mmmmnn UC-NRLF Bq 5^3 bm n, o. :n^o. 200 .TTTUDE, AZIMUTH, and LINE OF POSITION >MPR!SING TABLES FOR WORKING SIGHT OF HEAVFi^LY BODY FOR LINE OF POSITION BY 'HIE COSINE.HAVEBSINE FORMULA, MAKCQ SAINT HILAIRE METtiOD AQlJINer limb, ^f • Table ni. Logaiithiric Sinefr aflil Logarithrnic Cofinos . . « Tabk IV, Logaritarmc !-2ayeii,ines and Natural HaYeisme^ , , Table V. Th§ Finding of tie Azim'jitlis , . » , Expiaiialion of Atfjbo'c Methoa ... ... Table VI. AquinoV Sf^erical Traverse Table . . ; . ; . . ;- . Table Vli, Change of Aldhide per Minute of Are of l-JoiBr An^e ^ Table Vni. Change oi Azimuth per Mi'sote of AJtiUide , . , , Table IX. ConveitiQMol Am^Txme .,..., ^ PUKJSHED BY TKE HYDROGRAPHIC Ornca 1 UNDER THE AUTOORmr OF THE r SECRETARY OF THE NAVY IThird Rcpriatl WASHINGTON GOVEW^MEMT HlifmKO OFfJCf, 191S 3 201. 3 IS 320 v\ \. Example: At sea, January 15, 1916, about 8.30 a. ra., in Lat. by D. R. 30° 10^ N., Long, by D. R. 45° 15^ W., the sextant altitude of the sun's lower limb, bearing sout^liward and eastward, was 17° 40^ 50^'. Index correc- tion+i" OO-"-' liright of eye, 29 feet. Watch time, 8^' 30"' W; C.-W. 3" 02"» 40». Chronometer slow of G. M. T., 7"» 10^ Required: The altitude difference and the azimuth for laying down the line of position from the D. K. position. Formula: hav 2=hav (L'~(/)+cos L cos (/ ha V f =hav (L'^d)+hav 9 Times. Declination. H. D. Eq. of T. H. D. gh 3om iQ3 " G. M. noon, 1c 3 02 40 Jan. 15. f ______ (Jorr. S. W. T. C.-W. is. 21' 18^ N. 0' G. M. T. . ii> Eq. of T. (-)toM. T. ym lis 4 ^ o» Corr. — .3 — 9 C. T. G. C. G. M. T. \ 14th Jan.; or 15th Jan. 11 32 50 7 10 S.21 ]9'.0 Corr. S. 0.1 23 40 00 - 20 00 G. M. T. Long. W. 23 40 00 3 01 00 L. M. T. ' 20 39 00 Eq. ofT. - 9 ILl L. A.T. 20, = 3 29 30 48.9 n. 1 SOLUTION. L— N. 30° lO'.O rf-S. 21 19.0 ll.«l log hav=9. 29213 log cos=9. 93680 log cos=9. 96922 L'-N-'d* Calculated /i= Observed h-Q- Alt. diff. = 51° 29'.0 ©log hav=9. 19815a e nat hav= . 15782 nathav= . 18863 17 17 06 53 49 55 05 59 nat hav= . 34645 3' 06''=3^ 1 9-lLl Corr. 0.3 Altitude. By obs. 17° 40' 50' Index corr. + 1 OU Tab. I + 8 09 /j-e-17 49 59 Azimuths. 51° E. from Table V [as explained in the preface to that table]. a Since loparithraic haversines and natural haversines an: set down side by side in Table IV, the natural haversine may be found from the logarithmic haversine without taking out the vahie of the corresponding angle. Example: At sea, August 18, 1916, in the early morning, in Lat, by D. R. 34° 10' S., Long, by D. R. 172° 26' 30' E., the sextant altitude of the star Sirius, bearing eastward, was 25° 48' 50'^. Index correction +3' 10". Height of eye 40 feet. Watch time of observation, 4'» 30™ 15^ C.-W., 0>' 29"^ 45\ Chronometer fast of G. M. T., 13°» 40^ Required: The altitude difference and the azimuth for laying down the line of position from the D. R. position. Times. W. T. 4h 30°^ 15» C.-W. 29 45 C. T. C. C. 5 00 13 00 40 G. M. T. 17th Aug. R.A.M.S. 9 46 42 20 54.5 G. S. T. Long. E. 14 11 29 29 14.5 46 L. S. T. R. A. star 1 6 59 41 00.5 28.2 t= 4 42 27. 7 [From Nautical Almanac] R. A. Star. Dec. star. Aug. 1<» 0^=(j^ 41°^ 27^ 8 S. 16° 35'. 9 Sept. 1 =6 41 28 . 6 16 35 . 8 Aug. 17'^ S^^^e 41 28 . 2 16 35 . 8 SOLUTION. t= 4" 42'»27^7 L=S. 34° 10^ d=S. 16 35.8 log hav=9. 52381 log cos=9. 91772 log cos=9. 08152 elog hav=9. 4230^ L~d= Calculated h= Observed /8>j< Alt. diff. 17° 34'. 2 64° 56' 15" 25 03 45 25 43 48 nat hav=0. 26487 nat hav=0. 02333 nat hav=0. 28820 40' 03"=40'.05 R. A. mean sun. Aug. 17^ 0^=d^ 42™ 07«.5 Reduction"! n ^r, « forG.M.T.r 47.0 R.A.M.S. 9 42 54.5 Altitude. By obs. 25° 48' 50" Index corr. + 3 10 Table I 25 52 00 -» 8 12 71*25 43 48 Azimuth S. 86° E. from Table V [as explained in the preface to that table]. TABLE I GORRECTIONS TO BE APPLIED TO THE OBSERVED ALTITUDE OF THE SUN'S LOWER LIMB, OR OF A STAR OR PLANET l^^h" ^ ;^ Page 4] TABLE I. Astren. ( Corrections* to be Applied to the Observed Altitude of a Star or of the Sun 'a Lower Limb, to Find the True Altitude. Obs. Alt. HEIGHT OF THE EYE. 1 8 Feet. 9 Feet. 10 Feet. 11 Feet. 1 12 Feet. 13 Feet. 1 O * O * O * O * O * O * Sun's Star's Sun's Star's Sun's Star's Sun's Star's Sun's Star's Sun's Star's Corr. Corr. Con. Corr. Corr. Corr. Corr. Corr. Corr. Corr. Corr. Corr. (+) (-) (+) (-) (+) (-) (+) (-) (+) (-) (+) (-) 6 30 5 29 10 40 5 19 10 50 5 09 11 00 5 00 11 09 4 51 11 18 4 43 11 26 40 5 39 10 30 5 29 10 40 5 19 10 50 5 10 10 59 5 01 11 08 4 53 11 16 50 5 49 10 20 5 39 10 30 5 29 10 40 5 20 10 49 5 11 10 58 5 03 11 06 7 00 5 59 10 10 5 49 10 20 5 39 10 30 5 30 10 39 5 21 10 48 5 13 10 56 10 6 08 10 01 5 58 10 11 5 48 10 21 5 39 10 30 5 30 10 39 5 22 10 47 20 6 17 9 52 6 07 10 02 5 57 10 12 5 48 10 21 5 39 10 30 5 31 10 38 7 30 6 26 9 43 6 16 9 53 6 06 10 03 5 57 10 12 5 48 10 21 5 40 10 29 40 6 34 9 35 6 24 9 45 6 14 9 55 6 05 10 04 5 56 10 13 5 48 10 21 50 6 42 9 27 6 32 9 37 6 22 9 47 6 13 9 56 6 04 10 05 5 56 10 13 8 00 6 50 9 19 6 40 9 29 6 30 9 39 6 21 9 48 6 12 9 57 6 04 10 05 10 6 57 9 12 6 47 9 22 6 37 9 32 6 28 9 41 6 19 9 50 6 11 9 58 20 7 04 9 05 6 54 9 15 6 44 9 25 6 35 9 34 6 26 9 43 6 18 9 51 8 30 7 11 8 58 7 01 9 08 6 51 9 18 6 42 9 27 6 33 9 36 6 25 9 44 40 7 18 8 51 7 08 9 01 6 58 9 11 6 49 9 20 6 40 9 29 6 32 9 37 50 7 24 8 45 7 14 8 55 7 04 9 05 6 55 9 14 6 46 9 23 6 38 9 31 9 00 7 30 8 39 7 20 8 49 7 10 8 59 7 01 9 08 6 52 9 17 6 44 9 25 20 7 42 8 27 7 32 8 37 7 22 8 47 7 13 8 56 7 04 9 05 6 56 9 13 40 7 53 8 16 7 43 8 26 7 33 8 36 7 24 8 45 7 15 8 54 7 07 9 02 10 00 8 04 8 05 7 54 8 15 7 44 8 25 7 35 8 34 7 26 8 43 7 18 8 51 20 8 14 7 55 8 04 8 05 7 54 8 15 7 45 8 24 7 36 8 33 7 28 8 41 40 8 23 7 46 8 13 7 56 8 03 8 06 7 54 8 15 7 45 8 24 7 37 8 32 11 00 8 32 7 37 8 22 7 47 8 12 7 57 8 03 8 06 7 54 8 15 7 46 8 23 30 8 44 7 25 8 34 7 35 8 24 7 45 8 15 7 54 8 06 8 03 7 58 8 11 12 00 8 55 7 14 8 45 7 24 8 35 7 34 8 26 7 43 8 17 7 52 8 09 8 00 30 9 06 7 03 8 56 7 13 8 46 7 23 8 37 7 32 8 28 7 41 8 20 7 49 13 00 9 16 6 53 9 06 7 03 8 56 7 13 8 47 7 22 8 38 7 31 8 30 7 39 30 9 25 6 44 9 15 6 54 9 05 7 04 8 56 7 13 8 47 7 22 8 39 7 30 14 00 9 33 6 36 9 23 6 46 9 13 6 56 9 04 7 05 8 55 7 14 8 47 7 22 15 00 9 49 6 20 9 39 6 30 9 29 6 40 9 20 6 49 9 11 6 58 9 03 7 06 16 00 10 02 6 07 9 52 6 17 9 42 6 27 9 33 6 36 9 24 6 45 9 16 6 53 17 00 10 15 5 54 10 05 6 04 9 55 6 14 9 46 6 23 9 37 6 32 9 29 6 40 18 00 10 25 5 44 10 15 5 54 10 05 6 04 9 56 6 13 9 47 6 22 9 39 6 30 19 00 10 35 5 34 10 25 5 44 10 15 5 54 10 06 6 03 9 57 6 12 9 49 5 20 20 00 10 43 5 25 10 33 5 35 10 23 5 45 10 14 5 54 10 05 6 03 9 57 6 11 22 00 10 59 5 09 10 49 5 19 10 39 5 29 10 30 5 38 10 21 5 47 10 13 5 55 24 00 11 12 4 56 11 02 5 06 10 52 5 16 10 43 5 25 10 34 5 34 10 26 5 42 26 00 11 23 4 45 11 13 4 55 11 03 5 05 10 54 5 14 10 45 5 23 10 37 5 31 28 00 11 33 4 35 11 23 4 45 11 13 4 55 11 04 5 04 10 55 5 13 10 47 5 21 30 00 11 41 4 27 11 31 4 37 11 21 4 47 11 12 4 56 11 03 5 05 10 55 5 13 32 00 11 49 4 19 11 39 4 29 11 29 4 39 11 20 4 48 11 11 4 57 11 03 5 05 34 00 11 56 4 12 11 46 4 22 11 36 4 32 11 27 4 41 11 18 4 50 11 10 4 58 36 00 12 02 4 06 11 52 4 16 11 42 4 26 11 33 4 35 11 24 4 44 11 16 4 52 38 00 12 07 4 01 11 57 4 11 11 47 4 21 11 38 4 30 11 29 4 39 11 21 4 47 40 00 12 12 3 55 12 02 4 05 11 52 4 15 11 43 4 24 11 34 4 33 11 26 4 41 45 00 12 23 3 44 12 13 3 54 12 03 4 04 11 54 4 13 11 45 4 22 11 37 4 30 50 00 12 31 3 35 12 21 3 45 12 11 3 55 12 02 4 04 11 53 4 13 11 45 4 21 55 00 12 38 3 27 12 28 3 37 12 18 3 47 12 09 3 56 12 00 4 05 11 52 4 13 60 00 12 44 3 20 12 34 3 30 12 24 3 40 12 15 3 49 12 06 3 58 11 58 4 06 65 00 12 51 3 13 12 41 3 23 12 31 3 33 12 22 3 42 12 13 3 51 12 05 3 59 70 00 12 56 3 07 12 46 3 17 12 36 3 27 12 27 3 36 12 18 3 45 12 10 3 53 75 00 13 00 3 02 12 50 3 12 12 40 3 22 12 31 3 31 12 22 3 40 12 14 3 48 80 00 13 06 2 56 12 56 3 06 12 46 3 16 12 37 3 25 12 28 3 34 12 20 3 42 85 00 13 10 2 51 13 00 3 01 12 50 3 11 12 41 3 20 12 32 3 29 12 24 3 37 90 00 13 14 2 46 13 04 2 56 12 54 3 06 12 45 3 15 12 36 3 24 12 28 3 32 1 Additio ■^AL COEB. Day of month. Jan. Feb. Mar. Apr May. June. July. Aug. Sept. Oct. Nov. Dec. „ „ „ „ „ „ „ „ „ „ „ „ FOE SC rs'9 Alt. l9t 1 to 15th... +18 +15 +8 - 8 -13 -14 -11 -5 +3 +11 +16 16th to 3l8t.. +17 +12 +4 -4 -11 -14 -13 -9 -1 +7 +14 +18 *Thecc rrections for the ob? erved altitude of a £ tar or Planet involves the dip and the refraction; md for the observed altitude of the Sun 's lower limb, the di p, refraction, paralls X, and mean somidiameter, w hich is taken at 16'. A supplementary correction taking ace ount of the variatioi 1 of the Sim's semidi ameter in the different month. 5 of the year is given at the foot of the main table. C3oa5A.CYN-6vvw v-> JwViX" TABLE I. [Page 5 Corrections to be Applied to the ObBcrved Altitude of a Star or of the Sun'e the True Altitude — Continued. Lower Limb, to Find Obs. Alt. HEIGHT OF THE EYE. 1 14 Feet. 15 Feet. 16 Feet. 17 Feet. 18 Feet. 19 Feet. 1 O Sun's Corr. (+) * star's Corr. (-) O Sun's Corr. (+) * Star's Corr. (-) O Sun's Corr. (+) star's Corr. (-) O Sun's Corr. (+) * star's Corr. (-) O Sun's Corr. (+) * star's Corr. (-) O Sun's Corr. (+) * Star's Corr. (-) 6 30 4 35 11 34 4 27 11 42 4 20 11 49 4 13 11 56 4 06 12 03 3 59 / // 12 10 40 4 45 11 24 4 37 11 32 4 30 11 39 4 23 11 46 4 16 11 53 4 09 12 00 50 4 55 11 14 4 47 11 22 4 40 11 29 4 33 11 36 4 26 11 43 4 19 11 50 7 00 5 05 11 04 4 57 11 12 4 50 11 19 4 43 11 26 4 36 11 33 4 29 11 40 10 5 14 10 55 5 06 11 03 4 59 11 10 4 52 11 17 4 45 11 24 4 38 11 31 20 5 23 10 46 5 15 10 54 5 08 11 01 5 01 11 08 4 54 11 15 4 47 11 22 7 30 5 32 10 37 5 24 10 45 5 17 10 52 5 10 10 59 5 03 11 06 4 56 11 13 40 5 40 10 29 5 32 10 37 5 25 10 44 5 18 10 51 5 11 10 58 5 04 11 05 50 5 48 10 21 5 40 10 29 5 33 10 36 5 26 10 43 5 19 10 50 5 12 10 57 8 00 5 56 10 13 5 48 10 21 5 41 10 28 5 34 10 35 5 27 10 42 5 20 10 49 10 6 03 10 06 5 55 10 14 5 48 10 21 5 41 10 28 5 34 10 35 5 27 10 42 20 6 10 9 59 6 02 10 07 5 55 10 14 5 48 10 21 5 41 10 28 5 34 10 35 8 30 6 17 9 52 6 09 10 00 6 02 10 07 5 55 10 14 5 48 10 21 5 41 10 28 40 6 24 9 45 6 16 9 53 6 09 10 00 6 02 10 07 5 55 10 14 5 48 10 21 50 6 30 9 39 6 22 9 47 6 15 9 54 6 08 10 01 6 01 10 08 5 54 10 15 9 00 6 36 9 33 6 28 9 41 6 21 9 48 6 14 9 55 6 07 10 02 6 00 10 09 20 6 48 9 21 6 40 9 29 6 33 9 36 6 26 9 43 6 19 9 50 6 12 9 57 40 6 59 9 10 6 51 9 18 6 44 9 25 6 37 9 32 6 30 9 39 6 23 9 46 10 00 7 10 8 59 7 02 9 07 6 55 9 14 6 48 9 21 6 41 9 28 6 34 9 35 20 7 20 8 49 7 12 8 57 7 05 9 04 6 58 9 11 6 51 9 18 6 44 9 25 40 7 29 8 40 7 21 8 48 7 14 8 55 7 07 9 02 7 00 9 09 6 53 9 16 11 00 7 38 8 31 7 30 8 39 7 23 8 46 7 16 8 53 7 09 9 00 7 02 9 07 30 7 50 8 19 7 42 8 27 7 35 8 34 7 28 8 41 7 21 8 48 7 14 8 55 12 00 8 01 8 08 7 53 8 16 7 46 8 23 7 39 8 30 7 32 8 37 7 25 8 44 30 8 12 7 57 8 04 8 05 7 57 8 12 7 50 8 19 7 43 8 26 7 36 8 33 13 00 8 22 7 47 8 14 7 55 8 07 8 02 8 00 8 09 7 53 8 16 7 46 8 23 30 8 31 7 38 8 23 7 46 8 16 7 53 8 09 8 00 8 02 8 07 7 55 8 14 14 00 8 39 7 30 8 31 7 38 8 24 7 45 8 17 7 52 8 10 7 59 8 03 8 06 15 00 8 55 7 14 8 47 7 22 8 40 7 29 8 33 7 36 8 26 7 43 8 19 7 50 16 00 9 08 7 01 9 00 7 09 8 53 7 16 8 46 7 23 8 39 7 30 8 32 7 37 17 00 9 21 6 48 9 13 6 56 9 06 7 03 8 59 7 10 8 52 7 17 8 45 7 24 18 00 9 31 6 38 9 23 6 46 9 16 6 53 9 09 7 00 9 02 7 07 8 55 7 14 19 00 9 41 6 28 9 33 6 36 9 26 6 43 9 19 6 50 9 12 6 57 9 05 7 04 20 00 9 49 6 19 9 41 6 27 9 34 6 34 9 27 6 41 9 20 6 48 9 13 6 55 22 00 10 05 6 03 9 57 6 11 9 50 6 18 9 43 6 25 9 36 6 32 9 29 6 39 24 00 10 18 5 50 10 10 5 58 10 03 6 05 9 56 6 12 9 49 6 19 9 42 6 26 26 00 10 29 5 39 10 21 5 47 10 14 5 54 10 07 6 01 10 00 6 08 9 53 6 15 28 00 10 39 5 29 10 31 5 37 10 24 5 44 10 17 5 51 10 10 5 58 10 03 6 05 30 00 10 47 5 21 10 39 5 29 10 32 5 36 10 25 5 43 10 18 5 50 10 11 5 57 32 00 10 55 5 13 10 47 5 21 10 40 5 28 10 33 5 35 10 26 5 42 10 19 5 49 34 00 11 02 5 06 10 54 5 14 10 47 5 21 10 40 5 28 10 33 5 35 10 26 5 42 36 00 11 08 5 00 11 00 5 08 10 53 5 15 10 46 5 22 10 39 5 29 10 32 5 36 38 00 11 13 4 55 11 05 5 03 10 58 5 10 10 51 5 17 10 44 5 24 10 37 5 31 40 00 11 18 4 49 11 10 4 57 11 03 5 04 10 56 5 11 10 49 5 18 10 42 5 25 45 00 11 29 4 38 11 21 4 46 11 14 4 53 11 07 5 00 11 00 5 07 10 53 5 14 50 00 11 37 4 29 11 29 4 37 11 22 4 44 11 15 4 51 11 06 4 58 11 01 5 05 55 00 11 44 4 21 11' 36 4 29 11 29 4 36 11 22 4 43 11 15 4 50 11 08 4 57 60 00 11 50 4 14 11 42 4 22 11 35 4 29 11 28 4 36 11 21 4 43 11 14 4 50 65 00 11 57 4 07 11 49 4 15 11 42 4 22 11 35 4 29 11 28 4 36 11 21 4 43 70 00 12 02 4 01 11 54 4 09 11 47 4 16 11 40 4 23 11 33 4 30 11 26 4 37 75 00 12 06 3 56 11 58 4 04 11 51 4 11 11 44 4 18 11 37 4 25 11 30 4 32 80 00 12 12 3 50 12 04 3 58 11 57 4 05 11 50 4 12 11 43 4 19 11 36 4 26 85 00 12 16 3 45 12 08 3 53 12 01 4 00 11 54 4 07 11 47 4 14 11 40 4 21 90 00 12 20 3 40 12 12 3 48 12 05 3 55 11 58 4 02 11 51 4 09 11 44 4 16 1 1 Additional Core. Day of Month. Jan. Feb. Mar. Apr. May. i rune. July. Aug. Sept. Oct. Nov. Dec, // // // // // // // // // // It » FOE Sun's Alt, lstt< 16th )15th... to 31st.. .+18 .+17 +15 +12 +8 +4 -4 -8 - -11 - -13 -14 -14 -13 -11 - 9 -5 -1 +3 +7 +11 +14 +16 +18 * The corrections for the obs of the Sun's lower lunb, the dip taking account of the variation erved altitude of a Star or Planet involves the dip and the refraction; , refraction, parallax, and mean seinidiameter, which is taken as 16'. of the Sun's semidiameter in the difierent months of the year is given md for the observed altitude A supplementary correction it the foot of the main table. 380074 Page 6] TABLE I. Corrections to be Applied to the Observed Altitude of a Star or of the Sun's Lower Limb, to Find the True Altitude — Continued. Ob9. Alt. HEIGHT OF THK EYE. 1 20 Feet. 21 Feet. 22 Feet. 23 Feet. 24 Feet. 25 Feet. 1 O * O * O * G * O * O * Sun's Star's Sun's Star's Sun's Star's Sun's star's Sun's Star's Sun's star's Corr. Corr. Corr. Corr. Corr. Corr. Corr. Corr. Corr. Corr. Corr. Corr. (+) (-) (+) (-) (+) (-) (+) (-) (+) (-) (+) (-) / 6 30 3 52 12 17 3 46 / // 12 23 3 39 12 30 3 33 12 36 3 27 12 42 3 21 12 48 40 4 .2 12 07 3 56 12 13 3 49 12 20 3 43 12 26 3 37 12 32 3 31 12 38 50 4 12 11 57 4 06 12 03 3 59 12 10 3 53 12 16 3 47 12 22 3 41 12 28 7 00 4 22 11 47 4 16 11 53 4 09 12 00 4 03 12 06 3 57 12 12 3 51 12 18 10 4 31 11 38 4 25 11 44 4 18 11 51 4 12 11 57 4 06 12 03 4 00 12 09 20 4 40 11 29 4 34 11 35 4 27 11 42 4 21 11 48 4 15 11 54 4 09 12 00 7 30 4 49 11 20 4 43 11 26 4 36 11 33 4 30 11 39 4 24 11 45 4 18 11 51 40 4 57 11 12 4 51 11 18 4 44 11 25 4 38 11 31 4 32 11 37 4 26 11 43 50 5 05 11 04 4 59 11 10 4 52 11 17 4 46 11 23 4 40 11 29 4 34 11 35 8 00 5 13 10 56 5 07 11 02 5 00 11 09 4 54 11 15 4 48 11 21 4 42 11 27 10 5 20 10 49 5 14 10 55 5 07 11 02 5 01 11 08 4 55 11 14 4 49 11 20 20 5 27 10 42 5 21 10 48 5 14 10 55 5 08 11 01 5 02 11 07 4 56 11 13 8 30 5 34 10 35 5 28 10 41 5 21 10 48 5 15 10 54 5 09 11 00 5 03 11 06 40 5 41 10 28 5 35 10 34 5 28 10 41 5 22 10 47 5 16 10 53 5 10 10 59 50 5 47 10 22 5 41 10 28 5 34 10 35 5 28 10 41 5 22 10 47 5 16 10 53 9 00 5 53 10 16 5 47 10 22 5 40 10 29 5 34 10 35 5 28 10 41 5 22 10 47 20 6 05 10 04 5 59 10 10 5 52 10 17 5 46 10 23 5 40 10 29 5 34 10 35 40 6 16 9 53 6 10 9 59 6 03 10 06 5 57 10 12 5 51 10 18 5 45 10 24 10 00 6 27 9 42 6 21 9 48 6 14 9 55 6 08 10 01 6 02 10 07 5 56 10 13 20 6 37 9 32 6 31 9 38 6 24 9 45 6 18 9 51 6 12 9 57 6 06 10 03 40 6 46 9 23 6 40 9 29 6 33 9 36 6 27 9 42 6 21 9 48 6 15 9 54 11 00 6 55 9 14 6 49 9 20 6 42 9 27 6 36 9 33 6 30 9 39 6 24 9 45 30 7 07 9 02 7 01 9 08 6 54 9 15' 6 48 9 21 6 42 9 27 6 36 9 33 12 00 7 18 8 51 7 12 8 57 7 05 9 04 6 59 9 10 6 53 9 16 6 47 9 22 30 7 29 8 40 7 23 8 46 7 16 8 53 7 10 8 59 7 04 9 05 6 58 9 11 13 00 7 39 8 30 7 33 8 36 7 26 8 43 7 20 8 49 7 14 8 55 7 08 9 01 30 7 48 8 21 7 42 8 27 7 35 8 34 7 29 8 40 7 23 8 46 7 17 8 52 14 00 7 56 8 13 7 60 8 19 7 43 8 26 7 37 8 32 7 31 8 38 7 25 8 44 15 00 8 12 7 57 8 06 8 03 7 59 8 10 7 53 8 16 7 47 8 22 7 41 8 28 16 00 8 25 7 44 8 19 7 50 8 12 7 57 8 06 8 03 8 00 8 09 7 54 8 15 17 00 8 38 7 31 8 32 7 37 8 25 7 44 8 19 7 50 8 13 7 56 8 07 8 02 18 00 8 48 7 21 8 42 7 27 8 35 7 34 8 29 7 40 8 23 7 46 8 17 7 52 19 00 8 58 7 11 8 52 7 17 8 45 7 24 8 39 7 30 8 33 7 36 8 27 7 42 20 00 9 06 7 02 9 00 7 08 8 53 7 15 8 47 7 21 8 41 7 27 8 35 7 33 22 00 9 22 6 46 9 16 6 52 9 09 6 59 9 03 7 05 8 57 7 11 8 51 7 17 24 00 9 35 6 33 9 29 6 39 9 22 6 46 9 16 6 52 9 10 6 58 9 04 7 04 26 00 9 46 6 22 9 40 6 28 9 33 6 35 9 27 6 41 9 21 6 47 9 15 6 53 28 00 9 56 6 12 9 50 6 18 9 43 6 25 9 37 6 31 9 31 6 37 9 25 6 43 30 00 10 04 6 04 9 58 6 10 9 51 6 17 9 45 6 23 9 39 6 29 9 33 6 35 32 00 10 12 5 56 10 06 6 02 9 59 6 09 9 53 6 15 9 47 6 21 9 41 6 27 34 00 10 19 5 49 10 13 5 55 10 06 6 02 10 00 6 08 9 54 6 14 9 48 6 20 36 00 10 25 5 43 10 19 5 49 10 12 5 56 10 06 6 02 10 00 6 08 9 54 6 14 38 00 10 30 5 38 10 24 5 44 10 17 5 51 10 11 5 57 10 05 6 03 9 59 6 09 40 00 10 35 5 32 10 29 5 38 10 22 5 45 10 16 5 51 10 10 5 57 10 04 6 03 45 00 10 46 5 21 10 40 5 27 10 33 5 34 10 27 5 40 10 21 5 46 10 15 5 52 50 00 10 54 5 12 10 48 5 18 10 41 5 25 10 35 5 31 10 29 5 37 10 23 5 43 55 00 11 01 5 04 10 55 5 10 10 48 5 17 10 42 5 23 10 36 5 29 10 30 5 35 60 00 11 07 4 57 11 01 5 03 10 54 5 10 10 48 5 16 10 42 5 22 10 36 5 28 65 00 11 14 4 50 11 08 4 56 11 01 5 03 10 55 5 09 10 49 5 15 10 43 5 21 70 00 11 19 4 44 11 13 4 50 11 06 4 57 11 00 5 03 10 54 5 09 10 48 5 15 75 00 11 23 4 39 11 17 4 45 11 10 4 52 11 04 4 58 10 58 5 04 10 52 5 10 80 00 11 29 4 33 11 23 4 39 11 16 4 46 11 10 4 52 11 04 4 58 10 58 5 04 85 00 11 33 4 28 11 27 4 34 11 20 4 41 11 14 4 47 11 08 4 53 11 02 4 59 90 00 11 37 4 23 11 31 4 29 11 24 4 36 11 18 4 42 11 12 4 48 11 06 4 54 1 Addihoi UL Core. Day of Month. Jan. Feb. Mar. Apr May. June. July. Aug. Sept. Oct. Nov. Dec. // // „ // // // // tt « It n ,, Foa So N's Alt. Istt ol5th.... +18 +15 f-8 -8 -13 -14 -11 -5 +3 +11 +16 16th to 31st... +17 +12 f-4 -4 -11 -14 -13 - 9 -1 +7 +14 +18 *Theo orrections for the oh served altitude of a J 3taror Ph met involves the dir > and the refraction; and for the observed altitude of the Sun s lower lunb, the dl p, refraction, paralla X, and ni( jan semidiameter, w hichistakenasl6'. A supplementary correction at the foot of the main table. taking aco }UQt of the variatiot 1 of the Sun's semidi ameter in the different month s of the year is given TABLE I. [Page 7 1 Corrections* to be Applied to the Observed Altitude of a Star or of the Sun's Lower Limb, the True Altitude — Continued. to Find Obs. Alt. HEIGHT OF THE EYE. 1 26 Feet. 27 Feet. 28 Feet. 29 Feet. 30 Feet. 1 Sun's Corr. (+) * Star's Corr. (-) Sun's Corr. (+) * star's Corr. (-) Sim's Corr. (+) * Star's Corr. (-) Sun's Corr. (+) * star's Corr. (-) Sun's Corr. ( + ) * star's Corr. (-) e / 6 30 3 15 12 54 3 09 13 00 3 04 13 05 2 58 13 11 2 53 / n 13 16 40 3 25 12 44 3 19 12 50 3 14 12 55 3 08 13 01 3 03 13 06 50 3 35 12 34 3 29 12 40 3 24 12 45 3 18 12 51 3 13 12 56 7 00 3 45 12 24 3 39 12 30 3 34 12 35 3 28 12 41 3 23 12 46 10 3 54 12 15 3 48 12 21 3 43 12 26 3 37 12 32 3 32 12 37 20 4 03 12 06 3 57 12 12 3 52 12 17 3 46 12 23 3 41 12 28 7 30 4 12 11 57 4 06 12 03 4 01 12 08 3 55 12 14 3 50 12 19 40 4 20 11 49 4 14 11 55 4 09 12 00 4 03 12 06 3 58 12 11 50 4 28 11 41 4 22 11 47 4 17 11 52 4 11 11 58 4 06 12 03 8 00 4 36 11 33 4 30 11 39 4 25 11 44 4 19 11 50 4 14 11 55 10 4 43 11 26 4 37 11 32 4 32 11 37 4 26 11 43 4 21 11 48 20 4 50 11 19 4 44 11 25 4 39 11 30 4 33 11 36 4 28 11 41 8 30 4 57 11 12 4 51 11 18 4 46 11 23 4 40 11 29 4 35 11 34 40 5 04 11 05 4 58 11 11 4 53 11 16 4 47 11 22 4 42 11 27 50 5 10 10 59 5 04 11 05 4 59 11 10 4 53 11 16 4 48 11 21 9 00 5 16 10 53 5 10 10 59 5 05 11 04 4 59 11 10 4 54 11 15 20 5 28 10 41 5 22 10 47 5 17 10 52 5 11 10 58 5 06 11 03 40 5 39 10 30 5 33 10 36 5 28 10 41 5 22 10 47 5 17 10 52 10 00 5 50 10 19 5 44 10 25 5 39 10 30 5 33 10 36 5 28 10 41 20 6 00 10 09 5 54 10 15 5 49 10 20 5 43 10 26 5 38 10 31 40 6 09 10 00 6 03 10 06 5 58 10 11 5 52 10 17 5 47 10 22 11 00 6 18 9 51 6 12 9 57 6 07 10 02 6 01 10 08 5 56 10 13 30 6 30 9 39 6 24 9 45 6 19 9 50 6 13 9 56 6 08 10 01 12 00 6 41 9 28 6 35 9 34 6 30 9 39 6 24 9 45 6 19 9 50 30 6 52 9 17 6 46 9 23 6 41 9 28 6 35 9 34 6 30 9 39 13 00 7 02 9 07 6 56 9 13 6 51 9 18 6 45 9 24 6 40 9 29 30 7 11 8 58 7 05 9 04 7 00 9 09 6 54 9 15 6 49 9 20 14 00 7 19 8 50 7 13 8 56 7 08 9 01 7 02 9 07 6 57 9 12 15 00 7 35 8 34 7 29 8 40 7 24 8 45 7 18 8 51 7 13 8 56 16 00 7 48 8 21 7 42 8 27 7 37 8 32 7 31 8 38 7 26 8 43 17 00 8 01 8 08 7 55 8 14 7 50 8 19 7 44 8 25 7 39 8 30 18 00 8 11 7 58 8 05 8 04 8 00 8 09 7 54 8 15 7 49 8 20 19 00 8 21 7 48 8 15 7 54 8 10 7 59 8 04 8 05 7 59 8 10 20 00 8 29 7 39 8 23 7 45 8 18 7 50 8 12 7 56 8 07 8 01 22 00 8 45 7 23 8 39 7 29 8 34 7 34 8 28 7 40 8 23 7 45 24 00 8 58 7 10 8 52 7 16 8 47 7 21 8 41 7 27 8 36 7 32 26 00 9 09 6 59 9 03 7 05 8 58 7 10 8 52 7 16 8 47 7 21 28 00 9 19 6 49 9 13 6 55 9 08 7 00 9 02 7 06 8 57 7 11 30 00 9 27 6 41 9 21 6 47 9 16 6 52 9 10 6 58 9 05 7 03 32 00 9 35 6 33 9 29 6 39 9 24 6 44 9 18 6 50 9 13 6 55 34 00 9 42 6 26 9 36 6 32 9 31 6 37 9 25 6 43 9 20 6 43 36 00 9 48 6 20 9 42 6 26 9 37 6 31 9 31 6 37 9 26 6 42 38 00 9 53 6 15 9 47 6 21 9 42 6 26 9 36 6 32 9 31 6 37 40 00 9 58 6 09 9 52 6 15 9 47 6 20 9 41 6 26 9 36 6 31 45 00 10 09 5 58 10 03 6 04 9 58 6 09 9 52 6 15 9 47 6 20 50 00 10 17 5 49 10 11 5 55 10 06 6 00 10 00 6 06 9 55 6 11 55 00 10 24 5 41 10 18 5 47 10 13 5 52 10 07 5 58 10 02 6 03 60 00 10 30 5 34 10 24 5 40 10 19 5 45 10 13 5 51 10 08 5 56 65 00 10 37 5 27 10 31 5 33 10 26 5 38 10 20 5 44 10 15 5 49 70 00 10 42 5 21 10 36 5 27 10 31 5 32 10 25 5 38 10 20 5 43 75 00 10 46 5 16 10 40 5 22 10 35 5 27 10 29 5 33 10 24 5 38 80 00 10 52 5 10 10 46 5 16 10 41 5 21 10 35 5 27 10 30 5 32 85 00 10 56 5 05 10 50 5 11 10 45 5 16 10 39 5 22 10 34 5 27 90 00 11 00 5 00 10 54 5 06 10 49 5 11 10 43 5 17 10 38 5 22 1 ADDrnONAL Co BB. Da y of Month Jan. Feb. Mai . Apr. 1 klay. June July. Aug. Sept. Oct. Nov. Dec. // /' / // // » >f // // f /' " FOB Sun's Ai -T. 1st 16t to 15th.. hto3l8t. ..+18 ■ .-1+17 - +15 fl2 +e \ - [ -4 - - 8 -11 -13 -14 -14 -13 -11 - 9 -5 -1 +3 +7 +] + ] 11 L4 +16 +18 ♦The correct] of the Sun's lowei taking account of ons for the ■ limb, the the variati abserved al Jip.refracti an of the Si titudeofaS on, parallax in'ssemidia tar or Planet involves the dip and the refraction; and for c, and mean semidiameter, which is taken as 16'. A supp oneter in the different months of the year is given at the fc the observe lementary tot of the m d altitude correction lain table. Page 8] TABLE I. Corrrectiona to be Applied to the Observed Altitude of a Star or of the Sun's Lower Limb, to Find the True Altitude — Continued. Ob8. Alt. 6 30 40 50 7 00 10 20 7 30 40 50 8 00 10 20 8 30 40 50 9 00 20 40 10 00 20 40 11 00 30 12 00 30 13 00 30 14 00 15 00 16 00 17 00 18 00 19 00 20 00 22 00 24 00 26 00 28 00 30 00 32 00 34 00 36 00 38 00 40 00 45 00 50 00 55 00 60 00 65 00 70 00 75 00 80 00 85 00 90 00 HEIGHT OF THE EYE. 31 Feet. O Sun's Corr. (+) 48 58 08 18 27 36 45 53 01 09 16 23 30 37 43 49 01 12 23 33 42 51 03 14 6 25 6 35 6 44 6 52 star's Corr. (-) 08 21 34 44 54 8 02 8 18 8 31 8 42 8 52 9 00 9 08 9 15 9 21 9 26 9 31 9 42 9 50 9 57 10 03 10 10 10 15 10 19 10 25 10 29 10 33 13 21 13 11 13 01 12 51 12 42 12 33 12 24 12 16 12 08 12 00 11 53 11 46 11 39 11 32 11 26 11 20 11 08 10 57 10 46 10 36 10 27 10 18 10 06 9 55 9 44 9 34 9 25 9 17 9 01 8 48 8 35 8 25 8 15 8 06 32 Feet. Sun's Corr. (+) 6 53 6 47 6 42 6 36 6 25 6 16 6 08 6 01 54 48 43 37 32 27 star's Corr. (-) 6 08 6 19 6 29 6 38 6 46 8 12 8 25 8 36 8 46 8 54 9 02 9 09 9 15 9 20 9 25 9 36 9 44 9 51 9 57 10 04 10 09 10 13 10 19 10 23 10 27 13 27 13 17 13 07 12 57 12 48 12 39 12 30 12 22 12 14 12 06 11 59 11 52 11 45 11 38 11 32 11 26 11 14 11 03 10 52 10 42 10 33 10 24 10 12 10 01 9 50 9 40 9 31 9 23 9 07 8 54 8 41 8 31 8 21 8 12 33 Feet. O Sun's Corr. (+) 56 43 32 22 14 06 6 59 6 53 6 48 6 42 6 31 6 22 6 14 07 00 54 49 43 38 33 star's Corr. (-) 4 32 4 38 4 50 5 01 5 12 5 22 5 31 5 40 5 52 6 03 6 14 6 24 6 33 6 41 6 57 7 10 7 23 7 33 7 43 7 51 8 07 8 20 8 31 8 41 8 49 8 57 9 04 9 10 9 15 9 20 9 31 9 39 9 46 9 52 9 59 10 04 10 08 10 14 10 18 10 22 13 32 13 22 13 12 13 02 12 53 12 44 12 35 12 27 12 19 12 11 12 04 11 57 11 50 11 43 11 37 11 31 11 19 11 08 10 57 10 47 10 38 10 29 10 17 10 06 9 55 9 45 9 36 9 28 9 12 8 59 8 46 8 36 8 26 8 17 8 01 34 Feet. Sun's Corr. (+) 6 58 6 53 6 47 6 36 6 27 6 19 6 12 6 05 32 42 52 02 11 20 29 37 45 53 00 07 14 21 27 33 45 56 07 17 26 35 47 58 09 6 19 6 28 6 36 52 05 18 28 38 46 8 02 8 15 8 26 8 36 8 44 8 52 8 59 9 05 9 10 9 15 9 26 9 34 9 41 9 47 9 54 9 59 10 03 10 09 10 13 10 17 Star's Corr. (-) 13 37 13 27 13 17 13 07 12 58 12 49 12 40 12 32 12 24 12 16 12 09 12 02 11 55 11 48 11 42 11 36 11 24 11 13 11 02 10 52 10 43 10 34 10 22 10 11 10 00 9 50 9 41 9 33 9 17 9 04 8 51 8 41 8 31 8 22 35 Feet. 8 06 7 53 7 42 7 32 7 24 7 16 7 09 7 03 6 58 6 52 6 41 6 32 6 24 6 17 6 10 6 04 5 59 5 53 5 48 5 43 O Sun's Corr. (+) 27 37 47 57 06 15 24 32 40 48 55 02 09 16 22 28 40 51 02 12 5 21 5 30 5 42 5 53 6 04 6 14 6 23 6 31 6 47 7 00 7 13 7 23 7 33 7 41 7 57 8 10 8 21 8 31 S 39 8 47 8 54 9 00 9 05 9 10 9 21 9 29 9 36 9 42 9 49 9 54 9 58 10 04 10 08 10 12 Star's Corr. (-) 13 42 13 32 13 22 13 12 13 03 12 54 12 45 12 37 12 29 12 21 12 14 12 07 12 00 11 53 11 47 11 41 11 29 11 18 11 07 10 57 10 48 10 39 10 27 10 16 10 05 9 55 9 46 9 38 9 22 9 09 8 56 8 46 8 30 8 27 8 11 7 58 7 47 7 37 7 29 7 21 7 14 7 08 7 03 6 57 6 46 6 37 6 29 6 22 6 15 6 09 6 04 5 58 5 53 5 48 Additional Coer. FOB Sun's Alt. Day of Month. 1st to 15th.... 16th to 31st... Jan. Feb. Mar. Apr. May. June. July. Aug. Sept. Oct. Nov. +18 +17 +15 +12 +8 +4 -4 - 8 -11 -13 -14 -14 -13 ir -11 - 9 -5 -1 +3 +7 +11 +14 Dec. +16 +18 * The corrections for the observed altitude of a Star or Planet involves the dip and the refraction; and for the observed altitude of the Sun'slower limb, the dip, refraction, parallax, and mean semldiameter, which is taken as 16'. A supplementary correction taking account of the variation of the Sun's semidiameter in the different months of the year is given at the foot of the main table. TABLE I. [Page 9 Corrections* to be Applied to the Observed Altitude of a Star or of the Sun's Lower Limb, to Find the True Altitude — Contiuued. Obii. Alt. 6 30 40 50 7 00 10 20 7 30 40 50 8 00 10 20 8 30 40 50 9 00 20 40 10 00 20 40 11 00 30 12 00 30 13 00 30 14 00 15 00 16 00 17 00 18 00 19 GO 20 00 22 00 24 00 26 00 28 00 30 00 32 00 34 00 36 00 38 00 40 00 45 00 50 00 55 00 60 00 65 00 70 00 75 00 80 00 85 00 90 00 HEIGHT OF THE EYE. 36 Feet. O Sun's Corr. (+) 2 22 2 32 2 42 2 52 01 10 19 27 35 43 50 57 04 11 17 23 35 46 57 07 16 25 37 star's Corr. (-) 8 05 8 16 8 26 8 34 8 42 8 49 8 55 9 00 9 05 9 16 9 24 31 37 44 49 53 59 10 03 10 07 13 47 13 37 13 27 13 17 13 08 12 59 12 50 12 42 12 34 12 26 12 19 12 12 12 05 11 58 11 52 11 46 11 34 11 23 11 12 11 02 10 53 10 44 10 32 10 21 10 10 10 00 9 51 9 43 9 27 9 14 9 01 8 51 8 41 8 32 8 16 8 03 37 Feet. O Sun's Corr. (+) 2 17 2 27 2 37 2 47 2 56 05 14 22 30 38 45 52 59 06 12 18 30 41 52 02 11 20 32 43 54 04 13 21 37 50 03 13 23 31 47 8 00 8 11 8 21 8 29 8 37 8 44 8 50 8 55 9 00 9 11 9 19 9 26 9 32 9 39 9 44 9 48 9 54 9 58 10 02 Star's Corr. (-) 13 52 13 42 13 32 13 22 13 13 13 04 12 55 12 47 12 39 12 31 12 24 12 17 12 10 12 03 11 57 11 51 11 39 11 28 11 17 11 07 10 58 10 49 10 37 10 26 10 15 10 05 9 56 9 48 9 32 9 19 9 06 8 56 8 46 8 37 8 21 8 08 7 57 47 39 31 24 18 13 07 38 Feet. 7 7 7 7 7 7 7 6 56 6 47 6 39 6 32 6 25 6 19 6 14 6 08 6 03 5 58 O Sun's Corr. (+) 2 2 2 2 2 3 3 10 3 18 26 34 41 48 55 02 08 14 26 37 48 58 07 16 28 39 50 00 09 6 17 6 33 46 59 09 19 27 43 56 07 8 17 8 25 8 33 8 40 8 46 8 51 8 56 9 07 9 15 9 22 9 28 9 35 9 40 9 44 9 50 9 54 9 58 star's Corr. (-) 13 56 13 46 13 36 13 26 13 17 13 08 12 59 12 51 12 43 12 35 12 28 12 21 12 14 12 07 12 01 11 55 11 43 11 32 11 21 11 11 39 Feet. 11 02 10 53 10 41 10 30 10 19 10 09 10 00 9 52 9 36 9 23 9 10 9 00 8 50 8 41 8 25 8 12 8 01 7 51 7 43 7 35 7 28 7 22 7 17 7 11 7 00 6 51 6 43 6 36 6 29 6 23 6 18 6 12 6 07 6 02 o Sun's Corr. (+) 2 08 2 18 2 28 2 38 2 47 2 56 6 28 6 41 6 54 7 04 7 14 7 22 7 38 7 51 8 02 8 12 8 20 8 28 8 35 8 41 8 46 8 51 9 02 9 10 9 17 9 23 9 30 9 35 9 39 9 45 9 49 9 53 Star's Corr. (-) 14 01 13 51 13 41 13 31 13 22 13 13 13 04 12 56 12 48 12 40 12 33 12 26 12 19 12 12 12 06 12 00 11 48 11 37 11 26 11 16 11 07 10 58 10 46 10 35 10 24 10 14 10 05 9 57 9 41 9 28 9 15 9 05 8 55 8 46 8 30 8 17 8 06 40 Feet. 6 12 6 07 Sun's Corr. (+) 03 13 23 33 42 51 00 08 16 24 3] 38 45 52 58 04 16 27 38 48 57 06 18 29 5 40 5 50 5 59 6 07 6 23 6 36 6 49 6 59 7 09 7 17 7 33 7 46 7 57 8 07 8 15 8 23 8 30 8 36 8 41 8 4G 8 57 9 05 9 12 9 18 9 25 9 30 9 34 9 40 9 44 9 48 star's Corr. (-) 14 06 13 56 13 46 13 36 13 27 13 18 13 09 13 01 12 53 12 45 12 38 12 31 12 24 12 17 12 11 12 05 11 53 11 42 11 31 11 21 11 12 11 03 10 51 10 40 10 29 10 19 10 10 10 02 9 46 8 51 8 35 8 22 8 11 8 01 53 45 38 32 27 21 10 7 01 6 53 6 46 6 39 6 33 6 28 6 22 6 17 6 12 Additional Cork. FOE Sun's Alt. Day of Month. l8ttol5th... 16th to 31st. . Jan. Feb. Mar. Apr. May. June. July. Aug. Sept. Oct. Nov. +18 +15 +17 +12 +8 +4 -4 - 8 -11 -13 -14 -14 -13 -11 - 9 -5 -1 +3 +7 +11 +14 Dec +16 +18 * The corrections for the observed altitude of a Star or Planet involves the dip and the refraction; and for the observed altitude of the Sun's lower limb, the dip, refraction, parallax, and mean semidiameter, which is taken as 16'. A supplementary correction taking account of the variation of the Sun's semidiameter in the different months of the year is given at the foot of the main table. Page 10] TABLE I. Corrections* to be Applied to the Observed Altitude of a Star or of the Sun's Lower Limb, to Find the True Altitude — Continued. 1 HEIGHT OF THE EYE. 1 41 Feet. 43 Feet. 1 43 Feet. 1 44 Feet. 1 45 Feet. 46 Feet. 1 Obs. Alt. O * O ♦ O * O * O * O * Sun's Star's Sun's Star's Sun's Star's Sun's Star's Sun's star's Sun's Star's Corr. Corr. Corr. Corr. Corr. Corr. Corr. Corr. Corr. Corr. Corr. Corr. (+) (-) (+) (-) (+) (-) (+) (-) (+) (-) (+) (-) 6 30 1 58 14 11 1 54 14 15 1 49 1 II 14 20 1 44 14 25 1 39 14 30 / II 1 35 / II 14 34 40 2 08 14 01 2 04 14 05 1 59 14 10 1 54 14 15 1 49 14 20 1 45 14 24 50 2 18 13 51 2 14 13 55 2 09 14 00 2 04 14 05 1 59 14 10 1 55 14 14 7 00 2 28 13 41 2 24 13 45 2 19 13 50 2 14 13 55 2 09 14 00 2 05 14 04 10 2 37 13 32 2 33 13 36 2 28 13 41 2 23 13 46 2 18 13 51 2 14 13 55 20 2 46 13 23 2 42 13 27 2 37 13 32 2 32 13 37 2 27 13 42 2 23 13 46 7 30 2 55 13 14 2 51 13 18 2 46 13 23 2 41 13 28 2 36 13 33 2 32 13 37 40 3 03 13 06 2 59 13 10 2 54 13 15 2 49 13 20 2 44 13 25 2 40 13 29 50 3 11 12 58 3 07 13 02 3 02 13 07 2 57 13 12 2 52 13 17 2 48 13 21 8 00 3 19 12 50 3 15 12 54 3 10 12 59 3 05 13 04 3 00 13 09 2 56 13 13 10 3 26 12 43 3 22 12 47 3 17 12 52 3 12 12 57 3 07 13 02 3 03 13 06 20 3 33 12 36 3 29 12 40 3 24 12 45 3 19 12 50 3 14 12 55 3 10 12 59 8 30 3 40 12 29 3 36 12 33 3 31 12 38 3 26 12 43 3 21 12 48 3 17 12 52 40 3 47 12 22 3 43 12 26 3 38 12 31 3 33 12 36 3 28 12 41 3 24 12 45 50 3 53 12 16 3 49 12 20 3 44 12 25 3 39 12 30 3 34 12 35 3 30 12 39 9 00 3 59 12 10 3 55 12 14 3 50 12 19 3 45 12 24 3 40 12 29 3 36 12 33 20 4 11 11 58 4 07 12 02 4 02 12 07 3 57 14 12 3 52 12 17 3 48 12 21 40 4 22 11 47 4 18 11 51 4 13 11 56 4 08 12 01 4 03 12 06 3 59 12 10 10 00 4 33 11 36 4 29 11 40 4 24 11 45 4 19 11 50 4 14 11 55 4 10 11 59 20 4 43 11 26 4 39 11 30 4 34 11 35 4 29 11 40 4 24 11 45 4 20 11 49 40 4 52 11 17 4 48 11 21 4 43 11 26 4 38 11 31 4 33 11 36 4 29 11 40 11 00 5 01 11 08 4 57 11 12 4 52 11 17 4 47 11 22 4 42 11 27 4 38 11 31 30 5 13 10 56 5 09 11 00 5 04 11 05 4 59 11 10 4 54 11 15 4 50 11 19 12 00 5 24 10 45 5 20 10 49 5 15 10 54 5 10 10 59 5 05 11 04 5 01 11 08 30 5 35 10 34 5 31 10 38 5 26 10 43 5 21 10 48 5 16 10 53 5 12 10 57 13 00 5 45 10 24 5 41 10 28 5 36 10 33 5 31 10 38 5 26 10 43 5 22 10 47 30 5 54 10 15 5 50 10 19 5 45 10 24 5 40 10 29 5 35 10 34 5 31 10 38 14 00 6 02 10 07 5 58 10 11 5 53 10 16 5 48 10 21 5 43 10 26 5 39 10 30 15 00 6 18 9 51 6 14 9 55 6 09 10 00 6 04 10 05 5 59 10 10 5 55 10 14 16 00 6 31 9 38 6 27 9 42 6 22 9 47 6 17 9 52 6 12 9 57 6 08 10 01 17 00 6 44 9 25 6 40 9 29 6 35 9 34 6 30 9 39 6 25 9 44 6 21 9 48 18 00 6 54 9 15 6 50 9 19 6 45 9 24 6 40 9 29 6 35 9 34 6 31 9 38 19 00 7 04 9 05 7 00 9 09 6 55 9 14 6 50 9 19 6 45 9 24 6 41 9 28 20 00 7 12 8 56 7 08 9 00 7 03 9 05 6 58 9 10 6 53 9 15 6 49 9 19 22 00 7 28 8 40 7 24 8 44 7 19 8 49 7 14 8 54 7 09 8 59 7 05 9 03 24 00 7 41 8 27 7 37 8 31 7 32 8 36 7 27 8 41 7 22 8 46 7 18 8 50 26 00 7 52 8 16 7 48 8 20 7 43 8 25 7 38 8 30 7 33 8 35 7 29 8 39 28 00 8 02 8 06 7 58 8 10 7 53 8 15 7 48 8 20 7 43 8 25 7 39 8 29 30 00 8 10 7 58 8 06 8 02 8 01 8 07 7 56 8 12 7 51 8 17 7 47 8 21 32 00 8 18 7 50 8 14 7 54 8 09 7 59 8 04 8 04 7 59 8 09 7 55 8 13 34 00 8 25 7 43 8 21 7 47 8 16 7 52 8 11 7 57 8 06 8 02 8 02 8 06 36 00 8 31 7 37 8 27 7 41 8 22 7 46 8 17 7 51 8 12 7 56 8 08 8 00 38 00 8 36 7 32 8 32 7 36 8 27 7 41 8 22 7 46 8 17 7 51 8 13 7 55 40 00 8 41 7 26 8 37 7 30 8 32 7 35 8 27 7 40 8 22 7 45 8 18 7 49 45 00 8 52 7 15 8 48 7 19 8 43 7 24 8 38 7 29 8 33 7 34 8 29 7 38 50 00 9 00 7 06 8 56 7 10 8 51 7 15 8 46 7 20 8 41 7 25 8 37 7 29 55 00 9 07 6 58 9 03 7 02 8 58 7 07 8 53 7 12 8 48 7 17 8 44 7 21 60 00 9 13 6 51 9 09 6 55 9 04 7 00 8 59 7 05 8 54 7 10 8 50 7 14 65 00 9 20 6 44 9 16 6 48 9 11 6 53 9 06 6 58 9 01 7 03 8 57 7 07 70 00 9 25 6 38 9 21 6 42 9 16 6 47 9 11 6 52 9 06 6 57 9 02 7 01 75 00 9 29 6 33 9 25 6 37 9 20 6 42 9 15 6 47 9 10 6 52 9 06 6 56 80 00 9 35 6 27 9 31 6 31 9 26 6 36 9 21 6 41 •9 16 6 46 9 12 6 50 85 00 9 39 6 22 9 35 6 26 9 30 6 31 9 25 6 36 9 20 6 41 9 16 6 45 90 00 9 43 6 17 9 39 6 21 9 34 6 26 9 29 6 31 9 24 6 36 9 20 6 40 1 Additio NAL Core Day of Month. Jan. Feb. Mar. Apr . May. June. July. Aug. Sept. Oct. Nov. Dec. „ „ II II „ „ II „ „ II // FOR St. ra's Alt. 1st to 15th.... +18 +15 +8 c - 8 -13 -14 -11 -5 +3 +11 +16 16tt I to 31st... +17 + 12 +4 -4 -11 -14 -13 - 9 -1 +7 +14 +18 *The correction sfortheol )served altitude of a Star or Planet involves the dij ) and the refraction; and for the observed altitude of the Sun 's lower 111 nb.thedi p, refraction, paralla X, and mean semidiameter, w hich is taken as 16'. A supplementary correction is of the year is given at the foot of the main table. taking aco ount of th 3 variatior I of the Sun's semid ameter in the difierent month TABLE I. [Page 11 Corrections* to be Applied to the Observed Altitude of a Star or of the Sun'a Lower Limb, to Find | the True Altitude — Continued. 1 HEIGHT OF THE EYE. | 47 Feet. 48 Feet. 1 49 Feet. 1 50 Feet. 51 Feet. 52 Feet. 1 Obs. Alt. O * O * o * O * O * oO, * Sun's Star's Sun's Star's Sun's Star's Sun's Star's Sun's star's Sun's Star's Con. Corr. Corr. Corr. Corr. Corr. Corr. Corr. Corr. Corr. Corr. Corr. (+) (-) (+) (-) (+) (-) (+) (-) (+) (-) (+) (-) 6 30 1 31 14 38 1 27 14 42 1 23 / J/ 14 46 1 19 14 50 1 15 / II 14 54 1 11 14 58 40 1 41 14 28 1 37 14 32 1 33 14 36 1 29 14 40 1 25 14 44 1 21 14 48 50 1 51 14 18 1 47 14 22 1 43 14 26 1 39 14 30 1 35 14 34 1 31 14 38 7 00 2 01 14 08 1 57 14 12 1 53 14 16 1 49 14 20 1 45 14 24 1 41 14 28 10 2 10 13 59 2 06 14 03 2 02 14 07 1 58 14 11 1 54 14 15 1 50 14 19 20 2 19 13 50 2 15 13 54 2 11 13 58 2 07 14 02 2 03 14 06 1 59 14 10 7 30 2 28 13 41 2 24 13 45 2 20 13 49 2 16 13 53 2 12 13 57 2 08 14 01 40 2 36 13 33 2 32 13 37 2 28 13 41 2 24 13 45 2 20 13 49 2 16 13 53 50 2 44 13 25 2 40 13 29 2 36 13 33 2 32 13 37 2 28 13 41 2 24 13 45 S 00 2 52 13 17 2 48 13 21 2 44 13 25 2 40 13 29 2 36 13 33 2 32 13 37 10 2 59 13 10 2 55 13 14 2 51 13 18 2 47 13 22 2 43 13 26 2 39 13 30 20 3 06 13 03 3 02 13 07 2 58 13 11 2 54 13 15 2 50 13 19 2 46 13 23 8 30 3 13 12 56 3 09 13 00 3 05 13 04 3 01 13 08 2 57 13 12 2 53 13 16 40 3 20 12 49 3 16 12 53 3 12 12 57 3 08 13 01 3 04 13 05 3 00 13 09 50 3 26 12 43 3 22 12 47 3 18 12 51 3 14 12 55 3 10 12 59 3 06 13 03 9 00 3 32 12 37 3 28 12 41 3 24 12 45 3 20 12 49 3 16 12 53 3 12 12 57 20 3 44 12 25 3 40 12 29 3 36 12 33 3 32 12 37 3 28 12 41 3 24 12 45 40 3 55 12 14 3 51 12 18 3 47 12 22 3 43 12 26 3 39 12 30 3 35 12 34 10 00 4 06 12 03 4 02 12 07 3 58 12 11 3 54 12 15 3 50 12 19 3 46 12 23 20 4 16 11 53 4 12 11 57 4 OS 12 01 4 04 12 05 4 00 12 09 3 56 12 13 40 4 25 11 44 4 21 11 48 4 17 11 52 4 13 11 56 4 09 12 00 4 05 12 04 11 00 4 34 11 35 4 30 11 39 4 26 11 43 4 22 11 47 4 18 11 51 4 14 11 55 30 4 46 11 23 4 42 11 27 4 38 11 31 4 34 11 35 4 30 11 39 4 26 11 43 12 00 4 57 11 12 4 53 11 16 4 49 11 20 4 45 11 24 4 41 11 28 4 37 11 32 30 5 08 11 01 5 04 11 05 5 00 11 09 4 56 11 13 4 52 11 17 4 48 11 21 13 00 5 18 10 51 5 14 10 55 5 10 10 59 5 06 11 03 5 02 11 07 4 58 11 11 30 5 27 10 42 5 23 10 46 5 19 10 50 5 15 10 54 5 11 10 58 5 07 11 02 14 00 5 35 10 34 5 31 10 38 5 27 10 42 5 23 10 46 5 19 10 50 5 15 10 54 15 00 5 51 10 18 5 47 10 22 5 43 10 26 5 39 10 30 5 35 10 34 5 31 10 38 16 GO 6 04 10 05 6 00 10,09 5 56 10 13 5 52 10 17 5 48 10 21 5 44 10 25 17 00 6 17 9 52 6 13 9 56 6 09 10 00 6 05 10 04 6 01 10 08 5 57 10 12 18 00 6 27 9 42 6 23 9 46 6 19 9 50 6 15 9 54 6 11 9 58 6 07 10 02 19 00 6 37 9 32 6 33 9 36 6 29 9 40 6 25 9 44 6 21 9 48 6 17 9 52 20 00 6 45 9 23 6 41 9 27 6 37 9 31 6 33 9 35 6 29 9 39 6 25 9 43 22 00 7 01 9 07 6 57 9 11 6 53 9 15 6 49 9 19 6 45 9 23 6 41 9 27 24 00 7 14 8 54 7 10 8 58 7 06 9 02 7 02 9 06 6 58 9 10 6 54 9 14 26 00 7 25 8 43 7 21 8 47 7 17 8 51 7 13 8 55 7 09 8 59 7 05 9 03 28 00 7 35 8 33 7 31 8 37 7 27 8 41 7 23 8 45 7 19 8 49 7 15 8 53 30 00 7 43 8 25 7 39 8 29 7 35 8 33 7 31 8 37 7 27 8 41 7 23 8 45 32 00 7 51 8 17 7 47 8 21 7 43 8 25 7 39 8 29 7 35 8 33 7 31 8 37 34 00 7 58 8 10 7 54 8 14 7 50 8 18 7 46 8 22 7 42 8 26 7 38 8 30 36 00 8 04 8 04 8 00 8 08 7 56 8 12 7 52 8 16 7 48 8 20 7 44 8 24 38 00 8 09 7 59 8 05 8 03 8 01 8 07 7 57 8 11 7 53 8 15 7 49 8 19 40 00 8 14 7 53 8 10 7 57 8 06 8 01 8 02 8 05 7 58 8 09 7 54 8 13 45 00 8 25 7 42 8 21 7 46 8 17 7 50 8 13 7 54 8 09 7 58 8 05 8 02 50 00 8 33 7 33 8 29 7 37 8 25 7 41 8 21 7 45 8 17 7 49 8 13 7 53 55 00 8 40 7 25 8 36 7 29 8 32 7 33 8 28 7 37 8 24 7 41 8 20 7 45 60 00 8 46 7 18 8 42 7 22 8 38 7 26 8 34 7 30 8 30 7 34 8 26 7 38 65 00 8 53 7 11 8 49 7 15 8 45 7 19 8 41 7 23 8 37 7 27 8 33 7 31 70 00 8 58 7 05 8 54 7 09 8 50 7 13 8 46 7 17 8 42 7 21 8 38 7 25 75 00 9 02 7 00 8 58 7 04 8 54 7 08 8 50 7 12 8 46 7 16 8 42 7 20 80 00 9 08 6 54 9 04 6 58 9 00 7 02 8 56 7 06 8 52 7 10 8 48 7 14 85 00 9 12 6 49 9 08 6 53 9 04 6 57 9 00 7 01 8 56 7 05 8 52 7 09 90 00 9 16 6 44 9 12 6 48 9 08 6 52 9 04 6 56 9 00 7 00 8 56 7 04 1 Additjo NAL Core Day of Month. Jan. Feb. Mar. Apr . May. June. July. Aug. Sept. Oct. Nov. Dec. // // // / ft // ,1 II // // // It 70B Si m'3 Alt. 1st to 15th.... +18 +15 +8 C - 8 -13 -14 -11 -5 +3 + 11 +16 16tl 1 to 3l8t... +17 +12 +4 -4 -11 -14 -13 - 9 -1 +7 +14 +18 *The correction 3 for the ot )served altitude of a Star or Planet involves the dip and the refraction; and for the observed altitude of the Sun 's lower lii mb.thedi p, refraction, paralk ix, and mean semidiameter, which is taken as 16'. A supplementary correction ameter in the different months of the year is given at the foot of the main table. takihgacc ountof th e variatioi] I of the Sun's semid Page 12] TABLE I. Corrections* to be Applied to the Observed Altitude of a Star or of the Sun's Lower Limb, to Find the True Altitude — Continued. Obs. Alt. HEIGHT OF THE EYE. 1 53 Feet. 54 Feet. 55 Feet. 56 Feet. 57 Feet. 58 Feet. 1 O * G * O * O >» O * O * Sun's Star's Sun's Star's Sun's Star's Sun's Star's Sun's Star's Sun's Star's Corr. Corr. Corr. Corr. Corr. Corr. Corr. Corr. Corr. Corr. Corr. Corr. (+) (-) (+) (-) (+) (-) (+) (-) (+) (-) (+) (-) 6 30 1 07 15 02 1 03 15 06 59 15 10 / It 55 15 14 » II 51 / 11 15 18 48 15 21 40 1 17 14 52 1 13 14 56 1 09 15 00 1 05 15 04 1 01 15 08 58 15 11 50 1 27 14 42 1 23 14 46 1 19 14 50 1 15 14 54 1 11 14 58 1 08 15 01 7 00 1 37 14 32 1 33 14 36 1 29 14 40 1 25 14 44 1 21 14 48 1 18 14 51 10 1 46 14 23 1 42 14 27 1 38 14 31 1 34 14 35 1 30 14 39 1 27 14 42 20 1 55 14 14 1 51 14 18 1 47 14 22 1 43 14 26 1 39 14 30 1 36 14 33 7 30 2 04 14 05 2 00 14 09 1 56 14 13 1 52 14 17 1 48 14 21 1 45 14 24 40 2 12 13 57 2 08 14 01 2 04 14 05 2 00 14 09 1 56 14 13 1 53 14 16 50 2 20 13 49 2 16 13 53 2 12 13 57 2 08 14 01 2 04 14 05 2 01 14 08 8 00 2 28 13 41 2 24 13 45 2 20 13 49 2 16 13 53 2 12 13 57 2 09 14 00 10 2 35 13 34 2 31 13 38 2 27 13 42 2 23 13 46 2 19 13 50 2 16 13 53 20 2 42 13 27 2 38 13 31 2 34 13 35 2 30 13 39 2 26 13 43 2 23 13 46 8 30 2 49 13 20 2 45 13 24 2 41 13 28 2 37 13 32 2 33 13 36 2 30 13 39 40 2 56 13 13 2 52 13 17 2 48 13 21 2 44 13 25 2 40 13 29 2 37 13 32 50 3 02 13 07 2 58 13 11 2 54 13 15 2 50 13 19 2 46 13 23 2 43 13 26 9 00 3 08 13 01 3 04 13 05 3 00 13 09 2 56 13 13 2 52 13 17 2 49 13 20 20 3 20 12 49 3 16 12 53 3 12 12 57 3 08 13 01 3 04 13 05 3 01 13 08 40 3 31 12 38 3 27 12 42 3 23 12 46 3 19 12 50 3 15 12 54 3 12 12 57 10 00 3 42 12 27 3 38 12 31 3 34 12 35 3 30 12 39 3 26 12 43 3 23 12 46 20 3 52 12 17 3 48 12 21 3 44 12 25 3 40 12 29 3 36 12 33 3 33 12 36 40 4 01 12 08 3 57 12 12 3 53 12 16 3 49 12 20 3 45 12 24 3 42 12 27 11 00 4 10 11 59 4 06 12 03 4 02 12 07 3 58 12 11 3 54 12 15 3 51 12 18 30 4 22 11 47 4 18 11 51 4 14 11 55 4 10 11 59 4 06 12 03 4 03 12 06 12 00 4 33 11 36 4 29 11 40 4 25 11 44 4 21 11 48 4 17 11 52 4 14 11 55 30 4 44 11 25 4 40 11 29 4 36 11 33 4 32 11 37 4 28 11 41 4 25 11 44 13 00 4 54 11 15 4 50 11 19 4 46 11 23 4 42 11 27 4 38 11 31 4 35 11 34 30 5 03 11 06 4 59 11 10 4 55 11 14 4 51 11 18 4 47 11 22 4 44 11 25 14 00 5 11 10 58 5 07 11 02 5 03 11 06 4 59 11 10 4 55 11 14 4 52 11 17 15 00 5 27 10 42 5 23 10 46 5 19 10 50 5 15 10 54 5 11 10 58 5 08 11 01 16 00 5 40 10 29 5 36 10 33 5 32 10 37 5 28 10 41 5 24 10 45 5 21 10 48 17 00 5 53 10 16 5 49 10 20 5 45 10 24 5 41 10 28 5 37 10 32 5 34 10 35 18 00 6 03 10 06 5 59 10 10 5 55 10 14 5 51 10 18 5 47 10 22 5 44 10 25 19 00 6 13 9 56 6 09 10 00 6 05 10 04 6 01 10 08 5 57 10 12 5 54 10 15 20 00 6 21 9 47 6 17 9 51 6 13 9 55 6 09 9 59 6 05 10 03 6 02 10 06 22 00 6 37 9 31 6 33 9 35 6 29 9 39 6 25 9 43 6 21 9 47 6 18 9 50 24 00 6 50 9 18 6 46 9 22 6 42 9 26 6 38 9 30 6 34 9 34 6 31 9 37 26 00 7 01 9 07 6 57 9 11 6 53 9 15 6 49 9 19 6 45 9 23 6 42 9 26 28 00 7 11 8 57 7 07 9 01 7 03 9 05 6 59 9 09 6 55 9 13 6 52 9 16 30 00 7 19 8 49 7 15 8 53 7 11 8 57 7 07 9 01 7 03 9 05 7 00 9 08 32 00 7 27 8 41 7 23 8 45 7 19 8 49 7 15 8 53 7 11 8 57 7 08 9 00 34 00 7 34 8 34 7 30 8 38 7 26 8 42 7 22 8 46 7 18 8 50 7 15 8 53 36 00 7 40 8 28 7 36 8 32 7 32 8 36 7 28 8 40 7 24 8 44 7 21 8 47 38 00 7 45 8 23 7 41 8 27 7 37 8 31 7 33 8 35 7 29 8 39 7 26 8 42 40 00 7 50 8 17 7 46 8 21 7 42 8 25 7 38 8 29 7 34 8 33 7 31 8 36 45 00 8 01 8 06 7 57 8 10 7 53 8 14 7 49 8 18 7 45 8 22 7 42 8 25 50 00 8 09 7 57 8 05 8 01 8 01 8 05 7 57 8 09 7 53 8 13 7 50 8 16 55 00 8 16 7 49 8 12 7 53 8 08 7 57 8 04 8 01 8 00 8 05 7 57 8 08 60 00 8 22 7 42 8 18 7 46 8 14 7 50 8 10 7 54 8 06 7 58 8 03 8 01 65 00 8 29 7 35 8 25 7 39 8 21 7 43 8 17 7 47 8 13 7 51 8 10 7 54 70 00 8 34 7 29 8 30 7 33 8 26 7 37 8 22 7 41 8 18 7 45 8 15 7 48 75 00 8 38 7 24 8 34 7 28 8 30 7 32 8 26 7 36 8 22 7 40 8 19 7 43 80 00 8 44 7 18 8 40 7 22 8 36 7 26 8 32 7 30 8 28 7 34 8 25 7 37 85 00 8 48 7 13 8 44 7 17 8 40 7 21 8 36 7 25 8 32 7 29 8 29 7 32 90 00 8 52 7 08 8 48 7 12 8 44 7 16 8 40 7 20 8 36 7 24 8 33 7 27 1 Additio NAL COER Day of Month. Jan. Feb. Mar. Apr. May. June. July. Aug. Sept. Oct. Nov. Dec. „ „ „ „ II „ „ „ „ „ „ // FOR St m's Alt. Ist1 to 15th.... +18 +15 +8 - 8 -13 -14 -11 -5 +3 + 11 +16 leti I to 31st... + 17 +12 +4 -4 -11 -14 -13 - 9 -1 +7 + 14 +18 *The correction sfortheol jserved altitude of a Star or Planet involves the dij ) and the refraction; and for the observed altitude of the Sun 's lower lii mb.thedl p, refraction, parallf IX, and mean semidiameter, w hichistakenasl6'. A supplementary correction at the foot of the main table. taking ace ountof th evariatior I of the Sun's semid tameter in the diSerent month is of the year is given TABLE I. [Page 13 Corrections* to be Applied to the Observed Altitude of a Star or of the Sun's Lower Limb, to Find the True Altitude — Continued. Obs. Alt HEIGHT OF THE EYE. 1 59 Feet. 60 Feet. 61 Feet. 62 Feet. 63 Feet. 64 Feet. 1 G * O * O * O * O * O * Sun's Star's Sun's Star's Sun's Star's Sun's Star's Sun's Star's Sun's Star's Corr. Corr. Corr. Corr. Corr. Corr. Corr. Corr. Corr. Corr. Corr. Corr. (+) (-) (+) (-) (+) (-) (+) (-) {+) (-) (+) (-) 6 30 44 15 25 40 15 29 36 15 33 32 15 37 29 15 40 25 I II 15 44 40 54 15 15 50 15 19 46 15 23 42 15 27 39 15 30 35 15 34 50 1 04 15 05 1 00 15 09 56 15 13 52 15 17 49 15 20 45 15 24 7 00 1 14 14 55 1 10 14 59 1 06 15 03 1 02 15 07 59 15 10 55 15 14 10 1 23 14 46 1 19 14 50 1 15 14 54 1 11 14 58 1 08 15 01 1 04 15 05 20 1 32 14 37 1 28 14 41 1 24 14 45 1 20 14 49 1 17 14 52 1 13 14 56 7 30 1 41 14 28 1 37 14 32 1 33 14 36 1 29 14 40 1 26 14 43 1 22 14 47 40 1 49 14 20 1 45 14 24 1 41 14 28 1 37 14 32 1 34 14 35 1 30 14 39 50 1 57 14 12 1 53 14 16 1 49 14 20 1 45 14 24 1 42 14 27 1 38 14 31 8 00 2 05 14 04 2 01 14 08 1 57 14 12 1 53 14 16 1 50 14 19 1 46 14 23 10 2 12 13 57 2 08 14 01 2 04 14 05 2 00 14 09 1 57 14 12 1 53 14 16 20 2 19 13 50 2 15 13 54 2 11 13 58 2 07 14 02 2 04 14 05 2 00 14 09 8 30 2 26 13 43 2 22 13 47 2 18 13 51 2 14 13 55 2 11 13 58 2 07 14 02 40 2 33 13 36 2 29 13 40 2 25 13 44 2 21 13 48 2 18 13 51 2 14 13 55 50 2 39 13 30 2 35 13 34 2 31 13 38 2 27 13 42 2 24 13 45 2 20 13 49 9 00 2 45 13 24 2 41 13 28 2 37 13 32 2 33 13 36 2 30 13 39 2 26 13 43 20 2 57 13 12 2 53 13 16 2 49 13 20 2 45 13 24 2 42 13 27 2 38 13 31 40 3 08 13 01 3 04 13 05 3 00 13 09 2 56 13 13 2 53 13 16 2 49 13 20 10 00 3 19 12 50 3 15 12 54 3 11 12 58 3 07 13 02 3 04 13 05 3 00 13 09 20 3 29 12 40 3 25 12 44 3 21 12 48 3 17 12 52 3 14 12 55 3 10 12 59 40 3 38 12 31 3 34 12 35 3 30 12 39 3 26 12 43 3 23 12 46 3 19 12 50 11 00 3 47 12 22 3 43 12 26 3 39 12 30 3 35 12 34 3 32 12 37 3 28 12 41 30 3 59 12 10 3 55 12 14 3 51 12 18 3 47 12 22 3 44 12 25 3 40 12 29 12 00 4 10 11 59 4 06 12 03 4 02 12 07 3 58 12 11 3 55 12 14 3 51 12 18 30 4 21 11 48 4 17 11 52 4 13 11 56 4 09 12 00 4 06 12 03 4 02 12 07 13 00 4 31 11 38 4 27 11 42 4 23 11 46 4 19 11 50 4 16 11 53 4 12 11 57 30 4 40 11 29 4 36 11 33 4 32 11 37 4 28 11 41 4 25 11 44 4 21 11 48 14 00 4 48 11 21 4 44 11 25 4 40 11 29 4 36 11 33 4 33 11 36 4 29 11 40 15 00 5 04 11 05 5 00 11 09 4 56 11 13 4 52 11 17 4 49 11 20 4 45 11 24 16 00 5 17 10 52 5 13 10 56 5 09 11 00 5 05 11 04 5 02 11 07 4 58 11 11 17 00 5 30 10 39 5 26 10 43 5 22 10 47 5 18 10 51 5 15 10 54 5 11 10 58 18 00 5 40 10 29 5 36 10 33 5 32 10 37 5 28 10 41 5 25 10 44 5 21 10 48 19 00 5 50 10 19 5 46 10 23 5 42 10 27 5 38 10 31 5 35 10 34 5 31 10 38 20 GO 5 58 10 10 5 54 10 14 5 50 10 18 5 46 10 22 5 43 10 25 5 39 10 29 22 00 6 14 9 54 6 10 9 58 6 06 10 02 6 02 10 06 5 59 10 09 5 55 10 13 24 00 6 27 9 41 6 23 9 45 6 19 9 49 6 15 9 53 <> 12 9 56 6 08 10 00 26 00 6 38 9 30 6 34 9 34 6 30 9 38 6 26 9 42 6 23 9 45 6 19 9 49 28 00 6 48 9 20 6 44 9 24 6 40 9 28 6 36 9 32 6 33 9 35 6 29 9 39 30 00 6 56 9 12 6 52 9 16 6 48 9 20 6 44 9 24 6 41 9 27 6 37 9 31 32 00 7 04 9 04 7 00 9 08 6 56 9 12 6 52 9 16 6 49 9 19 6 45 9 23 34 00 7 11 8 57 7 07 9 01 7 03 9 05 6 59 9 09 6 56 9 12 6 52 9 16 36 00 7 17 8 51 7 13 8 55 7 09 8 59 7 05 9 03 7 02 9 06 6 58 9 10 38 00 7 22 8 46 7 18 8 50 7 14 8 54 7 10 8 58 7 07 9 01 7 03 9 05 40 00 7 27 8 40 7 23 8 44 7 19 8 48 7 15 8 52 7 12 8 55 7 08 8 59 45 00 7 38 8 29 7 34 8 33 7 30 8 37 7 26 8 41 7 23 8 44 7 19 8 48 50 00 7 46 8 20 7 42 8 24 7 38 8 28 7 34 8 32 7 31 8 35 7 27 8 39 55 00 7 53 8 12 7 49 8 16 7 45 8 20 7 41 8 24 7 38 8 27 7 34 8 31 60 00 7 59 8 05 7 55 8 09 7 51 8 13 7 47 8 17 7 44 8 20 7 40 8 24 65 00 8 06 7 58 8 02 8 02 7 58 8 06 7 54 8 10 7 51 8 13 7 47 8 17 70 00 8 11 7 52 8 07 7 56 8 03 8 00 7 59 8 04 7 56 8 07 7 52 8 11 75 00 8 15 7 47 8 11 7 51 8 07 7 55 8 03 7 59 8 00 8 02 7 56 8 06 80 00 8 21 7 41 8 17 7 45 8 13 7 49 8 09 7 63 8 06 7 56 8 02 8 00 85 00 8 25 7 36 8 21 7 40 8 17 7 44 8 13 7 48 8 10 7 51 8 06 7 55 90 00 8 29 7 31 8 25 7 35 8 21 7 39 8 17 7 43 8 14 7 46 8 10 7 50 1 Additioi fAL CORR. Day of Month. Jan. Feb. Mar. Apr. May. 3 rune. July. Aug. Sept. Oct. Nov . Dec. ,/ ,1 „ ,1 „ „ „ II „ „ „ FOE Sir N's Alt. Istl^ 15th... .+18 +15 +8 - 8 - -13 -14 -11 -5 +3 +11 +16 16th to 3l8t. ..+17 +12 +4 -4 -11 - -14 -13 - 9 -1 +7 +14 +18 *Thec orrections for the ob served altitude of a £ tar or Planet involv es the dip and the refraction; ( ind for the observed altitude of the Sun' 5 lower limb , the dip , refraction, paralla K, and mean semidia meter, which is taken as 16'. A supplementary correction taking acco unt of the variation of the Sun's semidis imeter in the differe at months of the year is given at the foot of the main table. Page 14] TABLE I. Corrections* to be Applied to the Observed Altitude of a Star or of the Sun's Lower Limb, to Find the True Altitude — Continued. Obs. Alt. HEIGHT OF THE EYE. 1 65 Feet. 66 Feet. 67 Feet. 1 68 Feet. 69 Feet. 70 Feet. 1 O * O * O * O ♦ O * O * Sun's Star's Sun's Star's Sun's Star's Sun's star's Sun's Star's Sun's Star's COIT. Corr. Corr. Corr. Corr. Corr. Corr. Corr. Corr. Corr. Corr. Corr, (+) (-) (+) (-) (+) (-) (+) (-) (+) (-) (+) (-) 6 30 21 1 It 15 48 18 15 51 14 15 55 10 15 59 07 16 02 03 16 06 40 31 15 38 28 15 41 24 15 45 20 15 49 17 15 52 13 15 56 50 41 15 28 38 15 31 34 15 35 30 15 39 27 15 42 23 15 46 7 00 51 15 18 48 15 21 44 15 25 40 15 29 37 15 32 33 15 36 10 1 00 15 09 57 15 12 53 15 16 49 15 20 46 15 23 42 15 27 20 1 09 15 00 1 06 15 03 1 02 15 07 58 15 11 55 15 14 51 15 18 7 30 1 18 14 51 1 15 14 54 1 11 14 58 1 07 15 02 1 04 15 05 1 00 15 09 40 1 26 14 43 • 1 23 14 46 1 19 14 50 1 15 .14 54 1 12 14 57 1 08 15 01 50 1 34 14 35 1 31 14 38 1 27 14 42 1 23 14 46 1 20 14 49 1 16 14 53 8 00 1 42 14 27 1 39 14 30 1 35 14 34 1 31 14 38 1 28 14 41 1 24 14 45 10 1 49 14 20 1 46 14 23 1 42 14 27 1 38 14 31 1 35 14 34 1 31 14 38 20 1 56 14 13 1 53 14 16 1 49 14 20 1 45 14 24 1 42 14 27 1 38 14 31 8 30 2 03 14 06 2 00 14 09 1 56 14 13 1 52 14 17 1 49 14 20 1 45 14 24 40 2 10 13 59 2 07 14 02 2 03 14 06 1 59 14 10 1 56 14 13 1 52 14 17 50 2 16 13 53 2 13 13 56 2 09 14 00 2 05 14 04 2 02 14 07 1 58 14 11 9 00 2 22 13 47 2 19 13 50 2 15 13 54 2 11 13 58 2 08 14 01 2 04 14 05 20 2 34 13 35 2 31 13 38 2 27 13 42 2 23 13 46 2 20 13 49 2 16 13 53 40 2 45 13 24 2 42 13 27 2 38 13 31 2 34 13 35 2 31 13 38 2 27 13 42 10 00 2 56 13 13 2 53 13 16 2 49 13 20 2 45 13 24 2 42 13 27 2 38 13 31 20 3 06 13 03 3 03 13 06 2 59 13 10 2 55 13 14 2 52 13 17 2 48 13 21 40 3 15 12 54 3 12 12 57 3 08 13 01 3 04 13 05 3 01 13 08 2 57 13 12 11 00 3 24 12 45 3 21 12 48 3 17 12 52 3 13 12 56 3 10 12 59 3 06 13 03 30 3 36 12 33 3 33 12 36 3 29 12 40 3 25 12 44 3 22 12 47 3 18 12 51 12 00 3 47 12 22 3 44 12 25 3 40 12 29 3 36 12 33 3 33 12 36 3 29 12 40 30 3 58 12 11 3 55 12 14 3 51 12 18 3 47 12 22 3 44 12 25 3 40 12 29 13 00 4 08 12 01 4 05 12 04 4 01 12 08 3 57 12 12 3 54 12 15 3 50 12 19 30 4 17 11 52 4 14 11 55 4 10 11 59 4 06 12 03 4 03 12 06 3 59 12 10 14 00 4 25 11 44 4 22 11 47 4 18 11 51 4 14 11 55 4 11 11 58 4 07 12 02 15 00 4 41 11 28 4 38 11 31 4 34 11 35 4 30 11 39 4 27 11 42 4 23 11 46 16 00 4 54 11 15 4 51 11 18 4 47 11 22 4 43 11 26 4 40 11 29 4 36 11 33 17 00 5 07 11 02 5 04 11 05 5 00 11 09 4 56 11 13 4 53 11 16 4 49 11 20 18 00 5 17 10 52 5 14 10 55 5 10 10 59 5 06 11 03 5 03 11 06 4 59 11 10 19 00 5 27 10 42 5 24 10 45 5 20 10 49 5 16 10 53 5 13 10 56 5 09 11 00 20 00 5 35 10 33 5 32 10 36 5 28 10 40 5 24 10 44 5 21 10 47 5 17 10 51 22 db 5 51 10 17 5 48 10 20 5 44 10 24 5 40 10 28 5 37 10 31 5 33 10 35 24 00 6 04 10 04 6 01 10 07 5 57 10 11 5 53 10 15 5 50 10 18 6 46 10 22 26 00 6 15 9 53 6 12 9 56 6 08 10 00 6 04 10 04 6 01 10 07 5 57 10 11 28 00 6 25 9 43 6 22 9 46 6 18 9 50 6 14 9 54 6 11 9 57 6 07 10 01 30 00 6 33 9 m 6 30 9 38 6 26 9 42 6 22 9 46 6 19 9 49 6 15 9 53 32 00 6 41 9 27 6 38 9 30 6 34 9 34 6 30 9 38 6 27 9 41 6 23 9 45 34 00 6 48 9 20 6 45 9 23 6 41 9 27 6 37 9 31 6 34 9 34 6 30 9 38 36 00 6 54 9 14 6 51 9 17 6 47 9 21 6 43 9 25 6 40 9 28 6 36 9 32 38 00 6 59 9 09 6 56 9 12 6 52 9 16 6 48 9 20 6 45 9 23 6 41 9 27 40 00 7 04 9 03 7 01 9 06 6 57 9 10 6 53 9 14 6 50 9 17 6 46 9 21 45 00 7 15 8 52 7 12 8 55 7 08 8 59 7 04 9 03 7 01 9 06 6 57 9 10 50 00 7 23 8 43 7 20 8 46 7 16 8 50 7 12 8 54 7 09 8 57 7 05 9 01 55 00 7 30 8 35 7 27 8 38 7 23 8 42 7 19 8 46 7 16 8 49 7 12 8 53 60 00 7 36 8 28 7 33 8 31 7 29 8 35 7 25 8 39 7 22 8 42 7 18 8 46 65 00 7 43 8 21 7 40 8 24 7 36 8 28 7 32 8 32 7 29 8 35 7 25 8 39 70 00 7 48 8 15 7 45 8 18 7 41 8 22 7 37 8 26 7 34 8 29 7 30 8 33 75 00 7 52 8 10 7 49 8 13 7 45 8 17 7 41 8 21 7 38 8 24 7 34 8 28 80 00 7 58 8 04 7 55 8 07 7 51 8 11 7 47 8 15 7 44 8 18 7 40 8 22 85 00 8 02 7 59 7 59 8 02 7 55 8 06 7 51 8 10 7 48 8 13 7 44 8 17 90 00 8 06 7 54 8 03 7 57 7 59 8 01 7 55 8 05 7 52 8 08 7 48 8 12 1 Additto NAL Cork Day of Month. Jan. Feb. Mar. Apr . May. June. July. Aug. Sept. Oct. Nov. Dec. n „ It „ n „ „ „ „ „ „ FOE St rN's Alt. 1st to 15th.... +18 +15 +8 c - 8 -13 -14 -11 -5 +3 + 11 +16 16tl: I to 31st... +17 +12 +4 -4 -11 -14 -13 - 9 -1 +7 +14 +18 *The< jorrection. 5 for the ol served altitude of a Star or Planet involves the dip and the refraction; and for the observed altitude of the Sun s lower lii nb.thedi p, refraction, paralls X, and mean semidiameter, which is taken as 16'. A supplementary correction at the Toot of the main table. taking aco ountof th B variation of the Sun's semid ameter in the different months of the year is given TABLE I. [Page 15 Corrections* to be Applied to the Observed Altitude of a Star or of the Sun's Lower Limb, to Find | the True Altitude — Continued. 1 Obs. Alt. HEIGHT OF THE EYE. 1 71 Feet. 72 Feet. 73 Feet. 74 Feet. 75 Feet. 76 Feet. 1 Sun's Corr. (+) * * * * * * Star's Corr. (-) Sun's Corr. Star's Corr. (-) Sun's Corr. Star's Corr. (-) O Sun's Corr. Star's Corr. (-) Sun's Corr. Star's Corr. (-) Sun's Corr. Star's Corr. (-) 6 30 00 16 09 -0 04 16 13 -0 08 16 17 -0 11 16 20 -0 14 16 23 -0 17 16 26 40 10 15 59 +0 06 16 03 +0 02 16 07 -0 01 16 10 -0 04 16 13 -0 07 16 16 50 20 15 49 16 15 53 12 15 57 +0 09 16 00 +0 06 16 03 +0 03 16 06 7 00 30 15 39 26 15 43 22 15 47 1 19 15 50 16 15 53 13 15 56 10 39 15 30 35 15 34 31 15 38 1 28 15 41 25 15 44 22 15 47 20 48 15 21 44 15 25 40 15 29 1 37 15 32 34 15 35 31 15 38 7 30 57 15 12 53 15 16 49 15 20 1 46 15 23 43 15 26 40 15 29 40 1 05 15 04 1 01 15 08 57 15 12 1 54 15 15 51 15 18 48 15 21 50 1 13 14 56 1 09 15 00 1 05 15 04 1 02 15 07 59 15 10 56 15 13 8 00 1 21 14 48 1 17 14 52 1 13 14 56 1 10 14 59 1 07 15 02 1 04 15 05 10 1 28 14 41 1 24 14 45 1 20 14 49 117 14 52 1 14 14 55 1 11 14 58 20 1 35 14 34 1 31 14 38 1 27 14 42 1 24 14 45 1 21 14 48 1 18 14 51 8 30 1 42 14 27 1 38 14 31 1 34 14 35 1 31 14 38 1 28 14 41 1 25 14 44 40 1 49 14 20 1 45 14 24 1 41 14 28 1 38 14 31 1 35 14 34 1 32 14 37 50 1 55 14 14 1 51 14 18 1 47 14 22 1 44 14 25 1 41 14 28 1 38 14 31 9 00 2 01 14 08 1 57 14 12 1 53 14 16 1 50 14 19 1 47 14 22 1 44 14 25 20 2 13 13 56 2 09 14 00 2 05 14 04 2 02 14 07 1 59 14 10 1 56 14 13 40 2 24 13 45 2 20 13 49 2 16 13 53 2 13 13 56 2 10 13 59 2 07 14 02 10 00 2 35 13 34 2 31 13 38 2 27 13 42 2 24 13 45 2 21 13 48 2 18 13 51 20 2 45 13 24 2 41 13 28 2 37 13 32 2 34 13 35 2 31 13 38 2 28 13 41 40 2 54 13 15 2 50 13 19 2 46 13 23 2 43 13 26 2 40 13 29 2 37 13 32 11 00 3 03 13 06 2 59 13 10 2 55 13 14 2 52 13 17 2 49 13 20 2 46 13 23 30 3 15 12 54 3 11 12 58 3 07 13 02 3 04 13 05 3 01 13 08 2 58 13 11 12 00 3 26 12 43 3 22 12 47 3 18 12 51 3 15 12 54 3 12 12 57 3 09 13 00 30 3 37 12 32 3 33 12 36 3 29 12 40 3 26 12 43 3 23 12 46 3 20 12 49 13 00 3 47 12 22 3 43 12 26 3 39 12 30 3 36 12 33 3 33 12 36 3 30 12 39 30 3 56 12 13 3 52 12 17 3 48 12 21 3 45 12 24 3 42 12 27 3 39 12 30 14 00 4 04 12 05 4 00 12 09 3 56 12 13 3 53 12 16 3 50 12 19 3 47 12 22 15 00 4 20 11 49 4 16 11 53 4 12 11 57 4 09 12 00 4 06 12 03 4 03 12 06 16 00 4 33 11 36 4 29 11 40 4 25 11 44 4 22 11 47 4 19 11 50 4 16 11 53 17 00 4 46 11 23 4 42 11 27 4 38 11 31 4 35 11 34 4 32 11 37 4 29 11 40 18 00 4 56 11 13 4 52 11 17 4 48 11 21 4 45 11 24 4 42 11 27 4 39 11 30 19 00 5 06 11 03 5 02 11 07 4 58 11 11 4 55 11 14 4 52 11 17 4 49 11 20 20 00 5 14 10 54 5 10 10 58 5 06 11 02 5 03 11 05 5 00 11 08 4 57 11 11 22 00 5 30 10 38 5 26 10 42 5 22 10 46 5 19 10 49 5 16 10 52 5 13 10 55 24 00 5 43 10 25 5 39 10 29 5 35 10 33 5 32 10 36 5 29 10 39 5 26 10 42 26 00 5 54 10 14 5 50 10 18 5 46 10 22 5 43 10 25 5 40 10 28 5 37 10 31 28 00 6 04 10 04 6 00 10 08 5 56 10 12 5 53 10 15 5 50 10 18 5 47 10 21 30 00 6 12 9 56 6 08 10 00 6 04 10 04 6 01 10 07 5 58 10 10 5 55 10 13 32 00 6 20 9 48 6 16 9 52 6 12 9 56 6 09 9 59 6 06 10 02 6 03 10 05 34 00 6 27 9 41 6 23 9 45 6 19 9 49 6 16 9 52 6 13 9 55 6 10 9 58 36 00 6 33 9 35 6 29 9 39 6 25 9 43 6 22 9 46 6 19 9 49 6 16 9 52 38 00 6 38 9 30 6 34 9 34 6 30 9 38 6 27 9 41 6 24 9 44 6 21 9 47 40 00 6 43 9 24 6 39 9 28 6 35 9 32 6 32 9 35 6 29 9 38 6 26 9 41 45 00 6 54 9 13 6 50 9 17 6 46 9 21 6 43 9 24 6 40 9 27 6 37 9 30 50 00 7 02 9 04 6 58 9 08 6 54 9 12 6 51 9 15 6 48 9 18 6 45 9 21 55 00 7 09 8 56 •7 05 9 00 7 01 9 04 6 58 9 07 6 55 9 10 6 52 9 13 60 00 7 15 8 49 7 11 8 53 7 07 8 57 7 04 9 00 7 01 9 03 6 58 9 06 65 00 7 22 8 42 7 18 8 46 7 14 8 50 7 11 8 53 7 08 8 56 7 05 8 59 70 00 7 27 8 36 7 23 8 40 7 19 8 44 7 16 8 47 7 13 8 50 7 10 8 53 75 00 7 31 8 31 7 27 8 35 7 23 8 39 7 20 8 42 7 17 8 45 7 14 8 48 80 00 7 37 8 25 7 33 8 29 7 29 8 33 7 26 8 36 7 23 8 39 7 20 8 42 85 00 7 41 8 20 7 37 8 24 7 33 8 28 7 30 8 31 7 27 8 34 7 24 8 37 90 00 7 45 8 15 +7 41 8 19 +7 37 8 23 +7 34 8 26 +7 31 8 29 +7 28 8 32 1 Additio ■^AL COER Day of Month. Jan. Feb. Mar. Apr May. June. July. Aug. Sept. Oct. Nov. Dec. „ „ „ „ „ „ „ „ „ ti „ „ FOE SU s'a Alt. Istt «15th.... +18 +15 +8 - 8 -13 -14 -11 -5 +3 + 11 +16 16th to 31st.. . +17 +12 +4 -4 -11 -14 -13 - 9 -1 +7 +14 +18 *Thec »iTections for the oh served altitude of a Star or Planet involves the dip and the refraction ; and for the observed altitude of the Sun s lower lii nb,thedi ), refraction, paralla X, and mean semidiameter, which is taken as 16'. A supplementary correction taking aca junt of th a variatior I of the Sun's semid iameter in the different months of the year is given at the footof the main table. Page 16] TABLE I. Corrections* to be Applied to the Observed Altitude of a Star or of the Sun's Lower Limb, to Find | the True Altitude — Continued. 