464 636 o 7326 8363 9472 1065 2 11905 1323 3 48 49 3893 465 i 5479 6376 7343 8381 949 i 1067 2 11927 13255 49 So 39 5 466 5 5493 6391 7360 8399 951 o 10693 "949 13278 50 39 1 7 4678 55o8 6407 7377 8417 9529 1071 3 11970 133 i 51 52 3929 469 i 5522 6423 7393 8435 9548 11992 13324 52 53 394 i 4704 553 6 6438 741 o 8453 9567 10754 1201 3 13347 53 54 395 3 \ 555 i 6454 7427 8471 9586 10774 1203 5 1337 54 55 3966 473 i 55 6 5 6469 7444 8489 960 6 I794 1205 7 13392 55 56 3978 4744 6485 7461 8507 9625 1081 5 1207 8 1341 5 56 57 3990 475 s 5594 650 I 7477 8525 9644 1083 5 1210 13438 57 58 400 2 477 i 5609 651 7 7494 8543 966 3 1085 6 1212 2 1346 i 58 59 401 4 4784 5623 6532 751 i 856 i 9683 1087 6 I2I43 1348 4 59 60 402 7 4798 6548 7528 8579 9702 10897 1216 5 13507 60 10 11 12 13 14 15 1 6 17 1 8 19 Latitude or Declination Latitude or Declination 20 21 22 23 24 25 26 27 28 29 i . 14924 1641 7 17987 19635 2136 2 23170 2506 o 2703 3 2909 o I 1353 H948 16443 1801 4 19663 21392 2320 i 2509 2 2706 6 2912 5 I 2 1355 3 '4973 1646 8 1804 i 1969 1 2142 I 2323 2 25124 2710 o 2916 o 2 3 14997 1649 4 1806 8 1971 9 2145 I 2326 2 2515 6 27 1 3 3 2919 6 3 4 '3599 1502 i 1651 9 1809 4 19748 2148 o 23293 2518 9 27167 2923 i t* Hour Sum f\r Hour or Diff. Angle (si Diff. Angle Diff. Angle Ol Diff. Angle or Diff. Angle o 60307 76033 o 6642 o 7393 6 7 7281 6 71940 i 7949 5 734 5 86454 68212 i 60 I 6040 7 75997 2 66524 73902 6 72925 71907 6 79609 70003 4 86573 681824 59 2 6050 6 759 6r 4 66628 73868 6 73034 718752 7972 3 69972 4 8669 I 681527 58 3 6060 6 75925 6 6673 3 738346 73H 3 718427 79836 69941 4 8681 o 68123 * 57 4 6070 6 758899 66837 73800 6 7325 3 71810 3 79950 69910 5 86928 68093 4 56 5 60806 758542 66942 73766 6 73362 71778 o 8006 4 69879 5 87047 68063 8 55 6 6090 6 75818 6 6704 6 737327 7347 i 71745 6 8017 8 69848 6 8716 6 68034 2 54 7 6100 6 75783 o 6715 i 73698 8 7358 i 7!7 J 3 3 8029 3 698177 87285 68004 6 53 8 6110 6 75747 4 6725 6 73664 9 73690 71681 o 8040 7 69786 8 87403 67975 * 52 9 6120 6 757 11 8 67361 73631 i 7380 o 716487 8052 i 697560 87522 67945 5 Si 10 6130 6 75676 3 67466 73597 3 739 10 71616 4 8063 6 69725 2 87642 67916 o 50 ii 6140 7 75640 8 6757 i 73563 5 7401 9 715842 8075 o 69694 3 8776 i 67886 5 49 12 61507 75605 3 67676 735297 74129 715520 8086 5 69663 6 8788 o 678570 48 J 3 6160 7 755698 6778 i 73496 o 7423 9 715198 80979 69632 8 87999 67827 6 47 14 61708 755344 67887 73462 3 74349 714876 8109 4 69602 i 8811 8 67798 i 46 15 6180 9 75499 67992 73428 6 74459 7H55 5 8120 9 69571 3 88238 67768 7 45 16 6190 9 75463 7 6809 8 733949 7457 7H234 81324 69540 7 88357 67739 3 44 17 6201 o 75428 3 6820 3 7336i 3 7468 o 7*39* 3 8i439 69510 o 88477 67710 o 43 18 6211 i 75393 i 6830 9 73327 7 74790 713592 8i554 69479 3 88597 67680 6 42 19 6221 2 753578 6841 4 73294 i 74901 713272 81669 69448 7 8871 6 67651 3 4i 20 6231 3 75322 5 6852 o 73260 5 7501 i 712952 8178 4 69418 i 8883 6 67622 o 40 21 6241 4 752873 68626 732270 75122 71263 2 81899 69387 5 8895 6 675927 22 625 1 5 75252 2 68732 73193 5 75232 71231 2 8201 4 693570 89076 67563 4 38 23 6261 7 752170 68838 73160 i 75343 7II993 8213 o 693264 8919 6 67534 2 37 24 6271 8 75181 9 68944 73126 6 75454 711674 82245 69295 9 89316 67505 o 36 25 6281 9 751468 6905 o 73093 2 75565 7"355 8236 i 69265 4 89436 67475 7 35 26 6292 i 75111 7 69*57 73059 8 75676 711036 82477 69235 89557 67446 6 34 2 7 63023 75076 7 6926 3 73026 4 75787 71071 8 82592 69204 5 89677 674174 33 28 63124 75041 7 6936 9 72993 * 75898 71040 o 8270 8 69174 i 89798 67388 3 S 2 29 6322 6 75006 7 6947 6 729598 7600 9 71008 2 82824 69H3 7 8991 8 67359 * 3i 30 63328 74971 8 6958 2 72926 5 7612 o 70976 4 8294 o 691133 90039 673300 30 31 63430 74936 9 6968 9 72893 3 76232 70944 7 8305 6 69083 o 9015 9 67300 9 32 6353 2 74902 o 69796 72860 o 76343 70913 o 83172 69052 6 9028 o 67271 9 28 33 63634 74867 i 69903 72826 8 7645 5 70881 3 8328 8 69022 ' 9040 i 67242 8 27 34 6373 6 74832 3 70009 72793 6 76566 70849 6 83404 68992 o 90522 672138 26 35 63838 74797 5 7011 6 72760 5 76678 70818 o 83521 68961 8 90643 671848 25 36 63940 74762 7 70223 72727 4 76790 70786 3 83637 68931 5 90764 671558 24 37 6404 3 74728 o 733 i 72694 3 76902 70754 7 83754 68901 - 9088 5 67126 9 23 38 64145 74693 3 7043 8 72661 2 7701 3 70723 2 83870 68871 i 9100 6 67097 9 22 39 6424 8 74658 6 70545 72628 2 77'25 70691 6 83987 68840 9 91127 67069 o 21 40 6435 74623 9 7065 2 72595 * 77238 70660 i 8410 4 688107 91249 67040 i 20 4i 6445 3 74589 3 7076 o 72562 I 7735 70628 6 84220 68780 6 91370 67011 2 19 42 6455 6 745547 70867 72529 2 77462 70597 i 8433 7 68750 5 91492 669824 18 43 64659 74520 i 797 5 72496 2 77574 70565 6 84454 68720 4 9161 3 66953 5 17 44 64762 74485 6 71083 72463 3 77687 7534 2 8457 * 68690 '. 9*735 66924 7 16 45 6486 5 74451 o 71190 72430 4 77799 70502 8 8468 8 68660 3 91857 66895 9 15 46 64968 74416 6 71298 72397 5 7791 2 70471 4 84806 686302 91979 66867 j 14 47 6507 i 74382 i 71406 72364 7 78024 70440 o 84923 68600 2 9210 o 66838 4 13 48 65174 74347 7 7I5M 7233 1 9 78i37 70408 7 8504 o 68570 3 9222 2 66809 7 12 49 65278 74313 3 7162 2 72299 i 78250 70377 4 85158 68540 3 92345 66780 9 II 5 6538 i 74278 9 7 J 73 72266 3 78362 70346 i 85275 685103 92467 667522 10 5 1 65485 74244 6 7 l8 3 9 72233 6 78475 703148 85393 68480 4 92589 66723 6 9 S 2 65588 74210 2 7 J 947 72200 9 78588 70283 6 85510 68450 5 9271 I 66694 9 8 53 6569 2 74 J 75 9 7205 5 72168 2 78701 702524 85628 68420 7 9283 3 66666 3 7 54 65795 74141 7 72164 72135 5 78815 70221 2 85746 68390 8 92956 66637 6 6 55 65899 74107 4 72272 72102 9 78928 70190 o 85864 68361 o 93078 66609 5 56 6600 3 74073 2 72381 72070 3 79041 70158 8 8598 2 68331 i 9320 i 66580 5 4 57 6610 7 74039 i 72490 72037 7 79*54 701277 86100 68301 4 93324 66551 9 3 58 6621 i 74004 9 7259 8 72005 2 79268 70096 6 8621 8 68271 6 93446 66523 3 2 59 6631 5 73970 8 72707 719726 7938 i 70065 5 86336 68241 8 93569 66494 8 I 60 6642 o 739367 7281 6 71940 i 79495 70034 5 86454 68212 i 93692 66466 3 Alt. Hour Angle Alt. Hour Angle Alt. Hour Angle Alt Hour Angle Alt. Hour Angle / 69 339 68 338 67 337 66 336 65 335 14* 2, 5 2( ) 2! 7 2i 1 2C > / Sum Hour Sum Hour Sum rtf* Hour Sum i-\t* Hour Sum At" Hour or Diff. Angle or Diff. Angle Ul Diff. Angle or Diff. Angle HI Diff. Angle o 9369 2 66466 3 IOI20 6 64791 2 10899 3 63181 5 117052 61632 5 12538 o 601400 60 I 938i 5 66437 8 10133 3 64763 8 10912 6 63155 2 11718 9 61607 2 12552 I 60115 ^ 59 2 9393 8 66409 4 10146 i 64736 5 10925 8 63128 9 11732 6 61581 8 12566 2 60091 2 58 3 9406 i 66380 9 10158 9 64709 2 10939 o 63102 6 11746 2 615565 12580 4 60066 8 4 9418 5 66352 5 10171 7 64681 9 10952 2 63076 4 "759 9 6I53 1 3 J2594 5 60042 5 56 ,j 94308 66324 i 101844 64654 6 10965 5 63050 i 117736 61506 o 12608 6 60018 i 55 5 9443 * 66295 7 10197 2 64627 4 10978 7 63023 9 117873 614808 12622 8 59993 8 54 7 9455 5 66267 4 IO2IO O 64600 i 10992 o 62997 7 11801 o 6i455 5 12636 9 59969 4 53 8 94678 66239 10222 8 64572 9 II005 2 62971 5 118147 614303 12651 i 59945 i S 2 9 9480 2 66210 7 10235 7 64545 7 11018 5 62945 4 11828 4 61405 i 12665 2 59920 8 Si 10 9492 5 661824 10248 5 64518 5 11031 8 62919 2 H842 2 61379 9 12679 4 59896 5 5 IX 95049 66154 i 10261 3 64491 3 11045 I 62893 i 11855 9 613548 12693 6 59872 3 49 12 95*73 66125 8 10274 2 64464 2 11058 4 62867 o 11869 6 613296 12707 8 59848 o 48 13 95 2 97 66097 6 10287 o 64437 11071 7 62840 9 11883 4 61304 5 12722 o 59823 8 47 14 9542 i 66069 3 10299 9 64409 9 11085 o 628148 11897 2 61279 3 12736 2 59799 5 46 15 9554 5 66041 i 103127 64382 8 11098 3 62788 7 11910 9 612542 12750 4 59775 3 45 16 95669 66012 9 10325 6 6 4355 7 inn 6 62762 7 119247 61229 x 127646 5975 1 i 44 17 9579 3 65984 8 10338 5 64328 7 11124 9 62736 6 "938 5 61204 i 12778 8 59726 9 43 18 959 1 7 65956 6 10351 4 64301 6 11138 3 62710 6 11952 3 61179 12793 i 59702 8 42 19 96042 65928 5 10364 2 64274 6 11151 6 62684 6 11966 i 61153 9 12807 *4 59678 6 4i 20 96166 65900 4 10377 I 64247 6 11165 o 62658 6 "9799 61128 9 12821 6 59654 5 40 21 9629 i 65872 3 10390 I 64220 6 11178 3 62632 6 "993 7 61103 9 12835 8 59630 3 22 9 6 4i 5 65844 2 10403 o 64193 6 11191 7 62606 7 12007 5 61078 9 12850 i 59606 2 38 23 96540 65816 10415 9 64166 7 11205 i 62580 8 I202I 3 61053 9 12864 3 59582 I 37 2 4 9666 5 65788 10428 8 641397 11218 5 625548 12035 I 61028 9 12878 6 595580 36 2C 9678 9 65760 10441 8 64112 8 11231 8 62528 9 12049 61004 12892 9 59534 35 2O 9691 4 6 5732 10454 7 64085 9 11245 2 62503 o 12062 8 60979 12907 2 59509 9 34 27 9703 9 6 574 10467 7 64059 o 11258 7 62477 2 12076 7 60954 i 12921 5 59485 9 33 28 97164 65676 10480 6 64032 2 11272 i 6245 x 3 12090 5 60929 2 12935 8 59461 i 32 29 9728 9 65648 2 10493 6 64005 3 11285 5 62425 5 121044 60904 3 12950 i 59437 8 3i 3 974i 5 65620 3 10506 6 63978 5 11298 9 62399 7 12118 3 60879 4 12964 4 594I3 8 30 31 9754 655924 "S^S 63951 6 113123 62373 9 I2I32 2 60854 6 12978 8 593898 32 9766 5 65564 5 105325 63924 8 113258 62348 i 12146 I 60829 7 12993 i 59365 9 28 33 9779 i 655366 I0 545 5 63898 i 113392 62322 3 12160 o 60804 9 13007 4 59341 9 27 1 S 4 979 1 6 65508 8 I0 55 8 5 63871 3 113527 62296 5 12173 9 60780 i 13021 593i8o 26 35 9804 2 65480 9 10571 6 63844 6 11366 2 62270 8 121878 60755 3 13036 i 592940 25 36 9816 7 6 5453 i 10584 6 63817 8 113796 62245 i I22OI 7 60730 5 13050 5 59270 i 24 37 9829 3 65425 3 10597 6 63791 i "393 i 62219 4 12215 6 60705 7 13064 c 59246 2 2 3 38 9841 9 65397 6 10610 6 63764 4 11406 6 62193 7 12229 6 60680 9 13079 3 59222 3 22 39 9 8 545 65369 8 10623 7 63737 7 11420 i 621680 12243 5 60656 2 13093 6 59*98 5 21 40 98671 65342 i 10636 7 63711 i H4336 62142 3 12257 5 60631 5 13108 o 59*746 2O 4 1 98797 6 53H3 10649 8 63684 4 11447 i 62116 7 12271 4 60606 8 13122 4 591508 J 9 42 98923 652866 10662 9 63657 8 i 1460 6 62091 i 12285 4 60582 i 131368 59126 9 1 8 43 9904 9 652590 10675 9 63631 2 114742 62065 4 122994 605574 13151 3 59 I0 3 * 17 44 99i7 5 65231 3 10689 o 63604 6 114877 62039 9 123133 605327 '3 l6 57 59079 3 16 45 99302 65203 7 10702 i 63578o II50I 2 62014 3 12327 3 60508 i 13180 i 5955 5 15 46 99428 65176 o 10715 2 6355 1 5 115148 619887 12341 3 60483 /] 131946 59031 8 J 4 47 9955 5 651484 10728 3 63524 9 11528 3 61963 2 !2355 3 60458 8 132090 59008 o 13 48 9968 i 65120 8 10741 4 63498 4 11541 9 619376 123693 60434 2 13223 4 58984 3 12 49 9980 8 6 593 3 i754 5 6347 1 9 "5555 61912 I 12383 3 60409 6 132379 58960 5 II 50 9993 5 65065 7 10767 7 63445 4 115690 6l8866 "3974 60385 o 132524 58936 8 IO Si 10006 i 65038 2 10780 8 634190 11582 6 6l86l I 12411 4 60360 5 13266 9 58913 i 52 10018 8 65010 7 10793 9 63392 5 "5962 6l8357 12425 4 60335 9 13281 3 588894 53 10031 5 64983 * 10807 i 63366 i 116098 6l8lO 2 I2 439 5 60311 4 132958 58865 7 7 54 10044 2 64955 7 10820 2 63339 6 "6234 617848 12453 5 60286 8 133103 58842 i 6 55 10056 9 64928 2 108334 633132 116370 617594 12467 6 60262 j 133248 588184 5 56 10069 6 64900 8 10846 6 63286 9 11650 7 617339 12481 7 60237 9 133393 58794 8 4 57 10082 4 64873 4 10859 8 63260 5 11664 3 61708 6 12495 8 60213 4 X 3353 9 58771 2 3 58 10095 i 64846 o 10872 9 63234 i 116779 61683 2 12509 8 60188 9 133684 58747 6 2 59 10107 8 64818 6 10886 i 63207 8 11691 6 616578 12523 9 60164 f 133829 587240 I 60 IOI20 6 64791 2 10899 3 63181 5 117052 61632 5 125380 60140 o J 3397 5 58700 4 o Hour Hour Hour Hour Hour Alt Angle Alt. Angle Alt. Angle Alt. Angle Alt. Angle 6 4 334 |6 3 333 62 332 61 331 60 330 15' 30 31 32 33 34 / Sum At* Hour Sum f\t* Hour Sum Of* Hour Sum f\f Hour Sum Hour 1/1 Diff. Angle \JL Diff. Angle \Ji Diff. Angle \JL Diff. Angle or Diff. Angle 13397 5 58700 4 14283 3 573'Q i '5'95 2 55966 2 161.329 54665 8 17096 2 534o6 5 60 I 134120 58676 8 14298 3 57287 3 15210 6 55944 ' 16148 8 54644 5 I7II25 533858 59 2 13426 6 58653 3 i43'32 57264 6 15226 o 55922 2 161646 54623 2 17128 8 533652 58 3 '344' i 58629 7 14328 2 57241 8 15241 5 55900 2 16180 5 54601 9 17145 i 53344 5 57 4 I345S7 58606 2 '4343 3 572191 152569 55878 2 16196 4 5458o 6 17161 4 533239 56 5 1 3470 3 585827 14358 3 571964 152723 558562 16212 2 545593 171777 53303 3 55 6 134849 58559 2 '4373 3 57'737 15287 8 558342 16228 i 54538 i 171940 532827 54 7 134994 585357 H388 3 57151 o '5303 3 558123 162440 545168 172103 53262 i 53 8 '35'4o 585122 14403 4 57128 3 '53i87 5579 4 162599 54495 6 17226 6 53241 5 S 2 9 135287 58488 8 144184 57'5 6 '53342 55768 4 16275 8 54474 4 17242 9 53221 o Si 10 13543 3 58465 3 '4433 4 57083 o '53497 55746 5 16291 7 54453 ' 17259 3 53200 4 50 IZ '35579 58441 9 14448 5 57060 3 153652 55724 6 16307 6 5443' 9 17275 6 53'79 8 49 12 '357*5 58418 5 14463 6 57037 7 153807 5572 7 16323 6 544107 17291 9 53'593 48 13 '35 8 72 58395 ' 14478 6 57oi5 i 153962 556808 163395 54389 6 I73o8 3 531388 47 14 13601 8 58371 7 '4493 7 56992 5 i54"7 556590 163554 54368 4 173247 53"83 46 15 136164 58348 3 14508 8 569699 15427 2 55637 ' '6371 4 54347 2 '734' o 53097 8 45 16 13631 i 583249 H523 9 56947 3 154427 556i53 '63873 54326 i '73574 53077 3 44 17 13645 8 58301 6 '4539 56924 8 15458 3 555934 16403 3 54304 9 '7373 8 530568 43 18 13660 4 58278 3 '4554!' 56902 2 '5473 8 5557' 6 164193 54283 8 17390 2 53036 3 42 19 '3 6 75 ' 582549 145692 568797 154894 555498 16435 2 54262 7 17406 6 530158 4i 20 13689 8 58231 6 145844 56857 I 155049 55528o 16451 2 54241 6 17423 o 52995 4 4 21 i374 5 58208 3 '4599 5 56834 6 155205 555062 16467 2 54220 5 '74394 5 2 974 9 22 137192 58185 o 14614 6 56812 i '5536o 55484 5 16483 2 54'994 '7455 8 52954 5 38 23 '3733 9 58161 8 146298 567896 I555I 6 55462 7 164992 54178 3 17472 2 52934 ' 37 24 13748 6 581385 14644 9 56767 i 155672 5544' o '65152 54'573 17488 7 529137 36 25 i37 6 3 4 58"5 3 14660 i 56744 7 155828 554192 16531 2 541362 17505 ' 52893 3 35 26 13778 i 58092 i 14675 2 56722 2 155984 55397 5 ' 6 547 3 54"52 '752i 5 52872 9 34 27 137928 58068 8 14690 4 56699 8 15614 o 55375 8 16563 3 54094 2 i7538o 52852 5 33 28 13807 6 58045 6 14705 6 56677 4 15629 6 55354 ' 165793 54073 2 '75544 52832 i 32 29 138223 58022 4 14720 8 5 6 6549 15645 2 553324 '6595 4 54052 2 175709 528118 31 30 13837 * 57999 3 147360 56632 5 15660 9 553107 16611 4 54031 2 175874 52791 4 3 ! 