1 Obs. Alt. HEIGHT OF THE EYE. | 77 Feet. 1 78 Feet. 1 79 Feet. 1 80 Feet. 1 81 Feet. 1 82 Feet. J ^ * * * * * Sun's Corr. Star's Corr. (-) Sun's Corr. Star's Corr. (-) Sun's Corr. Star's Corr. (-) Sun's Corr. star's Corr. (-) Sun's Corr. star's Corr. (-) Sim's Corr. Star's Corr. (-) 6 30 -0 21 16 30 -0 24 16 33 -0 28 16 37 -0 31 16 40 / n -0 34 16 43 -0 37 16 46 40 -0 11 16 20 -0 14 16 23 -0 18 16 27 -0 21 16 30 -0 24 16 33 -0 27 16 36 50 -0 01 16 10 -0 04 16 13 -0 08 16 17 -0 11 16 20 -0 14 16 23 -0 17 16 26 7 00 +Q 09 16 00 +0 06 16 03 +0 02 16 07 -0 01 16 10 -0 04 16 13 -0 07 16 16 10 18 15 51 15 15 54 11 15 58 +0 08 16 01 +0 05 16 04 +0 02 16 07 20 27 15 42 24 15 45 20 15 49 17 15 52 14 15 55 11 15 58 7 30 36 15 33 33 15 36 29 15 40 26 15 43 23 15 46 20 15 49 40 44 15 25 41 15 28 37 15 32 34 15 35 31 15 38 28 15 41 50 52 15 17 49 15 20 45 15 24 42 15 27 39 15 30 36 15 33 8 00 1 00 15 09 57 15 12 53 15 16 50 15 19 47 15 22 44 15 25 10 1 07 15 02 1 04 15 05 1 00 15 09 57 15 12 54 15 15 51 15 18 20 1 14 14 55 1 11 14 58 1 07 15 02 1 04 15 05 1 01 15 08 58 15 11 8 30 1 21 14 48 1 18 14 51 1 14 14 55 1 11 14 58 1 08 15 01 1 05 15 04 40 1 28 14 41 1 25 14 44 1 21 14 48 1 18 14 51 1 15 14 54 1 12 14 57 50 1 34 14 35 1 31 14 38 1 27 14 42 1 24 14 45 1 21 14 48 1 18 14 51 9 00 1 40 14 29 1 37 14 32 1 33 14 36 1 30 14 39 1 27 14 42 1 24 14 45 20 1 52 14 17 1 49 14 20 1 45 14 24 1 42 14 27 1 39 14 30 1 36 14 33 40 2 03 14 06 2 00 14 09 1 56 14 13 1 53 14 16 1 50 14 19 1 47 14 22 10 00 2 14 13 55 2 11 13 58 2 07 14 02 2 04 14 05 2 01 14 08 1 58 14 11 20 2 24 13 45 2 21 13 48 2 17 13 52 2 14 13 55 2 11 13 58 2 08 14 01 40 2 33 13 36 2 30 13 39 2 26 13 43 2 23 13 46 2 20 13 49 2 17 13 52 11 00 2 42 13 27 2 39 13 30 2 35 13 34 2 32 13 37 2 29 13 40 2 26 13 43 30 2 54 13 15 2 51 13 18 2 47 13 22 2 44 13 25 2 41 13 28 2 38 13 31 12 00 3 05 13 04 3 02 13 07 2 58 13 11 2 55 13 14 2 52 13 17 2 49 13 20 30 3 16 12 53 3 13 12 56 3 09 13 00 3 06 13 03 3 03 13 06 3 00 13 09 13 00 3 26 12 43 3 23 12 46 3 19 12 50' 3 16 12 53 3 13 12 56 3 10 12 59 30 3 35 12 34 3 32 12 37 3 28 12 41 3 25 12 44 3 22 12 47 3 19 12 50 14 00 3 43 12 26 3 40 12 29 3 36 12 33 3 33 12 36 3 30 12 39 3 27 12 42 15 00 3 59 12 10 3 56 12 13 3 52 12 17 3 49 12 20 3 46 12 23 3 43 12 26 16 00 4 12 11 57 4 09 12 00 4 05 12 04 4 02 12 07 3 59 12 10 3 56 12 13 17 00 4 25 11 44 4 22 11 47 4 18 11 51 4 15 11 54 4 12 11 57 4 09 12 00 18 00 4 35 11 34 4 32 11 37 4 28 11 41 4 25 11 44 4 22 11 47 4 19 11 50 19 00 4 45 11 24 4 42 11 27 4 38 11 31 4 35 11 34 4 32 11 37 4 29 11 40 20 00 4 53 11 15 4 50 11 18 4 46 11 22 4 43 11 25 4 40 11 28 4 37 11 31 22 00 5 09 10 59 5 06 11 02 5 02 11 06 4 59 11 09 4 56 11 12 4 53 11 15 24 00 5 22 10 46 5 19 10 49 5 15 10 53 5 12 10 56 5 09 10 59 5 06 11 02 26 00 5 33 10 35 5 30 10 38 5 26 10 42 5 23 10 45 5 20 10 48 5 17 10 51 28 00 5 43 10 25 5 40 10 28 5 36 10 32 5 33 10 35 5 3^ 10 38 5 27 10 41 30 00 5 51 10 17 5 48 10 20 5 44 10 24 5 41 10 27 5 38 10 30 5 35 10 33 32 00 5 59 10 09 5 56 10 12 5 52 10 16 5 49 10 19 5 46 10 22 5 43 10 25 34 00 6 06 10 02 6 03 10 05 5 59 10 09 5 56 10 12 5 53 10 15 5 50 10 18 36 00 6 12 9 56 6 09 9 59 6 05 10 03 6 02 10 06 5 59 10 09 5 56 10 12 38 00 6 17 9 51 6 14 9 54 6 10 9 58 6 07 10 01 6 04 10 04 6 01 10 07 40 00 6 22 9 45 6 19 9 48 6 15 9 52 6 12 9 55 6 09 9 58 6 06 10 01 45 00 6 33 9 34 6 30 9 37 6 26 9 41 6 23 9 44 6 20 9 47 6 17 9 50 50 00 6 41 9 25 6 38 9 28 6 34 9 32 6 31 9 35 6 28 9 38 6 25 9 41 55 00 6 48 9 17 6 45 9 20 6 41 9 24 6 38 9 27 6 35 9 30 6 32 9 33 60 00 6 54 9 10 6 51 9 13 6 47 9 17 6 44 9 20 6 41 9 23 6 38 9 26 65 00 7 01 9 03 6 58 9 06 6 54 9 10 6 51 9 13 6 48 9 16 6 45 9 19 70 00 7 06 8 57 7 03 9 00 6 59 9 04 6 56 9 07 6 53 9 10 6 50 9 13 75 00 7 10 8 52 7 07 8 55 7 03 8 59 7 00 9 02 6 57 9 05 6 54 9 08 80 00 7 16 8 46 7 13 8 49 7 09 8 53 7 06 8 56 7 03 8 59 7 00 9 02 85 00 7 20 8 41 7 17 8 44 7 13 8 48 7 10 8 51 7 07 8 54 7 04 8 57 90 00 +7 24 8 36 +7 21 8 39 +7 17 8 43 +7 14 8 46 +7 11 8 49 +7 08 8 52 1 Additio NAL Cork. Day of Month. Jan. Feb. Mar. Apr. May. June. July. Aug. Sept. Oct. Nov. Dec. „ „ // // // It // II // " /' " FOR Si jn's Alt. 1st to 15th.... +18 +15 +8 - 8 -13 -14 -11 -5 +3 +11 +16 16tl 1 to 31st... +17 +12 +4 -4 -11 -14 -13 - 9 -1 +7 +14 +18 *The corrections for the ol jserved altitude of a Star or Planet involves the dip and the refraction; and for the observed altitude lof theSun 's lower limb, the d p, refraction, paralh IX, and mean semidiameter, which is taken as 16'. A supplementary correction ameter in the diflerent months of the year is given at the foot of the main table. Itakingaa »unt of the variatioi 1 of the Sun's semid TABLE I. [Page 17 CorrectionB* to be Applied to the Observed Altitude of a Star or of the Sun's Lower Limb, to Find the True Altitude — Continued. 1 Obs. Alt. HEIGHT OF THE EYE. 1 83 Feet. 84 Feet. 85 Feet. 1 86 Feet. 1 87 Feet. 88 Feet. 1 * * * « if * Sun's Corr. Star's Corr. (-) Sun's Corr. Star's Corr. (-) Sun's Corr. Star's Corr. (-) Sun's Corr. Star's Corr. (-) O Sun's Corr. Star's Corr. (-) O Sim's Corr. Star's Corr. (-) 6 30 -0 41 16 50 -0 44 16 53 -0 47 16 56 -0 50 16 59 -0 53 17 02 -0 57 17 06 40 -0 31 16 40 -0 34 16 43 -0 37 16 46 -0 40 16 49 -0 43 16 52 -0 47 16 56 50 -0 21 16 30 -0 24 16 33 -0 27 16 36 -0 30 16 39 -0 33 16 42 -0 37 16 46 7 00 -0 11 16 20 -0 14 16 23 -0 17 16 26 -0 20 16 29 -0 23 16 32 -0 27 16 36 10 -0 02 16 11 -0 05 16 14 -0 08 16 17 -0 11 16 20 -0 14 16 23 -0 18 16 27 20 +0 07 16 02 +0 04 16 05 +0 01 16 08 -0 02 16 11 -0 05 16 14 -0 09 16 18 7 30 16 15 53 13 15 56 10 15 59 +0 07 16 02 +0 04 16 05 00 16 09 40 24 15 45 21 15 48 18 15 51 15 15 54 12 15 57 +0 08 16 01 50 32 15 37 29 15 40 26 15 43 23 15 46 20 15 49 16 15 53 8 00 40 15 29 37 15 32 34 15 35 31 15 38 28 15 41 24 15 45 10 47 15 22 44 15 25 41 15 28 38 15 31 35 15 34 31 15 38 20 54 15 15 51 15 18 48 15 21 45 15 24 42 15 27 38 15 31 8 30 1 01 15 08 58 15 11 55 15 14 52 15 17 49 15 20 45 15 24 40 1 08 15 01 1 05 15 04 1 02 15 07 59 15 10 56 15 13 52 15 17 50 1 14 14 55 1 11 14 58 1 08 15 01 1 05 15 04 1 02 15 07 58 15 11 9 00 1 20 14 49 1 17 14 52 1 14 14 55 1 11 14 58 1 08 15 01 1 04 15 05 20 1 32 14 37 1 29 14 40 1 26 14 43 1 23 14 46 1 20 14 49 1 16 14 53 40 1 43 14 26 1 40 14 29 1 37 14 32 1 34 14 35 1 31 14 38 1 27 14 42 10 00 1 54 14 15 1 51 14 18 1 48 14 21 1 45 14 24 1 42 14 27 1 38 14 31 20 2 04 14 05 2 01 14 08 1 58 14 11 1 55 14 14 1 52 14 17 1 48 14 21 40 2 13 13 56 2 10 13 59 2 07 14 02 2 04 14 05 2 01 14 08 1 57 14 12 11 00 2 22 13 47 2 19 13 50 2 16 13 53 2 13 13 56 2 10 13 59 2 06 14 03 30 2 34. 13 35 2 31 13 38 2 28 13 41 2 25 13 44 2 22 13 47 2 18 13 51 12 00 2 45 13 24 2 42 13 27 2 39 13 30 2 36 13 33 2 33 13 36 2 29 13 40 30 2 56 13 13 2 53 13 16 2 50 13 19 2 47 13 22 2 44 13 25 2 40 13 29 13 00 3 06 13 03 3 03 13 06 3 00 13 09 2 57 13 12 2 54 13 15 2 50 13 19 30 3 15 12 54 3 12 12 57 3 09 13 00 3 06 13 03 3 03 13 06 2 59 13 10 14 00 3 23 12 46 3 20 12 49 3 17 12 52 3 14 12 55 % 11 12 58 3 07 13 02 15 00 3 39 12 30 3 36 12 33 3 33 12 36 3 30 12 39 3 27 12 42 3 23 12 46 16 GO 3 52 12 17 3 49 12 20 3 46 12 23 3 43 12 26 3 40 12 29 3 36 12 33 17 00 4 05 12 04 4 02 12 07 3 59 12 10 3 56 12 13 3 53 12 16 3 49 12 20 IS 00 4 15 11 54 4 12 11 57 4 09 12 00 4 06 12 03 4 03 12 06 3 59 12 10 19 00 4 25 11 44 4 22 11 47 4 19 11 50 4 16 11 53 4 13 11 56 4 09 12 00 20 00 4 33 11 35 4 30 11 38 4 27 11 41 4 24 11 44 4 21 11 47 4 17 11 51 22 00 4 49 11 19 4 46 11 22 4 43 11 25 4 40 11 28 4 37 11 31 4 33 11 35 24 00 5 02 11 06 4 59 11 09 4 56 11 12 4 53 11 15 4 50 11 18 4 46 11 22 26 00 5 13 10 55 5 10 10 58 5 07 11 01 5 04 11 04 5 01 11 07 4 57 11 11 28 00 5 23 10 45 5 20 10 48 5 17 10 51 5 14 10 54 5 11 10 57 5 07 11 01 30 00 5 31 10 37 5 28 10 40 5 25 10 43 5 22 10 46 5 19 10 49 5 15 10 53 32 00 5 39 10 29 5 36 10 32 5 33 10 35 5 30 10 38 5 27 10 41 5 23 10 45 34 00 5 46 10 22 5 43 10 25 5 40 10 28 5 37 10 31 5 34 10 34 5 30 10 38 36 00 5 52 10 16 5 49 10 19 5 46 10 22 5 43 10 25 5 40 10 28 5 36 10 32 38 00 5 57 10 11 5 54 10 14 5 51 10 17 5 48 10 20 5 45 10 23 5 41 10 27 40 00 6 02 10 05 5 59 10 08 5 56 10 11 5 53 10 14 5 50 10 17 5 46 10 21 45 00 6 13 9 54 6 10 9 57 6 07 10 00 6 04 10 03 6 01 10 06 5 57 10 10 50 00 6 21 9 45 6 18 9 48 6 15 9 51 6 12 9 54 6 09 9 57 6 05 10 01 55 00 6 28 9 37 6 25 9 40 6 22 9 43 6 19 9 46 6 16 9 49 6 12 9 53 60 00 6 34 9 30 6 31 9 33 6 28 9 36 6 25 9 39 6 22 9 42 6 18 9 46 65 00 6 41 9 23 6 38 9 26 6 35 9 29 6 32 9 32 6 29 9 35 6 25 9 39 70 00 6 46 9 17 6 43 9 20 6 40 9 23 6 37 9 26 6 34 9 29 6 30 9 33 75 00 6 50 9 12 6 47 9 15 6 44 9 18 6 41 9 21 6 38 9 24 6 34 9 28 80 00 6 56 9 06 6 53 9 09 6 50 9 12 6 47 9 15 6 44 9 18 6 40 9 22 85 00 7 00 9 01 6 57 9 04 6 54 9 07 6 51 9 10 6 48 9 13 6 44 9 17 90 00 +7 04 8 56 +7 01 8 59 +6 58 9 02 +6 55 9 05 +6 52 9 08 +6 48 9 12 J Additio NAL COEE Day of Month. Jan. Feb. Mar. Apr . May. June. July. Aug. Sept. Oct. Nov. Dec. n '/ It n // " n It /' 11 " // FOB St rN's Alt. Istl to 15th.... +18 +15 +8 - 8 -13 -14 -11 -5 +3 +11 +16 16th L to Slst... +17 +12 +4 -4 -11 -14 -13 - 9 -1 +7 +14 +18 ♦The 3orrectionj sfortheot served altitude of a Star or Planet involves the dip and the refraction; and for the observed altitude of the Sun 's lower lii nb, the dr p, refraction, paralla X, and mean semidiameter, w hich is taken as 16'. A supplementary correction s of the year is given at the foot of the main table. taking ace ount of th evariatioi 1 of the Sun's semid ameter in the diSerent month 55901°— IJ Page 18] TABLE I. 1 Corrections* to be Applied to the Observed Altitude of a Star or of the Sun's Lower Limb, to Find 1 the True Altitude — Continued. 1 Ob8. Alt. HEIGHT OF THE EYE. 1 89 Feet. 90 Feet. 91 Feet. 92 Feet. 93 Feet. 94 Feet. 1 * « 4> * * Id Son's Con. Star's Corr. (-) Sun's Corr. Star's Corr. (-) Sun's Corr. Star's Corr, (-) Sun's Corr. Star's Corr. (-) Sun's Corr. star's Corr. (-) Sun's Corr. Star's Corr. (-) 6 30 1 >/ -1 00 17 09 -1 03 17 12 -1 06 17 15 -1 09 / 1/ 17 18 -1 12 17 21 -1 15 17 24 40 -0 50 16 59 -0 53 17 02 -0 56 17 05 -0 59 17 08 -1 02 17 11 -1 05 17 14 50 -0 40 16 49 -0 43 16 52 -0 46 16 55 -0 49 16 58 -0 52 17 01 -0 55 17 04 7 00 -0 30 16 39 -0 33 16 42 -0 36 16 45 -0 39 16 48 -0 42 16 51 -0 45 16 54 10 -0 21 16 30 -0 24 16 33 -0 27 16 36 -0 30 16 39 -0 33 16 42 -0 36 16 45 20 -0 12 16 21 -0 15 16 24 -0 18 16 27 -0 21 16 30 -0 24 16 33 -0 27 16 36 7 30 -0 03 16 12 -0 06 16 15 -0 09 16 18 -0 12 16 21 -0 15 16 24 -0 18 16 27 40 +0 05 16 04 +0 02 16 07 -0 01 16 10 -0 04 16 13 -0 07 16 16 -0 10 16 19 50 13 15 56 10 15 59 +0 07 16 02 +0 04 16 05 +0 01 16 08 -0 02 16 11 8 00 21 15 48 18 15 51 15 15 54 12 15 57 09 16 00 +0 06 16 03 10 28 15 41 25 15 44 22 15 47 19 15 50 16 15 53 13 15 56 20 35 15 34 32 15 37 29 15 40 26 15 43 23 15 46 20 15 49 8 30 42 15 27 39 15 30 36 15 33 33 15 36 30 15 39 27 15 42 40 49 15 20 46 15 23 43 15 26 40 15 29 37 15 32 34 15 35 50 55 15 14 52 15 17 49 15 20 46 15 23 43 15 26 40 15 29 9 00 1 01 15 08 58 15 11 55 15 14 52 15 17 49 15 20 46 15 23 20 1 13 14 56 1 10 14 59 1 07 15 02 1 04 15 05 1 01 15 08 58 15 11 40 1 24 14 45 1 21 14 48 1 18 14 51 1 15 14 54 1 12 14 57 1 09 15 00 10 00 1 35 14 34 1 32 14 37 1 29 14 40 1 26 14 43 1 23 14 46 1 20 14 49 20 1 45 14 24 1 42 14 27 1 39 14 30 1 36 14 33 1 33 14 36 1 30 14 39 40 1 54 14 15 1 51 14 18 1 48 14 21 1 45 14 24 1 42 14 27 1 39 14 30 11 00 2 03 14 06 2 00 14 09 1 57 14 12 1 54 14 15 1 51 14 18 1 48 14 21 30 2 15 13 54 2 12 13 57 2 09 14 00 2 06 14 03 2 03 14 06 2 00 14 09 12 00 2 26 13 43 2 23 13 46 2 20 13 49 2 17 13 52 2 14 13 55 2 11 13 58 30 2 37 13 32 2 34 13 35 2 31 13 38 2 28 13 41 2 25 13 44 2 22 13 47 13 00 2 47 13 22 2 44 13 25 2 41 13 28 2 38 13 31 2 35 13 34 2 32 13 37 30 2 56 13 13 2 53 13 16 2 50 13 19 2 47 13 22 2 44 13 25 2 41 13 28 14 00 3 04 13 05 3 01 13 08 2 58 13 11 2 55 13 14 2 52 13 17 2 49 13 20 15 00 3 20 12 49 3 17 12 52 3 14 12 55 3 11 12 58 3 08 13 01 3 05 13 04 16 00 3 33 12 36 3 30 12 39 3 27 12 42 3 24 12 45 3 21 12 48 3 18 12 51 17 00 3 46 12 23 3 43 12 26 3 40 12 29 3 37 12 32 3 34 12 35 3 31 12 38 18 00 3 56 12 13 3 53 12 16 3 50 12 19 3 47 12 22 3 44 12 25 3 41 12 28 19 00 4 06 12 03 4 03 12 06 4 00 12 09 3 57 12 12 3 54 12 15 3 51 12 18 20 00 4 14 11 54 4 11 11 57 4 08 12 00 4 05 12 03 4 02 12 06 3 59 12 09 22 00 4 30 11 38 4 27 11 41 4 24 11 44 4 21 11 47 4 18 11 50 4 15 11 53 24 00 4 43 11 25 4 40 11 28 4 37 11 31 4 34 11 34 4 31 11 37 4 28 11 40 26 00 4 54 11 14 4 51 11 17 4 48 11 20 4 45 11 23 4 42 11 26 4 39 11 29 28 00 5 04 11 04 5 01 11 07 4 58 11 10 4 55 11 13 4 52 11 16 4 49 11 19 30 00 5 12 10 56 5 09 10 59 5 06 11 02 5 03 11 05 5 00 11 08 4 57 11 11 32 00 5 20 10 48 5 17 10 51 5 14 10 54 5 11 10 57 5 08 11 00 5 05 11 03 34 00 5 27 10 41 5 24 10 44 5 21 10 47 5 18 10 50 5 15 10 53 5 12 10 56 36 00 5 33 10 35 5 30 10 38 5 27 10 41 5 24 10 44 5 21 10 47 5 18 10 50 38 00 5 38 10 30 5 35 10 33 5 32 10 36 5 29 10 39 5 26 10 42 5 23 10 45 40 00 5 43 10 24 5 40 10 27 5 37 10 30 5 34 10 33 5 31 10 36 5 28 10 39 45 00 5 54 10 13 5 51 10 16 5 48 10 19 5 45 10 22 5 42 10 25 5 39 10 28 50 00 6 02 10 04 5 59 10 07 5 56 10 10 5 53 10 13 5 50 10 16 5 47 10 19 55 00 6 09 9 56 6 06 9 59 6 03 10 02 6 00 10 05 5 57 10 08 5 54 10 11 60 00 6 15 9 49 6 12 9 52 6 09 9 55 6 06 9 58 6 03 10 01 6 00 10 04 65 00 6 22 9 42 6 19 9 45 6 16 9 48 6 13 9 51 6 10 9 54 6 07 9 57 70 00 6 27 9 36 6 24 9 39 6 21 9 42 6 18 9 45 6 15 9 48 6 12 9 51 75 00 6 31 9 31 6 28 9 34 6 25 9 37 6 22 9 40 6 19 9 43 6 16 9 46 80 00 6 37 9 25 6 34 9 28 6 31 9 31 6 28 9 34 6 25 9 37 6 22 9 40 85 00 6 41 9 20 6 38 9 23 6 35 9 26 6 32 9 29 6 29 9 32 6 26 9 35 90 00 +6 45 9 15 +6 42 9 18 +6 39 9 21 +6 36 9 24 +6 33 9 27 +6 30 9 30 1 Additio NAL CORR. Day of Month. Jan. Feb. Mar. Apr May. June. July. Aug. Sept. Oct. Noi r. Dec. // It /, „ „ II // II // II / 1 II FOE Sr rN's Alt. 1st to 15th.... +18 +15 +8 - 8 -13 -14 -11 -5 +3 +1] L +16 16tl 1 to 3l8t.. +17 +12 +4 -4 -11 -14 -13 - 9 -1 +7 +1^ I +18 *The corrections for the o Dserved altitude of a Star or Planet involves the dip and the refraction; and for the observed altitude ol the Sun 'slower limb, the di p, refraction, paralU IX, and mean semidiameter, which is taken as 16'. A supplementary correction ameter in the diflerent months of the year is given at the foot of the main table. takmgaoo ount of thev ariatior I of the Sun's semid TABLE I. [Page 19 Corrections* to be Applied to the Observed Altitude of a Star or of the Sun's Lower Limb, to Find | the True Altitude — Continued. Obs. Alt. HEIGHT OF THE EYE. 1 95 Feet. 1 96 Feet. 1 97 Feet. 1 98 Feet. 1 99 Feet. 1 100 Feet. 1 :» * * * * * Sun's Corr. Star's Corr. (-) Sun's Corr. star's Corr. (-) Sun's Corr. Star's Corr. (-) Sun's Corr. star's Corr. (-) Sun's Corr. Star's Corr. (-) Sun's Corr. Star's Corr. (-) c , / /' / // 1 II / // / /, / II , 1, 1 II / II / II 1 II I II 6 30 -1 18 17 27 -1 21 17 30 -1 24 17 33 -1 27 YJ 36 -1 30 17 39 -1 33 Yl 42 40 -1 08 17 17 -1 11 17 20 -1 14 17 23 -1 17 17 26 -1 20 17 29 -1 23 17 32 50 -0 58 17 07 -1 01 17 10 -1 04 17 13 -1 07 17 16 -1 10 17 19 -1 13 17 22 7 00 -0 48 16 57 -0 51 17 00 -0 54 17 03 -0 57 17 06 -1 00 17 09 -1 03 17 12 10 -0 39 16 48 -0 42 16 51 -0 45 16 54 -0 48 16 57 -0 51 17 00 -0 54 17 03 20 -0 30 16 39 -0 33 16 42 -0 36 16 45 -0 39 16 48 -0 42 16 51 -0 45 16 54 7 30 -0 21 16 30 -0 24 16 33 -0 27 16 36 -0 30 16 39 -0 33 16 42 -0 36 16 45 40 -0 13 16 22 -0 16 16 25 -0 19 16 28 -0 22 16 31 -0 25 16 34 -0 28 16 37 50 -0 05 16 14 -0 08 16 17 -0 11 16 20 -0 14 16 23 -0 17 16 26 -0 20 16 29 8 00 +0 03 16 06 00 16 09 -0 03 16 12 -0 06 16 15 -0 09 16 18 -0 12 16 21 10 10 15 59 +0 07 16 02 +0 04 16 05 +0 01 16 08 -0 02 16 11 -0 05 16 14 20 17 15 52 14 15 55 11 15 58 08 16 01 +0 05 16 04 +0 02 16 07 8 30 24 15 45 21 15 48 18 15 51 15 15 54 12 15 57 09 16 00 40 31 15 38 28 15 41 25 15 44 22 15 47 19 15 50 16 15 53 50 37 15 32 34 15 35 31 15 38 28 15 41 25 15 44 22 15 47 9 00 43 15 26 40 15 29 37 15 32 34 15 35 31 15 38 28 15 41 20 55 15 14 52 15 17 49 15 20 46 15 23 43 15 26 40 15 29 40 1 06 15 03 1 03 15 06 1 00 15 09 57 15 12 54 15 15 51 15 18 10 00 1 17 14 52 1 14 14 55 1 11 14 58 1 08 15,01 1 05 15 04 1 02 15 07 20 1 27 14 42 1 24 14 45 1 21 14 48 1 18 14 51 1 15 14 54 1 12 14 57 40 1 36 14 33 1 33 14 36 1 30 14 39 1 27 14 42 1 24 14 45 1 21 14 48 11 00 1 45 14 24 1 42 14 27 1 39 14 30 1 36 14 33 1 33 14 36 1 30 14 39 30 1 57 14 12 1 54 14 15 1 51 14 18 1 48 14 21 1 45 14 24 1 42 14 27 12 00 2 08 14 01 2 05 14 04 2 02 14 07 1 59 14 10 1 56 14 13 1 53 14 16 30 2 19 13 50 2 16 13 53 2 13 13 56 2 10 13 59 2 07 14 02 2 04 14 05 13 00 2 29 13 40 2 26 13 43 2 23 13 46 2 20 13 49 2 17 13 52 2 14 13 55 30 2 38 13 31 2 35 13 34 2 32 13 37 2 29 13 40 2 26 13 43 2 23 13 46 14 00 2 46 13 23 2 43 13 26 2 40 13 29 2 37 13 32 2 34 13 35 2 31 13 38 15 00 3 02 13 07 2 59 13 10 2 56 13 13 2 53 13 16 2 50 13 19 2 47 13 22 16 00 3 15 12 54 3 12 12 57 3 09 13 00 3 06 13 03 3 03 13 06 3 00 13 09 17 00 3 28 12 41 3 25 12 44 3 22 12 47 3 19 12 50 3 16 12 53 3 13 12 56 18 00 3 38 12 31 3 35 12 34 3 32 12 37 3 29 12 40 3 26 12 43 3 23 12 46 19 00 3 48 12 21 3 45 12 24 3 42 12 27 3 39 12 30 3 36 12 33 3 33 12 36 20 00 3 59 12 12 3 53 12 15 3 50 12 18 3 47 12 21 3 44 12 24 3 41 12 27 22 00 4 12 11 56 4 09 11 59 4 06 12 02 4 03 12 05 4 00 12 08 3 57 12 11 24 00 4 25 11 43 4 22 11 46 4 19 11 49 4 16 11 52 4 13 11 55 4 10 11 58 26 00 4 36 11 32 4 33 11 35 4 30 11 38 4 27 11 41 4 24 11 44 4 21 11 47 28 00 4 46 11 22 4 43 11 25 4 40 11 28 4 37 11 31 4 34 11 34 4 31 11 37 30 00 4 54 11 14 4 51 11 17 4 48 11 20 4 45 11 23 4 42 11 26 4 39 11 29 32 00 5 02 11 06 4 59 11 09 4 56 11 12 4 53 11 15 4 50 11 18 4 47 11 21 34 00 5 09 10 59 5 06 11 02 5 03 11 05 5 00 11 08 4 57 11 11 4 54 11 14 36 00 5 15 10 53 5 12 10 56 5 09 10 59 5 06 11 02 5 03 11 05 5 00 11 08 38 00 5 20 10 48 5 17 10 51 5 14 10 54 5 11 10 57 5 08 11 00 5 05 11 03 40 00 5 25 10 42 5 22 10 45 5 19 10 48 5 16 10 51 5 13 10 54 5 10 10 57 45 00 5 36 10 31 5 33 10 34 5 30 10 37 5 27 10 40 5 24 10 43 5 21 10 46 50 00 5 44 10 22 5 41 10 25 5 38 10 28 5 35 10 31 5 32 10 34 5 29 10 37 55 00 5 51 10 14 5 48 10 17 5 45 10 20 5 42 10 23 5 39 10 26 5 36 10 29 60 00 5 57 10 07 5 54 10 10 5 51 10 13 5 48 10 16 5 45 10 19 5 42 10 22 65 00 6 04 10 00 6 01 10 03 5 58 10 06 5 55 10 09 5 52 10 12 5 49 10 15 70 00 6 09 9 54 6 06 9 57 6 03 10 00 6 00 10 03 5 57 10 06 5 54 10 09 75 00 6 13 9 49 6 10 9 52 6 07 9 55 6 04 9 58 6 01 10 01 5 58 10 04 80 00 6 19 9 43 6 16 9 46 6 13 9 49 6 10 9 52 6 07 9 55 6 04 9 58 85 00 6 23 9 38 6 20 9 41 6 17 9 44 6 14 9 47 6 11 9 50 6 08 9 53 90 00 6 27 9 33 +6 24 9 36 +6 21 9 39 +6 IS 9 42 +6 15 9 45 +6 12 9 48 1 Additio NAL COEK. Day of Month. Jan. Feb. J ifar. Apr . May. Jime. July. Aug Sept. Oct. Nov. Dec. „ // It , 1 ,1 „ // // II // II /' FOB 8t ra's Alt. 1st to 15th. .. +18 +15 +8 ( ) - 8 -13 — 14 -11 -5 +3 +11 +16 16tl 1 to 3l8t ... +17 +12 +4 -A [ -11 -14 — 13 - 9 -1 +7 +14 +18 *Tlie corrections for the o )served al titudeofa Star or Planet involves the dip and the refraction ; and for the observed altitude of the Sun 'slower limb, the d p, refract on, paraUs IX, and mean semidiameter, which is ta ken as 16'. A supplementary correction sar is given at the foot of the main table. Itakliigaoc ountof thevariatioi X of the Si n's semidj ameter in the different months of the y( TABLE II CORRECTIONS TO BE APPLIED TO THE OBSERVED ALTITUDE OF THE MOON'S UPPER LIMB, AND ALSO OF THE LOWER UMB The height of the eye is assumed to be 35 feet, and the cor- rection for other elevations is given at the bottom of the table, and is ta be added or subtracted according as the height of the eye is less or greater than 35 feet 21 Page 22] TABLE II. Corrections for the Observed Altitudes of the Moon's Lower Limb. Obs. Alt. Lower HORIZONTAL PARALLAX. Limb. 54' 65' 66' 67' 68' 69' 60' 61' 5 30 6 ooa 6 305 53 46 54 22 54 51 55 03 56 38 56 08 56 19 66 54 67 24 57 36 58 11 58 40 58 53 59 28 59 57 60 09 60 44 61 13 * ft 61 27 62 01 62 29 62 44 63 18 63 46 7 00 7 30 8 00 55 17 55 39 55 58 56 33 56 55 67 15 57 50 58 12 58 31 59 06 59 28 59 47 60 22 60 44 61 03 61 38 62 00 62 19 62 54 63 16 63 36 64 11 64 33 64 52 8 30 9 00 9 30 56 15 56 29 56 42 57 31 57 45 57 58 58 47 59 01 59 13 60 03 60 16 60 29 61 19 61 33 61 45 62 35 62 49 63 01 63 62 64 05 64 17 65 08 65 20 65 32 10 00 11 12 56 54 57 10 57 22 58 10 58 26 68 37 59 25 59 41 59 52 60 40 60 56 61 07 61 56 62 12 62 23 63 11 63 27 63 39 64 27 64 43 64 54 65 43 65 53 66 09 13 14 15 57 29 57 35 57 35 68 45 58 50 58 50 59 59 60 04 60 04 61 14 61 18 61 18 62 30 62 33 62 33 63 45 63 48 63 48 65 00 65 03 65 03 66 15 66 17 66 17 16 17 18 57 33 57 30 57 22 58 47 58 44 58 36 60 01 59 57 59 49 61 15 61 11 61 03 62 30 62 25 62 17 63 45 63 39 63 31 64 59 64 53 64 46 66 13 66 07 65 59 19 20 21 57 15 57 05 55 53 58 28 58 18 58 06 59 41 59 31 59 18 60 54 60 44 60 31 62 08 61 57 61 44 63 21 63 10 62 56 64 36 64 23 64 09 65 49 65 36 65 22 22 23 24 56 40 56 26 56 09 57 52 57 38 57 20 59 03 58 49 58 31 60 15 60 00 59 42 61 28 61 12 60 54 62 40 62 24 62 06 63 53 63 36 63 18 65 05 64 48 64 29 25 26 27 55 51 55 32 55 12 57 02 56 43 56 22 58 13 57 53 57 32 59 24 59 03 58 41 60 36 60 14 59 51 61 47 61 25 61 01 62 58 62 36 62 12 64 08 63 46 63 22 28 29 30 54 51 54 28 54 04 56 00 55 37 55 13 57 09 56 46 56 21 58 18 57 55 57 29 59 29 59 05 58 38 60 38 60 14 59 47 61 48 61 23 60 56 62 57 62 33 62 05 31 32 33 53 39 53 14 52 47 54 47 54 22 53 64 55 55 55 29 55 01 57 03 56 36 56 08 58 12 57 44 57 15 59 20 58 52 58 22 60 28 60 00 59 29 61 36 61 07 60 36 34 35 36 52 20 51 51 51 21 53 26 52 56 52 26 54 31 54 01 53 30 55 37 55 06 54 35 56 44 56 12 56 41 57 50 57 18 56 46 58 57 58 24 57 51 60 03 59 30 58 65 37 38 39 50 51 50 19 49 47 51 54 51 23 50 50 52 57 52 26 51 52 54 02 53 29 52 55 55 07 54 33 53 58 56 12 55 37 55 02 57 17 56 41 56 05 58 22 57 45 57 08 40 41 42 49 13 48 38 48 03 50 15 49 40 49 04 51 16 50 41 50 04 52 18 61 43 61 05 53 21 52 45 52 07 54 24 53 47 53 09 55 27 54 49 54 11 56 30 55 50 55 12 43 44 45 47 28 46 51 46 13 48 28 47 51 47 12 49 28 48 49 48 10 50 29 49 49 49 09 51 30 50 49 50 09 52 29 51 48 51 08 53 30 52 48 52 07 54 30 53 47 53 06 46 47 48 45 35 44 55 44 15 46 33 45 53 45 13 47 30 46 50 46 09 48 28 47 48 47 06 49 27 48 46 48 03 50 26 49 43 48 59 51 24 50 41 49 56 52 22 51 38 50 52 49 50 51 43 36 42 54 42 12 44 32 43 50 43 07 45 27 44 44 44 01 46 23 45 39 44 55 47 19 46 34 45 50 48 15 47 30 46 44 49 11 48 25 47 38 50 06 49 20 48 32 52 53 54 41 30 40 46 40 02 42 23 41 39 40 54 43 16 42 31 41 45 44 09 43 24 42 37 45 04 44 17 43 30 45 57 45 09 44 21 46 51 46 02 45 13 47 44 46 54 46 04 55 56 57 39 17 38 33 37 47 40 09 39 23 38 37 40 59 40 13 39 26 41 50 41 02 40 14 42 42 41 53 41 04 43 32 42 44 41 53 44 23 43 34 42 43 45 14 44 24 43 32 58 59 60 37 01 36 15 35 28 37 50 37 03 36 15 38 38 37 49 37 00 39 25 38 36 37 46 40 14 39 24 38 34 41 03 40 11 39 20 41 52 40 69 40 06 42 39 41 46 40 52 61 62 63 34 39 33 50 33 02 35 25 34 35 33 46 36 10 35 19 34 29 36 66 36 04 35 13 37 42 36 49 35 57 38 27 37 34 36 41 39 13 38 19 37 25 39 58 39 03 38 08 TABLE II. [Page 23 Corrections for the Observed Altitudes of the Moon's Lower Limb. Obs. Alt. Lower Limb. HORIZONTAL PARALLEX. 54' 65' 56' 67' 68' 69' 60' 61' 64 65 66 32 13 31 23 30 33 32 56 32 06 31 14 / // 33 38 32 47 31 54 34 21 33 28 32 35 t n 35 05 34 11 33 17 35 47 34 52 33 57 36 30 35 34 34 38 37 13 36 16 35 19 67 6S 69 29 42 28 51 27 59 30 22 29 31 28 38 31 01 30 09 29 15 31 41 30 47 29 53 32 22 31 27 30 32 33 01 32 06 31 10 33 41 32 45 31 48 34 21 33 24 32 26 70 71 72 27 07 26 15 25 23 27 46 26 52 25 58 28 22 27 27 26 32 28 59 28 04 27 08 29 36 28 40 27 43 30 14 29 16 28 19 30 51 29 53 28 54 31 27 30 28 29 28 73 74 75 24 30 23 37 22 44 25 05 24 11 23 16 25 38 24 43 23 47 26 12 25 16 24 19 26 46 25 49 24 53 27 21 26 22 25 25 27 55 26 56 25 57 28 29 27 28 26 28 76 77 78 21 51 20 57 20 02 22 22 21 27 20 32 22 52 21 56 21 00 23 23 22 26 21 29 23 55 22 57 21 59 24 26 23 27 22 27 24 57 23 57 22 56 25 27 24 26 23 25 79 80 81 19 08 18 13 17 19 19 36 18 41 17 45 20 04 19 07 18 10 20 31 19 33 18 35 2100 20 01 19 02 21 27 20 27 19 27 21 56 20 55 19 55 22 23 21 22 20 21 82 83 84 16 24 15 29 14 33 16 49 15 53 14 57 17 13 16 16 15 19 17 37 16 40 15 42 18 03 17 04 16 05 18 28 17 27 16 27 18 54 17 52 16 50 19 IS 18 16 17 13 85 86 87 13 38 12 43 11 47 14 00 13 04 12 08 14 21 13 24 12 26 14 43 13 45 12 46 15 05 14 06 13 06 15 27 14 27 13 26 15 49 14 48 13 46 16 10 15 08 14 05 88 89 90 10 52 9 56 9 00 11 11 10 15 9 18 11 28 10 31 9 34 11 47 10 49 9 50 12 06 11 07 10 07 12 24 11 24 10 23 12 44 11 42 10 41 13 82 11 59 10 57 Height of Eye Coeeection. Height in feet. Correction. 10 +2 42 12 +2 24 14 +2 08 16 + 1 53 18 + 1 39 20 + 1 25 22 + 1 12 24 + 1 00 26 +0 48 28 +0 37 30 +0 26 35 00 40 -0 24 45 -0 48 50 -1 08 55 -1 28 60 -1 47 65 -2 06 70 -2 24 75 -2 41 80 -2 58 85 -3 14 90 -3 30 95 -3 45 100 -4 00 Page 24] TABLE II. Corrections for the Observed Altitude of the Moon's Upper Limb. Obs. Alt. Upper Limb. HORIZONTAL PARALLAX. 65' 56' 68' 59' 60' 61' 5 30 6 00 6 30 7 00 7 30 8 00 8 30 9 00 9 30 10 00 n 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 46 46 47 48 49 60 51 62 53 64 55 66 57 58 59 60 61 62 63 23 38 24 18 24 52 25 21 25 47 26 09 26 28 26 45 27 00 27 10 27 31 27 45 27 54 27 59 28 01 28 01 27 58 27 51 27 44 27 34 27 23 27 10 26 55 26 39 26 22 26 03 25 43 25 21 24 59 24 36 24 12 23 45 23 19 22 51 22 22 21 53 21 23 20 51 20 19 19 46 19 11 18 37 18 00 17 24 16 46 16 07 15 28 14 48 14 07 13 26 12 44 12 02 11 19 10 36 9 51 9 06 8 21 7 35' 6 48 6 00 5 12 4 23 3 35 24 21 25 01 25 35 26 04 26 30 26 52 27 U 27 27 27 42 27 53 28 13 28 27 28 36 28 40 28 42 28 42 28 39 28 32 28 24 28 13 28 03 27 49 27 33 27 17 27 00 26 40 26 20 25 68 25 35 25 11 24 47 24 20 23 53 23 24 22 56 22 25 21 54 21 22 20 49 20 15 19 40 19 05 18 27 17 50 17 12 16 33 15 53 15 12 14 31 13 49 13 06 12 23 11 39 10 54 10 09 9 23 8 37 7 50 7 02 6 13 5 24 4 35 3 46 25 05 25 44 26 18 26 48 27 13 27 35 27 64 28 10 28 24 28 36 28 55 29 10 29 18 29 22 29 24 29 23 29 20 29 13 29 05 28 54 28 43 28 29 28 12 27 66 27 38 27 18 26 68 26 35 26 12 25 47 25 22 24 55 24 27 23 68 23 28 22 68 22 26 21 53 21 20 20 45 20 09 19 33 18 55 18 17 17 38 16 58 16 18 15 36 14 65 14 11 13 27 12 44 11 59 11 13 10 27 9 40 8 53 8 05 7 17 6 27 5 37 4 48 3 57 25 48 26 27 27 02 27 31 27 56 28 18 28 37 28 63 29 06 29 19 29 38 29 62 30 00 30 05 30 06 30 04 30 01 29 54 29 45 29 34 29 23 29 08 28 52 28 35 28 17 27 56 27 36 27 12 26 48 26 24 25 57 25 30 25 01 24 32 24 01 23 30 22 58 22 24 21 50 21 15 20 38 20 01 19 23 18 45 18 04 17 24 16 43 16 00 15 17 14 34 13 49 13 05 12 19 11 32 10 45 9 58 9 10 8 21 7 32 6 41 5 50 5 00 4 08 26 31 27 10 27 44 28 13 28 39 29 01 29 20 29 36 29 49 30 01 30 21 30 34 30 42 30 47 30 48 30 45 30 42 30 34 30 26 .30 14 30 02 29 47 29 30 29 13 28 65 28 34 28 12 27 48 27 24 26 59 26 32 26 04 25 35 25 05 24 34 24 02 23 29 22 54 22 20 21 45 21 06 20 29 19 60 19 11 18 30 17 49 17 07 16 24 15 40 14 66 14 10 13 25 12 38 11 61 11 03 10 15 9 26 8 36 7 46 6 55 6 04 5 12 4 19 27 13 27 54 28 28 28 57 29 22 29 44 30 03 30 19 30 32 30 44 31 03 31 16 31 24 31 29 31 30 31 27 31 23 31 15 31 06 30 54 30 41 30 27 30 09 29 52 29 33 29 12 28 49 28 25 28 01 27 35 27 07 26 39 26 09 25 39 25 07/ 24 34 24 00 23 25 22 50 22 14 21 35 20 57 20 18 19 37 18 56 18 14 17 32 16 48 16 04 15 19 14 32 13 46 12 59 12 11 11 23 10 32 9 43 8 62 8 01 7 09 6 17 5 23 4 30 27 56 28 37 29 11 29 40 30 05 30 27 30 46 31 02 31 15 31 27 31 46 31 58 32 07 32 11 32 11 32 09 32 04 31 55 31 46 31 34 31 21 31 06 30 49 30 31 30 11 29 49 29 26 29 03 28 37 28 10 27 43 27 14 26 43 26 12 25 40 25 07 24 31 23 56 23 20 22 43 22 04 21 25 20 45 20 04 19 22 18 40 17 57 17 12 16 27 15 41 14 54 14 07 13 19 12 30 11 41 10 49 9 59 9 07 8 16 7 23 6 29 5 35 4 40 28 38 29 19 29 54 30 24 30 48 31 09 31 28 31 44 31 57 32 09 32 28 32 40 32 49 32 52 32 52 32 50 32 45 32 35 32 26 32 15 32 01 31 45 31 27 31 10 30 48 30 26 30 03 29 39 29 12 28 46 28 18 27 48 27 17 26 45 26 12 25 39 25 03 24 28 23 50 23 12 22 33 21 54 21 13 20 32 19 48 19 05 18 21 17 36 16 50 16 03 15 15 14 27 13 38 12 49 11 69 11 06 10 15 9 22 8 30 7 36 6 42 5 46 4 61 TABLE II. [Page 25 Corrections for the Observed Altitude of the Moon's Upper Limb. Obs. Alt. Uppee Limb. HORIZONTAL PARALLAX. 64' 55' 56' 67' 58' 5^ 60' 61' o n , n , n / If / H , n / It , „ , ,, 64 65 66 2 46 1 56 1 06 2 56 204 1 14 3 06 2 13 1 22 3 16 2 23 1 31 3 26 2 32 1 39 3 36 2 42 1 47 3 46 2 51 1 55 3 56 3 00 2 03 67 68 69 16 22 29 37 44 51 04 58 02 1 06 008 36 1 27 30 1 22 24 1 17 17 1 11 Oil 1 06 102 57 51 70 g 72 g 2 19 3 11 4 03 2 15 3 OS 4 01 2 11 3 05 3 59 2 06 3 01 3 56 2 02 2 58 3 54 1 58 2 55 3 52 1 54 2 52 3 50 1 50 2 48 3 48 73 g 74 75 4 55 5 49 6 43 4 56 5 50 6 44 4 54 5 49 6 44 4 52 5 48 6 45 4 51 5 48 6 46 4 50 5 48 6 47 4 49 5 48 6 48 4 47 5 47 6 48 76 77 78 7 37 8 31 9 25 7 39 8 34 9 29 7 40 8 37 9 33 7 42 8 39 9 36 7 44 8 42 9 40 7 45 8 44 9 44 7 47 8 47 9 48 7 49 8 50 9 51 79 80 81 10 19 11 13 12 08 10 24 11 20 12 15 10 29 11 26 12 22 10 33 11 31 12 28 10 38 11 37 12 35 10 43 11 43 12 42 10 48 11 49 12 50 10 52 11 54 12 57 82 83 84 13 03 13 58 14 53 13 11 14 07 15 04 13 19 14 16 15 14 13 27 14 25 15 23 13 34 14 34 15 33 13 43 14 43 15 44 13 51 14 52 15 54 13 59 15 01 16 03 85 86 87 15 48 16 44 17 39 16 00 16 57 17 53 16 11 17 09 18 06 16 21 17 20 18 18 16 33 17 32 18 32 16 44 17 45 18 45 16 55 17 57 18 59 17 06 18 08 19 11 88 89 90 18 35 19 31 20 26 18 50 19 47 20 43 19 04 20 02 21 00 19 18 20 16 21 15 19 32 20 31 21 31 19 46 20 47 21 48 20 00 21 03 22 04 20 14 21 17 22 20 Height of Ete Coeeection. Height in feet. Correction. 10 +2 42 12 +2 24 14 +2 08 16 + 1 53 18 + 1 39 20 + 1 25 22 + 1 12 24 + 1 00 26 + 48 28 + 37 30 +0 26 35 00 40 -0 24 45 -0 48 50 -1 08 55 -1 28 60 -1 47 65 -2 06 70 -2 24 75 -2 41 80 -2 58 85 -3 14 90 -3 30 95 -3 45 100 -4 00 TABLE III LOGARITHMIC SINES AND LOGARITHMIC COSINES 27 Page 28] TABLE III. Log . Sines. 0° 0' 0° 10' 2 Eh "'.2 0° 20' ■a d 0° 30' 0° 40' t3§ ■OH 0° 60' •oS 1° 0' •oS 1° 10' T3§ ''■2 •o 3 1° 20' -OH + 0' 10" 20 30 40 60 ■(- 1' 10" 20 30 40 60 + 2' 10" 20 30 40 60 4- 3' 10" 20 30 40 60 + 4' 10" 20 30 40 60 + 5' 10' 20 30 40 60 + 6' 10" 20 30 40 60 4- 7' 10' 20 30 40 60 + 8' 10" 20 30 40 60 + 9' 10" 20 30 40 60 flO' — oo 7.46373 1 7.76475 1 2 2 2 2 2 2 2 2 2 7.94084 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 8.06578 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 5 5 5 5 8.16268 6 6 5 5 6 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 7 7 7 7 8.24186 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 9 9 9 9 9 9 9 9 9 9 9 9 8.30879 9 9 9 9 9 9 9 9 9 9 9 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 12 12 12 12 12 12 S. 36678 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 13 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 14 15 15 15 15 15 15 15 15 6.68557 5.98660 6. 16270 6.28763 6.38454 .47090 . 47797 .48491 .49175 .49849 .76836 .77193 .77548 .77899 .78248 7.94325 7.94564 7.94802 7.95039 7.95274 .06758 .06938 .07117 .07295 .07473 .16413 .16557 .16700 .16843 .16986 .24306 .24426 .24546 . 24665 .24785 .30983 .31086 .31188 .31291 .31393 .36768 .36858 . 36948 .37038 .37128 6. 46373 .50512 .78594 7.95508 .07650 . 17128 .24903 .31495 .37217 6.53067 6.58866 6.63982 6.6S557 6.72697 .51165 . 51808 . 52442 .53067 .53683 . 78938 . 79278 .79616 . 79952 .80284 7.95741 7.95973 7. 96203 7.96432 7. 96660 .07826 .08002 .08176 .08350 .08524 .17270 .17411 . 17552 .17692 .17832 .25022 .25140 .25258 .25375 .25493 .31597 .31699 .31800 .31901 .32002 .37306 .37395 .37484 .37573 .37662 6.76476 .54291 .80615 7.96887 .08696 . 17971 .25609 .32103 .37750 6. 79952 6.83170 6.86167 6.88969 6.91602 .54890 . 55481 .56064 . 56639 .57206 .57767 . 80942 .81268 . 81591 .81911 .82229 7.97113 7.97337 7. 97560 7.97782 7. 98003 .08868 .09040 .09210 .09380 .09550 .18110 . 18249 .18387 .18524 .18662 .25726 .25842 .25958 .26074 .26189 .32203 .32303 .32403 .32503 .32602 .37838 .37926 .38014 .38101 .38189 6.94085 .82545 7.98223 .09718 . 18798 .26304 .32702 .38276 6.96433 6.9S660 7.00779 7.02800 7.04730 .58320 . 58866 .59406 . 59939 .60465 .82859 .83170 .83479 .83786 .84091 7.98442 7.98660 7.98876 7.99092 7.99306 .09886 .10054 .10220 .10386 .10552 . 18935 .19071 .19206 .19341 .19476 .26419 .26533 .26648 .26761 .26875 .32801 .32899 .32998 .33096 .33195 .38363 .38450 .38537 .38624 .38710 7.06579 .60985 .84393 7.99520 .10717 .19610 .26988 .3.3292 .38796 7.08351 7. 10055 7.11694 7. 13273 7. 14797 .61499 .62007 .62509 . 63006 .63496 .84694 .84992 .85289 .85583 .85876 7.99732 7.99943 8.00154 8.00363 8.00571 . 10881 .11044 .11207 .11370 .11531 .19744 .19877 .20010 .20143 .20275 .27101 .27214 .27326 .27438 . 27550 .33390 .33488 .33585 .33682 .33779 .38882 .38968 .39054 .39139 .39225 7. 16270 .63982 .86166 8.00779 . 11693 .20407 .27661 .33875 .39310 7. 17694 7. 19072 7.20409 7.21705 7.22964 . 6-1461 . 64936 .65406 .65870 .66330 .86455 .86741 .87026 .87309 .87590 8.00985 8.01190 8.01395 8.01598 8.01801 .11853 .12013 . 12172 . 12331 . 12489 .20538 .20669 .20800 .20930 .21060 .27773 .27883 . 27994 .28104 .28215 .33972 .34068 .34164 .34260 .34355 .39395 . 39480 .39565 . 39649 .39734 7.24188 .66784 .87870 8.02002 .12647 .21189 .28324 .34450 .39818 7.25378 7.26536 7.27664 7.28763 7.29836 .67235 .67680 .68121 .68557 .68989 .88147 .88423 .88697 .88969 .89240 8.02203 8.02402 8.02601 8.02799 8.02996 .12804 .12961 .13117 . 13272 .13427 .21319 .21447 .21576 .21703 .21831 .28434 .28543 .28652 .28761 .28869 .34546 .34640 .34735 .34830 .34924 .39902 ,39986 .40070 .40156 .40237 7.30882 .69417 .89509 8.03192 .13581 .21958 .28977 .35018 .40320 7.31904 7.32903 7.33879 7.34833 7.35767 .69841 . 70261 .70676 . 71088 .71496 .89776 .90041 .90305 .90568 .90829 8.03387 8.03581 8.03775 8.03967 8.04159 .13735 . 13888 . 14041 . 14193 .14344 .22085 .22211 .22337 .22463 .22588 .29085 .29193 .29300 .29407 .29514 .35112 .35206 .35299 .35392 .35485 .40403 .4W86 .48569 .40651 . 40734 7. 36682 . 71900 .91088 8.04350 .14495 .22713 .29621 .35578 . 40816 7.37577 7.38454 7.39314 7.40158 7.40985 .72300 . 72697 .7,3090 .73479 . 73865 .91346 . 91602 .91857 .92110 .92362 8. 04.540 8.04729 8.04918 8.05105 8. 05292 .14646 . 14796 . 14945 .15094 . 15243 .22838 .22962 .23086 .23210 .23333 .29727 .29833 .29939 .30044 .30150 .35671 .35764 .35856 .35948 . 36040 .40898 .40980 . 41062 .41144 .41225 7.41797 .74248 .92612 8. 05478 .15391 .23456 .30255 .36131 .41307 7.42594 7.43376 7.44145 7.44900 7.45643 .74627 .75003 .75376 . 75745 .76112 .92861 .93108 .93354 .93599 .93842 8.05663 8. 05848 8.06a31 8.06214 8.06396 . 15538 .15685 .15832 . 15978 .16123 .23578 .23700 .23822 .23944 .24065 .30359 .30464 .30568 .30672 .30776 .36223 .36314 .36405 .36496 .36587 .41388 .41469 .41550 .41631 .41711 7.46373 .76475 .94084 8.06578 . 16268 .24186 .30879 .36678 .41792 TABLE III. [Page 29 Log. Sines. 1 T.S t3 03 n S Tl 9 •rt S ^i ■d rt r,S nS 1''30' 1''40' ■OH < u 1°50' 3°0' 2° 10' ■T3b< •Z' 20' 2° 30' ■dH < u 2° 40' ■OH 2" 50' +0' 10" 8.41792 15 15 8.46366 18 18 8.50504 22 22 8. 51282 26 27 8.57757 31 31 8.60973 36 36 8. 63968 41 41 8.66769 47 47 S. 69400 53 53 .41872 .46439 .50570 .54342 .57812 .61025 .64016 . 66814 .69442 20 .41952 15 .46511 19 .50636 22 .54402 27 .57868 31 .61077 36 .64064 42 .66859 47 .6948.5 54 30 .42032 15 .46583 19 .50701 22 .54462 27 .57923 31 .61128 36 .64112 42 .66904 47 .69.527 64 40 .42112 15 . 46655 19 .50767 23 . 54522 27 .57979 31 .61180 36 .64160 42 .66949 47 .69570 64 50 + 1' 10" .4219C 15 15 15 .46727 19 19 19 .50^2 23 23 23 .54582 27 27 27 .58034 31 32 32 .61231 36 37 37 .64208 42 42 42 .66994 48 48 48 .69612 54 54 54 .42272 . 46799 . 50897 .54642 .58089 .61282 .64256 .67039 . 69654 .42351 . 46870 .50963 .54702 .58144 .61334 . 64304 .67084 .69897 20 . 42430 15 . 46942 19 . 51028 23 .54762 27 .58200 32 .61385 37 . 64352 42 .67129 48 . 697.39 54 30 .42510 15 . 47013 19 .51092 23 .54821 27 .58255 32 .61436 37 .04400 42 .67174 48 .69781 64 40 . 42589 15 .47084 19 .51157 23 .54881 27 .58310 32 .61487 37 .64448 42 .67219 48 . 69823 64 60 +2' 10" . 42667 15 16 16 .47155 19 19 19 .51222 23 23 23 . 54940 27 27 27 .58364 32 32 32 .61538 37 37 37 . 64495 42 42 43 .67263 48 48 48 . 69865 64 54 54 . 42746 . 47226 .51287 .54999 .58419 .61589 .64543 . 67308 .69907 . 42825 .47297 ..51351 .55059 .58474 .61640 .64590 . 67353 .69949 20 . 42903 16 .47368 19 .51416 23 .55118 28 .58529 32 .61691 37 . 64638 43 . 67397 48 . 69991 66 30 . 42982 16 .47439 19 . 51480 23 .55177 28 .58583 32 . 61742 37 .64685 43 . 67442 49 .70033 56 40 .43060 16 .47509 19 .51544 23 .55236 28 .58638 32 .61792 37 .64733 43 . 67486 49 .70075 66 50 +3' 10" .43138 16 16 16 .47580 19 19 20 .51609 23 23 24 .55295 28 28 28 .58693 32 33 33 .61843 37 38 38 .64780 43 43 43 .67531 49 49 49 .70117 55 55 55 .43216 . 47650 .51673 .55354 .58747 .61894 .64827 .67575 .70159 .43293 .47720 .51737 .55413 .58801 .61944 .64875 .67619 .70201 20 .43371 16 .47790 20 .51801 24 . 55471 28 .58856 33 .61995 38 .04922 43 .67664 49 .70242 56 30 .43448 16 .47860 20 . 51864 24 .55530 28 . 58910 33 .62045 3S .64969 43 .67708 49 . 70284 66 40 . 43526 16 .47930 20 .51928 24 . 55589 28 .58964 33 .62096 38 .6.5016 43 . 67752 41' .70326 55 60 +4' 10" .43603 16 16 16 .48000 20 20 20 .51992 24 24 24 .55647 28 28 28 .59018 33 33 33 .62146 38 38 38 .65063 43 44 44 .67796 49 49 49 .70367 66 56 56 .43680 .48069 .52055 .55705 .59072 .62196 .65110 .67841 .70409 .43757 .48139 .52119 .55764 .59126 .62246 .65157 .67885 .70451 20 .43834 16 .48208 20 .52182 24 .55822 28 .59180 33 .62297 38 .65204 44 .67929 50 .70492 66 30 .43910 16 .48278 20 .52245 24 .55880 28 .59234 33 .62347 38 .65251 44 .67973 60 .70534 56 40 .43987 16 .48347 20 .52308 24 .55938 29 .59288 33 . 62397 38 .65298 44 .68017 50 . 70575 66 50 +5' 10" .44063 17 17 17 .48416 20 20 20 .52371 24 24 24 .55996 29 29 29 .59341 33 33 34 .62447 39 39 39 .65344 44 44 44 .68060 50 50 SO .70616 66 56 56 .44139 .48485 .52434 .56054 .59395 .62497 .65391 .68104 .70558 .44216 .48554 .52497 .56112 .59448 .62546 . 65 138 .68148 .70699 20 .44292 17 .48622 20 .52560 24 .56170 29 .59502 34 .62596 39 .6.5184 44 .68192 50 . 70740 6V 30 .44367 17 .48691 20 .52623 25 .56227 29 .59555 34 .62646 39 . 65531 44 .68236 60 .70781 57 40 .44443 17 .48760 21 .5268.5 25 .56285 29 .59609 34 .62696 39 .65577 45 .68279 50 .70823 6V 50 +6' 10" . 44519 17 17 17 .48828 21 21 21 .52748 25 25 25 .56342 29 29 29 .59662 34 34 34 .62745 39 39 39 .65624 45 45 45 .68323 50 51 51 .70864 57 57 57 .44594 .48896 .52810 .56400 .59715 .62795 .65670 .68367 .70905 . 44669 .48965 .52872 .56457 .59768 . 62844 .65717 .68410 .70946 20 .44745 17 .49033 21 . 52935 25 .56515 29 .59821 34 .62894 39 .65763 45 .68454 61 .70987 57 30 . 44820 17 .49101 21 .52997 25 .56572 29 .59874 34 .62943 39 .65809 46 .68497 61 . 71028 67 40 .44895 17 .49169 21 .53059 25 .56629 29 .59927 34 . 62993 40 .65855 45 . 68540 51 .71069 57 50 + 7' 10" . 44969 17 17 17 .49236 21 21 21 . 53121 25 25 25 .56686 30 30 30 . 59980 34 34 35 .63042 40 40 40 .65901 45 45 45 .68584 51 51 51 .71110 6V 58 58 .45044 .49304 .53183 .56743 .60033 .63091 .65947 .68627 .71151 .45119 . 49372 .53245 .56800 .60086 .63140 .65994 .68670 .71192 20 .45193 17 .49439 21 . 53306 25 .56857 30 .60139 35 .63189 40 .66040 46 .68714 51 . 71232 68 30 . 45267 17 .49506 21 .53368 25 . 56914 30 .60191 35 .63238 40 .66085 46 . 68757 61 .71273 68 40 .45341 IS .49574 21 . 53429 25 .56970 30 .60244 35 .63288 40 .66131 46 .68800 52 .71314 68 50 +8' 10" .45415 18 IS 18 .49641 21 21 22 .53491 26 26 26 .57027 30 30 30 .60296 35 35 35 . 63336 40 40 40 .66177 46 46 46 . 68843 52 52 52 .713.5.5 68 58 58 .45489 .49708 . 53552 .57084 .60349 .63385 .66223 . 68886 .71395 .45563 . 49775 .53614 .57140 .60401 .63434 .66269 .68929 .71436 20 .45637 18 .49842. 22 .53675 26 .57196 30 .60454 35 .63483 40 .66314 46 .68972 52 .71476 68 30 . 45710 18 .49908 22 .53736 26 .57253 30 .60506 35 .63532 41 .66360 46 .69015 62 .71517 69 40 .45784 IS .49975 22 .53797 26 .57309 30 .60558 35 .63580 41 .66406 46 .69058 62 .71557 69 50 +9' 10" .45857 18 18 IS .50042 22 22 22 .53858 26 26 26 . 57365 31 31 31 .60610 35 36 36 .63629 41 41 41 .66451 46 46 47 .69101 62 52 53 .71598 69 59 59 .45930 .50108 .53919 .57421 .60662 .63678 .66497 .69144 .71638 .46003 . .50174 .53979 .57477 .60714 .&3726 .66542 .69187 . 71679 20 .46076 IS .50241 22 . 54040 26 .575.33 31 .60766 36 .63775 41 .66588 47 .69229 53 .71719 69 30 .46149 IS .50307 22 .54101 26 ..57589 31 . 60818 36 .63823 41 .66633 47 . 69272 ,63 .71759 59 40 .46222 18 .50373 22 .54161 26 .57645 31 .60870 36 .63871 41 .66678 47 .69315 ^i .71800 .69 50 .46294 18 18 .50439 22 22 .54222 26 26 .57701 31 31 .60922 36 36 .63920 41 41 .66724 47 47 .69357 63 53 . 71840 69 60 + 10' .46366 .50504 ..54282 .57757 .60973 .63968 .66769 . 69400 .71880 Page 30] TABLE III. Log. Sines. 3° O' Add for Tan. 3° lO' Add for Tan. 3° 20^ Add for Tan. 3° 30' Add for Tan. 3° 40' Add for Tan. 3° 50' Add for Tan. + o' 20 30 40 50 + r 20 30 40 50 + 2^ 20 30 40 50 + 3^ 20 30 40 50 + i' 20 30 40 50 + 5' 20 30 40 50 + 6^ 20 30 40 50 + r 20 30 40 50 + 8' lO'' 20 30 40 50 + 9' 20 30 40 50 +10' 8. 71880 60 60 60 60 60 60 60 60 60 60 61 61 61 61 61 61 61 61 62 62 62 62 62 62 62 62 62 63 63 63 63 63 63 63 63 63 64 64 64 64 64 64 64 64 65 65 65 65 65 65 65 65 65 66 66 66 66 66 66 66 66 8. 74226 66 66 67 67 67 67 67 67 67 67 68 68 68 68 68 68 68 68 68 69 69 69 69 69 69 69 69 70 70 70 70 70 70 70 70 71 71 71 71 71 71 71 71 71 72 72 72 72 72 72 72 72 73 73 73 73 73 73 73 73 74 8. 76451 74 74 74 74 74 74 74 74 75 75 75 75 75 75 75 75 76 76 76 76 76 76 76 76 77 77 77 77 77 77 77 77 78 78 78 78 78 78 78 78 79 79 79 79 79 79 79 79 80 80 80 80 80 80 80 80 81 81 81 81 81 8. 78568 81 81 81 81 82 82 82 82 82 82 82 82 83 83 83 83 83 83 83 84 84 84 84 84 84 84 85 85 85 85 85 85 85 85 86 86 86 86 86 86 86 86 87 87 87 87 87 87 87 88 88 88 88 88 88 88 88 89 89 89 89 8. 80585 89 89 89 89 90 90 90 90 90 90 90 90 91 91 91 91 91 91 91 92 92 92 92 92 92 92 93 93 93 93 93 93 93 93 94 94 94 94 94 94 94 95 95 95 95 95 95 95 96 96 96 96 96 96 96 97 97 97 97 97 97 8. 82513 97 97 98 98 98 98 98 98 98 99 99 99 99 99 99 99 100 100 100 100 100 100 100 101 101 101 101 101 101 101 102 102 102 102 102 102 102 103 103 103 103 103 103 103 104 104 104 104 104 104 104 105 105 105 105 105 105 105 106 106 106 8. 71920 8. 71960 8. 72000 8. 72040 8. 72080 8. 74264 8. 74302 8. 74340 8. 74378 8. 74416 8. 76487 8. 76523 8. 76559 8. 76595 8. 76631 8. 78602 8. 78636 8. 78671 8. 78705 8. 78739 8. 80618 8. 80651 8. 80684 8. 80716 8. 80749 8. 82544 8. 82576 8. 82607 8. 82639 8. 82670 8. 72120 8. 74454 8. 76667 8. 78774 8. 80782 8. 82701 8. 72160 8. 72200 8. 72240 8. 72280 8. 72320 8. 74491 8. 74529 8. 74567 8. 74605 8. 74642 8. 76703 8. 76739 8. 76775 8. 76811 8. 76847 8. 78808 8. 78842 8. 78876 8. 78910 8. 78945 8. 80815 8. 80847 8. 80880 8. 80913 8. 80945 8. 82732 8. 82764 8. 82795 8. 82826 8. 82857 8. 72359 8. 74680 8. 76883 8. 78979 8. 80978 8. 82888 8. 72399 8. 72439 8. 72478 8. 72518 8. 72558 8. 74718 8. 74755 8. 74793 8. 74831 8. 74868 8. 76919 8. 76954 8. 76990 8. 77026 8. 77061 8. 79013 8. 79047 8. 79081 8. 79115 8. 79149 8. 81010 8. 81043 8. 81075 8. 81108 8. 81140 8. 82920 8. 82951 8. 82982 8. 83013 8. 83044 8. 72597 8. 74906 8. 77097 8. 79183 8. 81173 8. 83075 8. 72637 8. 72676 8. 72716 8. 72755 8. 72794 8. 74943 8. 74980 8. 75018 8. 75055 8. 75092 8. 77133 8. 77168 8. 77204 8. 77239 8. 77275 8. 79217 8. 79251 8. 79284 8. 79318 8. 79352 8. 81205 8. 81237 8. 81270 8. 81302 8. 81334 8. 83106 8. 83137 8. 83168 8. 83199 8. 83230 8. 72834 8. 75130 8. 77310 8. 79386 8. 81367 8. 83261 8. 72873 8. 72912 8. 72951 8. 72991 8. 73030 8. 75167 8. 75204 8. 75241 8. 75279 8. 75316 8. 77346 8. 77381 8. 77416 8. 77452 8. 77487 8. 79420 8. 79453 8. 79487 8. 79521 8. 79555 8. 81399 8. 81431 8. 81463 8. 81496 8. 81528 8. 83292 8. 83322 8. 83353 8. 83384 8. 83415 8. 73069 8. 75353 8. 77522 8. 79588 8. 81560 8. 83446 8. 73108 8. 73147 8. 73186 8. 73225 8. 73264 8. 75390 8. 75427 8. 75464 8. 75501 8. 75538 8. 77558 8. 77593 8. 77628 8. 77663 8. 77698 8. 79622 8. 79655 8. 79689 8. 79722 8. 79756 8. 81592 8. 81624 8. 81656 8. 81688 8. 81720 8. 83476 8. 83507 8. 83538 8. 83568 8. 83599 8. 73303 8. 75575 8. 77733 8. 79789 8. 81752 8. 83630 8. 73342 8. 73380 8. 73419 8. 73458 8. 73497 8. 75612 8. 75648 8. 75685 8. 75722 8. 75759 8. 77768 8. 77803 8. 77838 8. 77873 8. 77908 8. 79823 8. 79856 8. 79890 8. 79923 8. 79956 8. 81784 8. 81816 8. 81848 8. 81880 8. 81912 8. 83660 8. 83691 8. 83721 8. 83752 8. 83783 8. 73535 8. 75795 8. 77943 8. 79990 8. 81944 8. 83813 8. 73574 8. 73613 8. 73651 8. 73690 8. 73728 8. 75832 8. 75869 8. 75905 8. 75942 8. 75979 8. 77978 8. 78013 8. 78048 8. 78083 8. 78118 8. 80023 8. 80056 8. 80090 8. 80123 8. 80156 8. 81975 8. 82007 8. 82039 8. 82071 8. 82103 8. 83844 8. 83874 8. 83904 8. 83935 8. 83965 8. 73767 8. 76015 8. 78152 8. 80189 8. 82134 8. 83996 8. 73805 8. 73844 8. 73882 8. 73920 8. 73959 8. 76052 8. 76088 8. 76125 8. 76161 8. 76197 8. 78187 8. 78222 8. 78257 8. 78291 8. 78326 8. 80222 8. 80255 8. 80289 8. 80322 8. 80355 8. 82166 8. 82198 8. 82229 8. 82261 8. 82292 8. 84026 8. 84056 8. 84087 8. 84117 8. 84147 8. 73997 8. 76234 8. 78360 8. 80388 8. 82324 8. 84177 8. 74035 8. 74073 8. 74112 8. 74150 8. 74188 8. 76270 8. 76306 8. 76343 8. 76379 8. 76415 8. 78395 8. 78430 8. 78464 8. 78499 8. 78533 8. 80421 8. 80454 8. 80487 8. 80519 8. 80552 8. 82356 8. 82387 8. 82419 8. 82450 8. 82482 8.84208 8. 84238 8. 84268 8. 84298 8. 84328 8. 74226 8. 76451 8. 78568 8. 80585 8. 82513 8. 84358 TABLE III. Log. Sines. [Page 31 4° O' Add for Tan. 4° W Add for Tan. 4° W Add for Tan. 4° W Add for Tan. 4° 4r Add for Tan. 4° 50^ Add for Tan. + 0" 20 30 40 50 + I' 20 30 40 50 + r 20 30 40 50 + 3' 20 30 40 50 + 4' 20 30 40 50 + 5' 20 30 40 50 + 6^ 20 30 40 50 + r 20 30 40 50 + 8^ 20 30 40 50 + 9^ 20 30 40 50 8. 84358 106 106 106 106 107 107 107 107 107 107 107 108 108 108 108 108 108 108 109 109 109 109 109 109 109 110 110 110 110 110 110 111 111 111 111 111 111 111 112 112 112 112 112 112 113 113 113 113 113 113 113 114 114 114 114 114 114 114 115 115 115 8. 86128 115 115 115 115 116 116 116 116 116 116 116 117 117 117 117 117 117 118 118 118 118 118 118 118 119 119 119 119 119 119 120 120 120 120 120 120 121 121 121 121 121 121 121 122 122 122 122 122 122 123 123 123 123 123 123 124 124 124 124 124 124 8. 87829 124 124 125 125 125 125 125 125 126 126 126 126 126 126 127 127 127 127 127 127 128 128 128 128 128 128 129 129 129 129 129 129 129 130 130 130 130 130 130 131 131 131 131 131 131 132 132 132 132 132 132 133 133 133 133 133 133 134 134 134 134 8. 89464 134 134 134 135 135 135 135 135 135 136 136 136 136 136 136 137 137 137 137 137 137 138 138 138 138 138 138 139 139 139 139 139 139 140 140 140 140 140 140 141 141 141 141 141 141 142 142 142 142 142 142 143 143 143 143 143 144 144 144 144 144 8. 91040 8. 91066 8. 91092 8.91118 8. 91143 8. 91169 144 144 145 145 145 145 145 145 146 146 146 146 146 146 147 147 147 147 147 147 148 148 148 148 148 149 149 149 149 149 149 150 150 150 150 150 150 151 151 151 151 151 152 152 152 152 152 152 153 153 153 153 153 153 154 154 154 154 154 155 155 8. 92561 155 155 155 155 155 156 156 156 156 156 156 157 157 157 157 157 158 158 158 158 158 159 159 159 159 159 159 160 160 160 160 160 160 161 161 161 161 161 162 162 162 162 162 162 163 163 163 163 163 164 164 164 164 164 164 165 165 165 165 165 165 8. 84389 8.84419 8.84449 8. 84479 8. 84509 8. 86157 8. 86186 8. 86215 8. 86244 8. 86273 8. 87856 8. 87884 8. 87912 8. 87940 8. 87967 8. 89491 8. 89518 8. 89545 8. 89571 8. 89598 8. 92586 8. 92611 8. 92636 8. 92660 8. 92685 8. 84539 8. 86301 8. 87995 8. 89625 8. 91195 8.92710 8. 84569 8. 84599 8. 84629 8. 84659 8. 84688 8. 86330 8. 86359 8. 86388 8. 86416 8. 86445 8. 88023 8. 88050 8. 88078 8. 88106 8. 88133 8. 89651 8. 89678 8. 89704 8. 89731 8. 89758 8. 91221 8. 91246 8.91272 8. 91298 8. 91323 8. 92735 8. 92760 8. 92784 8. 92809 8. 92834 8. 84718 8. 86474 8. 88161 8. 89784 8. 91349 8. 92859 8. 84748 8. 84778 8. 84808 8. 84838 8. 84867 8. 86502 8. 86531 8. 86560 8. 86588 8. 86617 8. 88188 8. 88216 8. 88243 8. 88271 8. 88298 8. 89811 8. 89837 8. 89864 8. 89890 8. 89917 8. 91374 8. 91400 8. 91426 8. 91451 8. 91477 8. 92883 8. 92908 8. 92933 8. 92957 8. 92982 8. 84897 8. 86645 8. 88326 8. 89943 8. 91502 8. 93007 8. 84927 8. 84957 8. 84986 8. 85016 8. 85045 8. 86674 8. 86703 8. 86731 8. 86760 8. 86788 8. 88353 8. 88381 8. 88408 8. 88435 8. 88463 8. 89970 8. 89996 8. 90023 8. 90049 8. 90075 8. 91528 8. 91553 8. 91579 8. 91604 8. 91630 8. 93031 8. 93056 8. 93081 8. 93105 8. 93130 8. 85075 8. 86816 8. 88490 8. 90102 8. 91655 8. 93154 8. 85105 8. 85134 8. 85164 8. 85193 8. 85223 8. 86845 8. 86873 8. 86902 8. 86930 8. 86958 8. 88518 8. 88545 8. 88572 8. 88600 8. 88627 8. 90128 8. 90154 8. 90181 8. 90207 8. 90233 8. 91680 8. 91706 8.91731 8. 91757 8. 91782 8. 93179 8. 93203 8. 93228 8. 93253 8. 93277 8. 85252 8. 86987 8. 88654 8. 90260 8. 91807 8. 93301 8. 85282 8. 85311 8. 85341 8. 85370 8. 85400 8. 87015 8. 87043 8. 87072 8. 87100 8. 87128 8. 88681 8. 88709 8. 88736 8. 88763 8. 88790 8. 90286 8. 90312 8. 90338 8. 90364 8. 90391 8. 91833 8. 91858 8. 91883 8. 91909 8. 91934 8. 93326 8. 93350 8. 93375 8. 93399 8. 93424 8. 85429 8. 87156 8. 88817 8. 90417 8. 91959 8. 93448 8. 85458 8. 85488 8. 85517 8. 85546 8. 85576 8. 87185 8. 87213 8. 87241 8. 87269 8. 87297 8. 88845 8. 88872 8. 88899 8. 88926 8. 88953 8. 90443 8. 90469 8. 90495 8. 90521 8. 90548 8. 91984 8. 92010 8. 92035 8. 92060 8. 92085 8. 93472 8. 93497 8. 93521 8. 93546 8. 93570 8. 85605 8. 87325 8. 88980 8. 90574 8. 92110 8. 93594 8. 85634 8. 85663 8. 85693 8. 85722 8. 85751 8. 87354 8. 87382 8. 87410 8. 87438 8. 87466 8. 89007 8. 89034 8. 89061 8. 89088 8. 89115 8. 90600 8. 90626 8. 90652 8. 90678 8. 90704 8. 92135 8. 92161 8. 92186 8. 92211 8. 92236 8. 93619 8. 93643 8. 93667 8. 93691 8. 93716 8. 85780 8. 87494 8. 89142 8. 90730 8. 92261 8. 93740 8. 85809 8. 85838 8. 85867 8. 85896 8. 85926 8. 87522 8. 87550 8. 87578 8. 87606 8. 87634 8. 89169 8. 89196 8. 89223 8. 89250 8. 89277 8. 90756 8. 90782 8. 90808 8. 90834 8. 90859 8. 92286 8. 92311 8. 92336 8. 92361 8. 92386 8. 93764 8. 93788 8. 93812 8. 93837 8. 93861 8. 85955 8. 87661 8. 89304 8. 90885 8. 92411 8. 93885 8. 85984 8. 86013 8. 86042 8. 86070 8. 86099 8. 87689 8.87717 8. 87745 8. 87773 8. 87801 8. 89330 8. 89357 8. 89384 8. 89411 8. 89438 8. 90911 8. 90937 8. 90963 8. 90989 8. 91015 8. 92436 8. 92461 8. 92486 8. 92511 8. 92536 8. 93909 8. 93933 8. 93957 8. 93981 8. 94006 +10^ 8. 86128 8. 87829 8. 89464 8. 91040 8. 92561 8. 94030 Page 32] TABLE III. Log. Sines. Time. Arc. Oh 20m 5° Oh 24^ 6° Oh 2Sm 7° Oh 32m 8° Oh 36m 9° Arc. Time. m. s. ' Sine. P. P. Sine. P. P. Sine. P. P. Sine. P. P. Sine. P. P. ' s. m. 8.94030 142 9.01923 lis 9.08589 102 9.14356 89 9.19433 79 60 +4 4 8 12 1 2 3 8.94174 8.94317 8.94461 14 28 43 9.02043 9.02163 9.02283 12 24 35 9.08692 9.08795 9.08897 10 20 31 9.14445 9.14535 9.14624 9 18 27 9.19513 9.19592 9.19672 8 16 24 59 58 57 56 52 48 16 20 24 4 5 6 8.94603 8.94746 8.94887 57 71 85 9.02402 9.02520 9.02639 47 59 71 9.08999 9.09101 9.09202 41 51 61 9.14714 9.14803 9.14891 36 45 53 9.19751 9.19830 9.19909 32 40 47 56 55 54 U 40 36 28 32 36 •3 S 9 8.95029 8.95170 8.95310 99 114 128 9.02757 9.02874 9.02992 83 94 106 9.09304 9.09405 9.09506 71 82 92 9.14980 9.15069 9.15157 62 71 80 9.19988 9.20067 9.20145 55 63 71 53 52 51 32 28 24 40 10 8.95450 138 9.03109 116 9.09606 99 9.15245 87 9.20223 78 50 20 44 48 52 11 12 13 8.95589 8.95728 8.95867 14 28 41 9.03226 9.03342 9.03458 12 23 35 9.09707 9.09807 9.09907 10 20 30 9.15333 9.15421 9.15508 9 17 26 9.20302 9.20380 9.20458 8 16 23 49 48 47 16 12 8 56 +1 4 14 15 16 8.96005 8.96143 8.96280 55 69 83 9.03574 9.03690 9.03805 46 58 70 9.10006 9.10106 9.10205 40 50 59 9.15596 9.15683 9.15770 35 44 52 9.20535 9.20613 9.20691 31 39 47 46 45 44 4 +3 56 8 12 16 n 18 19 8.96417 8.96553 8.96689 97 110 124 9.03920 9.04034 9.04149 81 93 104 9.10304 9.10402 9.10501 69 79 89 9.15857 9.15944 9.16030 61 70 78 9.20768 9.20845 9.20922 55 62 70 43 42 41 52 48 44 20 20 8.96825 133 9.04262 113 9.10599 97 9.16116 85 9.20999 76 40 40 24 28 32 21 22 23 8.96960 8.97095 8.97229 13 27 40 9.04376 9.04490 9.04603 11 23 34 9.10697 9.10795 9.10893 10 19 29 9.16203 9.16289 9.16374 9 17 26 9.21076 9.21153 9.21229 8 15 23 39 38 37 36 32 28 36 40 44 24 25 26 (8.97363 8.97496 8.97629 53 67 80 9.04715 9.04828 9.04940 45 57 68 9.10990 9.11087 9.11184 39 49 58 9.16460 9.16545 9.16631 34 43 51 9.21308 9.21382 9.21458 30 38 46 36 35 34 24 20 16 48 52 56 27 28 29 8.97762 8.97894 8.98026 93 106 120 9.05052 9.05164 9.05275 79 90 102 9.11281 9.11377 9.11474 68 78 87 9.16716 9.16801 9.16886 60 68 77 9.21534 9.21610 9.21685 53 61 68 33 32 31 12 8 4 +2 30 8.98157 129 9.05386 110 9.11570 95 9.16970 84 9.21761 75 30 +2 4 8 12 31 32 33 8.98288 8.98419 8.98549 13 26 39 9.05497 9.05607 9.05717 11 22 33 9.11666 9.11761 9.11857 10 19 29 9.17055 9.17139 9.17223 8 17 25 9.21836 9.21912 9.21987 8 15 23 29 28 27 56 52 48 16 20 24 34 35 36 8.98679 8.98808 8.98937 52 65 77 9.05827 9.05937 9.06046 44 55 66 9.11952 9.12047 9.12142 38 48 57 9.17307 9.17391 9.17474 34 42 50 9.22062 9.22137 9.22211 30 38 45 26 25 24 44 40 36 28 32 36 37 38 39 8.99066 8.99194 8.99322 90 103 116 9.06155 9.06264 9.06372 77 88 99 107 9.12236 9.12331 9.12425 67 76 86 9.17558 9.17641 9.17724 59 67 76 9.22286 9.22361 9.22435 53 60 68 23 23 21 32 28 24 40 40 8.99450 125 9.06481 9.12519 93 9.17807 82 9.22509 74 20 20 U 48 52 41 42 43 8.99577 8.99704 8.99830 13 25 38 9.06589 9.06696 9.06804 11 21 32 9.12612 9.12706 9.12799 9 19 28 9.17890 9.17973 9.18055 8 16 25 9.22583 9.22657 9.22731 7 15 22 19 18 17 16 12 8 56 +3 4 44 45 46 8.99956 9.00082 9.00207 50 63 75 9.06911 9.07018 9.07124 43 54 64 9.12892 9.12985 9.13078 37 47 56 9.18137 9.18220 9.18302 33 41 49 9.22805 9.22878 9.22952 30 37 44 16 15 14 4 +1 56 8 12 16 #7 48 49 9.00332 9.00456 9.00581 88 100 113 9.07231 9.07337 9.07442 75 86 96 9.13171 9.13263 9.13355 65 74 84 9.18383 9.18465 9.18547 57 66 74 9.23025 9.23098 9.23171 52 59 67 13 12 11 52 48 44 20 50 9.00704 122 9.07548 104 9.13447 91 9.18628 81 9.23244 73 10 40 24 28 32 51 52 53 9.00828 9.00951 9.01074 12 24 37 9.07653 9.07758 9.07863 10 21 31 9.13539 9.13630 9.13722 9 18 27 9.18709 9.18790 9.18871 8 16 24 9.23317 9.23390 9.23462 7 14 22 9 8 7 36 32 28 36 40 U 54 55 56 9.01196 9.01318 9.01440 49 61 73 9.07968 9.08072 9.08176 42 52 62 9.13813 9.13904 9.13994 36 46 55 9.18952 9.19033 9.19113 32 41 49 9.23535 9.23607 9.23679 29 36 43 6 5 4 24 20 16 48 52 56 57 58 59 9.01561 9.01682 9.01803 85 98 110 9.08280 9.08383 9.08486 73 83 94 9.14085 9.14175 9.14266 64 73 82 9.19193 9.19273 9.19353 57 65 73 9.23752 9.23823 9.23895 50 58 65 3 2 1 12 8 4 +4 60 9.01923 9.08589 9.14356 9.19433 9.23967 Cos. Cos. Cos. Cos. Cos. 84° 5h 36m 83° 5h 32m 82° 5h 28m | 81° 5h 24m 80° 5h 20m Log. Cosines. TABLE III. [Page 33 Log. Sines. Time. Arc. Oh 40m 10° Oh 44m 11° Oh 48m 12° Oh 52m 13° Oh 56m 14° Arc. Time. m. s. ' Sine. P. P. Sine. P. P. Sine. P. P. Sine. P. P. Sine. P. P. ' s. ra. 9.23967 71 9.28060 65 9.31788 59 9.35209 54 9.38368 51 60 +4 8 12 1 2 3 9.24039 9.24110 9.24181 7 14 21 9.28125 9.28190 9.28254 7 13 20 9.31847 9.31907 9.31966 6 12 18 9.35263 9.35318 9.35373 5 11 16 9.38418 9.38469 9.38519 5 10 15 59 58 57 56 52 48 16 20 24 4 5 6 9.24253 9.24324 9.24395 28 36 43 9.28319 9.28384 9.28448 26 33 39 9.32025 9.32084 9.32143 24 30 35 41 47 53 9.35427 9.35481 9.35536 22 27 32 9.38570 9.38620 9.38670 20 26 31 56 55 54 44 40 36 28 S2 36 7 8 9 9.24466 9.24536 9.24607 50 57 64 9.28512 9.28577 9.28641 46 52 59 9.32202 9.32261 9.32319 9.35590 9.35644 9.35698 38 43 49 9.38721 9.38771 9.38821 36 41 46 53 53 51 32 28 24 40 10 9.24677 70 9.28705 63 9.32378 58 9.35752 54 9.38871 50 50 20 44 48 52 11 13 13 9.24748 9.24818 9.24888 7 14 21 9.28769 9.28833 9.28896 6 13 19 9.32437 9.32495 9.32553 6 12 17 9.35806 9.35860 9.35914 5 11 16 9.38921 9.38971 9.39021 5 10 15 49 48 47 16 12 8 56 +1 4 14 15 16 9.24958 9.25028 9.25098 28 35 42 9.28960 9.29024 9.29087 25 32 38 9.32612 9.32670 9.32728 23 29 35 9.35968 9.36022 9.36075 22 27 32 9.39071 9.39121 9.39170 20 25 30 46 45 44 4 +3 56 8 12 16 17 18 19 9.25168 9.25237 9.25307 49 56 63 9.29150 9.29214 9.29277 44 50 57 9.32786 9.32844 9.32902 41 46 52 9.36129 9.36182 9.36236 38 43 49 9.39220 9.39270 9.39319 35 40 45 43 42 41 52 48 44 20 30 9.25376 69 9.29340 63 9.32960 58 9.36289 53 9.39369 49 40 40 24 28 32 31 33 33 9.25445 9.25514 9.25583 7 14 21 9.29403 9.29466 9.29529 6 12 19 9.33018 9.33075 9.33133 6 12 17 9.36342 9.36395 9.36449 5 11 16 9.39418 9.39467 9.39517 5 10 15 39 38 37 36 32 28 36 40 U 34 35 36 9.25652 9.25721 9.25790 28 35 41 9.29591 9.29654 9.29716 25 31 37 9.33190 9.33248 9.33305 23 29 35 41 46 52 9.36502 9.36555 9.36608 21 27 32 9.39566 9.39615 9.39664 20 25 29 36 35 34 24 20 16 12 8 4 48 52 56 37 38 39 9.25858 9.25927 9.25995 48 55 62 9.29779 9.29841 9.29903 43 50 56 9.33362 9.33420 9.33477 9.36660 9.36713 9.36766 37 42 48 9.39713 9.39762 9.39811 34 39 44 33 33 31 +3 30 9.26063 68 9.29966 63 9.33534 57 9.36819 53 9.39860 49 30 +3 4 8 12 33 * 33 9.26131 9.26199 9.26267 7 14 20 9.30028 9.30090 9.30151 6 12 19 9.33591 9.33647 9.33704 6 11 17 9.36871 9.36924 9.36976 5 10 16 21 26 31 9.39909 9.39958 9.40006 5 10 15 39 38 37 56 52 48 16 20 24 34 35 36 9.26335 9.26403 9.26470 27 34 41 9.30213 9.30275 9.30336 25 31 37 9.33761 9.33818 9.33874 23 29 34 9.37028 9.37081 9.37133 9.40055 9.40103 9.40152 20 25 29 36 35 34 44 40 36 28 32 36 37 38 39 9.26538 9.26605 9.26672 48 54 61 9.30398 9.30459 9.30521 43 50 56 9.33931 9.33987 9.34043 40 46 51 9.37185 9.37237 9.37289 36 42 47 9.40200 9.40249 9.40297 34 39 44 33 33 31 32 28 24 40 40 9.26739 67 9.30582 61 9.34100 56 9.37341 53 9.40346 48 30 20 44 48 52 41 43 43 9.26806 9.26873 9.26940 7 13 20 9.30643 9.30704 9.30765 6 12 18 9.34156 9.34212 9.34268 6 11 17 9.37393 9.37445 9.37497 5 10 16 9.40394 9.40442 9.40490 5 10 14 19 18 17 16 12 8 56 +3 4 M 45 . 