31 13851 8 57976 i 14751 2 56610 2 156765 55289 ' 16627 5 54010 2 17603 9 52771 ' 32 13866 6 57953 14766 4 565878 15692 i 552674 16643 5 539892 17620 3 5 2 75o8 28 33 13881 4 57929 8 14781 6 565654 157078 55245 8 16659 6 53968 3 17636 8 52730 5 27 1 34 138962 57906 7 14796 8 56543 I 157234 55224 i 166757 53947 3 17653 3 527102 26 j 35 13911 o 57883 6 14812 i 565207 '5739 ' 55202 5 16691 8 53926 4 17669 8 526899 25 36 13925 8 57860 5 14827 3 56498 4 157548 551809 16707 9 53905 4 176864 526696 24 37 139406 578374 14842 5 56476 i 157704 55'593 16724 o 538845 17702 9 52649 3 23 38 '39554 578i4 3 14857 8 56453 8 15786 i 55'377 16740 i 53863 6 177194 526290 22 39 13970 2 5779' 3 14873 i 56431 5 15801 8 551162 167562 53842 7 '7735 9 52608 8 21 40 13985 I 57768 2 14888 3 56409 2 '58i75 55094 6 16772 3 53821 8 17752 5 52588 5 20 4i '3999 9 57745 2 14903 6 563869 '58332 55073 ' 16788 5 53801 o 17.769 o 52568 3 J 9 42 14014 8 57722 2 14918 9 563647 158489 555' 5 16804 6 5378o i 17785 6 52548 i 18 43 14029 6 57699 2 14934 2 563424 158646 550300 16820 7 537593 17802 2 52527 9 17 44 14044 5 57676 2 '4949 5 56320 2 158804 55oo8 5 168369 53738 4 17818 7 52507 7 16 45 14059 4 57653 2 14964 8 56298 o 15896 i 54987 16853 o 537I7 6 17835 3 52487 5 15 46 14074 2 57 6 3 3 14980 i 56275 8 15911 8 54965 5 16869 2 53696 8 17851 9 52467 3 J 4 47 14089 I 57607 3 '4995 4 562536 159276 54944 o 16885 4 536760 17868 5 52447 ' *3 48 14104 o 575844 15010 7 56231 4 '5943 3 54922 5 16901 6 536552 17885 i 52427 o 12 49 14118 9 5756i 4 15026 i 56209 2 '5959 ' 54901 i 169177 536344 17901 7 52406 8 II 50 HI338 57538 5 15041 4 56187 I '5974 9 54879 6 '6933 9 536136 17918 3 523867 IO 5i 14148 7 575'5 6 150567 561649 159906 54858 2 16950 i 535928 '79349 523665 9 52 14163 6 57492 7 15072 i 561428 16006 4 54836 8 16966 3 535721 '795' 5 523464 8 53 14178 6 57469 9 150875 56120 7 l6o22 2 548i54 16982 6 5355' 4 17968 2 523263 7 54 '4'935 57447 15102 8 56098 6 16038 o 54794 o 16998 8 535306 17984 8 52306 2 6 55 14208 4 57424 2 15118 2 56076 5 16053 8 54772 6 17015 o 535099 18001 5 52286 I 5 56 14223 4 574' 3 151336 560544 16069 6 5475' 2 17031 2 534892 18018 i 52266 o 4 57 14238 4 57378 5 151490 56032 3 16085 4 54729 8 17047 5 53468 5 18034 8 522460 3 58 '4253 3 573557 151644 56010 3 16101 3 547o8 5 17063 7 53447 8 18051 4 52225 9 2 59 14268 3 573329 151798 559882 16117 i 54687 i 17080 o 53427 i 18068 i 52205 9 I 60 14283 3 57310 i '5'95 2 559662 16132 9 54665 8 17096 2 534o6 5 180848 521858 O | Hour Hour Hour Hour Hour Alt. Angle Alt. Angle Alt. Angle Alt. Angle Alt. Angle / 59 329 58 328 57 327 56 326 55 325 16* 35 36 37 38 39 / Sum Hour Sum Hour Sum Hour Sum Hour Sum Hour or Diff. Angle or Diff. Angle or Diff. Angle or Diff. Angle or Diff. Angle 18084 8 52185 8 19098 3 51001 8 20136 4 49852 4 21198 9 48735 8 22285 4 4765 5 60 I 18101 5 52165 8 191154 50982 3 20154 o 49833 5 212168 487175 22303 7 47632 6 59 2 18118 2 52145 8 19132 5 50962 9 20171 5 498146 212348 48699 i 22322 o 476148 H 3 181349 52125 8 19149 6 5943 5 20189 o 49795 8 212527 48680 8 22340 4 47597 57 4 18151 6 52105 8 19166 7 50924 i 20206 5 49776 9 21270 6 48662 5 22358 7 47579 2 56 5 18168 3 52085 8 19183 9 50904 7 20224 i 4975 8 * 21288 6 48644 2 22377 4756i 4 55 6 18185 52065 8 19201 o 50885 3 20241 6 49739 3 21306 5 48625 9 22395 4 47543 6 54 7 18201 8 52045 8 19218 i 50865 9 20259 2 49720 4 213244 48607 6 22413 7 47525 8 53 8 18218 5 52025 9 *9235 3 50846 5 20276 7 49701 6 213424 48589 3 22432 i 47508 o 52 9 18235 2 52005 9 19252 5 50827 2 20294 3 49682 8 21360 4 4857 1 i 22450 4 4749 3 Si 10 18252 o 51986 o 19269 6 50807 8 20311 8 49664 o 21378 3 485528 22468 8 47472 5 So IX 18268 7 51966 i 19286 8 50788 5 20329 4 49645 2 213963 48534 5 22487 2 47454 8 49 12 18285 5 51946 i 19304 o 50769 2 20347 o 49626 5 2I4H3 485163 22505 6 47437 o 48 13 18302 3 51926 2 19321 i 50749 8 20364 6 49607 7 214323 48498 i 22523 9 47419 3 47 14 18319 i 519063 19338 3 573o 5 20382 2 495890 214503 48479 8 22542 3 47401 6 46 IS 183358 51886 5 *9355 5 50711 2 20399 8 49570 2 21468 3 48461 6 22560 7 47383 8 45 16 183526 51866 6 *93727 50691 9 20417 4 4955 1 5 21486 3 48443 4 22579 i 47366 i 44 17 183694 518467 19389 9 50672 7 20435 o 4953 2 7 215043 48425 2 22597 6 47348 4 43 18 18386 2 518269 19407 2 5 6 53 4 20452 7 495140 215224 48407 o 22616 o 473307 42 19 18403 o 51807 o 194244 5 6 34 i 20470 3 49495 3 215404 48388 8 22634 4 473130 4i 20 184199 5^872 19441 6 506149 20487 9 49476 6 215584 4837 6 22652 8 47295 4 40 21 18436 7 5'7 6 73 19458 9 50595 6 20505 6 49457 9 215765 48352 5 22671 3 47277 7 22 l8 453 5 5 '747 5 19476 i 557 6 4 20523 2 49439 2 215945 48334 3 22689 7 47260 o 38 23 18470 4 517277 19493 4 5557 2 20540 9 49420 6 21612 6 483162 22708 2 47242 4 37 2 4 18487 2 517079 19510 6 50537 9 20558 5 49401 9 21630 6 48298 o 22726 6 47224 7 36 2 5 18504 i 51688 i *95279 55 l8 7 20576 2 49383 2 21648 7 48279 9 22745 i 47207 i 35 26 18520 9 51668 4 *9545 2 5499 5 20593 9 49364 6 216668 48261 8 22763 6 47 l8 9 5 34 27 185378 5 i 648 6 195624 50480 4 20611 6 49345 9 216849 48243 6 22782 i 47171 8 33 28 185547 51628 8 *95797 50461 2 20629 3 49327 3 21703 o 48225 5 22800 5 47*542 32 29 18571 6 51609 i 195970 504420 20647 o 493o8 7 21721 i 48207 4 22819 471366 3i 30 18588 4 5^893 196143 50422 8 20664 7 49290 i 217392 481893 22837 5 471190 30 31 18605 3 515696 19631 6 5 403 7 20682 4 49271 5 217573 48171 3 22856 o 47101 4 32 18622 2 5 r 549 9 19648 9 503846 2,0700 i 49252 9 21775 4 481532 22874 6 47083 9 28 33 18639 2 515302 19666 2 50365 4 20717 8 49234 3 21793 5 48i35 J 22893 i 47066 3 27 34 18656 i S 1 S* $ 19683 6 50346 3 20735 6 492157 21811 7 481171 22911 6 47 48 7 26 35 18673 514908 19700 9 50327 2 20753 3 49197 2 218298 48099 o 22930 i 47031 2 25 36 18689 9 51471 i 19718 2 50308 i 20771 o 49178 6 218480 48081 o 22948 7 47013 6 24 37 18706 9 5H5 1 5 *9735 6 50289 o 20788 8 49160 o 21866 i 48062 9 22967 2 46996 i 2 3 38 18723 8 5H3' 8 *975 2 9 50269 9 20806 5 49141 5 21884 3 48044 9 22985 8 46978 5 22 39 18740 8 51412 i 19770 3 50250 8 20824 3 49 I2 3 219024 48026 9 23004 3 46961 o 21 40 187577 5*392 5 197877 50231 8 20842 i 49104 4 21920 6 48008 9 23022 9 46943 5 2O 4 1 18774 7 5*3729 19805 o 502127 20859 9 49085 9 21938 8 47990 9 23041 5 46926 o 19 42 18791 6 5*353 3 19822 4 50193 6 20877 6 49067 4 219570 47972 9 23060 o 46908 5 18 43 18808 6 51333 6 198398 50174 6 20895 4 49048 9 21975 i 47954 9 23078 6 46891 o 17 44 18825 6 S^HO 198572 5 OI 55 6 20913 2 49030 4 21993 3 47936 9 23097 2 46873 5 16 45 18842 6 5*2945 19874 6 50136 6 20931 o 49012 o 2201 I 6 479190 231158 468560 15 46 18859 6 512749 19892 o 50117 5 20948 8 48993 5 22029 8 47901 o 231344 46838 6 J 4 47 18876 6 5*255 3 199094 50098 5 20966 7 48975 o 22048 o 47883 i 231530 46821 i J 3 48 18893 6 5*235 7 19926 9 50079 6 20984 5 48956 6 22066 2 47865 i 23171 6 46803 7 12 49 18910 6 5I2l6 2 19944 3 50060 6 21002 3 48938 i 22084 4 47847 2 231903 46786 2 IX 50 18927 7 51196 6 19961 7 50041 6 21020 2 489197 22102 7 47829 3 23208 9 46768 8 10 5i 189447 51177 i 19979 2 50022 6 21038 o 48901 3 22120 9 478n 3 23227.5 4675 l 3 9 52 18961 7 5**57 6 19996 6 50003 7 210559 48882 8 221392 47793 4 23246 2 4 6 733 9 8 53 18978 8 51138 i 20014 i 49984 7 21073 7 48864 4 221574 47775 5 232648 467165 7 54 18995 8 51118 6 20031 5 49965 8 21091 6 48846 o 221757 47757 6 23283 5 46699 i 6 55 19012 9 51099 i 20049 o 49946 9 21109 5 48827 6 22194 o 47739 8 23302 i 46681 7 5 S^ 19030 o 51079 6 20066 5 49927 9 211273 48809 3 22212 2 47721 9 23320 8 46664 3 4 57 19047 o 51060 i 20084 o 49909 o 2II45 2 4879 9 22230 5 47704 o 23339 5 46646 9 3 58 19064 i 510407 20101 5 49890 i 21163 I 48772 5 22248 8 47686 2 23358 2 46629 6 2 59 19081 2 5I02I 2 20118 9 49871 2 21181 o 48754 2 22267 I 47668 3 23376 9 46612 2 I 60 19098 3 51001 8 20136 4 498524 21198 9 48735 8 22285 4 47650 5 23395 6 46594 8 O Hour Hour Hour Hour Hour Alt. Angle Alt. Angle Alt. Angle Alt. Angle Alt. Angle / 54 324 53 323 52 322 5i 321 50 320 17* 40 41 42 43 44 1 I Sum e\r Hour Sum f\f Hour Sum r\f* Hour Sum Hour Sum Hour vi Diff. Angle ur Diff. Angle or Diff. Angle or Diff. Angle or Diff. Angle o 23395 6 46594 8 24529 o 45567 5 25685 5 44567 i 26864 6 43592 5 28066 o 42642 5 60 I 234H 3 46577 5 24548 i 455506 25705 o 44550 6 26884 5 4357 6 4 28086 2 42626 8 59 2 23433 o 46560 i 24567 2 455337 25724 5 44534 2 26904 3 43560 4 28106 4 426ll 2 58 3 2345 * 7 46542 8 24586 3 455^68 25743 9 445178 26924 2 43544 4 28126 7 42595 6 57 4 23470 4 4 6 5 2 5 5 24605 4 455000 25763 4 445i 3 26944 o 43528 4 28146 9 42580 o Is 5 23489 i 46508 2 24624 5 45483 i 25782 9 44484 9 26963 9 435*24 28167 i 425644 55 6 23507 9 46490 8 24643 7 45466 2 25802 4 44468 5 26983 8 43496 4 281874 42548 8 54 7 23526 6 46473 5 24662 8 45449 4 25821 9 44452 i 27003 7 4348o 4 28207 6 42533 2 53 8 23545 3 46456 2 24681 9 45432 6 25841 4 44435 7 27023 5 43464 4 28227 9 425176 S 2 9 23564 i 46439 o 24701 i 45415 7 25860 9 44419 3 27043 4 43448 4 28248 i 42502 o Si 10 23582 9 46421 7 24720 2 45398 9 25880 5 44402 9 27063 3 43432 4 28268 4 42486 4 50 ii 23601 6 46404 4 24739 4 45382 i 25900 o 44386 5 27083 2 434i6 5 28288 7 42470 9 49 12 236204 46387 i 24758 5 45365 3 259195 44370 i 27103 I 43400 5 28308 9 42455 3 48 13 23639 2 46369 9 24777 7 45348 5 25939 * 44353 8 271230 433846 28329 2 42439 8 47 M 23658 o 46352 6 24796 8 45331 7 25958 6 44337 4 27143 o 43368 6 28349 5 42424 2 46 15 23676 8 463354 248160 453H9 25978 2 44321 i 27162 9 433527 283698 42408 7 45 16 23695 6 46318 2 24835 2 45298 i 25997 7 44304 7 271828 433368 28390 i 42393 * 44 17 237H4 46300 9 24854 4 4528i 3 26017 3 44288 4 27202 8 433208 28410 4 42377 6 43 18 23733 2 46283 7 24873 6 45264 6 26036 9 44272 o 272227 43304 9 28430 7 42362 i 42 19 237520 46266 5 24892 8 45247 8 26056 5 44255 7 27242 7 43289 o 28451 o 42346 6 4i 20 23770 8 46249 3 24912 o 45231 i 26076 i 44239 4 27262 6 43273 i 28471 4 42331 i 40 21 23789 6 46232 i 24931 2 452143 26095 7 44223 i 27282 6 43257 2 28491 7 42315 6 22 23808 5 462149 24950 4 451976 26115 2 44206 8 27302 6 43241 3 28512 o 42300 i 38 23 23827 3 461977 24969 7 451809 26134 9 44190 5 27322 5 43225 4 285324 42284 6 37 2 4 23846 2 461806 24988 9 45164 i 261545 44174 2 27342 5 43209 6 285527 42269 i 36 25 23865 o 461634 25008 i 45H74 26174 i 441579 27362 5 431937 28573 i 42253 6 35 26 23883 9 46146 2 25027 4 45*307 261937 44141 7 27382 5 431778 28593 4 42238 2 34 27 23902 8 46129 I 25046 6 451140 26213 3 441254 27402 5 431620 28613 8 42222 7 33 28 23921 6 461 12 O 25065 9 45097 3 26233 o 44109 i 27422 5 43146 i 28634 2 42207 3 32 29 23940 5 46094 8 25085 2 45080 7 26252 6 44092 9 27442 5 43*3 3 28654 6 42191 8 3i 30 239594 46077 7 251044 450640 26272 3 44076 6 27462 6 43"44 28675 o 421764 30 31 23978 3 46060 6 25*237 4547 3 26291 9 44060 4 27482 6 43098 6 28695 3 42160 9 32 23997 2 46043 5 25H30 450307 26311 6 44044 2 27502 6 43082 8 287157 42145 5 28 33 24016 i 46026 4 251623 450140 26331 3 44027 9 27522 7 43067 o 28736 i 42130 i 27 34 24035 o 46009 3 25181 6 44997 4 26350 9 4401 i 7 27542 7 435! 2 28756 6 421147 26 35 24053 9 45992 2 25200 9 44980 7 26370 6 43995 5 27562 8 43035 4 28777 o 42099 2 25 36 24072 9 45975 i 25220 2 44964 i 26390 3 43979 3 27582 8 43019 6 28797 4 42083 8 24 37 24091 8 45958 o 252395 44947 5 26410 o 43963 i 27602 9 43003 8 288178 42068 4 23 38 241107 45941 o 25258 8 44930 8 26429 7 43946 9 27622 9 42988 o 28838 3 42053 o 22 39 24129 7 45923 9 25278 2 44914 2 26449 4 4393 7 27643 o 42972 2 28858 7 42037 7 21 40 24148 6 45906 9 25297 5 44897 6 26469 i 439H 5 27663 i 42956 5 28879 i 42022 3 20 4i 24167 6 458898 253168 44881 o 26488 8 43898 4 27683 2 42940 7 28899 6 42006 9 19 42 241866 45872 8 253362 44864 4 26508 5 43882 2 2773 3 42924 9 28920 i 4*99* 5 18 43 24205 5 458558 25355 5 44847 9 26528 3 43866 I 27723 4 42909 2 28940 5 419762 17 44 24224 5 45838 7 25374 9 44831 3 26548 o 43849 9 27743 5 42893 4 28961 o 419608 16 45 24243 5 45821 7 25394 3 448147 26567 7 43833 8 27763 6 42877 7 28981 5 4^945 5 15 46 24262 5 45804 7 25413 6 44798 2 26587 5 438176 27783 7 42862 o 29001 9 41930 i M 47 24281 5 45787 7 25433 o 44781 6 26607 3 43801 5 27803 8 42846 3 29022 4 419148 13 48 24300 5 45770 7 254524 44765 i 26627 o 43785 4 27824 o 42830 5 29042 9 418995 12 49 24319 5 45753 8 25471 8 44748 5 26646 8 43769 3 27844 i 428148 29063 4 418842 II 50 24338 5 45736 8 25491 2 44732 o 26666 6 43753 2 27864 3 42799 i 29083 9 41868 8 10 Si 24357 5 457198 255106 44715 5 26686 3 43737 i 27884 4 42783 4 291044 41853 5 9 52 24376 6 45702 9 255300 44699 o 26706 i 43721 o 27904 6 42767 7 29125 o 418382 8 53 24395 6 45685 9 25549 4 44682 4 26725 9 43704 9 27924 7 42752 i 29H5 5 41822 9 7 54 24414 6 45669 o 25568 8 44665 9 26745 7 43688 8 27944 9 4 2 736 4 29166 o 41807 6 6 55 24433 7 456520 25588 3 44649 4 26765 5 43672 7 27965 i 42720 7 29186 5 417924 5 56 24452 8 45635 i 25607 7 44633 o 26785 3 43 6 567 27985 2 42705 o 29207 i 41777 i 4 57 24471 8 45618 2 25627 2 44616 5 26805 i 43640 6 28005 4 42689 4 29227 6 41761 8 3 5 24490 9 45601 3 25646 6 44600 o 26825 o 43624 5 28025 6 42673 7 29248 2 41746 5 2 59 245100 455844 25666 i 44583 5 26844 8 43608 5 28045 8 42658 i 29268 8 4i73i 3 I 60 24529 o 45567 5 25685 5 44567 i 26864 6 43592 5 28066 o 42642 5 29289 3 41716 o Hour Hour Hour Hour Hour Alt Angle Alt. Angle Alt. Angle Alt. Angle Alt. Angle t 49 319 48 318 47 317 46 316 45 315 i 18= 45 46 47 48 49 / Sum Hour Sum Hour Sum Hour Sum Hour Sum Hour or Diff. Angle or Diff. Angle or Diff. Angle or Diff. Angle or Diff. Angle 29289 3 41716 o 3 5342 40812 2 31800 2 39930 330869 39068 7 34394 i 38227 3 60 I 29309 9 41700 8 30555 i 4797 3 318214 39915 5 33108 6 3954 5 344160 382134 59 2 2933 5 41685 5 30576 o 40782 4 318427 39901 o 331302 39040 3 34438 o 38199 6 58 3 29351 i 416703 30597 o 40767 6 31864 o 39886 5 33I5 1 8 39026 i 34460 o 381857 57 4 29371 6 41655 i 30617 9 40752 7 318853 398720 33173 5 39012 o 34482 o 38I7 1 9 5<> 29392 2 416399 30638 9 40737 9 31906 6 39857 5 33195 i 38997 8 34503 9 38158 i 55 29412 8 41624 6 30659 8 40723 o 319279 39843 o 332167 38983 6 34525 9 381442 54 7 29433 4 416094 30680 8 40708 2 31949 2 39828 5 332384 38969 5 34547 9 381304 53 8 29454 i 41594 2 30701 7 40693 3 3i97 5 398140 33260 i 38955 3 34569 9 381166 52 9 29474 7 41579 30722 7 40678 5 31991 9 39799 5 33281 7 38941 2 3459 1 9 381028 5i 10 29495 3 4i5 6 3 9 30743 7 40663 7 32013 2 39785 3333 4 38927 i 346i39 38089 o 50 i ii 29515 9 41548 7 30764 7 40648 9 32034 5 39770 f 33325 * 389129 34635 9 38075 2 49 12 29536 6 4'533 5 30785 7 40634 i 32055 9 39756 i 333468 38898 8 34657 9 38061 4 48 13 29557 2 4*5 l8 3 30806 7 40619 3 32077 2 39741 7 333684 388847 34680 o 38047 6 47 14 29577 9 41503 2 30827 7 40604 5 32098 6 39727 z 3339 i 38870 6 34702 o 38033 8 46 15 29598 5 41488 o 30848 7 405897 321199 397128 334" 8 388565 34724 o 38020 o 45 16 29619 2 41472 8 30869 7 40574 9 32141 3 39698 3 33433 5 388424 34746 I 38006 2 44 17 29639 9 4*457 7 30890 7 40560 i 321627 39683 9 33455 2 38828 3 34768 I 379924 43 18 2966* 5 41442 6 30911 8 40545 3 32184 o 39669 5 33477 o 388142 34790 2 37978 7 42 19 29681 z 414274 309328 453 5 32205 4 39655 i 33498 7 38800 i 348122 37964 9 4i 20 29701 9 414123 30953 8 405158 32226 8 39640 6 335204 387860 34834 3 3795 1 2 40 21 29722 6 413972 3974 9 40501 o 32248 2 39626 2 33542 i 387720 34856 3 37937 4 22 29743 3 41382 i 3995 9 40486 3 32269 6 39611 8 335639 38757 9 34878 4 37923 7 38 23 29764 o 41366 9 31017 o 40471 5 32291 o 395974 335856 38743 8 349 5 3799 9 37 2 4 29784 7 4i35i 8 31038 o 46456 8 323124 39583 33607 4 38729 8 34922 6 37896 2 36 25 29805 4 413367 31059 i 40442 o 323338 39568 7 33629 i 387157 34944 7 37882 5 35 26 29826 i 41321 7 31080 2 40427 3 323552 395543 33659 38701 7 34966 8 37868 7 34 27 29846 9 41306 6 31101 3 40412 6 323767 395399 336727 38687 6 34988 9 37855 33 28 29867 6 41291 5 311224 40397 9 32398 * 39525 5 33694 4 38673 6 35011 o 37841 3 32 29 29888 3 412764 3 JI 434 40383 2 324195 395112 337162 386596 35033 i 37827 6 3i 30 29909 i 41261 4 31164 5 40368 5 32441 o 39496 8 33738 o 38645 5 350552 378i39 30 31 29929 8 412463 31185 6 40353 8 32462 4 39482 4 33759 s 38631 5 35077 3 37800 2 32 29950 6 41231 2 312068 40339 * 32483 9 39468 i 33781 6 386175 350994 37786 5 28 33 29971 3 41216 2 312279 40324 4 32505 3 39453 8 33803 4 38603 5 35121 6 37772 8 27 34 29992 i 4I20I I 312490 40309 7 325268 39439 4 33825 2 385895 35*437 37759 i 20 35 30012 9 41186 I 312701 40295 o 32548 3 39425 * 33847 38575 5 35^59 37745 4 25 36 30033 7 41171 I 31291 2 40280 4 325698 394108 33868 8 38561 5 35188 o 3773i8 24 37 354 5 411561 313124 40265 7 32591 2 39396 5 33890 6 38547 5 352102 377i8 i 23 q8 30075 2 41141 o 3*333 5 40251 o 326127 39382 i 339*25 38533 5 352323 37704 4 22 39 30096 o 41126 o 3^3547 402364 32634 2 393678 339343 385196 352545 37690 8 21 40 30116 8 41111 o 3 r 375 8 40221 7 326557 39353 5 3395 6 * 3855 6 352767 37677 i 2O 41 3 OI 377 41096 o 3 r 397 40207 i 32677 2 393392 33978 o 38491 6 35298 8 37663 5 19 42 30158 5 41081 o 31418 2 40192 5 32698 7 393249 339998 38477 7 35321 o 37649 8 18 43 3 OI 79 3 41066 o 3*439-3 40177 8 32720 3 393107 34021 7 3 8 463 7 35343 2 376362 17 44 30200 i 41051 1 3*4605 40163 2 32741 8 392964 34043 5 38449 8 353654 37622 6 16 45 30221 o 41036 I 3H8i 7 40148 6 32763 3 39282 i 34065 4 38435 8 353876 37608 9 15 46 30241 8 41021 I 315029 401340 32784 9 39267 8 34087 3 38421 9 35409 8 37595 3 M 47 30262 6 41006 2 3*524 * 401194 32806 4 39253 6 341092 38407 9 354320 3758i7 13 48 30283 5 40991 2 3*545 3 40104 8 32827 9 39239 3 34I3 1 383940 354542 37568 i 12 49 334 3 40976 3 3*5665 40090 2 32849 5 39225 i 341529 38380 i 35476 4 37554 5 II 50 30325 2 40961 3 315877 40075 6 32871 o 39210 8 34174 8 38366 2 35498 7 37540 9 10 5i 30346 I 40946 4 31608 9 40061 o 32892 6 39196 6 341967 383523 35520 9 37527 3 9 52 30367 o 40931 4 316302 40046 4 329142 39182 3 34218 6 383384 35543 i 375*37 8 53 303878 40916 5 31651 4 40031 9 32935 8 39168 i 34240 6 38324 5 355 6 5 4 375oo i 7 54 30408 7 40901 6 31672 6 40017 3 32957 3 39*539 34262 5 38310 6 355876 37486 5 6 55 30429 6 40886 7 3*693 9 40002 7 32978 9 391397 34284 4 38296 7 35609 9 37473 5 56 345 5 40871 8 3*7*5 i 39988 2 33000 5 39*25 5 3436 3 38282 8 356321 37459 4 4 57 3 47i 4 40856 9 3*7364 39973 6 33022 i 391" 3 34328 3 38268 9 356544 37445 8 3 58 30492 3 40842 o 3*757 6 39959 * 33043 7 3997 * 343502 382550 356767 37432 3 2 59 30513 2 40827 i 31778 9 39944 6 33065 3 39082 9 34372 * 38241 2 35699 o 374187 I 60 3534 2 408 122 31800 2 399300 33086 9 39068 7 34394 * 38227 3 35721 2 37405 2 Hour Hour Hour Hour Hour Alt. Angle Alt. Angle Alt. Angle Alt. Angle Alt. Angle / 44 314 43 313 42 312 41 3H 40 310 19' 50 5i 52 53 54 / Sum Hour Sum f\f Hour Sum f\r Hour Sum Hour Sum Hour or Diff. Angle Ol Diff. Angle Or Diff. Angle or Diff. Angle or Diff. Angle 35721 2 3745 2 37068 o 36601 6 38433 9 358158 39818 5 35047 3 41221 5 34295 3 60 I 35743 5 3739 1 6 37090 6 36588 3 38456 8 35802 9 39841 7 35034 6 41245 o 342829 59 2 35765 8 37378 i 371132 36575 i 38479 7 357899 39865 o 35021 9 41268 5 34270 5 58 3 35788 i 37364 6 371358 36561 9 38502 6 35777 39888 2 35009 3 41292 i 34258 2 57 4 358104 3735 1 o 37*584 36548 6 385256 357640 399 11 5 34996 6 413156 34245 8 56 5 35 8 32 7 37337 5 37181 i 365354 38548 5 35751 i 39934 7 34984 o 413392 34233 4 55 6 35855 373240 37203 7 36522 2 3857 1 5 3573 s 2 39958 o 3497 1 3 413628 34221 o 54 7 35 8 77 4 373^5 37226 3 36509 o 385944 35725 3 39981 2 3495 s 7 413863 34208 7 53 8 35 8 99 7 37297 o 37249 36495 8 386174 357*23 40004 5 34946 i 41409 9 34*963 52 9 35922 o 37283 5 37271 6 36482 6 38640 4 356994 40027 8 34933 4 4H33 5 341839 Si 10 35944 3 37270 o 37294 3 36469 4 38663 3 35686 5 40051 i 34920 8 4H57 l 34*7* 6 50 ii 35966 7 37256 5 37317 36456 2 38686 3 356736 40074 4 34908 2 41480 6 341592 49 12 35989 37243 37339 6 36443 38709 3 356607 40097 6 34895 6 415042 34146 9 48 13 36011 4 37229 5 37362 3 36429 8 38732 3 35647 8 40120 9 34882 9 415278 341345 47 14 36033 7 372160 37385 o 36416 6 38755 3 356350 40144 2 34870 3 4*55*4 341222 46 IS 36056 i 37202 6 37407 7 36403 5 38778 3 35622 i 40167 5 348577 4I575 34109 9 45 16 36078 5 37 l8 9 i 3743 3 36390 3 38801 3 35609 2 40190 8 34845 * 41598 6 34097 5 44 17 36100 8 37175 6 37453 o 36377 i 38824 3 35596 3 40214 2 34832 5 41622 3 34085 2 43 18 36123 2 371622 37475 7 363640 38847 3 35583 5 40237 5 34820 o 41645 9 34072 9 42 19 36145 6 37H8 7 37498 4 3635 8 38870 3 355706 40260 8 34807 4 41669 5 34060 6 41 20 36168 o 37'35 3 37521 i 363377 38893 3 355577 40284 i 34794 8 41693 i 34048 3 40 21 36190 4 37121 8 37543 9 36324 6 389164 355449 40307 5 34782 2 41716 8 34036 o 22 36212 8 371084 37566 6 363" 4 389394 355320 40330 8 34769 6 41740 4 34023 7 38 23 36235 2 37095 o 37589 3 36298 3 38962 4 355*93 403542 34757 i 41764 o 34011 4 37 24 36257 6 378i 5 37612 o 36285 2 38985 5 355064 40377 5 34744 5 41787 7 33999 i 36 25 36280 o 37068 i 37634 8 36272 o 39008 5 35493 5 40400 9 34732 o 41811 4 339868 35 26 36302 4 3754 7 37657 5 36258 9 39031 6 354807 40424 2 347*94 41835 o 33974 5 34 27 3 6 324 9 374i 3 37680 3 36245 8 39054 6 354679 40447 6 34706 9 418587 339622 33 28 36347 3 37027 9 37703 o 36232 7 39077 7 35455 40471 o 34694 3 41882 4 339499 32 29 36369 7 37 OI 4 5 37725 8 36219 6 39100 8 354422 40494 3 34681 8 41906 o 339377 3i 30 36392 2 37001 i 37748 5 36206 5 39'239 354294 405177 34669 2 419297 33925 4 30 31 36414 6 369877 3777 1 3 36i934 391469 354166 40541 i 34656 7 419534 339*3 * 32 3 6 437 r 36974 3 37794 i 36180 3 391700 35403 8 40564 5 34644 2 41977 i 339oo 9 28 33 36459 5 36960 9 378169 36167 2 39 r 93 i 3539 10 40587 9 34631 7 42000 8 33888 6 27 34 36482 o 36947 6 378396 361542 392l6 2 35378 2 40611 3 346192 42024 5 338764 26 35 36504 5 36934 2 378624 36141 I 39239 3 35365 4 40634 7 34606 6 42048 2 33864 i 25 36 36526 9 36920 8 37885 2 36128 o 392624 353526 40658 i 34594 i 42071 9 33851 9 24 37 36549 4 36907 5 37908 o 361149 39285 5 353399 40681 5 3458i 6 42095 6 338397 23 38 3 6 57 J 9 36894 i 3793 8 36101 9 39308 6 35327 i 40704 9 345 6 9 i 421193 338274 22 39 36594 4 368808 37953 6 36088 8 393318 353M3 40728 4 345566 42143 o 338152 21 40 36616 9 36867 4 3797 6 5 36075 8 393549 35301 6 40751 8 34544 2 42166 8 33803 o 20 4i 36639 4 36854 i 3799 3 36062 7 39378 o 35288 8 40775 2 34531 7 42190 5 3379 8 19 42 36661 9 36840 7 38022 i 36049 7 39401 2 352760 40798 7 345*92 42214 2 33778 6 18 43 36684 4 368274 38044 9 360367 39424 3 35263 3 40822 i 34506 7 42238 o 33766 3 17 44 36706 9 368141 38067 8 36023 6 39447 4 352506 40845 6 34494 2 42261 7 33754 * 16 45 3 6 729 5 36800 8 38090 6 36010 6 39470 6 352378 40869 o 34481 8 42285 5 3374i 9 15 46 367520 36787 5 38113 5 35997 6 39493 8 35225 i 40892 5 34469 3 42309 2 337297 14 47 36774 5 36774 i 381363 35984 6 395169 352123 40916 o 34456 9 42333 337175 13 48 36797 i 36760 8 381592 35971 6 39540 i 351996 40939 4 34444 4 423568 33705 4 12 49 36819 6 3 6 747 5 381820 35958 6 39563 3 35i86 9 40962 9 34432 o 42380 5 33693 2 II 5 36842 2 36734 2 38204 9 35945 6 395864 35*742 40986 4 34419 5 42404 3 33681 o 10 51 36864 7 36721 o 38227 8 359326 39609 6 35*6i 5 41009 9 34407 * 42428 i 33668 8 9 52 36887 3 36707 7 38250 6 359196 396328 351488 410334 34394 6 42451 9 336567 8 53 36909 8 36694 4 38273 5 35906 6 39656 o 35*36i 41056 9 34382 2 42475 7 33644 5 7 54 36932 4 36681 i 382964 358936 39679 2 35*234 41080 4 34369 8 42499 5 336323 6 55 36955 36667 8 383193 358806 39702 4 351107 41103 9 34357 4 42523 3 336202 5 S^ 36977 6 366546 38342 2 35867 6 39725 6 35098 o 411274 34344 9 42547 * 33608 o 4 57 37000 2 36641 3 38365 * 358547 39748 8 35085 3 411509 34332 5 4257 9 335959 3 58 37022 8 36628 i 383880 3584i 7 39772 o 35072 6 411744 34320 i 42594 7 335837 2 59 3745 4 366148 384109 35828 8 39795 3 350599 411979 3437 7 42618 5 3357 1 6 I 60 37068 o 36601 6 38433 9 358i58 398185 35047 3 41221 5 34295 3 42642 4 335594 Hour Hour Hour Hour Hour Alt. Angle Alt. Angle Alt Angle Alt. Angle Alt. Angle / 39 309 38 308 37 307 36 306 35 305 20' 55 56 57 58 59 / Sum Hour Sum Hour Sum Hour Sum f%fl* Hour Sum nt* Hour or Diff. Angle or Diff. Angle or Diff. Angle ur Diff. Angle ur Diff. Angle o 42642 4 335594 44080 7 32839 i 45536 i 321337 47008 i 314429 48496 2 30766 i 60 I 42666 2 33547 3 441048 32827 2 455 6 5 32122 i 47032 7 3*43* 5 48521 I 30755 59 2 42690 o 33535 * 441290 328153 455849 321105 47057 4 31420 i 48546 I 30743 8 58 3 42713 9 33523 i 44153 i 32803 5 45609 3 32098 8 47082 i 314087 48571 o 30732 6 57 4 42737 7 335i9 441772 32791 6 456337 32087 2 471068 313973 48596 o 30721 5 56 5 42761 6 33498 8 44201 3 327797 45658 i 32075 6 47i3i 5 313859 48620 9 30710 3 55 6 42785 4 33486 7 44225 5 32767 9 45682 6 32064 o 471562 3*3746 48645 9 30699 2 54 7 42809 3 33474 6 44249 6 327560 45707 o 320524 471809 313632 48670 8 30688 i 53 8 42 8 33 i 33462 5 44273 8 32744 2 4573 1 4 32040 8 47205 6 3*35*8 48695 8 30676 9 52 9 42857 o 334504 44297 9 32732 3 45755 8 32029 2 47230 3 3*3405 48720 8 30665 8 5i 10 42880 9 33438 3 44322 i 32720 5 4578o 3 320176 47255 313291 48745 7 306547 50 XX 42904 8 33426 2 44346 3 32708 6 45804 7 32006 o 472797 3*3*78 4877 7 30643 5 49 12 42928 6 334HI 4437 4 32696 8 458292 319944 4734 4 313064 48795 7 306324 48 13 42952 5 33402 i 44394 6 32685 o 45853 6 319828 47329 i 31295 i 48820 7 30621 3 47 14 42976 4 3339oo 44418 8 32673 2 45878 i 3I97I2 47353 9 3*2837 48845 7 306102 46 i| 43000 3 333779 44443 o 32661 3 45902 5 319597 47378 6 312724 488707 30599 * 45 16 43024 2 333658 44467 2 32649 5 45927 31948 I 47403 3 31261 i 48895 7 305880 44 T Z 43048 I 333538 44491 4 326377 4595 1 5 3I93 6 5 47428 i 312497 489207 30576 9 43 18 43072 o 33341 7 445^6 32625 5 459760 319250 47452 8 312384 48945 7 30565 8 42 19 43096 o 333297 44539 8 32614 i 46000 4 3 I 9 I 34 47477 6 312271 489707 30554 7 4 1 20 431199 333176 44564 o 32602 3 46024 9 31901 8 47502 3 312157 48995 7 30543 6 40 21 43H3 8 33305 6 44588 2 325905 46049 4 318903 47527 i 312044 49020 8 30532 5 22 431677 33293 5 446124 32578 7 46073 9 318787 47551 9 3"93 * 49045 8 30521 4 38 23 43*9! 7 3328i 5 44636 6 325669 46098 4 318672 47576 6 31181 8 49070 8 305103 37 24 432156 332695 44660 8 325552 46122 9 318557 47601 4 3"7 5 49095 9 30499 3 36 25 43239 6 332574 44685 i 32543 4 46147 4 318441 47626 2 3"592 49120 9 30488 2 35 26 43263 5 33245 4 44709 3 32531 6 46171 9 318326 476510 3H479 49*45 9 30477 i 34 27 43287 5 332334 44733 6 325198 461965 31821 i 47675 8 311366 49171 o 30466 i 33 25 433 11 4 33221 4 44757 8 32508 i 46221 o 318095 47700 5 311253 49196 o 30455 32 29 433354 332094 44782 o 3249 6 3 46245 5 317980 47725 3 311140 49221 i 30443 9 3 1 30 433594 331973 44806 3 32484 5 46270 o 317865 47750 i 31102 8 49246 2 30432 9 3<> 31 433834 331853 44830 6 32472 8 46294 6 3i775o 47774 9 31091 5 49271 2 30421 8 32 43407 3 33173 3 448548 32461 o 463191 3!7 6 3 5 47799 8 31080 2 49296 3 30410 8 28 33 43431 3 331614 44879 * 32449 3 46343 7 317520 47824 6 31068 9 49321 4 3399 7 27 34 43455 3 33H94 44903 4 32437 6 46368 2 3*7405 47849 4 310577 49346 4 30388 7 20 35 43479 3 331374 44927 6 32425 8 46392 8 317290 47874 2 310464 4937 1 5 30377 7 25 36 4353 3 331254 4495 * 9 32414 i 46417 3 3*7*75 47899 o 31035 2 49396 6 30366 6 24 37 43527 3 33^34 44976 2 32402 4 46441 9 317060 47923 9 31023 9 49421 7 303556 23 38 43551 3 33 IQ i 4 45000 5 32390 6 46466 4 316945 47948 7 310127 49446 8 30344 6 22 39 43575 3 33089 5 45024 8 32378 9 46491 o 316830 47973 5 31001 4 49471 9 30333 6 21 40 43599 3 33077 5 4.5049 * 32367 2 465156 31671 6 47998 4 30990 2 49497 30322 5 20 4i 43 6 23 4 33065 5 45073 4 32355 5 46540 2 31660 i 48023 2 30978 9 49522 i 30311 5 19 42 43647 4 33053 6 45097 7 32343 8 46564 8 316486 48048 I 30967 7 49547 2 30300 5 18 43 43671 4 33041 6 45122 o 323321 465893 316372 48072 9 30956 5 49572 3 30289 5 17 44 43695 5 330297 451464 323204 46613 9 316257 48097 8 30945 2 49597 5 30278 5 16 45 43719 5 330177 451707 32308 7 46638 5 316142 481227 30934 o 49622 6 30267 5 15 46 43743 6 33005 8 451950 322970 46663 i 316028 481475 30922 8 49647 7 30256 5 14 47 43767 6 32993 9 452193 32285 3 46687 8 3i59i 3 481724 30911 6 49672 9 30245 5 13 48 4379 1 7 32981 9 45243 7 32273 6 467124 3*5799 48i973 30900 4 49698 o 30234 6 12 49 438157 32970 o 45268 o 32261 9 46737 o 315685 48222 2 308892 49723 I 30223 6 ii So 438398 32958 i 452924 322502 46761 6 3I557 48247 I 30878 o 49748 3 30212 6 10 5i 43863 9 32946 2 453i67 322386 46786 2 3*545 6 48272 o 30866 8 49773 4 30201 6 9 52 43887 9 329342 45341 i 322269 46810 9 31534 * 48296 9 30855 6 49798 6 30190 6 8 53 439120 32922 3 453654 32215 2 46835 5 315227 48321 8 30844 4 49823 8 301797 7 54 43936 i 329104 45389 8 32203 6 46860 i 3i5"3 48346 7 30833 2 49848 9 30168 7 6 55 43960 2 32898 5 454142 32191 9 46884 8 3H999 48371 6 30822 o 49874 i 301577 5 56 43984 3 32886 6 45438 5 321803 46909 4 314885 48396 5 308108 49899 3 30146 8 4 57 44008 4 328747 45462 9 32168 6 46934 i 3H77I 48421 4 30799 6 49924 4 30*358 3 58 44032 5 32862 8 45487 3 321570 46958 7 3*4657 48446 3 30788 5 49949 6 301249 .2 59 44056 6 328510 455 ir 7 32145 3 46983 4 3H543 48471 3 3777 3 49974 8 301139 X 60 44080 7 32839 i 45536i 321337 47008 i 3*4429 48496 2 30766 i 50000 o 30103 o O Hour Hour Hour Hour Hour Alt Angle Alt. Angle Alt. Angle Alt Angle Alt. Angle / 34 304 33 303 32 302 31 301 30 300 60 61 62 63 64 / Sum Hour Sum Hour Sum Hour Sum Hour Sum Hour Diff. Angle Diff. Angle Diff. Angle or Diff. Angle or Diff. Angle 50000 o 30103 o 5*5*90 29453 i 53052 8 28816 i 54600 < 28191 5 56162 9 275790 60 I 50025 2 30092 i 5*5445 29442 4 53078 5 28805 6 54626 9 28181 2 56189 o 27568 9 59 2 50050 i 30081 i 5*5699 2943* 7 28795 o 54652 8 28170 9 562152 27558 8 58 3 50075 6 30070 2 5*5954 29421 o 53*299 28784 5 54678 7 28160 6 56241 3 27548 7 57 4 50100 8 30059 3 51620 8 294102 531556 28774 o 54704 6 28150 56267 5 27538 6 56 5 50126 o 30048 '_. 