46 9.27007 9.27073 9.27140 27 34 40 9.30826 9.30887 9.30947 24 31 37 9.34324 9.34380 9.34436 22 28 34 9.37549 9.37600 9.37652 21 26 31 9.40538 9.40586 9.40634 19 24 29 16 15 14 4 +1 56 8 12 16 47 48 49 9.27206 9.27273 9.27339 47 54 60 9.31008 9.31068 9.31129 43 49 55 9.34491 9.34547 9.34602 39 45 50 9.37703 9.37755 9.37806 36 42 47 9.40682 9.40730 9.40778 34 38 43 13 13 11 52 48 44 20 50 9.27405 66 9.31189 60 9.34658 55 9.37858 51 9.40825 47 10 40 24 28 32 51 53 53 9.27471 9.27537 9.27602 7 13 20 9.31250 9.31310 9.31370 6 12 18 9.34713 9.34769 9.34824 6 11 17 9.37909 9.37960 9.38011 5 10 15 9.40873 9.40921 9.40968 5 9 14 9 8 7 36 32 28 36 40 U 54 55 56 9.27668 9.27734 9.27799 26 33 40 9.31430 9.31490 9.31549 24 30 36 9.34879 9.34934 9.34989 22 28 33 9.38062 9.38113 9.38164 20 26 31 9.41016 9.41063 9.41111 19 24 28 6 5 4 24 20 16 48 52 56 57 58 59 9.27864 9.27930 9.27995 46 53 59 9.31609 9.31669 9.31728 42 48 54 9.35044 9.35099 9.35154 39 44 50 9.38215 9 38266 9.38317 36 41 46 9.41158 9.41205 9.41252 33 38 42 3 3 1 12 8 4 +4 60 9.28060 9.31788 9.35209 9.38368 9.41300 Cos. Cos. Cos. Cos. Cos. 79° . 5hl6m 78° 5h 12m 77° 5h 8m 76° 5h 4m 75° 5h om Log. Cosines. 55901' Page 34] TAJBLE III. Log. Sines. Time. Arc. ih Om 15° Ih^m 16° Ihgm 17° lhi2m 18° Ih 16m 19° Arc. Time. m. s. ' Sine. P. P. Sine. P. P. Sine. P. P. Sine. P. P. Sine. P. P. ' s. m. 9.41300 47 9.44034 44 9.46594 41 9.48998 39 9.51264 36 60 +i 4 8 12 1 2 3 9.41347 9.41394 9.41441 5 9 14 9.44078 9.44122 9.44166 4 9 13 9.46635 9.46676 9.46717 4 8 12 9.49037 9.49076 9.49115 4 8 12 9.51301 9.51338 9.51374 4 7 11 59 58 57 56 52 48 16 20 U 4 5 6 9.41488 9.41535 9.41582 19 24 28 9.44210 9.44253 9.44297 18 22 26 9.46758 9.46800 9.46841 16 21 25 9.49153 9.49192 9.49231 16 20 23 9.51411 9.51447 9.51484 14 18 22 56 55 54 44 40 36 28 32 36 7 8 9 9.41628 9.41675 9.41722 33 38 42 9.44341 9.44385 9.44428 31 35 40 9.46882 9.46923 9.46964 29 33 37 9.49269 9.49308 9.49347 27 31 35 9.51520 9.51557 9.51593 25 29 32 53 52 51 32 28 24 40 10 9.41768 46 9.44472 43 9.47005 41 9.49385 39 9.51629 36 50 20 44 48 52 11 12 13 9.41815 9.41861 9.41908 5 9 14 9.44516 9.44559 9.44602 4 9 13 9.47045 9.47086 9.47127 4 8 12 9.49424 9.49462 9.49500 4 8 12 9.51666 9.51702 9.51738 4 7 11 49 48 47 10 12 8 56 +1 4 14 15 16 9.41954 9.42001 9.42047 18 23 28 9.44646 9.44689 9.44733 17 22 26 9.47168 9.47209 9.47249 16 21 25 9.49539 9.49577 9.49615 16 20 23 9.51774 9.51811 9.51847 14 18 22 48 45 44 4 +3 56" 8 12 16 17 18 19 9.42093 9.42140 9.42186 32 37 41 9.44776 9.44819 9.44862 30 34 39 9.47290 9.47330 9.47371 29 33 37 9.49654 9.49692 9.49730 27 31 35 9.51883 9.51919 9.51955 25 29 32 43 42 41 52 48 44 20 20 9.42232 46 9.44905 43 9.47411 40 9.49768 38 9.51991 38 40 40 24 28 32 21 22 23 9.42278 9.42324 9.42370 5 9 14 9.44948 9.44992 9.45035 4 9 13 9.47452 9.47492 9.47533 4 8 12 9.49806 9.49844 9.49882 4 8 11 9.52027 9.52063 9.52099 4 7 11 39 38 37 36 32 28 36 40 U 24 25 26 9.42416 9.42461 9.42507 18 23 28 9.45077 9.45120 9.45163 17 22 26 9.47573 9.47613 9.47654 16 20 24 9.49920 9.49958 9.49996 15 19 23 9.52135 9.52171 9.52207 14 18 22 36 35 34 24 20 16 48 52 56 27 28 29 9.42553 9.42599 9.42644 32 37 41 9.45206 9.45249 9.45292 30 34 39 9.47694 9.47734 9.47774 28 32 36 9.50034 9.50072 9.50110 27 30 34 9.52242 9.52278 9.52314 25 29 32 33 32 31 12 8 4 +3 30 9.42690 45 9.45334 42 9.47814 40 9.50148 38 9.52350 35 30 +2 4 8 12 31 32 33 9.42735 9.42781 9.42826 5 9 14 9.45377 9.45419 9.45462 4 8 13 9.47854 9.47894 9.47934 4 8 12 9.50185 9.50223 9.50261 4 8 11 9.52385 9.52421 9.52456 4 7 11 29 28 27 .56- 52 48 16 20 24 34 35 36 9.42872 9.42917 9.42962 18 23 27 9.45504 9.45547 9.45589 17 21 25 9.47974 9.48014 9.48054 16 20 24 9.50298 9.50336 9.50374 15 19 23 9.52492 9.52527 9.52563 14 18 21 26 25 24 U 40 36 28 32 36 37 38 39 9.43008 9.43053 9.43098 32 36 41 9.45632 9.45674 9.45716 29 34 38 9.48094 9.48133 9.48173 28 32 36 9.50411 9.50449 9.50486 27 30 34 9.52598 9.52634 9.52669 25 28 32 23 22 21 32 28 24 40 40 9.43143 45 9.45758 42 9.48213 40 9.50523 37 9.52705 35 20 20 44 48 52 41 42 43 9.43188 9.43233 9.43278 5 9 14 9.45801 9.45843 9.45885 4 8 13 9.48252 9.48292 9.48332 4 8 12 9.50561 9.50598 9.50635 4 7 11 9.52740 9.52775 9.52811 4 7 11 19 18 17 16 12 8 56 +3 4 44 45 46 9.43323 9.43367 9.43412 18 23 27 9.45927 9.45969 9.46011 17 21 25 9.48371 9.48411 9.48450 16 20 24 9.50673 9.50710 9.50747 15 19 22 9.52846 9.52881 9.52916 14 18 21 16 15 14 4 +1 56 8 12 16 47 48 49 9.43457 9.43502 9.43546 32 36 41 9.4G053 9.46095 9.46136 29 34 38 9.48490 9.48529 9.48568 28 32 36 9.50784 9.50821 9.50858 26 30 33 9.52951 9.52986 9.53021 25 28 32 13 12 11 52 48 U 20 50 9.43591 44 9.46178 41 9.48607 39 9.50896 37 9.53056 35 10 40 24 28 32 51 52 53 9.43635 9.43680 9.43724 4 9 13 9.46220 9.46262 9.46303 4 8 12 9.48647 9.48686 9.48725 4 8 12 9.50933 9.50970 9.51007 4 7 11 9.53092 9.53126 9.53161 4 7 11 9 8 7 36 32 28 36 40 44 54 55 56 9.43769 9.43813 9.43857 18 22 26 9.46345 9.46386 9.46428 16 21 25 9.48764 9.48803 9.48842 16 20 23 9.51043 9.51080 9.51117 15 19 22 9.53196 9.53231 9.53266 14 18 21 6 5 4 24 20 16 4S 52 56 67 68 59 9.43901 9.43946 9.43990 31 35 40 9.46469 9.46511 9.46552 29 33 37 9.48881 9.48920 9.48959 27 31 35 9.51154 9.51191 9.51227 26 30 33 9.53301 9.53336 9.53370 25 28 32 3 2 1 12 8 4 +* 69 9.44034 9.46594 9.48998 9.51264 9.53405 Cos. Cos. Cos. Cos. Cos. 74° 4'^ 56m 73° 4^ 52m 72° 4^ 48m 71° 4^ -f^'" 70° 4h 40m Log, Coaines. TABLE III. [Page 35 Log. Sines. Time. Arc. 1^ 20m 20° lh2pn 21° lh2Sm 22° Ih 32m 23° 1^ 06m 24° Arc. Time. m. s. ' Sine. P. P. Sine. P. P. Sine. P. P. Sine. P. P. Sine. P. P. ' s. m. 9.53405 35 9.55433 33 9.57358 31 9.59188 30 9.60931 28 60 +4 4 8 12 1 2 3 9.53440 9.53475 9.53509 4 7 11 9.55466 9.55499 9.55532 3 7 10 9.57389 9.57420 9.57451 3 6 9 9.59218 9.59247 9.59277 3 6 9 9.60960 9.60988 9.61016 3 6 8 59 58 57 56 55 54 56 52 48 44 40 36 16 •20 24 1 5 6 9.53544 9.53578 9.53613 14 18 21 9.55564 9.55597 9.55630 13 17 20 9.57482 9.57514 9.57545 12 16 19 9.59307 9.59.336 9.59366 12 15 18 9.61045 9.61073 9.61101 11 14 17 28 32 36 7 8 9 9.53647 9.53682 9.53716 25 28 32 9.55663 9.55695 9.55728 23 26 30 9.57576 9.57607 9.57638 22 25 28 9.59396 9.59425 9.59455 21 24 27 9.61129 9.61158 9.61186 20 22 25 53 52 51 32 28 24 40 10 9.53751 34 9.55761 32 9.57669 31 9.59484 29 9.61214 28 50 20 U 48 52 11 12 13 9.53785 9.53819 9.53854 3 7 10 9.55793 9.55826 9.55858 3 6 10 9.57700 9.57731 9.57762 3 6 9 9.59514 9.59543 9.59573 3 6 9 9.61242 9.61270 9.61298 3 6 8 49 48 47 16 12 8 36 +1 4 11 15 16 9.53888 9.53922 9.53957 14 17 20 9.55891 9.55923 9.55956 13 16 19 9.57793 9.57824 9.57855 12 16 19 9.59602 9.59632 9.59661 12 15 17 9.61326 9.61354 9.61382 11 14 17 46 45 44 43 42 41 4 +3 56 8 12 16 17 18 19 9.53991 9.54025 9.54059 24 27 31 9.55988 9.56021 9.56053 22 26 29 9.57885 9.57916 9.57947 22 25 28 9.59690 9.59720 9.59749 20 23 26 9.61411 9.61438 9.61466 20 22 25 52 48 44 20 20 9.54093 34 9.56085 32 9.57978 30 9.59778 29 9.61494 28 40 40 24 28 32 21 22 23 9.54127 9.54161 9.54195 3 7 10 9.56118 9.56150 9.56182 3 6 10 9.58008 9.58039 9.58070 3 6 9 9.59808 9.59837 9.59866 3 6 9 9.61522 9.61550 9.61578 3 6 8 39 38 37 36 32 28 36 40 44 24 25 26 9.54229 9.54263 9.54297 14 17 20 9.56215 9.56247 9.56279 13 16 19 9.58101 9.58131 9.58162 12 15 18 9.59895 9.59924 9.59954 12 15 17 9.61606 9.61634 9.61662 11 14 17 36 35 34 24 20 16 48 52 56 27 28 29 9.54331 9.54365 9.54399 24 27 31 9.56311 9.56343 9.56375 22 26 29 9.58192 9.58223 9.58253 21 24 27 9.59983 9.60012 9.60041 20 23 26 9.61689 9.61717 9.61745 20 22 25 33 32 31 12 8 4 +2 30 9.54433 34 9.56408 32 9.58284 30 9.60070 29 9.61773 28 30 +2 4 8 12 31 32 33 9.54466 9.54500 9.54534 3 7 10 9.56440 9.56472 9.56504 3 6 10 9.58314 9.58345 9.58375 3 6 9 9.60099 9.60128 9.60157 3 6 9 9.61800 9.61828 9.61856 3 6 8 29 28 27 56 52 48 16 20 24 34 35 36 9.54567 9.54601 9.54635 14 17 20 9.56536 9.56568 9.56599 13 16 19 9.58406 9.58436 9.58467 12 15 18 9.60186 9.60215 9.60244 12 15 17 9.61883 9.61911 9.61939 11 14 17 26 25 24 U 40 36 28 32 36 37 38 39 9.54668 9.54702 9.54735 24 27 31 9.56631 9.56663 9.56695 22 26 29 9.58497 9.58527 9.58557 21 24 27 9.60273 9.60302 9.60331 20 23 26 9.61966 9.61994 9.62021 20 22 25 23 22 21 32 28 24 40 40 9.54769 33 9.56727 32 9.58588 30 9.60359 29 9.62049 27 20 20 U 48 52 41 42 43 9.54802 9.54836 9.54869 3 7 10 9.56759 9.56790 9.56822 3 6 10 9.58618 9.58648 9.58678 3 6 9 9.60388 9.60417 9.60446 3 6 9 9.62076 9.62104 9.62131 3 5 8 19 18 17 16 12 8 56 +3 4 44 45 46 9.54903 9.54936 9.54969 13 17 20 9.56854 9.56886 9.56917 13 16 19 9.58709 9.58739 9.58769 12 15 18 9.60474 9.60503 9.60532 12 15 17 9.62159 9.62186 9.62214 11 14 16 16 15 14 4 +1 56 8 12 16 47 48 49 9.55003 9.55036 9.55069 23 26 30 9.56949 9.56980 9.57012 22 26 29 9.58799 9.58829 9.58859 21 24 27 9.60561 9.60589 9.60618 20 23 26 9.62241 9.62268 9.62296 19 22 24 13 12 11 52 48 U 20 50 9.55102 33 9.57044 31 9.58889 30 9.60646 29 9.62323 27 10 40 24 28 32 51 52 53 9.55136 9.55169 9.55202 3 7 10 9.57075 9.57107 9.57138 3 6 9 9.58919 9.58949 9.58979 3 6 9 9.60675 9.60704 9.60732 3 6 9 9.62350 9.62377 9.62405 3 5 8 9 8 7 36 32 28 36 40 U 54 55 56 9.55235 9.55268 9.55301 13 17 20 9.57169 9.57201 9.57232 12 16 19 9.59009 9.59039 9.59069 12 15 18 9.60761 9.60789 9.60818 12. 15 17 9.62432 9.62459 9.62486 11 14 16 6 5 4 24 20 16 4S 52 56 57 58 59 9.55334 9.55367 9.55400 23 26 30 9.57264 9.57295 9.57326 22 25 28 9.59098 9.59128 9.59158 21 24 27 9.60846 9.60875 9.60903 20 23 26 9.62513 9.62541 9.62568 19 22 24 3 2 1 12 8 4 +4 60 9.55433 9.57358 9.59188 9.60931 9.62595 Cos. Cos. Cos. Cos. Cos. 69° 4^ 36m 68° 4h 32-m 67° 4^ 28m 66° 4^ 24m 65° 4^ 20m Log. Cosines. Page 36] TABLE III. Log Sines. Time. Arc. 1^40171 25° Ih 44m 36° lh4Sm 270 lh52'm 38° ift 56'm 39° Arc. Time. m. s. ' Sine. P. P. Sine. P. P. Sine. P. P. Sine. P. P. Sine. P. P. ' m. s. 9.62595 27 9.64184 26 9.65705 25 9.67161 24 9.68557 23 60 +4 4 8 12 1 3 9.62622 9.62G49 9.62676 3 5 8 9.64210 9.64236 9.64262 3 5 8 9.65729 9.65754 9.65779 3 5 8 9.67185 9.67208 9.67232 2 5 7 9.68580 9.68603 9.68625 2 5 7 59 58 57 56 52 48 16 20 24 4 5 6 9.62703 9.62730 9.62757 11 14 16 9.64288 9.64313 9.64339 10 13 16 9.G5804 9.65828 9.65853 10 13 15 9.67256 9.67280 9.67303 10 12 14 9.68648 9.68671 9.68694 9 12 14 56 55 54 U 40 36 28 32 36 7 8 9 9.62784 9.62811 9.62838 19 22 24 9.64365 9.64391 9.64417 18 21 23 9.65878 9.65902 9.65927 18 20 23 9.67327 9.67350 9.67374 17 19 22 9.68716 9.68739 9.68762 16 18 21 53 52 51 32 28 24 40 10 9.62865 37 9 64442 36 9.65952 35 9.67398 23 9.68784 23 50 20 U 48 52 11 12 13 9.62892 9.62918 9.62945 3 5 8 9.64468 9.64494 9.64519 3 5 8 9.65976 9.66001 9.66025 3 5 8 9.67421 9.67445 9.67468 2 5 7 9.68807 9.68829 9.68852 2 5 7 49 48 47 16 12 8 56 +1 4 14 15 16 9.62972 9.62999 9.63026 11 14 16 9.64545 9.64571 9.64596 10 13 16 9.66050 9.66075 9.66099 10 13 15 9.67492 9.67515 9.67539 9 12 14 9.68875 9.68897 9.68920 9 12 14 46 45 44 4 +3 56 8 12 16 17 18 19 9.63052 9.63079 9.63106 19 22 24 9.64622 9.64647 9.64673 18 21 23 9.66124 9.66148 9.66173 18 20 23 9.67562 9.67586 9.67609 16 18 21 9.68942 9.68965 9.68987 16 18 21 43 42 41 52 48 44 20 20 9.63133 37 9.64698 35 9.66197 34 9.67633 23 9.69010 23 40 40 24 28 32 31 32 23 9.63159 9.63186 9.63213 3 5 8 9.64724 9.64749 9.64775 3 5 8 9.66221 9.66246 9.66270 2 5 7 9.67656 9.67680 9.67703 2 5 7 9.69032 9.69055 9.69077 2 4 7 39 38 37 36 32 28 36 40 44 24 25 26 9.63239 9.63266 9.63292 11 14 16 9.64800 9.64826 9.64851 10 13 15 9.66295 9.66319 9.66343 10 12 14 9.67726 9.67750 9.67773 9 12 14 9.69100 9.69122 9.69144 9 11 13 36 35 34 24 20 16 48 52 56 37 28 29 9.63319 9.63345 9.63372 19 22 24 9.64877 9.64902 9.64927 18 20 23 9.66368 9.66392 9.66416 17 19 22 9.67796 9.67820 9.67843 16 18 21 9.69167 9.69189 9.69212 15 18 20 33 32 31 12 8 4 +2 30 9.63398 36 9.64953 25 9.66441 34 9.67866 23 9.69234 23 30 +2 4 8 12 31 32 33 9.63425 9.63451 9.63478 3 5 8 9.64978 9.65003 9.65029 3 5 8 9.66465 9.66489 9.66513 2 5 7 9.67890 9.67913 9.67936 2 5 7 9.69256 9.69279 9.69301 2 4 i 39 38 37 56 52 48 16 20 24 28 32 36 34 35 36 37 38 39 9.63504 9.63531 9.63557 10 13 16 9.65054 9.65079 9.65104 10 13 15 9.66537 9.66562 9.66586 10 12 14 9.67959 9.67982 9.68006 9 12 14 9.69323 9.69345 9.69368 9 11 13 36 35 34 44 40 36 9.63583 9.63610 9.63636 18 21 23 9.65130 9.65155 9.65180 18 20 23 9.66610 9.66634 9.66658 17 19 22 9.68029 9.68052 9.68075 16 18 21 9.69390 9.69412 9.69434 15 18 20 33 32 31 32 28 24 40 40 9.63662 36 9.65205 25 9.66682 34 9.68098 23 9.69456 33 30 20 44 48 52 41 43 43 9.63689 9.63715 9.63741 3 5 8 9.65230 9.65255 9.65281 3 5 8 9.66706 9.66731 9.66755 2 5 7 9.68121 9.68144 9.68167 2 5 7 9.69479 9.69501 9.69523 2 4 7 19 28 17 16 12 8 56 +3 4 44 45 46 9.63767 9.63794 9.63820 10 13 16 9.65306 9.65331 9.65356 10 13 15 9.66779 9.66803 9.66827 10 12 14 9.68190 9.68213 9.68237 9 12 14 9.69545 9.69567 9.69589 9 11 13 16 15 14 4 +1 56 8 12 16 47 48 49 9.63846 9.63872 9.63898 18 21 23 9.65381 9.65406 9.65431 18 20 23 9.66851 9.66875 9.66899 17 19 22 9.68260 9.68283 9.68305 16 18 21 9.69611 9.69633 9.69655 15 18 20 13 12 11 52 48 U 20 50 9.63924 36 9.65456 35 9.66922 34 9.68328 33 9.09677 32 10 40 24 28 32 51 53 53 9.63950 9.63976 9.64002 3 5 8 9.65481 9.65506 9.65531 3 5 8 9.66946 9.66970 9.66994 2 5 7 9.68351 9.68374 9.68397 2 5 7 9.69699 9.69721 9.69743 2 4 7 9 8 7 36 32 28 36 40 U 54 55 56 9.64028 9.64054 9.64080 10 13 16 9.65556 9.65580 9.65605 10 13 15 9.67018 9.67042 9.67066 10 12 14 9.68420 9.68443 9.68466 9 12 14 9.69765 9.69787 9.69809 9 11 13 6 5 4 24 20 16 48 52 56 57 58 59 9.64106 9.64132 9.64158 18 21 23 9.65630 9.65655 9.65680 18 20 23 9.67090 9.67113 9.67137 17 19 22 9.6S489 9.68512 9.68534 16 18 21 9.69831 9.69853 9.69875 15 18 20 3 2 1 12 8 4 +4 60 9.64184 ( 9.65705 9.67161 9.68557 9.69897 Cos. Cos. Cos. Cos. Cos. ! 64° 4^ 16m 63° 4^ 12^ 62° 4^ 5"» 61° 4^ 4"* 60° 4^ 0^ Log. Coaiues. TABLE III. [Page 37 Log Sines. Time. Arc. 2h om 30° 2h 4m 31° on sm 32° 2h 12m 33° 2h 16m 34° Arc. Time. m. s. ' Sine. P. P. Sine. P. P. Sine. P. P. Sine. P. P. Sine. P. P. ' s. m. +4 9.69897 22 9.71184 21 9.72421 20 9.73611 19 9.74756 19 60 4 8 12 1 3 3 9.69919 9.69941 9.69963 2 4 7 9.71205 9.71226 9.71247 2 4 6 9.72441 9.72461 9.72482 2 4 6 8 10 12 9.73630 9.73650 9.73669 2 4 6 9.74775 9.74794 9.74812 2 4 6 59 58 57 56 52 48 16 20 24 5 6 9.69984 9.70006 9.70028 9 11 13 9.71268 9.71289 9.71310 8 11 13 9.72502 9.72522 9.72542 9.73689 9.73708 9.73727 8 10 11 9.74831 9.74850 9.74868 8 10 11 56 55 54 44 40 36 28 32 36 7 8 9 9.70050 9.70072 9.70093 15 18 20 9.71331 9.71352 9.71373 15 17 19 9.72562 9.72582 9.72602 14 16 18 9.73747 9.73766 9.73785 9.73805 13 15 17 19 9.74887 9.74906 9.74924 13 15 17 53 52 51 32 28 24 40 10 9.70115 22 9.71393 21 9.72622 20 9.74943 19 50 20 U 48 52 11 13 13 9.70137 9.70159 9.70180 2 4 7 9.71414 9.71435 9.71456 4 6 9.72643 9.72663 9.72683 2 4 6 9.73824 9.73843 9.73863 2 4 6 9.74961 9.74980 9.74999 2 4 6 49 48 47 16 12 8 56 +1 4 U 15 16 9.70202 9.70224 9.70245 9 11 13 9.71477 9.71498 9.71519 8 11 13 9.72703 9.72723 9.72743 8 10 12 9.73882 9.73901 9.73921 8 10 11 9.75017 9.75036 9.75054 8 10 11 46 45 44 4 +3 56 8 12 16 17 18 19 9.70267 9.70288 9.70310 15 18 20 9.71539 9.71560 9.71581 15 17 19 9.72763 9.72783 9.72803 14 16 18 9.73940 9.7.3959 9.73978 13 15 17 9.75073 9.75091 9.75110 13 15 17 43 42 41 52 48 U 20 20 9.70332 21 9.71602 31 9.72823 20 9.73997 19 9.75128 18 40 40 24 28 32 21 22 23 9.70353 9.70375 9.70396 2 4 6 9.71622 9.71643 9.71664 2 4 6 9.72843 9.72863 9. 72883 2 4 6 9.74017 9.74036 9.74055 2 4 9.75147 9.75165 9.75184 2 4 5 39 38 37 36 32 28 36 40 U 24 25 26 9.70418 9.70439 9.70461 8 11 13 9.71685 9.71705 9.71726 8 11 13 9.72902 9.72922 9.72942 8 10 12 9.74074 9.74093 9.74113 8 10 11 9.75202 9.75221 9.75239 7 9 11 36 35 34 24 20 16 48 52 56 27 28 29 9.70482 9.70504 9.70525 15 17 19 9.71747 9.71767 9.71788 15 17 19 9.72962 9.72982 9.73002 14 16 18 9.74132 9.74151 9.74170 13 15 17 9.75258 9.75276 9.75294 13 14 16 33 32 31 12 S 4 +3 30 9.70547 21 9.71809 21 9.73022 20 9.74189 19 9.75313 18 30 +2 4 8 12 31 32 33 9.70568 9.70590 9.70611 2 4 6 9.71829 9.71850 9.71870 2 4 6 9.73041 9.73061 9.73081 2 4 6 9.74208 9.74227 9.74246 2 4 6 9.75331 9.75350 9.75368 2 4 5 29 28 27 56 52 48 16 20 24 34 35 36 9.70633 9.70654 9.70675 8 11 13 9.71891 9.71911 9.71932 8 11 13 9.73101 9.73121 9.73140 8 10 12 9.74265 9.74284 9.74303 8 10 11 9.75386 9.75405 9.75423 7 9 11 26 25 24 44 40 36 28 32 36 37 38 39 9.70697 9.70718 9.70739 15 17 19 9.71952 9.71973 9.71994 15 17 19 9.73160 9.73180 9.7.3200 14 16 18 9.74322 9.74341 9.74360 13 15 17 9.75441 9.75459 9.75478 13 14 16 23 22 21 32 28 24 40 40 9.70761 21 9.72014 30 9.73219 20 9.74379 19 9.75496 18 20 20 44 48 52 41 42 43 9.70782 9.70803 9.70824 2 4 6 9.72034 9.72055 9.72075 2 4 6 9.73239 9.73259 9.73278 2 4 6 9.74398 9.74417 9.74436 2 4 6 9.75514 9.75533 9.75551 2 4 5 19 18 17 16 12 8 56 +3 4 44 45 46 9.70846 9.70867 9.70888 8 11 13 9.72096 9.72116 9.72137 8 10 12 9.73298 9.73318 9.73337 8 10 12 9.74455 9.74474 9.74493 8 10 11 9. 755(69 9.75587 9.75605 7 9 11 16 15 14 4 + 1 56 8 12 16 47 48 49 9.70909 9.70931 9.70952 15 17 19 9.72157 9.72177 9.72198 14 16 18 9.73357 9.73377 9.73396 14 16 18 9.74512 9.74531 9.74549 13 15 17 9.75624 9.75642 9.75660 13 14 16 13 12 11 52 48 44 20 50 9.70973 21 9.72218 20 9.73416 20 9.74568 19 9.75678 18 10 40 24 28 32 51 52 53 9.70994 9.71015 9.71036 2 4 6 9.72238 9.72259 9.72279 2 4 6 9.73435 9.73455 9.73474 2 4 6 9.74587 9.74606 9.74625 2 4 6 9.75696 9.75714 9.75733 2 4 5 9 8 7 36 32 28 36 40 U 54 55 56 9.71058 9.71079 9.71100 8 11 13 9.72299 9.72320 9.72340 8 10 12 9.73494 9.73513 9.73533 8 10 12 9.74644 9.74662 9.74681 8 10 11 9.75751 9.75769 9.75787 7 9 11 6 5 4 24 20 16 48 52 56 57 58 59 9.71121 9.71142 9.71163 15 17 19 9.72360 9.72381 9.72401 14 16 18 9.73552 9.73572 9.73591 14 16 18 9.74700 9.74719 9.74737 13 15 17 9.75805 9.75823 9.75841 13 14 16 3 2 1 12 8 4 +* 60 9.71184 9.72421 9.73611 9.74756 9.75859 Ck)s. Cos Cos. Cos. Cos. 59° 3h 56m 58° 3fi 52in 57° 3h48m 56° 3h 44m 55° 3^ 4Qm Log Cosines. Page 38] TABLE III. Log. Sines. Time. Arc. 2^ 20m 35° 2h 24^ 36° 2h 28m 37° 2^ 32m 38° 2^ S6m 39° Arc. Time. m. s. ' Sine. P. P. Sine. P. P. Sine. J'. ]'. Sine. P. P. Sine. P. P. / s. m. 9.75859 18 9.76922 17 9.77946 17 9.78934 16 9.79887 16 60 +4 4 8 12 1 2 3 9.75877 9.75895 9.75913 2 4 5 9.76939 9.76957 9.76974 2 3 5 9.77963 9.77980 9.77997 2 3 5 9.78950 9.78967 9.78983 2 3 5 9.79903 9.79918 9.79934 2 3 5 59 58 57 56 52 48 16 20 24 4 5 6 9.75931 9.75949 9.75967 7 9 11 9.70991 9.77009 9.77026 7 9 10 9.78013 9.78030 9.78047 7 9 10 9.78999 9.79015 9.79031 6 8 10 9.79950 9.79965 9.79981 6 8 10 56 55 54 44 40 36 28 32 36 7 8 9 10 9.75985 9.76003 9.76021 13 14 16 9.77043 9.77061 9.77078 12 14 15 9.78063 9.78080 9.78097 12 14 15 9.79047 9.79063 9.79079 11 13 14 16 9.79996 9.80012 9.80027 9.80043' 11 13 14 15 53 53 51 32 28 24 40 9.76039 18 9.77095 17 9.78113 17 9.79095 50 20 44 48 52 11 13 13 9.76057 9.76075 9.76093 2 4 5 9.77112 9.77130 9.77147 2 3 5 9.78130 9.78147 9.78163 2 3 5 9.79111 9.79128 9.79144 2 3 5 9.80058 9.80074 9.80089 2 3 5 49 48 47 16 12 8 56 +1 4 14 15 16 9.76111 9.76129 9.76146 7 9 11 9.77164 9.77181 9.77199 7 9 10 9.78180 9.78197 9.78213 7 9 10 9.79160 9.79176 9.79192 6 8 10 9.80105 9.80120 9.80136 6 8 9 46 45 44 4 +3 56 8 12 16 17 18 19 9.76164 9.76182 9.76200 13 14 16 9.77216 9.77233 9.77250 12 14 15 9.78230 9.78246 9.78263 12 14 15 9.79208 9.79224 9.79240 11 13 14 9.80151 9.80166 9.80182 11 12 14 43 42 41 52 48 44 20 30 9.76218 18 9.77268 17 9.78280 16 9.79256 16 9.80197 15 40 40 24 28 32 31 33 33 9.76236 9.76253 9.70271 2 4 5 9.77285 9.77302 9.77319 2 3 5 9.78296 9.78313 9.78329 2 3 5 9.79272 9.79288 9.79304 2 3 5 9.80213 9.80228 9.80244 2 3 5 39 38 37 36 32 28 36 40 U 34 35 26 9.76289 9.76307 9.76324 7 9 11 9.77336 9.77353 9.77370 7 9 10 9.78346 9.78362 9.78379 6 8 10 9.79319 9.79335 9.79351 6 8 10 9.80259 9.80274 9.80290 6 8 9 36 35 34 24 20 16 48 52 56 37 38 39 9.76342 9.76360 9.76378 13 14 16 9.77387 9.77405 9.77422 12 14 15 17 9.78395 9.78412 9.78428 11 13 14 9.79367 9.79383 9.79399 11 13 14 9.80305 9.80320 9.80336 11 12 14 33 33 31 12 8 4 +2 30 9.76395 18 9.77439 9.78445 16 9.79415 16 9.80351 15 30 +2 4 8 12 31 33 33 9.76413 9.76431 9.76448 2 4 5 9.77456 9.77473 9.77490 2 3 5 9.78461 9.78478 9.78494 2 3 5 9.79431 9.79447 9.79463 2 3 5 9.80366 9.80382 9.80397 2 3 5 39 38 37 56 52 48 16 20 24 34 35 36 9.76466 9.76484 9.76501 7 9 11 9.77507 9.77524 9.77541 .7 9 10 9.78510 9.78527 9.78543 6 8 10 9.79478 9.79494 9.79510 6 8 10 11 13 14 9.80412 9.80428 9.80443 6 8 9 36 35 34 44 40 36 28 32 36 37 38 39 9.76519 9.76537 9.76554 13 14 16 9.77558 9.77575 9.77592 12 14 15 9.78560 9.78576 9.78592 11 13 14 9.79526 9.79542 9.79558 9.80458 9.80473 9.80489 11 12 14 33 33 31 30 32 28 24 40 40 9.76572 17 9.77609 17 9.78609 16 9.79573 16 9.80504 15 20 44 48 52 41 43 43 9.76590 9.76607 9.76625 2 3 5 9.77626 9.77643 9.77660 2 3 5 9.78625 9.78642 9.78658 2 3 5 9.79589 9.79605 9.79621 2 3 5 9.80519 9.80534 9.80550 2 3 5 19 18 17 16 12 8 56 +3 4 44 45 46 9.70642 9.76660 9.76677 7 9 10 9.77677 9.77694 9.77711 7 9 10 9.78674 9.78691 9.78707 6 8 10 9.79636 9.79652 9.79668 6 8 10 9.80565 9.80580 9.80595 6 8 9 16 15 14 4 +1 56 8 12 16 47 48 49 9.76695 9.76712 9.76730 12 14 15 9.77728 9.77744 9.77761 12 14 15 9.78723 9.78739 9.78756 11 13 14 9.79684 9.79699 9.79715 11 13 14 9.80610 9.80625 9.80641 11 12 14 13 13 11 52 48 U 20 50 9.76747 17 9.77778 17 9.78772 16 9.79731 16 9.80656 15 10 40 24 28 32 51 53 53 9.76765 9.76782 9.76800 2 3 5 9.77795 9.77812 9.77829 2 3 5 9.78788 9.78805 9.78821 2 3 5 9.79746 9.79762 9.79778 2 3 5 9.80671 9.806S6 9.80701 2 3 5 9 8 7 36 32 28 36 40 44 54 55 56 9.76817 9.76835 9.76852 7 9 10 9.77846 9.77862 9.77879 7 9 10 9.78837 9.78853 9.78869 6 8 10 9.79793 9.79809 9.79825 6 8 10 9.80716 9.80731 9.80746 6 8 9 6 5 4 24 20 16 48 52 56 57 58 59 9.76870 9.76887 9.76904 12 14 15 9.77896 9.77913 9.77930 12 14 15 9.78886 9.78902 9.78918 11 13 14 9.79840 9.79856 9.79872 11 13 14 9.80762 9.80777 9.80792 11 12 14 3 2 1 12 8 4 +4 60 9.76922 9.77946 ! 9.78934 9.79887 9.80807 1 Cos. Cos. Cos. Cos. Cos. 54° Sn 36m 53° Sh 33'n 53° 3h 28m 61° .5ft 24"^ 50° 3h 20m Log. Cosines. TABLE III. [Page 39 Log. Sines. Time. Arc. 2h 40m 40° 2h 44m 41° ^h 48m 42° 2h 52m 43° 2h 56m 44° Arc. Time. m. s. ' Sine. P. P. Sine. P. P. Sine. P. P. Sine. P. P. Sinp. P. P. ' s. m. 9.80807 15 9.81694 14 9.82551 9.82565 9.82579 9.82593 14 9.83378 14 9.84177 13 60 +4 4 8 12 1 2 3 9.80822 9.80837 9.80852 2 3 5 9.81709 9.81723 9.81738 1 3 4 1 3 4 9.83392 9.83405 9.83419 1 3 4 9.84190 9.84203 9.84216 1 3 4 59 58 57 56 52 4S 16 20 24 4 5 6 9.80867 9.80882 9.80897 6 8 9 9.81752 9.81767 9.81781 6 7 8 9.82607 9.82621 9.82635 9.82649 9.82663 9.82677 6 7 8 9.83432 9.83446 9.83459 7 8 9.84229 9.84242 9.84255 5 7 8 56 55 54 44 40 36 28 32 36 1 8 9 9.80912 9.80927 9.80942 11 12 14 9.81796 9.81810 9.81825 10 11 13 10 11 13 9.83473 9.83486 9.83500 10 11 13 9.84269 9.84282 9.84295 9 10 12 53 52 51 32 28 24 40 10 9.80957 15 9.81839 14 9.82691 14 9.83513 13 9.84308 13 50 20 44 48 52 11 12 13 9.80972 9.80987 9.81002 2 o 5 9.81854 9.81868 9.81882 1 3 4 9.82705 9.82719 9.82733 1 3 4 9.83527 9.83540 9.83554 1 3 4 9.84321 9.84334 9.84347 1 3 4 49 48 47 46 45 44 16 12 8 56 +1 4 15 16 9.81017 9.81032 9.81047 6 8 9 9.81897 9.81911 9.81926 6 7 8 9.82747 9.82761 9.82775 6 7 8 9.83567 9.83581 9.83594 5 7 8 9.84360 9.84373 9.84385 5 7 8 4 +3 56 8 12 16 17 18 19 9.81061 9.81076 9.81091 11 12 14 9.81940 9.81955 9.81969 10 11 13 9.82788 9.82802 9.82816 10 11 13 9.83608 9.83621 9.83634 9 10 12 9.84398 9.84411 9.84424 9 10 12 43 42 41 52 48 44 20 20 9.81106 15 9.81983 14 9.82830 14 9.83648 13 9.84437 13 40 40 24 28 32 21 23 23 9.81121 9.81136 9.81151 2 3 5 9.81998 9.82012 9.82026 1 3 4 9.82844 9.82858 9.82872 1 3 4 9.83661 9.83674 9.83688 1 3 4 5 7 8 9.84450 9.84463 9.84476 1 3 4 39 38 37 36 32 28 36 40 U U 25 26 9.81166 9.81180 9.81195 6 8 9 9.82041 9.82055 9.82069 6 7 8 9.82885 9.82899 9.82913 6 7 8 9.83701 9.83715 9.83728 9.84489 9.84502 9.84515 5 7 8 36 35 34 24 20 16 48 52 56 27 28 29 9.81210 9.81225 9.81240 11 12 14 9.82084 9.82098 9.82112 10 11 13 9.82927 9.82941 9.82955 10 11 13 9.83741 9.83755 9.83768 9 10 12 9.84528 9.84540 9.84553 9 10 12 33 32 31 12 8 4 +3 30 9.81254 15 9.82126 14 9.82968 14 9.83781 13 9.84566 13 30 +2 4 8 12 31 32 33 9.81269 9.81284 9.81299 3 5 9.82141 9.82155 9.82169 1 3 4 9.82982 9.82996 9.83010 1 3 4 9.83795 9.83808 9.83821 1 3 4 9.84579 9.84592 9.84605 1 4 29 28 27 56 52 48 16 20 24 34 35 36 9.81314 9.81328 9.81343 6 8 9 9.82184 9.82198 9.82212 6 7 8 9.83023 9.83037 9.83051 6 7 8 9.83834 9.83848 9.83861 5 7 8 9.84618 9.84630 9.84643 5 7 8 26 25 24 44 40 36 28 32 36 37 38 39 9.81358 9.81372 9.81387 11 12 14 9.82226 9.82240 9.82255 10 11 13 9.83065 9.83078 9.83092 10 11 13 9.83874 9.83887 9.83901 9 10 12 9.84656 9.84669 9.84682 9 10 12 23 23 31 32 28 24 40 40 9.81402 15 9.82269 14 9.83106 14 9.83914 13 9.84694 13 20 20 44 48 52 41 42 43 9.81417 9.81431 9.81446 2 3 5 9.82283 9.82297 9.82311 1 3 4 9.83120 9.83133 9.83147 1 4 9.83927 9.83940 9.83954 1 3 4 9.84707 9.84720 9.84733 1 3 4 19 18 17 16 12 8 56 4-3 4 44 45 46 9.81461 9.81475 9.81490 6 8 9 9.82326 9.82340 9.82354 6 7 8 9.83161 9.83174 9.83188 6 n i 8 9.83967 9.83980 9.83993 5 7 8 9.84745 9.84758 9.84771 5 7 8 16 15 14 4 +1 56 8 12 16 47 48 49 9.81505 9.81519 9.81534 11 12 14 9.82368 9.82382 9.82396 9.82410 10 11 13 9.83202 9.83215 9.83229 10 11 13 14 9.84006 9.84020 9.84033 9 10 12 9.84784 9.84796 9.84809 9 10 12 13 12 11 52 48 U 20 50 9.81549 14 14 9.83242 9.84046 13 1 3 4 9.84822 13 10 40 24 28 32 51 52 53 9.81563 9.81578 9.81592 1 3 4 9.82424 9.82439 9.82453 1 3 4 9.83256 9.83270 9.83283 1 3 4 9.84059 9.84072 9.84085 9.84835 9.84847 9.84860 1 3 4 9 8 7 36 32 28 36 40 44 54 55 56 9.81007 9.81622 9.81636 6 7 8 9.82467 9.82481 9.82495 6 7 8 9.83297 9.83310 9.83324 6 7 8 9.84098 9.84112 9.84125 5 7 8 9.84873 9.84885 9.84898 5 7 8 6 5 4 24 20 16 48 52 56 57 58 59 9.81651 9.81665 9.81680 10 11 13 9.82509 9.82523 9.82537 10 11 13 9.83338 9.83351 9.83365 10 11 13 9.84138 9.84151 9.84164 9 10 12 9.84911 9.84923 9.84936 9 10 12 3 2 1 12 8 4 +4 1 60 9.81694 9.82551 9.83378 9.84177 9.84949 Cos. Cos. Cos. Cos. Cos. 49° 3h -?6™ 48° .5^ lom 47° 3h Sm 46° 3h 4m 45° Jft 0^ Log. Cosines. Page 40] TABLE III. Log. Sines. Time. Arc. 3^ 0"> 45° 3h 4m 46° Sh 8m 47° 3Ji 12m 48° 3h 16m 490 Arc. Time. m. s. ' Sine. P.P. Sine. P.P. Sine. P.P. Sine. P.P. Sine. P.P. ' s. m. 9.84949 13 9.85693 12 9.86413 12 9.87107 11 9.87778 11 60 +4 4 8 12 1 2 3 9.84961 9.84974 9.84986 1 3 4 9.85706 9.85718 9.85730 1 2 4 9.86425 9.86436 9.86448 1 2 4 9.87119 9.87130 9.87141 1 2 3 9.87789 9.87800 9.87811 1 2 3 59 58 57 56' 52 48 16 20 24 4 5 6 9.84999 9.85012 9.85024 5 7 8 9.85742 9.85754 9.85766 5 6 7 9.86460 9.86472 9.86483 9.86495 9.86507 9.86518 5 6 7 8" 10 11 9.87153 9.87164 9.87175 4 6 7 8 9 10 9.87822 9.87833 9.87844 4 6 56 55 54 44 40 36 32 28 24 20 28 32 36 7 8 9 9.85037 9.85049 9.85062 9 10 12 9.85779 9.85791 9.85803 8 10 11 12 9.87187 9.87198 9.87209 9.87855 9.87866 9.87877 8 9 10 53 52 51 50 40 10 9.85074 13 9.85815 9.86530 12 9.87221 11 9.87887 11 U 4S 52 11 n 13 9.85087 9.85100 9.85112 1 3 4 9.85827 9.85839 9.85851 1 2 4 9.86542 9.86554 9.86565 1 2 4 9.87232 9.87243 9.87255 1 2 3 9.87898 9.87909 9.87920 1 2 3 49 48 47 16 12 8 56 +1 4 14 15 16 9.85125 9.85137 9.85150 5 7 8 9.85864 9.85876 9.85888 5 6 7 9.86577 9.86589 9.86600 5 6 7 9.87266 9.87277 9.87288 4 6 7 9.87931 9.87942 9.87953 4 6 7 46 45 44 4 4-3 56 8 12 16 17 18 19 9.85162 9.85175 9.85187 9 10 12 9.85900 9.85912 9.85924 8 10 11 9.86612 9.86624 9.86635 9.86647 8 10 11 9.87300 9.87311 9.87322 8 9 10 9.87964 9.87975 9.87985 8 9 10 43 42 41 52 48 44 20 20 9.85200 13 9.85936 12 12 9.87334 11 9.87996 11 40 40 24 28 32 21 22 23 9.85212 9.85225 9.85237 1 2 4 9.85948 9.85960 9.85972 1 2 4 9.86659 9.86670 9.86682 1 2 4 9.87345 9.87356 9.87367 1 2 3 9.88007 9.88018 9.88029 1 2 3 39 38 37 36 32 28 36 40 44 24 25 26 9.85250 9.85262 9.85274 5 6 7 9.85984 9.85996 9.86008 5 6 7 9.86694 9.86705 9.86717 5 6 7 9.87378 9.87390 9.87401 4 6 7 9.88040 9.88051 9.88061 4 6 7 36 35 34 33 32 31 24 20 16 ^t8 52 56 +3 27 28 29 9.85287 9.85299 9.85312 8 10 11 9.86020 9.86032 9.86044 8 10 11 9.86728 9.86740 9.86752 8 10 11 9.87412 9.87423 9.87434 ' 8 9 10 9.88072 9.88083 9.88094 8 9 10 12 8 4 30 9.85324 12 9.86056 12 9.86763 12 9.87446 11 9.88105 11 30 +2 4 8 12 31 32 33 9.85337 9.85349 9.85361 1 2 4 5 6 7 9.86068 9.86080 9.86092 9.86104 9.86116 9.86128 1 2 4 5 6 7 9.86775 9.86786 9.86798 1 2 4 9.87457 9.87468 9.87479 1 2 3 9.88115 9.88126 9.88137 1 2 3 29 28 27 56 52 48 16 20 24 34 35 36 9.85374 9.85386 9.85399 9.86809 9.86821 9.86832 5 6 7 9.87490 9.87501 9.87513 4 6 7 9.88148 9.88158 9.88169 4 6 7 26 25 24 44 40 36 28 32 36 37 38 39 9.85411 9.85423 9.85436 8 10 11 9.86140 9.86152 9.86164 8 10 11 9.86844 9.86855 9.86867 8 10 11 9.87524 9.87535 9.87546 8 9 10 11 9.88180 9.88191 9.88201 8 9 10 23 22 21 32 28 24 40 40 9.85448 12 9.86176 12 9.86879 11 9.87557 9.88212 11 20 20 44 48 52 41 42 43 9.85460 9.85473 9.85485 1 2 4 9.86188 9.86200 9.86211 1 2 4 9.86890 9.86902 9.86913 1 2 3 9.87568 9.87579 9.87590 1 2 3 9.88223 9.88234 9.88244 1 2 3 19 18 17 16 12 8 56 +3 4 44 45 46 9.85497 9.85510 9.85522 5 6 7 9.86223 9.86235 9.86247 5 6 7 9.86924 9.86936 9.86947 4 6 7 9.87601 9.87613 9.87624 4 6 7 9.88255 9.88266 9.88276 4 6 7 16 15 14 4 +1 56 8 12 16 47 48 49 9.85534 9.85547 9.85559 8 10 11 9.86259 9.86271 9.86283 8 10 11 9.86959 9.86970 9.86982 8 9 10 9.87635 9.87646 9.87657 8 9 10 9.88287 9.88298 9.88308 8 9 10 13 12 11 52 48 44 20 50 9.85571 12 9.86295 12 9.86993 11 9.87668 11 9.88319 11 10 40 24 28 32 51 52 53 9.85583 9.85596 9.85608 1 2 4 9.86306 9.86318 9.80330 1 2 4 9.87005 9.87016 9.87028 1 2 3 9.87679 9.87690 9.87701 1 2 3 9.88330 9.88340 9.88351 1 2 3 9 8 7 36 32 28 36 40 U 54 55 56 9.85620 9.85632 9.85645 5 6 7 9.86342 9.86354 9.86366 9.86377 9.86389 9.86401 5 6 7 9.87039 9.87050 "9.87062 4 6 7 9.87712 9.87723 9.87734 4 6 7 9.88362 9.88372 9.88383 9.88394 9.88404 9.88415 4 6 7 6 5 4 24 20 le 48 52 56 57 58 59 9.85657 9.85669 9.85681 8 10 11 8 10 11 9.87073 9.87085 9.87096 8 9 10 9.87745 9.87750 9.87767 8 9 10 8 9 10 3 2 1 12 8 4 +4 60 9.85693 9.86413 9.87107 9.87778 9.88425 1 Cos. Cos. Cos. Cos. Cos. 44° 2h 56m 43° 2h 52m 42° 2h 48m 41° 2h44m 40° 2h 40m Log. Cosines. TABLE III. [Page 41 Log. Sines. Time. Arc. 3^1 20'm. 50° 3fi' 24'm 51° 3h 28^ 52° 3h 32m 53° ,3h 3r,m 540 Arc. Time. m. s. ' Sine. P.P. Sine. P.P. Sine. P.P. Sine. P.P. Sine. P.P. ' s. m. 9.88425 11 9.89050 10 9.89653 10 9.90235 9 9.90796 9 60 +4 A 8 12 1 2 3 9.88436 9.884-47 9.88457 1 2 3 9.89060 9.89071 9.89081 1 2 3 9.89663 9.89673 9.89683 1 2 .3 9.90244 9.90254 9.90263 1 2 9.90805 9.90814 9.90823 1 2 59 58 57 56- 52 48 16 20 24 4 5 6 9.88468 9.88478 9.88489 4 6 7 9.89091 9.89101 9.89112 4 5 6 9.89693 9.89702 9.89712 4 5 6 9.90273 9.90282 9.90292 4 5 5 9.90832 9.90842 9.90851 4 5 5 56 55 54 44 40 36 2S 32 36 7 8 9 9.88499 9.88510 9.88521 8 9 10 9.89122 9.89132 9.89142 7 8 9 9.89722, 9.89732' 9.89742 7 8 9 9.90301 9.90311 9.90320 6 7 8 9.90860 9.90869 9.90878 6 7 8 53 52 51 32 28 24 40 10 9.88531 11 9.89152 10 9.89752 10 9.90330 9 9.90887 9 1 50 20 44 48 52 11 12 13 9.88542 9.88552 9.88563 1 2 3 9.89162 9.89173 9.89183 1 2 3 9.89761 9.89771 9.89781 1 9.90339 2 9.90349 3 9.90358 1 3 9.90896 9.90906 9.90915 1 49 48 47 16 12 8 • 56 +1 4 14 15 16 9.88573 9.88584 9.88594 4 6 7 9.89193 9.89203 9.89213 4 5 6 9.89791 9.89801 9.89810 4 5 6 9.90308 9.90377 9.90386 4 5 5 9.90924 9.90933 9.90942 4 5 5 46 45 44 4 +3 56 8 12 16 17 18 19 9.88605 9.88615 9.88626 8 9 10 9.89223 9.89233 9.89244 7 8 9 9.89820 9.89830 9.89840 7 8 9 9.90396 9.90405 9.90415 6 7 8 9.90951 9.90960 9.90969 6 7 8 43 42 41 52 48 44 20 20 9.83636 10 9.89254 10 9.89849 10 9.90424 9 9.90978 9 49 40 24 28 32 21 22 23 9.88647 9.88657 9.88668 1 2 3 9.89264 9.89274 9.89284 1 2 3 9.89859 9.89869 9.89879 1 2 3 9.90434 9.90443 9.90452 1 2 3 9.90987 9.90996 9.91005 1 39 38 37 36 32 28 36 40 44 24 25 26 9.88678 9.88688 9.88699 4 5 6 9.89294 9.89304 9.89314 9.89324 9.89334 9.89344 4 5 6 9.89888 9.89898 9.89908 4 5 6 9.90462 9.90471 9.90480 4 5 5 9.91014 9.91023 9.91033 4 5 5 36 35 34 24 20 16 48 52 56 27 28 29 9.88709 9.88720 9.88730 7 8 9 7 8 9 9.89918 9.89927 9.89937 7 8 9 9.90490 9.90499 9.90509 6 7 8 9.91042 9.91051 9.91060 6 1 8 33 32 31 12 8 4 +2 30 9.88741 10 9.89354 10 9.89947 10 9.90518 9 9.91069 9 30 +2 4 8 12 31 32 33 9.88751 9.88761 9.88772 1 2 3 9.89364 9.89375 9.89385 1 2 3 9.89956 9.89966 9.89976 1 2 3 9.90527 9.90537 9.90546 1 2 3 9.91078 9.91087 9.91096 1 29 28 27 56 52 48 16 20 24 34 35 36 9.88782 9.88793 9.88803 4 5 6 9.89395 9.89405 9.89415 4 5 6 9.89985 9.89995 9.90005 4 5 6 9.90555 9.90565 9.90574 4 5 5 9.91105 9.91114 9.91123 4 5 5 26 25 24 4.i 40 36 28 32 36 37 38 39 9.88813 9.88824 9.88834 7 8 9 9.89425 9.89435 9.89445 7 8 9 9.90014 9.90024 9.90034 7 8 9 9.90583 9.90592 9.90002 6 7 8 9.91132 9.91141 9.91149 6 8 23 22 21 32 28 24 40 40 9.88844 10 9.89455 10 9.90043 10 9.90G11 9 9.91158 9 20 20 44 48 52 41 42 43 9.88855 9.88865 9.88875 1 2 3 9.89465 9.89475 9.89485 1 2 3 9.90053 9.90063 9.90072 1 2 3 9.90620 9.90630 9.90G39 1 2 3 9.91167 9.91176 9.91185 1 3 19 18 17 16 12 8 56 +3 4 44 45 46 9.88886 9.88896 9.88906 4 5 6 9.89495 9.89504 9.89514 4 5 6 9.90082 9.90091 9.90101 4 5 6 9.90648 9.90657 9.906G7 4 5 5 9.91194 9.91203 9.91212 4 5 5 16 15 14 4 +1 56 8 12 16 47 48 49 9.88917 9.88927 9.88937 7 8 9 9.89524 9.89534 9.89544 7 8 9 9.90111 9.90120 9.90130 7 8 9 9.90676 9.90G85 9.90694 6 7 8 9.91221 9.91230 9.91239 6 7 8 13 12 11 52 48 44 20 50 9.88948 10 9.89554 10 9.90139 10 9.90704 9 9.91248 9 10 40 24 28 32 51 52 63 9.88958 9.88968 9.88978 1 2 3 9.89564 9.89574 9.89584 1 2 3 9.90149 9.90159 9.90168 1 2 .3 9.90713 9.90722 9.90731 1 2 3 9.91257 9.91266 9.91274 1 3 9 8 7 36 32 28 36 40 44 54 55 56 9.88989 9.88999 9.89009 4 5 6 9.89594 9.89604 9.89014 4 5 6 9.90178 9.90187 9.90197 4 5 6 9.90741 9.90750 9.90759 4 5 5 9.91283 9.91292 9.91301 4 5 5 6 5 4 24 20 16 48 52 56 57 58 59 9.89010 9.89030 9.89040 7 8 9 9.89624 9.89633 9.89643 7 8 9 9.90206 9.90216 9.90225 7 8 9 9.90768 9.90777 9.90787 6 7 8 9.91310 9.91319 9.91328 6 7 8 3 2 1 12 8 4 +4 60 9.89050 9.89653 9.90235 9.90796 9.91336 ! Cos. Cos. Cos. Cos. Cos. 39° 2^ 36m 38° 2h 32^ 37° i?'* 28m 36° 2h 24m 35° 2^ 20m Lo<^. Casinos. Page 42] TABLE III. Log. Sines. Time. Are. 3^ 40m 55° Sh 44m 56° 3h4Sm 57° S^ 52m 58° Sh 56m 59° Arc. Time. m. s. ' Sine. P. P. Sine. P. P. Sine. P. P. Sine. P. P. Sine. P. P. / s. m. 9.91336 9 9.91857 8 9.92359 8 9.92842 8 9.93307 8 60 +4 4 8 12 1 2 3 9.91345 9.91354 9.91363 1 2 3 9.91866 9.91874 9.91883 1 2 2 3 4 5 9.92367 9.92376 9.92384 1 2 2 9.92850 9.92858 9.92866 1 2 2 9.93314 9.93322 9.93329 9.93337 9.93344 9.93352 1 2 2 3 4 5 59 58 57 56 55 54 53 52 51 56 52 48 16 20 24 4 5 6 9.91372 9.91381 9.91389 4 5 5 9.91891 9.91900 9.91908 9.92392 9.92400 9.92408 3 4 5 9.92874 9.92881 9.92889 9.92897 9.92905 9.92913 3 4 5 U 40 36 28 32 36 7 8 9 9.91398 9.91407 9.91416 6 7 8 9.91917 9.91925 9.91934 6 6 7 9.92416 9.92425 9.92433 6 6 7 6 6 7 9.93360 9.93367 9.93375 6 6 7 32 28 24 40 10 9.91425 9 9.91942 8 9.92441 8 9.92921 8 9.93382 8 50 20 48 52 56 +1 4 11 12 13 14 15 16 9.91433 9.91442 9.91451 1 2 3 9.91951 9.91959 9.91968 1 2 2 9.92449 9.92457 9.92465 1 2 2 9.92929 9.92936 9.92944 1 2 2 9.93390 9.93397 9.93405 1 2 2 49 48 47 16 12 8 9.91460 9.91469 9.91477 4 5 5 9.91976 9.91985 9.91993 3 4 5 9.92473 9.92482 9.92490 3 4 5 6 6 7 9.92952 9.92960 9.92968 3 4 5 9.93412 9.93420 9.93427 3 4 5 46 45 44 4 +3 56 8 12 16 17 18 19 9.91486 9.91495 9.91504 6 7 8 9.92002 9.92010 9.92018 6 6 7 9.92498 9.92506 9.92514 9.92976 9.92983 9.92991 6 6 7 9.93435 9.93442 9.93450 6 6 7 43 42 41 52 48 44 20 24 28 32 20 9.91512 9 9.92027 8 9.92522 8 9.92999 8 9.93457 7 40 40 21 22 23 9.91521 9.91530 9.91538 1 2 3 4 5 5 9.92035 9.92044 9.92052 9.92060 9.92069 9.92077 1 2 2 9.92530 9.92538 9.92546 1 2 2 9.93007 9.93014 9.93022 1 2 2 9.93465 9.93472 9.93480 1 1 2 39 38 37 36 32 28 36 40 44 24 25 26 9.91547 9.91556 9.91565 3 4 5 9.92555 9.92563 9.92571 3 4 5 9.93030 9.93038 9.93046 3 4 5 9.93487 9.93495 9.93502 3 4 4 36 35 34 24 20 16 48 52 56 27 28 29 9.91573 9.91582 9.91591 6 7 8 9.92086 9.92094 9.92102 6 6 7 9.92579 9.92587 9.92595 6 6 7 9.93053 9.93061 9.93069 6 6 7 9.93510 9.93517 9.93525 5 6 6 33 32 31 12 8 4 +2 30 9.91599 9 9.92111 8 9.92603 8 9.93077 8 9.93532 7 30 +2 4 8 12 31 32 33 9.91608 9.91617 9.91625 1 2 3 9.92119 9.92127 9.92136 9.92144 9.92152 9.92161 1 2 2 9.92611 9.92619 9.92627 1 2 2 9.93084 9.93092 9.93100 1 2 2 9.93539 9.93547 9.93554 1 1 2 29 28 27 56 52 48 16 20 24 34 35 36 9.91634 9.91643 9.91651 4 5 5 6 7 8 3 4 5 9.92635 9.92643 9.92651 3 4 5 9.93108 9.93115 9.93123 3 4 5 9.93562 9.93569 9.93577 3 4 4 26 25 24 U 40 36 28 32 36 37 38 39 9.91660 9.91669 9.91677 9.92169 9.92177 9.92186 6 6 7 9.92659 9.92667 9.92675 6 6 7 9.93131 9.93138 9.93146 6 6 7 9.93584 9.93591 9.93599 5 6 6 23 22 21 32 28 24 40 40 9.91686 9 9.92194 8 9.92683 8 9.93154 8 9.93606 7 20 20 44 48 52 41 42 43 9.91695 9.91703 9.91712 1 2 3 9.92202 9.92211 9.92219 1 2 2 9.92691 9.92699 9.92707 1 2 2 9.93161 9.93169 9.93177 1 2 2 9.93614 9.93621 9.93628 1 1 2 19 18 17 16 12 8 56 +3 4 44 45 46 9.91720 9.91729 9.91738 4 5 5 9.92227 9.92235 9.92244 3 4 5 9.92715 9.92723 9.92731 3 4 5 9.93184 9.93192 9.93200 3 4 5 9.93636 9.93643 9.93650 3 4 4 16 15 14 4 +1 56 8 12 16 47 48 49 9.91746 9.91755 9.91763 6 7 8 9.92252 9.92260 9.92269 6 6 7 9.92739 9.92747 9.92755 6 6 7 9.93207 9.93215 9.93223 6 6 7 9.93658 9.93665 9.93673 5 6 6 13 12 11 52 48 U 20 50 9.91772 1 9 9.92277 8 9.92763 8 9.93230 8 9.93680 7 10 40 24 28 32 51 52 53 9.91781 9.91789 9.91798 1 2 3 9.92285 9.92293 9.92302 1 2 2 9.92771 9.92779 9.92787 1 2 2 9.93238 9.93246 9.93253 1 2 2 9.93687 9.93695 9.93702 1 1 2 9 8 7 36 32 28 36 40 44 54 55 56 9.91806 9.91815 9.91823 4 5 5 9.92310 9.92318 9.92326 3 4 5 9.92795 9.92803 9.92810 3 4 5 9.93261 9.93269 9.93276 3 4 5 9.93709 9.93717 9.93724 3 4 4 6 5 4 24 20 16 48 52 56 57 58 59 9.91832 9.91840 9.91849 6 7 8 9.92335 9.92343 9.92351 6 6 7 9.92818 9.92826 9.92834 6 6 7 9.93284 9.93291 9.93299 6 6 7 9.93731 9.93738 9.93746 5 6 6 3 2 1 12 8 4 +* 60 9.91857 9.92359 9.92842 9.93307 9.93753 Cos. Cos. Cos. Cos. Cos. 34° 2hl6m 33° 2hl2m 32° 2h sm 31° 2h4m 30° 2h Om Log. Cosines. TABLE III. [Page 43 Log. Siuea. Time. Arc. 4^0m 60° | 4h 4m 61° 4h sm 62° 4h 12m 63° 4h 16m 64° Arc. Time. m. s. ' Sine. P. P. 1 Sine. P. P. Sine. P. P. Sine. P. P. Sine. P. P. ' s. in. 9.93753 7 9.94182 7 9.94593 7 1 1 2 9.94988 9.94995" 9.95001 9.95007 6 9.95366 6 60 +4 A 8 12 1 3 9.93760 9.93768 9.93775 1 1 2 9.94189 9.94196 9.94203 1 1 2 9.94600 9.94607 9.94614 1 1 2 9.95372 9.95378 9.95384 1 1 2 59 58 57 56 52 48 16 20 24 4 5 6 9.93782 9.93789 9.93797 3 4 4 9.94210 9.94217 9.94224 3 4 4 9.94620 9.94627 9.94634 3 4 4 9.95014 9.95020 9.95027 2 3 4 9.95391 9.95397 9.95403 2 3 4 56 55 54 53 52 51 44 40 36 28 32 36 7 8 9 9.93804 9.93811 9.93819 5 6 6 9.94231 9.94238 9.94245 5 6 6 9.94640 9.94647 9.94654 5 6 6 9.95033 9.95039 9.95046 4 5 5 9.95409 9.95415 9.95421 4 5 5 32 28 24 40 10 9.93826 7 9.94252 7 9.94660 7 9.95052 6 9.95427 6 50 20 U 48 52 11 12 13 9.93833 9.93840 9.93847 1 1 2 9.94259 9.94266 9.94273 1 1 2 9.94667 9.94674 9.94680 1 1 2 9.95059 9.95065 9.95071 1 1 2 9.95434 9.95440 9.95446 1 1 2 49 48 47 16 12 8 56 +1 4 14 15 16 9.93855 9.93862 9.93869 3 4 4 9.94279 9.94286 9.94293 3 4 4 9.94687 9.94694 9.94700 3 4 4 9.95078 9.95084 9.95090 2 3 4 9.95452 9.95458 9.95464 2 3 4 46 45 44 4 +3 56 S 12 16 18 19 9.93876 9.93884 9.93891 5 6 6 9.94300 9.94307 9.94314 5 6 6 9.94707 9.94714 9.94720 5 6 6 9.95097 9.95103 9.95110 4 5 5 9.95470 9.95476 9.95482 4 5 5 43 43 41 52 48 U 20 30 9.93898 7 9.94321 7 9.94727 7 9.95116 6 9.95488 6 40 40 24 28 32 32 23 9.93905 9.93912 9.93920 1 1 2 9.94328 9.94335 9.94342 1 1 2 9.94734 9.94740 9.94747 1 1 2 9.95122 9.95129 9.95135 1 1 2 9.95494 9.95500 9.95507 i 1 2 39 38 37 36 32 28 36 40 U 24 25 26 9.93927 9.93934 9.93941 3 4 4 9.94349 9.94355 9.94362 3 4 4 9.94753 9.94760 9.94767 3 4 4 9.95141 9.95148 9.95154 2 3 4 9.95513 9.95519 9.95525 2 3 4 36 35 34 24 20 16 48 52 56 27 28 29 9.93948 9.93955 9.93963 5 6 6 9.94369 9.94376 9.94383 5 6 6 9.94773 9.94780 9.94786 5 6 6 9.95160 9.95167 9.95173 4 5 5 9.95531 9.95537 9.95543 4 5 5 33 32 31 12 8 4 +2 30 9.93970 7 9.94390 7 9.94793 7 9.95179 6 9.95549 6 30 +3 4 8 12 31 33 33 9.93977 9.93984 9.93991 1 1 2 9.94397 9.94404 9.94410 1 1 2 9.94799 9.94806 9.94813 1 1 2 9.95185 9.95192 9.95198 1 1 2 9.95555 9.95501 9.95567 1 1 2 29 28 27 56 52 48 16 20 24 34 35 36 9.93998 9.94005 9.94012 3 4 4 9.94417 9.94424 9.94431 3 4 4 9.94819 9.94826 9.94832 3 4 4 9.95204 9.95211 9.95217 2 3 4 9.95573 9.95579 9.95585 2 3 4 36 35 24 U 40 36 28 32 36 37 38 39 9.94020 9.94027 9.94034 5 6 6 9.94438 9.94445 9.94451 5 6 6 9.94839 9.94845 9.94852 5 6 9.95223 9.95229 9.95236 4 5 5 9.95591 9.95597 9.95603 4 5 5 23 23 31 32 28 24 40 40 9.94041 7 9.94458 7 9.94858 7 9.95242 6 9.95609 6 30 20 44 48 52 41 43 43 9.94048 9.94055 9.94062 1 1 2 9.94465 9.94472 9.94479 1 1 2 9.94865 9.94871 9.94878 1 1 2 9.95248 9.95254 9.95261 1 »1 2 9.95615 9.95621 9.95627 1 1 2 19 18 17 16 12 8 56 +3 4 44 45 46 9.94069 9.94076 9.94083 3 4 4 9.94485 9.94492 9.94499 3 4 4 9.94885 9.94891 9.94898 3 4 4 9.95267 9.95273 9.95279 2 3 4 9.95633 9.95639 9.95645 2 3 4 16 15 14 4 +1 56 8 12 16 47 48 49 9.94090 9.94098 9.94105 5 6 6 9.94506 9.94513 9.94519 5 6 6 9.94904 9.94911 9.94917 5 6 6 9.95286 9.95292 9.95298 4 5 5 9.95651 9.95657 9.95663 4 5 5 13 13 11 52 48 44 20 50 9.94112 7 9.94526' 7 9.94923 7 9.95304 6 9.95668 6 10 40 24 28 32 51 53 53 9.94119 9.94126 9.94133 1 1 2 9.94533 9.94540 9.94546 1 1 2 9.94930 9.94936 9.94943 1 1 2 9.95310 9.95317 9.95323 1 1 2 9.95074 9.95680 9.95686 1 1 2 9 8 7 36 32 28 36 40 44 54 55 56 9.94140 9.94147 9.94154 3 4 4 9.94553 9.945C0 9.94567 3 4 4 9.94949 9.94956 9.94962 3 4 4 9.95329 9.95335 9.95341 2 3 4 9.95692 9.95698 9.95704 2 3 4 6 5 4 24 20 16 48 52 56 57 58 59 9.94161 9.94168 9.94175 5 6 6 9.94573 9.94580 9.94587 5 6 6 9.94969 9.94975 9.94982 5 6 6 9.95348 9.95554 9.95360 4 5 5 9.95710 9.95716 9.95722 4 5 5 3 1 12 8 4 +* 60 9.94182 9.94593 9.94988 9.95366 9.95728 1 Cos. Cos. Cos. Cos. Cos. 39° iJi 56^ 28° lh52m 27° Ih 48m 26° IhU^ 25° Ih 40m Log. Cosinea. Page 44] TABT.E III. Log. Sines. Time. Arc. 4^ 20m 65° 4^ 24"^ 66° 4h 28m 67° 4^1 32m 68° 4^ 36m 69° Arc. Time. m. s. Sine. P. P. Sine. P. P. Sine. P. P. Sine. P. P. Sine. P. P. ' s. m. 9.95728 6 9.96073 6 9.96403 5 9.96717 5 9.97015 5 60 +4 4 8 12 1 2 3 9.95783 9.95739 9.95745 1 1 2 9.96079 9.96084 9.96090 1 1 2 9.96408 9.96413 9.96419 1 1 2 9.96722 9.96727 9.9G732 1 1 2 9.97020 9.97025 9.97030 1 1 2 59 58 57 56 52 48 16 20 24 4 5 6 9.95751 9.95757 9.95763 2 3 4 9.96095 9.96101 9.96107 2 3 4 9.96424 9.96429 9.96435 2 3 3 9.96737 9.96742 9.96747 2 3 3 9.97035 9.97039 9.97044 2 3 3 56 55 54 44 40 36 28 32 36 7 8 9 9.95769 9.95775 9.95780 4 5 5 9.96112 9.96118 9.96123 4 5 5 9.96440 9.96445 9.96451 4 4 5 9.96752 9.96757 9.96762 4 4 5 9.97049 9.97054 9.97059 4 4 5 53 52 51 32 28 24 40 10 9.95786 6 9.96129 6 9.96456 5 9.96767 5 9.97063 5 50 20 44 48 52 11 12 13 9.95792 9.95798 9.95804 1 1 2 9.96135 9.96140 9.96146 1 1 2 9.96461 9.96467 9.96472 1 1 2 9.96772 9.96778 9.96783 1 1 2 9.97068 9.97073 9.97078 1 1 2 49 48 47 16 12 8 56 +1 4 14 15 16 9.95810 9.95815 9.95821 2 3 4 9.96151 9.96157 9.96162 2 3 4 9.96477 9.96483 9.96488 2 3 3 9.96788 9.96793 9.96798 2 3 3 9.97083 9.97087 9.97092 3 3 46 45 44 4 +3 56 8 12 16 17 18 19 9.95827 9.95833 9.95839 4 5 5 9.96168 9.96174 9.96179 4 5 5 9.96493 9.96498 9.96504 4 4 5 9.96803 9.96808 9.96813 4 4 5 9.97097 9.97102 9.97107 4 4 5 43 42 41 52 48 44 20 20 9.95844 6 9.96185 5 9.96509 5 9.96818 5 9.97111 5 40 40 24 28 32 21 22 23 9.95850 9.95856 9.95862 1 1 2 9.96190 9.96196 9.96201 1 1 2 9.96514 9.96520 9.96525 1 1 2 9.96823 9.96828 9.96833 1 1 2 9.97116 9.97121 9.97126 1 1 2 39 38 37 36 32 28 36 40 44 24 25 26 9.95868 9.95873 9.95879 2 3 4 9.96207 9.96212 9.96218 2 3 3 9.96530 9.96535 9.96541 2 3 3 9.96838 9.96843 9.96848 2 3 3 9.97130 9.97135 9.97140 2 3 3 36 35 34 24 20 16 48 52 56 27 28 29 9.95885 9.95891 9.95897 4 5 5 9.96223 9.96229 9.96234 4 4 5 9.96546 9.96551 9.96556 4 4 5 9.96853 9.96858 9.96863 4 4 5 9.97145 9.97149 9.97154 4 4 5 33 32 31 12 8 4 +2 4 8 12 30 9.95902 6 9.96240 5 9.96562 5 9.96868 5 9.97159 5 30 +2 31 32 33 9.95908 9.95914 9.95920 1 1 2 9.96245 9.96251 9.96256 1 1 2 9.96567 9.96572 9.96577 1 1 2 9.96873 9.96878 9.96883 1 1 2 9.97163 9.97168 9.97173 1 1 2 29 28 27 56 52 48 16 20 24 34 35 36 9.95925 9.95931 9.95937 2 3 4 9.96262 9.96267 9.96273 2 3 3 9.96582 9.96588 9.96593 2 3 3 9.96888 9.96893 9.96898 2 3 3 9.97178 9.97182 9.97187 2 3 3 26 25 24 44 40 36 28 32 36 37 38 39 9.95942 9.95948 9.95954 4 5 5 9.96278 9.96284 9.96289 4 4 5 9.96598 9.96603 9.96608 4 4 5 9.96903 9.96907 9.96912 4 4 5 9.97192 9.97196 9.97201 4 4 5 23 22 21 32 28 24 40 40 9.959G0 6 9.96294 5 9.96614 5 9.96917 5 9.97206 5 20 20 44 48 52 41 42 43 9.95965 9.95971 9.95977 1 1 2 9.96300 9.96305 9.96311 1 1 2 9.96619 9.96624 9.96629 1 1 2 9.96922 9.96927 9.96932 1 1 2 9.97210 9.97215 9.97220 1 1 2 19 18 17 16 12 8 56 +3 4 44 45 46 9.95982 9.95988 9.95994 2 3 4 9.96316 9.96322 9.96327 2 3 3 9.96634 9.96640 9.96645 2 3 3 9.96937 9.96942 9.96947 2 3 3 9.97224 9.97229 9.97234 2 3 3 16 15 14 4 +1 56 8 12 16 47 48 49 9.96000 9.96005 9.96011 4 5 5 9.96333 9.96338 9.96343 4 4 5 9.96650 9.96655 9.96660 4 4 5 9.96952 9.96957 9.96962 4 4 5 9.97238 9.97243 9.97248 4 4 5 13 12 11 52 48 44 20 24 28 32 50 9.96017 6 9.96349 5 9.96665 9.96670 9.96676 9.96681 5 9.96966 5 9.97252 5 10 40 51 52 53 9.96022 9.96028 9.96034 1 1 2 9.96354 9.96360 9.96365 1 1 2 1 1 2 9.96971 9.96976 9.96981 1 1 2 9.97257 9.97262 9.97266 1 1 2 9 8 7 36 32 28 36 40 44 54 55 56 9.96039 9.96045 9.96050 2 3 4 9.96370 9.96376 9.96381 2 3 3 9.96686 9.96691 9.96696 2 3 3 9.96986 9.96991 9.96996 2 3 3 9.97271 9.97276 9.97280 2 3 3 6 5 4 24 20 16 48 52 56 57 58 59 9.96056 9.96062 9.96067 4 5 5 9.96387 9.96392 9.96397 4 4 5 9.96701 9.96706 9.96711 4 4 5 9.97001 9.97005 9.97010 4 4 5 9.97285 9.97289 9.97294 4 4 5 3 2 1 12 8 4 +* 60 9.96073 9.96403 9.96717 9.97015 9.97299 Cos. Cos. Cos. Cos. Cos. 24° Ih 36^ 23° Ih 32m 22° ih 28m 21°, J A 24"^ 20° 1^ 20m 1 Log. Cosines. TiySLE III. [Page 45 Log. Sin 68. Time. Arc. 4h 40m 70° 4h 44m 71° 4h 48m 72° 4h 52m 73° 4h 56m 74° Arc. Time. m. s. ' Sine. P. P. Sine. P. P. Sine. P. P. Sine. P. P. Sine. P. P. ' 8. m. 9.97299 5 9.97567 4 9.97821 4 9.98060 4 9.98284 4 60 44 4 8 12 1 2 3 9.97303 9.97308 9.97312 1 1 2 9.97571 9.97576 9.97580 1 1 9.97825 9.97829 9.97833 1 1 9.98063 9.98067 9.98071 1 1 9.98288 9.98291 9.98295 1 1 59 58 57 56 52 48 16 20 2A 4 5 6 9.97317 9.97322 9.97326 2 3 3 9.97584 9.97589 9.97593 2 2 2 9.97837 9.97841 9.97845 2 2 2 9.98075 9.98079 9.98083 2 2 2 9.98299 9.98302 9.98306 2 2 2 56 55 54 44 40 36 28 32 36 7 8 9 9.97331 9.97335 9.97340 4 4 5 9.97597 9.97602 9.97606 3 4 9.97849 9.97853 9.97857 3 3 4 9.98087 9.98090 9.98094 3 3 4 9.98309 9.98313 9.98317 3 3 4 53 52 51 32 28 24 40 10 9.97344 5 9.97610 4 9.97861 4 9.98098 4 9.98320 4 50 20 44 48 52 11 13 13 9.97349 9.97353 9.97358 1 1 2 9.97615 9.97619 9.97623 1 1 9.97866 9.97870 9.97874 1 1 9.98102 9.98106 9.98110 1 1 9.98324 9.98327 9.98331 1 1 49 48 47 16 12 8 56 +1 4 14 15 16 9.97363 9.97367 9.97372 2 3 3 9.97628 9.97632 9.97636 2 2 2 9.97878 9.97882 9.97886 2 2 2 9.98113 9.98117 9.98121 2 2 2 9.98334 9.98338 9.98342 2 2 2 46 45 44 4 +3 56 8 12 16 17 18 19 9.97376 9.97381 9.97385 4 4 5 9.97640 9.97645 9.97649 3 3 4 9.97890 9.97894 9.97898 3 3 4 9.98125 9.98129 9.98132 3 3 4 9.98345 9.98349 9.98352 3 3 4 43 42 41 52 48 44 20 20 9.97390 4 9.97653 4 9.97902 4 9.98136 4 9.98356 4 40 40 24 28 32 21 22 23 9.97394 9.97399 9.97403 1 1 9.97657 9.97662 9.97666 1 1 9.97906 9.97910 9.97914 1 1 9.98140 9.98144 9.98147 1 1 9.98359 9.98363 9.98366 1 1 2 2 2 39 38 37 36 35 34 36 32 28 36 40 U 24 25 26 9.97408 9.97412 9.97417 2 2 2 9.97670 9.97674 9.97679 2 2 2 9.97918 9.97922 9.97926 2 2 2 9.98151 9.98155 9.98159 2 2 2 9.98370 9.98373 9.98377 24 20 16 48 52 56 27 28 29 9.97421 9.97426 9.97430 3 3 4 9.97683 9.97687 9.97691 3 3 4 9.97930 9.97934 9.97938 3 3 4 9.98162 9.98166 9.98170 3 3 4 9.98381 9.98384 9.98388 3 3 4 33 32 31 12 8 4 +3 30 9.97435 4 9.97696 4 9.97942 4 9.98174 4 9.98391 3 30 +2 4 8 12 31 32 33 9.97439 9.97444 9.97448 1 1 9.97700 9.97704 9.97708 1 1 9.97946 9.97950 9.97954 1 1 9.98177 9.98181 9.98185 1 1 9.98395 9.98398 9.98402 1 1 29 28 27 56 52 48 16 20 24 34 35 36 9.97453 9.97457 9.97461 2 2 2 9.97713 9.97717 9.97721 2 2 2 9.97958 9.97962 9.97966 2 2 2 9.98189 9.98192 9.98196 2 2 2 9.98405 9.98409 9.98412 1 2 2 26 25 24 U 40 36 28 32 36 37 38 39 9.97466 9.97470 9.97475 3 3 4 9.97725 9.97729 9.97734 3 3 4 9.97970 9.97974 9.97978 3 3 4 9.98200 9.98204 9.98207 3 3 4 9.98415 9.98419 9.98422 2 2 3 23 22 21 32 28 24 40 40 9.97479 4 9.97738 4 9.97982 4 9.98211 4 9.98426 3 20 20 44 48 52 41 42 43 9.97484 9.97488 9.97492 1 1 9.97742 9.97746 9.97750 1 1 9.97986 9.97989 9.97993 1 1 9.98215 9.98218 9.98222 1 1 9.98429 9.98433 9.98436 1 1 19 18 17 16 12 8 56 +3 4 44 45 46 9.97497 9.97501 9.97506 2 2 2 9.97754 9.97759 9.97763 2 2 2 9.97997 9.98001 9.98005 2 2 2 9.98226 9.98229 9.98233 2 2 2 9.98440 9.98443 9.98447 1 2 2 16 15 14 4 56 8 12 16 47 48 49 9.97510 9.97515 9.97519 3 3 4 9.97767 9.97771 9.97775 3 3 4 9.98009 9.98013 9.98017 3 3 4 9.98237 9.98240 9.98244 3 3 4 9.98450 9.98453 9.98457 2 2 3 13 12 11 52 48 U 20 50 9.97523 4 9.97779 4 9.98021 4 9.98248 4 9.98460 3 10 40 24 28 32 51 52 53 9.97528 9.97532 9.97536 1 1 9.97784 9.97788 9.97792 1 1 9.98025 9.98029 9.98032 1 1 9.98251 9.98255 9.98259 1 1 9.98464 9.98467 9.98471 1 1 9 8 7 36 32 28 36 40 44 54 55 56 9.97541 9.97545 9.97550 2 2 2 9.97796 9.97800 9.97804 2 2 2 9.98036 9.98040 9.98044 2 2 9.98262 9.98266 9.98270 2 2 2 3 3 4 9.98474 9.98477 9.98481 1 2 2 6 5 4 24 20 16 48 52 56 57 58 59 9.97554 9.97558 9.97563 3 3 4 9.97808 9.97812 9.97817 3 3 4 9.98048 9.98052 9.98056 3 3 4 9.98273 9.98277 9.98281 9.98484 9.98488 9.98491 2 2 3 3 2 1 12 8 4 +4 60 9.97567 9.97821 9.98060 9.98284 9.98494 Cos. Cos. Cos. Cos. Cos. 1 19" Ih 16m 18° 7 A 12m 17° Ih Sm 16° Ih 4"^ 15° ih om Log. CoaLaes. Page 46] TABLE III. Log. Sines. Time. Arc. 5h Om 75° oh 4m 76° 5h sm 77° 5h 12m 78° 5h um 79° Arc. Time. m. s. / Sine. P. P. Sine. P. P. Sine. P.P. Sine. P. P. Sine. P. P. t s. m. 9.98494 3 9.98690 3 9.98872 3 9.99040 3 9.99195 9.99197 9.99200 9.99202 2 60 +4 4 8 12 16 20 24 1 2 3 9.98498 9.98501 9.98505 1 1 9.98694 9.98697 9.98700 1 1 9.98875 9.98878 9.98881 ] 1 9.99043 9.99046 9.99048 1 1 59 58 57 56 52 48 4 5 6 9.98508 9.98511 9.98515 1 2 2 9.98703 9.98706 9.98709 1 2 2 9.98884 9.98887 9.98890 1 2 2 9.99051 9.99054 9.99056 1 2 2 9.99204 9.99207 9.99209 T 56 55 54 44 40 36 32 28 U 28 32 36 7 8 9 9.98518 9.98521 9.98525 2 2 3 9.98712 9.98715 9.98719 2 2 3 9.98893 9.98896 9.98898 2 2 3 9.99059 9.99062 9.99064 2 2 3 9.99212 9.99214 9.99217 2 2 53 52 51 AO 10 9.98528 3 9.98722 3 9.98901 3 9.99067 3 9.99219 2 50 20 U 48 52 11 13 13 9.98531 9.98535 9.98538 1 1 9.98725 9.98728 9.98731 1 1 9.98904 9.98907 9.98910 1 1 9.99070 9.99072 9.99075 1 1 9.99221 9.99224 9.99226 1 49 48 47 16 12 8 56 +1 4 14 15 16 9.98541 9.98545 9.98548 1 •7 2 9.98734 9.98737 9.98740 1 2 2 9.98913 9.98916 9.98919 1 2 2 9.99078 9.99080 9.99083 1 2 2 9.99229 9.99231 9.99233 1 1 1 46 45 44 4 +3 56 8 12 16 17 18 19 9.98551 9.98555 9.98558 2 2 3 9.98743 9.98746 9.98750 2 2 3 9.98921 9.98924 9.98927 2 3 9.99086 9.99088 9.99091 2 2 3 9.99236 9.99238 9.99241 1 2 2 43 42 41 52 48 44 20 30 9.98561 3 9.98753 3 9.98930 3 9.99093 3 9.99243 3 40 40 24 28 32 21 23 33 9.98565 9.98568 9.98571 1 1 9.98756 9.98759 9.98762 1 1 9.98933 9.98936 9.98938 1 1 9.99096 9.99099 9.99101 1 1 9.99245 9.99248 9.99250 1 39 38 37 36 32 28 36 40 44 34 35 36 9.98574 9.98578 9.98581 1 2 2 9.98765 9.98768 9.98771 1 2 2 9.98941 9.98944 9.98947 1 2 2 9.99104 9.99106 9.99109 1 2 2 9.99252 9.99255 9.99257 1 1 1 36 35 34 24 20 16 48 52 56 37 28 29 9.98584 9.98588 9.98591 2 2 3 9.98774 9.98777 9.98780 2 2 3 9.98950 9.98953 9.98955 2 2 3 9.99112 9.99114 9.99117 2 2 3 9.99260 9.99262 9.99264 1 2 2 33 32 31 12 8 4 +3 30 9.98594 3 9.98783 3 9.98958 3 9.99119 3 9.99267 3 30 +2 4 8 12 31 33 33 9.98597 9.98601 9.98604 1 1 9.98786 9.98789 9.98792 i 9.98961 9.98964 9.98967 1 1 9.99122 9.99124 9.99127 1 1 9.99269 9.99271 9.99274 29 38 37 56 52 48 16 20 24 34 35 36 9.98607 9.98610 9.98614 1 2 2 9.98795 9.98798 9.98801 1 2 9.98969 9.98972 9.98975 1 2 2 9.99130 9.99132 9.99135 1 2 2 9.99276 9.99278 9.99281 36 35 34 44 40 36 28 32 36 37 38 39 9.98617 9.98620 9.98623 2 2 3 9.98804 9.98807 9.98810 2 2 3 9.98978 9.98980 9.98983 2 3 9.99137 9.99140 9.99142 2 2 3 9.99283 9.99285 9.99288 2 2 33 32 21 32 28 24 40 40 9.98627 3 9.98813 3 9.989S6 3 9.99145 3 9.99290 3 20 20 44 ■'t8 52 41 43 43 9.98630 9.98633 9.98636 1 1 9.98816 9.98819 9.98822 1 1 9.98989 9.98991 9.98994 1 1 9.99147 9.99150 9.99152 1 1 9.99292 9.99294 9.99297 19 18 17 16 12 8 56 +3 4 44 45 46 9.98640 9.98643 9.98646 1 2 2 9.98825 9.98828 9.98831 1 2 2 9.98997 9.99000 9.99002 1 2 2 9.99155 9.99157 9.99160 1 2 2 9.99299 9.99301 9.99304 16 15 14 4 +1 56 52 48 U 8 12 16 47 48 49 9.98649 9.98652 9.98656 2 2 3 9.98834 9.98837 9.98840 2 2 3 9.99005 9.99008 9.99011 2 2 3 9.99162 9.99165 9.99167 2 2 3 9.99306 9.99308 9.99310 2 2 13 13 11 20 50 9.98659 3 9.98843 3 9.99013 3 9.99170 2 9.99313 2 10 40 24 28 32 51 52 53 9.98662 9.98665 9.98668 1 1 9.98846 9.98849 9.98852 1 1 9.99016 9.99019 9.99022 1 1 9.99172 9.99175 9.99177 9.99315 9.99317 9.99319 9 8 7 36 32 28 36 40 44 54 55 56 9.98671 9.98675 9.98678 1 2 2 9.98855 9.98858 9.98861 1 2 2 9.99024 9.99027 9.99030 1 2 2 9.99180 9.99182 9.99185 9.99322 9.99324 9.99326 6 5 4 24 20 16 48 52 56 57 58 59 9.98681 9.98684 9.98687 2 2 3 9.98864 9.98867 9.98869 2 2 3 9.99032 9.99035 9.99038 2 2 3 9.99187 9.99190 9.99192 2 2 9.99328 9.99331 9.99333 2 2 3 2 1 12 8 4 +4 60 9.98690 9.98872 9.99040 9.99195 9.99335 Cos. Cos. Cos. Cos. Cos. 10° < 14° Oh 56m 13° Oh 52m 12° Oh 48m 11° Oh 4.'tm Jh40m Log. Cosines. TABLE III. [Page 47 •^^ ^^ Cor ■^°=' ^"^^• Time. Arc. 5h 20m- 80° 5h 24m 81° 5h 28m 82° 5h 32m 83° 5h .36m 84° Arc. Time. m. s. ' Sine. P.P. Sine. P. P. Sine. P. P. Sine. P. P. Sine. P. P. ' s. m. 9.99335 2 9.99462 2 9.99575 2 9.99675 2 9.99761 1 60 +4 4 8 12 1 2 3 9.99337 9.99340 9.99342 9.99464 9.99466 9.99468 9.99577 9.99579 9.99581 9.99G77 9.99678 9.99680 9.99763 9.99764 9.99765 59 58 57 56- 52 48 16 20 24 4 5 6 9.99344 9.99346 9.99348 9.99470 9.99472 9.99474 9.99582 9.99584 9.99586 9.99681 9.99683 9.99684 9.99767 9.99768 9.99769 56 55 54 44 40 36 28 32 36 7 8 9 9.99351 9.99353 9.99355 2 o 9.99476 9.99478 9.99480 2 2 9.99588 9.99589 9.99591 2 2 9.99686 9.99687 9.99689 2 2 9.99771 9.99772 9.99773 53 52 51 32 28 24 40 10 9.99357 2 9.99482 2 9.99593 2 9.99690 1 9.99775 50 20 44 48 52 11 12 13 9.99359 9.99362 9.99364 9.99484 9.99486 9.99488 9.99595 9.99596 9.99598 9.99692 9.99693 9.99695 9.99776 9.99777 9.99778 49 48 47 16 12 8 56 +1 4 14 15 16 9.99366 9.99368 9.99370 9.99490 9.99492 9.99494 9.99600 9.99601 9.99603 9.99696 9.99698 9.99699 9.99780 9.99781 9.99782 46 45 44 4 +3 56 8 12 16 17 18 19 9.99372 9.99375 9.99377 2 2 9.99495 9.99497 9.99499 2 2 9.99605 9.99607 9.99608 2 2 9.99701 9.99702 9.99704 9.99783 9.99785 9.99786 43 42 41 52 48 U 20 20 9.99379 2 9.99501 2 9.99610 2 9.99705 9.99787 1 40 40 24 28 32 21 22 23 9.99381 9.99383 9.99385 9.99503 9.99505 9.99507 9.99612 9.99613 9.99615 1 9.99707 9.99708 9.99710 9.99788 9.99790 9.99791 39 38 37 36 32 28 36 40 44 24 25 26 9.99388 9.99390 9.99392 9.99509 9.99511 9.99513 9.99617 9.99618 9.99620 1 1 1 9.99711 9.99713 9.99714 9.99792 9.99793 9.99795 36 35 34 24 20 16 48 52 56 27 28 29 9.99394 9.99396 9.99398 2 2 9.99515 9.99517 9.99518 2 2 9.99622 9.99624 9.99625 1 2 2 9.99716 9.99717 9.99718 9.99796 9.99797 9.99798 33 32 31 12 8 4 +2 30 9.99400 2 9.99520 2 9.99627 2 9.99720 9.99800 30 +2 4 8 12 31 32 33 9.99402 9.99404 9.99407 9.99522 9.99524 9.99526 9.996:9 9.99630 9.99632 9.99721 9.99723 9.99724 9.99801 9.99802 9.99803 29 28 27 56 52 48 16 20 24 34 35 36 9.99409 9.99411 9.99413 9.99528 9.99530 9.99532 1 I" 9.99633 9.99635 9.99637 9.99726 9.99727 9.99728 9.99804 9.99806 9.99807 26 25 24 44 40 36 28 32 36 37 38 39 9.99415 9.99417 9.99419 2 2 9.99533 9.99535 9.99537 2 2 9.99638 9.99640 9.99642 2 2 9.99730 9.99731 9.99733 9.99808 9.99809 9.99810 23 22 21 32 28 24 40 40 9.99421 2 9.99539 2 9.99643 2 9.99734 9.99812 20 20 44 48 52 41 42 43 9.99423 9.99425 9.99427 1 9.99541 9.99543 9.99545 1 9.99645 9.99647 9.99648 9.99736 9.99737 9.99738 9.99813 9.99814 9.99815 19 18 17 16 12 8 56 +3 4 44 45 46 9.99429 9.99432 9.99434 1 1 1 9.99546 9.99548 9.99550 1 1 1 9.99650 9.99651 9.99653 9.99740 9.99741 9.99742 9.99816 9.99817 9.99819 16 15 14 4 +1 56 8 12 16 47 48 49 9.99436 9.99438 9.99440 1 2 2 9.99552 9.99554 9.99556 1 2 9.99655 9.99656 9.99658 2 2 9.99744 9.99745 9.99747 9.99820 9.99821 9.99822 13 12 11 52 48 44 20 50 9.99442 2 9.99557 2 9.99659 2 9.99748 9.99823 10 40 24 28 32 51 53 53 9.99444 9.99446 9.99448 1 9.99559 9.99561 9.99563 1 9.99661 9.99663 9.99664 9.99749 9.99751 9.99752 9.99824 9.99825 9.99827 9 8 7 36 32 28 36 40 U 54 55 56 9.99450 9.99452 9.99454 1 1 1 9.99565 9.99566 9.99568 1 1 1 9.99666 9.99667 9.99689 9.99753 9.99755 9.99756 9.99828 9.99829 9.99830 6 5 4 24 20 16 48 52 56 57 58 59 9.99456 9.99458 9.99460 1 2 2 9.99570 9.99572 9.99574 1 2 2 9.99670 9.99672 9.99674 2 2 9.99757 9.99759 9.99760 9.99831 9.99832 9.99833 3 2 1 12 8 4 +4 60 9.99462 1 9.99575 9.99675 9.99761 9.99834 Cos. Cos. Cos. Cos. Cos. 9° 0^ 30m 8° Oft 32m 7° 0^ 28^ 6° Oh 24"^ 5° Oh 20m Log. Cosines. Page 48J TABLE III. Log. Sines. Time. Arc. oh 40m 85° 5h 44m 86° 5h4Sm 87° 5h 52m 88° 5h 56m 89° Arc. Time. m. s. ' Sine. P. P. i^ine. P. P. Sine. Sine. Sine. ' s. m. 9.99834 1 9.99894 1 9.99940 9.99974 9.99993 60 +4 4 8 12 16 20 24 1 2 3 9.99836 9.99837 9.99838 9.99895 9.99896 9.99897 9.99941 9.99942 9.99942 9.99974 9.99974 9.99975 9.99994 9.99994 9.99994 9.99994 9.99994 9.99995 59 58 57 56 55 54 56 52 48 44 40 36 32 28 24 4 5 6 9.99839 9.99840 9.99841 9.99842 9.99843 9.99844 9.99898 9.99898 9.99899 9.99960 9.99901 9.99902 9.99943 9.99944 9.99944 9.99975 9.99976 9.99976 9.99977 9.99977 9.99977 28 32 36 7 8 9 9.99945 9.99946 9.99940 9.99995 9.99995 9.99995 53 52 51 40 10 9.99845 9.99903 9.99947 9.99978 9.99995 50 20 44 48 52 11 12 13 9.99846 9.99847 9.99848 9.99904 9.99904 9.99905 9.99948 9.99948 9.99949 9.99949 9.99950 9.99951 9.99978 9.99979 9.99979 9.99996 9.99996 9.9999G 9.99996 9.99996 9.99996 49 48 47 46 45 44 16 12 8 56 +1 4 14 15 16 9.99850 9.99851 9.99852 9.99906 9.99907 9.99908 9.99979 9.99980 9.99980 4 +3 56 8 12 16 1? 