5*6463 29399 5 53i8i3 28763 5 54730 6 28140 o 56293 7 27528 5 55 6 50151 2 30037 I 51671 8 29388 8 532070 28753 i 54756 5 28129 7 5 6 3*98 275*84 54 7 50*764 30026 5 516972 29378 i 532327 28742 6 54782 5 28119 ' 563460 27508 3 53 8 50201 7 30015 6 5*7227 29367 4 532584 28732 i 54808 4 28109 * 563722 27498 3 S 2 9 50226 c 30004 7 51748 2 293567 532842 28721 6 548344 28098 9 56398 3 27488 2 10 50252 i 29993 8 5*7737 29346 i 533099 28711 i 5486o 3 28088 6 56424 5 27478 i So ii 50277 4 29982 < 5*799 * 293354 533356 28700 6 54886 3 28078 3 564507 27468 o 49 12 50302 6 29972 o 518246 29324 7 5336i 3 28690 2 549*22 28068 o 56476 9 27458 o 48 13 50327 8 29961 i 51850 i 293*4 53387 * 286797 54938 2 28057 8 56503 * 27447 9 47 14 50353 i 299502 518756 29303 3 534*28 286692 54964 2 28047 5 565293 27437 8 46 15 50378 3 299393 51901 i 292927 53438 5 28658 8 54990 2 28037 2 56555 5 27427 8 45 16 50403 6 29928 4 51926 6 29282 o 53464 3 28648 3 55016 I 28027 565817 274*77 44 17 50428 9 299*75 5*952i 29271 3 53490 o 28637 9 55042 1 280167 56607 9 27407 6 43 18 5454 i 29906 7 5*9776 29260 7 535*58 286274 55068 I 28006 5 56634 i 27397 6 42 19 5479 4 29895 8 52003 2 29250 o 5354i 5 286169 55094 1 27996 2 56660 3 27387 5 20 50504 7 29884 9 52028 7 292394 535673 28606 5 551201 279860 566865 27377 5 4 21 50529 9 29874 i 520542 29228 7 53593 i 28596 i 55*46 I 27975 8 567127 27367 5 22 50555 2 29863 2 52079 7 29218 i 53618 8 28585 6 55*72 I 279 6 5 5 567390 273574 38 23 50580 5 298523 52*053 29207 4 53644 6 28575 2 55*98 I 27955 3 56765 2 27347 4 37 24 50605 8 29841 5 521308 291968 536704 285648 55224 I 27945 i 56791 4 27337 4 36 2 5 50631 i 29830 6 521564 29186 i 536962 285543 552501 27934 8 568177 27327 3 35 26 50656 4 29819 8 52181 9 29*75 5 53722 28543 9 55276 1 27924 6 56843 9 273*73 34 27 50681 7 29808 9 52207 4 29164 9 53747 7 28533 5 553021 279*44 56870 i 27307 3 33 28 50707 o 29798 i 522330 291542 53773 5 28523 i 55328 2 27904 2 568964 27297 3 32 29 50732 3 29787 3 52258 6 291436 537993 285127 553542 27894 o 56922 6 27287 2 30 50757 6 29776 4 52284 i 291330 53825 i 285022 553802 27883 8 56948 9 27277 2 30 31 50783 o 29765 6 523097 291224 538509 28491 8 55406 2 27873 6 56975 * 27267 2 32 50808 3 29754 8 52335 3 29111 8 538767 28481 4 55432 3 27863 4 27257 2 28 33 50833 6 29743 9 523608 29101 2 53902 6 28471 o 554583 278532 57027 7 27247 2 27 34 50858 9 29733 i 523864 29090 6 53928 4 28460 6 554844 27843 o 57053 9 27237 2 26 35 50884 3 29722 3 524120 29080 o 539542 284502 555104 27832 8 57080 2 27227 2 25 36 50909 6 297** 5 52437 6 29069 4 539800 28439 8 555365 27822 6 57*065 272172 24 37 5935 29700 7 52463 2 29058 8 54005 8 28429 5 555625 278124 57*328 27207 2 23 38 50960 3 29689 9 52488 8 29048 2 5403 1 7 28419 i 555886 27802 2 57*59 271972 22 39 50985 7 29679 i 525*44 29037 6 54057 5 28408 7 556147 27792 o 57i853 27187 3 21 40 51011 o 29668 3 52540 o 29027 o 54083 3 28398 3 556407 27781 9 57211 6 27*77 3 20 5*0364 29657 5 52565 6 29016 4 54*09 2 28387 9 556668 27771 7 57237 9 271673 19 42 51061 7 29646 7 52591 2 29005 9 54*35 28377 6 556929 27761 5 57264 2 27*573 18 43 51087 i 29635 9 526168 28995 3 54*609 28367 2 557*9 27751 3 5729 5 27*474 17 44 ;ni2 5 29625 i 526424 289847 54*867 283568 557450 27741 2 573*68 27*374 IO 45 51137 9 296144 52668 o 28974 i 542126 28346 5 55771 i 27731 o 57343 i 27*274 15 46 5** 6 3 3 29603 6 52693 7 28963 6 54238 5 28336 i 55797 2 27720 9 573 6 94 27117 5 14 47 51188 6 29592 8 527*93 289530 54264 3 28325 8 558233 277107 573957 27107 5 13 48 51214 o 29582 i 52744 9 28942 5 54290 2 283154 558494 27700 6 57422 i 27097 6 12 49 5*2394 2957 1 3 5277 6 28931 9 543*6 i 28305 i 55875 5 27690 4 57448 4 27087 6 II 50 512648 29560 5 527962 28921 4 54342 o 28294 7 55901 6 27680 3 57474 7 27077 7 10 1290 2 29549 8 52821 8 28910 8 54367 8 282844 559277 27670 i 57501 o 27067 7 9 52 1315 6 295390 52847 5 28900 3 54393 7 28274 i 559538 27660 o 575274 27057 8 8 53 1341 o 29528 3 52873 * 288897 544196 28263 7 55980 o 27649 9 575537 27 47 8 7 54 13665 295*75 52898 8 288792 54445 5 282534 56006 i 276397 575801 27037 9 6 55 *39* 9 29506 8 52924 5 28868 7 54471 4 28243 i 560322 27629 6 57606 4 27028 o 5 S^ *4*73 29496 o 5295 * 28858 i 54497 3 282327 56058 3 276195 576327 27018 o 4 57 14427 29485 3 52975 8 28847 6 545232 282224 56084 5 27609 4 57659 i 27008 I 3 58 1468 2 29474 6 53o* 5 28837! 5454-9 i 28212 i 56110 6 27599 3 57685 4 26998 2 2 59 1493 6 29463 8 53027 2 288266 54575 o 28201 8 561367 27589 i 577*i8 26988 3 I 60 15190 29453 i 530528 288161 54600 9 28191 5 56162 9 27579 57738 2 26978 4 Alt. Hour Angle Alt Hour Angle Alt. Hour Angle Alt. Hour Angle Alt. Hour Angle , 29 299 28 298 27 297 26 296 25 295 22' 65 66 67 68 6 9 / Sum S\f* Hour Sum />f Hour Sum f\r Hour Sum r*t* Hour Sum nt* Hour or Diff. Angle OF Diff. Angle Ul Diff. Angle vJi Diff. Angle Ul Diff. Angle 57738 2 26978 3 59326 3 26389 i 60926 9 25811 i 62539 3 25243 8 64163 2 24687 2 60 I 577 6 4 5 26968 4 593529 26379 4 60953 7 25801 5 62566 3 252345 641904 24678 o 59 2 57790 9 26958 5 59379 5 26369 7 60980 4 25792 o 62593 3 25225 i 64217 5 24668 8 58 3 578i73 26948 6 59406 i 263600 61007 2 257824 62620 3 252158 642447 24659 6 57 4 57843 7 26938 7 59432 7 26350 2 610340 25772 9 62647 2 25206 4 64271 9 24650 5 56 5 57870 o 26928 8 59459 * 26340 5 61060 8 25763 4 62674 2 251970 64299 o 24641 3 55 5 57896 4 26918 9 59485 8 26330 8 61087 6 25753 8 62701 2 251877 64326 2 24632 i 54 7 57922 8 26909 o 595124 26321 i 611144 25744 3 62728 2 251784 64353 4 24622 9 53 8 57949 2 26899 i 59539 263114 61141 2 25734 8 62755 2 25169 o 64380 6 24613 8 5 2 9 57975 6 268892 595 6 5 6 26301 7 61168 o 25725 3 62782 2 2 5!597 64407 7 24604 6 5i 10 58002 o 26879 4 59592 2 26292 o 611948 257158 62809 2 251503 644349 24595 4 5 XI 58028 4 26869 5 59618 9 26282 3 61221 6 25706 3 62836 2 251410 64462 i 245863 49 12 58054 8 26859 6 59645 5 26272 6 61248 4 256967 62863 2 25*317 64489 3 24577 i 48 13 58081 2 26849 7 59672 i 26262 9 61275 3 256872 62890 2 25122 3 645165 24568 o 47 14 581076 26839 8 59698 7 26253 3 61302 i 25677 7 62917 2 251130 64543 7 24558 8 46 15 581340 268300 59725 3 26243 6 61328 9 25668 2 62944 3 251037 6457 9 24549 7 45 16 581604 26820 i 597520 26233 9 6l 3557 25658 7 62971 3 25094 4 64598 i 24540 5 44 J Z 581869 26810 2 59778 6 26224 2 61382 6 25649 2 62998 3 25085 i 64625 3 24531 4 43 18 582133 26800 4 59805 2 262145 614094 256398 63025 3 2 575 7 64652 5 24522 2 42 19 582397 26790 5 59831 9 26204 9 614362 256303 63052 3 25066 4 64679 7 245*3 I 4 1 20 58266 i 26780 7 59858 5 26195 2 61463 i 25620 8 63079 4 25057 * 64706 9 24504 o 4 21 58292 6 26770 8 59885 i 26185 5 614899 25611 3 631064 25047 8 64734 2 24494 8 22 583190 26761 o 599118 26175 9 615168 25601 8 631335 25038 5 64761 4 24485 7 38 23 58345 5 26751 i 599384 26l66 2 6 i543 6 25592 3 631605 25029 2 64788 6 24476 6 37 2 4 5837 1 9 26741 3 599 6 5 * 26156 6 615705 255829 631875 250199 64815 8 24467 4 36 ' 25 58398 4 26731 5 59991 7 26146 9 6l 5973 255734 63214 6 250106 64843 i 24458 3 35 26 58424 8 26721 6 60018 4 261373 616242 255639 63241 6 250013 64870 3 24449 2 34 27 58451 3 26711 8 60045 i 26127 6 61651 o 255545 632687 24992 I 64897 5 24440 i 33 28 58477 7 26702 o 60071 7 261180 616779 25545 63295 7 24982 8 64924 8 24431 o 3 2 29 58504 2 26692 i 60098 4 26108 3 61704 8 255356 63322 8 24973 5 64952 o 24421 9 3i 30 585307 26682 3 60125 * 26098 7 617317 25526 i 633499 24964 2 64979 3 24412 8 3 31 58557 i 26672 5 60151 8 26089 i 61758 5 2 55 l6 7 63376 9 24954 9 65006 5 24403 7 32 58583 6 26662 7 60178 4 26079 4 617854 25507 2 63404 o 24945 7 65033 8 24394 6 28 33 58610 i 26652 9 60205 i 26069 8 61812 3 25497 8 63431 i 249364 65061 o 24385 5 27 34 586366 26643 i 60231 8 26060 2 618392 25488 3 63458 2 24927 i 65088 3 24376 4 26 35 58663 i 26633 3 60258 5 26050 6 61866 i 25478 9 63485 2 24917 9 65"55 24367 3 25 36 586896 26623 5 60285 2 26041 o 61893 25469 4 635123 24908 6 651428 24358 2 24 37 587160 266137 60311 9 26031 3 619199 25460 o 635394 24899 3 651701 24349 i 23 38 58742 5 26603 9 60338 6 26021 7 619468 25450 6 63566 5 24890 i 6 5 ' 97 3 24340 o 22 39 58769 o 26594 i 60365 3 26012 i 61973 7 25441 i 63593 6 24880 8 65224 6 2433 9 21 40 58795 5 26584 3 60392 o 26002 5 62000 6 25431 7 636207 24871 6 65251 9 24321 8 2O 4i 588220 26574 5 60418 7 25992 9 62027 5 25422 3 63647 8 24862 3 65279 i 243128 19 42 58848 6 26564 7 60445 4 25983 3 620544 254129 63674 9 24853 i 653064 24303 7 18 43 58875 i 265549 60472 2 25973 7 62081 3 25403 5 63702 o 24843 9 653337 24294 6 17 44 58901 6 26545 i 60498 9 25964 i 62108 2 253940 63729 i 24834 6 65361 o 24285 6 16 45 58928 i 265354 60525 6 25954 5 62135 i 253846 63756 2 24825 4 65388 3 24276 5 15 i 46 58954 6 26525 6 60552 3 25945 62162 i 25375 2 63783 3 24816 i 654156 24267 4 J 4 47 58981 2 265158 60579 * 259354 62189 o 25365 8 638104 24806 9 65442 9 24258 4 13 48 59007 7 26506 i 60605 8 25925 8 622159 253564 638375 24797 7 65470 2 24249 3 12 49 90342 26496 3 60632 5 259162 62242 9 25347 63864 7 24788 5 65497 5 24240 3 XI 50 90608 26486 5 60659 3 25906 6 62269 8 25337 6 63891 8 24779 2 655248 24231 2 XO 5i 90873 26476 8 606860 25897 * 622967 25328 2 639189 24770 o 655521 24222 2 9 52 91138 26467 o 60712 8 258875 62323 7 253188 639460 24760 8 655794 24213 I 8 53 91404 26457 3 60739 5 258779 623506 25309 5 63973 2 24751 6 65606 7 24204 I 7 54 9166 9 26447 5 60766 3 258684 62377 6 25300 i 6^000 3 24742 4 656340 241950 6 55 9193 5 26437 8 60793 258588 62404 5 252907 64027 5 24733 2 65661 3 24186 o 5 56 9220 i 26428 i 60819 8 25849 2 62431 5 25281 3 64054 6 24724 o 65688 7 241770 4 57 9246 6 26418 3 60846 6 258397 62458 4 25271 9 64081 7 247148 65716 o 241679 3 58 92732 26408 6 60873 3 258301 62485 4 25262 6 64108 9 24705 6 65743 3 241589 2 g 92998 26398 9 60900 i 258206 625124 252532 64136 o 24696 4 657706 241499 X 60 93263 26389 i 60926 9 25811 I 625393 25243 8 64163 2 24687 2 65798 o 241409 Alt Hour Angle Alt. Hour Angle Alt Hour Angle Alt. Hour Angle Alt. Hour Angle / 24 294 23 293 22 2 9 2 21 291 20 290 23* 70 71 72 73 74 / Sum or Hour Sum or Hour Sum or Hour Sum or Hour Sum f*m Hour Diff. Angle Diff. Angle Diff. Angle wl Diff. Angle Of Diff. Angle I o 65798 o 24140 9 67443 2 23604 6 69098 3 23078 i 70762 8 22561 2 72436 3 22053 7 60 1 I 65825 3 24131 9 67470 7 235957 69126 o 23069 4 70790 6 225527 72464 2 22045 3 2 658527 24122 { 67498 2 23586 9 691536 23060 7 70818 5 22544 2 72492 2 22036 9 58 3 65880 o 241138 67525 7 235780 69181 3 23052 i 70846 3 22535 6 725202 22028 6 57 4 65907 3 24104 8 67553 2 235692 69209 o 23043 4 70874 i 22527 I 72548 I 22020 2 ft 5 659347 24095 8 675807 235604 692367 23034 7 70901 9 22518 6 72576 I 2201 1 8 55 6 65962 o 24086 8 67608 3 23551 5 69264 3 23026 o 70929 8 22510 i 72604 I 22003 4 54 7 65989 4 24077 8 67635 8 235427 69292 o 230173 70957 6 22501 5 72632 I 21995 i 53 8 66016 7 24068 67663 3 235338 693197 23008 7 70985 4 22493 o 72660 o 219867 52 9 66044 r 24059 8 67690 8 235250 69347 4 23000 o 710133 22484 5 72688 o 21978 4 5i 10 66071 5 24050 67718 4 235162 69375 i 22991 3 71041 i 22476 o 727160 219700 50 ii 66098 8 24041 S 67745 9 2 357 4 69402 8 22982 7 71069 o 22467 5 72744 21961 6 49 12 66126 2 24032 8 67773 4 23498 5 69430 5 22974 o 71096 8 224590 72772 o 2*9533 48 13 661536 24023 67801 o 23489 7 69458 2 22965 3 711247 22450 5 72800 o 219449 47 14 66180 9 24014 8 67828 5 23480 9 69485 9 229567 7^525 22442 o 72828 o 21936 6 46 15 66208 3 24005 9 678560 23472 i 695136 22948 o 71180 4 22433 5 728560 21928 2 45 16 66235 7 23996 9 67883 6 23463 3 6954i 3 229394 71208 2 22425 o 72883 9 219199 44 17 66263 i 23987 9 67911 i 234544 69569 o 22930 7 71236 I 22416 5 72911 9 21911 6 43 18 66290 5 23978 9 6 7938 7 23445 6 69596 7 22922 i 71263 9 22408 o 72940 o 21903 2 42 19 663179 23970 o 67966 3 23436 8 69624 4 229134 71291 8 22399 5 72968 o 218949 4i 20 66345 2 23961 o 67993 8 23428 o 69652 i 22904 8 7 I 3 I 97 22391 o 72996 o 218866 40 21 66372 6 239520 68021 4 234192 69679 8 22896 i 7*347 5 223825 73024 o 21878 2 22 66400 o 23943 i 68048 9 234104 69707 6 22887 5 713754 22374 i 730520 21869 9 38 23 66427 4 23934 i 68076 5 23401 6 69735 3 22878 9 7*403 3 22365 6 73080 o 21861 6 37 24 66454 8 23925 2 68104 l 233928 69763 o 22870 2 71431 2 22357 i 73108 o 218532 36 25 66482 2 23916 2 68131 6 23384 i 6979 7 22861 6 714590 22348 6 731360 218449 35 26 66509 7 2397 3 68159 2 23375 3 69818 5 228530 71486 9 22340 2 731641 218366 34 27 66537 i 23898 3 68l868 23366 5 69846 2 22844 4 7*5*48 223317 731921 21828 3 33 28 66564 5 238894 682144 233577 69874 o 228357 7*5427 22323 2 73220 1 21820 o 32 29 66591 9 238804 68241 9 23348 9 69901 7 22827 i 715706 223H8 73248 I 21811 7 3i 3<> 66619 3 23871 5 68269 5 23340 2 69929 4 22818 5 7*598 5 22306 3 73276 2 21803 4 30 31 66646 7 23862 6 68297 i 2333M 69957 2 22809 9 716264 22297 9 73304 2 2*79'5 * ! 