18 19 9.99853 9.99854 9.99855 9.99909 9.99909 9.99910 9.99951 9.99952 9.99952 9.99981 9.99981 9.99981 9.99997 9.99997 9.99997 43 43 41 52 48 44 20 30 9.99856 9.99911 9.99953 9.99982 9.99997 40 40 24 28 32 21 22 33 9.99857 9.99858 9.99859 9.99912 9.99913 9.99913 9.99954 9.99954 9.99955 9.99982 9.99982 9.99983 9.99997 9.99997 9.99997 9.99998 9.99998 9.99998 39 38 37 36 35 34 36 32 28 36 40 44 24 25 26 9.99860 9.99861 9.99862 1 1 9.99914 9.99915 9.99916 9.99955 9.99956 9.99956 9.99983 9.99983 9.99984 24 20 . 16 48 52 56 27 28 29 9.99863 9.99864 9.99865 1 1 1 9.99917 9.99917 9.99918 9.99957 9.99958 9.99958 9.99984 9.99984 9.99985 9.99998 9.99998 9.99998 33 32 31 12 8 4 +3 30 9.99866 1 9.99919 9.99959 9.99985 9.99998 30 +2 4 8 12 31 32 33 9.99867 9.99868 9.99869 9.99920 9.99920 9.99921 9.99959 9.99960 9.99960 9.99985 9.99986 9.99986 9.99998 9.99999 9.99999 29 28 27 56' 52 48 16 20 24 34 35 36 9.99870 9.99871 9.99872 1 1 9.99922 9.99923 9.99923 9.99961 9.99961 9.99962 9.99986 9.99987 9.99987 9.99999 9.99999 9.99999 26 25 24 44 40 36 32 28 24 28 32 36 37 38 39 9.99873 9.99874 9.99875 1 1 1 9.99924 9.99925 9.99926 9.99962 9.99963 9.99963 9.99987 9.99988 9.99988 9.99999 9.99999 9.99999 23 22 31 40 40 9.99876 1 9.99926 9.99964 9.99988 9.99999 30 20 i48 52 41 42 43 9.99877 9.99878 9.99879 9.99927 9.99928 9.99929 9.99964 9.99965 9.99966 9.99989 9.99989 9.99989 9.99999 9.99999 9.99999 19 18 17 16 12 8 56 +3 4 44 45 46 9.99879 9.99880 9.99881 9.99929 9.99930 9.99931 9.99966 9.99967 9.99967 9.99989 9.99990 9.99990 0.00000 0.00000 0.00000 16 15 14 4 +1 56 8 12 16 47 48 49 9.99882 9.99883 9.99884 9.99932 9.99932 9.99933 9.99967 9.99968 9.99968 9.99990 9.99990 9.99991 0.00000 0.00000 0.00000 13 13 11 52 48 44 20 50 9.99885 9.99934 9.99969 9.99991 0.00000 10 40 24 28 32 51 52 53 9.99886 9.99887 9.99888 9.99934 9.99935 9.99936 9.99969 9.99970 9.99970 9.99991 9.99992 9.99992 0.00000 0.00000 0.00000 9 8 7 36 32 28 36 40 44 54 55 56 9.99889 9.99890 9.99891 1 1 9.99936 9.99937 9.99938 9.99971 9.99971 9.99972 9.99992 9.99992 9.99992 0.00000 0.00000 0.00000 6 5 4 24 20 16 48 52 56 57 58 59 9.99891 9.99892 9.99893 1 1 1 9.99938 9.99939 9.99940 9.99972 9.99973 9.99973 9.99993 9.99993 9.99993 0.00000 0.00000 0.00000 3 2 1 12 8 4 +4 60 9.99894 9.99940 9.99974 9.99993 0.00000 Cos. Cos. Cos. Cos. Cos. 4° Qh 16in 3° oh 12'"^ 2° Oh sm 1° Oh 4m 0° Qhom Log. Cosines. 1 TABLE IV NATURAL HAVERSINES AND LOGARITHMIC HAVERSINES 55901°— IS 4 49 Page 50] TABLE IV. Havereines. B ' 0^ 0^ 0° c OA 2m 0° W Oh 4m 1° (K U||^6"» 1° sr Oh8mZ°^ 60 Log.nav. Natnav. Log. nav. Nat, Hav. Log. Hav. Nat. Hav. ^Hpfav. Nat. Hav. Log. Hav. Nat Hav. -00 0.00000 5.27963 0.00002 5.88168 0.00008 6.23385 0.00017 6.48371 0.00030 S 1.72333 .00000 .29399 .00003 .88889 .00008 .23866 .00017 .48732 .00031 58 4+ 1 2.32539 .00000 .30811 .00003 .89604 .00008 .24345 .00018 .49092 .00031 56 6 2.67757 .00000 .32201 .00003 .90313 .00008 .24821 .00018 .49450 .00031 54 8+ 2 2.92745 0.00000 5.335G9 0.00003 5.91016 0.00008 6.25294 0.00018 6.49807 0.00031 52 10 3.12127 .00000 .34916 .00003 .91714 .00008 .25765 .00018 .50162 .00032 50 12-\- 3 3.279G3 .00000 .36242 .00003 .92406 .00008 .26233 .00018 .50516 .00033 48 U 3.41353 .00000 .37548 .00003 .93093 .00009 .26699 .00018 .50868 .00033 46 16+ 4 3.52951 0.00000 5.38835 0.00003 5.93774 0.00009 6.27162 0.00019 6.51219 0.00033 44 18 3.63182 .00000 .40103 .00003 .94450 .00009 .27623 .00019 .515G8 .00033 42 20+ 5 3.72333 .00000 .41352 .00003 .95121 .00009 .28081 .00019 .51916 .00033 40 22 3.80612 .00000 .42585 .00003 .95786 .00009 0.00009 .28537 .00019 .52263 .00033 38 24+ 6 3.88169 0.00000 5.43799 0.00003 5.96447 6.28991 0.00019 6.52608 0.00034 36 26 3.95122 .00000 .44997 .00003 .97102 .00009 29442 .00030 .52952 .00034 34 28+ 7 4.01559 .00000 .46179 .00003 .97753 .00010 .29891 .00030 .53295 .00034 32 SO 4.07551 .00000 .47345 .00003 .98399 .00010 .30337 .00030 .53636 .00034 SO S2+ 8 4.13157 0.00000 5.48496 0.00003 5.99040 0.00010 6.30781 0.00030 6.53976 0.00035 28 S4 .18423 .00000 .49631 .00003 5.99676 .00010 .31223 .00031 .54315 .00035 26 36+ 9 .23388 .00000 .50752 .00003 6.00308 .00010 .31663 .00031 .54652 .00035 24 S8 .28084 .00000 .51858 .00003 .00935 .00010 .32101 .00031 .54988 .00035 22 40+10 4.32539 0.00000 5.52951 0.00003 6.01557 0.00010 6.32536 0.00031 6.55323 0.00036 20 42 .36777 .00000 .54030 .00003 .02176 .00011 .32969 .00021 .55656 .00036 18 44+11 .40818 .00000 .55095 .00004 .02789 .00011 .33400 .00032 .55988 .00036 16 46 .44679 .00000 .56148 .00004 .03399 .00011 .33829 .00022 .56319 .00037 14 48+12 4.48375 0.00000 5.57189 0.00004 6.04004 0.00011 6.34256 0.00022 6.56649 0.00037 12 SO .51921 .00000 .58216 .00004 .04605 .00011 .34081 .00022 .56977 .00037 10 52+lZ .55328 .00000 .59232 .00004 .05202 .00011 .35103 .00033 .57304 .00037 8 54 .58606 .00000 .60236 .00004 .05795 .00011 .35524 .00033 .57630 .00038 6 56+U 4.61765 0.00000 5.61229 0.00004 6.06384 0.00013 6.35943 0.00033 6.57955 0.00038 4 58 4.64813 0.00000 5.62211 0.00004 6.06969 0.00013 6.36359 0.00033 6.58278 0.00038 2 23Ji 59m 23h 57m 23h 55m 2Sh 53^ 2Sh 5m B ' 0+15 Oh im 0° O' Oh sm 0° 30^ Oh sm 1° (K Oh 7m 1° 30^ Oh Qm 3° 0^ s 60 4.67757 0.00000 5.63181 0.00004 6.07550 0.00013 6.36774 •0.00033 6.58600 0.00039 S .70605 .00000 .64141 .00004 .08127' .00013 .37186 .00034 .58921 .00039 58 4+16 .73363 .00001 .65090 .00004 .08700 .00013 .37597 .00034 .59241 .00039 56 6 .76036 .00001 .66029 .00005 .09270 .00013 .38006 .00034 .59560 .09039 54 8+n 4.78629 0.00001 5.66958 0.00005 6.09836 0.00013 6.38412 0.00034 6.59878 0.00040 h2 10 .81147 .00001 .M877 .W787 .0000^ .10398 .00013 .38817 .^034 .60194 .00040 50 12+lS .83594 .00001 .OOOOfli.10956 .00013 .39220 .00035 .60509 .00040 48 14 .85973 .00001 .69687 .00005 .11511 .00013 .39622 .00025 .60823 .00041 46 16+19 4.88290 0.00001 5.70578 0.00005 6.12063 0.00013 6.40021 0.00025 6.61136 0.00041 4^ 18 .90546 .00001 .71460 .00005 .12611 .00013 .40418 .00035 .61448 .00941 42 20+20 .92745 .00001 .72332 .00005 .13155 .00014 .40814 .00026 .61759 .00041 40 22 .94890 .00001 .73197 .00005 .13696 .00014 .41208 .00026 .62068 .09043 38 24+21 4.96983 0.00001 5.74052 0.00006 6.14234 0.00014 6.41600 0.00026 6.62377 0.00042 36 26 4.99027 .00001 .74900 .00006 .14769 .00014 .41990 .00026 .62684 .00042 34 28+22 5.01024 .00001 .75739 .00006 .15300 .00014 .42379 .00037 .62991 .00043 32 SO .02976 .00001 .76570 .00006 .15828 .00014 .42766 .00037 .63296 .00043 30 S2+23 5.04885 0.00001 5.77394 0.00006 6.16353 0.00015 6.43151 0.00027 6.63600 0.00043 28 S4 .06753 .00001 .78209 .00006 .16874 .00015 .43534 .00037 .63903 .00044 26 56+24 .08581 .00001 .79017 .00006 .17393 .00015 .43916 .00037 .64205 .00044 24 S8^ .M"2 .00001 .79818 .00006 .17908 .00015 .44296 .00028 .64504 .00044 22 40+^ l^m 0.00001 5.8(1011 .8f397 0.00006 6.18421 0.00015 6.44675 0.00028 6.64806 0.00044 20 42 ^ JHP .00001 .00007 .18930 .00015 .45052 .00028 .65105 .00045 18 44+2^JI^3mi .00001 .82176 .00007 .19437 .00016 .45427 .00028 .65403 .00045 16 46 .17188 .00001 .82948 .00007 .19940 .00016 .45800 .00029 .65700 .00045 14 48+211 5.18812 0.00003 5.83713 0.00007 6.20441 0.00016 6.4G172 0.00029 6.65996 0.00046 12 60 .20406 .00003 .84472 .00007 .20938 .00016 .46543 .00029 .66291 .00046 10 52+2S .21971 .00003 ^224 .00007 .21433 .00016 .46911 .00029 .66585 .00046 8 54 .23508 .00003 ^^69 .00007 .21925 .00017 .47279 .00030 .66878 .00047 e 56+29 5.25019 0.00003MR709 0.00007 6.22415 0.00017 6.47644 0.00030 6.67170 0.00047 4 58 .26503 .OO0O^K7442 .00008 .22901 .00017 .48008 .00030 .67461 .00047 2 60+30 5.27^63 0.000i!Wr.88168 0.00008 6.23385 0.00017 6.48371 0.00030 6.67751 0.00048 2Sh 5Sm j 23h 56^ 2Sh 54m Oj]h S9m 2Sh 50m ] TABLE IV. [Page 51 1 Haversines. s ' Oh iom 2° 30^ o'^j^JH^r Qh 14m 3° 30^ 1 Qh 16m 4° 0^ Oh 18m 4° 30' s Log. Hav. Nat. Hav. Log. na^ BK. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Ilav. Log. Hav. Nat. Hav. 6.67751 0.00048 6.83584 0.00069 6.96970 0.00093 7.08564 0.00133 7.18790 0.00154 60 2 .68040 .00048 .83825 .00069 .97176 .00094 .08745 .00133 .18950 .00155 58 4+ 1 .68328 .00048 .84065 .00069 .97382 .00094 .08925 .00133 .19111 .00155 56 6 .68615 .00049 .84304 .00070 .97588 .00095 .09105 .00133 .19271 .00156 54 S+ 2 6.68901 0.00049 6.84543 0.00070 6.97793 0.00095 7.09284 0.00134 7.19430 0.00156 52 10 .69186 .00049 .84782 .00070 .97997 .00095 .09464 .00134 .19590 .00157 50 12+ 3 .69470 .00050 .85019 .00071 .98201 .00096 .09642 .00125 .19749 .00158 48 14 .69754 .00050 .85256 .00071 .98405 .00096 .09821 .00125 .19908 .00158 46 16-\- 4 6.70036 0.00050 6.85492 0.00073 6.98608 0.00097 7.09999 0.00126 7.20066 0.00159 44 18 .70318 .00050 .85728 .00073 .98811 .00097 .10177 .00126 .20225 .00159 42 20+ 5 .70598 .00051 .859G3 .00073 .99013 .00098 .10354 .00127 .20383 .00160 40 22 .70878 .00051 .86197 .00073 .99214 .00098 .10531 .00127 .20540 .00160 38 24+ 6 6.71157 0.00051 6.86431 0.00073 6.99416 0.00099 7.10708 0.00138 7.20698 0.00161 36 26 .71435 .00053 .86664 .00074 6.99616 .00099 .10884 .00138 .20855 .00162 34 2S+ 7 .71712 .00053 .86897 .00074 6.99817 .00100 .11060 .00139 .21012 .00162 32 SO .71988 .00053 .87129 .00074 7.00017 .00100 .11236 .00130 .21168 .00163 30 32+8 6.72263 0.00053 6.87360 0.00075 7.00216 0.00101 7.11411 0.00130 7.21325 0.00163 28 34 .72537 .00053 .87591 .00075 .00415 .00101 .11586 .00131 .21481 .00164 26 36+ 9 .72811 .00053 .87821 .00076 .00613 .00101 .11760 .00131 .21636 .00165 24 38 .73084 .00054 .88050 .00076 .00811 .00103 .11934 .00133 .21792 .00165 0.00166 22 20 ^0+10 6.73355 0.00054 6.88279 0.00076 7.01009 0.00103 7.12108 0.00133 7.21947 42 .73626 .00054 .88507 .00077 .01206 .00103 .12282 .00133 .22102 .00166 18 u+u .73896 .00055 .88735 .00077 .01403 .00103 .12455 .00133 .22256 .00167 16 46 .74166 .00055 .88962 .00078 .01599 .00104 .12627 .00134 .22411 .00168 14 48+n 6.74434 0.00056 6.89188 0.00078 7.01795 0.00104 7.12800 0.00134 7.22565 0.00168 12 50 .74702 .00056 .89414 .00078 .01990 .00105 .12972 .00135 .22718 .00169 10 52+13 .74969 .00056 .89639 .00079 .02185 .00105 .13144 .00135 .22872 .00169 8 54 .75235 .00057 .89864 .00079 0.00080 .02379 .00106 .13315 .00136 .23025 .00170 6 56+14 6.75500 0.00057 6.90088 7.02573 0.00106 7.13486 0.00136 7.23178 0.00171 4 58 6.75764 0.00057 6.90312 0.00080 7.02767 0.00107 7.13657 0.00137 7.23331 0.00171 2 231 49m 23h 47m 23^ 45m 23h4^m 23 h 41m 0+15 Oh lim 2° 30^ Oh ISm 3° 0^ Oh 15^ 3° 30' Oh 17m 4° 0' Oh 19m 4° 30^ s 60 6.76028 0.00058 6.^535 0.00080 7.02960 0.00107 7.13827 0.00137 7.23483 0.00173 2 .76290 .00058 .90757 .00081 .03153 .00108 .13997 .00138 .23635 .00173 58 4+16 .76552 .00058 .90979 .00081 .03345 .00108 .14167 .00139 .23787 .00173 56 6 .76814 .00059 .91200 .00083 .03537 00108 .14337 .00139 .23939 .00174 54 ^+17 6.77074 0.00059 6.91421 0.00083 7.03729 0.00109 7.14506 0.00140 7.24090 0.00174 52 10 .77334 .00059 ' .91641 .00083 .03920 .00109 .14674 , .00140 .24241 .00175 50 12+^ .77592 .00060 .91860 .00083 .04110 .00110 .14843 .00141 .24392 .00175 48 14 .77851 .00060 .92079 .00083 .04300 .00110 .15011 .00141 .24543 .00176 46 i6+19 6.78108 0.00060 6.92298 0.00084 7.04490 0.00111 7.15179 0.00143 7.24693 0.00177 44 18 .78364 .00061 .92516 .00084 .04680 .00111 .15346 .00143 .24843 .00177 42 20+^ .78620 .00061 .92733 .00085 .04869 .00113 .15513 .00143 .24993 .00178 40 22 .78875 .00061 .92950 6.93166 .00085 .05057 .00112 0.00113 .15680 .00143 .25143 .00178 38 24+^1 6.79129 0.00063 0.00085 7.05245 7.15846 0.00144 7.25292 0.00179 36 26 .79383 .00063 .93382 .00086 .05433 .00113 .16013 .00145 .25441 .00180 34 28+1S2 .79630 .00063 .93597 .00086 .05620 .00114 .16178 .00145 .25590 .00180 32 30 .79888 .00063 .93812 .00087 .05807 .00114 .16344 .00146 .25738 .00181 SO 32+^ 6.80139 0.00063 6.94026 0.00087 7.05994 0.00115 7.16509 0.00146 7.25886 0.00181 28 34 .80390 .00064 .94239 .00088 .06180 .00115 .16674 .00147 .26034 .00183 26 36+U .80640 .00064 .94453 .00088 .06366 .00116 .16839 .00147 .26182 .00183 24 38 .80889 .00064 .94665 .OOOSS .06551 .00116 0.00117 .17003 7.17167 .00148 .26330 .0018^ 0.00184 22 20 40+25 6.81137 0.00065 6.94877 0.00089 7.06736 0.00148 7.264^ .2663? 42 .81385 .00065 .95089 .00089 .06920 .00117 .17331 .00149 .00185 18 44+^ .81632 .00086 .95300 .00090 .07105 .00118 .17494 .00150 .26771 .00185 16 46 .81879 .C00G6 .95510 .00090 .07288 .00118 .17657 .00150 .26917 .00186 U 48+Z^ 6.82124 0.00066 6.95720 0.00091 7.07472 0.00119 7.17820 0.00151 7.27064 0.00186 12 50 .82369 .00067 .95930 .00091 .07655 .00119 .17982 .00151 .27210 .00187 10 5:^+28 .82614 .00067 .96139 .00091 .07837 .00120 .18144 .00153 .27355 .00188 8 54 .82857 .00067 .96347 .00093 .08019 .00130 .18306 .00153 .27501 .00188 6 56+39 6.83100 0.00068 6.96555 0.00093 7.08201 0.00121 7.18468 0.00153 7.27646 0.00189 4 58 .83342 .00068 .66763 .00093 .08383 .00121 .18629 .00154 .27791 .00190 2 6(7+30 6.83584 0.00069 6.96970 0.00093 7.08564 0.00133 7.18790 0.00154 7.27936 0.00190 23 h 48 m. 23h 46"* 23h 44^ 23h42r<^ 23 h 40'" Page 52] TABLE IV. Haversines. s ' 0Af0"»5°0' Oh tzr^ 5° 30'' Oft 24^" 6° 0' ...0Jkj?6™ 6° 30^ Oh 28^ 7° O' s Log. Hav Nat. Hav. Log. Hav. Nat. Hav. Log. Ilav. Nat. Hav. Lb^.Hav. Nat. Hav. Log. Hav. Nat. Hav. 7.27936 0.00190 7.36209 0.00230 7.43760 0.00274 7.50706 0.00321 7.57135 0.00373 60 o .28080 .00191 .36340 .00231 .43880 .00275 .50817 .00323 .57238 .00374 58 4+ 1 .28225 .00193 .36471 .00233 .44001 .00275 .50928 .00333 .57341 .00374 56 6 .28369 .00193 .36602 7.36733 .00333 0.00333 .44121 7.44241 .00276 0.00277 .51039 .00324 .57444 .00375 54 52 8+ 3 7.28513 0.00193 7.51149 0.00325 7.57547 0.00376 10 .28656 .00193 .36864 .00334 .44361 .90278 .51260 .00326 .57650 .00377 50 12+ 3 .28800 .00194 .36994 .00334 .44480 .00278 .51370 .00326 .57752 .00378 48 14 .28943 .00195 .37124 .00235 .44600 .00279 .51481 .00327 .57855 .00379 46 16+ 4 7.29086 0.00195 7.37254 0.00236 7.44719 0.00280 7.51591 0.00328 7.57957 0.00380 u 18 .29228 .00196 .37384 .00237 .44838 .00281 .51701 .00329 .58060 .00381 42 20+ 5 .29371 .00197 .37514 .00337 .44957 .00283 .51811 .00330 .58162 .00382 40 22 .29513 .00197 .37643 .00338 .45076 .00283 .51921 .00331 .58264 .00383 38 24+ 6 7.29655 0.00198 7.37773 0.00339 7.45194 0.00383 7.52030 0.00331 7.58366 0.00383 36 26 .29797 .00199 .37902 .00339 .45313 .00384 .52140 .00332 .58467 .00384 34 28+ 7 .29938 .00199 .38030 .00340 .45431 .00385 .52249 .00333 .58569 .00385 32 SO .30079 .00200 .38159 .00341 .45549 .00385 .52358 .00334 .58670 .00386 30 S2+ 8 7.30220 0.00201 7.38288 0.00341 7.45667 0.00386 7.52467 0.00335 7.58772 0.00387 28 S4 .30361 .00301 .38416 .00343 .45785 .00387 .52576 .00336 .58873 .00388 26 se+ 9 .30502 .00302 .38544 .00343 .45903 .00288 .52685 .00336 .58974 .00389 24 S8 .30642 .00203 .38672 .00344 .46020 .00289 .52794 .00337 .59075 .00390 22 40+10 7.30782 0.00203 7.38800 0.00244 7.46138 0.00289 7.52902 0.00338 7.59176 0.00391 20 42 .30922 .00304 .38927 .00345 .46255 .00290 .53011 .00339 .59277 .00393 18 44+\\ .31062 .00304 .39054 .00246 .46372 .00291 .53119 .00340 .59378 .00392 16 46 .31201 .00205 .39182 .00347 .46489 .00393 .53227 .00341 .59478 .00393 14 48+i2 7.31340 0.00306 7.39309 0.00347 7.46605 0.00393 7.53335 0.00341 7.59579 0.00394 12 50 .31479 .00266 .39435 .00348 .46722 .00393 .53443 .00343 .59679 .00395 10 52+lZ .31618 .00207 .39562 .00349 .46838 .00394 .53550 .00343 .59779 .00396 8 54 .31757 .00308 .39688 .00349 .46955 .00395 .53658 .00344 .59879 .00397 6 56+14 7.31895 0.00208 7.39815 0.00350 7.47071 0.00396 7.53706 0.00345 7.59979 0.00398 4 58 7.32033 6.00309 7.39941 0.00251 7.47187 0.00396 7.53873 0.00346 7.60079 0.00399 2 23T^ 39^ 23^ ^7™ 23 h 35^ 23»' 33>n f-SftJim 8 ' 0+15 0^21r'*5°0' OA 23-^ 5° 30^ Oft 25"^ 6° 0^ Oft 27^ 6° W Oft 29^ 7° 0' 3 60 7.32171 6.00310 7.40067 0.00353 7.47302 0.00397 7.53980 0.00347 7.60179 0.00400 f .32309 .00310 .40192 .00352 .47418 .00398 .54087 .00347 .60279 .00401 58 4+16 .32446 .00311 .40318 .00253 .47533 .00399 .54194 .00348 .60378 .09403 56 6 ,32583 .00213 .40443 .00254 .47649 .00300 .54301 .00349 .60478 .00403 54 5+17 7.32720 0.00313 7.40568 0.00255 7.47764 0.00300 7.54407 0.00350 7.60577 0.00403 52 10 .32857 .00313 .40693 .00255 .47879 .00301 .54514 .00351 .60676 .00404 50 12+1'i .32994 .00314 .40818 .00256 .47994 .00303 .54620 .00352 .60775 .00405 48 14 .33130 .00314 .40943 .00357 .48109 .00303 .54727 .00353 .60874 .00406 46 16+19 7.33266 0.00315 7.41067 0.00357 7.48223 0.00304 7.54833 0.00353 7.60973 0.00407 44 18 .33402 .00316 .41191 .00358 .48337 .00304 .54939 .00354 .61072 .00408 42 20+2(i .33538 .00316 .41315 .00359 .48452 .00305 .55045 .00355 .61170 .00409 40 22 .33673 .00217 .41439 .00360 .48566 .00306 .55150 .00356 .61269 7.61367 .00410 38 24+n 7.33809 0.00218 7.41563 0.00360 7.48680 0.00307 7.55256 0.00357 0.00411 36 26 .33944 .00218 .41686 .00361 .48794 .00308 .55361 .00358 .61466 .00413 34 28+n .34079 .00219 .41810 .00363 .48907 .00308 .55467 .00359 .61564 .00413 32 SO .34213 .00230 .41933 .00363 .49021 .00309 .55572 .00360 .61662 .00414 30 32+ZS 7.34348 0.00331 7.42056 0.00363 7.49134 0.00310 7.55677 0.00360 7.61760 0.00415 28 S4 .34482 .00331 .42179 .00364 .49247 .00311 .55782 .00361 .61858 .00416 26 S6+24: .34616 .00333 .42301 .00265 .49360 .00313 .55887 .00362 .61955 .00416 24 S8 .34750 .00323 .42424 .00266 .49473 .00312 .55992 .00363 .62053 .00417 22 40+35 7.34884 0.00233 7.42546 0.00266 7.49586 0.00313 7.56096 0.00364 7.62151 0.00418 20 42 .35017 .00334 .42668 .00267 .49699 .00314 .56201 .00365 .62248 .00419 18 44+26 .35150 .00335 .42790 .00368 .49811 .00315 .56305 .00366 .62345 .00430 16 46 .35283 .00335 .42912 .00389 .49923 .00316 .56409 .00367 .62442 .00431 14 48+21t 7.35416 0.00336 7.43034 0.00369 7.50036 0.00316 7.56513 0.00367 7.62540 0.00433 12 50 .35549 .00337 .43155 .00370 .50148 .00317 .56617 .00368 .62666 .00433 10 52+28 .35681 .00337 .43277 .00371 .50259 .00318 .56721 .00369 .62733 .00434 8 54 .35813 .00338 .43398 7.43519 .00373 .50371 .00319 .56825 .00370 .62830 .00435 6 4 56+29 7.35945 0.00339 0.00373 7.50483 0.00330 7.56928 0.00371 7.62927 0.00426 58 .36077 .00339 .43639 .00273 .50594 .00331 .57032 .00372 .63023 .00427 2 60+30 7.36209 0.00330 7.43760 0.00274 7.50706 0.00321 7.57135 0.00373 7.63120 0.00428 23 h 38^ 23^ 36"^ 23h 34"^ 23'' 32"i g5ft .SO" 1 TABLE IV. [Page 53 Haversines. s ' Qh 30^'^ 7° 30^ Oh, S2m 8° 0' Oh 34^ 8° 30' Oft 56'" 9° O' 1 Oft 55'" 9° SO' | 3 Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. 7.63120 0.0043S 7.68717 0.00487 7.73974 0.00549 7.78929 0.00616 7.83615 0.00686 60 f .63216 .00429 .68807 .00488 .74059 .00550 .79009 .00617 .83691 .00687 68 4+ 1 .63312 .00430 .68897 .00489 .74143 .00551 .79089 .00618 .83767 .00688 66 6 .63408 .00431 .68987 .00490 .74228 .00552 .79169 .00619 .83842 .00689 64 8+ % 7.63504 0.00432 7.69077 0.00491 7.74313 0.00554 7.79249 0.00620 7.83918 0.00691 62 10 .63600 .00433 .69167 .00492 .74398 .00555 .79329 .00621 .83994 .00692 60 12+ 3 .63696 .00433 .69257 .00493 .74482 .00556 .79409 .00622 .84070 .00693 48 U .63792 .00434 .G9347 .00494 .74567 .00557 .79489 .00624 .84145 .00694 46 16+ 4 7.63887 0.00435 7.69437 0.00495 7.74651 0.00558 7.79568 0.00625 7.84221 0.00695 U 18 .63983 .00436 .69526 .00496 74735 .00559 .79648 .00626 .84296 .00697 42 20+ 5 .64078 .00437 .69616 .00497 .74819 .00560 .79728 .00627 .84372 .00698 40 22 .64173 .00438 .69705 o00498 .74904 .00561 .79807 .00628 .84447 .00699 38 24+ 6 7.64269 0.00439 7.69794 0.00499 7.74988 0.00562 7.79886 0.00629 7.84522 0.00700 36 26 .64364 .00440 .69883 .00500 .75072 .00563 .79966 .00630 .84597 .00701 34 28+ 7 .64458 .00441 .69972 .00501 .75155 .00564 .80045 .00632 .84672 .00703 32 SO .64553 .00442 .70061 .00502 .75239 .00565 .80124 .00633 .84747 .00704 30 32+ 8 7.64648 0.00443 7.70150 0.00503 7.75323 0.00567 7.80203 0.00634 7.84822 0.00705 28 54 .64743 .00444 .70239 .00504 .75407 .00568 .80282 .00635 .84897 .00706 26 56+ 9 .64837 .00445 .70328 .00505 .75490 .00569 .80361 .00636 .84972 .00707 24 38 .64932 .00446 .70416 .00506 .75574 .00570 .80440 .00637 .85047 .00709 22 40+10 7.65026 0.00447 7.70505 0.00507 7.75657 0.00571 7.80519 0.00639 7.85122 0.00710 20 42 .65120 .0044S .70593 .00508 .75740 .00572 .80598 .00640 .85196 .00711 18 44+n .65214 .00449 .70682 .00509 .75824 .00573 .80677 .00641 .85271 .00712 16 46 .65308 .00450 .70770 .00510 .75907 .00574 .80755 .00642 .85346 .00714 14 48+n 7.65402 0.00451 7.70858 0.00511 7.75990 0.00575 7.80834 0.00643 7.85420 0.00715 12 60 .65496 .00452 .70946 .00512 .76073 .00576 .80912 .00644 .85494 .00716 10 5^+13 .65590 .00453 .71034 .00513 .78156 .00578 .80991 .00646 .85569 .00717 8 64 .65683 .00454 .71122 .00514 .76239 .00579 .81069 .00647 .85643 .00719 6 66+14: 7.65777 0.00455 7.71210 0.00515 7.76321 0.00580 7.81147 0.00648 7.85717 0.00720 4 58 7.65870 0.00456 7.71298 0.00516 7.76404 0.00581 7.81225 0.00649 7.85791 0.00721 2 23k 29-'» 23h 27 m 55 A 25m 2Sh 2Sm 23h 21m 8 ' 0+15 0h31r»7°Z0' Oh 33m 8° O' Oh S5m 8° 30' Oh 37 m 9° 0' Oh 39m 9° 30' s 60 7.65964 0.00457 7.71385 0.00517 7.76487 0.00582 7.81303 0.00650 7.85866 0.00722 2 .66057 .00458 .71473 .00518 .76569 .00583 .81382 .00651 .85940 .00723 68 ■^+16 .66150 .00459 .71560 .00520 .76652 .00584 .81459 .00653 .86014 .00725 66 6 .66243 .00460 .71648 .00521 .76734 .00585 .81537 .00654 .86087 .00726 54 62 8+17 7.66336 0.00461 7.71735 0.00522 7.76816 0.00586 7.81615 0.00655 7.86161 0.00727 10 .66429 .00462 .71822 .00523 .76898 .00587 .81693 .00656 .86235 .00728 60 12+18 .66521 .00463 .71909 .00524 .76981 .00589 .81771 .00657 .86309 .00730 48 14 .66614 .00464 .71996 .00525 .77063 .00590 .81848 .00658 .86382 .00731 46 16+19 7.66706 0.00465 7.72083 0.00526 7.77145 0.00591 7.81926 0.00660 7.86456 0.00732 44 18 .66799 .00466 .72170 .00527 .77227 .00592 .82003 .00661 .86530 .00733 42 20+20 .66891 .00467 .72257 .00528 .77308 .00593 .82081 .00662 .86603 .00735 40 22 .66983 .00468 .72343 .00529 .77390 .00594 0.00595 .82158 7.82235 .00663 .86676 .00736 0.00737 38 36 24+21 7.67075 0.00469 7.72430 0.00530 7.77472 0.00664 7.86750 26 .67167 .00470 .72516 .00531 .77553 .00596 .82313 .00665 .86823 .00738 34 28+HZ .67259 .00471 .72603 .00532 .77635 .00598 .82390 .00667 .86896 .00740 32 30 .67351 .00472 .72689 .00533 .77716 .00599 .82467 .00668 .86969 .00741 30 32+2S 7.67443 0.00473 7.72775 0.00534 7.77798 0.00600 7.82544 0.00669 7.87042 0.00742 28 34 .67535 .00474 .72801 .00535 .77879 .00601 .82621 .00670 .87115 .00743 26 56+24 .67626 .00475 .72948 .00536 .77960 .00602 .82698 .00671 .87188 .00745 24 38 .67718 .00476 .73034 .00537 .78041 .06603 .82774 .00673 .87261 .00746 22 40+25 7.67809 0.00477 7.73119 0.00539 7.78122 0.00604 7.82S51 0.00674 7.87334 0.00747 20 42 .67900 .00478 .73205 .00540 .78203 .00605 .82928 .00675 .87407 .00748 18 44+26 .67991 .00479 .73291 .00541 .78284 .00607 .83004 .00676 .87480 .00750 16 46 .68082 .00480 .73377 .00542 .78365 .00608 .83081 .00677 .87552 .00751 14 48+27 7.68173 0.00481 7.73462 0.00543 7.78446 0.00609 7.83157 0.00679 7.87625 0.00752 12 50 .68264 .00482 .73548 .00544 .78526 .00610 .83234 .00680 .87697 .00753 10 52 +2S .68355 .00483 .73633 .00545 .78607 .00611 .83310 .00681 .87770 .00755 8 54 .68445 .00484 .73718 .00546 .78688 .00612 .83386 .00682 .87842 .00756 6 66+29 7.68536 0.00485 7.73803 0.00547 7.78768 0.00613 7.83463 0.00683 7.87915 0.00757 4 58 .68627 .00486 .73889 .00548 .78848 .00614 .83539 .00685 .87987 .00758 i 60+30 7.68717 0.00487 7.73974 0.00549 7.78929 0.00616 7.83615 0.00686 7.88059 0.00760 2Sh 28-^ 23h 26m 2Sh 24m 2Sh 22m 23h 20m Page 54] TABLE IV. Haversinea. s ' o "4+ 1 6 Oh 40^ 10° 0' Oh 42m 10° 30' Oh 44m 11° 0' Oh 46m 11° 30' Oh 48m 13° O' s Log. Ilav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. 7.8S059 .88131 .88203 .88276 0.00760 .00761 .00763 .00763 7.92286 .92354 .92423 .92492 0.00837 .00839 .00840 .00841 7.96315 .96380 .96446 .96511 0.00919 .00930 .00931 .00933 8.00103 .00226 .00289 .00351 0.01004 .01005 .01007 .01008 8.03847 .03907 .03967 .04027 0.01093 .01094 .01096 .01097 60 58 56 54 8+ 2 10 12+ 3 14 16+ 4 IS 20+ 5 22 7.88348 .88419 .88491 .88563 7.88635 .88707 88778 .88850 0.00765 .00766 .00767 .00768 0.00770 .00771 .00773 .00774 7.92560 .92629 .92697 .92766 7.92834 .92902 .92970 .93039 0.00843 .00844 .00845 .00847 0.00848 .00849 .00851 .00853 7.96577 .96642 .96707 .96773 7.96838 .96903 .96968 .97033 0.00934 .00936 .00937 .00928 0.00930 .00931 .00933 .00934 8.00414 .00476 .00539 .00601 8.00664 .00726 .00788 .00851 0.01010 .01011 .01013 .01014 0.01015 .01017 .01018 .01030 8.04087 .04147 .04207 .04267 8.04326 .04386 .04446 .04506 0.01099 .01100 .01102 .01103 0.01105 .01106 .01108 .01109 52 50 48 46 44 42 40 38 36 34 32 30 28 26 24 22 24+ 26 28+ 7 30 32+ 8 34 36+ 9 38 7.88921 .88993 .89064 .89135 7.89207 .89278 .89349 .89420 0.00775 .00776 .00777 .00779 0.00780 .00781 .00783 .00784 7.93107 .93175 .93243 .93311 7.93379 .93447 .93514 .93582 0.00853 .00855 .00856 .00857 0.00859 .00860 ,00861 .00863 7.97098 .97163 .97228 .97293 7.97358 .97423 .97478 .97552 0.00935 .00937 .00938 .00940 0.00941 .00943 .00944 .00945 8.00913 .00975 .01037 .01099 8.01161 .01223 .01285 .01347 0.01031 .01033 .01024 .01026 0.01027 .01029 .01030 .01032 8.04565 .04625 .04684 .04744 8.04803 .04863 .04922 .04981 0.01111 .01112 .0U14 .01115 0.01117 .01118 .0U20 .01122 40+10 42 44+11 46 48+12 50 52+13 B4 7.89491 .89562 .89633 .89704 7.89775 .89846 .89916 .89987 0.00785 .00786 .00788 .00789 0.00790 .00793 .00793 .00794 7.93650 .93717 .93785 .93852 7.93920 .93987 .94055 .94122 0.00864 .00865 .00867 .00868 0.00869 .00871 .00873 .00873 7.97617 .97681 .97746 .97810 7.97875 .97939 .98003 .98068 0.00947 .00948 .00949 .00951 0.00953 .00954 .00955 .00956 8.01409 .01471 .01532 .01594 8.01656 .01717 .01779 .01840 0.01033 .01034 .01036 .01037 0.01039 .01040 .01042 .01043 8.05041 .05100 .05159 .05218 8.05277 .05336 .05395 .05454 0.01133 .01125 .01126 .01128 0.01129 .01131 .01132 .01134 20 IS 16 14 12 10 8 6 56+14 58 7.90057 7.90128 0.00795 0.00797 7.94189 7.94257 0.00875 0.00876 7.98132 7.98196 0.00958 0.00959 8.01902 8.01963 0.01045 0.01046 8.05513 8.05572 0.0U35 0.0U37 4 2 23!^ 19^ 23h 17m 23h 15m 2Sh 13m 2Sh 11m 0+15 i -♦+16 6 Oh 41m 10° r Oh4Sm 10° 30' Oh 45m 11° O' Oh 47m 11° 30^ Oh 49m 12° O' s 7.90198 .90269 .90339 .90409 0.00798 .00799 .00801 .00802 7.94324 .94391 .94458 .94525 0.00877. .00879 .00880 .00882 7.98260 .98325 .98389 .98453 0.00961 .00963 .00964 .00965 8.02025 .02086 .02148 .02209 0.01048 .01049 .01051 .01052 8.05631 .05690 .05749 .05808 0.01138 .01140 .01142 .01143 60 58 56 54 8+11 10 12+18 14 16+10 18 20+20 22 7.90480 .90550 .90620 .90690 7.90760 .90830 .90900 .90970 0.00803 .00804 .00806 .00807 0.0080S .00810 .00811 .00813 7.94592 .94659 .94726 .94792 7.94859 .94926 .94992 .95059 0.00883 .00884 .00886 .00887 0.00888 .00890 .00891 .00892 7.98517 .98581 .98644 .98708 7.98772 .98836 .98899 .98963 0.00966 .00968 .00969 .00971 0.06973 .00974 .00975 .00976 8.02270 .02331 .02392 .02453 8.02515 .02576 .02637 .02697 0.01054 .01055 .01057 .01058 0.01060 .01061 .01063 .01064 8.05866 .05925 .05984 .06042 8.06101 .06159 .06218 .06276 0.01145 .01146 .01148 .01149 0.01151 .01152 .01154 .01155 52 50 48 46 U 42 40 38 24+21 26 28+22 SO S2+23 34 56+24 38 7.91039 .91109 .91179 .91248 7.91318 .91387 .91457 .91526 0.00814 .00815 .00816 .00817 0.00819 .00820 .00821 .00833 7.95126 .95192 .95259 .95325 7.95391 .95458 .95524 .95590 0.00894 .00895 .00897 .00898 0.00899 .00901 .00902 .00903 7.99027 99090 .99154 .99217 7.99281 .99344 .99407 .99470 0.00978 .00979 .00981 .00983 0.00984 .00985 .00986 .00988 8.02758 .02819 .02880 .02941 8.03001 .03062 .03123 .03183 0.01066 .01067 .01089 .01070 0.01072 .01073 .01075 .01076 8.06335 .06393 .06451 .06510 8.06568 .06626 .06684 .06742 0.01157 .01159 .01160 .01162 0.01163 .01165 .01166 .01168 36 34 32 SO 28 26 24 22 40+25 42 44+20 46 48+21 50 52+28 54 7.91596 .91665 .91734 .91803 7.91872 .91941 .92010 .92079 0.00834 .00835 .00837 .00838 0.00839 .00831 .00833 .00833 7.95656 .95722 .95788 .95854 7.95920 .95986 .96052 .96118 0.00905 .00906 .00908 .00909 0.00910 .00912 .00913 .00914 7.99534 .99597 .99660 .99723 7.99786 .99849 .99912 7.99975 0.00989 .00991 .00993 .00994 0.00995 .00997 .00998 .00999 8.03244 .03304 .03365 .03425 8.03486 .03546 .03606 .03666 0.01078 .01079 .01081 .01082 0.01084 .01085 .01087 .01088 8.06800 .06859 .06917 .06975 8.07032 .07090 .07148 .07206 0.01170 .01171 .01173 .01174 0.01176 .01177 .01179 .01180 20 18 16 14 12 10 8 6 56+39 58 60+30 7.92148 .92217 7.92286 0.00835 .00836 0.00837 7.96183 .96249 7.96315 0.00916 .00917 0.00919 8.00038 .00100 8.00163 0.01001 .01003 0.01004 8.03727 .03787 8.03847 0.01090 .01091 0.01093 8.07264 .07322 8.07379 0.01183 .01184 0.01185 4 2 23 h 18m 23h 16m 23h 14m 23h 12m 23h 10m TxVBLE IV. [Page 65 Haversinea. s ' Ofe 50r^ 13° 30' Qh 52^ 13° 0' Oft 5-^'" 13° 30' Oft 56"» 14° 0' Oft 5 2Sh Im B ' 0+15 Oh 51m 12° SO' Oft 55'" 13° r Oft 55^ 13° 30' Oft 57 m 14° 0' Qh 59^ 14° 30' s 60 8.09092 0.01233 8.12419 0.01331 8.15622 0.01433 8.18709 0.01538 8.21688 0.01648 2 .09149 .01234 .12473 .01333 .15674 .01435 .18759 .01540 .21737 .01650 58 4+16 .09205 .01236 .12528 .01334 .15726 .01436 .18810 .01542 .21785 .01651 56 6 .09262 .01338 .12582 .01336 .15779 .01438 .18860 .01544 .21834 .01653 54 59. 8+11 8.09318 0.01239 8.12636 0.01338 8.15831 0.01440 8.18910 0.01546 8.21883 0.01655 10 .09374 .01241 .12691 .01339 .15883 .01442 .18961 .01547 .21932 .01657 50 12+19> .09431 .01343 .12745 .01341 .15935 .01443 .19011 .01549 .21980 .01659 48 14 .09487 .01344 .12799 .01343 .15987 .01445 .190G2 .01551 .22029 .01661 46 16+1^ 8.09543 0.01346 8.12853 0.01344 8.16040 0.01447 8.19112 0.01553 8.22077 0.01663 44 18 .09600 .01247 .12907 .01346 .16092 .01448 .19162 .01555 .22126 .01664 4^. 20+20 .09656 .01249 .12961 .01348 .16144 .01450 .19212 .01556 .22175 .01666 40 22 .09712 .01251 .13015 .01349 .16196 .01452 .19263 8.19313 .01558 0.01560 .22223 .01668 38 36 24+21 8.09768 0.01252 8.13069 0.01351 8.16248 0.01454 8.22272 0.01670 26 .09824 .01254 .13123 .01353 .16300 .01455 .19363 .01563 .22320 .01672 34 28+22 .09880 .01255 .13177 .01354 .10352 .01457 .19413 .01564 .22368 .01674 39 SO .09936 .01357 .13231 .01356 .16404 .01459 .19463 .01565 .22417 .01676 30 5^+23 8.09992 0.01359 8.13285 0.01358 8.16456 0.01461 8.19513 0.01567 8.22465 0.01677 28 34 .10048 .01360 .13339 .01360 .10508 .01463 .19563 .01509 .22514 .01679 96 36+U .10104 .01262 .13392 .01361 .16559 .01464 .19613 .01571 .22562 .01681 H 38 .10160 .01264 .13446 .01363 .16611 .01466 .19663 .01573 .22610 .01683 22 40+25 8.10216 0.01265 8.13500 0.01365 8.16603 0.01468 8.19713 0.01574 8.22658 0.01685 90 42 .10271 .01267 .13554 .01366 .16715 .01469 .19763 .01576 .22707 .01687 18 44+26 .10327 .01268 .13607 .01368 .16766 .01471 .19813 .01578 .22755 .01689 16 46 .10383 .01370 .13661 .01370 .16818 .01473 .19863 .01580 .22803 .01691 14 48+21 8.10439 0.01272 8.13714 0.01371 8.16870 0.01475 8.19913 0.01582 8.22851 0.01692 1?. 50 .10494 .01273 .13768 .01373 .16921 .01476 .19963 .01584 .22899 .01694 10 52+2% .10550 .01375 .13822 .01375 .16973 .01478 .20012 .01585 .22947 .01696 8 54 66+29 .10605 .01377 .13875 .01376 .17024 8.17076 .01480 0.01483 .20062 8.20112 .01587 .22996 .01698 6 4 8.10661 0.01278 8.13928 0.01378 0.01589 8.23044 0.01700 58 .10716 .01280 .13982 .01380 .17127 .01483 .20162 .01591 .23092 .01702 ?. 60+30 8.10772 0.01282 8.14035 0.01383 8.17179 0.01485 8.20211 0.01593 8.23140 0.01704 23h S'" 1 23^ 6^ 1 23h 4"^ 1 foft 2™ fjft 0^ 1 Page 56] TABLE IV. Haversines. s Ih Om 15° 0' Ihlm 15° 15' j Ih 2m 15° W IhSm 15° 4.5' lh4ml(i°0' s Log. Ilav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. 1 2 S 8.23140 .23164 .23188 .23212 .01704 .01705 .01706 .01707 8.24567 .24591 .24614 .24638 .01761 .01763 .01763 .01764 8.25971 .25994 .26017 .26040 .01818 .01819 .01830 .01831 8.27352 .27375 .27398 .27420 .01877 .01878 .01879 .01880 8.28711 .28734 .28756 .28779 .01937 .01938 .01939 .01940 60 59 58 57 + r 5 6 7 8.23235 .23259 .23283 .23307 .01707 .01708 .01709 .01710 8.24661 .24685 .24708 .24732 .01764 .01765 .01766 .01767 8.260G4 .26087 .26110 .26133 .01833 .01823 .01824 .01825 8.27443 .27466 .27489 .27512 .01881 .01882 .01883 .01884 8.28801 .28823 .28846 .28868 .01941 .01942 .01943 .01944 56 55 54 53 + 3^ 9 10 11 8.23331 .23355 ,23379 .23403 .01711 .01713 .01713 .01714 8.24755 .24779 .24803 .24826 .01768 .01769 .01770 .01771 8.26156 .26179 .26203 .26226 .01826 .01827 .01828 .01829 8.27534 .27557 .27580 .27603 .01885 .01886 .01887 .01888 8.28891 .28913 .28936 .28958 .01945 .01946 .01947 .01948 52 51 50 49 + 3' 13 u 15 8.23427 .23451 .23475 .23499 .01715 .01716 .01717 .01718 8.24850 .24873 .24897 .24920 .01773 .01773 .01774 .01775 8.26249 .26272 .26295 .26318 .01830 .01831 .01832 .01833 8.27626 .27648 .27671 .2-7694 .01889 .01890 .01891 .01892 8.28980 .29003 .29025 .29048 .01949 .01950 .01951 .01952 48 47 46 45 + 4' 17 18 19 8.23523 .23546 .23570 .23594 .01719 .01720 .01731 .01733 8.24944 .24967 .24991 .25014 .01776 .01777 .01778 .01779 8.26341 .26364 .26388 .26411 .01834 .01835 .01836 .01837 8.27717 .27739 .27762 .27785 .01893 .01894 .01895 .01896 8.29070 .29092 .29115 .29137 .01953 .01954 .01955 .01956 U 43 42 41 + 5' 21 22 23 8.23618 .23642 .23666 .23690 .01733 .01734 .01734 .01725 8.25037 .25061 .25084 .25108 .01780 .01781 .01782 .01783 8.26434 .26457 .26480 .26503 .01838 .01839 .01840 .01841 8.27807 .27830 .27853 .27876 .01897 .01898 .01899 .01900 8.29159 .29182 .29204 .29226 .01957 .01958 .01959 .01960 40 39 38 37 + 6' 25 26 27 8.23713 .23737 .23761 .23785 .01736 .01737 .01738 .01739 8.25131 .25155 .25178 .25202 .01784 .01785 .01786 .01787 8.26526 .26549 .26572 .26595 .01842 .01843 .01844 .01845 8.27898 .27921 .27944 .27966 .01901 .01902 .01903 .01904 8.29249 .29271 .29293 .29316 .01961 .01962 .01963 .01964 36 35 34 33 + r 29 SO 31 8.23809 .23832 .23856 .23880 .01730 .01731 .01733 .01733 8.25225 .25248 .25272 .25295 .01788 .01789 .01789 .01790 8.26618 .26641 .26664 .26687 .01846 .01847 .01848 .01849 8.27989 .28012 .28034 .28057 .01905 .01906 .01907 .01908 8.29338 .29360 .29383 .29405 .01965 .01966 .01967 .01968 32 SI 30 29 + 8' S3 S4 35 8.23904 .23928 .23951 .23975 .01734 .01735 .01736 .01737 8.25319 .25342 .25365 .25389 ,01791 .01793 .01793 .01794 8.26710 .26733 .26756 .26779 .01850 .01851 .01853 .01853 8.28080 .28102 .28125 .28147 .01909 .01910 .01911 .01913 8.29427 .29449 .29472 .29494 .01969 .01970 .01971 .01972 28 27 26 25 + 9^ S7 S8 39 8.23999 .24022 .24046 .24070 .01738 .01739 .01740 .01741 8.25412 .25435 .25459 .25482 .01795 .01796 .01797 .01798 8.26802 .26825 .26848 .26871 .01854 .01855 .01856 .01857 8.28170 .28193 .28215 .28238 .01913 .01914 .01915 .01916 8.29516 .29539 .29561 .29583 .01973 .01974 .01975 .01976 24 23 22 21 + W 41 42 43 8.24094 .24118 .24141 .24165 .01743 .01743 .01743 .01744 8.25505 .25529 .25552 .25575 .01799 .01800 .01801 .01802 8.26894 .26917 .26940 .26963 .01858 .01859 .01860 .01861 8.28260 .28283 .28306 .28328 .01917 .01918 .01919 .01930 8.29605 .29628 .29650 .29672 .01977 .01978 .01979 .01980 20 19 18 17 16 15 U 13 + 11' 45 46 47 8.24189 .24212 .24236 .24260 .01745 .01746 .01747 .01748 8.25599 .25622 .25645 .25669 .01863 .01804 .01805 .01806 8.26986 .27009 .27032 .27055 .01861 .01862 .01863 .01864 8.28351 .28373 .28396 .28418 .01931 .01923 .01923 .01924 8.29694 .29716 .29739 .29761 .01981 .01982 .01983 .01984 + 13' 49 50 51 8.24283 .24307 .24331 .24354 .01749 .01750 .01751 .01752 8.25692 .25715 .25738 .25762 .01807 .01808 .01809 .01810 8.27078 .27100 .27123 .27146 .01865 .01866 .01867 .01868 8.28441 .28464 .28486 .28509 .01925 .01926 .01927 .01938 8.29783 .29805 .29827 .29850 .01985 .01986 .01987 .01988 12 11 10 9 + 13' 53 64 65 8.24378 .24402 .24425 .24449 .01753 .01754 .01755 .01756 8.25785 .25808 .25831 .25855 .01811 .01813 .01813 .01814 8.27169 .27192 .27215 .27238 .01869 .01870 .01871 .01872 8.28531 .28554 .28576 .28599 .01939 .01930 .01931 .01932 8.29872 .29894 .29916 .29938 .01989 .01990 .01991 .01992 8 7 6 5 + 14' 57 58 59 8.24473 .24496 .24520 .24543 .01757 .01758 .01759 .01760 8.25878 .25901 .25924 .25948 .01815 .01816 .01817 .01818 8.27261 .27283 .27306 .27329 .01873 .01874 .01875 .01876 8.28621 .28644 .28666 .28689 .01933 .01934 .01935 .01936 8.29960 .29982 .30005 .30027 .01993 .01994 .01995 .01997 4 S 2 1 + 15' 8.24567 .01761 8.25971 .01818 8.27352 .01877 8.28711 .01937 8.30049 .01998 22h69^ 22f^ 58 m 22^ 57 m 22^ 56"> 22 h 55^ TABLE IV. [Page 57 Haversines. s ik 5m 16° 15' Ih 6m 16° 30' ift7"»16°45' IhS^lTQ' Ih 9m 17° 15' s Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. 1 2 S 8.30049 .30071 .30093 .30115 .01998 .01999 .03000 .03001 8.31366 .31388 .31410 .31431 .03059 .03060 .03061 .03063 8.32663 .32684 .32706 .32727 .03131 .03133 .03124 .03135 8.33940 .33962 .33983 .34004 .03185 .03186 .03187 .03188 8.35199 .35220 .35241 .35261 .03349 .03250 .03351 .03352 60 59 68 67 + r 5 6 7 8.30137 .30159 .30182 .30204 .03003 .03003 .03004 .03005 8.31453 .31475 .31497 .31518 .03063 .03064 .03065 .03066 8.32749 .32770 .32792 .32813 .03136 .03137 .03138 .03139 8.34025 .34046 .34067 .34088 .03189 .03190 .03191 .03193 8.35282 .35303 .35324 .35345 .03353 .03254 .02255 .03357 66 65 64 63 + 2' 9 10 11 8.30226 .30248 .30270 .30292 .02006 .03007 .03008 .03009 8.31540 .31562 .31584 .31605 .02067 .03068 .02069 .03070 8.32834 .32856 .32877 .32899 .03130 .03131 .03133 .03133 8.34109 .34130 .34152 .34173 .03193 .03194 .03195 .03196 8.35365 .35386 .35407 .35428 .03358 .03359 .03360 .03361 52 61 60 49 48' 47 46 45 + 3' IS 14 15 8.30314 .30336 .30358 .30380 .03010 .03011 .03013 .03013^ 8.31627 .31649 .31670 .31692 .03071 .03073 .03074 .03075 8.32920 .32941 .32963 .32984 .03134 .03135 .03136 .02137 8.34194 .34215 .34236 .34257 .03198 .03199 .03300 .03201 8.35449 .35469 .35490 .35511 .03363 .03363 .03264 .03365 n 18 19 8.30402 .30424 .30446 .30468 .03014 .03015 .03016 .02017 8.31714 .31735 .31757 .31779 .03076 .03077 .03078 .03079 8.33006 .33027 .33048 .33070 .03138 .02139 .02140 .03141 8.34278 .34299 .34320 .34341 .02203 .03303 .03304 .02305 8.35532 .35552 .35573 .35594 .02266 .03367 .03368 .03370 44 43 42 41 + 6' ;25 8.30490 .30512 .30534 .30556 .03018 .03019 .03030 .03031 8.31800 .31822 .31844 .31865 .03080 .03081 .03083 .03083 8.33091 .33112 .33134 .33155 .03143 .03143 .03145 .03146 8.34362 .34383 .34404 .34425 .03306 .03307 .03308 .03309 8.35614 .35635 .35656 .35677 .03371 .03373 .02273 .02274 40 39 38 37 + 6' 25 26 27 8.30578 .30600 .30622 .30644 .03033 .03033 .03034 .03035 8.31887 .31909 .31930 .31952 .03084 .02085 .02086 .02087 8.33176 .33198 .33219 .33240 .03147 .03148 .03149 .03150 8.34446 .34467 .34488 .34509 .02210 ,02211 .02313 .03314 8.35697 .35718 .85739 .35759 .02275 .02276 .03377 .03378 36 35 34 33 + r 29 SO SI 8.30666 .30688 .30710 .30732 .03036 .03037 .03038 .03039 8.31974 .31995 .32017 .32039 .03088 .02089 .02090 .02091 8.33262 .33283 .33304 .33325 .03151 .03153 .03153 .03154 8.34530 .34551 .34572 .34593 .03315 .02316 .03317 .03318 8.35780 .35801 .35821 .35842 .03379 .03380 .03381 .03383 32 31 30 29 + 8' SS 34 35 8.30754 .30776 .30798 .30820 .03030 .03031 .03033 .03033 8.32060 .32082 .32103 .32125 .02093 .03093 .03094 .02095 8.33347 .33368 .33389 .33411 .03155 .03156 .03157 .03158 8.34614 .34635 .34656 .34677 .03319 .03330 .02331 .03333 8.35863 .35883 .35904 .35925 .02384 .03385 .03386 .03387 28 27 26 25 24 23 22 21 + 9' 37 38 39 8.30842 .30863 .30885 .30907 .03034 .03035 .03036 .02037 8.32147 .32168 .32190 .32211 .03096 .03097 .02098 .03099 8.33432 .33453 .33474 .33496 .03159 .03160 .03161 .03163 8.34698 .34719 .34740 .34761 .03333 .03334 .03335 .03236 8.35945 .35966 .35987 .36007 .03388 .03389 .03390 .03391 + W 41 42 43 8.30929 .30951 .30973 .30995 .03038 .03039 .03040 .03043 8.32233 .32254 .32276 .32297 .03101 .03103 .02103 .02104 8.33517 .33538 .33559 .33580 .03164 .03165 .03166 .03167 8.34782 .34803 .34823 .34844 .03337 .03339 .03330 .02231 8.36028 .36048 .36069 .36090 .03293 .03393 .03295 .03396 20 19 IS 17 16 15 14 13 + ir 45 46 47 8.31017 .31039 .31060 .31082 .03043 .03044 .03045 .03046 8.32319 .32341 .32362 .32384 .02105 .02106 .02107 .03108 8.33602 .33623 .33644 .33665 .03168 .03169 .03170 .03171 8.34865 .34886 .34907 .34928 .03333 .03333 .03334 .03335 8.36110 .36131 .36151 .36172 .03397 .03398 .03399 .03300 + 13' 49 50 51 8.31104 .31126 .31148 .31170 .03047 .03048 .03049 .02050 8.32405 .32427 .32448 .32470 .03109 .02110 .02111 .03113 8.33686 .33708 .33729 .33750 .03173 .03173 .03174 .02175 8.34949 .34970 .34991 .35011 .03336 .03337 .03338 .03339 8.36193 .36213 .36234 .36254 .02301 .03303 .03303 .03304 12 11 10 9 + 13' 53 54 55 8.31192 .31213 .31235 .31257 .03051 .03053 .03053 .03054 8.32491 .32513 .32534 .32556 .03113 .03114 .02115 .03116 8.33771 .33792 .33814 .33835 .03176 .03177 .03178 .03179 8.35032 .35053 .35074 .35095 .03340 .03341 .03343 .03344 8.36275 .36295 .36316 .36337 .03305 .03307 .03308 .03309 8 7 6 5 4 3 2 1 + U' 57 58 59 8.31279 .31301 .31322 .31344 .03055 .03056 .03057 .03058 8.32577 .32599 .32620 .32642 .03117 .03118 .03119 .02130 8.33856 .33877 .33898 .33919 .03181 .02183 .03183 .03184 8.35116 .35137 .35157 .35178 .03345 .03346 .03347 .03348 8.36357 .36378 .36398 .36419 .02310 .02311 .02313 .03313 + 15' 8.31366 .03059 8.32663 .03131 8.33940 .03185 8.35199 .03349 8.36439 .03314 22 h 54"' ff A 5Sm 22!^ 52^ 22^ 5i™ 22''- 50^ Page 58] TABLE IV. Haversines. s jAio^nsr 1 i/. i/". 17° 45' 1 JAi;?"»18°0' m3mlS°15' 11^ 14"^ 18° W 1 s Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. 1 2 S 8.36439 .36460 .36480 .36501 .03314 .03316 .03316 .03317 8.37662 .37682 .37702 .37722 .03380 .03381 .03383 .03384 8.38867 .38886 .38906 .38926 .03447 .03448 .03449 .03451 8.40055 .40074 .40094 .40114 .03515 .03516 .03517 .03518 8.41226 .41246 .41265 .41284 .03584 .03686 .03586 .03587 60 59 58 67 + r 5 6 7 8.36521 .36542 .36562 .36583 .03319 .03330 .03331 .03333 8.37742 .37763 .37783 .37803 .03385 .03386 .03387 .03388 8.38946 .38966 .38986 .39006 .03453 .03453 .03454 .03455 8.40133 .40153 .40172 .40192 .03530 .03531 .03533 .03533 8.41304 .41323 .41343 .41362 .03588 .03590 .03591 .03593 66 65 64 63 + r 9 10 11 8.36603 .36624 .36644 .36665 .03333 .03334 .03335 .03336 8.37823 .37843 .37864 .37884 .03389 .03390 .03391 .03393 8.39026 .39046 .39066 .39086 .03456 .03457 .03458 .03460 8.40212 .40231 .40251 .40271 .03534 .03535 .03536 .03538 8.41381 .41401 .41420 .41439 .03593 .03594 .03596 .03597 52 51 60 49 + 3' 13 14 15 8.36685 .36706 .36726 .36746 .03337 .03338 .03339 .03331 .03333 .03333 .03334 .03335 8.37904 .37924 ■ .37944 .37964 .03394 .03395 .03396 .03397 8.39105 .39125 .39145 .39165 .03461 .03463 .03463 .03464 8.40290 .40310 .40329 .40349 .03539 .03530 .03531 .03533 8.41459 .41478 .41497 .41517 .03598 .03699 .03600 .03601 48 47 46 45 + 4' 17 18 19 8.36767 .36787 .36808 .36828 8.37985 .38005 .38025 .38045 .03398 .03399 .03400 .03401 8.39185 .39205 .39225 .39245 .03465 .03466 .03467 .03469 8.40369 .40388 .40408 .40427 .03533 .03534 .03536 .03537 8.41536 .41555 .41575 .41594 .03603 .03603 .03606 .03606 44 43 42 41 + 5' 21 22 23 8.36849 .36869 .36889 .36910 .03336 .03337 .03338 .03339 8.38065 .38085 .38105 .38126 .03403 .03404 .03405 .03406 8.39264 .39284 .39304 .39324 .03470 .03471 .03473 .03473 8.40447 .40467 .40486 .40506 .03538 .03539 .03540 .03541 8.41613 .41632 .41652 .41671 .03607 .03608 .03609 .03610 40 39 38 37 H- 6' 25 26 27 8.36930 .36951 .36971 .36991 .03340 .03343 .03343 .03344 8.38146 .38166 .38186 .38206 .03407 .03408 .03409 .03410 8.39344 .39364 .39384 .39403 .03474 .03475 .03476 .03478 8.40525 .40545 .40564 .40584 .03543 .03544 .03545 .03546 8.41690 .41710 .41729 .41748 .03613 .03613 .03614 .03615 36 35 34 33 + r 29 SO 31 8.37012 .37032 .37053 .37073 .03345 .03346 .03347 .03348 8.38226 .38246 .38266 .38286 .03411 .03413 .03414 .03415 8.39423 .39443 .39463 .39482 .03479 .03480 .03481 .03483 8.40603 .40623 .40642 .40662 .03547 .03548 .03549 .03550 8.41767 .41787 .41806 .41825 .03616 .03617 .03619 .03630 32 31 30 29 + 8' 33 34 35 8.37093 .37114 .37134 .37154 .03349 .03350 .03351 .03353 8.38306 .38326 .38346 .38367 .03416 .03417 .03418 .03419 8.39502 .39522 .39542 .39562 .03483 .03484 .03486 .03487 8.40681 .40701 .40721 .40740 .03553 .03553 .03554 .03555 8.41845 .41864 .41883 .41902 .03631 .03633 .03633 .03634 28 27 26 25 24 23 22 21 + 9^ 37 38 39 8.37175 .37195 .37215 .37236 .03354 .03355 .03356 .03357 8.38387 .38407 .38427 .38447 .03430 .03431 .03433 .03434 8.39581 .39601 .39621 .39641 .03488 .03489 .03490 .03491 8.40760 .40779 .40799 .40818 .03656 .03557 .03559 .03560 8.41921 .41941 .41960 .41979 .03636 .03637 .03638 .03639 + 10' 41 42 43 8.37256 .37276 .37297 .37317 .03358 .03359 .03360 .03361 8.38467 .38487 .38507 .38527 .03436 .03436 .03437 .03438 8.39660 .39680 .39700 .39720 .03493 .03493 .03495 .03496 8.40837 .40857 .40876 .40896 .03561 .03563 .03663 .03564 8.41998 .42018 .42037 .42056 .03630 .03631 .03633 .03834 20 19 18 17 + ir 45 46 47 8.37337 .37358 .37378 .37398 .03363 .03364 .03365 .03366 .03367 .03368 .03369 .03370 8.38547 .38567 .38587 .38607 .03439 .03430 .03431 .03433 8.39739 .39759 .39779 .39799 .03497 .03498 .03499 .03500 8.40915 .40935 .40954 .40974 .03565 .03567 .03568 .03569 8.42075 .42095 .42114 .42133 .03635 .03636 .03637 .03638 16 15 14 13 12 11 10 9 + 13' 49 50 51 8.37419 .37439 .37459 .37479 8.38627 .38647 .38667 .38687 .03434 .03435 .03436 .03437 8.39818 .39838 .39858 .39877 .03501 .03503 .03504 .03505 8.40993 .41013 .41032 .41052 .03570 .03571 .03673 .03673 8.42152 .42171 .42190 .42210 .03639 .03641 .03643 .03643 + 13' 53 54 55 8.37500 .37520 .37540 .37560 .03371 .03373 .03374 .03375 8.38707 .38727 .38747 .38767 .03438 .03439 .03440 .03443 8.39897 .39917 .39937 .39956 .03506 .03507 .03508 .03509 8.41071 .41090 .41110 .41129 .03575 .03676 .03677 .03678 8.42229 .42248 .42267 .42286 .03644 .03645 .03646 .03648 8 7 6 5 + 14' 57 55 59 8.37581 .37601 .37621 .37641 .03376 .03377 .03378 .03379 8.38787 .38807 .38827 .38847 .03443 .03444 .03445 .03446 8.39976 .39996 .40015 .40035 .03510 .03513 .03513 .03514 8.41149 .41168 .41187 .41207 .03679 .03680 .03683 .03683 8.42305 .42324 .42344 .42363 .03649 .03650 .03651 .03653 4 3 2 1 + 16' 8.37662 .03380 8.38867 .03447 8.40055 .03515 8.41226 .03684 8.42382 .03653 22^ 49^ 22 1^ 4S^ 22^ 47m 22k 46m 22>^45m TABLE IV. [Page 59 Haversines. s iftJ5"» 18° 45' 1 iniemi%°iy 1 Ihnm 19° 15/ l^lSm 19° 30' Ih 19m 19° 45' s Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. 1 2 S 8.42382 .42401 .42420 .42439 .03653 .02655 .03656 .03657 8.43522 .43541 .43560 .43578 .03724 .02725 .02726 .02738 8.44647 .44665 .44684 .44703 .03796 .03797 .03798 .03799 8.45757 .45775 .45794 .45812 .02868 .02869 .02870 .02871 8.46852 .46871 .46889 .46907 .03941 .03943 .03944 .02945 60 59 58 57 + r 5 6 7 8.42458 .42477 .42497 .42516 .02658 .03659 .03661 .03663 8.43597 .43616 .43635 .43654 .02729 .03730 .02731 .02733 8.44721 .44740 .44758 .44777 .02800 .02803 .03803 .02804 8.45830 .45849 .45867 .45885 .02873 .02874 .02875 .02876 8.46925 .46943 .46961 .46979 .02946 .02947 .02949 .02950 56 55 54 53 + r 9 10 11 8.42535 .42554 .42573 .42592 .02663 .03664 .02665 .02666 8.43673 .43692 .43710 .43729 .02734 .02735 .02736 .02737 8.44796 .44814 .44833 .44851 .02805 .02806 .03808 .03809 8.45904 .45922 .45940 .45959 .02878 .02879 .02880 .02881 8.46998 .47016 .47034 .47052 .02951 .02952 .02954 .02955 52 51 50 49 + 3' IS 14 15 8.42G11 .42630 .42649 .42668 .02668 .02669 .03670 .03671 8.43748 .43767 .43786 .43805 .02738 .02739 .02741 .02743 8.44870 .44889 .44907 .44926 .03810 .02811 .03813 .02814 8.45977 .45995 .46014 .46032 .02883 .02884 .02885 .02886 8.47070 .47088 .47106 .47124 .02956 .02957 .02958 ,02960 48 47 46 45 + 4' 17 18 19 8.42687 .42706 .42725 .42745 .02673 .02673 .02675 .02676 8.43823 .43842 .43861 .43880 .03743 .02744 .02745 .02747 8.44944 .44963 .44981 .45000 .02815 .02816 ,02817 .03818 8.46050 .46069 .46087 .4G105 .02887 .02889 .03890 .02891 8.47142 .47160 .47178 .47197 ,02961 ,03962 ,03963 ,02965 44 43 42 41 + 5' 21 22 23 8.42764 .42783 .42802 .42821 .02677 .02678 .02679 .02680 8.43899 .43917 .43936 .43955 .02748 .02749 .02750 .02751 8.45018 .45037 .45055 .45074 .02820 .02821 .02822 .03823 8.46124 .46142 .46160 .46179 .02893 .02893 .02895 .02896 8.47215 .47233 .47251 .47269 .03966 .02967 .02968 .02970 40 39 38 37 + 6' 25 26 27 8.42840 .42859 .42878 .42897 .02683 .02683 .03684 .03685 8.43974 .43992 .44011 .44030 .02753 .03754 .02755 .02756 8.45093 .45111 .45130 .45148 .02824 .02826 .02827 .02828 8.46197 .46215 .46233 .46252 .02897 .03898 .03900 .02901 8.47287 .47305 .47323 .47341 .02971 .02972 .02973 .03974 36 35 34 33 + r 29 30 31 8.42916 .42935 .42954 .42973 .03686 .03688 .03689 .02690 8.44049 .44067 .44086 .44105 .02757 .02759 .02760 .02761 8.45167 .45185 .45204 .45222 .02829 .02830 .02833 .03833 8.46270 .46288 .46306 .46325 .02902 .02903 .02904 .02906 8.47359 .47377 .47395 .47413 .03976 .03977 .03978 .02979 32 31 SO 29 + 8' 33 84 35 8.42992 .43011 .43030 .43049 .02691 .02693 .03693 .03695 8.44124 .44142 .44161 .44180 .02762 .03763 .03764 .03766 8.45241 .45259 .45278 .45296 .02834 .02835 .02836 .02838 8.46343 .46361 .46379 .46398 .02907 .02908 .02909 ,02911 8.47431 .47449 .47467 .47485 .02981 .02982 .02983 .02984 28 27 26 25 + 9^ 37 38 39 8.43068 .43087 .43106 .43125 .02696 .02697 .02698 .02699 8.44199 .44217 .44236 .44255 .03767 .03768 .03769 .02771 8.45315 .45333 .45352 .45370 .02839 .02840 .02841 .02843 8.46416 .46434 .46452 .46471 .02913 .02913 .02914 .02915 8.47503 .47521 .47539 .47557 .0298« ,02987 ,02988 ,02989 24 23 22 21 + ir 41 42 43 8.43144 .43163 .43181 .43200 .02700 .03703 .02703 .02704 8.44273 .44292 .44311 .44330 .02772 .02773 .02774 .03775 8.45388 .45407 .45425 .45444 .02844 .02845 .02846 .02847 8.46489 .46507 .46525 .46544 .02917 .02918 .02919 .02920 8.47575 .47593 .47611 .47629 .02991 .02993 .03993 .03994 20 19 18 17 + 11' 45 46 47 8.43219 .43238 .43257 .43276 .02705 .02706 .02708 .02709 8.44348 .44367 .44386 .44404 .03776 .03778 .03779 .02780 8.45462 .45481 .45499 .45518 .02849 .02850 .02851 .02852 8.46562 .46580 .46598 .46616 .02922 .02923 .02924 .02925 8.47647 .47665 .47683 .47701 .03996 .03997 .03998 .02999 16 15 14 IS + 13' 49 50 51 8.43295 .43314 .43333 .43352 .02710 .02711 .02713 .02713 8.44423 .44442 .44460 .44479 .02781 .02782 .02784 .02785 8.45536 .45554 .45573 .45591 .02853 ,02855 .02856 .02857 8.46634 .46653 .46671 .46689 .02926 ,02928 ,02929 .02930 8.47719 .47737 .47755 .47773 .03000 .03003 .03093 .03004 12 11 ■10 9 + 13' 53 54 55 8.43371 .43390 .43409 .43427 .02715 .02716 .02717 .02718 8.44498 .44516 .44535 .44554 .03786 .02787 .03788 .03790 8.45610 .45628 ,45646 .45665 .02858 .02859 .02861 .02862 8.46707 .46725 .46744 .46762 .02931 .02933 .02934 ,02935 8.47791 .47809 .47827 .47844 .03005 .03007 .03008 .03009 8 7 6 5 + 14' 57 58 59 8.43446 .43465 .43484 .43503 .02719 .02721 .02722 .02723 8.44572 .44591 .44610 .44628 .02791 .02793 .02793 .03794 8.45683 .45702 .45720 .45738 .02863 .02864 .02866 .02867 8.46780 .46798 .46816 .46834 ,02936 ,02938 ,02939 ,02940 8.47862 .47880 .47898 .47916 .03010 .03013 .03013 .03014 4 3 2 1 + 15' 8.43522 .03734 8.44647 .03796 8.45757 .02868 8.46852 ,03941 8.47934 .03015 221^ 44"" 22^43^ 22J>' 42^ 22h 41"* 22J<'40^ Page 60] TABLE IV. Haversines. s Ih 20m 30° (y 1 in2im2Q°W jh ogm 20° 30^ 1^23^20° 4:5' :?'i.M"'-31°0' 1 s 60 59 58 57 Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. 1 2 3 8.47934 .47952 .47970 .47988 .03015 .03017 .03018 .03019 8.49002 .49020 .49037 .49055 .03090 .03093 .03093 .03091 8.50056 .50074 .50091 .50109 .03166 .03168 .03169 .03170 8.51098 .51115 .51132 .51150 .03313 .03315 .03316 .03317 8.52127 .52144 .52161 .52178 .03331 .03323 .03331 .03335 + r 5 6 7 8.48006 .48024 .48041 .48059 .03020 .03033 .03033 .03031 8.49073 .49090 .49108 .49126 .03095 .03097 .03098 .03099 8.50126 .50144 .50161 .50179 .03171 .03173 .03171 .03175 8.51167 .51184 .51201 .51219 .03318 .03350 .03251 .03353 8.52195 .52212 .52229 .52246 .03336 .03338 .03329 .03330 56 55 54 53. + 3^ 9 10 11 8.48077 .48095 .48113 .48131 .03035 .03037 .03038 .03039 8.49143 .49161 .49179 .49196 .03101 .03103 .03103 .03101 8.50196 .50214 .50231 .50248 .03177 .03178 .03179 .03180 8.51236 .51253 .51270 .51287 .03351 .03355 .03356 .03357 8.52263 .52280 .52297 .52314 .03331 .03333 .03331 .03335 52 51 50 49 + 3- 13 14 15 8.48149 .48167 .48184 .48202 .03030 .03033 .03033 .03031 8.49214 .49232 .49249 .49267 .03106 .03107 .03108 .03109 8.50266 .50283 .50301 .50318 .03183 .03183 .03181 .03186 8.51305 .51322 .51339 .51356 .03359 .03360 .03361 .03363 8.52331 .52348 .52365 .52382 .03337 .03338 .03339 .03311 48 47 46 45 n 18 19 8.48220 .48238 .48256 .48274 .03035 .03037 .03038 .03039 8.49284 .49302 .49320 .49337 .03111 .03113 .03113 .03111 8.50335 .50353 .50370 .50388 .03187 .03188 .03189 .03191 8.51374 .51391 .51408 .51425 .03361 .03365 .03366 .03368 8.52399 .52416 .52433 .52450 .03313 .03313 .03314 .03316 U 43 42 41 + 6^ 21 22 23 8.48292 .48309 .48327 .48345 .03010 .03013 .03013 .03011 8.49355 .49373 .49390 .49408 .03116 .03117 .03118 .03119 8.50405 .50422 .50440 .50457 .03193 .03193 .03191 .03196 8.51442 .51459 .51477 .51494 .03369 .03370 .03373 .03373 8.52467 .52484 .52501 .52518 .03317 .03348 .03350 .03351 40 39 38 37 + 6^ 25 26 27 8.48363 .48381 .48399 .48416 .03015 .03017 ,03018 .03019 8.49425 .49443 .49461 .49478 .03131 .03133 .03133 .03135 8.50475 .50492 .50509 .50527 .03197 .03198 .03300 .03301 8.51511 .51528 .51545 .51562 .03371 .03375 .03377 .03378 8.52535 .52552 .52569 .52585 .03353 .03351 .03355 .03356 36 35 34 33 + r 29 SO 31 8.48434 .48452 .48470 .48488 .03050 .03053 .03053 .03051 8.49496 .49513 .49531 .49548 .03136 .03137 .03138 .03130 8.50544 .50561 .50579 .50596 .03303 .03301 .03305 .03306 8.51580 .51597 .51614 .51631 .03379 .03381 .03383 .03383 8.52602 .52619 .52636 .52653 .03358 .03359 .03360 .03361 32 31 30 29 + 8^ 33 34 35 8.48505 .48523 .48541 .48559 .03055 .03057 .03058 .03059 8.49566 .49584 .49601 .49619 .03131 .03133 .03133 .03135 8.50614 .50631 .50648 .50666 .03307 .03309 .03310 .03311 8.51648 .51665 .51682 .51700 .03385 .03386 .03387 .03388 8.52670 .52687 .52704 .52721 .03363 .03361 .03365 .03367 28 27 26 25 + 9^ 37 38 39 8.48576 .48594 .48612 .48630 .03060 .03063 .03063 .03061 8.49636 .49654 .49671 .49689 .03136 .03137 .03138 .03110 8.50683 .50700 .50718 .50735 .03313 .03311 .03315 .03316 8.51717 .51734 .51751 .51768 .03390 .03391 .03393 .03391 8.52738 .52755 .52772 .52789 .03368 .03369 .03371 .03373 24 23 22 21 + W 41 42 43 8.48648 .48665 .48683 .48701 .03065 .03067 .03068 .03069 8.49706 .49724 .49742 .49759 .03111 .03143 .03111 .03115 8.50752 .50770 .50787 .50804 .03318 .03319 .03230 .03331 8.51785 .51802 .51819 .51836 .03395 .03396 .03398 .03399 8.52806 .52822 .52839 .52856 .03373 .03375 .03376 .03377 20 19 18 17 + il' 45 46 47 8.48719 .48736 .48754 .48772 .03070 .03073 .03073 .03071 8.49777 .49794 .49812 .49829 .03116 .03117 .03119 .03150 8.50821 .50839 .50856 .50873 .03333 .03331 .03325 .03337 8.51854 .51871 .51888 .51905 .03300 .03301 .03303 .03301 8.52873 .52890 .52907 .52924 .03379 .03380 .03381 .03383 16 15 14 13 + n' 49 50 51 8.48789 .48807 .48825 .48843 .03075 .03077 .03078 .03079 8.49847 .49864 .49882 .49899 .03151 .03153 .03151 ,03155 8.50891 .50908 .50925 .50943 .03338 .03239 .03330 .03333 8.51922 .51939 .51956 .51973 .03305 .03307 .03308 .03309 8.52941 .52958 .52974 .52991 .03381 .03385 .03386 .03388 12 11 10 9 + W 53 54 55 8.48860 .48878 .48896 .48914 .03080 .03083 .03083 .03081 8.49917 .49934 .49952 .49969 .03156 .03157 .03159 .03160 8.509G0 .50977 .50994 .51012 .03333 .03331 .03336 .03337 8.51990 .52007 .52024 .52041 .03311 .03313 .03313 .03311 8.53008 .53025 .53042 .53059 .03389 .03390 .03392 .03393 8 7 6 5 + ir 57 58 59 8.48931 .48949 .48967 .48984 .03085 .03087 .03088 .03089 8.49987 .50004 .50022 .50039 .03161 .03163 .03161 .03165 8.51029 .51046 .51063 .51081 .03338 .03339 .03311 .03313 8.52058 .52076 .52093 .52110 .03316 .03317 .03318 .03330 8.53076 .53092 .53109 .53126 .03391 .03396 .03397 .03398 4 3 2 1 + W 8.49002 .03090 8.50056 .03166 8.51098 .03313 8.52127 .03331 8.53143 .03100 22h son, 22^ 38m 22h S7m 22h S6m 22h 35m TABLE IV. Haversinea. [Page 61 s jh 25m 31° 15' Ih 26m 21° 30' Ihzim, 21° 45' Ih 28m 23° 0' Ih 29m 23° 15' S Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. 