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Angle Alt. Angle Alt. Angle Alt. Angle Alt. Angle / 19 289 1 8 288 17 287 1 6 286 15 285 24* 75 76 77 78 79 / Sum Hour Sum Hour Sum /\f* Hour Sum f\f Hour Sum Hour or Diff. Angle or Diff. Angle or Diff. Angle ur Diff. Angle or Diff. 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9 3798 331 2 2859 243 9 205 3 170 o 8 53 607 2 545 4863 431 o 3790 3304 2851 2432 2047 1695 7 54 606 I 5440 4854 430 i 3296 2844 242 6 204 i 1689 6 55 605 o 543 4844 4292 , 3773 3288 2837 241 9 203 5 1684 5 56 604 o 5420 4835 4283 37 6 5 328 o 2830 241 2 2028 1678 57 602 9 541 o 4825 4274 : 375 6 3273 2822 240 6 202 2 167 2 3 58 601 8 5400 481 6 426 5 i 3748 3265 281 5 2399 201 6 1667 2 59 6008 539 4806 425 6 ; 3740 3257 2808 2392 201 166 o I 60 5997 538o 4797 4247 373 i 3249 280 i 2386 200 4 165 6 O 199 198 197 196 195 194 193 I92 191 I90 Hour Angle ' 35* , Hour Angle 170 171 172 173 174 175 176 177 178 179 165 6 i34 i 1059 81 i 59 6 4i 4 265 149 66 7 60 I 165 o 133 6 105 5 807 592 41 i 262 H7 65 6 2 164 5 133 i 105 o 80 3 589 408 26 o 146 64 5 eg 3 163 9 1326 104 6 799 586 405 258 144 63 5 57 4 1634 132 i 104 2 795 582 403 256 142 62 4 56 5 1628 131 6 1037 792 579 40 o 254 H i 61 4 55 6 162 3 131 i 1033 788 576 39~7 25 2 139 60 3 54 i 7 161 7 130 6 102 9 784 573 394 249 '37 59 3 53 ! 8 161 2 130 i 102 4 780 5 6 9 392 247 136 58 2 52 9 1606 129 6 102 776 566 389 245 134 57 2 51 10 1 60 i 129 2 ioi 6 773 563 38 6 243 13 3 56 I 50 ii 1596 128 7 IOI I 769 56 o 384 24 I 5 5 I 49 12 159 o 128 2 100 7 765 557 38 i 239 130 54 I 48 | 13 1585 1277 100 3 761 553 378 237 128 53 O 47 '579 1272 998 758 55 376 235 127 52 46 1C 1574 126 7 994 754 547 373 23 3 125 5 i 09 45 ID 126 2 99 544 37 i 23 i 124 5 09 44 17 ^63 125 8 985 746 54 i 368 228 12 2 49 09 43 18 1558 1253 98! 743 537 365 226 12 I 48 08 42 19 155 2 1248 977 739 534 363 224 ii 9 47 08 41 I 2O 1547 1243 973 73 5 53 i 36 o 22 2 ii 8 46 07 40 1 21 1542 1238 968 732 528 358 22 ii 6 45 07 22 1536 1234 964 728 525 355 21 8 " 5 44 07 38 23 153 I 122 9 96 o 724 522 353 21 6 " 3 43 06 37 24 152 6 122 4 95 6 72 i 5 1 9 350 21 4 112 42 06 * 2 5 1521 121 9 952 71 7 51 6 347 21 2 II 4 i 06 35 1 26 1515 121 5 947 7i 3 51 3 345 21 O 10 9 4 i 5 34 i 27 151 o 121 943 71 o 5 1 342 208 10 8 40 5 33 | 28 1 S 5 120 5 939 70 6 5 7 34 20 6 10 6 39 05 32 29 1499 120 I 935 7 3 5 3 337 205 105 38 04 31 30 1494 1196 93 i 699 50 o 33 5 203 103 37 04 30 1489 119 I 927 695 497 332 20 I IO 2 36 04 32 1484 118 7 923 69 2 494 330 199 10 I 36 04 28 33 1478 118 2 91 8 688 49 i 328 197 99 3 5 03 27 34 1473 "77 91 4 685 488 325 195 98 34 03 26 35 1468 "73 91 o 68 i 485 323 193 97 3 3 3 25 36 1463 1168 90 6 678 482 320 95 3 2 3 24 37 1458 "63 902 674 479 318 18 9 94 32 2 23 38 145 2 "59 898 671 476 31 5 187 93 3 i 2 22 39 1447 "54 894 667 473 31 3 18 6 9 ! 3 O 2 21 40 1442 "49 890 664 47 i 31 i 184 90 29 2 2O 4 1 1437 "45 886 660 468 308 182 89 29 O 2 J 9 42 H3 2 114 o 882 657 465 30 6 18 o 87 28 I 18 43 1427 113 6 878 653 462 3 4 178 8 6 27 O 17 44 1422 "3 i 874 65 o 459 301 176 85 27 16 9 141 6 141 i 1127 112 2 870 866 646 643 456 45 3 299 29 6 175 1 7 3 84 8 2 26 25 o 15 14 47 140 6 in 7 862 639 450 294 17 i 8 i 24 o 13 48 140 i in 3 858 63 6 447 292 16 9 8 o 24 12 49 1396 no 8 854 633 444 28 9 168 79 23 II 50 '39 ! no 4 85 o 62 9 442 287 166 78 23 oo 10 51 138 6 1099 846 626 43 9 285 164 76 2 2 oo 9 52 138 i 1095 842 622 436 283 162 75 2 I oo 8 53 I37 6 109 o 838 61 9 433 28 o 16 i 74 2 I 7 54 137 i 108 6 834 61 6 430 27 '8 J 59 73 2 00 6 55 1366 108 i 830 61 2 427 276 157 72 9 oo 5 56 136 i 1077 826 60 9 425 274 156 7 l 9 o o 4 57 135 6 1073 822 606 422 27 * '54 69 8 O 3 58 Z 35 1 1068 81 9 602 41 9 26 9 152 68 8 O 2 1346 i34i 106 4 i5 9 815 81 i 599 59 6 416 4i 4 267 265 149 67 66 7 7 o o i 189 1 88 187 186 185 184 I83 182 181 1 80 t Hour Angle 36' THE "NEWEST" NAVIGATION ALTITUDE AND AZIMUTH TABLES FOR FACILITATING THE DETERMINATION OF LINES OF POSITION AND GEOGRAPHICAL POSITION AT SEA THE SIMPLEST AND READIEST IN SOLUTION Plane and Spherical Traverse Tables for Solving all Problems of Navigation By LIEUTENANT RADLER DE AQUINO BRAZILIAN NAVY SECOND STEREOTYPED EDITION ENLARGED AND IMPROVED Sights " may be practically worked out so as to give the ship's place as accurately as it can be deduced from the observations, with hardly any calculation " One of the advantages in the use of this method is that no logarithmic work is required." SIR WILLIAM THOMSON (LORD KELVIN). "Tables for Facilitating Sumner's Method at Sea." London, 1876. pp. iv. and v. " E' facile persuadersi che, dopo avere acquistata un po' di pratica, le operazioni descritte possono esser fatte con grande speditezza : 1' uso della Tavola e facile e le regole da applicare sono indiscutibilmente semplici." DOTT. ALBERTO ALESSJO, R.I.N. " Sulla Teoria e la Pratica della Nuova Navigazione Astronomica." Rivista Marittima for March 1909, Appendice, p. 59. 1912 LONDON J. D. POTTER Admiralty Agent for Charts 145, MINORIES, E.C. RIO DE JANEIRO D. N ORRIS Admiralty Sub-Agent for Charts 36, RUA DA ASSEMBLEA [COPYRIGHT] Price 10s. 6d. net GENERAL PRINCIPLE AND EQUATIONS In Fig. 2, P is the elevated pole and PMZ is the astronomical triangle of position projected on the plane of the horizon. If we let fall a perpendicular from M on PZ, it will divide the triangle of position into two right-angled triangles. 1 Let us call the perpendicular a and the two parts into which PZ is divided 90 -b and 90 -B. The perpendicular a is common to .the two triangles and there- fore to (a and 90 in triangle MPm correspond 90 ^ and t a 90 - and vice versa, or to and vice versa. *and{^ MZm correspond d and t, h Z 90-* 1 The principle upon which these tables are based is as old as Spherical Trigo- nometry itself, and naturally it was the only way of solving spherical triangles until, as DOTT. PESCI informs us, ALBATANI (880-928 A.D.) discovered the well-known relation (erroneously attributed to Euler) between the three sides and an angle of a spherical triangle cos a = cos b cos c+ sin b sin c cos A. xii o.8io 0-795 0.781 IV a = 510' a = 51 30' a = 520' Y V \ \ d 60^ X f A \ d 60' 1 \ * A \d 60' I \ * A A \ s \ h \ A z \ 60"' h \ A Z \ 60' \ T 6y c \ \ o o * / / / o / / o O 1.58 51 o o.oo o o 1.62 51 30 o.oo 1.62 52 o o.oo go 90.0 I 38 1.58 .02 37 1.58 30 .02 37 1.62 .02 8 89.2 2 i 16 1.62 I .02 i 15 1.62 31 .02 i 14 1.62 I .02 88 88.4 3 53 1.58 2 03 52 1.62 32 03 1.62 2 .03 87 87.7 4 2 31 1.58 4 03 2 29 1.58 34 03 2 28 1.62 4 3 86 86.9 5 3 9 1.58 6 0.05 3 7 1.62 36 0.05 3 5 1.67 6 0.05 85 86.1 6 47 1.62 9 .07 44 1.62 39 .05 1.62 9 .05 84 85.3 7 4 24 1.58 13 .07 4 21 1.62 42 .07 4 18 1.62 12 .07 83 8 5 2 1.62 17 .07 58 1.62 46 .08 55 1.62 16 .08 82 83-7 9 39 1.62 21 .08 5 35 1.62 .08 5 32 i.6 7 21 .08 81 82.9 10 6 16 1.58 26 0.08 6 12 1.62 56 O.o8 6 8 1.62 26 0.08 80 82.1 ii 54 1.62 31 .10 49 1.62 52 i .10 45 1.67 31 .10 79 81.5 12 7 3i 1.62 37 .12 7 26 1.62 7 .10 7 21 1.62 37 .10 78 80.6 13 8 8 1.62 44 .12 8 3 1.62 13 .12 58 i.6 7 43 .12 77 79.8 14 45 1.62 .12 40 1.67 20 '3 8 34 1.67 50 '3 76 79.0 15 9 22 1.62 58 O.I 3 9 16 1.62 28 0.13 9 10 1.67 58 O.I 3 75 78.2 16 59 1.62 52 6 53 1.67 36 '5 46 1.67 53 6 '3 74 77-4 17 10 36 1.62 15 .15 10 29 1.67 45 *$ IO 22 1.67 14 .15 73 76-5 18 ii 13 1.67 24 .17 ii 5 1.67 54 '5 58 1.67 23 '7 72 75-7 19 49 1.62 34 '7 4i 1.67 53 3 '7 ii 34 1.71 33 '7 71 74-9 20 12 26 1.67 44 0.18 12 I 7 1.67 13 0.18 12 9 i.6 7 43 0.18 70 74.1 21 13 2 1.67 55 .18 53 1.67 24 .18 45 1.71 54 .18 O9 73-3 22 38 1.67 53 6 .20 13 29 1.67 35 .20 13 20 1.71 54 5 .20 Oo 72.5 23 14 14 1.67 18 .20 i4 5 1.71 47 .22 55 1.71 17 .20 67 71.6 24 50 1.67 30 .22 40 1.71 54 o .22 14 30 1.71 29 .22 66 70.8 25 15 26 1.71 43 0.23 i5 15 1.71 13 0.22 15 5 1.71 42 0.22 65 70.0 26 16 i 1.71 57 23 1.71 26 .23 40 55 .23 64 69.1 27 36 1.71 54 ii .25 16 25 1.71 40 25 16 14 1.76 55 9 25 63 68.3 28 17 ii 1.71 26 .27 17 o 1.76 55 48 1.76 24 .25 62 67.4 29 46 1.76 42 .27 34 1.76 55 10 .27 17 22 1.76 39 .27 61 66.5 30 1 8 20 1.71 58 0.27 18 8 1.76 26 0.28 56 1.82 55 0.27 60 65-7 31 55 1.76 55 H .28 42 1.76 43 '.28 18 29 1.82 56 ii .28 C Q 64.8 3 2 19 29 1.76 3 19 16 1.82 56 o 3 19 2 1.82 28 3 5^ 63.9 33 20 3 1.76 49 3 49 1.82 18 3 35 1.82 46 3 57 63.1 34 37 1.82 56 7 32 20 22 1.82 36 3 2 20 8 1.82 57 4 32 56 62.2 35 21 IO 1.82 26 -33 55 1.82 55 0.32 4i 1.88 23 0.32 55 61.3 36 43 1.82 46 35 21 28 1.88 57 14 33 21 13 1.88 42 33 54 60.4 37 22 l6 1.88 57 7 35 22 1.88 34 35 45 1.88 58 2 35 53 59-5 38 48 1.88 28 35 32 1.88 55 37 22 17 1.94 23 35 52 58.0 39 23 20 1.88 49 37 23 4 1.94 58 17 37 48 1.94 44 37 51 57-6 40 52 1.94 58 ii 0.38 35 1.94 39 0.38 23 19 1.94 59 6 0.38 50 56.7 24 23 1.94 34 .40 24 6 1.94 59 2 .38 50 2.00 29 .38 49 55-8 42 54 1.94 58 .40 37 2.00 25 .40 24 2O 2.00 .52 .38 48 54-8 43 25 25 2.00 59 22 .42 25 7 2.00 49 .40 50 2.07 60 15 .42 4Z 53-9 44 55 2.00 47 .42 37 2.00 60 13 43 25 19 2.07 40 .42 46 52.9 45 26 25 6O 12 26 7 39 48 61 5 45 52.0 60/ II A 60' T A 60' || T A a a a a t A 1 6o~' A 6c/ A II 60"' . = 51=0' d = 5l 30' . = 52 0' 122 The " Newest " Navigation Altitude and Azimuth Tables, by Lieutenant Radler de Aquino, Brazilian Navy, second edition, enlarged and improved, London, 1912. Published by J. D. Potter, 145 Minories, London, E. Price IDS. 6d. net. A slightly improved method of finding the Altitude and Azimuth by means of my Tables has been developed recently whereby it is not necessary to interpolate and find the true values of b and / for the true value of declination d, as explained on pages xv, xxi, and xxv of my Tables. It is sufficient to find only in column a the values of b (always a whole degree) and of / that correspond to an approximate value of d. This approximate value of d, for con- venience, is always taken smaller than the true value, b is combined in the usual way with L A , (also always the whole degree nearest the dead reckoning latitude) to find C, and h' and Z'are found corresponding to the'tf and C. Now as this h' and Z' are for the approximate tabular value of d, we must correct h' and Z' for the difference &d between this approximate value and the true value of the declination. 1 We know from page xvii that a change of altitude A/j for a given change of declination Af is given by the formula: A/z = Adf cos M, where M is the paralatic angle. If we call, in Fig. 2 on page xii, the angle mMP : a. and the angle mMZ : ft, we have M=a+8. The value of a is found on the same line with b, d, and t (a being practically the same for all three values of a}. In the same way j3 is found on the same line opposite C, h, and Z. However, instead of finding C with L A . and b, it\is better to find L A . from b and C, as explained below. The working out of our typical example on page xix will show the great advantage of this improvement. Page 122. G. A. T. = 2o h 59 24 s a =52 o' t G . =30 36 E =45 9'.o E. ~b =17 ^'=10 7.2,' /^.=53 14.0 E a= 76.s d =10 27 G A = 8 5'.o W. Arf~= 5' C =54 '=21 13' Z'=S 57 42' E .0= 6o. 4 L A =yj A/% = -3-7 M=\itf.<) h A . =21 9'. 3 h =21 7 .o NOTE. Numbers taken out of the Tables by Inspection are black-faced in order to distinguish them from data given or found. In addition to the formulas given on page xxviii for finding L A , with b and C, we have added those for finding M with a and ft. d and L A , same name - \ L A _ > b \t > 90 L A . contrary names When / > 90 the sum C+b > 90 also, and we must subtract it from 180 to obtain L A . A simple inspection of these formulas shows that no difficult rules are necessary with this new process. A knowledge of the approximate value of L A , is always known by dead- reckoning, and, therefore, we can immediately find, in view of the fact that b and L A are always whole degrees, the value of Cthat combined with b will give us L A . The tabular value h' nearest to the true altitude h shows us opposite it also the value of C. The formulas show also that when we subtract b and C to find LA., we must add a and ft to obtain M. When we add b and C to find L A , we must subtract a and ft from one another to obtain M. The "Altitude correction" A// = 3'. 7 is given immediately by our Correction Table 2 where we enter at the top with A<^=5', and with M=i^j on the right hand side. If M is smaller than 90, enter the Table on the left hand side. The correction is plus ( + ) when M is smaller than 90, and minus ( ) when M is greater than 90, provided we always take the tabular value of the declination less than the true value. In this way Altitude and Azimuth are found by means of simple mnemonical rules without interpolating. 1 As Arf is generally only a few minutes of arc, Z f does not need in practice any correction. The formula on page xvii : AZ=sin^/sec h Ld shows us that AZ is always smaller than sec h. Under ^ = 60, AZ is always smaller than 2&d. 2 Also by our Plane Traverse Tables in LAT. column if we enter them with M as D and with M or 1 80 - M as Course. A FEW VALUABLE OPINIONS. RIVISTA MARITTIMA ITALIANA, February 1910. BlBLIOGRAFIA. " II procedimento del de Aquino e ingegnosissimo, poiche, spezzando in due triangoli sferici rettangoli il noto triangolo SPZ, conducendo 1'arco normale all'arco PZ, da una serie di relazioni ben note, che abilmente utilizzate, per mezzo di una tavola dialtezza ad azimut e tavole ausiliarie (pagg. 3-128), rende il conttegio pratico cosi semplice ed esatto per le esigenze nautiche da destare in verita meraviglia." E. MlLLOSEViCH, Director of the Observatory of Rome, Italy. ALMIRANTE GARCIA MANSILLA, DETERMINACION DEL PUNTO EN LA MAR, BUENOS AlRES, IQIO. " Sea como fuera, debo mencionar en primer term ino y con especial satisfaction, las tablas de Altura y Azimut, del sefior Radler de Aquino por ser, sin duda alguna, la mejor solution del problema que yo conozco." From Paper read before the Congreso Cientifico Internacional held at Buenos Aires, 1910. ANNALEN DER HYDROGRAPHIE UND MARITIMEN METEOROLOGIE, November 1910. RADLER DE AQUINO : Altitude and azimuth tables for facilitating the determination of lines of position and geographical position at sea. The simplest and readiest in solution. Spherical traverse tables for solving all problems of navigation. 