1 s 8.53143 .53160 .53177 .53193 .03400 .03401 .03403 .03404 8.54147 .54164 .54180 .54197 .03479 .03480 .03483 .03483 8.55139 .55156 55172 .55189 .03560 .03561 .03563 .03564 8.56120 .56136 .56152 .56169 .03641 .03642 .03644 .03645 8.57089 .57105 .57121 .57137 .03733 .03724 .03726 .03737 60 59 58 57 66 55 54 53 + r 5 6 7 8.53210 .53227 .53244 .53261 .03405 .03106 .0340S .03409 8.54214 .54230 .54247 .54263 .03484 .03486 .03487 .03488 8.55205 .55221 55238 .55254 .03565 .03566 .03568 .03569 8.56185 .56201 .56217 .56233 .03646 .03648 .03649 .03650 8.57153 .57169 .57185 .57201 .03738 .03730 .03731 .03733 + ^ 9 10 11 8.53277 .53294 .53311 .53328 .03410 .03411 .03413 .03414 8.54280 .54297 .54313 .54330 .03490 .03491 .03493 .03494 8.55271 .55287 .55303 .55320 .03570 .03573 .03573 .03574 8.56250 .56266 .56282 .56298 .03652 .03653 .03654 .03656 8.57217 .57233 .57230 .57266 .03734 .03735 .03737 .03738 52 51 50 49 + 3' IS 14 15 8.53345 .53361 .53378 .53395 .03415 .03417 .03418 .03419 8.54346 .54363 .54380 .54396 .03495 .03496 .03498 .03499 8.55336 .55353 .55369 .55385 .03576 .03577 .03578 .03580 8.56315 .56331 .56347 .56363 .03657 .03659 .03660 .03661 8.57282 .57298 .57314 .57330 .03740 .03741 .03743 .03744 48 47 46 45 + 4' 17 18 19 8.53412 .53429 .53445 .53462 .03431 .03423 .03433 .03435 8.54413 .54429 .54446 .54462 .03500 .03503 .03503 .03504 8.55402 .55418 .55435 .55451 .03581 .03583 .03584 .03585 8.56379 .56396 .56412 .56428 .03663 .03664 .03665 .03667 8.57346 .57362 .57378 .57394 .03745 .03746 .03748 .03749 44 43 42 41 + 5' 21 23 8.53479 .53496 .53512 .53529 .03436 .03437 .03439 .03430 8.54479 .54496 .54512 .54529 .03506 .03507 .03509 .03510 8.55467 .55484 .55500 .55516 .03587 .03588 .93589 .03591 8.56444 .56460 .56477 .56493 .03668 .03669 .03671 .03673 8.57410 .57426 .57442 .57458 .03751 .03752 .03753 .03755 40 39 38 37 + 6^ 25 26 27 8.53546 .53563 .53580 .53596 .03431 .03433 .03434 .03435 8.54545 .54562 . .54578 5.54595 .03511 .03513 .03514 .03515 . .03517 ;. 03518 ; .03519 -.03531 8.55533 <. 55549 1.55566 .55582 .03593 .03593 .03595 .03596 8.56509 .56525 .56541 .56557 .03674 .03675 .03676 .03678 8.57474 .57490 .57506 .57522 .03756 .03757 .03759 .03760 36 35 34 33 + r 29 SO 31 8.53613 .' .53630 .53646 .53663 .03437 .03438 .03439 .03441 8.54612 i. 54628 ) .54645 .54661 8.55598 .55615 .55631 .55647 .03597 r .03599 .03600 .03601 8.56574 .56590 .56606 .56622 .03679 .03680 .03682 .03683 8.57538 .57554 .57570 .57585 .03763 .03763 .03764 .03766 32 31 30 29 + 8' 33 34 35 8.53680 .53697 .53713 .53730 .03443 .03443 .03445 .03446 8.54678 -.54694 :. 54711 '.54727 .03533 .03533 '.03535 .03536 8.55664 .55680 .55696 .55713 .03603 .03604 .03605 .03607 8.56638 .56654 .56670 .56687 .03685 .03686 .03687 .03689 8.57601 .57617 .57633 .57649 .03767 .03769 .03770 .03771 28 27 26 25 + r 37 38 39 8.53747 .53764 .53780 .53797 .03447 .03449 .03450 .03451 8.54744 . .54760 .54777 .54793 .03537 .03539 .03530 .03531 8.55729 .55745 .55762 .55778 .03608 .03610 .03611 .03613 .03614 .03615 .03616 .03618 8.56703 .56719 .56735 .56751 .03680 .03691 .03693 .03694 8.57665 .57681 .57697 .57713 .03773 .03774 .03775 .03777 24 23 22 21 + W 41 42 43 8.53814 .53830 .53847 .53864 .03453 .03454 .03455 .03457 8.54810 .54826 ^.54843 -.54859 .03533 .03534 .03535 .03537 8.55794 .55811 .55827 .55843 8.56767 .56783 .56799 .56816 .03695 .03697 .03698 .03700 8.57729 .57745 .57761 .57777 .03778 .03780 .03781 .03782 20 19 18 17 16 15 14 13 + ir 45 46 47 8.53880 .53897 .53914 .53930 .03458 .03459 .03460 .03463 8.54876 .54892 -.54909 .54925 .03538 .03539 .03541 .03543 8.55859 .55876 .55892 .55908 .03619 .03630 .03633 .03633 8.56832 .56848 .56864 .56880 .03701 .03702 .03704 .03705 8.57793 .57809 .57825 .57841 .03784 .03785 .03787 .03788 + ir 49 50 51 8.53947 .53964 .53980 .53997 .03463 .03464 .03466 .03467 8.54942 .54958 .54975 .54991 .03543 .03545 .03346 .03547 8.55925 55941 .55957 .55973 .03634 .03636 .03637 .03629 8.56896 .56912 56928 .56944 .03706 .03708 .03709 .03711 8.57856 .57872 .57888 .57904 .03789 .03791 .03792 .03794 12 11 10 9 8 7 6 5 + W 53 54 55 8.54014 .54030 .54047 .45064 .03468 .03470 .03471 .03473 8.55008 .55024 .55041 .55057 .03549 .03550 .03551 .03553 8.55990 56006 .56022 .56039 .03630 .03631 .03633 .03634 8.56960 56977 .56993 .57009 .03713 .03713 .03715 .03716 8.57920 .57936 57952 .57968 .03795 .03796 .03798 .03799 + ir 57 58 59 8.54080 .54097 .54114 .54130 .03474 .03475 .03476 .03478 8.55073 .55090 .55106 .55123 8.55139 .03554 .03555 .03557 .03558 .03560 8.56055 .56071 .56087 .56104 .03635 .03637 .03638 .03639 8.57025 .57041 .57057 .57073 .03717 .03719 .03730 .03733 .03723 8.57984 .58000 .58015 .58031 .03800 .03802 .03803 .03805 4 3 2 1 + 15' 8.54147 .03479 8.56120 .03641 8.57089 8.58047 .03806 22^ 34m 22^ 33m 22^ 32m 22'^ 3pn 22h SOm Page 62] TABLE IV. Haversines. s 1AJ0™22°3(K 1 Ih Sim 22° 45' iA5^23°0' 1 JA5.JW23°15' IhSpn 23° 30' a 1 Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. 1 s 8.58047 .58063 .58079 .58095 .03806 .03807 .03809 .03810 8.58994 .59010 .59026 .59042 .03890 .03891 .03893 .03894 8.59931 .59947 .59962 .59978 .03975 .03976 .03978 .03979 8.60857 .60873 .60888 .60903 .04060 .04062 .04063 .04065 8.61773 61789 .61804 .61819 .04147 .04148 .04150 .04151 60 59 58 57 + r 5 6 7 8.58111 .58127 .58142 .58158 .03813 .03813 .03814 .03816 8.59057 .59073 .59089 .59104 .03896 .03897 .03898 .03900 8.59993 .60009 .60024 .60040 .03980 .03982 .03983 .03985 8.60919 .60934 .60949 .60965 .04066 .04068 .04069 .04070 8.61834 .61849 .61864 .61880 .04153 .04154 .04156 .04157 56 55 54 53 + ?/ 9 10 11 8.58174 .58190 .58206 .58222 .03817 .03819 .03830 .03831 8.59120 .59136 .59151 .59167 .03901 .03903 .03904 .03905 8.60055 .60071 .60086 .60102 .03986 .03988 .03989 .03990 8.60980 .60995 .61011 .61026 .04072 .04073 .04075 .04076 8.61895 .61910 .61925 .61940 .04159 .04160 .04163 .04163 52 51 50 49 + 3' IS u 15 8.58238 .58253 .58269 .58285 .03833 .03834 .03836 .03837 8.59183 .59198 .59214 .59230 .03907 .03908 .03910 .03911 8.60117 .60133 .60148 .60164 .03992 .03993 .03995 .03996 8.61041 .61057 .61072 .61087 .04078 .04079 .04081 .04083 8.61955 .61971 .61986 .62001 .04164 .04166 .04167 .04169 48 47 46 45 n 18 19 8.58301 .58317 .58333 .58348 .03838 .03830 .03831 .03833 8.59245 .59261 .59277 .59292 .03912 .03914 .03915 .03917 8.60179 .60195 .60210 .60226 .03998 .03999 .04000 .04002 8.61103 .61118 .61133 .61149 .04083 .04085 .04086 .04088 8.62016 .62031 .62046 .62061 .04170 .04172 04173 .04175 44 43 42 41 40 39 38 37 ■i + 6^ 22 ■'■ 2S 8.58364 .58380 .68396 .58412 .03834 .03835 .03837 .03838 8.59308 .59323 .59339 .59355 .03918 .03930 .03931 .03933 8.60241 .60256 .60272 .60287 .04003 .04005 .04006 .04007 8.61164 .61179 .61194 .61210 .04089 .04091 .04093 .04094 8.62077 .62092 .62107 .62122 .04176 .04177 .04179 .04180 ■- + 6' 25 26 '■■■ 27 ^ 8.58427 .58443 .58459 .58475 .03839 .03841 .03842 .03844 8.59370 .59386 .59402 .59417 .03934 .03925 .03927 .03938 8.60303 .60318 .60334 .60349 .04009 .04010 .04012 .04013 8.61225 .61240 .61256 .61271 .04095 .04096 .04098 .04099 8.62137 .62152 .62167 .62182 .04182 .04183 .04185 .04186 36 35 34 33 32 31 30 29 + r 29 . SO SI 8.58491 .58506 .58522 .58538 .03845 .03846 .03848, .03849^ 8.59433 .59448 .59464 '.59480 .03939 ^03931 1.03932 *. 03934 8.60365 .60380 .60396 .60411 .04015 .04016 .04017 .04019 8.61286 .61301 .61317 .61332 .04101 .04103 .04104 .04105 8.62197 .62213 .62228 .62243 .04188 .04189 .04191 .04192 + 8^ ss 34 35 8.58554 .58570 .58585 .58601 .03851 .03853 .03853 .03855 8.59495 .59511 ■ .59527 .59542 .03935 .03936 * .03938 -.03939 8.60426 .60442 .60457 ~ .60473 .04020 .04022 .04023 .04025 8.61347 .61362 .61378 .61393 .04106 .04108 .04109 .04111 8.62258 .62273 .62288 .62303 .04194 .04195 .04196 .04198 28 27 26 25 + 9^ 37 38 , 39 8.58617 .58633 .58648 .58664 .03856 .03858 .03859 .03860 8.59558 .59573 -.59589 .59604 .03941 .03943 ; .03944 .03945 8.60488 .60504 .60519 .60534 .04026 .04037 .04039 .04030 8.61408 .61423 .61439 .61454 .04113 .04114 .04115 .04117 8.62318 .62333 .62348 .62363 .04199 .04201 .04202 .04304 24 23 22 21 1 + W 41 - 42 43 8.58680 .58696 .58711 .58727 .03863 .03863 .03865 .03866 8.59620 .59636 .59651 .59667 .03946 i .03948 f. 03949 .03951 8.60550 .60565 .60581 .60596 .04033 .04033 .04035 .04036 8.61469 .61484 .61500 .61515 .04118 .04119 .04131 .04132 8.62379 .62394 .62409 .62424 .04305 .04307 .04208 .04210 20 19 18 17 + ir 45 46 47 8.58743 .58759 .58774 .58790 .03867 .03869 .03870 .03873 8.59682 .59698 .59714 .59729 .03952 .03953 .03955 .03956 8.60611 .60627 .60642 .60658 .04038 .04039 .04040 .04043 8.61530 .61545 .61561 .61576 .04124 .04125 .04127 .04128 8.62439 .62454 .62469 .62484 .04211 -04212 .04214 .04215 16 15 14 IS + 13' 49 50 i 51 8.58806 .58822 .58837 .58853 .03873 .03875 .03876 .03877 8.59745 .59760 .59776 .59791 .03958 .03959 .03961 .03962 8.60673 .60688 .60704 .60719 .04043 .04045 .04046 .04048 8.61591 .61606 .61621 .61637 .04130 .04131 .04133 .04134 .04135 .04137 .04138 .04140 8.62499 .62514 .62529 .62544 8.62559 .62574 .62589 .62604 .04217 .04218 .04220 .04221 .04223 .04224 .04226 .04237 12 11 10 9 8 7 6 5 + 13' 53 54 55 8.58869 .58885 .58900 .58916 .03879 .03880 .03883 .03883 8.59807 .59822 .59838 .59853 .03963 .03965 .03966 .03968 8.60734 .60750 .60765 .60781 .04049 .04050 .04053 .04053 8.61652 .61667 .61682 .61697 + W 57 58 59 8.58932 .58947 .58963 .58979 .03884 .03886 .03887 .03889 8.59869 .59885 .59900 .59916 .03969 .03971 .03973 .03973 8.60796 .60811 .60827 .60842 .04055 .04056 .04058 .04059 8.61713 .61728 .61743 .61758 .04141 .04143 .04144 .04146 8.62619 .62634 .62649 .62664 .04229 .04230 .04232 .04233 4 o 2 1 + 15' 8.58994 .03890 8.59931 .03975 8.60857 .04060 8.61773 .04147 8.62680 .04234 m. 22^ 29m • 22^ 28m ^4-:*' -'.'••■ f^^ 27m M- ^2^ 26m ^^^.1 22^ 25m TABLE IV. [Page 63 Haversines. s Jft55"»23°45' 1 iA56m24°0' Ih S7m 24° 15/ J?ft 55^24° 30' i'iJ9"»24°45' s 60 59 58 57 Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. 1 2 S 8.62680 .62695 .62710 .62725 .04234 .04236 .04237 .04239 8.63576 .63591 .63606 .63620 .04323 .04324 .04326 .04327 8.64463 .64477 .64492 .64507 .04412 .04413 .04415 .0441G 8.65340 .65355 .65369 .65384 .04502 .04503 .04505 .04506 8.66208 .66223 .66237 .66251 .04593 .04594 .04596 .04597 + 1^ 6 6 7 8.62740 .62755 .62770 .62785 .04240 .04242 .04243 .04245 8.63635 .63650 .63665 .63680 .04329 .04330 .04332 .04333 8.64521 .64536 .64551 .64565 .04418 .04419 .04421 .04422 8.65398 .65413 .65427 .65442 .04508 .04509 .04511 .04512 8.66266 .66280 .66295 .66309 .04599 .04600 .04602 .04604 56 55 54 53 + 3' 9 10 11 8.62800 .62815 .62830 .62845 .04246 .04248 .04249 .04251 8.63695 .63709 .63724 .63739 .04335 .04336 .04338 .04339 8.64580 .64595 .64609 .64624 .04424 .04425 .04427 .04428 8.65456 .65471 .65485 .65500 .04514 .04516 .04517 .04519 8.66323 .66338 .66352 .66366 .04605 .04607 .04608 .04610 52 51 50 49 + 3^ IS 14 15 8.62860 .62875 .62890 .62904 .04252 .04253 .04255 .04256 8.63754 .63769 .63784 .63798 .04340 .04342 .04343 .04345 8.64639 .64653 .64668 .64683 .04430 .04431 .04433 .04434 8.65514 .65529 .65543 .65558 .04520 .04522 .04523 .04525 8.66381 .66395 .66409 .66424 .04611 .04613 .04614 .04616 48 47 46 45 17 18 19 8.62919 .62934 .62949 .62964 .04258 .04259 .04261 .04262 8.63813 .63828 .63843 .63858 .04346 .04348 .04349 .04351 8.64697 .64712 .64727 .64741 .04436 .04437 .04439 .04440 8.65572 .65587 .65601 .65616 .04526 .04528 .04529 .04531 8.66438 .66453 .66467 .66481 .04617 .04619 .04620 .04622 44 43 42 41 + 5' 21 22 23 8.62979 .62994 .63009 .63024 .04264 .04265 .04267 .04268 8.63872 .63887 .63902 .63917 .04352 .04354 .04355 .04357 8.64756 .64771 .64785 .64800 .04442 .04443 .04445 .04446 8.65630 .65645 .65659 .65674 .04532 .04534 .04535 .04537 8.66496 .66510 .66524 .66539 .04623 .04625 .04626 .04628 40 39 38 37 36 35 34 33 + 6^ 25 26 27 8.63039 .63054 .63069 .63084 .04270 .04271 .04273 .04274 8.63932 .63946 .63961 .63976 .04358 .04360 .04361 .04363 8.64815 .64829 .64844 .64859 .04448 .04449 .04451 .04452 8.65688 .65703 .65717 .65732 .04538 .04540 .04541 .04543 8.66553 .66567 .66582 .66596 .04629 .04631 .04633 .04634 + r 29 30 31 8.63099 .63114 .63129 .63144 .04276 .04277 .04278 .04280 8.63991 .64006 .64020 .64035 .04364 .04366 .04367 .04369 8.64873 .64888 .64902 .64917 .04454 .04455 .04457 .04458 8.65746 .65761 .65775 .65790 .04544 .04546 .04547 .04549 8.66610 .66625 .66639 .66653 .04636 .04637 .04639 .04640 32 31 30 29 + 8' 33 34 35 8.63159 .63174 .63189 .63204 .04281 .04283 .04284 .04286 8.64050 .64065 .64079 .64094 .04370 .04372 .04373 .04375 8.64932 .64946 .64961 .64976 .04460 .04461 .04463 .04464 8.65804 .65819 .65833 .65848 .04550 .04552 .04553 .04555 8.66668 .66682 .66696 .66710 .04642 .04643 .04645 .04646 28 27 26 25 + 9" 37 38 39 8.63218 .63233 .63248 .63263 .04287 .04289 .04290 .04292 8.64109 .64124 .64139 .64153 .04376 .04378 .04379 .04381 8.64990 .65005 .65019 .65034 .04466 .04467 .04469 .04470 8.65862 .65876 .65891 .65905 .04556 .04558 .04559 .04561 8.66725 .66739 .66753 .66768 .04648 .04649 .04651 .04652 24 23 22 21 + 10' 41 42 43 8.63278 .63293 .63308 .63323 .04293 .04295 .04296 .04298 8.64168 .64183 .64198 .64212 .04382 .04384 .04385 .04387 8.65049 .65063 .65078 .65092 .04472 .04473 .04475 .04476 8.65920 .65934 .65949 .65963 .04562 .04564 .04565 .04567 8.66782 .66796 .66811 .66825 .04654 .04655 .04657 .04659 20 19 18 17 + u^ 45 46 47 8.63338 .63353 .63368 .63382 .04299 .04301 .04302 .04304 8.64227 .64242 .64257 .64271 .04388 .04390 .04391 .04393 8.65107 .65122 .65136 .65151 .04478 .04479 .04481 .04482 8.65978 .65992 .66006 .66021 .04569 .04570 .04572 .04573 8.66839 .66853 .66868 .66882 .04660 .04662 .04663 .04665 16 15 14 13 + ir 49 50 51 8.63397 .63412 .63427 .63442 .04305 .04306 .04308 .04309 8.64286 .64301 .64315 .64330 .04394 .04395 .04397 .04398 8.65165 .65180 .65194 .65209 .04484 .04485 .04487 .04488 8.66035 .66050 .66064 .66079 .04575 .04576 .04578 .04579 8.66896 .66911 .66925 .66939 .04666 .04668 .04669 .04671 12 11 10 9 8 7 6 5 + 13' 53 54 55 8.63457 .63472 .63487 .63502 .04311 .04312 .04314 .04315 8.64345 .64360 .64374 .64389 .04400 .04401 .04403 .04404 8.65224 .65238 .65253 .65267 .04490 .04491 .04493 .04494 8.66093 .66107 .66122 .66136 .04581 .04582 .04584 .04585 8.66953 .66968 .66982 .66996 .04672 .04674 .04675 .04677 + W 57 58 59 8.63516 .63531 .63546 .63561 .04317 .04318 .04320 .04321 8.64404 .64418 .64433 .64448 .04405 .04407 .04409 .04410 8.65282 .65296 .65311 .65325 .04496 .04497 .04499 .04500 8.66151 .66165 .66179 .66194 .04587 .04588 .04590 .04591 8.67010 .67025 .67039 .67053 .04678 .04680 .04682 .04683 4 3 2 1 + 15' 8.63576 .04323 8.64463 .04412 8.65340 .04502 8.66208 .04593 8.67067 .04685 22'h' 24"* 22h 2 3m 22^ 22^ 22h 21m 22 f^ 20"* _ Page 64] TABLE IV. Haversines. B jh 40mZ5°B' 1 Ih^im 35° 15' lh42m 85° 30' Ih4,3m25°i5' | Ih ^m 26° r s Log. nav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. 1 2 3 8.67067 J67082 ' .67096 .67110 .046S5 .04686 .04688 .04689 8.67918 .67932 .67946 .67960 .04777 .04779 .047S0 .04782 8.68760 .68773 .68787 .68801 .04871 .04872 .04874 .04875 8.69593 .69607 .69620 .69634 .04965 .04967 .04908 .04970 8.70418 .70431 .70445 .70459 .05060 .05062 .05063 .05065 60 59 58 57 + r 5 6 7 8.67124 .67139 .67153 .67167 .04691 .04693 .04694 .04695 8.67974 .67988 .68002 .68016 .04783 .04785 .04787 .04788 8.68815 .68829 .68843 .68857 .04877 .04879 .04880 .04882 8.69648 .69662 .69676 .69690 .04971 .04973 .04975 .04976 8.70472 .70486 .70500 .70513 .05067 .05068 .05070 .05071 56 55 54 53 + ^ 9 10 11 8.67181 .67196 .67210 .67224 .04697 .04698 .04700 .04702 8.68030 .68045 .68059 .68073 .04790 .04791 .04793 .04794 8.68871 .68885 .68899 .68913 .04883 .04885 .04886 .04888 8.69703 .69717 .69731 .69745 .04978 .04979 .04981 .04983 8.70527 .70541 .70554 .70568 .05073 .05075 .05076 .05078 52 51 50 49 + 3' IS 14 15 8.67238 .67252 .67267 .67281 .04703 .04705 .04706 .04708 8.68087 .68101 .68115 .68129 .04796 .04797 .04799 .04801 8.68927 .68941 .68955 .68969 .04890 .04891 .04893 .04894 8.69758 .69772 .69786 .69800 .04984 .04986 .04987 .04989 8.70582 .70595 .70609 .70623 .05079 .05081 .05083 .05084 48 47 46 45 44 43 42 41 + 4' n 18 19 8.67295 .67309 .67323 .67338 .04709 .04711 .04712 .04714 8.68143 .68157 .68171 .68185 .04802 .04804 .04805 .04807 8.68983 .68996 .69010 .69024 .04896 .04897 .04899 .04901 8.69814 .69827 .69841 .69855 .04990 .04992 .04994 .04995 8.70636 .70650 .70664 .70677 .05086 .05087 .05089 .05091 + 5' 21 22 23 8.67352 .67366 .67380 .67394 .04715 .04717 .04718 .04720 8.68199 .68213 .68227 .68241 .04808 .04810 .04811 .04813 8.69038 .69052 .69066 .69080 .04902 .04904 .04905 .04907 8.69869 .69882 .69896 .69910 .04997 .04998 .05000 .05001 8.70691 .70704 .70718 .70732 .05092 .05094 .05095 .05097 40 39 38 37 + r 25 26 27 8.67409 .67423 .67437 .67451 .04722 .04723 .04725 .04726 8.68256 .68270 .68284 .68298 .04815 .04816 .04818 .04819 8.69094 .69108 .69122 .69136 .04908 .04910 .04912 .04913 8.69924 .69937 .69951 .69965 .05003 .05005 .05006 .05008 8.70745 .70759 .70773 .70786 .05099 .05100 .05102 .05104 36 35 34 33 32 3^1 30 29 28 27 26 25 + r 29 30 31 8.67465 .67480 .67494 .67508 .04728 .04729 .04731 .04732 8.68312 .68326 .68340 .68354 .04821 .04823 .04824 .04825 8.69149 .69163' .69177 .69191 .04915 .04916 .04918 .04919 8.69979 .69992 .70006 .70020 .05009 , .05011 .05013 .05014 8.70800 *.70813 *' .70827 .70841 .05105 .05107 .05108 .05110 + 8' 33 34 35 8.67522 .67536 .67550 .67565 .047»4 .04735 .04737 .04739 8.68368 .68382 .68396 .68410 .04827 .04839 .04830 .04832 8.69205 .69219 .69233 .69247 .04921 .04923 .04934 .04926 8.70034 .70047 .70061 .70075 .05016 .05017 .05019 .05031 8.70854 .70868 .70881 .70895 .05111 .05113 .05115 .05116 + 9^ 57 38 39 8.67579 .67593 .67607 .67621 .04740 .04743 .04743 .04745 8.68424 .68438 .68452 .68466 .04833 .04835 .04836 .04838 8.69260 .69274 .69288 .69302 .04937 .04929 .04930 .04932 8.70089 .70102 .70116 .70130 .05033 .05034 .05035 .05037 8.70909 .70922 .70936 .70949 .05118 .05119 .05121 .05133 24 23 22 21 + UK 42 43 8.67635 .67649 .67664 .67678 .04746 .04748 .04749 .04751 8.68480 .68494 .68508 .68522 .04839 .04841 .04843 .04844 8.69316 .69330 .69344 .69358 .04934 .04935 .04937 .04938 8.70144 .70157 .70171 .70185 .05028 .05030 .05032 .05033 8.70963 .70977 .70990 .71004 .05134 .05126 .05127 .05129 20 19 18 17 + 11' 45 46 47 8.67692 .67706 .67720 .67734 .04752 .04754 .04756 .04757 8.68536 .68550 .68564 .68578 .04846 .04847 .04849 .04850 8.69371 .69385 .69399 .69413 .04940 .04941 .04943 .04945 8.70198 .70212 .70226 .70240 .05035 .05036 .05038 .05040 8.71017 .71031 .71045 .71058 .05131 .05133 .05134 .05135 16 15 U IS + 12' ■49 50 51 8.67748 .67763 .67777 .67791 .04759 .04760 .04762 .04763 8.68592 .68606 .68620 .68634 .04852 .04854 .04855 .04857 8.69427 .69441 .69454 .69468 .04946 .04948 .04949 .04951 8.70253 .70267 ..70281 .70294 .05041 .05043 .05044 ,05046 8.71072 .71085 .71099 .71112 .05137 .05139 .05140 .05143 12 11 10 9 + 13' 55 54 55 8.67805 .67819 .67833 .67847 .04765 .04766 .04768 .04769 8.68648 .68662 .68676 .68690 .04858 .04860 .04861 .04863 8.69482 .69496 .69510 .69524 .04953 .04954 .04956 .04957 8.70308 .70322 .70336 .70349 .05048 .05049 .05051 .05052 8.71126 .71140 .71153 .71167 .05144 .05145 .05147 .05148 8 7 6 5 + U' 57 58 59 8.67861 .67875 .67890 .67904 .04771 .04773 .04774 .04776 8.68704 .68718 .68732 .68746 .04864 .04866 .04868 .04869 8.69537 .69551 .69565 .69579 .04959 .04960 .04963 .04964 8.70363 .70377 .70390 .70404 .05054 .05055 .05057 .05059 8.71180 .71194 .71207 .71221 .05150 .05153 .05153 .05155 4 3 2 1 + 15' 8.67918 .04777 8.68760 .04871 8.69593 .04966 8.70418 .05080 8.71234 .05156 22^ igm 22^ ISm 22^ nm 2S^ l&m 22h ISm TABLE IV. [Page 65 ^Haversines. s lh45m 36° 15' 1^ 46rn 26° SC Ih 47m 36° 45' Ih 48m 2V C - Ih 49m 370 15/ s Log. Hav. Nat. Hav Log. Hav Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. 1 2 S S.71234 .71248 .71261 .71275 .05156 .05158 .05160 .05161 8.72043 .72057 .72070 .72083 .05253 .05255 .05257 .05358 8.72844 .72857 .72871 .72884 .05351 .05353 .05354 .05356 8.73637 .73650 .73663 .73677 .05450 .05451 .05453 .05455 8.74423 .74436 .74449 .74462 .05549 .05551 .05552 .05554 60 59 58 51 + r 5 6 1 8.71289 .71302 .71316 .71329 .05163 .05164 .05166 .05168 8.72097 .72110 .72124 .72137 .05360 .05261 .05263 .05265 8.72897 .72910 .72924 .72937 .05358 .05359 .05301 .05363 8.73690 .73703 .73716 .73729 .05456 .05458 .05460 .05461 8.74475 .74488 .74501 .74514 .05556 .05557 .05559 .05561 56 55 54 53 + 3' 9 10 11 8.71343 .71356 .71370 .71383 .05169 .05171 .05173 .05174 8.72150 .72164 .72177 .72191 .05266 .05368 .05370 .05271 8.72950 .72963 .72977 .72990 .05364 .05366 .05367 .05369 8.73742 .73755 .73769 .73782 .05463 .05464 .05466 .05468 8.74527 .74540 .74553 .74566 .05562 .05564 .05566 .05567 52 51 50 49 48 41 46 45 44 43 42 41 + 3' 13 14 15 8.71397 .71410 .71424 .71437 .05176 .05177 .05179 .05181 8.72204 .72217 .72231 .72244 .05273 .05274 .05276 .05278 8.73003 .73016 .73030 .73043 .05371 .05373 .05374 .05376 8.73795 .73808 .73821 .73834 .05470 .05471 .05473 .05474 8.74579 .74592 .74605 .74618 .05569 .05571 .05573 .05574 + 4' 17 18 19 8.71451 .71464 .71478 .71491 .05182 .05184 .05185 .05187 8.72257 .72271 .72284 .72298 .05279 .05281 .05283 .05284 8.73056 .73069 .73083 .73096 .05377 .05379 .05381 .05383 8.73847 .73860 .73874 .73887 .05476 .05478 .05479 .05481 8.74631 .74644 .74657 .74670 .05576 .05577 .05579 .05581 + 5' 21 22 23 8.71505 .71518 .71532 .71545 .05189 .05190 .05193 .05193 8.72311 .72324 .72338 .72351 .05386 .05287 .05289 .05291 8.73109 .73122 .73136 .73149 .05384 .05385 .05387 .05389 8.73900 .73913 .73926 .73939 .05483 .05484 .05486 .05488 8.74683 .74696 .74709 .74722 .05582 .05584 .05586 .05587 40 39 38 31 + 6' 25 26 21 8.71559 .71572 .71586 .71599 .05195 .05197 .05198 .05200 8.72364 .72378 .72391 .72404 .05393 .05394 .05296 .05297 8.73162 .73175 .73189 .73202 .05390 .05392 .05394 .05395 8.73952 .73965 .73978 .73992 .05489 .05491 .05493 .05494 8.74735 .74748 .74761 .74774 .05589 .05591 .05593 .05594 36 35 34 33 + r 29 SO 31 8.71613 .71626 .71640 .71653 .05201 .05203 .05205 .05206 8.72418 .72431 .72445 .72458 .05299 .05300 .05302 .05304 8.73215 .73228 .73241 .73255 .05397 .05399 .05400 .05402 8.74005 .74018 .74031 .74044 .05496 .05498 .05499 .05501 8.74787 .74800 .74813 .74826 .05596 .05597 .05599 .05601 32 31 30 29 + 8' S3 34 35 8.71667 .71680 .71694 .71707 .05208 .05210 .05211 .05213 8.72471 .72485 .72498 .72511 .05305 .05307 .05309 .05310 8.73268 .73281 .73294 .73308 .05404 .05405 .05407 .05408 8.74057 .74070 .74083 .74096 .05503 .05504 .05506 .05508 8.74839 .74852 .74864 .74877 .05603 .05604 .05606 .05607 28 21 26 25 + 9^ 31 38 39 8.71721 .71734 .71748 .71761 .05214 .05216 .05218 .05319 8.72525 .72538 .72551 .72565 .05313 .05314 .05315 .05317 8.73321 .73334 .73347 .73360 .05410 .05412 ' .05413 .05415 8.74109 .74122 .74135 .74149 .05509 .05511 .05513* .05514 8.74890 .74903 .74916 .74929 .05609 .05611 .05613 .05614 24 23 22 21 + 1(K 41 42 43 8.71774 .71788 .71801 .71815 .05221 .05222 .05224 .05226 8.72578 .72591 .72605 .72618 .05318 .05320 .05322 .05323 8.73374 .73387 .73400 .73413 .05417 .05418 .05420 .05423 8.74162 .74175 .74188 .74201 .05516 .05518 .05519 .05521 8.74942 .74955 .74968 .74981 .05616 .05618 .05619 .05621 20 19 18 11 + ir 45 46 41 8.71828 .71842 .71855 .71869 .05327 .05229 .05231 .05332 8.72631 .72644 .72658 .72671 .05325 .05326 i .05338 .05330 8.73426 .73440 .73453 .73466 .05433 .05425 .05427 .05428 8.74214 .74227 .74240 ■ .74253 .05523 .05534 .05536 .05528 8.74994 .75007 .75020 .75033 .05623 .05624 .05626 .05638 16 15 14 13 + 12' 49 60 51 8.71882 .71895 .71909 .71922 .05234 .05335 .05237 .05239 8.72684 .72698 .72711 .72724 .05331 .05333 » .05335 ^ .05336 8.73479 .73492 i.73505 ^73519 .05430 .05431 .05433 .05435 8.74266 -.74279 .74292 .74305 .05529 .05531 .05533 .05534 8.75046 .75059 .75072 .75084 .05639 .05631 .05633 .05634 12 11 10 9 + 13' 53 54 55 8.71936 .71949 .71963 .71976 ,05340 .05343 .05344 .05345 8.72738 .72751 .72764 .72778 .0.5338 .05340 .05341 .05343 8.73532 , .73545 .73558 .73571 .05436 .05438 .05440 .05441 8.74318 .74331 .74344 .74357 .05536 .05537 .05539 .05541 8.75097 .75110 .75123 .75136 .05636 .05638 .05639 .05641 8 7 6 5 + w 57 58 59 8.71989 .72003 .72016 .72030 .05347 .05348 .05250 .05353 8.72791 .72804 .72817 .72831 .05345 .05346 .05348 .05349 8.73584 .73598 .73611 .73624 .05443 .05445 .05446 .05448 8.74371 .74384 .74397 .74410 .05542 .05544 .05546 .05547 8.75149 .75162 .75175 .75188 .05643 .05644 .05646 .05648 4 3 2 1 + 15' 8.72043 .05353 8.72844 .05351 8.73637 .05450 8.74423 .05549 8.75201 .05649 22h 14m 1 22h JSm • 22^ 12™' 22^ llm 1 22h 10^ 55901°— 18- Page 66] TABLE IV. Haversines. s 2 A 5(9« 27o W Ih 5im 27° 45' Ih 52rn' 28° C Ih 5Sm 28° 15' Ih 54"" 28° 30' s Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. 1 2 3 8.75201 .75214 .75227 .75239 .05649 .05651 .05653 .05655 8.75972 .75984 .75997 .76010 .05751 .05752 .05754 .05756 8.76735 .76748 .76760 .76773 .05853 .05854 .05856 .05858 8.77492 .77504 .77517 .77529 .05955 .05957 .05959 .05961 8.78241 .78254 .78266 .78278 .06059 .06061 .06063 .06064 60 59 58 57 + r 5 6 7 8.75252 .75265 .75278 .75291 .05656 .0565S .05660 .05661 8.76023 .76035 .76048 .76061 .05757 .05759 .05761 .05762 8.76786 .76798 76811 .76824 .05859 .05861 .05863 .05865 8.77542 .77554 .77567 .77579 .05962 .05964 .05966 .05968 8.78291 .78303 .78310 .78328 .06066 .06088 .06070 .06071 56 55 54 53 + 3' 9 10 11 8.75304 .75317 .75330 .75343 .05663 .05665 .05666 .05668 8.76074 .76086 .76099 .76112 .05764 .05766 .05768 .05769 8.76836 .76849 .76862 .76874 .05866 .05868 .05870 .05871 8.77592 .77604 .77617 .77630 .05969 .05971 .05973 .05974 8.78341 .78353 .78365 .78378 .06073 .06075 .06077 .06078 52 51 50 49 + 3' IS 14 15 8.75355 .75368 .75381 .75394 .05670 .05671 .05673 .05675 8.76125 .76138 .76150 .76163 .05771 .05773 .05774 .05776 8.76887 .76900 .76912 .76925 .05873 .05875 .05877 .05878 8.77642 .77655 .77667 .77680 .05976 .05978 .05980 .05981 8.78390 .78403 .78415 .78428 .06080 .06082 .06083 .08085 48 47 46 45 + 4' 17 18 19 8.75407 .75420 .75433 .75446 .05676 .05678 .05680 .05681 8.76176 .76189 .76201 .76214 .05778 .05779 .05781 .05783 8.76938 .76950 .76963 .76975 .05880 .05882 .05883 .05885 8.77692 .77705 .77717 .77730 .05983 .05985 .05986 .05988 8.78440 .78452 .78465 .78477 .06087 .06089 .06090 .96092 44 43 42 41 + 6' 21 22 23 8.75458 .75471 .75484 .75497 .05683 .05685 .05686 .05688 8.76227 .76240 .76252 .76265 .05785 .05786 .05788 .05790 8.76988 .77001 .77013 .77026 .05887 .05888 .05890 .05892 8.77742 .77755 .77767 .77780 .05990 .05992 .05993 .05995 8.78490 .78502 .78514 .78527 .06094 .08096 .06097 .08099 40 39 38 37 + 6' 25 26 27 8.75510 .75523 .75536 .75548 .05690 .05691 .05693 .05695 8.76278 .76291 .76303 .76316 .05791 .05793 .05795 .05796 8.77039 .77051 .77064 .77076 .05894 .05895 .05897 .05899 8.77792 .77805 .77817 .77830 .05997 .05999 .06000 .06002 8.78539 .78551 .78564 .78576 .06101 .06103 .06104 .06106 36 35 34 33 + r 29 SO 31 8.75561 .75574 .75587 .75600 .05697 .05698 .05700 .05702 8.76329 .76341 .76354 .76367 .05798 .05800 .05802 .05803 8.77089 .77102 .77114 .77127 .05901 .05902 .05904 .05906 8.77842 .77855 .77867 .77880 .06004 .06005 .06007 .06009 8.78589 .78601 .78613 .78626 .06108 .06110 .06111 .06113 32 31 30 29 + 8' 33 34 35 8.75613 .75626 .75638 .75651 .05703 .05705 .05707 .05708 8.76380 .76392 .76405 .76418 .05805 .05807 .05808 .05810 8.77139 .77152 .77165 .77177 .05907 .05909 .05911 .05913 8.77892 .77905 .77917 .77930 .06011 .08013 .06014 .06016 8.78638 .78651 .78663 .78675 .06115 .06117 .06118 .06120 28 27 26 25 24 23 22 21 20 19 18 17 + 9^ 37 38 39 8.75664 .75677 .75690 .75703 .05710 .05712 .05713 .05715 8.76431 .76443 .76456 .76469 .05812 .05813 .05815 .05817 8.77190 .77202 .77215 .77228 .05914 .05916 .05918 .05919 8.77942 .77955 .77967 .77980 .08018 .06019 .06021 .06023 8.78(i88 .78700 .78712 .78725 .06122 .06124 .06125 .06127 + 1(K 41 42 45 8.75715 .75728 .75741 .75754 .05717 .05718 .05720 .05722 8.76481 .76494 .76507 .76519 .05819 .05820 .05822 .05824 8.77240 .77253 .77265 .77278 .05921 .05923 .05925 .05926 8.77992 .78005 .78017 .78029 .06024 .08026 .06028 .06030 8.78737 .78749 .78762 .78774 .06129 .06130 .06132 .06134 + 11' 45 46 47 8.75767 .75779 .75792 .75805 .05724 .05725 .05727 .05729 8.76532 .76545 .76558 .76570 .05825 .05837 .05829 .05830 8.77291 .77303 .77316 .77328 .05928 .05930 .05931 .05933 8.78042 .78054 .78067 .78079 .06031 .06033 .08035 .06037 8.78787 .78799 .78811 .78824 .06136 .06137 .06139 .06141 16 15 14 13 12 11 10 9 + 12' 50 5i 8.75818 .75831 .75844 .75856 .05730 .05732 .05734 .05735 8.76583 .76596 .76608 .76621 .05832 .05834 .05836 .05837 8.77341 .77353 .77306 .77379 .05935 .05936 .05938 .05940 8.78092 .78104 .78117 .78129 .06038 .06040 .06042 .06044 8.78836 .78848 .78861 .78873 .06143 .06144 .06146 .06148 + 13' 55 54 55 8.75869 .75882 .75895 .75908 .05737 .05739 .05740 .05742 8.76634 .76646 .76659 .76672 .05839 .05841 .05842 .05844 8.77391 .77404 .77416 .77429 .05942 .05943 .05945 .05947 8.78142 .78154 .78167 .78179 .06045 .06047 .06049 .06050 8.78885 .78898 .78910 .78922 8.78935 .78947 .78959 .78972 .06150 .06151 .06153 .06155 8 7 6 5 + 14' 57 55 59 8.75920 .75933 .75946 .75959 .05744 .05745 .05747 .05749 8.76684 .76697 .76710 .76722 .05846 .05847 .05849 .05851 8.77441 .77454 .77466 .77479 .05949 .05950 .05952 .05954 8.78191 .78204 .78216 .78229 .06052 .06054 .06056 .06057 .06157 .06158 .08160 .06162 4 3 2 1 + 15' 8.75972 .05751 8.76735 .05853 8.77492 .05955 8.78241 .06059 8.78984 .06184 22^ 9m 22h Sm 22h7m 22h6m ff ft 5m TABLE IV. [Page 67 Haversines. s iA 55^28° 45' Ih 56m 29° 0' ^^1.57^39° 15' Ih SSm 39° 30' Ih 59^29° 45' s Log. Ilav. Nat. Ilav. Log. nav. Nat. Ilav. Log. Ilav. Nat. Uav. Log. Uav Nat. nav. Log. Ilav. Nat. Ilav. 1 2 3 8.78984 .78996 .79009 .79021 .06164 .06165 .06167 .06169 8.79720 .79732 .79744 . .79757 .06369 .06371 .06373 .06374 8.80449 .80462 .80474 .80486 .06375 .06377 .06379 .06381 8.81172 .81184 .81196 .81208 .06482 .06484 .06488 .06488 8.81889 .81901 .8-1913 .81925 .06590 .08592 .06594 .06595 60 59 58 57 + r 5 6 7 8.79033 .79046 .79058 .79070 .06171 .06173 .06174 .06176 8.79769 .79781 .79793 .79805 .06376 .06378 .06380 .06381 8.80498 .80510 .80522 .80534 .06383 .06384 .06386 .06388 8.81220 .81232 .81244 .81256 .06489 .06491 .08493 .06495 8.81937 .81948 .81960 .81972 .08597 .08599 .06601 .06603 56 55 54 53 + V 9 10 11 8.79082 .79095 .79107 .79119 .06178 .06179 .06181 .06183 8.79818 .79830 .79842 .79854 .06383 .06385 .06387 .06388 8.80546 .80558 .80570 .80582 .08389 .06391 .06393 .06395 8.81268 .81280 .81292 .81304 .06497 .06498 .06500 .08502 8.81984 .81996 .82008 .82020 .06805 .08808 .06808 .06610 52 51 50 49 + 3' IS 14 15 8.79132 .79144 .79156 .79169 .06185 .06186 .06188 .06190 8.79866 .79879 .79891 .79903 .06390 .06393 .06394 .06395 8.80595 ,80607 .80619 _. 80631 .06397 .06398 .06400 .06402 8.81316 .81328 .81340 .81352 .06504 .06505 .06507 .06509 8.82032 .82043 .82055 .82067 .06612 .06614 .08815 .06617 48 47 46 45 + ^' 17 18 19 8.79181 .79193 .79205 .79218 .06193 .06193 .06195 .06197 8.79915 .79927 .79940 .79952 .06397 .06399 .06301 .06303 8.80643 .80655 .80667 .80679 ^06404 .06405 .06407 .06409 8.81364 .81376 .81388 .81400 .06511 .06513 .06514 .08516 8.82079 .82091 .82103 .82115 .06619 .06621 .06623 .06634 44 43 42 41 + ^ 21 22 23 8.79230 .79242 .79255 .79267 .06199 .06300 .06203 .06304 8.79964 .79976 .79988 .80000 .06304 .06306 .06308 .06310 8.80691 .80703 .80715 .80727 .06411 .06413 .06414 .06416 8.81412 .81424 .81436 .81448 .08518 .06530 .06533 .06533 8.82126 .82138 .82150 .82162 .06636 .06628 .06630 .08633 40 39 38 37 + ^ 25 26 27 8.79279 .79291 .79304 .79316 .06306 .06307 .06309 .06311 8.80013 .80025 .80037 .80049 .06311 .06313 .06315 .06317 8.80739 .80751 .80764 .80776 .06418 .06420 .06421 .06433 8.81460 .81^72 .81484 .81496 .06535 .08527 .06539 .08531 8.82174 .82186 .82198 .82209 .08633 .06635 .06637 .06639 36 35 34 33 + r 29 30 -31 8.79328 .79341 .79353 .79365 .06313 .06314 .06316 .06318 8.80061 .80073 .80086 .80098 .06318 .06330 .06333 .06334 8.80788 .80800 .80812 .80824 .06435 :06437 w06429 .08430 8.81508 .81520 .81531 .81543 .06533 .06534 .06538 .06538 8.82221 .82233 .82245 .82257 .08841 .06643 .08844 .06648 32 31 30 29 + 8^ S3 34 35 8.79377 .79390 .79402 .79414 .06330 .06331 .06223 .06335 8.80110 .80122 .80134 .80146 .06336 .06327 .06329 .06331. 8.80836 .80848 .80860 .80872 .06433 .06434 .08436 .08438 8.81555 .81567 .81579 .81591 .06540 .06541 .06543 .06545 8.82269 .82280 .82292 .82304 .06648 .06850 .08653 .08653 28 27 26 25 + 9^ 37 38 39 8.79426 .79439 .79451 .79463 .06337 .06339 .06330 .06233 8.80158 .80171 .80183 .80195 .06333 .06334 .06336 .06338 8.80884 .80896 .80908 .80920 .08439 .08441 .08443 .06445 8.81603 .81615 .81627 .81639 .06547 .06549 .08550 .06553 8.82316 .82328 .82340 .82351 .08655 .08857 .08859 .06681 24 23 22 21 + ir 41 42 43 8.79475 .79488 .79500 .79512 .06334 .06336 .06337 .06339 8.80207 .80219 .80231 .80243 .06340 .06341 .06343 .06345 8.80932 .80944 .80956 .80968 .06446 .06448 .06450 .06453 8.81651 .81663 .81675 .81687 .06554 .06558 .06558 .08559 8.82363 .82375 .82387 .82399 .06663 .06884 .06686 .08668 20 19 18 17 + 11' 45 46 47 8.79524 .79537 .79549 .79561 .06341 .06343 .08344 .06346 8.80256 .80268 .80280 .80292 .06347 .06349 .06350 .06353 8.80980 .80992 .81004 .81016 .06454 .06455 .06457 .06459 8.81699 .81710 .81722 .81734 .06561 .06563 .06565 .06567 8.82410 .82422 .82434 .82446 .06670 .08871 .08673 .08675 16 15 U 13 + ir 49 50 51 8.79573 .79586 .79598 .79610 .06348 .06350 .06351 .06353 8.80304 .80316 .80328 .80340 .06354 .06356 .06357 .06359 8.81028 .81040 .81052 .81064 .08481 .08463 .06464 .06468 8.81746 .81758 .81770 .81782 .06568 .06570 .06573 .06574 8.82458 .82470 .82481 .82493 .08677 .06879 .08681 .06682 12 11 10 9 + 13' 53 54 55 8.79622 .79634 .79647 .79659 .06355 .06357 .06358 .06360 8.80353 .80365 .80377 .80389 .06361 .06363 .06365 .06386 8.81076 .81088 .81100 .81112 .06468 .06470 .06471 .06473 8.81794 .81806 .81818 .81830 .06576 .06577 .06529 .06581 8.82505 .82517 .82529 .82540 .08684 .06688 .06888 .06690 8 7 6 5 + 14' 57 68 59 8.79671 .79683 .79696 .79708 .06363 .06364 .06365 .06367 8.80401 .80413 .80425 .80437 .06368 .06370 .06373 .06373 8.81124 .81136 .81148 .81160 .06475 .06477 .06479 .06480 8.81841 .81853 .81865 .81877 .06583 .06585 .08586 .08588 8.82552 .82564 .82576 .82588 .08691 .08893 .06895 .06697 4 3 2 1 + 15' 8.79720 .06369 8.80449 .06375 8.81172 .06483 8.81889 .06590 8.82599 .08899 22^ 4m 22^1' Sm 22}'' jgw 1 22^^ im 22h (ym. 1 Page 68] TABLE IV. Haversinea. s 2h Orn 30° (K 1 ^h im 30° 15' 1 Oh 2m 30° 30' 2^ Sm 30° 45' 2h 4"» 31° 0' 1 s Log. Hav. Nat. Hav. Log. Hav. Nat. Kav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. 1 2 3 8.82599 .82611 .82623 .82635 .06699 .06701 .06703 .06701 8.83303 .83315 .83327 .83338 .06808 .06810 .06813 .06814 8.84002 .84013 .84025 .84036 .06919 .06920 .06923 .06934 8.84694 .84705 .84717 .84728 .07030 .07032 .07033 .07035 8.85380 .85391 .85403 .85414 .07143 .07144 .07145 .07147 60 59 58 57 + r 5 6 7 8.82646 .82658 .82670 .82682 .06706 .06708 .06710 .06711 8.83350 .83362 .83374 .83385 .06816 .06817 .06819 .06831 8.84048 .84059 .84071 .84083 .06936 .06938 .06930 .06931 8.84740 .84751 .84762 .84774 .07037 .07039 .07041 .07043 8.85425 .85437 .85448 .85459 .07149 .07151 .07153 .07155 56 55 54 53 + V 9 10 11 8.82694 .82705 .82717 .82729 .06713 .06715 .06717 .06719 8.83397 .83409 .83420 .83432 .06823 .06825 .06826 .06838 8.84094 .84106 .84117 .84129 .06933 .06935 .06937 .06939 8.84785 .84797 .84808 .84820 .07045 .07046 .07048 .07050 8.85471 .85482 .85494 .85505 .07157 .07158 .07160 .07162 52 51 50 49 + 3' 13 14 15 8.82741 .82752 .82764 .82776 .06731 .06723 .06731 .06736 8.83444 .83455 .83467 .83479 .06830 .06833 .06834 .06836 8.84140 .84152 .84164 .84175 .06941 .06943 .06944 .06946 8.84831 .84843 .84854 .84866 .07053 .07054 .07056 .07058 8.85516 .85528 .85539 .85550 .07164 .07166 .07168 .07170 48 47 46 45 44 43 42 41 + 4^ 17 18 19 8.82788 .82799 .82811 .82823 8.82835 .82846 .82858 .82870 .06728 .06730 .06731 .06733 8.83490 .83502 .83513 .83525 .06838 .06839 .06841 .06843 8.84187 .84198 .84210 .84221 .06948 .06950 .06952 .06954 8.84877 .84889 .84900 .84912 .07059 .07061 .07063 .07065 8.85562 .85573 .85585 .85596 .07172 .07173 .07175 .07177 + 5^ 21 22 23 .06735 .06737 .06739 .06741 8.83537 .83548 .83560 .83572 .06845 .06847 .06849 .06850 8.84233 .84244 .84256 .84268 .06956 .06957 .06959 .06961 8.84923 .84934 .84946 .84957 .07067 .07069 .07071 .07073 8.85607 .85619 .85630 .85641 .07179 .07181 .07183 .07185 40 39 38 37 + 6' 25 26 27 8.82882 .82893 .82905 .82917 .06743 .06744 .06746 .06748 8.83583 .83595 .83607 .83618 .06852 .06854 .06856 .06858 8.84279 .84291 .84302 .84314 .06963 .06965 .06967 .06968 8.84969 .84980 .84992 .85003 .07074 .07076 .07078 .07080 8.85653 .85664 .85675 .85687 .07187 .07189 .07190 .07192 36 35 34 33 + r 29 30 31 8.82929 .82940 .82952 .82964 .06750 .06753 .06753 .06755 8.83630 .83642 .83653 .83665 .06860 .06861 .06863 .06865 8.84325 .84337 .84348 .84360 .06970 .06972 .06974 .06976 8.85015 .85026 .85037 .85049 .07083 .07084 .07086 .07087 8.85698 .85709 .85721 .85732 .07194 .07196 .07198 .07300 32 31 30 29 + 8' 33 24 35 8.82976 .82987 .82999 .83011 .06757 .06759 .06761 .06763 8.83676 .83688 .83700 .83711 .06867 .06869 .06871 .06873 8.84371 .84383 .84394 .84406 .06978 .06980 .06981 .06983 8.85060 .85072 .85083 .85095 .07089 .07091 .07093 .07095 8.85743 .85755 \85766 .85777 .07303 .07304 .07305 .07307 28 27 26 25 + 9^ 57 SB 39 8.83023 .83034 .83046 .83058 .06764 .06766 .06788 .06770 8.83723 .83735 .83746 .83758 .06874 .06876 .06878 .06880 8.84417 .84429 .84441 .84452 .06985 .06987 .06989 .06991 8.85106 .85117 .85129 .85140 .07097 .07099 .07100 .07103 8.85789 .85800 .85811 .85823 .07309 .07311 .07313 .07315 24 23 22 21 + W 41 42 43 8.83069 .83081 .83093 .83105 .06772 .06773 .06775 .06777 8.83769 .83781 .83793 .83804 .06883 .06884 .06885 .06887 8.84464 .84475 .84487 .84498 .06993 .06994 .06996 .06998 8.85152 .85163 .85175 .85186 .07104 .07106 .07108 .07110 8.85834 .85845 .85857 .85868 .07217 .07219 .07230 .07223 20 19 18 17 + ir 45 46 47 8.83116 .83128 .83140 .83151 .06779 .06781 .06783 .06784 8.83816 .83828 .83839 .83851 .06889 .06891 .06893 .06895 8.84510 .84521 .84533 .84544 .07000 .07003 .07004 .07006 8.85197 .85209 .85220 .85232 .07112 .07114 .07115 .07117 8.85879 .85891 .85902 .85913 .07234 .07236 .07228 .07230 16 15 14 13 + 13' 49 50 51 8.83163 .83175 .83187 .83198 .06786 .06788 .06790 .06793 8.83862 .83874 .83886 .83897 .06896 .06898 .06909 .06903 8.84556 .84567 .84579 .84590 .07007 .07009 .07011 .07013 8.85243 .85254 .85266 .85277 .07119 .07121 .07123 .07135 8.85925 .85936 .85947 .85959 .07232 .07234 .07236 .07237 12 11 10 9 + 13' 53 54 55 8.83210 .83222 .83233 .83245 .06794 .06795 .06797 .06799 8.83909 .83920 .83932 .83944 .06904 .06906 .06907 .06909 8.84602 .84613 .84625 .84636 .07015 .07017 .07019 .07020 8.85289 .85300 .85311 .85323 .07137 .07139 .07130 .07133 8.85970 .85981 .85992 .86004 .07339 .07341 .07343 .07345 8 7 6 5 + 14' 57 59 8.83257 .83268 .83280 .83292 .06801 .06803 .06805 .06806 8.83955 .83967 .83978 .83990 .06911 .06913 .06915 .06917 8.84648 .84659 .84671 .84682 .07033 .07024 .07026 .07028 8.85334 .85346 .85357 .85368 .07134 .07136 .07138 .07140 8.86015 .86026 .86038 .86049 .07347 .07349 .07351 .07253 4 3 2 1 + 15' 8.83303 .06808 8.84002 .06919 8.84694 .07030 8.85380 .07143 8.86060 .07254 21^ 59m 21h58m 21h57m 21^ 56m 21h 55m TABLE IV. [Page 69 Haversjnes. s 2h jm 31° 15' 2^ 6"» 31° 30' 2h 7m 310 45/ f A 5m 32° C 2h gm 33° 15' 8 Log. Hav Nat. Hav Log. Hav. Nat. Hav Log. Hav. Nat. Hav. Log. Hav. Nat. llav Log. Hav. Nat. Hav. 1 2 S 8.86060 .86072 .86085 .86094 .07254 .07256 .07258 .07260 8.86735 .86746 .86757 .86769 .07368 .07370 .07372 .07374 8.87404 .87415 .87426 .87437 .07482 .07484 .07486 .07488 8.88068 .88079 .88090 .88101 .07598 .07600 .07601 .07603 8.88726 .88737 .88748 .88759 .07714 .07716 .07717 .07719 60 59 58 57 5 6 7 8.86105 .86117 .86128 .86139 .07262 .07264 .07266 .07268 8.86780 .86791 .86802 .86813 .07376 .07377 .07379 .07381 8.87448 .87460 .87471 .87482 .07490 .07492 .07494 .07496 8.88112 .88123 .88134 .88145 .07605 .07607 .07609 .07611 8.88769 .88780 .88791 .88802 .07721 .07723 .07725 .07727 66 55 54 63 + r 9 10 11 8.86151 .86162 .86173 .86184 .07270 .07271 .07273 .07275 8.86825 .86836 .86847 .86858 .07383 .07385 .07387 .07389 8.87493 .87504 .87515 .87526 .07498 .07500 .07502 .07503 8.88156 .88167 .88178 .88189 .07613 .07615 .07617 .07619 8.88813 .88824 .88835 .88846 .07729 .07731 .07733 .07735 52 51 60 49 + 3' IS 14 15 8.86196 .86207 .86218 .86229 .07277 .07279 .07281 .07283 8.86869 .86880 .86892 .86903 .07391 .07393 .07395 .07397 8.87537 .87548 .87559 .87570 .07505 .07507 .07509 .07511 8.88200 .88211 .88222 .88233 .07621 .07623 .07625 .07627 8.88857 .88868 .88879 .88890 .07737 .07739 .07741 .07743 48 47 46 45 + 4' 17 18 19 8.86241 .86252 .86263 .86275 .07285 .07287 .07288 .07290 8.86914 .86925 .86936 .86947 .07398 .07400 .07402 .07404 8.87582 .87593 .87604 .87615 .07513 .07515 .07517 .07519 8.88244 .88255 .88266 .88277 .07628 .07630 .07632 .07634 8.88900 .88911 .88922 .88933 .07745 .07747 .07749 .07751 44 43 42 41 + 5' 21 22 2S 8.86286 .86297 .86308 .86320 .07292 .07294 .07296 .07298 8.86959 .86970 .86981 .86992 .07406 .07408 .07410 .07412 8.87626 .87637 .87648 .87659 .07521 .07523 .07525 .07527 8.88288 .88299 .88310 .88321 .07636 .07638 .07640 .07642 8.88944 .88955 .88966 .88977 .07752 .07754 .07756 .07758 40 39 38 37 + 6' 25 26 27 8.86331 .86342 .86353 .86365 .07300 .07302 .07304 .07305 8.87003 .87014 .87026 .87037 .07414 .07416 .07417 .07419 8.87670 .87681 .87692 .87703 .07528 .07530 .07532 .07534 8.88332 .88343 .88354 .88364 .07644 .07646 .07648 .07650 8.88988 .88998 .89009 .89020 .07760 .07762 .07764 .07766 36 35 34 33 + r 29 SO SI 8.86376 .86387 .86398 .86410 .07307 .07309 .07311 .07323 8.87048 .87059 .87070 .87081 .07421 .07423 .07425 .07427 8.87714 .87725 .87737 .87748 .07536 .07538 .07540 .07542 8.88375 .88386 .88397 .88408 .07652 .07654 .07656 .07657 8.89031 .89042 .89053 .89064 .07768 .07770 .07772 .07774 32 31 30 29 + 8' ss S4 35 8.86421 .86432 .86443 .86455 .07315 .07317 .07319 .07321 8.87093 .87104 .87115 .87126 .07429 .07431 .07433 .07435 8.87759 .87770 .87781 .87792 .07544 .07546 .07548 .07549 8.88419 .88430 .88441 .88452 .07659 .07661 .07663 .07665 8.89075 .89086 .89096 .89107 .07776 .07778 .07780 .07782 28 27 26 25 + 9' S7 S8 S9 8.86466 .86477 .86488 .86499 .07322 .07324 .07326 .07328 8.87137 .87148 .87159 .87171 .07437 .07438 .07440 .07442 8.87803 .87814 .87825 .87836 .07551 .07553 .07555 .07557 8.88463 .88474 .88485 .88496 .07667 .07669 .07671 .07673 8.89118 .89129 .89140 .89151 .07784 .07786 .07788 .07789 24 23 22 21 + 10' 41 42 43 8.86511 .86522 .86533 .86544 .07330 .07332 .07334 .07336 8.87182 .87193 .87204 .87215 .07444 .07446 .07448 .07450 8.87847 .87858 .87869 .87880 .07559 .07561 .07563 .07565 8.88507 .88518 .88529 .88540 .07675 .07677 .07679 .07681 8.89162 .89172 .89183 .89194 .07791 .07793 .07795 .07797 20 19 18 17 16 15 14 13 + 11' 46 46 47 8.86556 .86567 .86578 .86589 .07338 .07340 .07341 .07343 8.87226 .87237 .87248 .87260 .07452 .07454 .07456 .07458 8.87891 .87902 .87913 .87924 .07567 .07569 .07571 .07573 8.88551 .88562 .88573 .88584 .07683 .07685 .07686 .07688 8.89205 .89216 .89227 .89238 .07799 .07801 .07803 .07805 + 12' 49 50 51 8.86600 .86611 .86623 .86634 .07345 .07347 .07349 .07351 8.87271 .87282 .87293 .87304 .07459 .07461 .07463 .07465 8.87935 .87946 .87957 .87968 .07574 .07576 .07578 .07580 8.88595 .88606 .88616 .88627 .07690 .07692 .07694 .07696 8.89248 .89259 .89270 .89281 .07807 .07809 .07811 .07813 12 11 10 9 8 7 6 5 + 13' 5S 54 55 8.86645 .86657 .86668 .86679 .07353 .07355 .07357 .07359 8.87315 .87326 .87337 .87349 .07467 .07469 .07471 .07473 8.87980 .87991 .88002 .88013 .07582 .07584 .07586 .07588 8.88638 .88649 .88660 .88671 .07698 .07700 .07702 .07704 8.89292 .89303 .89314 .89324 .07815 .07817 .07819 .07831 + 14' 57 58 59 8.86690 .86701 .86713 .86724 .07360 .07362 .07364 .07366 8.87360 .87371 .87382 .87393 .07475 .07477 .07479 .07480 8.88024 .88035 .88046 .88057 .07590 .07592 .07594 .07596 8.88682 .88693 .88704 .88715 .07706 .07708 .07710 .07712 8.89335 .89346 .89357 .89368 .07823 .07825 .07827 .07829 4 3 2 "1 + W 8.86735 .07368 8.87404 .07482 8.88068 .07598 8.88726 .07714 8.89379 .07830 21h 54'^ 1 2lT^5Sm 21h S2m 21hsim Sih 50m Page 70] TABLE IV. Havereines. s 2hl0mZZ°S(/ 1 ^AiJn»32°45' 1 ^A 12^ 33° 0' 1 2h 13m 33' 15' 2h 14m s^oZO" 1 s Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. 1 2 3 8.89379 .89389 .89400 .89411 .07830 .07833 .07834 .07836 8.90026 .90037 .90048 .90058 .07948 .07950 .07953 .07954 8.90668 .90679 .90690 .90700 .08066 .08068 .08070 .08073 8.91306 .91316 .91327 .91337 .08186 .08188 .08190 .08193 8.91938 .91948 .91959 .91969 .08306 .08308 .08310 .08312 60 59 58 57 + r 5 6 7 8.89422 .89433 .89444 .89454 .07838 .07840 .07842 .07844 8.90069 .90080 .90091 .90101 .07956 .07958 .07960 .07962 8.90711 .90722 .90732 .90743 .08074 .08076 .08078 .08080 8.91348 .91358 .91369 .91380 .08194 .08196 .08198 .08300 8.91980 .91990 .92001 .92011 .08314 .08316 .08318 .08330 56 55 54 S3 + 2' 9 10 11 8.89465 .89476 .89487 .89498 .07846 .07848 .07850 .07852 8.90112 .90123 .90134 .90144 .07964 .07966 .07968 .07970 8.90754 .90764 .90775 .90786 .08083 .08084 .08088 .08088 8.91390 .91401 .91411 .91422 .08203 .08304 .08306 .08308 8.92022 .92032 .92043 .92053 .08323 .08324 .08336 .08328 52 51 50 49 48 47 46 45 44 43 42 41 + 3' 13 14 15 8.89509 .89519 .89530 .89541 .07854 .07856 .07858 .07860 8.90155 .90166 .90176 .90187 .07973 .07974 .07976 .07978 8.90796 .90807 .90818 .90828 .08090 .08093 .08094 .08096 8.91432 .91443 .91454 .91464 .08310 .08313 .08314 .08316 8.92064 .92074 .92084 .92095 .08330 .08332 .08334 .08336 + 4' 17 18 19 8.89552 .89563 .89573 .89584 .07862 .07864 .07866 .07868 8.90198 .90209 .90219 .90230 .07980 .07983 .07983 .07985 8.90839 .90849 .90860 .90871 .08098 .08100 .08103 .08104 8.91475 .91485 .91496 .91506 .08318 .08330 .08333 .08334 8.92105 .92116 .92126 .92137 .08338 .08340 .08342 .08344 + 5' 21 22 23 8.89595 .89606 .89617 .89627 .07870 .07873 .07873 .07875 8.90241 .90252 .90262 .90273 .07987 .07989 .07991 .07993 8.90881 .90892 .90903 .90913 .08106 .08108 .08110 .08113 8.91517 .91527 .91538 .91549 .08336 .08338 .08330 .08333 8.92147 .92158 .92168 .92179 .08346 .08348 .08350 .08353 40 39 38 37 + 6' 25 26 27 8.89638 .89649 .89660 .89671 .07877 .07879 .07881 .07883 8.90284 .90294 .90305 .90316 .07995 .07997 .07999 .08001 8.90924 .90935 .90945 .90956 .08114 .08116 .08118 .08130 8.91559 .91570 .91580 .91591 .08334 .08336 .08338 .08340 8.92189 .92200 .92210 .92221 .08354 .08356 .08358 .08360 36 35 34 33 + r 29 30 31 8.89681 .89692 .89703 .89714 .07885 .07887 .07889 .07891 8.90326 .90337 .90348 .90359 .08003 .08005 .08007 .08009 8.90966 .90977 .90988 .90998 .08133 .08134 .08136 .08138 8.91601 .91612 .91622 .91633 .08343 .08344 .08346 .08348 8.92231 .92241 .92252 .92262 .08363 .08364 .08366 .08368 32 31 30 29 + 8' 33 34 35 8.89725 .89735 .89746 .89757 .07893 .07895 .07897 .07899 8.90369 .90380 .90391 .90401 .08011 .08013 .08015 .08017 8.91009 .91019 .91030 .91041 .08130 .08133 .08134 .08136 .08138 .08140 .08143 .08144 8.91643 .91654 .91664 .91675 .08350 .08353 .08254 .08356 8.92273 .92283 .92294 .92304 .08370 .08372 .08374 .08376 28 27 26 25 24 23 22 7i 20 19 18 n + 9' 37 38 39 8.89768 .89779 .89789 .89800 .07901 .07903 .07905 .07907 8.90412 .90423 .90433 .90444 .08019 .08031 .08033 .08035 8.91051 .91062 .91073 .91083 8.91685 .91696 .91707 .91717 .08358 .08360 .08363 .08364 8.92315 .92325 .92335 .92346 .08378 .08380 .08382 .08384 41 42 43 8.89811 .89822 .89832 .89343 .07909 .07911 .07913 .07915 8.90455 .90466 .90476 .90487 .08037 .08039 .08031 .08033 8.91094 .91104 .91115 .91126 .08146 .08148 .08150 .08153 8.91728 .91738 .91749 .91759 .08366 .08268 .08370 .08372 8.92356 .92367 .92377 .92388 .08386 .08388 .08390 .08393 + 11' 45 46 47 8.89854 .89865 .89875 .89886 .07917 .07919 .07931 .07933 8.90498 .90508 .90519 .90530 .08035 .08037 .08039 .08041 8.91136 .91147 .91157 .91168 .08154 .08156 .08158 .08160 8.91770 .91780 .91791 .91801 .08274 .08376 .08278 .08380 8.92398 .92409 .92419 .92429 .08394 .08396 .08398 .08400 16 15 14 13 + 12' 49 50 51 8.89897 .89908 .89919 .89929 .07934 .07936 .07938 .07930 8.90540 .90551 .90562 .90572 .08043 .08045 .08047 .08049 8.91179 .91189 .91200 .91210 .08163 .08164 .08166 .08168 8.91812 .91822 .91833 .91843 .08383 .08384 .08386 .08288 8.92440 .92450 .92401 .92471 .08403 .08404 .08406 .08408 12 11 10 9 + 13' 53 54 55 8.89940 .89951 .89962 .89972 .07933 .07934 .07936 .07938 8.90583 .90594 .90604 .90615 .08051 .08053 .08055 .08057 8.91221 .91232 .91242 .91253 .08170 .08172 .08174 .08176 8.91854 .91864 .91875 .91885 .08390 .08393 .08394 .08396 8.92482 .92492 .92502 .92513 .08410 .08412 .08414 .08416 8 1 6 5 4 3 2 1 + ir 57 58 59 8.89983 .89994 .90005 .90015 .07940 .07943 .07944 .07946 8.90626 .90636 .90647 .90658 .08059 .08061 .08063 .08065 8.91263 .91274 .91284 .91295 .08178 .08180 .08183 .08184 8.91896 .91906 .91917 .91927 .08398 .08300 .08303 .08304 8.92523 .92534 .92544 .92554 .08418 .08420 .08423 .08425 + 15' 8.90026 .07948 8.90668 .08066 8.91306 .08186 8.91938 .08306 8.92565 .08427 21h49m 21h4Sm 21^ 47m 21h46m 21h45m TABLE IV. Haversines. [Page 71 s 2h urn 33° 45' 2h 16m 34° 0" 2h 17m 34° 15' 2^ 18m 34° SO' 2h 19m 34° 45' s Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. 1 2 S 8.92565 .92575 .92586 .92596 .08437 .08429 .08431 .08433 8.93187 .93197 .93208 .93218 .08548 .08550 .08552 .08554 8.93805 .93815 .93825 .93835 .08671 .08673 .08675 .08677 8.94417 .94427 .94438 .94448 .08794 .08796 .08798 .08800 8.95025 .95035 .95045 .95055 .08918 .08920 .08922 .08924 60 59 58 57 + r 5 6 7 8.92607 .92617 .92627 .92638 .08435 .08437 .08439 .08441 8.93228 .93239 .93249 .93259 .08556 .08558 .08560 .08562 8.93846 .93856 .93866 .93876 .08679 .08681 .08683 .08685 8.94458 .94468 .94478 .94488 .08802 .08804 .08806 .08808 8.95065 .95076 .95086 .95096 .08926 .08928 .08930 .08933 .08934 .08936 .08938 .08940 56 55 54 53 62 51 50 49 + r 9 10 11 8.92648 .92659 .92669 .92679 .08443 .08445 .08447 .08449 8.93270 .93280 .93290 .93301 .08564 .08566 .08568 .08571 8.93886 .93897 .93907 .93917 .08687 .08689 .08691 .08693 8.94498 .94509 .94519 .94529 .08810 .08812 .08814 .08816 8.95106 .95116 .95126 .95136 + r 13 14 15 8.92690 .92700 .92710 .92721 .08451 .08453 .08455 .08457 8.93311 .93321 .93332 .93342 .08573 .08575 .08577 .08579 8.93927 .93938 .93948 .93958 .08695 .08697 .08699 .08701 8.94539 .94549 .94559 .94570 .08818 .08820 .08823 .08825 8.95146 .95156 .95166 .95176 .08943 .08945 .08947 .08949 48 47 46 45 + 4' 17 IS 19 8.92731 .92742 .92752 .92762 .08459 .08461 .08463 .08465 8.93352 .93363 .93373 .93383 .08581 .08583 .08585 .08587 8.93968 .93979 .93989 .93999 .08703 .08705 .08707 .08709 8.94580 .94590 .94600 .94610 .08827 .08829 .08831 .08833 8.95186 .95197 .95207 .95217 .08951 .08953 .08955 .08957 44 43 42 41 + 5' 21 22 23 8.92773 .92783 .92794 .92804 .08467 .08469 .08471 .08473 8.93393 .93404 .93414 .93424 .08589 .08591 .08593 .08595 8.94009 .94019 .91030 .94040 .08711 .08714 .08716 .08718 8.94620 .94630 .94641 .94651 .08835 .08837 .08839 .08841 8.95227 .95237 .95247 .95257 .08959 .08961 .08963 .08965 40 39 38 37 + 6^ 25 26 27 8.92814 .92825 .92835 .92845 .08475 .08477 .08479 .08481 8.93435 .93445 .93455 .93466 .08597 .08599 .08601 .08603 8.91050 .94060 .94071 .94081 .08720 .08722 .08724 .08726 8.94661 .94671 .94681 .94691 .08843 .08845 .08847 .08849 8.95267 .95277 .95287 .95297 .08967 .08970 .08973 .08974 36 35 34 S3 + r 29 30 31 8.92856 .92866 .92877 .92887 .08483 .08485 .08487 .08489 8.93476 .93486 .93496 .93507 .08605 .08607 .08609 .08611 8.94091 .94101 .94111 .94122 .08728 .08730 .08732 .08734 8.94701 .94712 .94722 .94732 .08851 .08853 .08856 .08858 8.95307 .95317 .95327 .95337 .08976 .08978 .08980 .08983 32 31 SO 29 + 8^ 33 34 35 8.92897 .92908 .92918 .92928 .08491 .08493 .08495 .08497 8.93517 .93527 .93538 .93548 .08613 .08615 .08617 .08619 8.94132 .94142 .94152 .94162 .08736 .08738 .08740 .08742 8.94742 .94752 .94782 .94772 .08860 .08862 .08864 .08866 8.95347 .95357 .95368 .95378 .08984 .08986 .08988 .08990 28 27 26 25 + 9^ 37 38 39 8.92939 .92949 .92960 .92970 .08499 .08501 .08503 .08505 8.93558 .93568 .93579 .93589 .08621 .08624 .08626 .08628 8.94173 .94183 .94193 .94203 .08744 .08746 .08748 .08750 8.94782 .94793 .94803 .94813 .08868 .08870 .08872 .08874 8.95388 .95398 .95408 .95418 .08992 .08994 .08997 .08999 24 23 22 21 20 19 18 17 + 1(K 41 42 43 8.92980 .92991 .93001 .93011 .08508 .08510 .08512 .08514 8.93599 .93610 .93620 .93630 .08630 .08632 .08634 .08636 8.94213 .94224 .94234 .94244 .08753 .08755 .08757 .08759 8.94823 .94833 .94843 .94853 .08876 .08878 .08880 .08883 8.95428 .95438 .95448 .95458 .09001 .09003 .09005 .09007 + ir 45 46 47 8.93022 .93032 .93042 .93053 .08516 .08518 .08520 .08522 8.93640 .93651 .93661 .93671 .08638 .08640 .08642 .08644 8.94254 .94264 .94275 .94285 .08761 .08763 .08765 .08767 8.94863 .94874 .94884 .94894 .08885 .08887 .08889 .08891 8.95468 .95478 .95488 .95498 .09009 .09011 .09013 .09015 16 15 14 13 + ir 49 50 51 8.93063 .93073 .93084 .93094 .08524 .08526 .08528 .08530 8.93681 .93692 .93702 .93712 .08646 .08648 .08650 .08652 8.94295 .94305 .94315 .94326 .08769 .08771 .08773 .08775 8.94904 .94914 .94924 .94934 .08893 .08895 .08897 .08899 8.95508 .95518 .95528 .95538 .09017 .09019 .09023 .09024 12 11 10 9 + 13^ 53 54 55 8.93104 .93115 .93125 .93135 .08532 .08534 .08536 .08538 8.93722 .93733 .93743 .93753 .086^4 .08656 .08658 .08660 8.94336 .94346 .94356 .94366 .08777 .08779 .08781 .08783 8.94944 .94954 .94965 .94975 .08901 .08903 .08905 .08907 8.95548 .95558 .95568 .95578 .09036 .09028 .09030 .09033 8 7 6 5 57 58 59 8.93146 .93156 .93166 .93177 .08540 .08542 .08544 .08546 8.93764 .93774 .93784 .93794 .08662 .08664 .08666 .08668 8.94376 .94387 .94397 .94407 .08785 .08788 .08790 .08792 8.94985 .94995 .95005 .95015 .08909 .08911 .08914 .08916 8.95588 .95598 .95608 .95618 .09034 .09036 .09038 .09040 4 S 2 1 + 15' 8.93187 .08548 8.93805 .08671 8.94417 .08794 8.95025 .08918 8.95628 .09042 21'h' 44m 21h 43m 21h 42m 21^ 41m 21^ 40m Page 7 2] TABLE IV. Haversines. 8 2h 20m 35° (K 2h 21m 35° 15' 2h 22^ 35° 3r 2k 23^ 35° 45' 2h 24m 36° r s Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. 1 2 3 8.95628 .95638 .95648 .95658 .09042 .09044 .09047 .09049 8.96227 .96237 .96247 .96257 .09168 .09170 .09172 .09174 8.96821 .96831 .96841 .96851 .09294 .09296 .09298 .09301 8.97411 .97421 .97431 .97441 .09431 .09433 .09436 .09438 8.97997 .98006 .98016 .98026 .09549 .09551 .09553 .09556 60 59 58 57 + r 5 6 7 8.95668 .95678 .95688 .95698 .09051 .09053 .09055 .09057 8.96267 .96277 .96287 .96297 .09176 .09178 .09181 .09183 8.96861 .96871 .96881 .96890 .09303 .09305 .09307 .09309 8.97450 .97460 .97470 .97480 .09430 .09433 .09434 .09436 8.98035 .98045 .98055 .98065 .09558 .09560 .09563 .09564 56 55 54 53 + V 9 10 11 8.95709 .95719 .95729 .95739 .09059 .09061 .09063 .09065 8.96307 .96317 .96326 .96336 .09185 .09187 .09189 .09191 8.96900 .96911) .96920 .96930 .09311 .09313 .09315 .09317 8.97489 .97499 .97509 .97519 .09438 .09440 .09443 .09445 8.98074 .98084 .98094 .98103 .09566 .09568 .09571 .09573 52 51 50 49 48 47 46 45 + 3' IS 14 15 8.95749 .95759 .95769 .95779 .09067 .09070 .09073 .09074 8.96346 .96356 .96366 .96376 .09193 .09195 .09197 .09199 8.96940 .96950 .96959 .96969 .09320 .09322 .09324 .09326 8.97529 .97538 .97548 .97558 .09447 .09449 .09451 .09453 8.98113 .98123 .98132 .98142 .09575 .09577 .09579 .09581 + *' 17 18 19 8.95789 .95799 .95809 .95819 .09076 .09078 .09080 .09082 8.96386 .96396 .96406 .96416 .09202 .09204 .09206 .09208 8.96979 .96989 .96999 .97009 .09328 .09330 .09332 .99334 8.97568 .97577 .97587 .97597 .09455 .09457 .09460 .09463 8.98152 .98162 .98171 .98181 .09583 .09586 .09588 .09590 44 43 42 41 + ^ 21 22 23 8.95828 .95838 .95848 .95858 .09084 .09088 .09088 .09030 8.96426 .96436 .96446 .96455 .09210 .09212 .09214 .09216 8.97018 .97028 .97038 .97048 .09337 .09339 .09341 .09343 8.97607 .97617 .97626 .97636 .094W .09466 .09468 .09470 8.98191 .98200 .98210 .98220 .09593 .09594 .09596 .09598 40 39 38 37 + r 25 26 27 8.95868 .95878 .95888 .95898 .09033 .09095 .09097 .09099 8.96465 .96475 .96485 .96495 .09218 .09220 .09223 .09225 8.97058 .97068 .97077 .97087 .09345 .09347 .09349 .09351 8.97646 .97656 .97665 .97675 .09473 .09474 .09477 .09479 8.98229 .98239 .98249 .9S259 .09601 .09603 .09605 .09607 36 35 34 33 + r 29 30 31 8.95908 .95918 .95928 .95938 .09101 .09103 .09105 .09107 8.96505 .96515 .96525 .96535 .09227 .09229 .09231 .09233 8.97097 .97107 .97117 .97127 .09353 .09356 .08358 .09360 8.97685 .97695 .97704 .97714 .09481 .09483 .09485 .09487 S.9S2bS .98278 .98288 .98297 .09609 .09611 .09613 .09616 32 31 30 29 + 8' 33 34 35 8.95948 .95958 .95968 .95978 .09109 .09111 .09113 .09116 8.96545 .96555 .96564 .96574 .09235 .09237 .09239 .09243 8.97136 .97146 .97156 .97166 .09362 .09364 .09366 .09368 8.97724 .97734 .97743 .97753 .09489 .09493 .09494 .09496 8.9S307 .98317 .98326 .98336 .09618 .09620 .09622 .09624 28 27 26 25 24 23 22 Vl 20 19 18 n + 9" 37 S8 39 8.95988 .95998 .96008 .96018 .09118 .09120 .09122 .09124 8.96584 .96594 .96604 .96614 .09244 .09246 .09248 .09250 8.97176 .97186 .97195 .97205 .09370 .09372 .03375 .09377 8.97763 .97773 .97782 .97792 .09498 .09500 .09503 .09504 8.98346 .98355 .98365 .98375 .09626 .09628 .09631 .09633 + W 41 42 43 8.96028 .96038 .96048 .96058 .09126 .09128 .09130 .09132 8.96624 .96634 .96644 .96653 .09253 .09254 .09356 .09258 8.97215 .97225 .97235 .97244 .09379 .09381 .09383 .09385 8.97802 .97812 .97821 .97831 .09506 .09509 .09511 .09513 8.9S3S4 .98394 .98404 .98413 .09635 .09637 .09639 .09641 + 11' 45 46 47 8.96068 .96078 .96088 .96098 .09134 .09136 .09139 .09141 8.96663 .96673 .96683 .96693 .09260 .09263 .09265 .09267 8.97254 .97264 .97274 .97284 .09387 .09389 .09392 .09394 8.97841 .97851 .97860 .97870 .09515 .09517 .09519 .09531 8.98423 .98433 .98442 .98452 .09643 .09646 .09648 .09650 16 15 14 13 + 12' 49 50 51 8.96108 .96118 .96128 .96138 .09143 .09145 .09147 .09149 8.96703 .96713 .96723 .96733 .09269 .09271 .09373 .09375 8.97294 .97303 .97313 .97323 .09396 .09398 .09400 .09402 8.97880 .97890 .97899 .97909 .09534 .09536 .09538 .09530 8.9S4G2 .98471 .98481 .98491 .09652 .09654 .09656 .09658 12 11 10 9 8 7 6 5 + 13^ 53 54 55 8.96148 .96158 .96167 .96177 .09151 .09153 .09155 .09157 8.96742 .96752 .96762 .96772 .09277 .09280 .09383 .09284 8.97333 .97343 .97352 .97362 .09404 .09406 .09409 .09411 8.97919 .97928 .97938 .97948 .09533 .09534 .09536 .09538 8.98500 .98510 .98520 .98529 .09661 .09663 .09665 .09667 + 1¥ 57 58 59 8.96187 .96197 .96207 .96217 .09160 .09162 .09164 .09166 8.96782 .96792 .96802 .96812 .09386 .09288 .09290 .09292 8.97372 .97382 .97392 .97401 .09413 .09415 .09417 .09419 8.97958 .97967 .97977 .97987 .09541 .09543 .09545 .09547 8.98539 .98549 .98558 .98568 .09669 .09671 .09673 .09676 4 3 1 + 15^ 8.96227 .09168 8.96821 .09294 8.97411 .09431 8.97997 .09549 8.98578 .09678 21f^ 39m 21^ 38^ 21f>' 37m 2in 36^ 21^ 35m TABLE IV [Page 73 Haversines. s 2^ 25m 36° 15' 2h 26m 36° 30' 2h 27m 36° 45' 2^ 2Sm 37° 0' 2h 29m 37° 15' s Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. 