8vo. 128 pp. London, 1910. J. D. Potter, and Rio de Janeiro, 1910. Radler de Aquino. Preis ics. 6d. Die Hohen- und Azimut-Tafeln des Leutnants RADLER DE AQUINO der brasilianischen Kriegs- Marine liefern ein recht bequemes Hilfsmittel, um die fur Anwendung der Marcq St. Hilaireschen Methode notwendigen Berechnungen der Hohe und des Azimuts ohne logarithmische Rechnung durchzufiihren. Durch Zer- legung des Poldreiecks in zwei rechtwinklige spharische Dreiecke (durch Fallen eines Lots vom Gestirnsort auf den Meridian) wird ermoglicht, dass die Losung der Haupt- aufgaben der nautischen Astronomic mit den Tafeln nach einheitlicher Methode zu erreichen ist. Um die Hohe und das Azimut eines Gestirns zu finden, geht man mit der Abweichung und dem Stundenwinkel in die Tafel und entnimmt zunachst Nahe- rungswerte zweier Hilfsgrossen (a und b). Mit diesen findet man durch nochmaligen Eingang den der Abweichung entsprechenden Wert von b und aus diesem den Wert eines Stundenwinkels, der anstatt des aus der gegissten Lange hergeleiteten Stunden- winkels benutzt wird. Das gefundene b und die zweckenfsprechend geandert Breite geben Hohe und Azimut, die also nicht fur den gegissten Ort, sondern fur einen Hilfspunkt gel ten. Es ist jedoch nach den in den Tafeln gegebenen Anweisungen nur mit wenig Mehrarbeit verkniipft, wenn man Hohe und Azimut fur das gegisste Besteck ermitteln will. Die Tafeln lassen sich, wie in der Gebrauchsanweisung aus- fuhrlich auseinander gesetzt wird, auch zur Losung anderer Aufgaben der nautischen Astronomic mit Vorteil verwenden. So lasst sich mit den Tafeln leicht ermitteln, wenn Hohe und Azimut eines Gestirnes beobachtet sind, zu welchem Gestirne diese Grossen gehoren. Auch die Ermittlung des Zeit- und des Zeithohen-Azimuts, der Amplitude und der Hohe eines Gestirns im Ersten Vertikal usw. lasst an Bequem- lichkeit nichts zu wiinschen iibrig, so dass sich diese Tafeln bald Freunde unter den Nautikern erwerben werden, die Hohenberechnungen ohne Benutzung der Loga- rithmentafeln bevorzugen. Sk. NAUTICAL MAGAZINE, February 1910. " Whether or no any marked simplification results from the use of the new processes is a point which the navigator may easily determine for himself, but we have no hesitation in endorsing the verdict of the Hydrographer of the U.S. Navy, that 'the plan of the work is sound in principle and scientific in conception. 3 The central idea is distinctly original, and the work forms an interesting addition to the literature of Nautical Astronomy." "Altogether the book is a remarkable triumph of ingenuity, and does credit to designer and printer and publisher." Rev. WILLIAM HALL, R.N., in the Nautical Magazine for November, 1910, page 486. BRAZILIAN NAVY OFFICIAL OPINIONS PARECERES OFFICIAES. Copia. Ministerio da Marinha. Estado Maior da Armada. Em 15 de setembro de 1910. Ao Sr. Vice-almirante Ministro da Marinha. Passo ds vossas maos com os presentes papeis o parecer apresentado pelo capitSo-tenente Augusto Cesar Burlamaqui, membro da commissao nomeada pelo capitao de mar e guerra Joao Baptista das Neves, commandante do encouragado Minas Geraes, para estudar o trabalho apresentado pelo capitao-tenente Radler de Aquino, intitulado Altitude and Azimuth Tables. Nao so pela leitura do referido parecer, como pela opiniao daquelle commandante, que diz que o uso dessas taboas tornou-se generalisado a bordo durante a longa commissao emprehendida pelo mesmo encouragado, do porto de Newcastle-on-Tyne ao desta Capital, facto este que demonstra a sua utilidade e o modo facil e pratico do seu emprego, podereis verificar que o trabalho desse intelli- gente e operoso official e digno de ser adoptado, pois torna de extrema facilidade o tragado da recta de posigao e resolve com um grau de precisao acceitavel para a navegagao um numeroso grupo de problemas. Saude e fraternidade. (Assignado) H. PiNHElRO GUEDES, Vice-almirante, Chefe do Estado Maior da Armada. Copia. Commando do encouragado Minas Geraes. Rio de Janeiro, 9 de setembro de 1910. N. 264. Sr. Contra-Almirante Commandante da Divisao de Encouragados. Cumpre-me enviar-vos o parecer apresentado pelo Sr. capitao- tenente Augusto Cesar Burlamaqui sobre o trabalho intitulado A Ititude and Azimuth Tables, do Sr. capitao tenente Radler de Aquino. Tendo apparecido este trabalho antes da partida deste encouracado do porto de Newcastle, nomeei uma commissao de tres officiaes do navio para dar parecer sobre o seu valor e utilidade ; esta com- missao era composta dos Srs. capitaes-tenentes Augusto Cesar Burlamaqui, Alfredo Dodsworth e Leopoldo Nobrega Moreira. Pela leitura do parecer, podereis verificar a opiniao favoravel da commissao, cabendo pela minha parte accrescentar que o uso dessas taboas tornou-se generalisado a bordo durante a commissao, facto este que demonstra a sua utilidade e o modo facil e pratico do seu emprego. Estas taboas representam mais um importante trabalho dado a" publicidade pelo seu illustre e operoso autor. Saude e fraternidade. JOAO BAPTISTA DAS NEVES, capitao de mar e guerra. Ilha Grande, 10 de abril de 1910. Passo ds vossas maos o parecer elaborado pela commissao por vos nomeada para emittir juizo sobre o trabalho da lavra do Sr. capitao-tenente Radler de Aquino, intitulado Altitude and Azimuth Tables. Em abono das referidas taboas do estudioso official da nossa marinha de guerra vem a longa commissao desempenhada pelo couragado Minas Geraes, sob o vosso com- mando, durante a qual foram verificados d saciedade os magnificos resultados forne- cidos pelas taboas em comparagao com os varios processos utilizados a bordo para o mesmo fim. O methodo Marcq, hoje defmitivamente adoptado, encontra no inestim- avel livro do Sr. capitao-tenente Radler de Aquino a sua resolucao simples, rapida e segura, tornando de extrema facilidade o tragado da recta de posigao e resolvendo com um grdo de precisao acceitavel para a navegagao um numeroso grupo de pro- blemas. Julgo que as taboas de 360 paginas, que o Sr. capitao-tenente Radler de Aquino promette publicar, facilitarao de modo tal o calculo das coordenadas da posigao do navio, que affirmo esperar o mais favoravel acolhimento por todos os que se interessam pelos progresses da navegagao. Augusto Cesar Burlamaqui, capitao- tenente, instructor de navegacao. Ao Sr. capitao de mar e guerra commandante do couragado Minas Geraes, Joao Baptista das Neves. OTHER WORKS OF THE AUTHOR NOT MENTIONED IN THESE TABLES O Methodo de Marcq Saint Hilaire para um observador determinar a sua posic^ao no mar, com taboas para a sua applicagao. Imprensa National, Rio de Janeiro, 1902. This work was printed by order of the Minister of Marine, and was first published in the Revista Maritima Brazileira for November, 1899, January, 1900, and October, 1900. Typos de calculo para o methodo de Marcq Saint Hilaire pela modificagao do Dr. Otto Fulst de Hamburgo. Imprensa National, Rio de Janeiro, 1902. Reprinted from the Revista Maritima Brazileira for December, 1901. Estudo theorico e pratico dos Instrumentos Nauticos de Lord Kelvin. DescripQao e theoria da agulha de Lord Kelvin. Magnetismo dos navios. Theoria geral dos desvios das agulhas e de sua compensagao. Imprensa National, Rio de Janeiro, 1902. Reprinted, by order of the Minister of Marine from the Revista Maritima Brazileira, August-September, 1900, January, 1901, and April-May, 1901. Causas da instabilidade do caracter magnetico de um navio. Prisma azimuthal de Lord Kelvin. Regulagao das agulhas por meio de azimuths. Determinagao do caracter magnetico de um navio. Compensagao horizontal das agulhas com azmuths. Balanga magnetica de Lord Kelvin. Compensate vertical do desvio de banda. Machina de sondar de Lord Kelvin. Indicadores : mecanico e chimico. Theoria e manejo pratico. Imprensa National, Rio de Janeiro, 1903. Reprinted from the Revista Maritima Brazileira, May and July, 1903, pages 1291 and 8, and March, 1902, page 1202. Compensagao e regulac.ao das agulhas sem azimuths. Deflector de Lord Kelvin. Theoria e manejo pratico. Methodo do Kaptain Clausen. Imprensa National, Rio de Janeiro, 1903. Reprinted from the Revista Maritima Brazileira, June, 1903. This work has been recently translated into English by Commander L. H. Chandler, U.S. Navy and published in the United States Naval Institute Proceedings for December, 1909. Estudo theorico e pratico dos Instrumentos Nauticos de Lord Kelvin. Mag- netismo dos navios. Compensagao e regulagao das agulhas com e sem azimuths. Sondagens no mar. New edition of above three works, by order of the Minister of Marine. Imprensa National, Rio de Janeiro, 1910. A Signaria Naval. Reprinted from the Revista Maritima Brazileira, January, 1903. Estudo elementar de Trigonometria Esphevica e algumas das suas applicagoes a" Astronomia Espherica, Navegagao e Geographia, edited by H. Gamier, Paris and Rio de Janeiro, 1903. Price 45. Relatorio annual da Associagao Protectora dos Homens do Mar de 1903-1904. Rio de Janeiro, 1904. JiU-JlTSU. Educagao Physica Japoneza, pelo Mr. H. Irving Hancock. Joint translation from English with the late Capitao de corveta J. A. dos Santos Porto. Rio de Janeiro, 1905. Price 45. Nomograms for Deducing Altitude and Azimuth and for Star Identification and Finding Course and Distance in Great Circle Sailing. Reprinted from the United States Naval Institute Proceedings for June, 1908. Nomogrammas para achar alturas e azimuths, &c. Reprinted from the Revista Maritima Brazileira, July, 1908. Taboas para achar alturas e azimuths facilitando a determinagao de rectas de posicao e o ponto observado no mar. Imprensa National, 1910. Reprinted from the Revista Maritima Brazileira, August, 1910. A Nomogram for Compass Deviations, with an Elementary Exposition of the Two Parallel Scale Nomograms. By Professor Guiseppe Pesci, Italian Navy. Translated from the original manuscript in Italian by Lieutenant Radler de Aquino. Reprinted from the United States Naval Institute Proceedings for December, 1910. And many other articles in the Revista Maritima Brazileira since 1899. LIST OF NAUTICAL WORKS PUBLISHED BY J, D. POTTER. 145, MINOBIES, LONDON, E.G. LIST OF NAUTICAL WORKS PUBLISHED BY J. D. POTTER. ADMIRALTY CHARTS. Official Catalogue of Admiralty Charts, Plans, and Sailing s. d. Directions, with 24 Index Charts. No charge. At Board of Trade inquiries reference is frequently made to the subject of charts (see p. 11) and sailing directions. It is doubtful, however, if the general public has the remotest idea of the vast number of charts, plans and sailing direcbions which have been brought into existence by the cartographer (see p. 12). The making of charts is a never-ending task, for the simple reason that new dangers to navigation in the way of uncharted rocks and shoals are constantly being reported. Some conception of the amount of work done is afforded by the catalogue of Admiralty charts, plans and sailing directions issued by J. D. Potter, of 145, Minories, E.G. The volume, which is published by order of the Lords Commissioners of the Admiralty, consists of 260 pages, index charts, &c., and may be obtained gratis from J. D. Potter. Shipping Gazette and Lloyd's List, May 7, 1909. On the Correction of Charts, Light Lists, and Sailing Directions; with a Short History of the Hydrographic Department of the British Admiralty. No charge. ALTITUDE TABLES. Computed for Intervals Of Four Minutes between the Parallels of Latitude 31 and 60 and Parallels of Declination and 24, designed for the Determination of the Position Line at all Hour Angles without Logarithmic Computation, by Frederick Ball, M.A. (late Scholar of Exeter College, Oxford), Chaplain and Naval Instructor in His Majesty's Fleet ... ... ... ... ... ... ... ... 15 Ditto, ditto, between the Parallels of Latitude and 30 and Parallels of Decimation and 24 15 Ditto, ditto, between the Parallels of Latitude 24 and 60 and Parallels of Declination 24 and 60 15 Altitude and Azimuth Tables, for Facilitating the Determination of Lines of Position and Geographical Position at Sea. The simplest and readiest in solution. Plane and Spherical Ti averse Tables for solving all problems of navigation. By Lieut. Radler de Aquino (Brazilian Navy). All sights for position are worked out by the same method without logarithms, with hardly any calculation. All the other problems in navigation are easily and rapidly solved by inspection without in- terpolation. This work has received the favourable endorsement of the United States Hydrographic Office. 2nd Stereotyped Edition 10 6 New Log and Versine Altitude Tables (Reprinted from the 2nd Edition of above Book), by Lieut. Radler de Aquino (Brazilian Navy). The simplest and readiest way of finding the Altitude by means of logarithms ... ... ... ... ... 2 6 ARTIFICIAL HORIZON. Description of an Artificial Horizon, invented by Capt. A. B. Becher, R.N., with examples of its application, afloat and ashore (1857) ... ... '-'- ... ... 1 gi List of Nautical Works published by J, D. POTTER, AZIMUTHS. s. d. Davis's Sun's True Bearing, or Azimuth Tables (30 N. to 30 S.), by J. E. and Percy L. H. Davis. The only means of ensuring a correct course at sea is by the use of calculated or tabular azimuths, and the latter render the operation speedy and accurate. Ihese tables, an addendum'to those of Capt. Burdwood, E.N., which preceded them, have been in very general use since their publication. The instructions in several European languages have proved of great service to foreign seamen 10 6 Davis's Supplementary Azimuth Tables (now published separately). The Time Azimnth Tables in general use do not often give azimuths near the meridian, which are in frequent demand for ex-meridian observations, but they will be found in this book, in addition to complete tables extending to latitude 64 8 Davis's Star Azimuth Tables, computed for all latitudes between 60 North and 60 South, by P. L. H. Davis. This book has followed on the very general adoption of stellar observations as a means of navigation, and supplies the seaman with the same details regarding stars, as he can get from "Burdwood and Davis" when the sun is concerned. Some ingenious altitude marks are used for the first time in these tables which materially aid in the identification of any hastily observed star, as to which doubt may exist ... ... ... ... ... ... 