1 2 S 8.98578 .98587 .98597 .98606 .09678 .09680 .09683 .09684 8.99154 .99164 .99173 .99183 .09807 .09809 .09811 .09814 8.99727 .99736 .99746 .99755 .09937 .09939 .09942 .09944 9.00295 .00305 .00314 .00324 .10068 .10070 .10073 .10075 9.00860 .00869 .00878 .00888 .10200 .10202 .10304 .10306 60 59 58 57 + V 5 6 7 '8.98616 .98626 .98635 .98645 .09686 .09689 .09691 .09693 8.99193 .99202 .99212 .99221 8.99231 .99240 .99250 .99260 .09816 .09818 .09830 .09833 .09834 .09837 .09839 .09831 8.99765 .99774 .99784 .99793 .09946 .09948 .09950 .09953 .09955 .09957 .09959 .09961 9.00333 .00342 .00352 .00361 .10077 .10079 .10081 .100S4 .10086 .10088 .10090 .10092 9.00897 .00906 .00916 .00925 .10309 .10311 .10213 .10315 .10318 .10330 .10332 .10324 56 55 54 53 52 51 50 49 + 3^ 9 10 11 8.98655 .98664 .98674 .98684 .09695 .09697 .09699 .09701 8.99803 .99812 .99822 .99831 9.00371 .00380 .00390 .00399 9.00935 .00944 .00953 .00963 + 3^ IS 14 15 8.98693 .98703 .98712 .98722 .09704 .09706 .09708 .09710 8.99269 .99279 .99288 .99298 .09833 .09835 .09837 .09840 8.99841 .99850 .99860 .99869 .09963 .09966 .09968 .09970 9.00408 .00418 .00427 .00437 .10095 .10097 .10099 .10101 9.00972 .00981 .00991 .01000 .10326 .10228 .10231 .10233 48 47 46 45 + i' 17 18 19 8.98732 .98741 .98751 .98761 .09712 .09714 .09717 .09719 8.99307 .99317 .99327 .99336 .09843 .09844 .09846 .09848 8.99879 .99888 .99898 .99907 .09973 .09974 .09977 .09979 9.00446 .00456 .00465 .00474 .10103 .10105 .10108 .10110 9.01009 .01019 .01028 .01037 .10235 .10237 .10240 .10242 U 43 42 41 40 39 38 37 + 5' 21 22 23 8.98770 .98780 .98790 .98799 .09731 .09733 .09735 .09737 8.99346 .99355 .99365 .99374 .09850 .09853 .09855 .09857 8.99917 .99926 .99936 .99945 .09981 .09983 .09985 .09987 9.00484 .00493 .00503 .00512 .10112 .10114 .10116 .10119 9.01047 .01056 .01065 .01075 .10244 .10246 .10248 .10251 + 6^ 25 26 27 8.98809 .98818 .98828 .98838 .09739 .09733 .09734 .09736 8.99384 .99393 .99403 .99412 .09859 .09861 .09863 .09866 8.99955 .99964 .99974 .99983 .09990 .09993 .09994 .09996 9.00522 .00531 .00540 .00550 .10121 .10133 .10125 .10137 9.01084 .01094 .01103 01112 .10253 .10255 .10257 .10259 36 35 34 33 + r 29 30 31 8.98847 .98857 .98866 .98876 .09738 .09740 .09743 .09745 8.99422 .99432 .99441 .99451 .09868 .09870 .09873 .09874 8.99993 9.00002 .00012 .00021 .09998 .10000 .10003 .10005 9.00559 .00569 .00578 .00587 .10130 .10133 .10134 .10136 9.01122 .01131 .01140 .01150 .10262 .10264 .10266 .10268 32 31 30 29 + 8' 33 34 35 8.98886 .98895 .98905 .98915 .09747 .09749 .09751 .09753 8.99460 .99470 .99479 .99489 .09876 .09879 .09881 .09883 9.00031 .00040 .00049 .00059 .10007 .10009 .10011 .10014 9.00597 .00606 .00616 .00625 .10138 .10141 .10143 .10145 9.01159 .01168 .01178 .01187 .10270 .10373 .10275 .10277 .10279 .10281 .10284 .10286 28 27 26 25 24 23 22 21 + 9" 37 38 39 8.98924 .98934 .98943 .98953 .09755 .09757 .09760 .09763 8.99498 .99508 .99517 .99527 .09885 .09887 .09890 .09892 9.00068 .00078 .00087 .00097 .10016 .10018 .10030 .10033 9.00634 .00644 .00653 .00663 .10147 .10149 .10152 .10154 9.01196 .01206 .01215 .01224 + W 41 42 43 8.98963 .98972 .98982 .98991 .09764 .09766 .09768 .09770 8.99536 .99546 .99556 .99565 .09894 .09896 .09898 .09900 9.00106 .00116 .00125 .00135 .10035 .10037 .10029 .10031 9.00672 .00681 .00691 .00700 .10156 .10158 .10160 .10163 9.01234 .01243 .01252 .01262 .10288 .10290 .10293 .10395 20 19 18 17 16 15 14 IS + ir 45 46 47 8.99001 .99011 .99020 .99030 .09773 .09775 .09777 .09779 8.99575 .99584 .99594 .99603 .09903 .09905 .09907 .09909 9.00144 .00154 .00163 .00172 .10033 .10035 .10038 .10040 9.00710 .00719 .00728 .00738 .10165 .10167 .10169 .10171 9.01271 .01280 .01289 .01299 .10397 .10399 .10301 .10304 + n' 49 50 51 8.99039 .99049 .99058 .99068 .09781 .09783 .09786 .09788 8.99613 .996.22 .99^:32 .99641 .09911 .09913 .09916 .09918 9.00182 .00191 .00201 .00210 .10042 .10044 .10046 .10049 9.00747 .00756 .00766 .00775 .10174 .10176 .10178 .10180 9.01308 .01317 .01327 .01336 .10306 .10308 .10310 .10312 12 11 10 9 + W 53 54 55 8.99078 .99087 .99097 .99106 .09790 .09792 .09794 .09796 8.99651 .99660 .99670 .99679 .09930 .09933 .09934 .09936 9.00220 .00229 .00239 .00248 .10051 .10053 .10055 .10057 9.00785 .00794 .00803 .00813 .10182 .10184 .10187 .10189 9.01345 .01355 .01364 .01373 .10315 .10317 .10319 .10321 8 7 6 5 57 58 59 8.99116 .99126 .99135 .99145 .09799 .09801 .09803 .09805 8.99689 .99698 .99708 .99717 .09939 .09931 .09933 .09935 9.00258 .00267 .00276 .00286 .10059 .10062 .10064 .10066 9.00822 .00831 .00841 .00850 .10191 .10193 .10196 .10198 9.01383 .01392 .01401 .01411 .10323 .10326 .10338 .10330 4 3 *^ 1 + 15^ 8.99154 .09807 8.99727 .09937 9.00295 .10068 9.00860 .10200 9.01420 .10333 2lh 34m 21h 33m 2111 32^ 2lh 3im 2lh SOm Page 74] TABLE IV. Havereines. s 2^ SOm 37° Sr 2h 3m 37° 45' 2h 32m 38° O' 1 2h 33m 38° 15' 2h 34'^ 38° 30' s Log. Hav Nat. Hav Log. Hav Nat. Hav Log. Hav Nat. Hav Log. Hav Nat. Hav Log. Hav Nat. Hav 1 2 3 9.01420 .01429 .01438 .01448 .10333 .10335 .10337 .10339 9.01976 .01985 .01995 .02004 .10466 .10468 .10470 .10473 9.02528 .02538 .02547 .02556 .10599 .10603 .10004 .10606 9.03077 .03086 .03095 .03104 .10734 .10736 .10739 .10741 9.03621 .03630 .03639 .03648 .10870 .10873 .10874 .10879 60 59 58 57 + r 5 6 7 9.01457 .01466 .01476 .01485 .10341 .10343 .10346 .10348 9.02013 .02022 .02031 .02041 .10474 .10477 .10479 .10481 9.02565 .02574 .02583 .02593 .10608 .10611 .10613 .10615 9.03113 .03122 .03131 .03141 .10743 .10745 .10748 .10750 9.03657 .03667 .03676 .03685 .10879 .10881 .10883 .10885 56 55 54 53 + 3^ 9 10 11 9.01494 .01504 .01513 .01522 .10350 .10353 .10354 .10357 9.02050 .02059 .02068 .02078 .10483 .10486 .10488 .10490 9.02602 .02611 .02620 .02629 .10617 .10630 .10633 .10634 9.03150 .03159 .03168 .03177 .10753 .10754 .10757 .10759 9.03694 .03703 .03712 .03721 .10888 .10890 .10893 .10895 52 51 50 49 + 3' 13 14 15 9.01531 .01541 .01550 .01559 .10359 .10361 .10363 .10366 9.02087 .02096 .02105 .02115 .10493 .10494 .10497 .10499 9.02638 .02648 .02657 .02666 .10636 .10639 .10631 .10633 9.03186 .03195 .03204 .03213 .10761 .10763 .10766 .10768 9.03730 .03739 .03748 .03757 .10897 .10899 .10901 .10904 48 47 46 45 44 43 42 41 + i' 17 18 19 9.015G9 .01578 .01587 .01596 .10368 .10370 .10373 .10374 9.02124 .02133 .02142 .02151 .10501 .10503 .10506 .10508 9.02675 .02684 .02693 .02702 .10635 .10638 .10640 .10643 9.03222 .03231 .03241 .03250 .10770 .10773 .10775 .10777 9.03766 .03775 .03784 .03793 .10906 .10908 .10910 .10913 + 5^ 21 22 73 9.01606 .01615 .01624 .01634 .10377 .10379 .10381 .10383 9.02161 .02170 .02179 .02188 .10510 .10513 .10515 .10517 9.02712 .02721 .02730 .02739 .10644 .10647 .10649 .10651 9.03259 .03268 .03277 .03286 .10779 .10781 .10784 .10786 9.03802 .03811 .03820 .03829 .10915 .10917 .10919 .10933 40 39 38 37 + 6' 25 26 27 9.01643 .01652 .01661 .01671 .10386 .10388 .10390 .10393 9.02197 .02207 .02216 .02225 .10519 .10531 .10533 .10536 9.02748 .02757 .02767 .02776 .10653 .10655 .10658 .10660 9.03295 .03304 .03313 .03322 .10788 .10790 .10793 .10795 9.03838 .03847 .03856 .03865 .10934 .10936 .10939 .10931 36 35 34 33 + r 29 30 31 9.01680 .01689 .01698 .01708 .10394 .10397 .10399 .10401 9.02234 .02244 .02253 .02262 .10538 .10530 .10533 .10535 9.02785 .02794 .02803 .02812 .10663 .10664 .10667 .10669 9.03331 .03340 .03350 .03359 .10797 .10799 .10803 .10804 9.03874 .03883 .03892 .03901 .10933 .10935 .10938 .10940 32 31 30 29 + 8' 33 34 35 9.01717 .01726 .01736 .01745 .10403 .10405 .10408 .10410 9.02271 .02280 .02290 .02299 .10537 .10539 .10541 .10544 9.02821 .02830 .02840 .02849 .10671 .10673 .10676 .10678 9.03368 .03377 .03386 .03395 .10806 .10809 .10811 .10813 9.03910 .03919 .03928 .03937 .10943 .10944 .10947 .10949 28 27 26 25 24 23 22 21 + 9" r;7 38 39 9.01754 .01763 .01773 .01782 .10413 .10414 .10417 .10419 9.02308 .02317 .02326 .02336 .10546 .10548 .10550 .10553 9.02858 .02867 .02876 .02885 .10680 .10683 .10685 .10687 9.03404 .03413 .03422 .03431 .10815 .10818 .10830 .10833 9.03946 .03955 .03964 .03973 .10951 .10953 .10956 .10958 + 10^ 41 42 43 9.01791 .01800 .01810 .01819 .10431 .10433 .10435 .10438 9.02345 .02354 .02363 .02372 .10555 .10557 .10559 .10561 9.02894 .02904 .02913 .02922 .10689 .10691 .10694 .10696 9.03440 .03449 .03458 .03467 .10834 .10837 .10839 .10831 9.03982 .03991 .04000 .04009 .10960 .10963 .10965 .10967 20 19 18 17 + ir 45 46 47 9.01828 .01837 .01847 .01856 .10430 .10433 .10434 .10436 9.02381 .02391 .02400 .02409 .10564 .10566 .10568 .10570 9.02931 .02940 .02949 .02958 .10698 .10700 .10703 .10705 9.03476 03486 .03495 .03504 .10833 .10836 .10838 .10840 9.04018 .04027 .04036 .04045 .10969 .10973 .10974 .10976 16 15 14 13 + 12' 49 50 51 9.01865 .01874 .01884 .01893 .10439 .10441 .10443 .10445 9.02418 .02427 .02437 .02446 .10573 .10575 .10577 .10579 9.02967 .02977 .02986 .02995 .10707 .10709 .10713 .10714 9.03513 .03522 .03531 .03540 .10843 .10845 .10847 .10849 9.04054 .04063 .04072 .04081 .10978 .10981 .10983 .10985 12 11 10 9 + 13' 53 54 55 9.01902 .01911 .01921 .01930 .10448 .10450 .10453 .10454 9.02455 .02464 .02473 .02483 .10583 .10584 .10586 .10588 9.03004 .03013 .03022 .03031 .10716 .10718 .10731 .10733 9.03549 .03558 .03567 .03576 .10851 .10854 .10856 .10858 9.04090 .04099 .04108 .04117 .10988 .10990 .10993 .10994 8 7 6 5 4 3 2 + W 57 58 59 9.01939 01948 .01958 .01967 .10457 .10459 .10461 .10463 9.02492 .02501 .02510 .02519 .10591 .10593 .10595 .10597 9.03040 .03050 .03059 .03068 .10735 .10737 .10730 .10733 9.03585 .03594 .03603 .03612 .10861 .10863 .10865 .10867 9.04126 .04135 .04144 .04153 .10997 .10999 .11001 .11004 + 15' 9.01976 .10486 9.02528 .10599 9.03077 .10734 9.03621 .10870 9.04162 .11006 — 21 h 29m 21^ 28'"^ 2lTi27m 1 21'!^ 26m j 21h25m TABLE IV. Haveraines. [Page 75 s f ft 55"» 38* 45' j ift 56'" 39° r 2h 37m 39° 16' f ft S8m 39° SO' f ft S9m 39° 45' s Log. Hav. Nat. Hav. Log. Hav. Nat. nav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. 1 .-> 3 9.04162 .04171 .04180 .04189 .11006 .11008 .11010 .11013 9.04699 .04708 .04717 .04726 .11143 .11145 .11147 .11150 9.05232 .05241 .05250 .05259 .11380 .11383 .11385 .11387 9.05762 .05771 .05780 .05788 .11419 .11431 .11433 .11436 9.06288 .06297 .06305 .06314 .11558 .11560 .11563 .11565 60 59 58 57 5 6 7 9.04198 .04207 .04216 .04225 .11015 .11017 .11019 .11033 9.04735 .04744 .04753 .04761 .11153 .11154 .11156 .11159 9.05268 .05277 .05285 .05294 .11390 .11393 .11394 .11396 9.05797 .05806 .05815 .05823 .11438 .11430 .11433 .11435 9.06323 .06332 .06340 .06349 .11567 .11569 .11573 .11574 56 55 54 53 + 3' .9 10 11 9.04234 .04243 .04252 .04261 .11034 .11036 .11039 .11031 9.04770 .04779 .04788 .04797 .11161 .11163 .11166 .11163 9.05303 .05312 .05321 .05330 .11399 .11301 .11303 .11306 9.05832 .05841 .05850 .05859 .11437 .11440 .11443 .11444 9.06358 .06367 .06375 .06384 .11577 .11579 .11581 .11584 52 51 50 49 + 3' 13 14 15 9.04270 .04279 .04288 .04297 .11033 .11035 .11038 .11040 9.04806 .04815 .04824 .04833 .11170 .11173 .11175 .11177 9.05339 .05347 .05356 .05365 .11308 .11310 .11313 .11315 9.05867 .05876 .05885 .05894 .11447 .11449 .11451 .11453 9.06393 .06401 .06410 .06419 .U586 .11588 .11590 .11593 48 47 46 45 44 43 42 41 40 39 38 37 + i' 17 18 19 9.04306 .04315 .04324 .04333 .11043 .11044 .11047 .11049 9.04842 .04851 .04859 .04868 .11179 .11183 .11184 11186 9.05374 .05383 .05392 .05400 .11317 .11330 .11333 .11334 9.0.5903 .05911 .05920 .05929 .11456 .11458 .11460 .11463 9.06428 .06436 .06445 .06454 .11595 .11597 .11600 .11603 + 5^ 21 22 23 9.04341 .04350 .04359 .04368 .11051 .11054 .11056 .11058 9.04877 .04886 .04895 .04904 .11189 .11191 .11193 .11195 9.05409 .05418 .05427 .05436 .11336 .11339 .11331 .11333 9.05938 .05946 .05955 .05964 .11465 .11467 .11470 .11473 9.06482 .06471 .06480 .06489 .11604 .11607 .11609 .11611 + 6^ 25 26 27 9.04377 .04386 .04395 .04404 .11060 .11063 .11065 .11067 9.04913 .04922 .04931 .04939 .11198 .11300 .11303 .11305 9.05445 .05453 .05462 .05471 .11336 .11338 .11340 .11343 9.05973 .05982 .05990 .05999 .11474 .11477 .11479 .11481 9.06497 .06506 .06515 .06523 .11614 .11616 .11618 .11631 36 35 34 33 + r 29 30 31 9.04413 .04422 .04431 .04440 .11070 .11073 .11074 .11076 9.04948 .04957 .04966 .04975 .11307 .11309 .11311 .11314 9.05480 .05489 .05498 .05506 .11345 .11347 .11349 .11353 9.06008 .06017 .06025 .06034 .11484 .11486 .11488 .11491 9.06532 .06541 .06550 .06558 .11633 .11635 .11638 .11630 32 31 30 29 + 8^ 33 34 35 9.04449 .04458 .04467 .04476 .11079 .11081 .11083 .11086 9.04984 .04993 .05002 .0.5011 .11316 .11318 .11331 .11333 9.05515 .05524 .05533 .05542 .11354 .11356 .11359 .11361 9.06043 .06052 .06060 .06069 .11493 .11495 .11498 .11500 9.06567 .06576 .06584 .06-593 .11633 .11635 .11637 .11639 28 27 26 25 + 9^ .57 38 39 9.04485 .04494 .04503 .04512 .11088 .11090 .11093 .11095 9.05019 .05028 .05037 .05046 .11335 .11338 .11330 .11333 9.05551 .05559 .05568 .05577 .11363 .11366 .11368 .11370 9.06078 .06087 .06095 .06104 .11503 .11504 .11507 .11509 9.06602 .06611 .06619 .06628 .11643 .11644 .11646 .11649 24 23 22 "21 + W 41 42 43 9.04520 .04529 .04538 .04547 .11097 .11099 .11103 .11104 9.050.55 .05064 .05073 .05082 .11334 .11337 .11339 .11341 9.05586 .0.5595 .05603 .05612 .11373 .11375 .11377 .11379 9.06113 .06122 .06131 .06139 .11511 .11514 .11516 .11518 9.06637 .06645 .06654 .06663 .11651 .11653 .11656 .11658 20 19 18 17 + 11^ 45 46 47 9.04556 .04565 .04574 .04583 .11106 .11108 .11111 .11113 9.05090 .05099 .05108 .05117 .11344 .11346 .11348 .11351 9.05621 .05630 .05639 .05648 .11383 .11384 .11386 .11389 9.06148 .06157 .06166 .06174 .11531 .11533 .11535 .11538 9.06671 .06680 .06689 .06697 .11660 .11663 .11665 .11667 16 15 14 13 49 50 51 9.04592 .04601 .04610 .04619 .11115 .11117 .11130 .11133 9.05126 .05135 .05144 .05153 .11353 .11355 .11357 .11360 9.05656 .05665 .05674 .05683 .11391 .11393 .11396 .11398 9.06183 .06192 .06201 .06209 .11530 .11533 .11535 .11537 9.06706 .06715 .06724 .06732 .11670 .11673 .11674 .11677 12 11 10 9 + 13^ 53 54 55 9.04628 .04637 .04646 .04654 .11134 .11137 .11139 .11131 9.05161 .05170 .05179 .05188 .11363 .11364 .11367 .11369 9.05692 .05700 .05709 .05718 .11400 .11403 .11405 .11407 9.06218 .06227 .06235 .06244 .11539 .11543 .11544 .11546 9.06741 .06750 .06758 .06767 .11679 .11681 .11684 .11686 8 7 6 5 + W 57 58 59 9.04663 .04672 .04681 .04690 .11134 .11136 .11138 .11140 9.05197 .05206 .05215 .05223 .11371 .11374 .11376 .11378 9.05727 .05736 .05744 .057.53 .11410 .11413 .11414 .11416 9.06253 .06262 .06270 .06279 .11549 .11551 .11553 .11556 9.06776 .06784 .06793 .06802 .11688 .11691 .11693 .11695 4 3 2 1 -r 15^ 9.04699 .11143 9.05232 .11380 9.05762 .11419 9.062S8 .11558 9.06810 .11698 21h 24"^ 21h 2.3m 21^ 22>n 21^ 21m 21h 20m Page 76] TABLE IV. Haversinea. s 2h 40^ 40° 0' 2h 4im 40° 15' 2h 42m 40° SO' ^ft 43m 40° 45' 2li 44m 41° 0' s Log. Hav. Nat. Ilav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. 1 2 S 9.06810 .06819 .06828 .06836 .11698 .11700 .11702 .11705 9.07329 .07338 .07346 .07355 .11838 .11841 .11843 .11845 9.07845 .07853 .07862 .07870 .11980 .11982 .11984 .11987 9.08357 .08365 .08374 .08382 .12122 .12124 .12127 .12129 9.08865 .08874 .08882 .08890 .13265 .12267 .12269 .12272 60 59 58 57 + r 5 6 7 9.06845 .06854 .06862 .06871 .11707 .11709 .11712 .11714 9.07364 .07372 .07381 .07390 .11848 .11850 .11852 .11855 9.07879 .07887 .07896 .07905 .11989 .11992 .11994 .11996 9.08391 .08399 .08408 .08416 .12131 .12134 .12136 .12138 9.08899 .08907 .08916 .08924 .12274 .12276 .12279 .12281 56 55 54 53 + r 9 10 11 9.06880 .06888 .06897 .06906 .11716 .11719 .11721 .11724 9.07398 .07407 .07415 .07424 .11857 .11860 .11862 .11864 9.07913 .07922 .07930 .07939 .11999 .12001 .12003 .12006 9.08425 .08433 .08442 .08450 .12141 .12143 .12146 .12148 9.08933 .08941 .08949 .08958 .12284 .12286 .12288 .12291 52 51 50 49 48 47 46 45 + 3' 13 14 15 9.06914 .06923 .06932 .06940 .11726 .11728 .11731 .11733 9.07433 .07441 .07450 .07458 .11867 .11869 .11871 .11874 9.07947 .07956 .07964 .07973 .12008 .12010 .12013 .12015 9.08459 .08467 .08475 .08484 .12150 .12153 .12155 .12157 9.08966 .08975 .08983 .08992 .12293 .12296 .12298 .12300 + 4^ 17 18 19 9.06949 .06958 .06966 .06975 .11735 .11738 .11740 .11742 9.07467 .07476 .07484 .07493 .11876 .11878 .11881 .11883 9.07981 .07990 ■ .07999 .08007 .12018 .12020 .12022 .12025 9.08492 .08501 .08509 .08518 .12160 .12162 .12165 .12167 9.09000 .09009 .09017 .09025 .12303 .12305 .12307 .12310 44 43 42 41 + 5' 21 22 23 9.06984 .06992 .07001 .07010 .11745 .11747 .11749 .11752 9.07501 .07510 .07519 .07527 .11885 .11888 .11890 oll892 9.08016 .08024 .08033 .08041 .12027 cl2029 .12032 .12034 9.08526 .08535 .08543 .08552 .12169 .12172 .12174 .12176 9.09034 .09042 .09051 .09059 .12312 .12315 .12317 .12319 40 39 38 37 + 6' 25 26 27 9.07018 .07027 .07036 .07044 .11754 .11756 .11759 .11761 9.07536 .07544 .07553 .07562 .11895 .11897 .11900 .11902 9.08050 .08058 .08067 .08075 .12036 .12039 .12041 .12044 9.08560 .08569 .08577 .08586 .12179 .12181 .12184 .12186 9.09068 .09076 .09084 .09093 .12322 .12324 .12327 .12329 36 35 34 33 + r 29 30 31 9.07053 .07062 .07070 .07079 .11763 .11766 .11768 .11770 9.07570 .07579 .07587 .07596 .11904 .11907 .11909 .11911 9.08084 .08092 .08101 .08110 .12046 .12048 .12051 .12053 9.08594 .08603 .08611 .08620 .12188 .12191 cl2193 .12195 9.09101 .09110 .09118 .09126 .12331 .12334 .12336 .12339 32 31 30 29 + ^ S3 34 35 9.07088 .07096 .07105 .07113 .11773 .11775 .11777 .11780 9.07605 .07613 .07622 .07630 .11914 .11916 .11918 .11921 9.08118 .08127 .08135 .08144 .12055 .12058 .12060 .12062 9.08628 .08637 .08645 .08654 .12198 .12200 .12203 .12205 9.09135 .09143 .09152 .09160 .13341 .13343 .12346 .12348 28 27 26 25 + 9^ 37 38 39 9.07122 .07131 .07139 .07148 .11782 .11784 .11787 .11789 9.07639 .07647 .07656 .07665 .11923 .11925 .11928 .11930 9.08152 .08161 .08169 .08178 .12065 .12067 .12070 .12072 9.08662 .08671 .08679 .08687 .12207 .12210 .12212 .12214 9.09169 .09177 .09185 .09194 .13351 .13353 .12355 .12358 24 23 22 21 + W 41 42 43 9.07157 .07165 .07174 .07183 .11791 .11794 .11796 .11798 9.07673 .07682 .07690 .07699 .11933 .11935 .11937 .11940 9.08186 .08195 .08203 .08212 .12074 .12077 .12079 .12081 9.08696 .08704 .08713 .08721 .12217 .12219 .12222 .12224 9.09202 .09211 .09219 .09227 .12360 .12363 .12365 .12367 20 19 18 17 + ir 45 46 47 9.07191 .07200 .07208 .07217 .11801 .11803 .11806 .11808 9.07708 .07716 .07725 .07733 .11942 .11944 .11947 .11949 9.08220 .08229 .08237 .08246 .12084 .12086 .12089 .12091 9.08730 .08738 .08747 .08755 .12226 .12229 .12231 .12233 9.09236 .09244 .09253 .09261 .13370 .12372 .12374 .12377 16 15 14 IS 12 11 10 9 + 12' 49 50 51 9.07226 .07234 .07243 .07252 .11810 .11813 .11815 .11817 9.07742 .07750 .07759 .07768 .11951 .11954 .11956 .11958 9.08254 .08263 .08271 .08280 .12093 .12096 .12098 .12100 9.08764 .08772 .08781 .08789 .12236 .12238 .12241 .12243 9.09269 .09278 .09286 .09295 .12379 .12382 .12384 .12386 + ir 53 54 55 9.07260 .07269 .07277 .07286 .11820 .11822 .11824 .11827 9.07776 .07785 .07793 .07802 .11961 .11963 .11966 .11968 9.08288 .08297 .08306 .08314 .12103 .12105 .12108 .12110 9.08797 .08806 .08814 .08823 .12245 .12248 .12250 .12253 9.09303 .09311 .09320 .09328 .12389 .12391 .12394 .12396 8 7 6 5 + W 57 58 59 9.07295 .07303 .07312 .07321 .11829 .11831 .11834 .11836 9.07810 .07819 .07827 .07836 .11970 .11973 .11975 .11977 9.08323 .08331 .08340 .08348 .12112 .12115 .12117 .12119 9.08831 .08840 .08848 .08857 .12255 .12257 .12260 .12262 9.09337 .09345 .09353 .09362 .13398 .13401 .12403 .13406 4 3 2 1 + 15' 9.07329 .11838 9.07845 .11980 9.08357 .12122 9.08865 .12265 9.09370 .12408 21h 19m 21h 18m 21h ijm 21h 16m 21^ 15m TABLE IV. Haversines. [Page 77 s ' 2h45m 41° 15' 2h jj.sm 41° 30' 2h47m 41° 45' 2^48^ 42° 0' 2h 49m 43° 15' s Log. Hav. Nat. llav. Log. Hav. Nat. Uav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. 1 2 9.09370 .09379 .09387 .09395 .13408 .12410 .12413 .12415 9.09872 .09880 .09889 .09897 .12552 .12555 .12557 .12559 9.10371 .10379 .10387 .10395 .13697 .12700 .12702 .12704 9.10866 .10874 .10882 .10891 .12843 .12845 .12848 .12850 9.11358 .11366 .11374 .11382 .13989 .13993 .13994 .13996 60 59 58 57 + r 5 6 7 9.09404 .09412 .09421 .09429 .12418 .12420 .13422 .13425 9.09905 .09914 .09922 .09930 .12562 .13564 .12567 .12569 9.10404 .10412 .10420 .10429 .12707 .13709 .13713 .13714 9.10899 .10907 .10915 .10923 .12852 .12855 .12857 .12860 9.11391 .11399 .11407 .11415 .12999 .13001 .13004 .13006 56 55 54 53 + 2' 9 10 11 9.09437 .09446 .09454 .09462 .13437 .13430 .13433 .12434 9.09939 .09947 .09955 .09964 .12572 .12574 .12576 .12579 9.10437 .10445 .10453 .10462 .13717 .13719 .13731 .13724 9.10932 .10940 .10948 .10956 .12862 .12865 .12867 .12870 9.11423 .11431 .11440 .11448 .13009 .13011 .13014 .13016 52 51 50 49 + 3' 13 14 15 9.09471 .09479 .09488 .09496 .12437 .12439 .12443 .12444 9.09972 .09980 .09989 .09997 .12581 .12584 .13586 .13588 9.10470 .10478 .10486 .10495 .12726 0I2729 .12731 .12733 9.10965 .10973 .10981 .10989 .13873 .13874 .12877 .12879 9.11456 .11464 .11472 .11480 .13018 .13031 .13023 .13036 43 47 46 45 + 4' 17 18 19 9.09504 .09513 .09521 .09529 .12446 .12449 .12451 .12454 9.10005 .10014 .10022 .10030 .13591 ,12593 .13596 .12598 9.10503 .10511 .10519 .10528 .12736 .12738 .12741 .12743 9.10997 .11006 .11014 .11022 .12882 .12884 .12887 .12889 9.11489 .11497 .11505 .11513 .13028 .13031 .13033 .13036 44 43 42 41 + 5' 21 22 23 9.09538 .09546 .09555 .09563 .12456 .12458 .12461 .12463 9.10039 .10047 .10055 .10064 .13600 .13603 .13605 .13608 9.10536 .10544 .10553 .10561 .13746 .12748 .13750 .13753 9.11030 .11038 .11047 .11055 .13891 .13894 .13896 .12899 9.11521 .11529 .11538 .11546 .13038 .13041 .13043 .13045 40 39 38 37 + 6' 25 26 27 9.09571 .09580 .09588 .09596 .12466 .13468 .12470 .12473 9.10072 .10080 .10088 .10097 .12610 .12613 .12615 .12617 9.10569 .10577 .10586 .10594 .13755 .13758 .13760 .13763 9.11063 .11071 .11079 .11088 .12901 .12904 .12906 .12909 9.11554 .11562 .11570 .11578 .13048 .13050 .13053 .13055 36 35 34 33 32 31 SO 29 + r 29 30 31 9.09605 .09613 .09622 .09630 .12475 .12478 .12480 .12482 9.10105 .10113 .10122 .10130 .12620 .12622 .12625 .12637 9.10602 .10610 .10619 .10627 .13765 .13767 .13770 .12773 9.11096 .11104 .11112 .11120 .12911 .12913 .13916 .13918 9.11586 .11595 .11603 .11611 .13058 .13060 .13063 .13065 + 8' S3 34 35 9.09638 .09647 .09655 .09663 .12485 .12487 .12490 .12492 9.10138 .10147 .10155 .10163 .13639 .13633 .13634 .12637 9.10635 .10643 .10652 .10660 .13775 .13777 .12780 .13783 9.11129 .11137 .11145 .11153 .13931 .13933 .13936 .13938 9.11619 .11627 .11635 .11643 .13067 .13070 .13072 .13075 28 27 26 25 + 9' 37 38 39 9.09672 .09680 .09688 .09697 .12494 .12497 .13499 .13503 9.10172 .10180 .10188 .10196 .12639 .12641 .12644 .12646 9.10668 .10676 .10685 .10693 .13784 .13787 .12789 .12792 9.11161 .11170 .11178 .11186 .13930 .13933 .12935 .13938 9.11652 .11660 .11668 .11676 .13077 .13080 .13082 .13085 24 23 22 "21 + W 41 42 43 9.09705 .09713 .09722 .09730 .13504 .13506 .13509 .13511 9.10205 .10213 .10221 .10230 .12649 .12651 .12654 .12656 9.10701 .10709 .10718 .10726 .13794 .13797 .13799 .13801 9.11194 .11202 .11211 .11219 .13940 .12943 .12945 .12948 9.11684 .11692 .11700 .11709 .13087 .13090 .13092 .13095 20 19 18 17 + 11' 45 46 47 9.09739 .09747 .09755 .09764 cl3514 .13510 ,13519 .13521 9.10238 .10246 .10255 .10263 .12658 .12661 .12663 .12666 9.10734 .10742 .10751 .10759 .12804 .12806 .13809 .13811 9.11227 .11235 .11243 .11252 .12950 .12952 .12955 .12957 9.11717 .11725 .11733 .11741 .13097 .13099 .13102 .13104 16 15 14 13 + 12' 49 50 51 9.09772 .09780 .09789 .09797 .13533 .13536 .13538 .13531 9.10271 .10279 .10288 .10296 .12668 .12671 .12673 .12675 9.10767 .10775 .10784 .10792 .13814 .13816 .12818 .12821 9.11260 .11268 .11276 .11284 .12960 .13963 .13965 .13967 9.11749 .11757 .11766 .11774 .13107 .13109 .13112 .13114 12 11 10 9 + 13' 53 54 55 9.09805 .09814 .09822 .09830 .13533 .13536 .13538 .13540 9.10304 .10313 .10321 .10329 .12678 .12680 .12683 .12685 9.10800 .10808 .10816 .10825 .12823 .12826 .12828 .12831 9.11292 .11301 .11309 .11317 .12970 .12972 .18974 .12977 9.11782 .11790 .11798 .11806 .13116 .13119 .13121 .13124 8 7 6 5 + 14' 57 58 59 9.09839 .09847 .09856 .09864 .12543 .12545 .12547 .12550 9.10337 .10346 .10354 .10362 .12687 .12690 .12692 .12695 9.10833 .10841 .10849 .10858 .12833 .12836 .12838 .12840 9.11325 .11333 .11342 .11350 .12979 .12982 .12984 .12987 9.11814 .11822 .11831 .11839 .13126 .13139 .13131 .13134 4 3 1 ! i + 15' 9.09872 .12552 9.10371 .13697 9.10866 .12843 9.11358 .13989 9.11847 .13136 21 h 14m 21h ISm ^Ih 12m 21h lim 21h lOm Page 78] TABLE IV. Havereines. s 2h 50m 43° 30' 2h5im 43° 45' 2h 52m 43° 0' fi 53^ 43° 15' 2h54m 43° 30' s Log. Hav. Nat. Hav. IjOg. Ilav. Nat. nav. Log. nav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. 1 2 S 9.11847 .11855 .11863 .11871 .13136 .13139 .13141 .13143 9.12332 .12341 .12349 .12357 .13384 .13386 .13289 .13291 9.12815 .12823 .12831 .12839 .13433 .13435 .13437 .13440 9.13295 .13303 .13311 .13319 .13581 .13584 .13586 .13589 9.13771 .13779 .13787 .13795 .13731 .13734 .13736 .13739 60 59 58 57 + r 5 6 7 9.11879 .11887 .11895 .11904 .13146 .13148 .13151 .13153 9.12365 .12373 .12381 .12389 .13294 .13396 .13399 .13301 9.12847 .12855 .12863 .12871 .13442 .13445 .13447 .13450 9.13326 .13334 .13342 .13350 .13591 .13594 .13596 .13599 9.13803 .13811 .13819 .13827 .13741 .13744 .13746 .13749 56 55 54 53 + 2' 9 10 11 9.11912 .11920 .11928 .11936 .13156 .13158 .13161 .13163 9.12397 .12405 .12413 .12421 .13304 .13306 .13309 .13311 9.12879 .12887 .12895 .12903 .13452 .13455 .13457 .13460 9.13358 .13366 .13374 .13382 .13601 .13604 .13607 .13609 9.13834 .13842 .13850 .13858 .13751 .13754 .13756 .13759 52 51 50 49 + 3' 13 14 15 9.11944 .11952 .11960 .11968 .13166 .13168 .13171 .13173 9.12429 .12437 .12445 .12453 .13314 .13316 .13318 .13331 9.12911 .12919 .12927 .12935 .13463 .13465 .13467 .13470 9.13390 .13398 .13406 .13414 .13611 .13614 .13616 .13619 9.13866 .13874 .13882 .13890 .13761 .13764 .13766 .13769 48 47 46 45 + 4' 17 18 19 9.11977 .11985 .11993 .12001 .13175 .13178 .13180 .13183 9.12461 .12470 .12478 .12486 .13323 .13336 .13328 .13331 9.12943 .12951 .12959 .12967 .13473 .13474 .13477 .13479 9.13422 .13430 .13438 .13446 .13621 .13624 .13626 .13629 9.13898 .13906 .13913 .13921 .13771 .13774 .13776 .13779 44 43 42 41 + 5' 21 22 23 9.12009 .12017 .12025 .12033 .13185 .13188 .13190 .13193 9.12494 .12502 .12510 .12518 .13333 .13336 .13338 .13341 9.12975 .12983 .12991 .12999 .13482 .13484 .13487 .13489 9.13454 .13462 .13470 .13478 .13631 .13634 .13636 .13639 9.13929 .13937 .13945 .13953 .13781 .13784 .13786 .13789 40 39 38 37 + 6' 25 26 27 9.12041 .12050 .12058 .12066 .13195 .13198 .13300 .13203 9.12526 .12534 .12542 .12550 .13343 .13346 .13348 .13351 9.13007 .13015 .13023 .13031 .13492 .13494 .13497 .13499 9.13486 .13494 .13501 .13509 .13641 .13644 .13646 .13649 9.13961 .13969 .13977 .13985 .13791 .13794 .13796 .13799 36 35 34 33 + r 29 30 31 9.12074 .12082 .12090 .12098 .13205 .13207 .13210 .13212 9.12558 .12566 .12574 .12582 .13353 .13356 .13358 .13360 9.13039 .13047 .13055 .13063 .13503 .13504 .13507 .13509 9.13517 .13525 .13533 .13541 .13651 .13654 .13656 .13659 9.13992 .14000 .14008 .14016 .13801 .13804 .13806 .13809 32 31 30 29 28 27 26 25 + 8' 33 34 35 9.12106 .12114 .12122 .12130 .13215 .13217 .13220 .13222 9.12590 .12598 .12606 .12614 .13363 .13365 .13368 .13370 9.13071 .13079 .13087 .13095 .13512 .13514 .13517 .13519 9.13549 .13557 .13565 .13573 .13661 .13664 .13666 .13669 9.14024 .14032 .14040 .14048 .13811 .13814 .13816 .13819 + JK 37 38 39 9.12139 .12147 .12155 .12163 .13225 .13227 .13230 .13233 9.12622 .12630 .12638 .12647 .13373 .13375 .13378 .13380 9.13103 .13111 .13119 .13127 .13533 .13524 .13537 .13539 9.13581 .13589 .13597 .13605 .13671 .13674 .13676 .13679 9.14056 .14063 .14071 .14079 .13833 .13834 .13827 .13829 ■24 23 22 21 + W 41 42 43 9.12171 .12179 .12187 .12195 .13235 .13237 .13239 .13242 9.12655 .12663 .12671 .12679 .13383 .13385 .13388 .13390 9.13135 .13143 .13151 .13159 .13532 .13534 .13537 .13539 9.13613 .13621 .13628 .13636 .13681 .13684 .13686 .13689 9.14087 .14095 .14103 .14111 .13832 .13834 ,13837 .13839 20 19 18 17 + ir 45 46 47 9.12203 .12211 .12219 .12228 .13344 .13347 .13349 .13252 9.12687 .12695 .12703 .12711 .13393 .13395 .13398 .13400 9.13167 .13175 .13183 .13191 .13542 .13544 .13547 .13549 9.13644 .13652 .13660 .13668 .13691 .13694 .13696 .13699 9.14119 .14127 .14134 .14142 .13842 .13844 .13847 .13849 16 15 14 13 + n' 49 50 51 9.12236 .12244 .12252 .12260 .13254 .13257 .13259 .13262 9.12719 .12727 .12735 .12743 .13403 .13405 .13408 .13410 9.13199 .13207 .13215 .13223 .13552 .13554 .13557 .13559 9.13676 .13684 .13692 .13700 .13701 .13704 .13706 .13709 9.14150 .14158 .14166 .14174 .13853 .13854 .13857 .13859 12 11 10 9 + 13' 53 54 55 9.12268 .12276 .12284 .12292 .13264 .13367 .13369 .13373 9.12751 .12759 .12767 .12775 .13412 .13415 .13417 .13430 9.13231 .13239 .13247 .13255 .13562 .13564 .13567 .13569 9.13708 .13716 .13724 .13732 .13711 .13714 .13716 .13719 9.14182 .14190 .14197 .14205 .13862 .13864 .13867 .13869 8 7 6 5 + 14' 57 58 59 9.12300 .12308 .12316 .12324 .13274 .13276 .13279 .13281 9.12783 .12791 .12799 .12807 .13432 .13425 .13427 .13430 9.13263 ,13271 .13279 .13287 .13571 .13574 .13576 ,13579 9.13739 .13747 .33755 .13763 .13731 .13734 .13736 .13739 9.14213 .14221 .14229 .14237 .13872 .13874 .13877 -13879 4 S 2 1 + 15' 9.12332 .13284 9.12815 .13432 9.13295 .13581 9.13771 .13731 9.14245 .13882 21fi gm 21^ Sm. 21h7m 21^ em 2lh 5m TABLE IV. Haversinee. [Page 79 s f A 55m 43° 45' 1 2h 56m 44° 0' | 2h 57m 14:° 15' 1 2h58mU°W \ 2h59mU°45' | s Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. 1 2 3 9.14245 .14252 .14260 .14268 .13883 .13884 .13887 .13889 9.14715 .14723 .14731 .14739 .14033 .14035 .146.38 .14041 9.15183 .15190 .15198 .15206 .14185 .14187 .14190 .14193 9.15647 .15655 .15663 .15670 .14337 .14340 .14343 .14345 9.16109 .16117 .16124 .16132 .14491 .14493 .14496 .14498 60 59 58 57 + r 5 6 7 9.14276 .14284 .14292 .14300 .13893 .13894 .13897 .13899 9.14746 .14754 .14762 .14770 .14043 .14046 .14048 .14051 9.15214 .15221 .15229 .15237 .14195 .14198 .14300 .14303 9.15678 .15686 .15694 .15701 .143^18 .14350 .14353 .14355 9.16140 .16147 .16155 .16163 .14501 .14504 .14506 .14509 56 55 54 53 + r 9 10 11 9.14307 .14315 .14323 .14331 .13903 .13904 .13907 .13909 9.14778 .14785 .14793 .14801 .14053 .14056 .14058 .14061 9.15245 .15253 .15260 .15268 .14305 .14308 .14310 .14313 9.15709 .15717 .15724 .15732 .14358 .14360 .143C3 .14366 .14368 .14371 .14373 .14376 9.16170 .16178 .16186 .16193 9.16201 .16209 .16216 .16224 .14511 .14514 .14516 .14519 .14521 .14524 .14537 .14529 52 51 50 49 4S 47 46 45 + 3' 13 14 15 9.14339 .14347 .14355 .14362 .13913 .13914 cl3917 .13930 9.14809 .14817 .14824 .14832 .14003 .14066 .14068 .14071 9.15276 .15284 .15291 .15299 .14315 .14318 .14330 .14333 9.15740 .15748 .15755 .15763 + 4' 17 18 19 9.14370 .14378 .14386 .14394 .13933 .13935 .13937 .13930 9.14840 .14848 .14856 .14863 .14073 .14076 .14079 .14081 9.15307 .15315 .15322 .15330 .14336 .14338 .14331 .14333 9.15771 .15778 .15786 .15794 .14378 .14381 .14383 .14386 9.16232 .16239 .16247 .16255 .14532 .14534 .14537 .14539 44 43 42 41 40 39 38 37 + 5' 21 22 23 9.14402 .14410 .14417 .14425 .13933 .13935 .13937 .13940 9.14871 .14879 .14887 .14895 .14084 .14086 .14089 .14091 9.15338 .15346 .15353 .15361 .14336 .14338 .14341 .14343 9.15802 .15809 .15817 .15825 .14388 .14391 .14394 .14396 9.16262 .16270 .16278 .16285 .14542 .14545 .14547 .14550 + 6' 25 26 27 9.14433 .14441 .14449 .14457 .13943 .13945 .13947 .13950 9.14902 .14910 .14918 .14926 .14094 .14096 .14099 .14101 9.15369 .15377 .15384 .15392 .14346 .14348 .14251 .14353 9.15832 .15840 .15848 .15855 .14399 .14401 .14404 .14406 9.16293 .16301 .16308 .16316 .14552 .14555 .14557 .14560 36 35 34 33 + r 29 SO 31 9.14465 .14472 .14480 .14488 .13953 .13955 .13957 .13960 9.14934 .14941 .14949 .14957 .14104 .14106 .14109 .14111 9.15400 .15408 .15415 .15423 .14356 .14359 .14361 .14364 9.15863 .15871 .15879 .15886 .14409 .14411 .14414 .14417 9.16324 .16331 .16339 .16346 .14562 .14565 .14568 .14570 32 31 30 29 + S' 33 34 35 9.14496 .14504 .14512 .14519 .13963 .13965 .13967 .13970 9.14965 .14973 .14980 .14988 .14114 .14116 .14119 .14133 9.15431 .15439 .15446 .15454 .14366 .14369 .14371 .14274 9.15894 .15902 .15909 .15917 .14419 .14432 .14434 .14437 9.16354 .16362 .16369 .16377 .14573 .14575 .14578 .14580 28 27 26 25 24 23 22 21 20 19 18 17 + 9' 37 38 39 9.14527 .14535 .14543 .14551 .13973 .13975 .13977 .13980 9.14996 .15004 .15012 .15019 .14134 .14137 .14139 .14133 9.15462 .15470 .15477 .15485 .14376 .14379 .14381 .14384 9.15925 .15932 .15940 .15948 .14439 .14432 .14434 .14437 9.16385 .16392 .16400 .16408 .14583 .14586 .14588 .14591 41 42 43 9.14559 .14566 .14574 .14582 .13983 .13985 .13988 .13990 9.15027 .15035 .15043 .15050 .14134 .14137 .14139 .14143 9.15493 .15500 .15508 .15516 .14387 .14289 .14293 .14394 9.15955 .15963 .15971 .15978 .14440 .14442 .14445 .14447 9.16415 .16423 .16431 .16438 .14593 .14596 .14598 .14601 + 11' 45 46 47 9.14590 .14598 .14606 .14613 .13993 .13995 .13998 .14000 9.15058 .15066 .15074 .15082 .14144 .14147 .14149 .14153 9.15524 .15531 .15539 .15547 .14297 .14299 .14302 .14304 9.15986 .15994 .16002 .16009 .14450 .14452 .14455 .14457 9.16446 .16453 .16461 .16469 .14604 .14606 .14609 .14611 16 15 14 13 + 13' 49 50 51 9.14621 .14629 .14637 .14645 .14003 .14005 .14008 .14010 9.15089 .15097 .15105 .15113 .14154 .14157 .14160 .14163 9.15555 .15562 .15570 .15578 .14307 .14309 .14312 .14315 9.16017 .16025 .16032 .16040 .14460 .14463 .14465 .14468 9.16476 .16484 .16492 .16499 .14614 .14616 .14619 .14622 12 11 10 9 + 13' 53 54 55 9.14653 .14660 .14668 .14676 .14013 .14015 .14018 .14030 9.15120 .15128 .15136 .15144 .14165 .14167 .14170 .14173 9.15585 .15593 .15601 .15609 .14317 .14320 .14322 .14335 9.16048 .16055 .16063 .16071 .14470 .14473 .14475 .14478 9.16507 .16515 .16522 .16530 .14624 .14637 .14639 .14632 8 7 6 5 + 14' 57 58 59 9.14684 .14692 .14699 .14707 .14033 .14035 .14038 .14030 9.15152 .15159 .15167 .15175 .14175 .14177 .14180 .14183 9.15616 .15624 .15632 .15640 .14327 .14330 .14332 .14335 9.16078 .16086 .16094 .16101 .14480 .14483 .14486 .14488 9.16537 .16545 .16553 .16560 .14634 .14637 .14639 .14643 4 S 2 1 + 15' 9.14715 .14033 9.15183 .14185 9.15647 .14337 9.16109 .14491 9.16568 .14645 21J1 ^m 21h3m 21f I ^m 21f> jm 21fi Om Page 80] TABLE lY. Haversines. s Sh om 45° 0' 3h im 450 15/ 1 ^A f m 45° 30^ Sh 3m 45° 45/ Sh 4m 46° (K s Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. 1 2 3 9.16568 .16576 .16583 .16591 .14645 .14frl7 .14650 .14653 9.17024 .17032 .17039 .17047 .14799 .14803 .14804 .14807 9.17477 .17485 .17492 .17500 .14955 .14957 .14960 .14963 9.17928 .17935 .17943 .17950 .15110 .15113 .15116 .15118 9.18376 .18383 .18390 .18398 .15367 .15370 .15373 .15375 60 59 58 57 + r 5 6 7 9.16598 .16606 .16614 .16621 .14655 .14658 .14660 .14663 9.17054 .17062 .17069 .17077 .14810 .14813 .14815 .14817 9.17507 .17515 .17522 .17530 .14965 .14968 .14970 .14973 9.17958 .17965 .17973 .17980 .15131 .15133 .15126 .15139 9.18405 .18413 .18420 .18428 .15278 .15380 .15383 .15385 56 55 54 53 + V 9 10 11 9.16629 .16637 .16644 .16652 .14665 .14668 .14670 .14673 9.17085 .17092 .17100 .17107 .14830 .14833 .14835 .14838 9.17538 .17545 .17553 .17560 .14975 .14978 .14981 .14983 9.17988 .17995 .18003 .18010 .15131 .15134 .15137 .15139 9.18435 .18443 .18450 .18457 .15388 .15391 .15393 .15396 52 51 50 49 + 3^ 13 14 15 9.16659 .16667 .16675 .16682 .14676 .14678 .14681 .14683 9.17115 .17122 .17130 .17138 .14830 .14833 .14835 .14838 9.17568 .17575 .17583 .17590 .14986 .14988 .14991 .14993 9.18018 .18025 .18033 .18040 .15143 .15144 .15147 .15150 9.18465 .18472 .18480 .18487 .15398 .15301 .15304 .15306 48 47 46 45 + 4' 17 18 19 9.16690 .16697 .16705 .16713 .14686 .14688 .14691 .14693 9.17145 .17153 .17160 .17168 .14841 .14843 .14846 .14848 9.17598 .17605 .17613 .17620 .14996 .14999 .15001 .15004 9.18048 .18055 .18062 .18070 .15153 .15155 .15157 .15160 9.18495 .18502 .18509 .18517 .15309 .15312 .15314 .15316 44 43 42 41 + 5' 21 22 23 9.16720 .16728 .16735 .16743 .14696 .14699 .11701 .14704 9.17175 .17183 .17191 .17198 .14851 .14853 .14856 .14859 9.17628 .17635 .17643 .17650 .15006 .15009 .15013 .15014 9.18077 .18085 .18092 .18100 .15163 .15165 .15168 .15170 9.18524 .18532 .18539 .18547 .15319 .15333 .15325 .15337 40 39 38 37 25 26 27 9.16751 .16758 .16766 .16774 .14706 .14709 .14713 .14714 9.17206 .17213 .17221 .17228 .14861 .14864 .14866 .14869 9.17658 .17665 .17673 .17680 .15017 .15019 .15033 .15035 9.18107 .18115 .18122 .18130 .15173 .15176 .15178 .15181 9.18554 .18561 .18569 .18576 .15330 .15333 .15335 .15337 36 35 34 33 29 30 31 9.16781 .16789 .16796 .16804 .14717 .14719 .14733 .14734 9.17236 .17243 .17251 .17259 .14873 .14874 .14877 .14879 9.17688 .17695 .17703 .17710 .15037 .15030 .15033 .15035 9.18137 .18145 .18152 .18160 .15183 .15186 .15189 .15191 9.18584 .18591 .18598 .18608 .15340 .15343 .15346 .15348 32 31 30 29 33 34 35 9.16812 .16819 .16827 .16834 .14737 .14730 .14733 .14735 9.17266 .17274 .17281 .17289 .14883 .14885 .14887 .14890 9.17718 .17725 .17733 .17740 .15038 .15040 .15043 .15045 9.18167 .18174 .18182 .18189 .15194 .15197 .15199 .15303 9.18613 .18621 .18628 .18636 .15351 .15353 .15356 .15359 28 27 26 25 + 9^ 37 38 39 9.16842 .16850 .16857 .16865 .14737 .14740 .14743 .14745 9.17296 .17304 .17311 .17319 .14893 .14895 .14898 .14900 9.17748 .17755 .17763 .17770 .15048 .15051 .15053 .15056 9.18197 .18204 .18212 .18219 .15304 .15207 .15310 .15313 9.18643 .18650 .18658 .18665 .15361 .15364 .15367 .15369 24 23 22 21 + W 41 42 43 9.16872 .16880 .16887 .16895 .14748 .14750 .14753 .14755 9.17327 .17334 .17342 .17349 .14903 .14905 .14908 .14910 9.17778 .17785 .17793 .17800 .15058 .15061 .15064 .15066 9.18227 .18234 .18242 .18249 .15315 .15317 .15330 .15323 9.18673 .18680 .18687 .18695 .15373 .15374 .15377 .15379 20 19 18 17 + 11' 45 46 47 9.16903 .16910 .16918 .16925 .14758 .14760 .14763 .14766 9.17357 .17364 .17372 .17379 .14913 .14916 .14918 .14931 9.17808 .17815 .17823 .17830 .15069 .15071 .15074 .15077 9.18256 .18264 .18271 .18279 .15335 .15338 .15330 .15333 9.18702 .18710 .18717 .18724 .15383 .15385 .15388 .15390 16 15 U 13 + ir 49 50 51 9.16933 .16941 .16948 .16956 .14768 .14771 .14773 .14776 9.17387 .17394 .17402 .17409 .14933 .14936 .14939 .14931 9.17838 .17845 .17853 .17860 .15079 .15083 .15084 .15087 9.18286 .18294 .18301 .18309 .15336 .15338 .15241 .15244 9.18732 .18739 .18747 .18754 .15393 .15395 .15398 .15401 12 11 10 9 + 13^ 53 64 55 9.16963 .16971 .16979 .16986 .14779 .14781 .14784 .14786 9.17417 .17425 .17432 .17440 .14934 .14936 .14939 .14943 9.17868 .17875 .17883 .17890 .15090 .15093 .15095 .15097 9.18316 .18324 .18331 .18338 .15246 .15249 .15251 .15254 9.18762 .18769 .18776 .18784 .15403 .15406 .15409 .15411 8 7 6 5 + U' 57 58 59 9.16994 .17001 .17009 .17016 .14789 .14791 .14794 .14797 9.17447 .17455 .17462 .17470 .14944 .14947 .14949 .14953 9.17898 .17905 .17913 .17920 .15100 .15103 .15105 .15108 9.18346 .18353 .18361 .18368 .15257 .15259 .15263 .15364 9.18791 .18798 .18806 .18813 .15414 .15416 .15419 .15433 4 3 Z 1 + W 9.17024 .14799 9.17477 .14955 9.17928 .15110 9.18376 .15367 9.18821 .15434 20h 59m 20h 55™ 20^ 57m 20h 56^ 20h 55m TABLE IV. Haversinea. [Page 81 s 3h 5m 46° 15' 3h em 46° 30' 3h7m t6°45' Sh 8m 47° C 3h 9m 47° 15' a Log. Hav. Nat. Hav. Log. Ilav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. 1 2 S 9.18821 .18828 .18835 .18843 .15424 .15437 .15430 .15432 9.19263 .19270 .19278 .19285 .15582 .15585 .15588 .15590 9.19703 .19710 .19717 .19725 .15741 .15743 .15746 .15748 9.20140 .20147 .20154 .20162 .15900 .15903 .15905 .15908 9.20574 .20582 .20589 .20596 .16060 .16063 .16065 .16068 60 59 58 57 + r 5 6 7 9.18850 .18858 .18865 .18872 .15435 .15437 .15440 .15443 9.19292 .19300 .19307 .19315 .15593 .15595 .15598 .15601 9.19732 .19739 .19747 .19754 .15751 .15754 .15757 .15759 9.20169 .20176 .20184 .20191 .15911 .15913 .15916 .15919 9.20603 .20611 .20618 .20625 .16071 .16073 .16076 .16079 56 55 54 53 + V 9 10 11 9.18880 .18887 .18895 .18902 .15445 .15448 .15451 .15453 9.19322 .19329 .19337 .19344 .15603 .15606 .15609 .15611 9.19761 .19769 .19776 .19783 .15762 .15765 .15767 .15770 9.20198 .20205 .20213 .20220 9.20227 .20234 .20242 .20249 .15921 .15924 .15927 .15929 .15933 .15935 .15937 .15940 9.20632 .20639 .20647 .20654 .16081 .16084 .16087 .16089 52 51 50 49 + 3' 13 14 15 9.18909 .18917 .18924 .18932 .15456 .15458 .15461 .15464 9.19351 .19359 .19366 .19373 .15614 .15617 .15619 .15622 9.19790 .19798 .19805 .19812 .15773 .15775 .15778 .15781 9.20661 .20668 .20675 .20683 .16092 .16095 .16097 .16100 48 47 46 45 + 4^ 17 18 19 9.18939 .18946 .18954 .18961 .15466 .15469 .15472 .15474 9.19381 .19388 .19395 .19403 .15625 .15627 .15630 .15632 9.19820 .19827 .19834 .19842 .15783 .15786 .15789 .15791 9.20256 .20263 .20271 .20278 .15943 .15945 .15948 .15951 9.20690 .20697 .20704 .20712 .16103 .16105 .16108 .16111 44 43 42 41 + 5^ 21 22 23 9.18968 .18976 .18983 .18991 .15477 .15479 .15482 .15485 9.19410 .19417 .19425 .19432 .15635 .15638 .15640 .15643 9.19849 .19856 .19863 .19871 .15794 .15796 .15799 .15803 9.20285 .20292 .20300 .20307 .15953 .15956 .15959 .15961 9.20719 .20726 .20733 .20740 .16113 .16116 .16119 .16121 40 39 38 37 + 6' 25 26 27 9.18998 .19005 .19013 .19020 .15487 .15490 .15493 .15495 9.19439 .19447 .19454 .19461 .15646 .15648 .15651 .15654 9.19878 .19885 .19893 .19900 .15804 .15807 .15810 .15813 9.20314 .20321 .20329 .20336 .15964 .15967 .15969 .15973 9.20748 .20755 .20762 .20769 .16124 .16127 .16139 .16133 36 35 34 33 + r 29 30 31 9.19027 .19035 .19042 .19050 .15498 .15501 .15503 .15506 9.19469 .19476 .19483 .19491 .15656 .15659 .15662 .15664 9.19907 .19914 .19922 .19929 .15815 .15818 .15830 .15833 9.20343 .20350 .20358 .20365 .15975 .15977 .15980 .15983 9.20776 .20784 .20791 .20798 .16135 .16137 .16140 .16143 32 31 30 29 + 8' 33 S4 35 9.19057 .19064 .19072 .19079 .15509 .15511 .15514 .15516 9.19498 .19505 .19513 .19520 .15667 .15670 .15672 .15675 9.19936 .19944 .19951 .19958 .15826 .15828 .15831 .15834 9.20372 .20379 .20386 .20394 .15985 .15988 .15991 .15993 9.20805 .20812 .20820 .20827 .16146 .16148 .16151 .16154 28 27 26 25 + a' 37 38 39 9.19086 .19094 .19101 .19109 .15519 .15522 .15524 .15527 9.19527 .19535 .19542 .19549 .15677 .15680 .15683 .15685 9.19965 .19973 .19980 .19987 .15836 .15839 .15843 .15844 9.20401 .20408 .20415 .20423 .15996 .15999 .16001 .16004 9.20834 .20841 .20848 .20856 .16156 .16159 .16163 .16164 24 23 22 21 + W 41 42 43 9.19116 .19123 .19131 .19138 .15530 .15532 .15535 .15537 9.19557 .19564 .19571 .19579 .15688 .15691 .15693 .15696 9.19995 .20002 .20009 .20016 .15847 .15850 .15853 .15855 9.20430 .20437 .20444 .20452 .16007 .16009 .16013 .16015 9.20863 .20870 .20877 .20884 .16167 .16170 .16173 .16175 20 19 18 n + 11' 45 46 47 9.19145 .19153 .19160 .19167 .15540 .15543 .15545 .15548 9.19586 .19593 .19600 .19608 .15699 .15701 .15704 .15706 9.20024 .20031 .20038 .20045 .15858 .15860 .15863 .15866 9.20459 .20466 .20473 .20481 .16017 .16030 .16033 .16035 9.20891 .20899 .20906 .20913 .16178 .16180 .16183 .18186 16 15 14 13 12 11 10 9 8 7 6 5 + 12' 49 50 51 9.19175 .19182 .19190 .19197 .15551 .15553 .15556 .15559 9.19615 .19622 .19630 .19637 .15709 .15713 .15714 .15717 9.20053 .20060 .20067 .20075 .15868 .15871 .15874 .15876 9.20488 .20495 .20502 .20509 .16038 .16031 .16033 .16036 9.20920 .20927 .20935 .20942 .16188 .16191 .16194 .16196 + 13' 53 54 55 9.19204 .19212 .19219 .19226 .15561 .15564 .15566 .15569 9.19644 .19652 .19659 .19666 .15730 .15733 .15735 .15728 9.20082 .20089 .20096 .20104 .15879 .15881 .15884 .15887 9.20517 .20524 .20531 .20538 .16039 .16041 .16044 .16047 9.20949 .20956 .20963 .20971 .16199 .16203 .16204 .16307 + 14' 57 58 59 9.19234 .19241 .19248 .19256 .15572 .15574 .15577 .15580 9.19674 .19681 .19688 .19696 .15730 .15733 .15736 .15738 9.20111 .20118 .20125 .20133 .15889 .15893 .15895 .15898 9.20546 .20553 .20560 .20567 .16049 .16052 .16055 .16057 9.20978 .20985 .20992 .20999 .16310 .16313 .16315 .16318 4 3 2 1 + 15' 9.19263 .15582 9.19703 .15741 9.20140 .15900 9.20574 .16060 9.21006 .16230 20h 54^ 20h 5Sm 20^ 52^ 20f>- 5im 20'!' 50m 55901= Page 82] TABLE IV. Eaversines. s Sh jom 47° 30' 3h 11m 47° 45' Sh 12m 48° C Sh iSm 48° 15' Sh 14m 48° 30' s Log. llav. Nat. Ilav. Log. Ilav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Ilav. Log. Hav. Nat. Hav. 1 2 3 9.21006 .21014 .21021 .21028 .16220 .16223 .16226 .16229 9.21436 .21443 .21450 .21457 .16382 .16384 .16387 .16390 9.21863 .21870 .21877 .21884 .16543 .16546 .16549 .16552 9.22287 .22294 .22301 .22308 .16706 .16709 .16711 .16714 9.22709 .22716 .22723 .22730 .16869 .16872 .16874 .16877 60 59 5S 57 5 6 7 9.21035 .21042 .21049 .21057 .16231 .16234 .16237 .16239 9.21464 .21471 .21479 .21486 .16392 .16395 .16398 .16401 9.21891 .21898 .21905 .21912 .16554 .16557 .16560 .16562 9.22315 .22322 .22329 .22336 .16717 .16720 .16722 .16725 9.22737 .22744 .22751 .22758 0I688O .16883 .16885 .16888 56 55 54 53 + 2" 9 10 11 9.21064 .21071 .21078 .21085 .16242 .16245 .16247 .16250 9.21493 .21500 .21507 .21514 .16403 .16406 .16409 .16411 9.21919 .21926 .21934 .21941 .16565 .16568 .16571 .16573 9.22343 .22350 .22358 .22365 .16728 .16730 .16733 .16736 9.22765 .22772 .22779 .22786 .16891 .16893 .16896 .16899 52 51 50 49 + 3^ IS 14 15 9.21092 .21100 .21107 .21114 .16253 .16255 .16358 .16261 9.21521 .21529 .21536 .21543 .16414 .16417 .16419 .16433 9.21948 .21955 .21962 .21969 .16576 .16579 .16581 .16584 9.22372 .22379 .22386 .22393 .16738 .16741 .16744 .16747 9.22793 .22800 .22807 .22814 .16902 .16904 .16907 .16910 48 47 46 45 + 4' 17 18 19 9.21121 .21128 .21135 .21143 .16263 .16266 .16269 .16271 9.21550 .21557 .21564 .21571 .16425 .16427 .16430 .16433 9.21976 .21983 .21990 .21997 .16587 .16589 .16593 .16595 9.22400 .22407 .22414 .22421 .16749 .16753 .16755 .16757 9.22821 .22828 .22835 .22842 .16913 .16915 .16918 .16921 U 43 42 41 + y 21 22 23 9.21150 .21157 .21164 .21171 .16274 .16277 .16280 .16282 9.21578 .21585 .21593 .21600 .16436 .16438 .16441 .16444 .16446 .16449 .16452 .16454 9.22004 .22011 .22019 .22026 .16598 .16600 .16603 .16606 9.22428 .22435 .22442 .22449 .16760 .16763 .16766 .16768 9.22849 .22856 .22863 .22870 .16924 .16926 .16921) .16932' 40 39 38 37 36 35 34 S3 + 6^ 25 26 21 9.21178 .21186 .21193 .21200 .16285 .16288 .16290 .16293 9.21607 .21614 .21621 .21628 9.22033 .22040 .22047 .22054 .16608 .16611 .16614 .16616 9.22456 .22463 .22470 .22477 .16771 .16774 .16777 .16779 9.22877 .22884 .22891 .22898 .16934 .16937 .16940 .16943 + r 29 30 31 9.21207 .21214 .21221 .21229 .16296 .16298 .16301 .16304 9.21635 .21642 .21650 .21657 .16457 .16460 .16462 .16465 9.22061 .22068- .22075 .22082 .16619 .16622 .16625 .16637 9.22484 .22491 .22498 .22505 .16783 .16785 .16787 .16790 9.22905 .22012 .22919 .22926 .16945 .16948 .16951 .16953 32 31 30 29 + 8' 33 34 35 9.21236 .21243 .21250 .21257 .16306 .16309 .16312 .16314 9.21664 .21671 .21678 .21685 .16468 .16471 .16473 .16476 9.22089 .22096 .22103 .22111 .16630 .16633 .16635 .16638 9.22512 .22519 .22526 .22533 .16793 .16795 .16798 .16801 9.22933 .22940 .22947 .22954 .16956 .16959 .16962 .16964 2S 27 26 25 + 9' 37 38 39 9.21264 .21272 .21279 .21286 .16317 .16320 .16323 .16325 9.21692 .21699 .21706 .21714 .16479 .16481 .16484 .16487 9.22118 .22125 .22132 .22139 .16641 .16644 .16646 .16649 9.22540 .22547 .22555 .22562 .16804 .16806 .16809 .16813 9.22961 .22968 .22975 .22982 .16967 .16970 .16973 .16975 24 23 2? 21 4- W 41 42 43 9.21293 .21300 .21307 .21314 .16328 .16331 .16333 .16336 9.21721 .21728 .21735 .21742 .16489 .16492 .16495 .16498 9.22146 .22153 .22160 .22167 .16652 .16654 .16657 .16660 9.22569 .22576 .22583 .22590 .16815 .16817 .16820 .16823 9.22989 .22996 .23003 .23010 .16978 .16981 .16984 .16986 20 19 18 17 + ir 45 46 47 9.21322 .21329 .21336 .21343 .16339 .16341 .16344 .16347 9.21749 .21756 .21763 .21770 .16500 .16503 .16506 .16508 9.22174 .22181 .22188 .22195 .16663 .16665 .16668 .16671 9.22597 .22604 .22611 .22618 .16825 .16828 .16831 .16834 9.23017 .23024 .23031 .23038 .16989 .16992 .16994 .16997 16 15 14 13 + 12^ 49 50 51 9.21350 .21357 .21364 .21372 .16349 .16352 .16355 .16357 9.21778 .21785 .21792 .21799 .16511 .16514 .16516 .16519 9.22202 .22209 .22216 222^^4 9.22231 .22238 .22245 .22252 .16673 .16676 .16679 .16681 9.22625 .22632 .22639 .22646 .16836 .16839 .16842 .16844 9.23045 .23052 .23059 .23066 .17000 .17003 .17005 .17008 12 11 10 9 8 7 6 5 + 13' 53 54 55 9.21379 .21386 .21393 .21400 .16360 .16363 .16366 .16368 9.21806 .21813 .21820 .21827 .16523 .16524 .16537 .16530 .16684 .16687 .16690 .16692 9.22653 .22660 .22667 .22674 .16847 .16850 .16853 .16855 9.23073 .23080 .23087 .23094 .17011 .17014 .17016 .17019 + ir 57 58 59 9.21407 .21414 .21422 .21429 .16371 .16374 .16376 .16379 9.21834 .21841 .21848 .21856 .16533 .16535 .16538 .16541 9.22259 .22266 .22273 .22280 .16695 .16698 .16701 .16703 9.22681 .22688 .22695 .22702 .16858 .16861 .16864 .16866 9.23100 .23107 .23114 .23121 .17022 .17024 .17027 .17030 4 S 2 '1 + 15' 9.21436 .16382 9.21863 .16543 9.22287 .16706 9.22709 .16869 9.23128 .17033 20h 43m 20^t' 48^ 20h J^jm 20h 46m 20^ 45m TABLE IV. [Page 83 Haversines. s Sh 157TI 48° 45' 3h 16^ 49° 0' 1 Sh nm 49° 15' 3h IS'"' 49° 30' 3h 19m 49° 45' s Log. Hav. Nat. Ha V. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Ilav. Nat. Hav. Log. Hav. Nat. Hav. 1 3 9.23128 .23135 .23142 .23149 .17033 .17035 .17038 .17041 9.23545 .23552 .23559 .23566 .17197 .17200 .17203 .17205 9.23960 .23967 .23974 .23981 .17362 .17365 .17368 .17370 9.24372 .24379 .24386 .24393 .17528 .17530 .17533 .17536 9.24782 .24789 .24796 .24803 .17694 .17697 .17699 .17702 60 59 58 57 + r 5 6 7 9.23156 .23163 .23170 .23177 .17044 .17046 .17049 .17052 9.23573 .23580 .23587 .23594 .17208 .17211 .17214 .17216 9.23988 .23994 .24001 .24008 .17373 .17376 .17379 .17381 9.24400 .24406 .24413 .24420 .17539 .17541 .17544 .17547 9.24809 .24816 .24823 .24830 .17705 .17708 .17710 .17713 56 55 54 53 + 2^ 9 10 11 9.23184 .23191 .23198 .23205 .17055 .17057 .17060 .17063 9.23601 .23608 .23615 .23622 .17219 .17222 .17225 .17227 9.24015 .24022 .24029 .24036 .17384 .17387 .17390 .17392 9.24427 .24434 .24441 .24448 .17550 .17552 ,17555 .17558 9.24837 .24843 .24850 .24857 .17716 .17719 .17722 .17724 52 51 50 49 48 47 46 45 + 3' 13 14 15 9.23212 .23219 .23226 .23233 .17066 .17068 .17071 .17074 9.23629 .23635 .23642 .23649 .17230 .17233 .17235 .17238 9.24043 .24050 .24056 .24063 .17395 .17398 .17401 .17403 9.24454 .24461 .24468 .24475 .17561 .17563 .17566 .17569 9.24864 .24871 .24877 .24884 .17727 .17730 .17733 .17735 + ^' 17 18 19 9.23240 .23247 .23254 .23261 .17076 .17079 .17082 .17085 9.23656 .23663 .23670 , .23677 .17241 .17244 .17246 .17249 9.24070 .24077 .24084 .24091 .17406 .17409 .17412 .17414 9.24482 .24489 .24495 .24502 .17572 .17575 .17577 .17580 9.24891 .24898 .24905 .24911 .17738 .17741 .17744 .17746 44 43 42 41 + 5' 21 22 23 9.23268 .23275 .23282 .23289 .17087 .17090 .17093 .17096 9.23684 .23691 .23698 .23705 .17252 .17255 .17257 .17260 9.24098 .24105 .24111 .24118 .17417 .17420 .17423 .17425 9.24509 .24516 .24523 .24530 .17583 .17586 .17588 .17591 9.24918 .24925 .24932 .24939 .17749 .17752 .17755 .17758 40 39 38 37 + 6^ 25 26 27 9.23295 .23302 .23309 .23316 .17098 .17101 .17104 .17107 9.23712 .23718 .23725 .23732 .17263 .17266 .17268 .17271 9.24125 .24132 .24139 .24146 .17428 .17431 .17434 .17436 9.24536 .24543 .24550 .24557 .17594 .17597 .17600 .17602 9.24945 .24952 .24959 .24966 .17760 .17763 .17766 .17769 36 35 34 33 + r 29 30 31 9.23323 .23330 .23337 .23344 .17109 .17112 .17115 .17117 9.23739 .23746 .23753 .23760 .17274 .17277 .17279 .17282 9.24153 .24160 .24166 .24173 .17439 .17442 .17445 .17447 9.24564 .24571 .24577 .24584 .17605 .17608 .17611 .17613 9.24973 .24979 .24986 .24993 .17772 .17774 .17777 .17780 32 31 SO 29 + 8' 33 34 35 9.23351 .23358 .23365 .23372 .17120 .17123 .17126 .17128 9.23767 .23774 .23781 .23788 .17285 .17288 .17290 .17293 9.24180 .24187 .24194 .24201 .17450 .17453 .17456 .17458 9.24591 .24598 .24605 .24612 .17616 .17619 .17622 .17624 9.25000 .25007 .25013 .25020 .17783 .17785 .17788 .17791 28 27 26 25 24 23 22 21 + 9' 37 38 39 9.23379 .233-86 .23393 .23400 .17131 .17134 .17137 .17139 9.23794 .23801 .23808 .23815 .17296 .17299 .17301 .17304 9.24208 .24215 .24221 .24228 .17461 .17464 .17467 .17470 9.24618 .24625 .24632 .24639 .17627 .17630 .17633 .17636 9.25027 .25034 .25040 .25047 .17794 .17797 .17799 .17802 + W 41 42 43 9.23407 .23414 .23421 .23427 .17142 .17145 .17148 .17150 9.23822 .23829 .23836 .23843 .17307 .17310 .17313 .17315 9.24235 .24242 .24249 .24256 .17472 .17475 .17478 .17481 9.24646 .24653 .24659 .24666 .17638 .17641 .17644 .17647 9.25054 .25061 .25068 .25074 .17805 .17808 .17811 .17813 20 19 18 17 + 11^ 45 46 47 ■ 9.23434 .23441 .23448 .23455 .17153 .17156 .17159 .17161 9.23850 .23857 .23863 .23870 .17318 .17321 .17323 .17326 9.24263 .24269 .24276 .24283 .17483 .17486 .17489 .17492 9.24G73 .24680 .24687 .24694 .17649 .17652 .17655 .17658 9.25081 .25088 .25095 .25102 .17816 .17819 .17822 .17824 16 15 14 IS + 12' 49 50 51 9.23462 .23469 .23478 .23483 .17164 .17167 .17170 .17172 9.23877 .23884 .23891 .23898 .17329 .17332 .17335 .17337 9.24290 .24297 .24304 .24311 .17494 .17497 .17500 .17503 9.24700 .24707 .24714 .24721 .17661 .17663 .17666 .17669 9.25108 .25115 .25122 .25129 .17827 .17830 .17833 .17836 12 11 10 9 + 13' 53 54 55 9.23490 .23497 .23504 .23511 .17175 .17178 .17181 .17183 9.23905 .23912 .23919 .23926 .17340 .17343 .17346 .17348 9.24317 .24324 .24331 .24338 .17505 .17508 .17511 .17514 9.24728 .24734 .24741 .24748 .17672 .17674 .17677 .17680 9.25135 .25142 .25149 .25156 .17838 .17841 .17844 .17847 8 7 6 5 + 14' 57 58 59 9.23518 .23525 .23532 .23538 .17186 .17189 .17192 .17194 9.23932 .23939 .23946 .23953 .17351 .17354 .17357 .17359 9.24345 .24352 .24359 .24365 .17517 .17519 .17522 .17525 9.24755 .24762 .24768 .24775 .17683 .17686 .17688 .17691 9.25163 .25169 .25176 .25183 .17849 .17852 .17855 .17858 4 3 2 1 + 15' 9.23545 .17197 9.23960 .17362 9.24372 .17528 9.24782 .17694 9.25190 1 .17861 20^ 44^ 20f>' 4Sin 20h 42m 20h4]m oQh 4om Page 84] TABLE IV. Haversines. s 5'» 20m 50° 0" Sh Sim 50° 15" Sh 22m 60° 30" 3h 2Sm 50° 45" Sh 24m 51° 6' s Log. Hav. Nat. Hav. Log. Hay. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav Nat. Hav. Log. Hav. Nat. Hav. 1 2 3 9.25190 .25196 .25203 .25210 .17861 .17863 .17866 .17869 9.25595 .25602 .25608 .25615 .18038 .18031 .18034 .18036 9.25998 .26005 .26011 .26018 .18196 .18199 .18303 .18305 9.26398 .26405 .26412 .26418 .18365 .18368 .18370 .18373 9.26797 .26804 .26810 .26817 .18534 .18537 .18540 .18542 60 59 58 57 + r 5 6 7 9.25217 .25224 .25230 .25237 .17873 .17875 .17877 .17880 9.25622 .25629 .25635 .25642 .18039 .18043 .18045 .18048 9.26025 .26031 .26038 .26045 .18307 .18310 .18313 .18316 9.26425 .26432 .26438 .26445 .18376 .18379 .18383 .18384 9.26823 .26830 .26837 .26843 .18545 .18548 .18551 .18554 56 55 54 53 + V 9 10 11 9.25244 .25251 .25257 .25264 .17883 .17886 .17888 .17891 9.25649 .25655 .25662 .25669 .18050 .18053 .18056 .18059 9.26051 .26058 .26065 .26071 .18319 .18231 .18334 .18327 9.26452 .26458 .26465 .26472 .18387 .18390 .18393 .18396 9.26850 .26856 .26863 .26870 .18557 .18559 .18563 .18565 52 51 50 49 + 3" 13 14 15 9.25271 .25278 .25284 .25291 .17894 .17897 .17900 .17903 9.25676 .25682 .25689 .25696 .18063 .18064 .18067 .18070 9.26078 .26085 .26091 .26098 .18330 .18333 .18335 .18238 9.26478 .26485 .26492 .26498 .18399 .18401 .18404 .18407 9.26876 .26883 .26890 .26896 .18568 .18571 .18574 .18576 4S 47 46 45 + 4" 17 18 19 9.25298 .25305 .25311 .25318 .17905 .17908 .17911 .17914 9.25703 .25709 .25716 .25723 .18073 .18076 .18078 .18081 9.26105 .26112 .26118 .26125 .18241 .18244 .18247 .18249 9.26505 .26512 .26518 .26525 .18410 .18413 .18415 .18418 9.26903 .26909 .26916 .26923 .18579 .18583 .18585 .18588 44 43 42 41 + 5" 21 22 23 9.25325 .25332 .25339 .25345 .17916 .17919 .17933 .17935 9.25729 ,25736 .25743 .25750 .18084 .18087 .18090 .18093 9.26132 .26138 .26145 .26152 .18352 .18255 .18358 .18261 9.26532 .26538 .26545 .26551 .18431 .18434 .18437 .18430 9.26929 .26936 .26942 .26949 .18591 .18593 .18596 .18599 40 39 38 37 + 6" 25 26 27 9.25352 .25359 .25366 .25372 .17928 .17930 .17933 .17936 9.25756 .25763 .25770 .25776 .18095 .18098 .18101 .18104 9.26158 .26165 .26172 .26178 .18263 .18366 .18369 .18373 9.26558 .26565 .26571 .26578 .18433 .18435 .18438 .18441 9.26956 .26962 .26969 .26975 .18603 .18605 .18608 .18610 36 35 34 33 + r 29 30 31 9.25379 .25386 .25393 .25399 .17939 .17941 .17944 .17947 9.25783 .25790 .25797 .25803 .18106 .18109 .18113 .18115 9.26185 .26192 .26198 .26205 .18275 .18277 .18280 .18283 9.26585 .26591 .26598 .26605 .18444 .18446 .18449 .18452 9.26982 .26989 .26995 .27002 .18613 .18616 .18619 .18633 32 31 SO 29 + 8" 33 34 35 9.25406 .25413 .25420 .25426 .17950 .17953 .17955 .17958 9.25810 .25817 .25823 .25830 .18118 .18130 .18133 .18136 9.26212 .26218 .26225 .26232 .18386 .18289 .18293 .18294 9.26611 .26618 .26625 .26631 .18455 .18458 .18461 .18463 9.27008 .27015 .27022 .27028 .18634 .18627 .18630 .18633 28 27 26 25 + 9' 37 38 39 9.25433 .25440 .25447 .25453 .17961 .17964 , .17967 .17969 9.25837 .25844 .25850 .25857 .18139 .118133 .18134 .18137 9.26238 .26245 .26252 .26259 .18297 .18300 .18303 .18306 9.26638 .26644 .26651 .26658 .18466 .18469 .18472 .18475 9.27035 .27041 .27048 .27055 .18636 .18639 .18641 .18644 24 23 22 21 + 10" 41 42 43 9.25460 .25467 .25474v .25480^ .17973 .17975 .17978 .17981 9.25864 .25870 .25877 .25884 .18140 .18143 .18146 .18148 9.26265 .26272 .26279 .26285 .18308 .18311 .18314 .18317 9.26664 .26671 .26678 .26684 .18478 .18480 .18483 .18486 9.27061 .27068 .27074 .27081 .18647 .18650 .18653 .18656 20 19 18 17 + 11' 45 46 47 9.25487 .25494 .25500 .25507 .17983 .17986 .17989 .17993 9.25891 .25897 .25904 .25911 .18151 .18154 .18157 .18160 9.26292 .26299 .26305 .26312 .18320 .18323 .18325 .18328 9.26691 .26697 .26704 .26711 .18489 .18492 .18494 ,18497 9.27088 .27094 .27101 .27107 .18658 .18661 .18664 .18667 16 15 14 IS + 13" 49 50 51 9.25514 .25521 .25528. .25534 .17995 .17997 .18000 .18003 9.25917 .25924 .25931 .25938 .18163 .18165 .18168 .18171 9.26319 .26325 .26332 .26339 .18331 .18334 .18337 .18339 9.26717 .26724 .26731 .26737 .18500 .18503 .18506 .18509 9.27114 .27121 .27127 .27134 .18670 .18673 .18675 .18678 12 11 10 9 + 13" 53 54 55 9.25541 .25548 .25544 .25561 .18006 .18008 .18011 .18014 9.25944 .25951 .25958 .25964 .18174 .18176 .18179 .18183 9.26345 .26352 .26359 .26365 .18342 .18345 .18348 .18351 9.26744 .26751 .26757 .26764 .18511 .18514 .18517 .18520 9.27140 .27147 .27154 .27160 .18681 .18684 .18687 .18690 8 7 6 5 4 3 2 1 + 14" 57 58 59 9.25568 .25575 .25581 .25588 .18017 .18030 .18033 .18035 9.25971 .25978 .25984 .25991 .18185 .18188 .18190 .18193 9.26372 .26378 .26385 .26392 .18353 .18356 .18359 .18363 9.26770 .26777 .26784 .26790 .18523 .18526 .18528 .18531 9.27167 .27173 .27180 .27186 .18693 .18695 .18698 .18701 + 15" 9.25595 .18038 9.25998 .18196 9.26398 .18365 9.26797 .18534 9.27193 .18704 _ 20^ 39m 1 20^ SS^ 20^ 37m 1 20h 36m 1 20^ S5m 1 TABLE IV. Haversines. [Page 85 Sfi 26m 51° 15' 3h 26m 51° 30' | 3h 27m 51° W 1 3h 28m 5%° 0^ Stt 29m 62° 15^ 1 s s Log. Hav. Nat. Hav. Log. Ilav. Nat. nav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. 1 2 S 9.27193 .27200 .27206 .27213 .18704 .18707 .18710 .18713 9.27587 .27594 .27600 .27607 .18874 .18877 .18880 .18883 9.27979 .27985 .27992 .27998 .19045 .19048 .19051 .19054 9.28368 .28375 .28381 .28388 .19217 .19220 .19223 .19226 9.28756 .28762 .28769 .28775 .19389 .19392 .19395 .19398 60 69 68 57 + r 5 6 7 9.27219 .27226 .27233 .27239 .18715 .18718 .18721 .18724 9.27613 .27620 .27626 .27633 .18886 .18888 .18891 .18894 9.28005 .28011 .28018 .28024 .19057 .19060 .19062 .19065 9.28394 .28401 .28407 .28414 .19228 .19231 .19234 .19237 9.28782 .28788 .28794 .28801 .19401 .19404 .19406 .19409 66 55 54 53 + ^ 9 10 11 9.27246 .27252 .27259 .27265 .18727 .18729 .18732 .18735 9.27639 .27646 .27652 .27659 .18897 .18900 .18903 .18906 9.28031 .28037 .28044 .28050 .19068 .19071 .19074 .19077 9.28420 .28427 .28433 .28440 .19240 .19243 .19246 .19248 9.28807 .28814 .28820 .28827 .19412 .19415 .19418 .19421 52 61 60 49 48 47 46 45 44 43 42 41 + 3^ 13 14 15 9.27272 .27279 .27285 .27292 .18738 .18741 .18744 .18746 9.27666 .27672 .27679 .27685 .18908 .18912 .18914 .18917 9.28057 .28063 .28070 .28076 .19080 .19082 .19085 .19088 9.28446 .28453 .28459 .28465 .19251 .19254 .19257 .19260 9.28833 .28840 .28846 .28852 .19424 .19427 .19429 .19432 + 4^ 17 18 19 9.27298 .27305 .27311 .27318 .18749 .18752 .18755 .18758 9.27692 .27698 .27705 .27711 .18920 .18923 .18926 .18928 9.28083 .28089 .28096 .28102 .19091 .19094 .19097 .19100 9.28472 .28478 .28485 .28491 .19263 .19266 .19269 .19271 9.28859 .28865 .28872 .28878 .19435 .19438 .19441 .19444 + ^ 21 22 23 9.27325 .27331 .27338 .27344 .18761 .18763 .18766 .18769 9.27718 .27724 .27731 .27737 .18931 .18934 .18937 .18940 9.28109 .28115 .28122 .28128 .19102 .19105 .19108 .19111 9.28498 .28504 .28511 .28517 .19274 .19277 .19280 .19283 9.28885 .28891 .28897 .28904 .19447 .19450 .19452 .19455 40 39 38 37 + ^ 25 26 27 9.27351 .27357 .27364 .27371 .18772 .18775 .18778 .18780 9.27744 .27751 .27757 .27764 .18943 .18945 .18948 .18951 9.28135 .28141 .28148 .28154 .19114 .19117 .19120 .19122 9.28524 .28530 .28537 .28543 .19286 .19289 .19291 .19294 9.28910 .28917 .28923 .28930 9.28936 .28942 .28949 .28955 .19458 .19461 .19464 .19467 36 36 34 33 32 31 30 29 + r 29 SO 31 9.27377 .27384 .27390 .27397 .18783 .18786 .18789 .18792 9.27770 .27777 .27783 .27790 .18954 .18957 .18960 .18963 9.28161 .28167 .28174 .28180 .19125 .19128 .19131 .19134 9.28549 .28556 .28562 .28569 .19297 .19300 .19303 .19306 .19470 .19473 .19475 .19478 + 9/ 33 34 35 9.27403 .27410 .27417 .27423 .18795 .18797 .18800 .18803 9.27796 .27803 .27809 .27816 .18965 .18968 .18971 .18974 9.28187 .28193 .28200 .28206 .19137 .19140 .19142 .19145 9.28575 .28582 .28588 .28595 .19309 .19311 .19314 .19317 9.28962 .28968 .28974 .28981 .19481 .19484 .19487 .19490 28 27 26 25 + 9^ 37 38 39 9.27430 .27436 .27443 .27449 .18806 .18809 .18812 .18815 9.27822 .27829 .27835 .27842 .18977 .18980 .18983 .18985 9.28213 .28219 .28226 .28232 .19148 .19151 .19154 .19157 9.28601 .28608 .28614 .28620 .19320 .19323 .19326 .19329 9.28987 .28994 .29000 .29007 .19493 .19496 .19499 .19501 24 23 22 21 20 19 18 17 16 16 14 13 + 1(K 41 42 43 9.27456 .27463 .27469 .27476 .18817 .18820 .18823 .18826 9.27848 .27855 .27861 .27868 .18988 .18991 .18994 .18997 9.28239 .28245 .28252 .28258 .19160 .19163 .19165 .19168 9.28627 .28633 .28640 .28646 .19332 .19335 .19337 .19340 9.29013 .29019 .29026 .29032 .19504 .19507 .19510 .19513 + 11^ 45 46 47 9.27482 .27489 .27495 .27502 .18829 .18832 .18834 .18837 9.27875 .27881 .27888 .27894 .19000 .19002 .19005 .19008 9.28265 .28271 .28278 .28284 .19171 .19174 .19177 .19180 9.28653 .28659 .28666 .28672 .19343 .19346 .19349 .19352 9.29039 .29045 .29051 .29058 .19516 .19519 .19522 .19524 + 1%' 49 60 61 9.27508 .27515 .27522 .27528 .18840 .18843 .18846 .18849 9.27901 .27907 .27914 .27920 .190U .19014 .19017 .19020 9.28291 .28297 .28304 .28310 .19183 .19185 .19188 .19191 9.28679 .28685 .28691 .28698 .19355 .19358 .19360 .19363 9.29064 .29071 .29078 .29084 .19527 .19530 .19533 .19536 12 11 10 9 + 13^ 63 54 66 9.27535 .27541 .27548 .27554 .18852 .18854 .18857 .18860 9.27927 .27933 .27940 .27946 .19022 .19025 .19028 .19031 9.28317 .28323 .28330 .28336 .19194 .19197 .19200 .19203 9.28704 .28711 .28717 .28724 .19366 .19369 .19372 .19375 9.29090 .29096 .29103 .29109 .19539 .19542 .19545 .19548 8 7 6 6 57 58 59 9.27561 .27567 .27574 .27580 .18863 .18866 .18869 .18871 9.27953 .27959 .27966 .27972 .19034 .19037 .19040 .19042 9.28342 .28349 .28355 .28362 .19205 .19208 .19211 .19214 9.28730 .28737 .28743 .28749 .19378 .19381 .19383 .19386 9.29116 .29122 .29128 .29135 .19550 .19553 .19556 .19559 4 3 2 1 + ly 9.27587 .18874 9.27979 .19045 9.28368 .19217 9.28756 .19389 9.29141 .19562 20h 34m 20h SSm 20h S2m 20h Sim 20hS0m Page 86] TABLE IV. Haveraines. s 3^ 30m 53° 30' 3h3im 62° 45' ShS2^ 53° C .5 A 33m 53° 15' 3h34m 53° 30' s Log. Hav. Nat. llav. Log. Hav. Nat. Hav. Log. Ilav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav Nat. Hav. 1 2 S 9.29141 .29148 .29154 .29160 .19563 .19565 .19568 .19571 9.29524 .29531 .29537 .29543 .19735 .19738 .19741 .19744 9.29906 .29912 .29918 .29925 .19909 .19913 .19915 .19918 9.30285 .30291 .30207 .30303 .20084 .20087 .30090 .20093 9.30662 .30068 .30674 .30680 .20359 .30363 .30366 .30368 60 59 58 57 56 55 54 53 52 51 50 49 + r 5 6 7 9.29167 .29173 .29180 .29186 .19573 .19576 .19579 .19583 9.29550 .29556 .29563 .29569 .19747 .19760 .19763 .19756 9.29931 .29937 .29943 .29950 .19931 .19934 .19927 .19930 9.30310 .30316 .30322 .30329 .20095 .30098 .30101 .30104 .20107 .20110 .20113 .20116 9.30687 .30693 .30699 .30705 9.30712 .30718 .30724 .30730 .30371 .30373 .30376 .20379 .20383 .20285 .20388 .30391 + 2' 9 10 11 9.29192 .29199 .29205 .29212 .19585 .19588 .19591 .19591 9.29575 .29582 .29588 .29594 .19758 .19761 .19764 .19767 9.29956 .29962 .29969 .29975 .19933 .19935 .19938 .19941 9.30335 .30341 .30348 .30354 + 3' 13 14 15 9.29218 .29224 .29231 .29237 .19597 .19599 .19603 .19605 9.29601 .29607 .29614 .29620 .19770 .19773 .19776 .19779 9.29981 .29988 .29994 .30000 .19944 .19947 .19950 .19953 9.30360 .30366 .30373 .30379 .20119 .20122 .20125 .20127 9.30737 .30743 .30749 .30755 .30294 .20297 .20300 .20303 48 47 46 45 + r 17 18 19 9.29244 .29250 .29256 .29263 .19608 .19611 .19614 .19617 9.29626 .29633 .29639 .29645 .19783 .19785 .19787 .19790 9.30007 .30013 .30019 .30026 .19956 .19959 .19963 .19964 9.30385 .30392 .30398 .30404 .20130 .20133 .20136 .20139 9.30762 .30768 .30774 .30780 .20308 .20309 .30313 .30314 u 43 42 41 + 5' 21 22 23 9.29269 .29276 .29282 .29288 .19630 .19633 .19635 .19638 9.29652 .29658 .29664 .29671 .19793 .19796 .19799 .19803 9.30032 .30038 .30045 .30051 .19967 .19970 .19973 .19976 9.30410 .30417 .30423 .30429 .20142 .20145 .20148 .20151 9.30787 .30793 .30799 .30805 .30317 .30330 .30333 .30326 40 39 38 37 36 35 34 33 + 6' 25 26 27 9.29295 .29301 .29307 .29314 .19631 .19634 .19637 .19640 9.29677 .29683 .29690 .29696 .19805 .19808 .19811 .19814 9.30057 .30064 .30070 .30076 .19979 .19982 .19985 .19988 9.30436 .30442 .30448 .30454 .20154 .20157 .20160 .20162 9.30812 .30818 .30824 .30830 .30339 .30333 .30336 .20338 + r 29 30 31 9.29320 .29327 .29333 .29339 .19643 .19646 .19649 .19651 9.29703 .29709 .29715 .29722 .19816 .19819 .19823 .19825 9.30083 .30089 .30095 .30102 .19991 .19994 .19996 .19999 9.30461 .30467 .30473 .30480 .20165 .20168 .20171 .20174 9.30837 .30843 .30849 .30855 .20341 .20344 .20347 .20350 .20352 .20355 .20358 .20361 32 31 30 29 28 27 26 25 + 8' 33 34 35 9.29346 .29352 .29359 .29365 .19654 .19657 .19660 .19663 9.29728 .29734 .29741 .29747 ■ .19828 .19831 .19834 .19837 9.30108 .30114 .30121 .30127 .30003 .30005 .30008 .30011 9.30486 .30492 .30498 .30505 .20177 .20180 .20183 .20186 9.30862 .30868 .30874 .30880 + r 57 38 39 9.29371 .29378 .29384 .29391 .19666 .19669 .19673 .19675 9.29753 .29760 .29766 .29772 .19840 .19843 .19845 .19848 9.30133 .30139 .30146 .30152 .20014 .20017 .20020 .20033 9.30511 .30517 .30524 .30530 .20189 .30193 .30195 .20198 9.30887 .30893 .30899 .30905 .20364 .20367 .20370 .20373 24 23 22 21 + 10' 41 42 43 9.29397 .29403 .29410 .29416 .19677 .19680 .19683 .19686 9.29779 .29785 .29791 .29798 .19851 .19854 .19857 .19860 9.30158 .30165 .30171 .30177 .20026 .20038 .20031 .20034 9.30536 .30542 .30549 .30555 .20300 .30303 .30306 .20209 9.30912 .30918 .30924 .30930 .20376 .20379 .20382 .20385 20 19 ■ 18 . 17 ' + 11' 45 46 47 9.29422 .29429 .29435 .29442 .19689 .19693 .19695 .19698 9.29804 .29810 .29817 .29823 .19863 .19866 .19869 .19873 9.30184 .30190 .30196 .30203 .20037 .20040 .20043 .20046 9.30561 .30567 .30574 .30580 .20212 .20216 .20218 .30331 9.30937 .30943 .30949 \30955 ' .30388 .20391 .20393 .20396 16 15 14 13 12 ■ 11 10 9 + ir 49 50 51 9.29448 .29454 .29461 .29467 .19701 .19703 .19706 .19709 9.29829 .29836 .29842 .29848 .19874 .19877 .19880 .19883 9.30209 .30215 .30222 .30228 .20049 .20052 .20055 .20058 9.30586 .30593 .30599 .30605 .20334 .30337 .30330 .20233 9.30962 .30968 .30974 .30980 .20399 .20402 .20405 .20408 + 13' 53 54 55 9.29473 .29480 .29486 .29493 .19713 .19715 .19718 .19731 9.29855 .29861 .29867 .29874 .19886 .19889 .19893 .19895 9.30234 .30240 .30247 .30253 .20060 .20063 .20066 .20069 9.30611 .30618 .30624 .30630 .20235 .20238 .20341 .30344 9.30987 .30993 .30999 .31005 .30411 .30414 .30417 .20430 8 7 6 5 + 14' 57 58 59 9.29499 .29505 .29512 .29518 .19734 .19737 .19730 .19733 9.29880 .29886 .29893 .29899 .19898 .19901 .19903 .19906 9.30259 .30266 .30272 .30278 .20073 .20076 .20078 .20081 9.30636 .30643 .30649 .30655 .30347 .30250 .20353 .20356 9.31012 .31018 .31024 .31030 .30433 .20426 .20429 .20432 4 3 2 1 + 15' 9.29524 .19735 9.29906 .19909 9.30285 .20084 9.30662 .20259 9.31036 .20436 20h 29^ 20^ 28^ 20'h' 27'"^ 20h 26>n | 20h S5m TABLE IV. [Page 87 Havereines. s 3h 35m 5Z°i5' 1 Sh 36m 54° 0' | Sh 37m u° w 3hS8m5i°W 3f^ 39m 5i°i5' | s Log. Hav. Nat. Hav. Log. Ilav. Nat. Ilav. Log. Ilav. Nat. Uav. Log. Ilav. Nat. Ilav. Log. Uav. Nat. Hav. 1 2 3 9.31036 .31043 .31049 .31055 .20435 .20437 .20440 .20443 9.31409 .31416 .31422 .31428 .20011 .30614 .30617 .20620 9.31780 .31786 .31793 .31799 .30788 .30790 .30793 .30796 9.32149 .32155 .32161 .32168 .30965 .20968 .20971 .20974 9.32516 .32522 .32528 .32534 .21143 .31146 .31149 .31153 60 59 58 57 + r 5 6 7 9.31061 .31068 .31074 .31080 .20446 .30449 .30452 .30455 9.31434 .31440 .31447 .31453 .20623 .30636 .30639 .30631 .30634 .20637 .30640 .30643 9.31805 .31811 .31817 .31823 .30799 .30803 .30805 .30808 9.32174 .32180 .32186 .32192 .30977 .30980 .20983 .20986 9.32541 .32547 .32553 .32559 9.32565 .32571 .32577 .32583 .31155 .31158 .31161 .31164 56 55 64 53 + 2^ 9 10 11 9.31086 .31093 .31099 .31105 .30458 .20461 .30464 .30467 9.31459 .31465 .31471 .31478 9.31830 .31836 .31842 .31848 .30811 .30814 .30817 .30830 9.32198 .32204 .32210 .32217 9.32223 .32229 .32235 .32241 .20989 .20991 .20994 .20997 .31167 .31169 .31173 .31175 52 51 50 49 48 47 46 45 + 3' 13 U 15 9.31111 .31117 .31124 .31130 .30470 .30473 .20476 .30479 9.31484 .31490 .31496 .31502 .30646 .30649 .30653 .30655 9.31854 .31860 .31867 .31873 .30833 .30836 .30839 .30833 .21000 .21003 .21006 .21009 9.32589 .32595 .32601 .32608 .31178 .31181 .31184 .31187 + 4' 17 18 19 9.31136 .31142 .31149 .31155 .30481 .30484 .30487 .30490 9.31508 .31515 .31521 .31527 .30658 .30661 .30664 .30667 9.31879 .31885 .31891 .31897 .30835 .30838 .30841 .30844 9.32247 .32253 .32259 .32266 .31013 .31015 .31018 .31031 9.32614 .32620 .32626 .32632 .31190 .31193 .31196 .21199 44 43 42 41 + 5' 21 22 23 9.31161 .31167 .31173 .31180 .30493 .30486 .30499 .30503 9.31533 .31539 .31546 .31552 .30670 .30673 .30675 .30678 9.31903 .31910 .31916 .31922 .30847 .30850 .30853 .30855 9.32272 .32278 .32284 .32290 .21024 .31027 .21030 .21033 9.32638 .32644 .32650 .32656 .21202 .21205 .21208 .21211 40 39 38 37 + 6^ 25 26 27 9.31186 .31192 .31198 .31205 .30505 .30508 .30511 .30514 9.31558 .31564 .31570 .31577 .30681 .30684 .30687 .20690 9.31928 .31934 .31940 .31947 .30858 .30861 .30864 .30867 9.32296 .32302 .32308 .32315 .31036 .31039 .31043 .21045 9.32662 .32668 .32675 .32681 .21214 .21217 .21220 .21233 36 35 34 S3 + r 29 30 31 9.31211 .31217 .31223 .31229 .30517 .30530 .30523 .20525 9.31583 .31589 .31595 .31601 .20693 .20696 .30699 .30702 9.31953 .31959 .31965 .31971 .30870 .30873 .30876 .30879 9.32321 .32327 .32333 .32339 .21048 .21051 .21054 .21057 9.32687 .32693 .32699 .32705 .31336 .31339 .31333 .21335 32 31 30 29 + 8' 33 34 35 9.31236 .31242 .31248 .31254 .20528 .20531 .20534 .20537 9.31607 .31614 .31620 .31626 .30705 .30708 .30711 .30714 9.31977 .31983 .31990 .31996 .30883 .30885 .30888 .30891 9.32345 .32351 .32357 .32363 .31060 .31063 .31066 .31069 9.32711 .32717 .32723 .32729 .21338 .31241 .31344 .31347 28 27 26 25 24 23 22 21 20 19 18 11 + r 37 38 39 9.31260 .31267 .31273 .31279 .20540 .20543 .20546 .20549 9.31632 .31638 .31644 .31651 .30717 .30730 .30723 .20726 9.32002 .32008 .32014 .32020 .30894 .30897 .30900 .20903 9.32370 .32376 .32382 .32388 .31072 .21074 .21077 .21080 9.32735 .32741 .32748 .32754 .31350 .31353 .31256 .21259 + 10^ 41 42 43 9.31285 .31291 .31298 .31304 .20553 .30555 .30558 .20561 9.31657 .31663 .31669 .31675 .20729 .20731 .20734 .20737 9.32026 .32033 .32039 .32045 .20906 .20909 .20912 .20915 9.32394 .32400 .32406 .32412 .21083 .21086 .21089 .21092 9.32760 .32766 .32772 .32778 .31363 .31265 .21268 .21271 + ir 45 46 47 9.31310 .31316 .31323 .31329 .30564 .30567 .30570 .30573 9.31682 .31688 .31694 .31700 .30740 .30743 .30746 .30749 9.32051 .32057 .32063 .32069 .30918 .30930 .30933 .30936 9.32418 .32425 .32431 .32437 .21095 .21098 .31101 .21104 9.32784 .32790 .32796 .32802 .31374 .31377 .21380 .31283 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 + n' 49 50 51 9.31335 .31341 .31347 .31354 .30575 .30578 .30581 .30584 9.31706 .31712 .31719 .31725 .30753 .30755 .20758 .30761 9.32076 .32082 .32088 .32094 .30939 .30933 .30935 .30938 9.32443 .32449 .32455 .32461 .21107 .21110 .21113 .21116 9.32808 .32814 .32820 .32827 .31385 .21388 .21291 .21394 + 13^ 53 54 55 9.31360 .31366 .31372 .31378 .30587 .30590 .30593 .30596 9.31731 .31737 .31743 .31749 .30764 .20767 .20770 .20773 9.32100 .32106 .32112 .32119 .30941 .30944 .30947 .30950 9.32467 .32473 .32480 .32486 .21119 .21122 .21125 .21128 9.32833 .32839 .32845 .32851 .31397 .21300 .21303 .21306 57 58 59 9.31385 .31391 .31397 .31403 .30599 .30603 .20605 .20608 9.31756 .31762 .31768 .31774 .30776 .30779 .30782 .20785 9.32125 .32131 .32137 .32143 .30953 .30956 .30959 .30963 9.32492 .32498 .32504 .32510 .31131 .31134 .31137 .21140 9.32857 .32863 .32869 .32875 .21309 .21312 .21315 .21318 + W 9.31409 .20611 9.31780 .30788 9.32149 .30965 9.32516 .21143 9.32881 .31321 20h 24^ 20h 23m 20^ 22m. 20^ 21m 20^ 20m Page 88] TABLE IV. Haversines. s 3^40^ » 55° 0' 3h4im 55° 15' 3h 42m 55° 3(K Sh 4Sm 55° 45' 3h 44m 56° 0' s Log. Hav. Nat. Hav. Log. Hav. Nat. Ilav. Log. Hav. Nat. Hav Log. Hav. Nat. Hav Log. Hav. Nat. Hav. 1 2 3 9.32881 .32887 .32893 .32899 .21331 .31334 .31337 .31330 9.33244 .33250 .33256 .33262 .21500 .21503 .21506 .21509 9.33605 .33611 .33617 .33623 .21680 .21683 .21686 .21689 9.33965 .33971 .33976 .33982 .21860 .21863 .21866 .21869 9.34322 .34328 .34334 .34340 .22040 .32043 .22046 .22049 60 59 58 57 + r 5 6 7 9.32905 .32911 .32918 .32924 .31333 .31336 .21339 .21342 9.33268 .33274 .33280 .33286 .21513 .21515 .21518 .21521 9.33629 .33635 .33641 .33647 .21692 .21695 .21698 .21701 9.33988 .33994 .34000 .34006 .21873 .31875 .31878 .21881 9.34346 .34352 .34358 .34363 .22053 .23055 .32058 .33061 56 55 54 53 + V 9 10 11 9.32930 .32936 .32942 .32948 .31345 .31348 .31351 .31354 9.33292 .33298 .33305 .33311 .21534 .21527 .21530 .21533 9.33653 .33659 .33665 .33671 .21704 .21707 .21710 .21713 9.34012 .34018 .34024 .34030 .21884 .21887 .21890 .21893 9.34369 .34375 .34381 .34387 .32064 .22067 .33071 .33074 52 51 50 49 + 3' 13 14 15 9.32954 .32960 .32966 .32972 .21357 .21360 .21363 .31366 9.33317 .33323 .33329 .33335 .21536 .21539 .21542 .21545 9.33677 .33683 .33689 .33695 .21716 .21719 .21722 .21725 9.34036 .34042 .34048 .34054 .31896 .31899 .21902 .21905 9.34393 .34399 .34405 .34411 .33077 .33080 .33083 .22086 48 47 46 45 + 4' 17 18 19 9.32978 .32984 .32990 .32996 .21369 .21372 .21375 .21378 9.33341 .33347 .33353 .33359 .21548 .21551 .21554 .21557 9.33701 .33707 .33713 .33719 .21728 .21731 .21734 .21737 9.34060 .34066 .34072 .34078 .21908 .21911 .21914 .21917 9.34417 .34423 .34429 .34435 .22089 .22092 .22095 .32098 44 43 42 41 + 5' 21 22 23 9.33002 .33008 .33014 .33021 .31381 .31384 .31387 .31390 9.33365 .33371 .33377 .33383 .21560 .21563 .21566 .21569 9.33725 .33731 .33737 .33743 .31740 .31743 .21746 .21749 9.34084 .34090 .34096 .34102 .21920 .21933 .31926 .31929 9.34441 .34446 .34452 .34458 .22101 .22104 .22107 .22110 40 39 38 37 + 6' 25 26 27 9.33027 .33033 .33039 .33045 .21393 .21396 .21399 .21402 9.33389 .33395 .33401 .33407 .21572 .21575 .21578 .21581 9.33749 .33755 .33761 .33767 .21752 .21755 .21758 .21761 9.34108 .34114 .34120 .34126 .21932 .21935 .21938 .21941 9.34464 .34470 .34476 .34482 .22113 .22116 .22119 .22123 36 35 34 33 + r 29 30 31 9.33051 .33057 .33063 .33069 .21405 .21408 .31411 .31414 9.33413 .33419 .33425 .33431 9.33437 .33443 .33449 .33455 .21584 .21587 .21590 .21593 .21596 .21599 .21602 .21605 9.33773 .33779 .33785 .33791 .21764 .21767 .21770 .21773 9.34132 .34137 .34143 .34149 .21944 .21947 .21950 .21953 9.34488 .34494 .34500 .34506 .32125 .22128 .22131 .22134 32 31 30 29 + 8' 33 34 35 9.33075 .33081 .33087 .33093 .21417 .21430 .21423 .21426 9.33797 .33803 .33809 .33815 .21776 .21779 .21782 .21785 9.34155 .34161 .34167 .34173 .21956 .31959 .21962 .21965 9.34512 .34518 .34524 .34529 .22137 .22140 .22143 .22146 28 27 26 25 + ^ 37 38 39 ^ 9.33099 .33105 .33111 .33117 .21429 .21431 .21434 .21437 9.33461 .33467 .33473 .33479 .21608 .21611 .21614 .21617 9.33821 .33827 .33833 .33839 .21788 .21791 .21794 .21797 9.34179 .34185 .34191 .34197 .21968 .21971 .21974 .21977 9.34535 .34541 .34547 .34553 .22149 .22152 .32155 .22158 24 23 22 Ti + W 41 42 43 9.33123 .33129 .33135 .33142 .21440 .21443 .21446 .21449 9.33485 .33491 .33497 .33503 .21630 .21623 .21626 .21629 9.33845 .33851 .33857 .33863 .21800 .21803 .21806 .31809 9.34203 .34209 .34215 .34221 .31980 .31983 .21986 .21989 9.34559 .34565 .34571 .34577 .22161 .22164 .22167 .22170 20 19 18 17 + 11^ 45 46 47 9.33148 .33154 .33160 .33166 .21452 .21455 .31458 .31461 9.33509 .33515 .33521 .33527 .31633 .21635 .21638 .21641 9.33869 .33875 .33881 .33887 .21812 .21815 .21818 .21821 .21834 .31837 .31830 .31833 9.34227 .34233 .34239 .34245 .31993 .21995 .21998 .22001 9.34583 .34589 .34595 .34600 .33173 .22176 .22179 .22182 16 15 14 13 12 11 10 9 + 13' 49 50 51 9.33172 .33178 .33184 .33190 .21464 .21467 .21470 .21473 9.33533 .33539 .33545 .33551 .21644 .21647 .21650 .21653 9.33893 .33899 .33905 .33911 9.34251 .34256 .34262 .34268 .22004 .22007 .22010 .22013 9.34606 .34612 .34618 .34624 .22185 .22188 .22191 .23194 + 13' 53 54 55 9.33196 .33202 .33208 .33214 .21476 .21479 .21482 .21485 9.33557 .33563 .33569 .33575 .21656 .21659 .21662 .21665 9.33917 .33923 .33929 .33935 .21836 .21839 .21843 .21845 9.34274 .34280 .34286 .34292 .22016 .22019 .33032 .22035 9.34630 .34636 .34642 .34648 .22197 .22300 .22303 .22206 8 7 6 5 + 14' 57 58 59 9.33220 .33226 .33232 .33238 .21488 .21491 .31494 .31497 9.33581 .33587 .33593 .33599 .21668 .21671 .21674 .21677 9.33941 .33947 .33953 .33959 .21848 .21851 .31854 .21857 9.34298 .34304 34310 .34316 .22028 .32031 .22034 .22037 9.34654 .34660 .34666 .34671 .22309 .22313 .22315 .22318 4 3 2 "1 + 16' 9.33244 .31500 9.33605 .21680 9.33965 .21860 9.34322 .22040 9.34677 .23321 20^ igm 20Jil8m 20h 17m 20h 16m- 1 20h 15m 1 TABLE IV. [Page 89 Haversines. s 3h 45m 56° 15' 3h 46m 56° 30^ 3h 47m 56° 45' 3^ 4Sm 67° 0' 3h 49m 67° 15' s Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat .Hav. 1 2 3 9.34677 .34683 .34689 .34695 .22231 .22225 .22338 .32331 9.35031 .35037 .35043 .35049 .23403 .33406 .33409 .33413 9.35383 .35389 .35394 .35400 .22585 .23588 .33591 .33594 9.35733 .35738 .35744 .35750 .22768 .23771 .33774 .33777 9.36081 .36086 .36092 .36098 .33951 .33954 .33957 .22960 60 59 58 57 + 1' 5 6 7 9.34701 .34707 .34713 .34719 .23334 .33337 .33340 .33343 9.35054 .35060 .35066 .35072 .33415 .33418 .33431 .33434 .33437 .23430 .33433 .33437 9.35406 .35412 .35418 .35424 .33598 .33601 .33604 .33607 9.35756 .35762 .35767 .35773 .33780 .33783 .33786 .33789 9.36104 .30110 .36115 .36121 .22964 .22967 .33970 .32973 56 55 54 53 + 2' 9 10 11 9.34725 .34730 .34736 .34742 .22246 .33349 .33353 .33355 9.35078 .35084 .35090 .35096 9.35429 .35435 .35441 .35447 .33610 .22613 .22616 .22619 9.35779 .35785 .35791 .35797 .33792 .22795 .22799 .22803 9.36127 .36133 .36139 .36144 .33976 .33979 .33982 .33985 52 51 50 49 + 3' 13 14 15 9.34748 .34754 .34760 .34766 .33258 .23361 .33364 .22267 9.35101 .35107 .35113 .35119 .33440 .33443 .33446 .33449 9.35453 .35459 .35464 .35470 .23632 .22625 .22628 .22631 9.35802 .35808 .35814 .35820 .33805 .33808 .33811 .33814 9.36150 .36156 .36162 .36167 .22988 .22991 .23994 .22997 48 47 46 45 + 4' 17 18 19 9.34772 .34778 .34784 .34789 .33370 .33373 .33376 .23379 9.35125 .35131 .35137 .35143 .22452 .22455 .22458 .23461 9.35476 .35482 .35488 .35494 .22634 .22637 .33640 .22643 9.35826 .35831 .35837 .35843 .33817 .32820 .22823 .22836 9.36173 .36179 .36185 .36191 .23000 .23003 .33006 .23009 44 43 42 41 40 39 38 37 + 5' 21 22 23 9.34795 .34801 .34807 .34813 .33383 .33385 .32288 .22291 9.35148 .35154 .35160 .35166 .22464 .22467 .22470 .33473 9.35500 .35505 .35511 .35517 .22646 .22649 .22652 .22655 9.35849 .35855 .35860 .35866 .33829 .33832 .22835 .22838 9.36196 .36202 .36208 .36214 .23013 .33016 .33019 .23033 + 6' f7 9.34819 .34825 .34831 .34837 .23294 .22297 .23300 .33303 9.35172 .35178 .35184 .35189 .23476 .33479 .22483 .22485 9.35523 .35529 .35535 .35540 .22658 .22661 .23664 .23667 9.35872 .35878 .35884 .35889 .22841 .22844 .22847 .22850 9.36219 .36225 .36231 .36237 .23025 .23028 .23031 .23034 36 35 34 33 + r 29 SO 31 9.34843 .34848 .34854 .34860 .33306 .33309 .33313 .33315 9.35195 .35201 .35207 .35213 .22488 .22491 .23494 .33497 9.35546 .35552 .35558 .35564 .33671 .22674 .22677 .22680 9.35895 .35901 .35907 .35913 .22853 .22857 .22860 .22863 9.36243 .36248 .36254 .36260 .23037 .23040 .23043 .23046 32 31 30 29 + 8' 33 34 35 9.34866 .34872 .34878 .34884 .32318 .22321 .22334 .23337 9.35219 .35225 .35230 .35236 .33500 .23503 .33506 .33509 9.35570 .35575 .35581 .35587 .22683 .22686 .33689 .33693 9.35918 .35924 .35930 .35936 .22866 .23869 .33873 .33875 9.36266 .36271 .36277 .36283 .23049 .33053 .23055 .23058 28 27 26 25 24 23 22 21 + y 57 55 59 9.34890 .34896 .34901 .34907 .22330 .22333 .33336 .22340 9.35242 .35248 .35254 .35260 .33513 .33515 .33518 .22522 9.35593 .35599 .35604 .35610 .22695 .22698 .23701 .22704 9.35942 .35947 .35953 .35959 .22878 .22881 .23884 .22887 9.36289 .36294 .36300 .36306 .23061 .23065 .23068 .23071 + W 41 42 43 9.34913 .34919 .34925 .34931 .33343 .32346 .22349 .22353 9.35266 .35271 .35277 .35283 .22535 .22528 .22531 .22534 9.35616 .35622 .35628 .35634 .23707 .33710 .22713 .22716 9.35965 .35971 .35976 .35982 .23890 .33893 .33896 .33899 9.36312 .36318 .36323 .36329 .23074 .23077 .23080 .23083 20 19 18 17 + ir 45 46 47 9.34937 .34943 .34949 .34954 .22355 .22358 .23361 .22364 9.35289 .35295 .35301 .35307 .33537 .32540 .23543 .33546 9.35639 .35645 .35651 .35657 .22719 .22722 .22735 .33738 9.35988 .35994 .36000 .36005 .33903 .33905 .33908 .33913 9.36335 .36341 .36346 .36352 .23086 .23089 .23092 .33095 16 15 14 13 + ir 49 50 51 9.34960 .34966 .34972 .34978 .23367 .22370 .22373 .22376 9.35312 .35318 .35324 .35330 .33549 .33553 .33555 .22558 9.35663 .35669 .35674 .35680 .22731 .23735 .33738 .22741 9.36011 .36017 .36023 .36029 .23915 .22918 .22931 .33934 9.36358 .36364 .36369 .36375 .33098 .33101 .33104 .23107 12 11 10 9 + W 53 54 55 9.34984 .34990 .34996 .35002 .23379 .33383 .22385 .23388 9.35336 .35342 .35348 .35353 .22561 .23564 .33567 .33570 9.35686 .35692 .35698 .35703 .22744 .22747 .22750 .22753 9.36034 .36040 .36046 .36052 .23927 .22930 .22933 .23936 9.36381 .36387 .36392 .36398 .23110 .23114 .23117 .23120 S 7 6 5 + U' 57 58 59 9.35007 .35013 .35019 .35025 .23391 .32394 .22397 .23400 9.35359 .35365 .35371 .35377 .33573 .22576 .22579 .22582 9.35709 .35715 .35721 .35727 .23756 .33759 .33763 .33765 9.36058 .36063 .36069 .36075 .33939 .33943 .33945 .32948 9.36404 .36410 .36415 .36421 .23123 .23126 .23139 .23132 4 3 2 1 + 15' 9.35031 .22403 9.35383 .22585 9.35733 .22768 9.36081 .23951 9.36427 .23135 20h 14m 1 20^ ISm 1 20h 12m 1 20^ lim 1 20h iffm 1 Page 90] TABLP] IV. Haversixiea. s 3h 50m 57° SCK 3h 5im 57° 45' 3h 52m 58° 0' 3^ 53m 58° 15' 3^ 54^ 58° 30' s Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat Hav. i 'I S 9.36427 .36433 .36439 .36444 .23135 .23138 .23141 .23144 9.36772 .36777 .36783 .36789 .23319 .23322 .23325 .23329 9.37114 .37120 .37126 .37131 .23504 .23507 .23510 .23513 9.37455 .37461 .37467 .37472 .23689 .23692 .23695 .23699 9.37794 .37800 .37806 .37811 .23875 .23878 .23881 .23884 60 59 58 67 + 1' .5 1 9.36450 .36456 .36462 .36467 .23147 .23150 .23153 .23156 9.36794 .36800 .36806 .36812 .23332 .23335 .23338 .23341 9.37137 .37143 .37148 .37154 .23516 .23519 .23523 .23526 9.37478 .37484 .37489 .37495 .23702 .23705 .23708 .23711 9.37817 .37823 .37828 .37834 .23887 .23891 .23894 .23897 56 55 54 53 + r. 9 ' 10 " 11 9.36473 .36479 .36485 .36490 .23160 .23163 .23166 .23169 9.36817 .36823 .36829 .36834 .23344 .23347 .23350 .23353 9.37160 .37166 .37171 .37177 .23529 .23532 .23535 .23538 9.37501 .37506 .37512 .37518 .23714 .23717 .23720 .23723 9.37840 .37845 .37851 .37856 .23900 .23903 .23906 .23909 62 51 50 49 + 3^ 13 14 15 9.36496 .36502 .36508 .36513 .23172 .23175 .23178 .23181 9.36840 .36846 .36852 .36857 .23356 .23359 .23362 .23365 9.37183 .37188 .37194 .37200 .23541 .23544 .23547 .23550 9.37523 .37529 .37535 .37540 .23726 .23729 .23733 .23736 9.37862 .37868 .37873 .37879 .23912 .23915 .23918 .23922 48 47 46 45 44 43 42 41 + i' 17 18 19 9.36519 .36525 .36531 .36536 .23184 .23187 .23190 .23193 9.36863 .36869 .36875 .36880 .23368 .23372 .23375 .23378 9.37205 .37211 .37217 .37222 .23553 .23556 .23560 .23563 9.37546 .37552 .37557 .37563 .23739 .23742 .23745 .23748 9.37885 .37890 .37896 .37902 .23925 .23928 .23831 .23934 + 5' 21 22 23 9.36542 .36548 .36554 .36559 .23196 .23199 .23203 .23206 9.36886 .36892 .36897 .36903 .23381 .23384 .23387 .23390 9.37228 .37234 .37239 .37245 .23566 .23569 .23572 .23575 9.37569 .37574 .37580 .37585 .23751 .23754 .23757 .23760 9.37907 .37913 .37918 .37924 .23937 .23940 .23943 .23946 40 39 38 37 + 6^ 25 26 27 9.36565 .36571 .36577 .36582 .23209 .23212 .23215 .23218 9.36909 .36915 .36920 .36926 .23393 .23396 .23399 .23402 9.37251 .37257 .37262 .37268 .23578 .23581 .23584 .23587 9.37591 .37597 .37602 .37608 .23764 .23767 .23770 .23773 9.37930 .37935 .37941 .37947 .23950 .23953 .23956 .23959 36 35 34 S3 + r 29 30 31 9.36588 .36594 .36599 .36605 .23221 .23224 .23227 .23230 9.36932 .36937 .36943 .36949 .23405 .23409 .23412 .23415 9.37274 .37279 .37285 .37291 .23590 .23594 .23597 .23600 9.37614 .37619 .37625 .37631 .23776 .23779 .23782 .23785 9.37952 .37958 .37963 .37969 .23962 .23965 .23968 .23971 32 31 30 29 + 8' 33 34 35 9.36611 .36617 .36622 .36628 .23233 .23236 .23239 .23242 9.36955 .36960 .36966 .36972 .23418 .23421 .23424 .23427 9.37296 .37302 .37308 .37313 .23603 .23606 .23609 .23612 9.37636 .37642 .37648 .37653 .23788 .23791 .23795 .23798 9.37975 .37980 .37986 .37992 .23974 .23977 .23981 .23984 28 27 26 25 + 9' 37 38 39 9.36634 .36640 .36645 .36651 .23246 .23249 .23252 .23255 9.36977 .36983 .36989 .36995 .23430 .23433 .23436 .23439 9.37319 .37325 .37330 .37336 .23615 .23618 .23621 .23624 9.37659 .37665 .37670 .37676 .23801 .23804 .23807 .23810 9.37997 .38003 .38008 .38014 .23987 .23990 .23993 .23996 24 23 22 21 + 10' 41 42 43 9.36657 .36663 .36668 .36674 .23258 .23261 .23264 .23267 9.37000 .37006 .37012 .37017 .23442 .23445 .23449 .23452 9.37342 .37347 .37353 .37359 .23627 .23631 .23634 .23637 9.37682 .37687 .37693 .37699 .23813 .23816 .23819 .23822 9.38020 .38025 .38031 .38037 .23999 .24002 .24005 .24009 20 19 18 17 + ir 45 46 47 9.36680 .36686 .36691 .36697 .23270 .23273 .23276 .23279 9.37023 .37029 .37034 .37040 .23455 .23458 .23461 .23464 9.37364 .37370 .37376 .37382 .23640 .23643 .23646 .23649 9.37704 .37710 .37715 .37721 .23825 .23829 .23832 .23835 9.38042 .38048 .38053 .38059 .24012 .24015 .24018 .24021 16 15 14 13 + ir 49 50 51 9.36703 .36708 .36714 .36720 .23282 .23285 .23289 .23292 9.37046 .37052 .37057 .37063 .23467 .23470 .23473 .23476 9.37.387 .37393 .37399 .37404 .23652 .23655 .23658 .23661 9.37727 .37732 .37738 .37744 .23838 .23841 .23844 .23847 9.38065 .38070 .38076 .38081 .24024 .24027 .24030 .24033 12 11 10 9 4- 13' 53 54 55 9.36726 .36731 .36737 .36743 .23295 .23298 .23301 .23304 9.37069 .37074 .37080 .37086 .23479 .23482 .23486 .23489 9.37410 .37416 .37421 .37427 .23665 .23668 .23671 .23674 9.37749 .37755 .37761 .37766 .23850 .23853 .23856 .23860 9.38087 .38093 .38098 .38104 .24036 .24040 .24043 .24046 .24049 .24052 .24055 .24058 8 7 6 5 4 3 2 1 + 14' 57 58 59 9.36749 .36754 .36760 .36766 .23307 .23310 .23313 .23316 9.37091 .37097 .37103 .37109 .23492 .23495 .23498 .23501 9.37433 .37438 .37444 .37450 .23677 .23680 .23683 .23686 9.37772 .37778 .37783 .37789 .23863 .23866 .23869 .23872 9.38110 .38115 .38121 .38126 + IS' 9.36772 .23319 9.37114 .23504 9.37455 .23689 9.37794 .23875 9.38132 .24061 fOApm 20hSm 20^ 7m, 20^ fim 20h5m TABLE IV. [Page 91 Havereinea. s 5ft 55m 68° 45' 3^ 56"* 59° 0' Sh 57m 59° 15' Sh 58m 59° ZQ' | 3h 59m 59° 45' s Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Ilav. Log. Hav. Nat. Hav. 1 2 S 9.38132 .38138 .38143 .38149 .34061 .24064 .24068 .24071 9.38468 .38473 .38479 .38485 .34348 .34351 .34354 .34357 9.38802 .38807 .38813 .38819 .34435 .24438 .24443 .34445 9.39134 .39140 .39145 .39151 .34633 .34636 .34639 .34633 9.39465 .39470 .39476 .39481 .348U .34814 .34818 .34831 60 59 58 57 + r 5 6 7 9.38154 .38160 .38166 .38171 .24074 .34077 .24080 .24083 9.38490 .38496 .38501 .38507 .24261 .34264 .34267 .34370 9.38824 .38830 .38835 .38841 .34448 .34451 .34454 .34457 9.39156 .39162 .39167 .39173 .34636 .34639 .34843 .34645 9.39487 .39492 .39498 .39503 .34834 .34837 .34830 .34833 56 55 54 53 + V 9 10 11 9.38177 .38182 .38188 .38194 .24086 .24089 .34092 .24096 9.38512 .38518 .38524 .38529 .24273 .24376 .34379 .34383 9.38846 .38852 .38857 .38863 .34460 .34463 .34467 .34470 9.39178 .39184 .39189 .39195 .34648 .34651 .34654 .34658 9.39509 .39514 .39520 .39525 .34836 .34840 .34843 .34846 52 51 50 49 48 47 46 45 + 3' 13 14 15 9.38199 .38205 .38210 .38216 .34099 .34102 .34105 .34108 9.38535 .38540 .38546 .38551 .24386 .34389 .34393 .34395 9.38868 .38874 .38880 .38885 .34473 .34476 .24479 .24482 9.39201 .39206 .39212 .39217 .34661 .34664 .34667 .34670 9.39531 .39536 .39542 .39547 .34849 .34853 .34855 .34858 + 4' 17 18 19 9.38222 .38227 .38233 .38239 .34111 .34114 .24117 .24130 9.38557 .38563 .38568 .38574 .34398 .34301 .34304 .34307 9.38891 .38896 .38902 .38907 .24485 .24488 .34492 .34495 9.39223 .39228 .39234 .39239 .34673 .34676 .34680 .34683 9.39553 .39558 .39564 .39569 .34863 .34865 .34868 .34871 44 43 42 41 + 6' 21 22 23 9.38244 .38250 .38255 .38261 .34134 .24137 .34130 .34133 9.38579 .38585 .38590 .38596 .34310 .34314 .34317 .34330 9.38913 .38918 .38924 .38929 .34498 .34501 .34504 .34507 9.39245 .39250 .39256 .39261 .34686 .34689 .34693 .34695 9.39575 .39580 .39586 .39591 .34874 .34877 .34880 .34884 40 39 38 37 + 6' 25 26 27 9.38267 .38272 .38278 .38283 .34136 .34139 .34143 .34145 9.38602 .38607 .38613 .38618 .34333 .34336 .34339 .34333 9.38935 .38941 .38946 .38952 .34510 .34514 .34517 .34530 9.39267 .39272 .39278 .39283 .34698 .34701 .34705 .34708 9.39597 .39602 .39608 .39613 .34887 .34890 .34893 .34896 36 35 34 33 ^9 30 31 9.38289 .38295 .38300 .38306 .34148 .34153 .34155 .34158 9.38624 .38629 .38635 .38641 .34335 .34339 .34343 .34345 9.38957 .38963 .38968 .38974 .34533 .34536 .34539 .34533 9.39289 .39294 .39300 .39305 .34711 .34714 .34717 .24730 9.39619 .39624 .39630 .39635 .34899 .34903 .34906 .34909 32 31 SO 29 28 27 26 25 + 8' 33 34 35 9.38311 .38317 .38322 .38328 .34161 .34164 .24167 .24170 9.38646 .38652 .38657 .38663 .24348 .24351 .34354 .34357 9.38979 .38985 .38990 .38996 .34535 .34539 .34543 .34545 9.39311 .39316 .39322 .39327 .34733 .34737 .34730 .34733 9.39641 .39646 .39652 .39657 .34913 .34915 .34918 .34931 + 9^ 37 38 39 9.38334 .38339 .38345 .38350 .24173 .24176 .24180 .24183 9.38668 .38674 .38680 .38685 .34360 .34364 .34367 .34370 9.39002 .39007 .39013 .39018 .34548 .34551 .34554 .34557 9.39333 .39338 .39344 .39349 .34736 .34739 .34743 .34745 9.396G3 .39668 .39674 .39679 .34934 .34938 .34931 .34934 24 23 22 21 + 10' 41 42 43 9.38356 .38362 .38367 .38373 .34186 .24189 .24193 .34195 9.38691 .38696 .38702 .38707 .34373 .34376 .34379 .34383 9.39024 .39029 .39035 .39040 .34560 .34564 .34567 .34570 9.39355 .39360 .39366 .39371 .34749 .34753 .34755 .34758 9.39685 .39690 .39695 .39701 .34937 .34940 .34943 .34946 .34950 .34953 .34956 .34959 20 19 18 17 16 15 14 13 + 11' 45 46 47 9.38378 .38384 .38390 .38395 .34198 .34301 .34304 .34308 9.38713 .38719 .38724 .38730 .34385 .34388 .34393 .34395 9.39046 .39051 .39057 .39062 .34573 .34576 .34579 .34583 9.39377 .39382 .39388 .39393 .34761 .34764 .34767 .34770 9.39706 .39712 .39717 .39723 + 12' 49 50 51 9.38401 .38406 .38412 .38418 .34211 .24214 .34217 .34330 9.38735 .38741 .38746 .38752 .34398 .34401 .34404 .34407 9.39068 .39073 .39079 .39085 .34586 .34589 .34593 .34595 9.39399 .39404 .39410 .39415 .34774 .34777 .34780 .34783 9.39728 .39734 .39739 .39745 .34963 .34965 .34969 .34973 12 11 10 9 + 13^ 53 54 55 9.38423 .38429 .38434 .38440 .34333 .34336 .34339 .34333 9.38757 .38763 .38769 .38774 .34410 .34413 .34417 .34430 9.39090 .39096 .39101 .39107 .24598 .24601 .34604 .34607 9.39421 .39426 .39432 .39437 .34786 .34789 .34793 .34796 9.39750 .39756 .39761 .39767 .34975 .34978 .34981 .34984 8 7 6 5 + W 57 58 59 9.38445 .38451 .38457 .38462 .34336 .34339 .34343 .34245 9.38780 .38785 .38791 .38796 9.38802' .34433 .34436 .34439 .34433 .34435 9.39112 .39118 .39123 .39129 .34611 .34614 .34617 .34630 9.39443 .39448 .39454 .39459 9.39465 .34799 .34803 .34805 .34808 9.39772 .39778 .39783 .39789 .34987 .34991 .34994 .24997 4 3 2 1 + 15' 9.38468 .34348 9.39134 .34623 .34811 9.39794 .35000 20^4^ 20hsm fOA^m 20h J»n 20f^0'^ Page 92] TABLE IV. Haversines. s 4h om 60° 0' 4h m 60° 15' 4h 2m 60° 30' 4h 3m 60° 45' 4h 4-^ 61° 0' s Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log.Hav. Nat. Hav. Log. Hav. Nat. Hav. 1 2 S 9.3979^ .39799 .39805 .39810 .25000 .25003 .25006 .25009 9.40121 .40127 .40132 .40138 .25189 .25192 .25195 .25199 9.40447 .40453 .40458 .40463 .25379 .25382 .25385 .25388 9.40771 .40777 .40782 .40787 .25569 .25572 .25575 .25578 9.41094 .41099 .41105 .41110 .25760 .25763 .25766 .25769 60 59 58 57 + r 5 6 7 9.39816 .39821 .39827 .39832 .25013 .25016 .25019 .25022 9.40143 .40149 .40154 .40159 .25202 .25205 .25208 .25211 9.40469 .40474 .40480 .40485 .25391 .25395 .25398 .25401 9.40793 .40798 .40804 .40809 .25582 .25585 .25588 .25591 9.41115 .41121 .41126 .41131 .25772 .25775 .25779 .25782 56 55 54 53 + 3' 9 10 11 9.39838 .39843 .39849 .39854 .25025 .25028 .25032 .25035 9.40165 .40170 .40176 .40181 .25214 .25218 .25221 .25224 9.40490 .40496 .40501 .40507 .25404 .25407 .25410 .25414 9.40814 .40820 .40825 .40831 .25594 .25597 .25601 .25604 9.41137 .41142 .41147 .41153 .25785 .25788 .25791 .25795 52 51 50 49 + 3^ IS 14 15 9.39860 .39865 .39871 .39876 .25038 .25041 .25044 .25047 9.40187 .40192 .40198 .40203 .25227 .25230 .25233 .25237 9.40512 .40518 .40523 .40528 .25417 .25420 .25423 .25426 9.40836 .40841 .40847 .40852 .25607 .25610 .25613 .25617 9.41158 .41163 .41169 .41174 .25798 .25801 .25804 .25807 48 47 46 45 + 4' 17 18 19 9.39881 .39887 .39892 .39898 .25050 .25054 .25057 .25060 9.40208 .40214 .40219 .40225 .25240 .25243 .25246 .25249 9.40534 .40539 .40545 .40550 .25429 .25433 .25436 .25439 9.40858 .40863 .40868 .40874 .25620 .25623 .25626 .25629 9.41180 .41185 .41190 .41196 .25810 .25814 .25817 .25820 44 43 42 41 + 5' 21 22 23 9.39903 .39909 .39914 .39920 .25063 .25066 .25069 .25072 9.40230 .40236 .40241 .40246 .25252 .25255 .25259 .25262 9.40555 .40561 .40566 .40572 .25442 .25445 .25448 .25452 9.40879 .40884 .40890 .40895 .25632 .25636 .25639 .25642 9.41201 .41206 .41212 .41217 .25823 .25826 .25830 .25833 40 39 38 37 36 35 34 33 + 6^ 25 26 27 9.39925 .39931 .39936 .39942 .25076 .25079 .25082 .25085 9.40252 .40257 .40263 .40268 .25265 .25268 .25271 .25274 9.40577 .40582 .40588 .40593 .25455 .25458 .25461 .25464 9.40900 .40906 .40911 40917 .25645 .25648 .25651 .25655 9.41222 .41228 .41233 .41238 .25836 .25839 .25842 .25845 + r 29 30 31 9.39947 .39952 .39958 .39963 .25088 .25091 .25095 .25098 9.40274 .40279 .40284 .40290 .25278 .25281 .25284 .25287 9.40599 .40604 .40609 .40615 .25467 .25471 .25474 .25477 9.40922 .40927 .40933 .40938 .25658 .25661 .25664 .25667 9.41244 .41249 .41254 .41260 .25849 .25852 .25855 .25858 32 '31 30 29 28 27 26 25 24 23 22 21 + S' 33 34 35 9.39969 .39974 .39980 .39985 .25101 .25104 .25107 .25110 9.40295 .40301 .40306 .40312 .25290 .25293 .25297 .25300 9.40620 .40626 .40631 .40636 .25480 .25483 .25487 .25490 9.40943 .40949 .40954 .40960 .25671 .25674 .25677 .25680 9.41265 .41270 .41276 .41281 .25861 .25865 .25868 .25871 + 9' 37 38 39 9.39991 .39996 .40002 .40007 .25113 .25117 .25120 .25123 9.40317 .40322 .40328 .40333 .25303 .25306 .25309 .25312 9.40642 .40647 .40653 .40658 .25493 .25496 .25499 .25502 9.40965 .40970 .40976 .40981 .25683 .25686 .25690 .25693 9.41287 .41292 .41297 .41303 .25874 .25877 .25880 .25884 + W 41 42 43 9.40012 .40018 .40023 .40029 .25126 .25129 .25132 .25136 9.40339 .40344 .40350 .40355 .25316 .25319 .25322 .25325 9.40663 .40669 .40674 .40680 .25506 .25509 .25512 .25515 9.40986 .40992 .40997 .41003 .25696 .25699 .25702 .25705 9.41308 .41313 .41319 .41324 .25887 .25890 .25893 .25896 20 19 18 17 + 11' 45 46 47 9.40034 .40040 .40045 .40051 .25139 .25142 .25145 .25148 9.40360 .40366 .40371 .40377 .25328 .25331 .25335 .25338 9.40685 .40690 .40696 .40701 .25518 .25521 .25525 .25528 9.41008 .41013 .41019 .41024 .25709 .25712 .25715 .25718 9.41329 .41335 .41340 .41345 .25900 .25903 .25906 .25909 16 15 14 13 + n' 49 50 51 9.40056 .40062 .40067 .40072 .25151 .25154 .25158 .25161 9.40382 .40388 .40393 .40398 .25341 .25344 .25347 .25350 9.40707 .40712 .40717 .40723 .25531 .25534 .25537 .25540 9.41029 .41035 .41040 .41046 .25721 .25724 .25728 .25731 9.41351 .41356 .41361 .41367 .25912 .25915 .25919 .25922 12 11 10 9 + 13^ 53 54 55 9.40078 .40083 .40089 .40094 .25164 .25167 .25170 .25173 9.40404 .40409 .40415 .40420 .25354 .25357 .25360 .25363 9.40728 .40734 .40739 .40744 .25544 .25547 .25550 .25553 9.41051 .41056 .41062 .41067 .25734 .25737 .25740 .25744 9.41372 .41377 .41383 .41388 .25925 .25928 .25931 .25935 8 7 6 5 + W 57 58 59 9.40100 .40105 .40111 .40116 .25177 .25180 .25183 .25186 9.40425 .40431 .40436 .40442 .25366 .25369 .25372 .25376 9.40750 .40755 .40761 .40766 .25556 .25559 .25563 .25566 9.41072 .41078 .41083 .41088 .25747 .25750 .25753 .25756 9.41393 .41399 .41404 .41409 .25938 .25941 .25944 .25947 4 3 2 1 + W 9.40121 .25189 9.40447 .25379 9.40771 .25569 9.41094 .25760 9.41415 .25951 19h 59m 19^ 58m 19h S7m 19k 56m 19^ 55m TABLE IV. [Page 93 Haversineg. s 4ft 5m 61° 15' 1 4ft 6"» 61° 3^ 1 4h 7m 61° 45' 4h 8^ 63° 0' 4f>' 9m 63° 15' | 3 Log. Ilav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. 1 2 3 9.41415 .41420 .41425 .41431 .25951 .25954 .25957 .25960 9.41734 .41739 .41745 .41750 .26142 .26145 .26148 .26152 9.42052 .42057 .42062 .42068 .26334 .36337 .26340 .26344 9.42368 .42373 .42378 .42384 .26526 .26530 .26533 .26536 9.42682 .42688 .42693 .42698 .26719 .26722 .26726 .36739 60 59 58 57 56 ' 55 54 53 + r 5 6 7 9.41436 .41441 .41447 .41452 .25963 .25966 .25970 .25973 9.41755 .41761 .41766 .41771 .26155 .26158 .26161 .26164 9.42073 .42078 .42083 .42089 .26347 .26350 .26353 .26356 9.42389 .42394 .42399 .42405 .26539 .26543 .26546 .26549 9.42703 .42709 .42714 .42719 .36732 .26735 .26739 .26742 + 2^ 9 10 11 9.41457 .41463 .41468 .41473 .25976 .25979 .25982 .25986 9.41776 .41782 .41787 .41792 .26168 .26171 .26174 .26177 9.42094 .42099 .42105 .42110 .26360 .26363 .26366 .26369 9.42410 .42415 .42420 .42426 .36552 .26555 .26559 .26562 9.42724 .42730 .42735 .42740 .26745 .26748 .26751 .26755 52 51 50 49 + 3' 13 14 15 9.41479 .41484 .41489 .41495 .25989 .25992 .25995 .25998 9.41798 .41803 .41808 .41814 .26180 .26184 .26187 .26190 9.42115 .42120 .42126 .42131 .26372 .26376 ' .26379 .26382 9.42431 .42436 .42441 .42447 .26565 ,26568 .26571 .26575 9.42745 .42750 .42756 .42761 .36758 .36761 .36764 .26768 48 47 46 45 + 4' 17 18 19 9.41500 .41505 .41511 .41516 .26002 .26005 .26008 .26011 9.41819 .41824 .41829 .41835 .26193 .26196 .26300 .26203 9.42136 .42141 .42147 .42152 .26385 .26389 .26393 .36395 9.42452 .42457 .42462 .42468 .26578 .26581 .26584 .26587 9.42766 .42771 .42777 .42782 .26771 .26774 .26777 .26780 44 4-3 42 41 + 5' 21 22 23 9.41521 .41527 .41532 .41537 .26014 .26017 .26021 .26024 9.41840 .41845 .41851 .41856 .26206 .26209 .26212 .26216 9.42157 .42163 .42168 .42173 .26398 .26402 .26405 .26408 9.42473 .42478 .42483 .42489 .36591 .36594 .36597 .26600 9.42787 .42792 .42797 .42803 .26784 .26787 .26790 .26793 40 39 38 37 + 6' 25 26 27 9.41543 .41548 .41553 .41559 .26027 .26030 .26033 .26037 9.41861 .41867 .41872 .41877 .26219 .26222 .26225 .26228 9.42178 .42184 .42189 .42194 .26411 .26414 .26417 .26421 9.42494 .42499 .42504 .42510 .26604 .26607 .26610 .26613 9.42808 .42813 .42818 .42824 .26797 .26800 .26803 .26806 36 35 34 33 29 SO 31 9.41564 .41569 .41575 .41580 .26040 .26043 .26046 .26049 9.41882 .41888 .41893 .41898 .26232 .26235 .26238 .26241 9.42199 .42205 .42210 .42215 .26434 .36437 .36430 .26433 9.42515 .42520 .42525 .42531 .26616 .26620 .26623 .26626 9.42829 .42834 .42839 .42844 .26809 .26813 .26816 .26819 32 31 SO 29 + 8' 33 34 35 9.41585 .41590 .41596 .41601 .26053 .26056 .26059 .26062 9.41904 .41909 .41914 .41920 .26244 .26248 .26251 .26254 9.42221 .42226 .42231 .42236 .26437 .26440 .26443 .26446 9.42536 .42541 .42546 .42552 .26629 .26632 .26636 .26639 9.42850 .42855 .42860 .42865 .26823 .26836 .26839 .36832 28 27 26 25 + 9^ 37 38 39 9.41606 .41612 .41617 .41622 .26065 .26069 .26072 .26075 9.41925 .41930 .41935 .41941 .26257 .26260 .26264 .26267 9.42242 .42247 .42252 .42257 .36449 26453 .26456 .26459 9.42557 .42562 .42567 .42573 .26643 .36645 .36649 .26652 9.42870 .42876 .42881 .42886 .26835 .26838 .26842 .36845 24 23 22 21 + 10' 41 42 43 9.41628 .41633 41638 .41644 .26078 .26081 .26085 .26088 9.41946 .41951 .41957 .41962 .26270 .26273 .26276 .26280 9.42263 .42268 .42273 .42278 .26462 .26465 .26469 .26472 9.42578 .42583 .42588 .42593 .26655 .26658 .26661 .26665 9.42891 .42897 .42902 .42907 .36848 .36851 .36855 .36858 20 19 18 17 + 11' 45 46 47 9.41649 .41654 .41660 .41665 .26091 .26094 .26097 .26101 9.41967 .41972 .41978 .41983 .26283 .26286 .26289 .26292 9.42284 .42289 .42294 .42300 .26475 .26478 .26481 .26485 9.42599 .42604 .42609 .42614 .26668 .26671 .26674 .26677 9.42912 .42917 .42923 .42928 .26861 .26864 .26867 .26871 16 15 14 13 + 12' 49 50 51 9.41670 .41676 .41681 .41686 .26104 .26107 .26110 .26113 9.41988 .41994 .41999 .42004 .26296 .26299 .26303 .26305 9.42305 .42310 .42315 .42321 .26488 .26491 .26494 .26498 9.42620 .42625 .42630 .42635 .26681 .26684 .26687 .26690 9.42933 .42938 .42943 .42949 .26874 .26877 .26880 .26883 12 11 10 9 8 7 6 5 + 13' 53 54 55 9.41692 .41697 .41702 .41707 .26117 .26120 .26123 .26126 9.42009 .42015 .42020 .42025 .26308 .26312 .26315 .26318 9.42326 .42331 .42336 .42342 .26501 .26504 .26507 .26510 9.42641 .42646 .42651 .42656 .26694 .26697 .26700 .26703 9.42954 .42959 .42964 .42969 .26887 .26890 .26893 .36896 + 14' 57 58 59 9.41713 .41718 .41723 .41729 .26129 .26132 .26136 .26139 9.42031 .42036 .42041 .42046 .26321 .26324 .26328 .26331 9.42347 .42352 .42357 .42363 .26514 .26517 .26520 .26523 9.42662 .42667 .42672 .42677 .26706 .26710 .36713 .26716 9.42975 .42980 .42985 .42990 .36900 .36903 .26906 .26909 4 3 2 1 + 15' 9.41734 .26142 9.42052 .26334 9.42368 .26526 9.42682 .26719 9.42996 .26913 19h 54^ 19^ 5Sm 19^ 52'm 19h 5im 19^50^ Page 94] TABLE IV. Haversines. s 4ft lOm 63° 30' 4h nm 62° 45' 4h 12'"> 63° 0' 4^ ISm 63° 15' 4h 14m 63° 3r a Log. Hav. Nat. Hav. Log. nav. Nat. Hav. Log. Hav Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. 1 2 3 9.42996 .43001 .43006 .43011 .26913 .26916 .26919 .26922 9.43307 .43312 .43317 .43323 .27106 .27110 .27113 .27116 9.43617 .43622 .43627 .43632 .27300 .27304 .27307 .37310 9.43926 .43931 .43936 .43941 .27495 .27498 .27502 .27505 9.44232 .44238 .44243 .44248 .37690 .27693 .27697 .27700 60 59 58 57 56 55 54 53 + r 5 6 7 9.43016 .43022 .43027 .43032 .26925 .26929 .26932 .26935 9.43328 .43333 .43338 .43343 .27119 .27122 .27126 .27129 9.43638 .43643 .43648 .43653 .37313 .27317 .27320 .37333 9.43946 .43951 .43956 .43961 .27508 .27511 .27515 .27518 9.44253 .44258 .44263 .44268 .27703 .27706 .27710 .37713 + 3' 9 10 11 9.43037 .43042 .43048 .43053 .26938 .26942 .26945 .26948 9.43348 .43354 .43359 .43364 .27132 .27135 .27139 .27142 9.43658 .43663 .43669 .43674 .37336 .27330 .27333 .27336 9.43967 .43972 .43977 .43982 .27521 .27524 .27528 .27531 9.44273 .44278 .44283 .44289 .37716 .37719 .37733 .37736 52 51 50 49 + 3^ IS 14 15 9.43058 .43063 .43068 .43074 .26951 .26955 .26958 .26961 9.43369 .43374 .43380 .43385 .27145 .27148 .27152 .27155 9.43679 .43684 .43689 .43694 .27339 .27343 .27346 .27349 9.43987 .43992 .43997 .44002 .27534 .27537 .27541 .27544 9.44294 .44299 .44304 .44309 .37739 .27733 .27736 .27739 48 47 46 45 + *' 17 18 19 9.43079 .43084 .43089 .43094 .26964 .26967 .26971 .26974 9.43390 .43395 .43400 .43405 .27158 .27161 .27165 .27168 9.43699 .43705 .43710 .43715 .27352 .27356 .27359 .27362 9.44008 .44013 .44018 .44023 .37547 .37550 .37554 .37557 9.44314 .44319 .44324 .44329 .27742 .27745 .37749 .37753 44 43 42 41 + 5' 21 22 23 9.43100 .43105 .43110 .43115 .26977 .26980 .26984 .26987 9.43411 .43416 .43421 .43426 .37171 .37174 .37177 .27181 9.43720 .43725 .43730 .43735 .27365 .27369 .27372 .27375 9.44028 .44033 .44038 .44043 .37560 .37563 .37567 .37570 9.44334 .44340 .44345 .44350 .27755 .37758 .37763 .27765 40 39 38 37 + 6' 25 26 27 9.43120 .43126 .43131 .43136 .26990 .26993 .26996 .27000 9.43431 .43436 .43442 .43447 .37184 .37187 .37190 .27194 9.43741 .43746 .43751 .43756 .27378 .27383 .37385 .37388 9.44048 .44054 .44059 .44064 .37573 .37576 .37580 .27583 9.44355 .44360 .44365 .44370 .27768 .27772 .27775 .27778 36 35 34 33 + r 29 30 31 9.43141 .43146 .43151 43157 .27003 .27006 .37009 .27013 9.43452 .43457 .43462 .43467 .27197 .37300 .37303 .37307 9.43761 .43766 .43771 .43777 .37391 .37394 .37398 .37401 9.44069 .44074 .44079 .44084 .37586 .37589 .37593 .37596 9.44375 .44380 .44385 .44390 .37781 .37785 .37788 .27791 32 31 SO 29 + 8' 33 34 35 9.43162 .43167 .43172 .43177 .27016 .27019 .27022 .27025 9.43473 .43478 .43483 .43488 .37210 .37313 .37316 .27330 9.43782 .43787 .43792 .43797 .27404 .27407 .27411 .27414 9.44089 .44095 .44100 .44105 .37599 .37603 .37606 .27609 9.44396 .44401 .44406 .44411 .37794 .37798 .27801 .37804 28 27 26 25 + 9^ 37 38 39 9.43183 .43188 .43193 .43198 .37029 .27032 .27035 .27038 9.43493 .43498 .43504 .43509 .27223 .27228 .27229 .37233 9.43802 .43807 .43813 .43818 .27417 .27420 .27424 .27437 9.44110 .44115 .44120 .44125 .37612 .27615 .27619 .27623 9.44416 .44421 .44426 .44431 .37807 .37811 .37814 .37817 24 23 22 21 + W 41 42 43 9.43203 .43209 .43214 .43219 .27043 .27045 .27048 .27051 9.43514 .43519 .43524 .43529 .27236 .27239 .27242 .27245 9.43823 .43828 .43833 .43838 .37430 .37433 .37437 .37440 9.44130 .44135 .44141 .44146 .37625 .27638 .37633 .37635 9.44436 .44441 .44446 .44452 .37830 .37834 .27827 .37830 20 19 18 17 + 11' 45 46 47 9.43224 .43229 .43234 .43240 .27055 .37058 .37061 .37064 9.43535 .43540 .43545 .43550 .27249 .27353 .37355 .27258 9.43843 .43849 ,43854 .43859 .37443 .37446 .37450 .37453 9.44151 .44156 .44161 .44166 .37638 .37641 .37645 .37648 9.44457 .44462 .44467 .44472 .37833 .27837 .37840 .37843 16 15 14 13 + n' 49 50 51 9.43245 .43250 .43255 .43260 .37068 .37071 .37074 .37077 9.43555 .43560 .43565 .43571 .27262 .37265 .27268 .27371 9.43864 .43869 .43874 .43879 .37456 .37459 .37463 .37466 9.44171 44176 .44181 .44187 .37651 .37654 .37658 .37661 9.44477 .44482 .44487 .44492 .37846 .37850 .37853 .27856 12 11 10 9 + 13^ 53 54 55 9.43266 .43271 .43276 .43281 .27080 .27084 .27087 .27090 9.43576 .43581 .43586 .43591 .27275 .27278 .27281 .27284 9.43884 .43890 .43895 .43900 .37469 .37473 .37476 .37479 9.44192 .44197 .44202 .44207 .37664 .37667 .37671 .37674 9.44497 .44502 .44507 .44513 .27859 .27863 .27866 .27869 8 7 6 5 4 3 2 1 57 58 59 9.43286 .43291 .43297 .43302 .27093 .27097 .27100 .27103 9.43596 .43602 .43607 .43612 .27288 .27291 .27294 .27297 9.43905 .43910 .43915 .43920 .37483 .37485 .37489 .37493 9.44212 .44217 .44222 .44227 .37677 .37680 .37684 .27687 9.44518 .44523 .44528 .44533 .27873 .27876 .27879 .27882 + 15^ 9.43307 c27106 9.43617 .27300 9.43926 .37495 9.44232 .27690 9.44538 .27886 19^ 49m Wft 4Sm 19h 47m 19^ 46/3 19fi 45m TABLE IV. [Page 95 Haversinea. s 4hl5m%3°i5' 1 4h lem 64° 0' 4h 17m 64° IS'' jfh 18m 64° 30' 4h 19m 64° 45' 3 Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. llav. Log. Hav. Nat. Hav. 1 2 3 9.44538 .44543 .44548 .44553 .37886 .37889 .37893 .37895 9.44842 .44847 .44852 .44857 9.44862 .44867 .44872 .44877 .38081 .38085 .38088 .38091 9.45144 .45149 .45155 .45160 .28278 .28381 .28284 .28288 9.45446 .45451 .45456 .45461 .38474 .38478 .38481 .38484 9.45745 .45750 .45755 .45760 .38673 .38675 .38678 .28681 60 59 58 57 56 55 54 53 + r 5 6 7 9.44558 .44563 .44568 .44573 .37899 .37903 .37905 .37908 .38095 .38098 .38101 .38104 9.45165 .45170 .45175 .45180 .28391 .28294 .28297 .28301 9.45460 .45471 ■ .45476 .45481 .38488 .28491 .28494 .28497 9.45765 .45770 .45775 .45780 .28685 .28688 .28691 .28695 + 2' 9 10 11 9.44579 .44584 .44589 .44594 .37913 .37915 .37918 .37931 9.44882 .44887 .44892 .44898 .38108 .38111 .38114 .38117 9.45185 .45190 ■ .45195 .45200 .28304 .38307 .38310 .38314 9.45486 .45491 .45496 .45501 .28501 .38504 .38507 .38511 9.45785 .45790 .45795 .45800 .28698 .28701 .28704 .38708 52 51 50 49 + 3' IS 14 15 9.44599 .44604 .44609 .44614 .37935 .37938 .37931 .37935 9.44903 .44908 .44913 .44918 .38131 .38134 .38137 .38130 9.45205 .45210 .45215 .45220 .38317 .38330 .38334 .38337 9.45506 .45511 .45516 .45521 .28514 .28517 .28530 .28534 9.45805 .45810 .45815 .45820 .28711 .28714 .38718 .38731 48 47 46 45 44 43 42 41 + 4^ 17 18 19 9.44619 .44624 .44629 .44634 .37938 .37941 .37944 .37948 9.44923 .44928 .44933 .44938 .38134 .38137 .38140 .38144 9.45225 .45230 .45235 .45240 .38330 .38333 .28337 .28340 9.45526 .45531 .45536 .45541 .38537 .38530 .28534 .28537 9.45825 .45830 .45835 .45840 .38734 .38737 .28731 .38734 + 5' 21 22 23 9.44639 .44645 .44650 .44655 .37951 .37954 .37957 .37961 9.44943 .44948 .44953 .44958 .38147 .38150 .38153 .38157 9.45245 .45250 .45255 .45260 .38343 .38347 .38350 .38353 9.45546 .45551 .45556 .45561 .38540 .38543 .38547 .28550 9.45845 .45850 .45855 .45860 .28737 .38741 .38744 .38747 40 39 38 37 + 6' 25 26 27 9.44660 .44665 .44670 .44675 .37964 .37967 .37970 .37974 9.44963 .44968 .44973 .44978 .38160 .38163 .38166 .38170 9.45265 .45270 .45275 .45280 .38356 .38360 .38363 .28366 9.45566 .45571 .45576 .45581 .28553 .28557 .28560 .28563 9.45865 .45870 .45875 .45879 .38751 .38754 .38757 .28760 36 35 34 33 + r 29 30 31 9.44680 .44685 .44690 .44695 .37977 .37980 .37983 .37987 9.44983 .44988 .44993 .44998 .38173 .38176 .38180 .38183 9.45285 .45290 .45295 .45300 .28369 .28373 .38376 .38379 9.45586 .45591 .45596 .45601 .28566 .28570 .28573 .28576 9.45884 .45889 .45894 .45899 .28764 .28767 .28770 .28774 32 31 30 29 28 27 26 25 + S' 33 34 35 9.44700 .44705 .44710 .44715 .37990 .37993 .37997 .38000 9.45003 .45009 .45014 .45019 .38186 .38189 .38193 .38196 9.45305 .45310 .45315 .45320 .38383 .38386 .38389 .38392 9.45006 .45610 .45615 .45620 .28580 .28583 .28586 .28589 9.45904 .45909 .45914 .45919 .28777 .28780 .28783 .28787 37 38 39 9.44721 .44726 .44731 .44736 .38003 .38006 .38010 .38013 9.45024 .45029 .45034 .45039 .38199 .38303 .38306 .38309 9.45325 .45330 .45335 .45340 .38396 .38399 .28403 .28406 9.45625 .45630 .45635 .45640 .28593 .28596 .28599 .38603 9.45924 .45929 .45934 .45939 .28790 .28793 .28797 .28800 .38803 .38807 .38810 .38813 24 23 22 21 20 19 18 17 + W 41 42 43 9.44741 .44746 .44751 .44756 .38016 .38019 .38033 .38036 9.45044 .45049 .45054 .45059 .38313 .38316 .38319 .38333 9.45345 .45350 .45355 .45360 .38409 .28413 .28415 .28419 9.45645 .45650 .45655 .45660 .28606 .28609 .28612 .28616 9.45944 .45949 .45954 .45959 + ir 45 46 47 9.44761 .44766 .44771 .44776 .38039 .38033 .38036 .38039 9.45064 .45069 .45074 .45079 .38335 .38339 .38333 .38335 9.45365 .45370 .45375 .45380 .38433 .38435 .38439 .38433 9.45665 .45670 .45675 .45680 .38619 .28622 .28636 .38639 9.45964 .45969 .45974 .45979 .38816 .38830 .28823 .28836 16 15 14 13 + 13^ 49 50 51 9.44781 .44786 .44791 .44796 .38043 .38046 .38049 .38053 9.45084 .45089 .45094 .45099 .38338 .38343 .28345 .38348 9.45385 .45390 .45395 .45400 .38435 .38438 .38443 .38445 9.45685 .45690 .45695 .45700 .38633 .28635 .28639 .28643 9.45984 .45989 .45994 .45999 .38830 .38833 .38836 .28839 12 11 10 9 + 13^ 53 54 55 9.44801 .44807 .44812 .44817 .38055 .38059 .38063 .38065 9.45104 .45109 .45114 .45119 .38353 .38355 .38358 .38361 9.45405 .45410 .45415 .45420 .38448 .38451 .38455 .38458 9.45705 .45710 .45715 .45720 .38645 .38649 .38653 .38655 9.46004 .46009 .46014 .46019 .28843 .28846 .28849 .28853 8 7 6 5 + 14^ 57 58 59 9.44822 .44827 .44832 .44837 .38068 .38073 .38075 .38078 9.45124 .45129 .45134 .45139 .38365 .28368 .38371 .38374 9.45426 .45431 .45436 .45441 .38461 .28465 .38468 .38471 9.45725 .45730 .45735 .45740 .38658 .38662 .28665 .28668 9.46023 .46028 .46033 .46038 .28856 .28859 .28863 .28866 4 3 2 1 + 15^ 9.44842 .38081 9.45144 .38378 9.45446 .28474 9.45745 .38673 9.46043 .28869 19h44m 19^ 4Sm 19^42^ igh 41m 19^40^^ Page 96] TABLE IV. Haversinea, s 4^ 20m 65° C 4h2im 65° 15' 4h 22^ 65° 30' 4h23'^ 66° 45' 4^24^ 66° C s Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. 