10 6 Short, Accurate, and Comprehensive Altitude-Azimuth Tables to show the true bearing of the Sun, Moon, Planets, &c., for latitude to 75 north or south ; altitudes to 75 ; and declination 30 north to 30 south ; also the Approximate Ship Time, by A. C. Johnson, R.N. (Published by request) 3 6 Time Azimuth Diagram, by Hugh Godfray, M.A 3 Captain Weir's Azimuth Diagram 1 6 CHRONOMETERS. Davis's " Chronometer " Tables ; or, hour angles for selected altitudes between latitudes and 50, with variations for V in all elements, by P. L. H. Davis. Means of working a Sun " Chronometer " arithmetically have been for many years a desideratum, and have been published, in 1793, by Lalande ; in 1827, by Lynn ; and by Hommey, in 1863 ; but Mr. Davis, by the omission of useless or undesirable altitudes, and the inclusion of Variations in 1' of Altitude, Latitude, and Declination, has made a table of great practical utility. The book, as a substitute for or a check on logarithmic calculation, is almost a necessity, and is especially useful in latitudes less than 45. A comparison has been made in actual work of the tabular results with those obtained in the ordinary way, showing practically identical results ... ... ... ... ... ... ... ... t 10 6 Notes on the Management of Chronometers and the Measurement of Meridian Distances, by Rear- Admiral Charles Shadwell, F.R.S. (1861) ... ... 4 6 COLUMBUS. The Landfall of Columbus on his First Voyage to America, with a Trans- Jation of The Baron Bonnefoux's History of his previous life, also a Chart showing his Track from the Landfall to Cuba, and an outline of his subsequent voyages, by Capt. A. B. Becker, J?.A r . (185G) 12 COOKERY. Ship's Cook and Steward's Guide, containing Hints for Management, and Two Hundred and Fifty Bccipes, by James B. Wilson \ List of Nautical Works published by J. D. POTTER. COMPASS. s. d. An Explanation of the Adjustment of Ships' Compasses, illustrated with numerous diagrams, by Captain the Honourable Wentworth Chetwynd, R.N. ... 2 Handbook to Bead's Compass Deviascope, by Captain George Beall, contains, in addition to a complete explanation of this well-known instrument, mnch information necessary to compass correction ... ... ... ... ... 1 6 Elementary Manual for the Deviations of the Compass in Iron Ships, intended for the nse of Seamen of the Royal Navy and Mercantile Marine, and Navigation Schools, by E. W. Creak, C.B., F.R.S., retired Captain, R.N. 6 6 Practical Information on the Deviation of the Compass, for the useoH Masters and Mates of Iron Ships, by J. T. Towson, F.R.G.S | AND I 4 Supplement to the above ; being the Questions on the Deviation of the Compass f issued by the Board of Trade for the Examination for Masters' and Extra Masters' j Certificates, and Answers to the Questions, by Capt. William Mayes, R.N. ... ...J The Pocket Compass Corrector. Makes an error in applying variation and deviation almost impossible ... ... ... ... ... ... ... ... 2 The Binnacle Compass, Corrected by itself, or the Deviation found with one Compass by both methods, and the Corrections applied, by Capt. A. B. Becher, R.N. 1 The Storm Compass, or Seaman's Hurricane Companion, containing a familiar explanation of the Hurricane Theory, by Capt. A. B. Becher, R.N., illustrated with Diagrams and Accounts of Hurricanes ... ... ... ... ... ... ... 1 6 Plain Deviation Curve Diagram, by Captain J. C. Robinson 6 CRUISE. Cruise Round the World of the Flying Squadron, 1869-1870, under the command of Rear -Admiral G. T. Phipps Hornby (illustrated), and Chart showing its Track ... 21 CURRENTS (See Tides). DEVIATION (See Compass). DOUBLE ALTITUDES. A Method for finding the Latitude by the Simultaneous Altitudes Of TWO Stars, by Capt. Burdwood, R.N. (reprinted 1896) 1 EQUAL ALTITUDES. Tables for Facilitating the Method of Equal Altitudes, by F. A. L. Kitchin, B.A., Naval Instructor, R.N. 1 EX-MERIDIANS. Davis's Ex-Meridian Tables and Supplementary Azimuths, by P. L. H. Davis. This important work contains Calculated Eeductions to the Meridian for hour angles less than 75 and altitudes lower than 84, Declinations and Latitudes 34 and 64 N. and S. The use of the book is quite easy to anyone familiar with the Azimuth Tables. The Supplementary Azimuths, which accompany it, give bearings too near the meridian for inclusion in " Burdwood and Davis," which are now in great request for position lines and ex-meridian work ... ... ... 10 6 Tables for the Reduction of Ex- Meridian Altitudes, by J.T. Towson, F.R.G.S. 1 o Ex-Meridian Diagram, by F. A. L. Kitchin, B.A., Naval Instructor, R.N. 1 GREAT CIRCLE SAILING. A Chart of South Latitudes, beyond 20degrees, to facilitate the practice of Great Circle Sailing; with an accompanying diagram for the determination of the courses and distances, by Hugh Godfray, M.A 3 List of Nautical Works published by J. D. POTTER. i _ _ _ . ..._.,. ; ^-^- ' . .. --; i^ ....:, ,- : ... T -..-; - j. ..,. --,:'- HOUR ANGLES. - S. d. Hour Angles Of the Sun, MOOrt, and Stars, for Latitude and Declination 3 -8(T, and Altitude 5 9 -64, together with Short Methods of finding the Longitude by Chron- ometer ; and the Latitude and Longitude by Two " Chronometers," by A. C. Johnson, R.N. 36 HYDROGBAPHICAL ENGINEERING. An Essay on Hydrographical Engineering, as applicable to Floating Sea Barriers, Harbours, Batteries, Coast Defences, and Naval Fortifications, by Capt. Adderly Sleigh, K.T.S., F.R.S.L. (with Illustrations), (1859) 10 INTERPOLATION. Notes on Interpolation, Mathematical and Practical, by Rear-Admiral C. Shadwell, F.R.S 2 LATITUDE AND LONGITUDE. On Finding the Latitude and Longitude in Cloudy Weather and at Other Times, by A. C. Johnson, R.N. Enlarged to 56 pages, with Appendix and Part II 5 Short Tables and Rules for finding Latitude and Longitude, by Single and Double Altitudes, Pole Star, Lnnars, &c., by A. C. Johnson, R.N. 3 Scales of Latitude from 5 to 60 proportional to a scale of Longi- tude, where $ in. = one mile, arranged to facilitate the finding of position from two Snmner lines, by R. E. Pealce, AM.I.G.E. ... ... ... per set 5 Charts to accompany above each 2 6 Tables showing the Length in Feet of a Degree, Minute, and Second Of Latitude and Longitude, with the corresponding number of Statute Miles in each Degree of Latitude ; and the number of Minutes of Latitude or Nautical Miles contained in a Degree of Longitude, under each Parallel of Latitude, by R. <7. Carrington, F.R.G.S. (1868) 1 See also Double Altitudes, Equal Altitudes, Ex- Meridians, Hour Angles, Lunars. LAW. Admiralty Procedure against Merchant Ships and Cargoes, &c., in the High Court of Justice and in County Courts, showing the various matters as to which proceedings in Admiralty can be taken, and the mode of commencing action, &c., by R. G. M. Browne, the Admiralty Marshal (1889) 10 Handbook on the Law and Practice relating to Apprentices to the Mercantile Marine Service, by F. W. Gardner (of the Middle Temple) ... 1 6 The Statute Law Of Merchant Shipping, comprised in an alphabetical Analysis, and a Summary of the unrepealed Merchant Shipping Acts, from 1821 to 1888, by R. G. M. Browne, the Admiralty Marshal (1889) 60 LIGHTS. Lights in Lyrics, or a Glance at the Channel Lights as Piloting Marks, on a run from Scilly to the Nore, accompanied by a Parting Precept on Compass Deviation, addressed to all younger Mariners. With a view of the Casquets, Notes and Charts. (1859) 1 a List of Nautical Works published by J. D. POTTER. LOGARITHMS. Davis's Requisite Tables (Logarithmic), by P. L. H. Daiis. Tables of e. d. Logarithms to five places of decimals only, for practical sea work. The typography and arrangement of the book will render it suitable for habitual use, and it contains a table of Logarithmic and Natural llaversines specially designed Tor modem navigation 7 6 Davis's Five-Figure Logs and Anti-Logs, by P. L. H. Davis. Specially pre- pared for use in Actuarial and General Calculations. These tables are very legible and do not fatigue the eye in use 5 Pitto ditto with Index Tabs 60 LUNARS. Notes on the Reduction of Lunar Observations, Mathematical and Practical, by Rear-Admiral C. Shadwell, F.R 8. (1881) ... 4 6 See also Latitude and Longitude. MAST-HEAD ANGLES. Tables Of Ma&t- Head Angles, for five feet intervals, from 30 to 280 feet, and varying distances from a cable's length to four miles, with their application to Nautical Surveying; also the determination of distance by sound, with an example... ... 2 MEASURES. Foreign Measures and their English Values, compiled from Official Sources, by R. C. Carrington, F.R.G.S. (1864) 7 6 MERCANTILE MARINE. A Voice from the Quarter-Deck on the State of our Mercantile Marine, by Joseph Mayne (Master Mariner) (1876) 1 An Address delivered to the Boys of the Training Ships " Chichester " and "Arethusa," by 0. M. Coxhead (1885) 4 METEOROLOGY. Solectr'lCS ; a theory explaining the causes of Tempests, Seismic and Volcanic Disturbances, and how to calculate their time and place. Illustrated by over 100 diagrams, by Alfred J. Cooper, Navigator, King's Medallist 10 The Causes of Weather and Earthquakes (with four Diagrams), by Alfred J. Cooper (1902) 2 Light as a Motive Power, a Series of Meteorological Essays (1875), by Lieut. R. H. Armit, R.N. 15 See also Winds. REVERSIBLE TRANSIT INSTRUMENT. Notes on the use of the Portable Reversible Transit, and the Method of Calculation of the Observations, with diagrams and photographs, by Capt. C. E. Monro, R.N. ... ... ... ... ... ... 3 ROYAL NAVY. Chart of the Navy of Great Britain, from the Earliest Period of History, compiled from Historical publications, old records, Parliamantary returns, and other authorities, by Frederick Perigal (of the Admiralty), 1860 ^ 3 6 SAIL-MAKING. Remarks on Rigging Ships with Flat Surface Sails, by Lieut. William Conpalton, R.N.R. (1965) 2 Q 7 List of Nautical Works published by J. D. POTTER. NAVIGATION AND NAUTICAL ASTRONOMY. *. d. Nautical Astronomy, by TF. P. Sy mends. f (E-z.-Commi&ioner of Surveys)* The beet . methods of calculating Hour- Angle, and finding Longitude and Latitude. The shortest Ex-Meridian method with New Table. Sidereal and Mean Time made clear. The New Navigation explained and the Modern methods of working Double Altitudes, and drawing Position lines. The Equation of Equal Altitudes made easy, and used for finding Longitude from Ex-Meridians, and for determining error in Latitude due to Ship moving N. or S. Lunars simplified. Chapters on finding Distances, the Tides, &o., with many diagrams ... Nautical Astronomy Made Easy, by A. C. Johnson, R.N. All the Rules being worked by a Small Table on One Page, designed to economise Time and Labour ... 3 An Introduction to the Practice of Navigation and Nautical Astronomy, by R. E. Hooppell, M.A., F.R.A.S. 3 6 The Practice of Navigation and Nautical Astronomy, complete with tables, by Lieut. Roper, R.N. (See also the " New " Navigation) 16 Nautical Tables, by Lieut. Roper, R.N. ( do., do. ) 10 6 Inman's Nautical Tables. A New Edition of this standard work, revised and brought thoroughly up to the present date, by the Rev. William Hall, R.N., and containing all the aids to rapid fixing of position which are essential in modern Navigation 16 Lectures on Elementary Navigation, by Rev. J. B. Harbord, M.A. (Retired Naval Instructor, R.N. ; late Inspector of Naval Schools, Admiralty ; Examiner in Navigation and Nautical Astronomy for the Department of Science and Art ; Author of " Glossary of Navigation ") ... ... ... ... ... ... ... 7 6 Navigation Simplified, by a System of Teaching based on First Principles, for Officers (from 2nd Mate to Extra Master) in the Mercantile Marine and Yachtsmen. Illustrated by numerous diagrams, by Captain P. Thompson, F.R.A.S., Younger Brother of the Trinity H( use, Senior Examiner of Masters and Mates, and Secretary to the Local Marine Boar (. of London ... ... ... ... ... ... ... 12 Examination Diagram? Simplified, for Navigation Students; illustrated by sixteen diagrams (including 5| inch Boxwood Scale), by Captain P. Thompson, F.R.A.S 2 6 Navigation, intended for Self -Instruction up to the Second Mate's Examination, by William Roy ... . 6 Practical Coastal Navigation, with numerous charts and diagrams, by Count de Miremont ... ... ... ... ... ... ... ... ... ... ... 4 Tables of Allowance for Current when affecting Compass Course and Ship's Speed, by Copt. G. E. Hoar, War Department Fleet. A small and convenient Table to give by inspection the correction to a Compass Course made necessary by a Current in any direction, and the resulting distance made good. A desirable book for all Coastwise Navigation ... ... ... ... ... ... 2 "THE 'NEW NAVIGATION." Appendix to Paper's Practice of Navigation. Being an explanation of the New Astronomical Navigation by the method of Calculated Zenith Distances, with Special Tables for Simplifying and Shortening the work, by William Hall, R.N., F.R.A.S., Chaplain and Naval Instructor (Chief Naval Instructor, Royal Australian Navy) ... ... ... ... ... ... ... ... ... ... 1 o See also Altitude Tables. RULES OP THE ROAD. The Rules Of the Road at Sea, comprising the Regulations for preventing collisions at Sea, 1897, and Eules in force in Harbours, Rivers, and Inland Waters ; with explanatory notes and observations, by H. Stuart Moore, of the Inner Temple and the Admiralty Court, Barrister-at- Law. (Third Edition) 7 C Diagrams, with Explanations, illustrating the Rule of the Road for Sailing Ships, by Copt. H. S. Blaclcburne 2 3 H (How's Her Head) Indicator and Rule of the Road at Sea, by George Spillane .,, .,. ... .,, ... ,,, it , ,,, ti> i Q 8 List of Nautical Works published by J. D. POTTER. SALVAGE. s. d. Salvage Operations, The floating of H.M. Battleship ".Howe." Illustrated by 23 plans and photographs, by Rear-Admiral G. T. H. Boycs, la.lc Flag-CaptainHM 8. "AnBon."(1900) ... .... ... ... t 5 How Ships are Lost, and How to Save Life and Property at Sea (Illustrated), by W. P. B. Manser (1877) 1 SEAMANSHIP. Under Square Sail, by Capt. Withers (1898) 2 o Under the Red Ensign; or, "Going to Sea," by Thomas Gray (1892) ... 1 6 SAILING DIRECTIONS. Canadian North Atlantic Steamship Routes between the British Isles and Canada* Distance, Latitude, Longitude, Variation, and true Course, by R. A. Woodward, Lieut. R.N.R 5 Correct Magnetic Courses and Distances, from and to Various Ports round the British Isles, by Arthur Underhill, LL.D., Commodore of the Royal Cruising Club, assisted by several Members of the Club. Second Edition 2 Concise Navigating Directions for the River Thames, including all the Pools, Reaches, and Channels, from London Bridge to the South Foreland and Orfordness, and for the English Channel to Beachy Head; also for the Port of Dunkerque and the approaches to the Scheldt, by Stephen Penny, Trinity Pilot, Gravesend (illustrated by nineteen Charts) 70 East Coast Rivers. Charts and Sailing Directions for the Rivers Roach, Crouch, Blackwater, Colne, Stour, Orwell, Deben, Ore and Aide; together with General Charts from the Thames to Southwold, by Lieut. 8. V. 8. C. Messum, R.tf. 5 The Pilot's Guide for the English Channel (with which is now incorporated "The Pilot's Handbook for the English Channel" by Staff Commander J. W. King, R.N.), comprising the South Coast of England, and general directions for the Navigation of the Channel; with numerous Charts and Plans of Harbours, edited by H. D. Jenkins, F.R.G.S 7 fi Yacht Cruising, illustrated with drawings and sketches, by Claud Worth. (This book consists partly of " logs " of cruises and partly of articles and notes on various matters connected with cruising) ... ... ... ... ... ... ... ... 7 A Chart of the Dutch Waterways, by J. & A. B. Powell 4 o From Calcutta to Bombay Coasting, being the Second Edition of the Hand- book to the Ports on the Coast of India between Calcutta and Bombay, including Ceylon and the Maldive and Laccadive Islands, with 11 Charts and 12 Photographs, by Lieut. H. 8. Brown, R.N.R., Port Officer, Marine Department, Madras Presidency. 10 Winds and Currents of the Mediterranean, by Capt. A. B. Becher, R.N., with remarks on its Navigation at different Seasons of the Year, compiled from various authorities, chiefly Spanish (1864) 30 Navigation Of the Atlantic Ocean, by Capt. A. B. Becher, R.N., with an account of the Winds, Weather and Currents found therein throughout the year (with Charts) (1892) 5 Navigation of the Indian Ocean, China and Australian Seas, by Capt. A. B. Becher, R.N., with an account of the Winds, Weather, and Currents found therein throughout the year (with Charts) (1864) 5 Chart of the Sulina Branch of the Danube (European Commission of the Danube), surveyed by Robert Hansford, Surveyor of the Commission, under the direction of C. A. Hartley, Engineer in Chief (showing 45 nautical miles of the River from Sulina), size 10 ft. x 2 ft. 3 in. (1860) 20 Notes On Cherbourg (Geographical and Historical description of, Ac.), and Chart (1858), by Commander Bedford Pirn, R.N., F.R.G.S ... 1 List of Nautical Works published by J. D. POTTER. SEXTANTS. s. d. Stars and Sextants. Star Distance Tables for facilitating the use of Lord Ellenborough's method of Correcting the Centring and Total Errors of Sextants at Sea, by John Abner Sprigge, Wm. Fraser DoaJc, M,A., F.R.A.S., T. Charlton Hudson, B.A., F.R.A.8., of H.M. Nautical Almanac Office, Admiralty, and Arthur 8. Cex, B.Sc.,A.R.C.S 2 6 Captains' and Officers' Bridge or Poop Companion, Tables for finding the distance of an object at sea by inspection (without the use of pencil or paper), at the same time giving the distance the ship will go wide of the object before getting to it, and the course to steer to obtain a required distance. The above gives, with the aid of a compass only, the distance of a moving ship from any fixed object. By A. Hutteroth 2 6 Course and Position by Sextant Observations of two known Objects, by Lt.-Col. English, late R.E 6 SHIPPING. Historical Notes on Shipping, by P. L. Isaac, M.I.N.A. (1879) 1 o SIGNALS. Signal Cards British System, with Plates, containing Instructions for Sema- phoring by Day, and with the Morse Code by Day or N ight, together with the principal " Urgent " Light or Sound Signals, in accordance with the New Code. Also, Sheet of New Code Flags (34 Flags, coloured). Compiled by J. Whitly Dixon (Retired Captain, Royal Navy). (Size, 24 x 19) 1 6 Ditto ditto mounted on thick card 2 SPEEDS. Speed and Consumption of Steam-Ships and Stability, with Algebraic Formula for Economical Speed, and Rules for calculating the alterations in Draught and Trim corresponding to Changes in Displacement, and for using the Hydrometer to estimate those due to Differences in the Specific Gravity of the Water ; for use in the Royal Navy and Mercantile Marine ; to which has been added a Chapter on Stability, with Practical Rules; Second Edition, Revised and Enlarged, by/. F. Ruthven, Master Mariner, late Lieut. R.N.R., AssocJnst.N.A., Younger Brother of the Trinity House, F.R.Q.8 4 Speed Tables, for finding the distance run in a given time at a given speed, between the limits of 10 to 18 knots, by J. D. Macpherson (Pacific Steam Navigation Co.) ... 1 STABILITY. A New Theory Of the Stability Of Ships, second edition, revised and enlarged (with 28 diagrams), by Alf. J. Cooper (1899) 2 See also Speed and Consumption of Steamships, STABS. The Bearings Of the Principal Bright Stars of greater declination than 23 north or 23 south ; also those of the Moon and Planets when similarly situated, by A. C. Johnson, R.N. (Published by request) ... ... ... ... ... ... 3 o Pole-Star Latitude : a Method of Finding the Latitude from an Altitude of the Pole Star, by Darnton Hution (Master Mariner), B.A., MJnst.C.E 1 Position-Line Star Tables, A new and simple method of fixing ship's position by observations of stars near Meridian and Prime Vertical without logarithmic calculation, by H. B. Qoodunn, R.N. ... ... ... ... ... ... ... ... 5 o Tables for Facilitating the Determination of the Latitude and Time at Sea by Observations Of the Stars, by Rear-Admiral C. Shadwell, F.R.S. 2 6 A Handbook for Star Double Altitudes, by A. C. Johnson, R.N., with directions for selecting the Stars ... ... ... ... ... ... ,., ... ... 2 6 See also Sextants. Id List of Nautical Works published by J. D. POTTEE. SURVEYING. s. d. Practical Nautical Surveying and the Handicraft of Navigation, by Com. T. A. Hull, R.N. 3 Practical Observations on Surveying (on determining the Position of a Vessel when Sounding), by Commander P. F. Shortland, R.N. 1 WINDS. The True Direction and Velocity of Wind, observed from Ships while Sailing, by James N. Miller (Member of the Liverpool Polytechnic Society), with Table for Indicating the Trne Direction of the Winds at Sea (1870) C The Wind in its Circuits: with the explanation of the Origin and Cause of Circular Storms and Equinoctial Gales ; illustrated with numerous Diagrams and a Chart of the Prevailing Winds of the World for Spring and Slimmer, by Lieut. R. H. Armit, R.N. (1870) 7 See also Meteorology and Sailing Directions. TIDES. Moxly's Theory Of the Tides, with numerous diagrams, Second Edition, Revised and Enlarged, by Capt. J. F. Ruthven, F.R.C1.S 5 Tide Charts of the English and Bristol Channels and entrance of the Thames, compiled from the Admiralty Tide Tables, by Algernon Heber Percy, late Lieut. Royal Navy 5 The Direction and Rate of the Tidal Streams at every Hour, for 48 Localities between the Nore and Scilly Isles, compiled from Admiralty Sources only, by F. Howard Col lins ... ... ... ... ... ... ... ... 2 The General Direction of the Tidal Streams in the North Sea for every Hour "before" and "after," and at High Water, Dover, compiled by Com. G. K. Gandy, R.N.R., from Official Publications (on one sheet, size 23 by 17 inches) 1 The Universal Tidal Ready Reckoner, calculated by Capt. w. E. Hutchinson. 1 6 The North Sea, Its Physical Characteristics, Tides, Currents and Fisheries, by W. H. Wheeler, H.Inst.C.E. 2 6 The Currents on the South-Eastern Coasts of Newfoundland and the Amount of Indraught into the Largest Bays on the South Coast, from Investigations of the Tidal and Current Survey in the Season of 1903, by W. Bell Daivson, H.A., D.Sc., F.R.S.C., H.Inst.C.E., Superintendent. Published by order of the Minister of Marine and Fisheries, Ottawa No char ye. The Currents in the Gulf of St. Lawrence, including the Anticosti Region, Belle Isle, and Cabot Straits, condensed from the Reports of the Survey of Tides and Currents for the Seasons of 1894, 1895, and 1896. Published by order of the Minister of Marine and Fisheries, Ottawa ... ... No chary c. The Currents at the entrance of the Bay of Fundy and on the Steam- ship Routes in or approaching Southern Nova Scotia, from investi- gations of the Tidal and Current Survey in the Season of 1904, by W. Bell Dawson, M.A., D.Sc., F.R.S.C., H.Inst.C.E., Superintendent. Published by the Department of Marine and Fisheries, Ottawa, Canada No charge. The Currents in Belle Isle Strait, from Investigations of the Tidal and Current Survey in the Seasons of 1894 and 1906. By W. Bell Dawson, M.A., D.Sc., F.R.S.C., M.Inst.C.E., Superintendent. Published by the Department of Marine and Fisheries, Ottawa, Canada ... ... ... ... ... ... ... ... ... No charge. Tables of Hourly Direction and Velocity of the Currents and Time of Slack Water in the Bay of Fundy and its Approaches as far as CapG Sable. From Investigations of the Tidal and Current Survey in the seasons of 1804 and 1907. By W. Bell Dawson, H.A., D.Sc., H.Inst.C.E., Superin- tendent. Published by the Department of Marine and Fisherits, Ottawa, Canada No charge. See also Time. 11 List of Nautical Works published by J. D. POTTER, TIME. s. d. How to Find the Time at Sea in less than a Minute, being a New and Accurate Method, with specially adapted Tables, by A. C. Johnson, R.N. 2 6 Time, Tide, and Distances. A handy book of reference for the Shipowner, Underwriter, or Traveller. Contains the World's Time compared with Greenwich ; the Tides round the British Coasts and those from Bergen via the Eastern Eoute to Japan with that at London Bridge ; approximate Distances from Home Ports to Home and Foreign Ports (over 13,000 references) ; and a Speed and Distance Table for Bates of Speed from 8 to 21 knots for distances up to 14,000 nautical miles, by J. McKirdy, R.N.R ... ,. 15 Time-Altitudes for Expediting the Calculation of Apparent-Time, &C,, by A. C. Johnson, R.N. ... 4 The Blue Coat Boys' Clock. A dial showing the simultaneous time of day at all parts of the earth's surface, size 20 x 17 inches. ... ... ... ... .... ...50 See also Azimuths, Chronometers, Tides. INCORRECT CHARTS. SPECIAL BOARD OF TRADE OFFICIAL NOTICE TO SHIPOWNERS. NOTICE TO SHIPOWNERS AND AGENTS. The attention of the Board of Trade has frequently been called to cases in which British vessels have been endangered or wrecked through Masters attempting to navigate them by means of antiquated or otherwise defective Charts. The Board of Trade desire, therefore, to direct the especial attention of Shipowners and their Servants and Agents to the necessity of seeing that the Charts taken or sent on. board their Ships are corrected down to the time of sailing. Neglect to supply a ship with proper Charts will be brought prominently before the Court ot Inquiry in the event of a wreck occurring from that cause. The Official Catalogue of Charts, plans and sailing directions, published by the Admiralty (issued annually in March), can be obtained free of charge on application to the Chart Agency, 145, Minories, London, B.C., or from any of the sub-agencies at the Home or Foreign Ports. P. HOWARD COLLINS'S SINGLE-HANDED DIVIDERS, Specially Designed for Navigators. THE advantages of these Single-handed Dividers are that they can be picked up from the table by one hand alone, and the legs opened or closed by the finger and thumb of the same hand, without any other assistance whatever. Navigators are thus enabled to work, and retain in position, the parallel ruler with one hand, while distances are being measured with the other. It is needless to say that this enables much time to be saved in laying off courses and distances, a matter for consideration in these days of steamers travelling a mile in less than two-and-a-half minutes. These Dividers are of the best make in German-silver, price 7s. 6d. per pair in Cardboard box, and with special cleat and screws for fixing to the chart-room bulk-head to hold them when not in use. 12 ADMIRALTY GHAUTS. Statement showing the number of New British Admiralty Charts Published and Corrections made t( the Chart Plates, &c., for the years 1885, 1890, 1895, 1900, 1905 and 1910. 1885 1890 1895 1900 1905 1910 New Chart Plates Engraved and Published 54 76 114 102 110 45 Chart Plates Improved by Additional Plans 32 10 34 30 36 33 Chart Plates Improved by Corrections and Additions 186 130 163 224 196 612 Corrections Made to the Chart Plates 2,750 4,750 5,300 4,520 5,320 8,500 Notices to Mariners, issued 243 723 728 874 1,392 1,809* Of each of these Notices 4,350 copies are printed off and distributed to H.M. Fleet, the British and Foreign Mercantile Marine Services, Yachting: centres, and the general Shipping: public. Books of Sailing Directions have been Published for every Sea. UNIVERSITY OF CALIFORNIA LIBRARY BERKELEY Return to desk from which borrowed. This book is DUE on the last date stamped below. ASTKCNOMY LIB 3ARY LD 21-100m-ll,'49(B7146sl6)476 UNIVERSITY OF CALIFORNIA LIBRARY