9.46043 .38869 9.46340 .29067 9.46635 .39365 9.46929 .39464 9.47222 .39663 60 J .46048 .28872 .46345 .29070 .46640 .39369 .46934 .29467 .47227 .39866 59 e .46053 .28876 .46350 .29074 .46645 .39272 .46939 .39471 .47231 .39670 58 s . .46058 .28879 .46355 .29077 .46650 .29275 .46944 .39474 .47236 .29673 51 + 1' 9.46063 .28882 9.46360 .39080 9.46655 .29279 9.46949 .39477 9.47241 .29676 56 6 .46068 .28886 .46365 .39084 .46660 .29282 .46954 .39481 .47246 .39680 55 6 .46073 .28889 .46370 .39087 .46665 .29285 .46959 .39484 .47251 .39683 54 7 .46078 .28892 .46375 .39090 .46670 .29389 .46963 .39487 .47256 .29686 53 + 2' 9.46083 .28895 9.46380 .39093 9.46675 .29392 9.46968 .29491 9.47261 .29690 52 9 .46088 .28899 .46384 .39097 .46680 .29295 .46973 .39494 .47266 .39693 51 10 .46093 .28902 .46389 .29100 .46684 .29398 .46978 .39497 .47270 .39696 50 11 .46098 .28905 .46394 .39103 .46689 .39302 .46983 .29501 .47275 .39700 49 + 3' 9.46103 .28909 9.46399 .39107 9.46694 .39305 9.46988 .29504 9.47280 .29703 48 IS .46108 .28912 .46404 .39110 .46699 .39308 .46993 .29507 .47285 .29706 41 14 .46113 .28915 ..46409 .39113 .46704 .39313 .46998 .29510 .47290 .29710 46 15 .46118 .28918 .46414 .39117 .46709 .29315 .47003 .29514 .47295 .29713 45 + i' 9.46123 .28922 9.46419 .39130 9.46714 .29318 9.47007 .29517 9.47300 .29716 44 11 .46128 .28925 .46424 .39133 .46719 .29322 .47012 .29520 .47304 .29720 43 18 .46132 .28928 .46429 .39136 .46724 .29325 .47017 .29524 .47309 .29723 42 19 .46137 .28932 .46434 .39130 .46729 .29338 .47022 .29527 .47314 .29726 41 40 + 5' 9.46142 .28935 9.46439 .39133 9.46733 . .39333 9.47027 .29530 9.47319 .29730 21 .46147 .38938 ..46444 .39136 .46738 .39335 .47032 .29534 .47324 .29733 39 22 .46152 .28943 .46448 .29140 .46743 .39338 .47037 .29537 .47329 .29736 38 23 .46157 .28945 .46453 .39143 .46748 .29341 .47042 .29540 .47334 .39740 31 + 6' 9.46162 .38948 9.46458 .39146 9.46753 .29345 9.47046 .29544 9.47338 .39743 36 25 .46167 .38953 .46463 .39150 .46758 .29348 .47051 .29547 .47343 .39746 35 26 .46172 .38955 .46468 .39153 .46763 .29351 .47056 .39550 .47348 .39750 34 21 .46177 .28958 .46473 .39156 .46768 .29355 .47061 .29554 .47353 .39753 33 + r 9.46182 .38961 9.46478 .39160 9.46773 .29358 9.47066 .29557 9.47358 .29756 32 29 .46187 .38965 .46483 .29163 .46778 .29361 .47071 .29560 .47363 .29760 31 30 .46192 .28968 .46488 .29166 .46782 .29365 .47076 .29564 .47367 .29763 30 31 .46197 .28971 .46493 .29169 .46787 .39368 .47081 .29567 .47372 .29766 29 + 8^ 9.46202 .28975 9.46498 .29173 9.46792 .39371 9.47085 .29570 9.47377 .29770 28 33 .46207 .28978 .46503 .29176 .46797 .39375 .47090 .29573 .47382 .39773 21 34 .46212 .28981 .46508 .29179 .46802 .39378 .47095 .29577 .47387 .39776 26 35 .46217 .28985 .46512 .39183 .46807 .39381 .47100 .29580 .47392 .39779 25 24 + 9^ 9.46222 .28988 9.46517 .39186 9.46812 .29385 9.47105 .29583 9.47397 .39783 31 .46226 .28991 .46522 .39189 .46817 .29388 .47110 .29587 .47401 .39786 23 38 .46231 .28994 .46527 .39193 .46822 .29391 .47115 .29590 .47406 .39789 22 39 .46236 .28998 .46532 .39196 .46827 .29394 .47120 .39593 .47411 .39793 21 + 10' 9.46241 .39001 9.46537 .39199 9.46831 .29398 9.47124 .39597 9.47416 .39796 20 41 .46246 .39004 .46542 .39303 .46836 .29401 .47129 .29600 .47421 .39799 19 42 .46251 .39008 .46547 .39306 .46841 .29404 .47134 .39603 .47426 .39803 18 43 .46256 .39011 .46552 .39309 .46846 .29408 .47139 .39607 .47431 .39806 11 + ir 9.46261 .39014 9.46557 .39313 9.46851 .29411 9.47144 .39610 9.47435 .39809 16 45 .46266 .39017 .46562 .39316 .46856 .29414 .47149 .39613 .47440 .39813 15 46 .46271 .29021 .46567 .29319 .46861 .39418 .47154 .39617 .47445 .29816 14 41 .46276 .29024 .46571 .39222 .46866 .39431 .47159 .39620 .47450 .39819 13 + n' 9.46281 .39027 9.46576 .29226 9.46871 .39424 9.47163 .29623 9.47455 .39833 12 49 ■ .46286 .39031 .46581 .29229 .46875 .39438 .47168 .29637 .47460 .39836 11 50 .46291 .39034 .46586 .39332 .46880 .39431 .47173 .29630 .47464 .39829 10 51 .46296 .39037 .46591 .29236 .46885 .39434 .47178 .29633 .47469 .29833 9 + 13' 9.46301 .39041 9.46596 .29239 9.46890 .39438 9.47183 .29637 9.47474 .29836 8 53 .46305 .39044 .46601 .29343 .46895 .29441 .47188 .29640 .47479 .29839 1 54 .46310 .29047 .46606 .39245 .46900 .29444 .47193 .29643 .47484 .29843 6 55 .46315 .29051 .46611 .29349 .46905 .29447 .47197 .39647 .47489 .29846 5 + W 9.46320 .39054 9.46616 .39253 9.46910 .29451 9.47202 .39650 9.47493 .29849 4 51 .46325 .39057 .46621 .39355 .46915 .39454 .47207 .39653 .47498 .29853 3 58 .46330 .39060 .46626 .39359 .46919 .39457 .47212 .39657 .47503 .29856 2 59 .46335 .39064 .46630 .39363 .46924 .39461 .47217 .39660 .47508 .39859 1 + 15' 9.46340 .39067 9.46635 .39365 9.46929 .39464 9.47222 .39663 9.47513 .29863 19h Sgm igh ssm 19h Sl'm 19h S6m 19^ 35^ 1 TABLE IV. Haversines. [Page 97 s 4^ 25m 66° 15' 4h 26m 66° W ^h ojm 66° 45' 4^ 2Sm 67° 0' 4^ 29m 67° 15' s Log. nav. Nat. Hav. Log. nav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Is at. Hav. Log. Hav. Nat. Hav. 1 2 3 9.47513 .47518 .47523 .47527 .29863 .29866 .29869 .29873 9.47803 .47807 .47812 .47817 .30063 .30066 .30069 .30073 9.48091 .48096 .48101 .48105 .30363 .30368 .30369 .30373 9.48378 .48383 .48387 .48392 .30463 .30467 .30470 .30473 9.48664 .48668 .48673 .48678 .30664 .30668 .30671 .30675 60 59 58 57 + r 5 6 7 9.47532 .47537 .47542 .47547 .29876 .29879 .29883 .29886 9.47822 .47827 .47831 .47836 .30076 .30079 .30083 .30086 9.48110 .48115 .48120 .48124 .30376 .30380 .30283 .30286 9.48397 .48402 .48407 .48411 .39477 .30480 .30484 .30487 9.48683 .48687 .48692 .48697 .30678 .30681 .30685 .30688 .30691 .30895 .30698 .30701 56 55 54 53 hi 51 50 49 + 2^ 9 10 11 9.47552 .47556 .47561 .47566 .29889 .29893 .29896 .29899 9.47841 .47846 .47851 .47856 .30089 .30093 .30096 .30099 9.48129 .48134 .48139 .48144 .30290 .30393 .30296 .30300 9.48416 .48421 .48426 .48430 .30490 .39494 .30497 .30500 9.48702 .48706 .48711 .48716 + 3^ 13 14 15 9.47571 .47576 .47581 .47585 .29903 .29906 .29909 .39913 9.47860 .47865 .47870 .47875 .30103 .30106 .30109 .30113 9.48148 .48153 .48158 .48163 .30303 .30306 .30310 .30313 9.48435 .48440 .48445 .48449 .30504 .30507 .30510 .30514 9.48720 .48725 .48730 .48735 .30705 .30708 .30711 .30715 48 47 46 45 + 4' 17 18 19 9.47590 .47595 .47600 .47605 .29916 .29919 .29923 .29926 9.47880 .47884 .47889 .47894 .30116 .30119 .30133 .30136 9.48168 .48172 .48177 .48182 .30316 .30330 .30323 .30336 9.48454 .48459 .48464 .48468 .30517 .30530 .30524 .30527 9.48739 .48744 .48749 .48754 .30718 .30731 .30725 .30728 44 43 42 41 + 6' 21 22 23 9.47610 .47614 .47619 .47624 .39939 .29933 .29936 .29939 9.47899 .47904 .47908 .47913 .30139 .30133 .30136 .30139 9.48187 .48192 .48196 .48201 .30330 .30333 .30336 .30340 9.48473 .48478 .48483 .48488 .30530 .30534 .30537 .30540 9.48758 .48763 .48768 .48773 .30733 .30735 .30738 .30742 40 39 38 37 + ^ 25 26 27 9.47629 .47634 .47639 .47643 .39943 .29946 .39949 .29953 9.47918 .47923 .47928 .47933 .30143 .30146 .30149 .30153 9.48206 .48211 .48215 .48220 .30343 .30346 .30350 .30353 9.48492 .48497 .48502 .48507 .30544 .30547 .30551 .30554 9.48777 .48782 .48787 .48792 .30745 .30748 .30753 .30755 36 35 34 33 32 31 30 29 + r 29 30 31 9.47648 .47653 .47658 .47663 .29956 .29959 .29963 .29966 9.47937 .47942 .47947 .47952 .30156 .30159 .30163 .30166 9.48225 .48230 .48235 .48239 .30356 .30360 .30363 .30366 9.48511 .48516 .48521 .48526 .30557 .30561 .30564 .30567 9.48796 .48801 .48806 .48811 .30758 .30763 .30765 .30768 + 8' 33 34 35 9.47668 .47672 .47677 .47682 .29969 .29973 .29976 .29979 9.47957 .47961 .47906 .47971 .30169 .30173 .30176 .30179 9.48244 .48249 .48254 .48258 .30370 .30373 .30376 .30380 9.48530 .48535 .48540 .48545 .30571 .30574 .30577 .30581 9.48815 .48820 .48825 .48830 .30772 .30775 .30779 .30782 28 27 26 25 + 9^ 37 38 39 9.47687 .47692 .47697 .47701 .39983 .29986 .29989 .29993 9.47976 .47981 .47985 .47990 .30183 .30186 .30189 .30193 9.48263 .48268 .48273 .48278 .30383 .30386 .30390 .30393 9.48549 .48554 .48559 .48564 .30584 .30587 .30591 .30594 9.48834 .48839 .48844 .48848 .30785 .30789 .30792 .30795 24 23 22 21 + ir 41 42 43 9.47706 .47711 .47716 .47721 .29996 .29999 .30003 .30006 9.47995 .48000 .48005 .48009 .30196 .30199 .30303 .30306 9.48282 .48287 .48292 .48297 .30397 .30400 .30403 .30407 9.48568 .48573 .48578 .48583 .30597 .30601 .30604 .30607 9.48853 .48858 .48863 .48867 .30799 .30802 .30805 .30809 20 19 18 17 + 11^ 45 46 47 9.47725 .47730 .47735 .47740 .30009 .30013 .30016 .30019 9.48014 .48019 .48024 .48029 .30309 .30313 .30316 .,30319 9.48302 .48306 .48311 .48316 .30410 .30413 .30417 .30430 9.48587 .48592 .48597 .48602 .30611 .30614 .30618 .30621 9.48872 .48877 .48882 .48886 .30813 .30815 .30819 .30833 16 15 14 IS 12 11 10 9 + 13' 49 50 51 9.47745 .47750 .47754 .47759 .30023 .30026 .30029 .30033 9.48033 .48038 .48043 .48048 .30333 .30336 .30339 .30333 9.48321 .48325 .48330 .48335 .30433 .30427 .30430 .30433 9.48607 .48011 .48016 .48621 .30634 .30638* .30631 .30634 9.48891 .48896 .48901 .48905 .30836 .30839 .30833 .30836 + 13' 53 54 55 9.47764 .47769 .47774 .47778 .30036 .30039 .30043 .30046 9.48053 .48057 .48002 .48067 .30336 .30339 .30343 .30346 9.48346 .48344 .48349 .48354 .30437 .30440 .30443 .30447 9.48626 .48630 .48635 .48640 .30638 .30641 .30644 .30648 9.48910 .48915 .48919 .48924 .30839 .30843 .30846 .30849 8 7 6 5 + IV 57 58 59 9.47783 .47788 .47793 .47798 .30049 .30053 .30056 .30059 9.48072 .48077 .48081 .48086 .30349 .30353 .30356 .30359 9.48359 .48364 .48368 .48373 .30450 .30453< .30457 .30460 9.48645 ^ .48649 .48654 .48659 .30651 .30655 .30658 .30661 9.48929 .48934 .48938 .48943 .30852 .30856 .30859 .30862 4 3 2 1 + W 9.47803 .30063 9.48091 .30363 9.48378 .30463 9.48664 .30664 9.48948 .30866 19^ 34m 19li3Sm 19h 32^ 19^ sm 19h 30m 1 55901°— IS- Page 98] TABLE IV. Haversines. B 4h Sffm 67° SO' 4^ Sim 67° 45' 4^ S2m 68° C 4hSsme^W 4^S4me8°W 8 Log. Hav. Nat. Hav Log. Hav Nat. Hav Log. Hav Nat. Hav Log. Hav. NaLHav Log. Hav. Nat. Hav. 1 2 S 9.48948 .48953 .48957 .489G2 .30866 .30869 .30873 .30876 9.49231 .49235 .49240 .49245 .31068 .31071 .31074 .31078 9.49512 .49517 .49522 .49526 .31370 .31373 .31376 .31380 9.49793 .49797 .49802 .49807 .31473 .31475 .31479 .31483 9.50072 .50076 .50081 .50085 .31675 .31678 .31682 .31685 60 59 58 57 + r 5 6 7 9.48967 .48971 .48976 .48981 .30879 .30883 .30886 .30889 9.49250 .49254 .49259 .49264 .31081 .31084 .31088 .31091 9.49531 .49536 .49540 .49545 .31383 .31387 .31390 .31393 9.49811 .49816 .49821 .49825 .31486 .31489 .31493 .31496 9.50090 .50095 .50099 .50104 .31688 .31693 .31695 .31699 56 55 54 53 + 2^ 9 10 11 9.48986 .48990 .48995 .49000 .30893 .30896 .30899 .30903 9.49268 .49273 .49278 .49282 .31095 .31098 .31101 .31105 9.49550 .49554 .49559 .49564 .31397 .31300 .31303 .31307 9.49830 .49835 .49839 .49844 .31499 .31503 .31506 .31509 9.50109 .50113 .50118 .50123 .31703 .31705 .31709 .31713 5^ 51 50 49 + 3' IS u 15 9.49004 .49009 .49014 .49019 .30906 .30910 .30913 .30916 9.49287 .49292 .49297 .49301 .31108 .31111 .31115 .31118 9.49568 .49573 .49578 .49583 .31310 .31314 .31317 .31330 9.49849 .49853 .49858 .49802 .31513 .31516 .31519 .31533 9.50127 .50132 .50136 .50141 .31716 .31719 .31733 .31736 48 47 46 45 44 43 42 41 40 39 38 37 36 35 34 33 + 4^ 17 18 19 9.49023 .49028 .49033 .49038 .30930 .30923 .30926 .30930 9.49306 .49311 .49315 .49320 .31131 .31125 .31128 .31133 9.49587 .49592 .49597 .49601 .31334 .31337 .31330 .31334 9.49867 .49872 .49876 .49881 .31536 .31530 .31533 .31536 9.50146 .50150 .50155 .50160 .31729 .31732 .31736 .31739 + 5' 21 22 23 9.49042 .49047 .49052 .49056 .30933 .30936 .30940 .30943 9.49325 .49329 .49334 .49339 .31135 .31138 .31143 .31145 9.49606 .49611 .49615 .49620 .31337 .31341 .31344 .31347 9.49886 .49890 .49895 .49900 .31540 .31543 .31546 .31550 9.50164 .50169 .50174 .50178 .31742 .31746 .31749 .31753 + 6' 25 26 27 9.49061 .49066 .49071 .49075 .30946 .30950 .30953 .30957 9.49344 .49348 .49353 .49358 .31148 .31153 .31155 .31158 9.49625 .49629 .49634 .49639 .31351 .31354 .31357 .31361 9.49904 .49909 .49914 .49918 .31553 .31557 .31560 .31563 9.50183 .50187 .50192 .50197 .31756 .31760 .31763 .31766 + r 29 SO 31 9.49080 .49085 .49089 .49094 .30960 .30963 .30967 .30970 9.49302 .49367 .49372 .49376 .31163 .31165 .31169 .31173 9.49643 .49648 .49653 .49657 .31364 .31367 .31371 .31374 9.49923 .49928 .49932 .49937 .31567 .31570 .31573 .31577 9.50201 .50206 .50211 .50215 .31770 .31773 .31776 .31780 32 31 30 29 28 27 26 25 + 8' 33 34 35 9.49099 .49104 .49108 .49113 .30973 .30977 .30980 .30983 9.49381 .49386 .49390 .49395 .31175 .31179 .31183 .31185 9.49662 .49667 .49671 .49676 .31378 .31381 .31384 .31388 9.49942 .49946 .49951 .49956 .31580 .31584 .31587 .31590 9.50220 .50224 .50229 .50234 .31783 .31787 .31790 .31793 + 9^ 37 SB 39 9.49118 .49122 .49127 .49132 .30987 .30990 .30994 .30997 9.49400 .49405 .49409 .49414 .31189 .31193 ^31190 .31199 9.49681 .49685 .49690 .49695 .31391 .31394 .31398 .31401 9.49960 .49965 .49969 .49974 .31594 .31597 .31601 .31604 9.50238 .50243 .50248 .50252 .31797 .31800 .31804 .31807 24 23 22 21 + ir 41 42 43 9.49137 .49141 .49146 .49151 .31000 .31004 .31007 .31010 9.49419 .49423 .49428 .49433 .31303 .31206 .31309 .31313 9.49699 .49704 .49709 .49713 .31405 .31408 .31411 .31415 9.49979 .49983 .49988 .49993 .31607 .31611 .31614 .31617 9.50257 .50261 .50266 .50271 .31810 .31814 .31817 .31820 20 19 18 17 16 15 14 IS + 11' 45 46 47 9.49155 .49160 .49165 .49170 .31014 .31017 .31020 .31024 9.49437 .49442 .49447 .49451 .31316 .31319 .31333 .31336 9.49718 .49723 .49727 .49732 .31418 .31431 .31425 .31428 9.49997 .50002 .50007 .50011 .31631 .31624 .31628 .31631 9.50275 .50280 .50284 .50289 .31824 .31827 .31831 .31834 + n' 49 50 51 9.49174 .49179 .49184 .49188 .31037 .31031 .31034 .31037 9.49456 .49461 .49465 .49470 .31339 .31333 .31336 .31339 9.49737 .49741 .49746 .49751 .31432 .31435 .31438 .31442 9.50016 .50021 .50025 .50030 .31634 .31638 .31641 .31644 9.50294 .50298 .50303 .50308 .31837 .31841 .31844 .31848 12 11 10 9 8 7 6 5 + 13' 53 54 55 9.49193 .49198 .49202 .49207 .31041 .31044 .31047 .31051 9.49475 .49480 .49484 .49489 .31343 .31346 .31349 .31353 9.49755 .49700 .49765 .49769 .31445 .31448 .31452 .31455 9.50034 .50039 .50044 .50048 .31648 .31651 .31655 .31658 9.50312 .50317 .50322 .50326 .31851 .31854 .31858 .31861 57 58 59 9.49212 .49217 .49221 .49226 .31054 .31057 .31061 .31064 9.49494 .49498 .49503 .49508 .31356 .31360 .31363 .31266 9.49774 .49779 .49783 .49788 .31459 .31462 .31465 .31469 9.50053 .50058 .50062 .50067 .31661 .31665 .31668 .31673 9.50331 .50335 .50340 .50345 .31865 .31868 .31871 .31875 4 3 2 1 + 15' 9.49231 .31068 9.49512 .31270 9.49793 .31473 9.50072 .31675 9.50349 .31878 J9h 29m 1 19^ 28m 1 19Ji 27m 1 19^ 26m 19h 25m TABLE IV. Havereines. [Page 99 s 4h S5m 68° 45' 4h 36m 69° 0' 4A SJm 69° 15' 4t^ SSm 69° 30' 4h S9m 69° 45' s 60 69 58 57 Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Ilav. Nat. Hav. Log. Hav. Nat. Hav. 1 2 S 9.50349 .50354 .50358 .50363 .31878 .31881 .31885 .31888 9.50626 .50630 .50635 .50639 .33083 .33085 .33088 .33093 9.50901 .50905 .50910 .50914 .32385 .33389 .33393 .33396 9.51174 .51179 .51184 .51188 .33490 .33493 .33496 .33500 9.51447 .51452 .51456 .51461 .33694 .33698 .33701 .33704 + 1' 5 6 7 9.50368 .50372 .50377 .50382 .31893 .31895 .31898 .31903 9.50644 .50649 .50653 .50658 .33095 .33099 .33103 .33105 9.50919 .50924 .50928 .50933 .33399 .33303 .32306 .32309 9.51193 .51197 .51202 .51206 .33603 .33507 .33510 .33513 9.51465 .51470 .51474 .51479 .33708 .33711 .33715 .33718 56 55» 54 53 62 61 50 49 + r 9 10 11 9.50386 .50391 .50395 .50400 .31905 .31909 .31913 .31915 9.50662 .50667 .50672 .50676 .33109 .33113 .33116 .32119 9.50937 .50942 .50946 .50951 .33313 .33316 .33319 .33333 9.51211 .51215 .51220 .51225 .33517 .33530 .33534 .33537 9.51483 .51488 .51492 .51497 .33731 .33735 .33738 .33733 + 3' 13 14 15 9.50405 .50409 .50414 .50418 .31919 .31933 .31936 .31939 9.50681 .50685 .50690 .50694 .33133 .33126 .32139 .33133 9.50956 .50960 .50965 .50969 .32336 .33330 .32333 .32336 9.51229 .51234 .51238 .51243 .33531 .33534 .33537 .33541 .33544 .33547 .33551 .33554 9.51501 .51506 .51510 .51515 .33735 .33738 .33742 .33745 4S 47 46 45 44 43 42 41 + *' 17 18 19 9.50423 .50428 .50432 .50437 .31933 .31936 .31939 .31913 9.50699 .50704 .50708 .50713 .33136 .33139 .33143 .33146 9.50974 .50978 .50983 .50988 .33340 .33343 .33347 .33350 9.51247 .51252 .51256 .51261 9.51519 .51524 .51529 .51533 .32749 .32753 .32756 .33759 + 5' 21 22 23 9.50442 .50446 .50451 .50455 .31946 .31949 .31953 .31956 9.50717 .50722 .50727 .50731 .33150 .33153 .33156 .33160 9.50992 .50997 .51001 .51006 .33353 .33357 .33360 .33364 9.51265 .51270 .51275 .51279 .33558 .33561 .33565 .33568 9.51538 .51542 .51547 .51551 .32762 .32766 .32769 .32773 40 39 38 37 + 6^ 25 26 27 9.50460 .50465 .50469 .50474 .31959 .31963 .31966 .31970 9.50736 .50740 .50745 .50750 .33163 .33166 .33170 .33173 9.51010 .51015 .51019 .51024 .33367 .33370 .33374 .33377 9.51284 .51288 .51293 .51297 .33571 .33575 .33578 .32582 9.51556 .51560 .51565 .51569 .33776 .33779 .33783 .33786 36 35 34 S3 + r 29 30 31 9.50478 .50483 .50488 .50492 .31973 .31976 .31980 .31983 9.50754 .50759 .50763 .50768 .32177 .33180 .33183 .33187 9.51029 .51033 .51038 .51042 .33381 .33384 .32388 .32391 9.51302 .51306 .51311 .51315 .32585 .32588 .33593 .32595 9.51574 .51578 .51583 .51587 .33790 .33793 .33797 .33800 32 31 30 29 + 8' 33 34 35 9.50497 .50501 .50506 .50511 .31987 .31990 .31993 .31997 9.50772 .50777 .50782 .50786 .32190 .32194 .32197 .32300 9.51047 .51051 .51056 .51061 .32394 .32398 .33401 .33405 9.51320 .51325 .51329 .51334 .32599 .32603 .32605 .32609 9.51592 .51596 .51601 .51605 .32803 .32807 .32810 .32814 28 27 26 25 + ^ 37 38 39 9.50515 .50520 .50524 .50529 .33000 .33004 .33007 .33010 9.50791 .50795 .50800 .50805 .33204 .32207 .33311 .33314 9.51065 .51070 .51074 .51079 .33408 .33411 .33415 .33418 9.51338 .51343 .51347 .51352 .32612 .33616 .33619 .33633 9.51610 .51614 .51619 .51623 .33817 .33830 .33834 .33837 24 23 22 21 + W 41 42 43 9.50534 .50538 .50543 .50547 .33014 .33017 .33031 .33034 9.50809 .50814 .50818 .50823 .33317 .33331 .33334 .33238 9.51083 .51088 .51092 .51097 .33433 .33435 .33438 .33433 9.51356 .51361 .51305 .51370 .33636 .33639 .33683 .32636 9.51628 .51633 .51637 .51642 .33831 .32834 .32838 .32841 20 19 18 17 + 11^ 45 46 47 9.50552 .50557 .50561 .50566 .33037 .33031 .32034 .33037 9.50827 .50832 .50837 .50841 .33331 .33335 .33338 .33341 9.51102 .51106 .51111 .51115 .33435 .33438 .33443 .33445 9.51374 .51379 .51384 .51388 .32640 .32643 .32646 .32650 9.51646 .51651 .51655 .51660 .32844 .32848 .32851 .32855 16 15 14 13 12 11 10 9 8 7 6 5 + 1%' 49 50 51 + 13' 53 54 55 9.50570 .50575 .50580 .50584 .33041 .33044 .33048 .33051 9.50846 .50850 .50855 .50860 .33245 .33348 .33351 .33355 9.51120 .51124 .51129 .51133 .33449 .33453 .33456 .33459 9.51393 .51397 .51402 .51406 .32653 .32657 .32660 .33663 9.51664 .51669 .51673 .51678 .33858 .33861 .33865 .33868 9.50589 .50593 .50598 .50603 .33054 .33058 .33061 .33065 9.50864 .50869 .50873 .50878 .33358 .33363 .33365 .33368 9.51138 .51143 .51147 .51152 .33463 .33466 .33469 .33473 9.51411 .51415 .51420 .51424 .33667 .33670 .33674 .33677 9.51682 .51687 .51691 .51696 .33873 .33875 .33878 .32882 + W 57 58 59 9.50607 .50612 .50616 .50621 .33068 .33071 .33075 .33078 9.50882 .50887 .50892 .50896 .33373 .33375 .32379 .33282 9.51156 .51161 .51165 .51170 .33476 .33479 .33483 .33486 9.51429 .51433 .51438 .51442 .33681 .32684 .32687 .32691 9.51700 .51705 .51709 .51714 .33885 .33889 .33892 .32896 4 3 2 1 + 15' 9.50626 .33083 9.50901 .32285 9.51174 .33490 9.51447 .32694 9.51718 .32899 19h 24m 19h 23m 19h 22ra 19^ 21m 19h 20m j Page 100] TABLE IV. Haversines. s 4h 40m 70'' C 4h 41m 70° 15' 4h 42m 70° 30' 4h 4sm 70° 45' 4h 44m 710 0' s Log. Hav. Nat. Hav Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav Nat. Hav. 1 5 S 9.51718 .51723 .51727 .51732 .32899 .32902 .32906 .32909 9.51988 .51993 .51997 .52002 .33104 .33108 .33111 .33114 9.52257 .52261 .52266 .52270 .33310 .33313 .33317 .33330 9.52525 .52529 .52533 .52538 .33515 .33519 .33532 .33526 9.52791 .52795 .52800 .52804 .33732 .33725 .33728 .33732 60 59 58 57 + r • 5 6 7 9.51736 .51741 .51745 .51750 .32913 .32916 .32920 .32923 9.52006 .52011 .52015 .52020 .33118 .33121 .33125 .33128 9.52275 .52279 .52284 .52288 .33323 .33327 .33330 .33334 9.52542 .52547 .52551 .52556 .33529 .33533 .33536 .33540 9.52809 .52813 .52817 .52822 .33735 .33739 .33742 .33746 56 55 54 53 52 51 50 49 48 47 46 45 + 2^ 9 10 11 9.51754 .51759 .51763 .51768 .32926 .32930 .32933 .32937 9.52024 .52029 .52033 .52038 .33132 .33135 .33138 .33142 9.52293 .52297 .52302 .52306 .33337 .33341 .33344 .33347 9.52560 .52565 .52569 .52573 .33543 .33546 .33550 .33553 9.52826 .52831 .52835 .52839 .33749 .33753 .33756 .33759 + 3' 13 U 15 9.51772 .51777 .51781 .51786 .32940 .32943 .32947 .32950 9.52042 .52047 .52051 .52056 .33145 .33149 .33152 .33156 9.52311 .52315 .52320 .52324 .33351 .33354 .33358 .33361 9.52578 .52582 .52587 .52591 .33557 .33560 .33564 .33567 9.52844 .52848 .52853 .52857 .33763 .33766 .33770 .33773 + 4' n 18 19 9.51790 .51795 .51799 .51804 .32954 .32957 .32961 .32964 9.52060 .52065 .52069 .52074 .33159 .33162 .33166 .33169 9.52328 .52333 .52337 .52342 .33365 .33368 .33371 .33375 9.52596 .52600 .52605 .52609 .33570 .33574 .33577 .33581 9.52862 .52866 .52870 .52875 .33777 .33780 .33783 .33787 44 43 42 41 + 5' 21 22 23 9.51808 .51813 .51817 .51822 .32967 .32971 .32974 .32978 9.52078 .52082 .52087 .52091 .33173 .33176 .33179 .33183 9.52346 .52351 .52355 .52360 .33378 .33382 .33385 .33389 9.52613 .52618 .52622 .52627 .33584 .33588 .33591 .33594 9.52879 .52884 .52888 .52893 .33790 .33794 .33797 .33801 40 39 SS 37 36 35 34 33 + 6' 25 26 27 9.51826 .51831 .51835 .51840 .32981 .32984 .33988 .32991 9.52096 .52100 .52105 .52109 .33186 .33190 .33193 .33197 9.52364 .52369 .52373 .52378 .33392 .33395 .33399 .33402 9.52631 .52636 .52640 .52645 .33598 .33601 .33605 .33608 9.52897 .52901 .52906 .52910 .33804 .33808 .33811 .33814 + r 29 SO SI 9.51844 .51849 .51853 .51858 .32995 .32998 .33002 .33005 9.52114 .52118 .52123 .52127 .33200 .33203 .33207 .33210 9.52382 .52386 .52391 .52395 .33406 .33409 .33413 .33416 9.52649 .52653 .52658 .52662 .33612 .33615 .33618 .33622 9.52915 .52919 .52923 .52928 .33818 .33821 .33835 .33838 32 31 30 29 28 27 26 25 24 23 22 21 + 8' SS 34 35 9.51862 .51867 .51871 .51876 .33008 .33012 .33015 .33019 9.52132 .52136 .52141 .52145 .33314 .33317 .33321 .33224 9.52400 .52404 .52409 .52413 .33419 .33423 .33426 .33430 9.52667 .52671 .52676 .52680 .33625 .33629 .33632 .33636 9.52932 .52937 .52941 .52946 .33833 .33835 .33839 .33842 + 9^ 57 5,? 39 9.51880 .51885 .51889 .51894 .33022 .33025 .33029 .33032 9.52150 .52154 .52159 .52163 .33227 .33231 .33234 .33338 9.52418 .52422 .52427 .52431 .33433 .33436 .33440 .33444 9.52684 .52689 .52693 .52698 .33639 .33643 .33646 .33649 9.52950 .52954 .52959 .52963 .33845 .33849 .33852 .33856 + W 41 42 43 9.51898 .51903 .51907 .51912 .33036 .33039 .33043 .33046 9.52168 .52172 .52177 .52181 .33241 .33345 .33348 .33251 9.52436 .52440 .52444 .52449 .33447 .33450 .33454 .33457 9.52702 .52707 .52711 .52715 .33653 .33656 .33660 .33663 9.52968 .52972 .52976 .52981 .33859 .33863 .33866 .33869 20 19 18 n + 11' 45 4S 47 9.51916 .51921 .51925 .51930 .33049 .33053 .33056 .33060 9.52185 .52190 .52194 .52199 .33255 .33258 .33263 .33265 9.52453 .52458 .52462 .52467 .33461 .33464 .33467 .33471 9.52720 .52724 .52729 .52733 .33667 .33670 .33673 .33677 9.52985 .52990 .52994 .52999 .33873 .33876 .33880 .33883 16 15 14 13 12 11 10 9 + 12' 49 50 51 9.51934 .51939 .51943 .51948 .33063 .33067 .33070 .33073 9.52203 .52208 .52212 .52217 .33269 .33272 .33275 .33279 9.52471 .52476 .52480 .52484 .33474 .33478 .33481 .33485 9.52738 .52742 .52747 .52751 .33680 .33684 .33687 .33691 9.53003 .53007 .53012 .53016 .33887 .33890 .33894 .33897 + 13' 53 54 55 9.51952 .51957 .51961 .51966 .33077 .33080 .33084 .33087 9.52221 .52226 .52230 .52235 .33383 .33286 .33289 .33293 9.52489 .52493 .52498 .52502 .33488 .33491 .33495 .33498 9.52755 .52760 .52764 .52769 .33694 .33698 .33701 .33704 9.53021 .53025 .53029 .53034 .33900 .33904 .33907 .33911 S 7 6 5 4 3 2 1 + 14' 57 58 59 9.51970 .51975 .51979 .51984 .33090 .33094 .33097 .33101 9.52239 .52244 .52248 .52253 .33396 .33399 .33303 .33306 9.52507 .52511 .52516 .52520 .33502 .33505 .33509 .33513 9.52773 .52778 .52782 .52786 .33708 .33711 .33715 .33718 9.53038 .53043 .53047 .53051 .33914 .33918 .33921 .33925 + 15' 9.51988 .33104 9.52257 .33310 9.52525 .33515 9.52791 .33722 9.53056 .33938 19h 19m 19hlgm igh 17m 1 19A 16m 19^ 15m TABLE IV. Haversinea. [Page 101 s 4h4Sm 71° 15' 4h46m 71° 30' 4h 47m 71° 4.5^ 4^ 4Sm 73° 0' .^A 49™ 73° 15' 1 s Log. Ilav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. 1 2 3 9.53056 .530G0 .53065 .53069 .33938 .33931 .33935 .33938 9.53320 .53324 .53328 .53333 .34135 .34138 .34143 .34145 9.53582 .53587 .53591 .53595 .34343 .34345 .34349 .34353 9.53844 .53848 .53852 .53857 .34549 .34553 .34556 .34560 9.54104 .54108 .54113 .54117 .34757 .34760 .34764 .34767 60 59 58 57 + r 5 6 7 9.53073 .53078 .53082 .53087 .33943 .33945 .33949 .33953 9.53337 .53342 .53346 .53350 .34149 .34153 .34155 .34159 9.63600 .53604 .53609 .53613 .34356 .34359 .34363 .34366 9.53861 .53865 .53870 .53874 .34563 .34566 .34570 .34573 9.54121 .54126 .54130 .54134 .34771 .34774 .34778 .34781 56 55 54 53 + V 9 10 11 9.53091 .53096 .53100 .53104 .33956 .33959 .33963 .33966 9.53355 .53359 .53364 .53368 .34163 .34166 .34169 .34173 9.53617 .53622 .53626 .53630 .34369 .34373 .34376 .34380 9.53879 .53883 .53887 .53892 .34577 .34580 .34584 .34587 9.54139 .54143 .54147 .54152 .34784 .34788 .34791 .34795 52 51 50 49 + 3' 13 14 15 9.53109 .53113 .53118 .53122 .33969 .33973 .33976 .33980 9.53372 .53377 .53381 .53385 .34176 .34180 .34183 .34186 9.53635 .53639 .53643 .53648 .34383 .34387 .34390 .34394 9.53896 .53900 .53905 .53909 .34591 .34594 .34598 .34601 9.54156 .54160 .54165 .54169 .34798 .34803 .34805 .34809 48 47 46 45 + 4' 17 18 19 9.53126 .53131 .53135 .53140 .33983 .33986 .33990 .33993 9.53390 .53394 .53399 .53403 .34190 .34193 .34197 .34300 9.53652 .53657 .53661 .53665 .34397 .34400 .34404 .34407 9.53913 .53918 .53922 .53926 .34604 .34608 .34611 .34615 9.54173 .54177 .54182 .54186 .34813 .34816 .34819 .34833 U 43 42 41 + 5' 21 22 23 9.53144 .53148 .53153 .53157 .33997 .34000 .34004 .34007 9.53407 .53412 .53416 .53421 .34304 .34307 .34311 .34314 9.53670 .53674 .53678 .53683 .34411 .34414 .34418 .34431 9.53931 .53935 .53939 .53944 .34618 .34623 .34635 .34639 9.54190 .54195 .54199 .54203 .34836 .34830 .34833 .34836 40 39 38 37 + 6' 25 26 27 9.53162 .53166 .53170 .53175 .34011 .34014 .34018 .34031 9.53425 .53429 .53434 .53438 .34318 .34331 .34334 .34338 9.53687 .53691 .53696 .53700 .34435 .34438 .34433 .34435 9.53948 .53952 .53957 .53961 .34633 .34636 .34639 .34643 9.54208 .54212 .54216 .54221 .34840 .34843 .34847 .34850 36 35 34 33 + r 29 30 31 9.53179 .53184 .53188 .53192 .34034 .34038 .34031 .34035 9.53442 .53447 .53451 .53456 .34331 .34335 .34338 .34343 9.53704. .53709 .53713 .53718 .34439 .34443 .34445 .34449 9.53966 .53970 .53974 .53978 .34646 .34649 .34653 .34656 9.54225 .54229 .54234 .54238 .34854 .34857 .34861 .34864 32 31 30 29 + 8' 33 34 35 9.53197 .53201 .53206 .53210 .34038 .34043 .34045 .34049 9.53460 .53464 .53469 .53473 .34345 .34349 .34353 .34356 9.53722 .53726 .53731 .53735 .34453 .34456 .34459 .34463 9.53983 .53987 .53991 .53996 .34660 .34663 .34667 .34670 9.54242 .54247 .54251 .54255 .34868 .34871 .34875 .34878 28 27 26 25 + r 37 38 39 9.53214 .53219 .53223 .53228 .34053 .34055 .34059 .34063 9.53477 .53482 .53486 .53491 .34359 .34363 .34366 .34369 9.53739 .53744 .53748 .53752 .34466 .34470 .34473 .34477 9.54000 .54004 .54009 .54013 .34674 .34677 .34681 .34684 9.54260 .54264 .54268 .54272 .34883 .34885 .34888 .34892 24 23 22 21 + W 41 42 43 9.53232 .53236 .53241 .53245 .34066 .34069 .34073 .34076 9.53495 .53499 .53504 .53508 .34373 .34376 .34380 .34383 9.53757 .53761 .53765 .53770 .34480 .34483 .34487 .34490 9.54017 .54022 .54026 .54030 .34688 .34691 .34694 .34698 9.54277 .54281 .54285 .54290 .34895 .34899 .34902 .34906 20 19 18 17 + 11' 45 46 47 9.53249 .53254 .53258 .53263 .34080 .34083 .34087 .34090 9.53512 .53517 .53521 .53526 .34387 .34390 .34393 .34297 9.53774 ■.53778 .5S783 .53787 .34494 .34497 .34501 .34504 9.54035 .54039 .54043 .54048 .34701 .34705 .34708 .34713 9.54294 .54298 .54303 .54307 .34909 .34913 .34916 .34930 16 15 U 13 + 13' 49 50 51 9.53267 .53271 .53276 .53280 .34093 .34097 .34100 .34104 9.53530 .53534 .53539 .53543 .34300 .34304 .34307 .34311 9.53792 .53796 .53800 .53805 .34508 .34511 .34515 .34518 9.54052 .54056 .54061 .54065 .34715 .34719 .34733 .34726 9.54311 .54316 .54320 .54324 .34933 .34927 .34930 .34933 12 11 10 9 + 13' 53 54 55 9.53285 .53289 .53293 .53298 .34107 .34111 .34114 .34118 9.53547 .53552 .53556 .53560 .34314 .34318 .34331 .34335 9.53809 .53813 .53818 .53822 .34531 .34535 .34528 .34533 9.54069 .54074 .54078 .54082 .34739 .34733 .34736 .34739 9.54329 .54333 .54337 .54341 .34937 .34940 .34944 .34947 8 7 6 5 + 14' 57 55 59 9.53302 .53307 .53311 .53315 .34131 .34134 .34138 .34131 9.53565 .53569 .53574 .53578 .34338 .34331 .34335 .34338 9.53826 .53831 .53835 .53839 .34535 .34539 .34543 .34546 9.54087 .54091 .54095 .54100 .34743 .34746 .34750 .34753 9.54346 .54350 .54354 .54359 .34951 .34954 .34958 .34961 4 3 2 1 + 15' 9.53320 .34135 9.53582 .34343 9.53844 .34549 9.54104 .34757 9.54363 .34965 19h 14m J9A 13m 19h 22m igh urn 19hi0m Page 102] TABLE IV. Haversinee. s 4^ 50m 72° Sr 4h 5im 72° 45/ 4^ 52m 730 0' 4h 53m 73° 15' 4h 54m 73° 30/ Log. Hav Nat. Hav Log. Hav Nat. Hav Log. Hav Nat. Hav Log. Hav Nat. Hav Log. Hav Nat. Hav 3 1 2 S 9.54363 .54367 .54372 .54376 .34965 .34968 .34972 .34975 9.54621 .54625 .54629 .54634 .35173 .35176 .35180 .35183 9.54878 .54882 .54886 .54890 .35381 .35385 .35388 .35392 9.55133 .55137 .55142 .55146 .35590 .35594 .35597 .35601 9.55387 .55392 .55396 .55400 .35799 .35803 .35806 .35810 60 59 58 57 + r 5 6 7 9.54380 .54385 .54389 .54393 .34979 .34983 .34986 .34989 9.54638 .54642 .54847 .54651 .35187 .35190 .35194 .35197 9.54895 .54899 .54903 .54907 .35395 .35399 .35403 .35406 9.55150 .55154 .55159 .55163 .35604 .35608 .35611 .35615 9.55404 .55409 .55413 .55417 .35813 .35817 .35830 .35834 56 55 54 53 52 51 50 49 4- 2' 9 10 11 9.54397 .54402 .54406 .54410 .34993 .34996 .34999 .35003 9.54655 .54659 .54664 .54668 .35301 .35304 .35308 .35311 9.54912 .54916 .54920 .54924 .35409 .35413 .35416 .35430 9.55167 .55171 .55176 .55180 .35618 .35633 .35625 .35638 9.55421 .55425 ,55430 .55434 .35837 .35831 .35834 .35838 + 3' 13 14 15 9.54415 .54419 .54423 .54428 .35006 .35010 .35013 .35017 9.54672 .54677 .54681 .54685 .35315 .35318 .35333 .35225 9.54929 .54933 .54937 .54942 .35433 .35437 .35430 .35434 9.55184 .55188 .55192 .55197 .35633 .35635 .35639 .35643 9.55438 .55442 .55447 .55451 .35841 .35845 .35848 .35853 48 47 46 45 + r 17 18 19 9.54432 .54436 .54440 .54445 .35030 .35034 .35037 .35031 9.54689 .54694 .54698 .54702 .35338 .35332 .35235 .35239 9.54946 .54950 .54954 .54959 .35437 .35441 .35444 .35448 9.55201 .55205 .55209 .55214 .35646 .35649 .35653 .35656 9.55455 .55459 .55463 .55468 .35855 .35859 .35863 .35865 44 43 42 41 + 5^ 21 22 23 9.54449 .54453 .54458 .54462 .35034 .35038 .35041 .35044 9.54707 .54711 .54715 .54719 .35343 .35346 .35249 .35253 9.54963 .54967 .54971 .54976 .35451 .35454 .35458 .35461 9.55218 .55222 .55226 .55231 .35660 .35663 .35667 .35670 9.55472 .55476 .55480 .55485 .35869 .35873 .35876 .35879 40 39 38 37 + 6^ 25 26 27 9.54466 .54471 .54475 .54479 .35048 .35651 .35055 .35058 9.54724 .54728 .54732 .54736 .35356 .35260 .35363 .35367 9.54980 .54984 .54988 .54993 .35465 .35468 .35473 .35475 9.55235 .55239 .55243 .55248 .35674 .35677 .35681 .35684 9.55489 .55493 .55497 .55501 .35883 .35886 .35890 .35893 36 35 34 33 + r 29 30 31 9.54483 .54488 .54492 .54496 .35063 .35065 .35069 .35073 9.54741 .54745 .54749 .54754 .35370 .35374 .35377 .35281 9.54997 .55001 .55005 .55010 .35479 .35483 .35486 .35489 9.55252 .55256 .55260 .55265 .35688 .35691 .35695 .35698 9.55506 .55510 .55514 .55518 .35897 .35900 .35904 .35907 32 31 30 29 28 27 26 25 + s' 33 34 35 9.54501 .54505 .54509 .54514 .35076 .35079 .35083 .35086 9.54758 .54762 .54766 .54771 .35384 .35288 .35391 .35394 9.55014 .55018 .55022 .55027 .35493 .35496 .35500 .35503 9.55269 .55273 .55277 .55282 .35703 .35705 .35709 .35713 9.55523 .55527 .55531 .55535 .35911 .35914 .35918 .35931 + r 37 38 39 9.54518 .54522 .54526 .54531 .35090 .35093 .35097 .35100 9.54775 .54779 .54784 .54788 .35398 .35301 .35305 .35308 9.55031 .55035 .55039 .55044 .35507 .35510 .35514 .35517 9.55286 .55290 .55294 .55298 .35716 .35719 .3^733 .35736 9.55539 .55544 .55548 .55552 .35935 .35938 .35932 .35935 24 23 22 21 + W 41 42 43 9.54535 .54539 .54544 .54548 .35103 .35107 .35110 .35114 9.54792 .54796 .54801 .54805 .35313 .35315 .35319 .35332 9.55048 .55052 .55057 .55061 .35531 .35534 .35538 .35531 9.55303 .55307 .55311 .55315 .35730 .35733 .35737 .35740 9.55556 .55561 .55565 .55569 .35939 .35942 .35946 .35949 20 19 18 17 + ir 45 46 47 9.54552 .54556 .54561 .54565 .35117 .35121 .35134 .35138 9.54809 .54813 .54818 .54822 .35326 .35329 .35333 .35336 9.55065 .55069 .55074 1 .55078 .35534 .35538 .35541 .35545 9.55320 .55324 .55328 .55332 .35743 .35747 .35750 .35754 9.55573 .55577 .55582 .55586 .35953 .35956 .35960 .35963 16 15 14 13 + 13' 49 50 51 9.54569 .54574 .54578 .54582 .35131 .35135 .35138 .35143 9.54826 .54831 .54835 .54839 .35340 .35343 .35347 .35350 9.55082 .55086 .55091 .55095 .35548 .35553 .35555 .35559 9.55337 .55341 .55345 .55349 .35757 .35761 .35764 .35768 9.55590 .55594 .55598 .55603 .35967 .35970 .35974 .35977 12 11 10 9 + 13' 53 54 55 9.54587 .54591 .54595 .54599 .35145 .35149 .35153 .35156 9.54843 .54848 .54852 .54856 .35354 .35357 .35361 .35364 9.55099 .55103 .55108 .55112 .35563 .35566 .35569 .35573 9.55354 .55358 .55362 .55366 .35771 .35775 .35778 .35783 9.55607 .55611 .55615 .55620 .35981 .35984 .35988 .35991 8 7 6 5 4 3 2 1 + W 57 58 59 9.54604 .54608 .54612 .54617 .35159 .35163 .35166 .35169 9.54860 .54865 .54869 .54873 .35368 .35371 .35374 .35378 9.55116 .55120 .55125 .55129 .35576 .35580 .35583 .35587 9.55370 .55375 .55379 .55383 .35785 .35789 .35793 .35796 9.55624 .55628 .55632 .55636 .35995 .35998 .36002 .36005 + 15' 9.54621 .35173 9.54878 1 .35381 9.55133 .35590 9.55387 .35799 9.55641 1 .36009 19h gm 19h 8m 1 19h7m 19h6m 19h 5m j TABLE IV. [Page 103 Haversinea. s 4f>' 55m 73° 45' \n 56^ 74° 0' 4h 57m 74° 15' 4h5smU°W 4h59^U°i5' 1 3 Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Ha>v. Nat. Hav. Log. Hav. Nat. Hav. 1 2 3 9.55641 .55645 .55649 .55653 .36009 .36013 .36016 .36019 9.55893 .55897 .55901 .55905 .36318 .36233 .36235 .36239 9.56144 .56148 .56152 .56156 .36438 .36431 .36435 .36438 9.56393 .56397 .56402 .56406 .36638 .38643 .36645 .36649 9.56642 .56646 .56650 .56654 .36848 .36853 .36855 .36859 60 59 58 57 56 55 54 53 4- V 5 6 7 9.55657 .55662 .55666 .55670 .36023 .36026 .36030 .36033 9.55909 .55914 .55918 .55922 .36232 .36336 .36339 .36243 9.56160 .56164 .56169 .56173 .36443 .36445 .36449 .36453 9.56410 .56414 .56418 .56422 .36652 .36656 .36659 .36663 9.56658 .56663 .56667 .56671 .36863 .36866 .36869 .36873 9 10 11 9.55674 .55678 .55683 .55687 .36036 .36040 .36043 .36047 9.55926 .55930 .55935 .55939 .36346 .36350 .36253 .36257 9.56177 .56181 .56185 .56189 .36456 .36459 .36463 .36466 9.56426 .56431 .56435 .56439 .36666 .36670 .36673 .36677 9.56675 .56679 .56683 .56687 .36877 .36880 .36884 .36887 52 51 50 49 + 3' 13 14 15 9.55691 .55695 .55699 .55704 .36030 .36054 .36057 .36061 9.55943 .55947 .55951 .55955 .36360 .36364 .36367 .36371 9.56194 .56198 .56202 .56206 .36470 .36473 .36477 .36480 9.56443 .56447 .56451 .56456 .36680 .36684 .36687 .38691 9.56692 .56696 .56700 .56704 .36891 .36894 .36898 .36901 48 47 46 45 + *^ 17 18 19 9.55708 .55712 .55716 .55721 .36064 .36068 .38071 .36075 9.55960 .55964 .55968 .55972 .36374 .36378 .36381 .36385 9.56210 .56214 .56219 .56223 .36484 .36487 .36491 .36494 9.56460 .56464 .56468 .56472 .36694 .36698 .36701 .36705 9.56708 .56712 .56716 .56720 .36905 .36908 .36913 .36915 44 43 42 41 + 5' 21 22 23 9.55725 .55729 .55733 .55737 .36078 .36083 .36085 .36089 9.55976 .55981 .55985 .55989 .36388 .36393 .36395 .36399 9.56227 .56231 .56235 .56239 .36498 .36501 .36505 .36508 9.56476 .56480 .56485 .56489 .36708 .38712 .36715 .36719 9.56725 .56729 .56733 .56737 .36919 .36933 .36926 .36939 40 39 38 37 36 35 34 S3 + 6' 25 26 27 9.55742 .55746 .55750 .55754 .36093 .36096 .36099 .36103 9.55993 .55997 .56001 .56006 .36303 .36306 .36309 .36313 9.56244 .56248 .56252 .56256 .36513 .36515 .36519 .36533 9.56493 .56497 .56501 .56505 .36722 .36736 .36739 .36733 9.56741 .56745 .56749 .56753 .36933 .36936 .36940 .36943 + r 29 SO SI 9.55758 .55763 .55767 .55771 .36106 .36110 .36113 .36117 9.56010 .56014 .56018 .56022 .36316 .36330 .36333 .36337 9.56260 .56264 .56269 .56273 .36536 .36539 .36533 .36536 9.56509 .56514 .56518 .56522 .36736 .36740 .36743 .36747 9.56758 .56762 .56766 .56770 .36947 .36950 .36954 .36957 32 31 30 29 + 8' S3 S4 S5 9.55775 .55779 .55784 .55788 .36120 .36134 .36137 .36131 9.56027 .56031 .56035 .56039 .36330 .36334 .36337 .36341 9.56277 .56281 .56285 .56289 .36549 .36543 .36547 .36551 9.56526 .56530 .56534 .56538 .36750 .36754 .36757 .36761 9.56774 .56778 .56782 .56786 .36961 .36964 .36968 .36971 28 27 26 25 -f 9^ S7 S8 S9 9.55792 .55796 .55800 .55805 .36134 .36138 .36141 .36145 9.56043 .56047 .56052 .56056 .36344 .36348 .36351 .36355 9.56294 .56298 .56302 .56306 .36554 .36558 .36561 .36565 9.56543 .56547 .56551 .56555 .36764 .36768 .36771 .36775 9.56791 .56795 .56799 .56803 .36975 .36978 .36983 .36985 24 23 22 21 + W 41 42 43 9.55809 .55813 .55817 .55821 .36148 .36153 .36155 .36159 9.56060 .56064 .56068 .56073 .36358 .36363 .36365 .36368 9.56310 .56314 .56318 .56323 .36568 .36573 .36575 .36579 9.56559 .56563 .56567 .56572 .36778 .36783 .36785 .36789 9.56807 .56811 .56815 .56819 .36989 .36993 .36996 .36999 20 19 18 17 + 11' 45 46 47 9.55826 .55830 .55834 .55838 .36163 .36166 .36169 .36173 9.56077 .56081 .56085 .56089 .36373 .36376 .36379 .36383 9.56327 .56331 .56335 .56339 .36583 .36586 .36589 .36593 9.56576 .56580 .56584 .56588 .36793 .36796 .36799 .36803 9.56824 .56828 .56832 .56836 .37003 .37006 .37010 .37013 16 15 U IS + 12' 49 50 51 9.55842 .55846 .55851 .55855 .36176 .36180 .36183 .36187 9.56093 .56098 .56102 .56106 .36386 .36389 .36393 .36396 9.56343 .56348 .56352 .56356 .36596 .36600 .36603 .36607 9.56592 .56596 .56601 .56605 .36806 .36810 .36813 .36817 9.56840 .56844 .56848 .56852 .37017 .37030 .37034 .37037 12 11 10 9 + 13' 53 54 55 9.55859 .55863 .55867 .55872 .36190 .36194 .36197 .36201 9.56110 .56114 .56118 .56123 .36400 .36403 .36407 .36410 9.56360 .56364 .56368 .56373 .36610 .36614 .36617 .36631 9.56609 .56613 .56617 .56621 .36830 .36834 .36837 .36831 9.56856 .56861 .56865 .56869 .37031 .37034 .37038 .37041 8 7 6 5 + 14' 57 58 59 9.55876 .55880 .55884 .55888 .36304 .36308 .36211 .36215 9.56127 .56131 .56135 .56139 .36414 .36417 .36421 .36424 9.56377 .56381 .56385 .56389 .36634 .36638 .36631 .36635 9.56625 .56630 .56634 .56638 .36834 .36838 .36841 .36845 9.56873 .56877 .56881 .56885 .37045 .37049 .37053 .37055 4 3 2 1 + 15' 9.55893 .3631S 9.56144 .36428 9.56393 .36638 9.56642 .36848 9.56889 .37059 19^ 4m ighsm igh^m ighim 19^ Qm Page 104] TABLE IV. Haversines. s 5ft Om 75° (K 5ft im 750 15/ 5h fro 75° 30' 5ft 5"* 75"* 45' 5h 4m 76° 0' s Log. Hav. Nat. Hav. Log. IIrv. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. 1 s 9.56889 .56893 .56898 .56902 .37059 .37063 .37066 .37070 9.57136 .57140 .57144 .57148 .37370 .37373 .37377 .37280 9.57381 .57385 .57389 .57393 .37481 .37485 .37488 .37493 9.57625 .57629 .57633 .57637 .37693 .37696 .37699 .37703 9.57868 .57872 .57876 .57881 .37904 .37907 .37911 .37914 6Q 59 58 57 56 55 54 53 + r 5 6 7 9.56906 .56910 .56914 .56918 .37073 .37077 .37080 .37084 9.57152 .57156 .57160 .57165 .37384 .37387 .37391 .37395 9.57397 .57402 .57406 .57410 .37495 .37499 .37503 .37506 9.57642 .57646 .57650 .57654 .37706 .37710 .37713 .37717 9.57885 .57889 .57893 .57897 .37918 .37923 .37925 .37929 + 2' 9 10 11 9.56922 .56926 .56931 .56935 .37087 .37091 .37094 .37098 9.57169 .57173 .57177 .57181 .37398 .37303 .37305 .37309 9.57414 .57418 .57422 .57426 .37509 .37513 .37516 .37530 9.57658 .57662 .57666 .57670 .37731 .37734 .37728 .37731 9.57901 .57905 .57909 .57913 .37933 .37936 .37939 .37943 52 51 50 49 + 3' IS 14 15 9.56939 .56943 .56947 .56951 .37101 .37105 .37108 .37112 9.57185 .57189 .57193 .57197 .37313 .37316 .37319 .37333 9.57430 .57434 .57438 .57442 .37533 .37537 .37530 .37534 9.57674 .57678 .57682 .57686 .37735 .37738 .37743 .37745 9.57917 .57921 .57925 .57929 .37946 .37950 .37953 .37957 48 47 46 45 + 4' 17 18 19 9.56955 .56959 .56963 .56968 .37115 .37119 .37133 .37126 9.57201 .57205 .57210 .57214 .37336 .37330 .37333 .37337 9.57446 .57450 .57454 .57459 .37537 .37541 .37544 .37548 9.57690 .57694 .57698 .57702 .37749 .37753 .37756 .37759 9.57933 .57937 .57941 .57945 .37960 .37964 .37967 .37971 44 43 42 41 + 5' 21 22 23 9.56972 .56976 .56980 .56984 .37139 .37133 .37136 .37140 9.57218 .57222 .57226 .57230 .37340 .37344 .37347 .37351 9.57463 .57467 .57471 .57475 .37551 .37555 .37558 .37563 9.57706 .57711 .57715 .57719 .37763 .37766 .37770 .37773 9.57949 .57953 .57957 .57961 .37974 .37978 .37983 .37985 40 39 38 31 + 6' 25 26 27 9.56988 .56992 .56996 .57000 .37143 .37147 .37150 .37154 9.57234 .57238 .57242 .57246 .37354 .37358 .37361 .37365 9.57479 .57483 .57487 .57491 .37566 .37569 .37573 .37576 9.57723 .57727 .57731 .57735 .37777 .37780 .37784 .37788 9.57965 .57969 .57973 .57977 .37989 .37993 .37996 .37999 36 35 34 33 + r 29 30 31 9.57005 .57009 .57013 .57017 .37157 .37161 .37164 .37168 9.57250 .57255 .57259 .57263 .37368 .37373 .37375 .37379 9.57495 .57499 .57503 .57507 .37580 .37583 .37587 .37590 9.57739 .57743 .57747 .57751 .37791 .37794 .37798 .37803 9.57981 .57986 .57990 .57994 .38003 .38006 .38010 .38013 32 31 30 29 + 8' 33 34 35 9.57021 .57025 .57029 .57033 .37171 .37175 .37179 .37183 9.57267 .57271 .57275 .57279 .37383 .37386 .37389 .37393 9.57511 .57516 .57520 .57524 .37594 .37597 .37601 .37604 9.57755 .57759 .57763 .57767 .37805 .37809 .37813 .37816 9.57998 .58002 .58006 .58010 .38017 .38030 .38034 .38037 28 21 26 25 + 9" 37 38 39 9.57037 .57042 .57046 .57050 .37186 .37189 .37193 .37196 9.57283 .57287 .57291 .57295 .37397 .37400 .37404 .37407 9.57528 .57532 .57536 .57540 .37608 .37611 .37615 .37618 9.57771 .57775 .57779 .57783 .37819 .37833 .37836 .37830 9.58014 .58018 .58022 .58026 .38031 .38034 .38038 .38043 24 23 22 21 20 19 18 17 + W 41 42 43 9.57054 .57058 .57062 .57066 .37300 .37303 .37307 .37310 9.57299 .57304 .57308 .57312 .37411 .37414 .37418 .37431 9.57544 .57548 .57552 .57556 .37633 .37635 .37639 .37633 9.57787 .57792 .57796 .57800 .37833 .37837 .37840 .37844 9.58030 .58034 .58038 .58042 .38045 .38049 .38053 .38056 + U' ■'^ 46 47 9.57070 .57074 .57078 .57083 .37314 .37317 ,37331 .37334 9.57316 .57320 .57324 .57328 .37435 .37438 .37433 .37435 9.57560 .57564 .57568 .57572 .37636 .37639 .37643 .37647 9.57804 .57808 .57812 .57816 .37847 .37851 .37855 .37858 9.58046 .58050 .58054 .58058 .38059 .38063 .38066 .38070 16 15 14 13 + 13' 49 50 51 9.57087 .57091 .57095 .57099 .37338 .37231 .37335 .37238 9.57332 .57336 .57340 .57344 .37439 .37443 .37446 .37449 9.57577 .57581 .57585 .57589 .37650 .37654 .37657 .37661 9.57820 .57824 .57828 .57832 .37863 .37865 .37869 .37873 9.58062 .58066 .58070 .58074 .38073 .38077 .38080 .38084 12 11 10 9 + 13' 53 54 55 + 14' 57 58 59 9.57103 .57107 .57111 .57115 .37343 .37345 .37349 .37353 9.57348 .57353 .57357 .57361 .37453 .37456 .37460 .37463 9.57593 .57597 .57601 .57605 .37664 .37668 .37671 .37675 9.57836 .57840 .57844 .57848 .37876 .37879 .37883 .37886 9.58078 .58082 .58086 .58090 .38087 .38091 .38095 .38098 8 7 6 5 9.57119 .57124 .57128 .57132 .37356 .37359 .37363 .37366 9.57365 .57369 .57373 .57377 .37467 .37470 .37474 .37477 9.57609 .57613 .57617 .57621 .37678 .37683 .37685 .37689 9.57852 .57856 .57860 .57864 .37890 .37893 .37897 .37900 9.58094 .58098 .58102 .58106 .38103 .38105 .38109 .38113 4 3 S 1 + 15' 9.57136 .37370 9.57381 .37481 9.57625 .37693 9.57868 .37904 9.58110 .38116 18h 59m 15ft 55m 18^ 57m 18^ 56^ i5ft 55m 1 TABLE IV. [Page 106 HaversincB. s 5^5mU°W 1 5h 6m 76° 30' | 5h jm 76° 45/ 5A 8m 77° 0' | 571577177015/ 1 Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. s 1 2 3 9.58110 .58114 .58118 .58122 .38116 .38119 .38133 .38126 9.58351 .58355 .58359 .58363 .38328 .38331 .38335 .38338 9.58591 .58595 .58599 .58603 .38540 .38544 .38547 .38551 9.58830 .58834 .58838 .58842 .38752 .38756 .38760 .38763 9.59068 .59072 .59076 .59079 .38965 .38969 .38972 .38976 60 59 58 57 + r 5 6 7 9.58126 .58131 .58135 .58139 .38130 .38133 .38137 .38140 9.58367 .58371 .58375 .58379 .38343 .38345 .38349 .38353 9.58607 .58611 .58615 .58619 .38554 .3a558 .38561 .38565 9.58846 .58850 .58854 .58858 ..?8767 .38770 .38774 .38777 9.59083 .59087 .59091 .59095 .38979 .38983 .38986 .38990 56 55 54 53 + 2^ 9 10 11 9.58143 .58147 .58151 .58155 .38144 .38148 .38151 .38155 9.58383 .58387 .58391 .58395 .38356 .38360 .38363 .38367 9.58623 .58627 .58631 .58635 .38568 .38572 .38575 .38579 9.58862 .58866 .58870 .58874 .38781 .38784 .38788 .38791 9.59099 .59103 .59107 .59111 .38994 .38997 .39001 .39004 52 51 50 49 + 3^ 13 14 15 9.58159 .58163 .58167 .58171 .38158 .38163 .38165 .38169 9.58399 .58403 .58407 .58411 .38370 .38374 .38377 .38381 9.58639 .58643 .58647 .58651 .38583 .38586 .38590 .38593 9.58878 .58882 .58885 .58889 .38795 .38799 .38803 .38806 9.59115 .59119 .59123 .59127 .39008 .39011 .39015 .39018 48 47 46 45 + 4^ 17 IS 19 9.58175 .58179 .58183 .58187 .38173 .38176 .38179 .38183 9.58415 .58419 .58423 .58427 .38384 .38388 .38391 .38395 9.58655 .58659 .58663 .58667 .38597 .38600 .38604 .38607 9.58893 .58897 .58901 .58905 .38809 .38813 .38816 .38830 9.59131 .59135 .59139 .59143 .39033 .39035 .39029 .39033 U 43 42 41 + 5^ 21 22 23 9.58191 .58195 .58199 .58203 .38186 .38190 .38193 .38197 9.58431 .58435 .58439 .58443 .38398 .38403 .38406 .38409 9.58671 .58675 .58679 .58683 .38611 .38614 .38618 .38631 9.58909 .58913 .58917 .58921 .38833 .38837 .38830 .38834 9.59147 .59151 .59155 .59158 .39036 .39040 .39043 .39047 40 39 38 37 + 6' 25 26 27 9.58207 .58211 .58215 .58219 .38300 .38304 .38308 .38311 9.58447 .58451 .58455 .58459 .38413 .38416 .38430 .38433 9.58687 .58691 .58695 .58699 .38635 .38638 .38632 .38636 9.58925 .58929 .58933 .58937 .38837 .38841 .38845 .38848 9.59162 .59166 .59170 .59174 .39050 .39054 .3tK»7 .39061 36 35 34 33 + r 29 SO 31 9.58223 .58227 .58231 .58235 .38315 .38318 .38333 .38335 9.58463 .58467 .58471 .58475 .38437 .38430 .38434 .38437 9.58703 .58707 .58711 .58715 .38639 .38643 .38646 .38650 9.58941 .58945 .58949 .58953 .38853 .38855 .38859 .38863 9.59178 .59182 .59186 .59190 .39064 .39068 .39073 .39075 32 31 30 29 + 8- 33 34 35 9.58239 .58243 .58247 .58251 .38339 .38333 .38336 .38339 9.58479 .58483 .58487 .58491 .38441 .38444 .38448 .38451 9.58719 .58723 .58727 .58731 .38653 .38657 .38660 .38664 9.58957 .58961 .58965 .58969 .38866 .38869 .38873 .38876 9.59194 .59198 .59202 .59206 .39079 .39083 .39086 .39089 28 27 26 25 + r 37 38 39 9.58255 .58259 .58263 .58267 .38343 .38346 .38350 .38354 9.58495 .58499 .58503 .58507 .38455 .38459 .38463 .38466 9.58735 .58739 .58742 .58746 .38667 .38671 .38675 .38678 9.58973 .58977 .58981 .58985 .38880 .38884 .38887 .38891 9.59210 .59214 .59218 .59222 .39093 .39096 .39100 .39103 24 23 22 21 + W 41 42 43 9.58271 .58275 .58279 .58283 .38357 .38361 .38364 .38368 9.58511 .58515 .58519 .58523 .38469 .38473 .38476 .38480 9.58750 .58754 .58758 .58762 .38682 .38685 .38689 .38693 9.58989 .58992 .58996 .59000 .38894 .38898 .38901 .38905 9.59225 .59229 .59233 .59237 .39107 .39111 .39114 .39118 20 19 18 17 + 11^ 45 46 47 9.58287 .58291 .58295 .58299 .38371 .38375 .38378 .38383 9.58527 .58531 .58535 .58539 .38483 .38487 .38490 .38494 9.58766 .58770 .58774 .58778 .38696 .38699 .38703 .38706 9.59004 .59008 .59012 .59016 .38908 .38913 .38915 .38919 9.59241 .59245 .59249 .59253 .39131 .39135 .39138 .39133 16 15 14 IS + ir 49 50 51 9.58303 .58307 .58311 .58315 .38385 .38389 .38393 .38396 9.58543 .58547 .58551 .58555 .38498 .38501' .38505 .38508 9.58782 .58786 .58790 .58794 .38710 .38713 .38717 .38731 9.59020 .59024 .59028 .59032 .38933 .38936 .38930 .38933 9.59257 .59261 .59265 .59269 .39135 .39139 .39143 .39146 12 11 10 9 + 13^ 53 54 55 9.58319 .58323 .58327 .58331 .38399 .38303 .38307 .38310 9.58559 .58563 .58567 .58571 .38513 .38515 .38519 .38533 9.58798 .58802 .58806 .58810 .38734 .38738 .38731 .38735 9.59036 .59040 .59044 .59048 .38937 .38940 .38944 .38947 9.59273 .59277 .59281 .59285 .39150 .39153 .39157 .39160 8 4 6 5 + W 57 58 59 9.58335 .58339 .58343 .58347 .38314 .38317 .38321 .38334 9.58575 .58579 .58583 .58587 .38536 .38539 .38533 .38536 9.58814 .58818 .58822 .58826 .38738 .38743 .38745 .38749 9.59052 .59056 .59060 .59064 .38951 .38954 .38958 .38963 9.59289 .59292 .59296 .59300 .39164 .39167 .39171 .39174 4 3 2 + W 9.58351 .38338 9.58591 .38540 9.58830 .38753 9.59068 .38965 9.59304 .39178 18^ 54"» 18^ 53m 18^ 52m 18h oim 18h 50m Page 106] TABLE IV. naversines. s 5fe iO™ 77° 30' 5fe nm 77° 45' 5h 12m 78° C 5A 13m 78° 15' 5h 14m 78° 30' s Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. 1 2 3 9.59304 .59308 .59312 .59316 .39178 .39183 .39185 .39189 9.59540 ..59544 .59548 .59552 .39391 .39395 .39398 .39402 9.59774 .59778 .59782 .59786 .39604 .39608 .39612 .39615 9.60008 .60012 .60016 .60020 .39818 .39821 .39825 .39829 9.60240 .60244 .60248 .60252 .40032 .40035 .40039 .40042 60 59 58 57 + r 5 6 7 9.59320 .59324 .59328 .59332 .39193 .39196 .39199 .39203 9.59556 .59559 .59563 .59567 .39405 .39409 .39412 .39416 9.59790 .59794 .59798 .59802 .39619 .39622 .39626 .39629 9.60023 .60027 .60031 .60035 .39832 .39836 .39839 .39843 9.60256 .60260 .60263 .60267 .40046 .40049 .40053 .40057 56 55 54 53 + 3' 9 10 11 9.59336 .59340 .59344 .59348 .39206 .39210 .39214 .39317 9.59571 .59575 .59579 .59583 .39420 .39423 .39427 .39430 9.59806 .59809 .59813 .59817 .39633 .39636 .39640 .39644 9.60039 .60043 .60047 .60051 .39846 .39850 .39854 .39857 9.60271 .60275 .60279 .60283 .40060 .40064 .40067 .40071 52 51 50 4a 48 47 46 45 + 3' 13 14 15 9.59351 .59355 .59359 .59363 .39221 .39224 .39238 .39331 9.59587 .59591 .59595 .59599 .39434 .39437 .39441 .39444 9.59821 .59825 .59829 .59833 .39647 .39651 .39654 .39658 9.60054 .60058 .60062 .60066 .39861 .39884 .39868 .39871 9.60287 .60291 .60294 .60298 .40074 .40078 .40081 .40085 + 4' 17 18 19 9.59367 .59371 .59375 .59379 .39335 .39338 .39242 .39245 9.59602 .59606 .59610 .59614 .39448 .39451 .39455 .39459 9.59837 .59841 .59845 .59848 .39661 .39665 .39668 .39672 9.60070 .60074 .60078 .60082 .39875 .39878 .39882 .39886 9.60302 .60306 .60310 .60314 .40089 .40092 .40096 .40099 U 43 42 41 + 5' 21 22 23 9.59383 .59387 .59391 .59395 .39249 .39253 .39256 .39260 9..59618 .59622 .59626 .59630 .39462 .3946G .39469 .39473 9.59852 .59856 .59860 .59864 .39676 .39679 .39683 .39686 9.60085 .60089 .60093 .60097 .39889 .39893 .39896 .39900 9.60318 .60321 .60325 .60329 .40103 .40106 .40110 .40114 40 39 38 37 + ^ 25 26 5 27 9.59399 .59403 ( .59406 .59410 .39263 .39267 .39270 .39274 9.59634 .59638 .59642 .59646 .39476 .39480 .39484 .39487 9.59868 .59872 .59876 .59880 .39890 .39693 .39697 .39700 9.60101 .60105 .60109 .60113 .39903 .39907 .39910 .39914 9.60333 .60337 .60341 .60345 .40117 .40121 .40124 .40128 36 35 34 33 + y 29 30 31 9.59414 .59418 .59422 .59426 .39277 .39281 .39285 .39288 9.59649 .59653 .59657 .59661 .39491 .39494 .39498 .39501 9.59883 .59887 .59891 .59895 .39704 .39708 .39711 .39715 9.60116 .60120 .60124 .60128 .39918 .39921 .39925 .39928 9.60348 .60352 .60356 .60360 .40131 .40135 .40139 .40142 32 31 30 29 + 8' 33 34 35 9.59430 .59434 .59438 .59442 .39292 .39295 .39299 .39302 9.59665 ..59669 .59673 .59677 .39505 .39508 .39512 .39516 9.59899 .59903 .59907 .59911 .39718 .39722 .39725 .39729 9.60132 .60136 .60140 .60144 .39932 .39935 .39939 .39943 9.60364 .60368 .60372 .60375 .40146 .40149 .40153 .40156 28 27 26 25 + 9^ 37 38 39 9.59446 .59450 .59454 .59458 .39306 .39309 .39313 .39317 9.59681 .59685 .59688 .59692 .39519 .39523 .39526 .39530 9.59915 .59918 .59922 .59926 .39733 .39736 .39739 .39743 9.60147 .60151 .60155 .60159 .39946 .39950 .39953 .39957 9.60379 .60383 .60387 .60391 .40160 .40163 .40167 .40171 24 23 22 21 + W 41 42 43 9.59461 .59465 .59469 .59473 .39330 .39324 .39327 .39331 9.59696 .59700 .59704 .59708 .39533 .39537 .39540 .39544 9.59930 .59934 .59938 .59942 .39746 .39750 .39754 .39757 9.60163 .60167 .60171 .60175 .39960 .39964 .39967 .39971 9.60395 .60399 .60402 .60406 .40174 .40178 .40181 .40185 20 19 18 17 + 11' 45 46 47 9.59477 .59481 .59485 .59489 .39334 .39338 .39341 .39345 9.59712 .59716 .59720 .59724 .39548 .39551 .39555 .39558 9.59946 .59950 .59953 .59957 .39761 .39765 '39768 .39772 9.60178 .60182 .60186 .60190 .39975 .39978 .39982 .39985 9.60410 .60414 .60418 .60422 .40188 .40192 .40196 .40199 16 15 14 13 + 12' 49 50 51 9.59493 .59497 .59501 .59505 .39348 .39352 .39356 .39359 9.59728 .59731 .59735 .59739 .39562 .39565 .39569 .39572 9.59961 .59965 .59969 .59973 .39775 .39779 .39782 .39786 9.60194 .60198 .60202 .60206 .39989 .39992 .39996 .40000 9.60426 .60429 .60433 .60437 .40203 .40206 .40210 .40213 12 11 10 9 + 13' 53 54 55 9.59508 .59512 ..59516 .59520 .39363 .39366 .39370 .39373 9.59743 .59747 .59751 .59755 .39576 .39580 .39583 .39587 9.59977 .59981 .59985 .59988 .39789 .39793 .39796 .39800 9.60209 .60213 .60217 .60221 .40003 .40007 .40010 .40014 9.60441 .60445 .60449 .60452 .40217 .40220 .40224 .40238 8 7 6 5 4 3 2 1 + 14' .57 59 9.59524 .59528 .59532 .59536 .39377 .39380 .39384 .39388 9.59759 .59763 .59767 .59770 .39590 .39594 .39597 .39601 9.59992 .59996 .60000 .60004 .39803 .39807 .39811 .39814 9.60225 .60229 .60233 .60236 .40017 .40021 .40034 .40038 9.60456 .60460 .60464 .60468 .40231 v40335 .40238 .40242 + 15' 9.59540 .39391 9.59774 .39604 9.60008 .39818 9.60240 .40033 9.60472 .40345 18^ 49m 18^ 48^ isn 4Tm 18h 46m 18fi45m TABLE IV. [Page 107 Haversines. s 5 A J.5m 78° 45' ofi 16^ 79° 0' 5h 17m 790 15' 5h ISm 79° 30' 5h 19m 79° iy s Log. Hav. Nat. Hav. Log. Hav. Nat. Hav Log. Hav Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. 1 2 3 9.60472 .60476 .60479 .60483 .40345 .40249 .40253 .40256 9.60702 .60706 .60710 .60714 .40460 .40483 .40467 .40470 9.60931 .60935 .60939 .60943 .40674 .40677 .40681 .40885 9.61160 .61164 .61167 .61171 .40888 .40893 .40895 .40899 9.61387 .61391 .61395 .61399 .41103 .41106 .41110 .41114 60 59 58 57 + 1' 5 6 7 9.60487 .60491 .60495 .60499 .40280 .40283 .40387 .40270 9.60717 .60721 .60725 .60729 .40474 .40477 .40481 .40485 9.60947 .60951 .60954 .60958 .40888 .40692 .40695 .40899 9.61175 .61179 .61183 .61186 .40903 .40906 .40910 .40913 9.61402 .61406 .61410 .61414 .41117 .41121 .41124 .41128 56 55 54 53 + ^ 9 10 11 9.60502 .60506 .60510 .60514 ,40274 .40277 .40281 .40285 9.60733 .60737 .60740 .60744 .40488 .40493 .40495 .40499 9.60962 .60966 .60970 .60973 .40702 .40708 .40710 .40713 9.61190 .61194 .61198 .61202 .40917 .40930 .40934 .40938 9.61417 .61421 .61425 .61429 .41131 .41135 .41139 .41143 52 51 50 49 + 3' IS 14 15 9.60518 .60522 .60526 .60529 .40288 .40393 .40295 .40299 9.60748 .60752 .60756 .60760 .40502 .40506 .40510 .40513 9.60977 .60981 .60985 .60989 .40717 .40720 .40724 .40727 9.61205 .61209 .61213 .61217 .40931 .40935 .40938 .40943 9.61433 .61436 .61440 .61444 .41146 .41149 .41153 .41156 48 47 46 45 + i' 17 18 19 9.60533 .60537 .60541 .60545 .40303 .40306 .40310 .40313 9.60763 .60767 .60771 .60775 .40517 .40520 .40524 .40537 9.60992 .60996 .61000 .61004 .40731 .40735 .40738 .40743 9.61221 .61224 .61228 .61232 .40945 .40949 .40953 .40956 9.61448 .61451 .61455 .61459 .41160 .41164 .41167 .41171 U 43 42 41 + 5' 21 22 23 9.60549 .60552 .60556 .60560 .40317 .40320 .40324 .40338 9.60779 .60783 .60786 .60790 ,40531 .40535 .40538 .40543 9.61008 .61012 .61015 .61019 .40745 .40749 '40753 .40756 9.61236 .61240 .61243 .61247 .40980 .40963 .40967 .40970 9.61463 .61467 .61470 .61474 .41174 .41178 .41183 .41185 40 39 38 37 + 6' 25 26 27 9.6056^ .60568 .60572 .60576 .40331 .40335 .40338 .40343 9.60794 .60798 .60802 .60805 .40545 .40549 .40553 .40556 9.61023 .61027 .61031 .61034 .40760 .40763 .40767 .40770 9.61251 .61255 .61258 .61262 .40974 .40978 .40981 .40985 9.61478 .61482 .61485 .61489 .41189 .41193 .41198 .41199 36 35 34 33 + r 29 • 30 1 31 ' 9.60579 .60583 .60587 .60591 .40345 .40349 .40353 .40356 9.60809 .60813 .60817 .60821 .40560 .40563 .40567 .40570 9.61038 .61042 .610i6 .61050 .40774 .40777 .40781 .40785 9.61266 .61270 .61274 .61277 .40988 .40993 .40996 .40999 9.61493 .61497 .61500 .61504 .41303 .41307 .41310 .41314 32 sli 30 29 + 8" 33 - 34 ' 35 ' 9.60595 .60599 .60602 .60606 .40360 .40363 .40367 .40370 9.60825 .60828 .60832 .60836 .40574 .40577 .40581 .40585 9.61053 .61057 .61061 .61065 .40788 .40793 .40795 .40799 9.61281 .61285 .61289 .61293 .41003 .41006 .41010 .41013 9.61508 .61512 .61516 .61519 .41317 .41331 .41225 .41228 28 27 26 25 + 9^ 37 - 38 39 9.60610 .60614 .60618 .60622 .40374 .40377 .40381 .40385 9.60840 .60844 .60847 .60851 .40588 .40593 .40595 .40599 9.61069 .61072 .61076 .61080 .40803 .40806 .40810 .40813 9.61296 .61300 .61304 .61308 .41017 .41031 .41024 .41028 9.61523 .61527 .61531 .61534 .41333 .41335 .41339 .41343 24 23 22 21 + 1(K 42 43 ' 9.60625 .60629 .60633 .60637 .40388 .40393 .40395 .40399 9.60855 .60859 .60863 .60867 .40603 .40606 .40610 .40613 9.61084 .61088 .61091 .61095 .40817 .40820 .40834 .40827 9.61312 .61315 .61319 .61323 .41031 .41035 .41039 .41042 9.61538 .61542 .61546 .61549 .41346 .41250 .41253 .41257 20 19 18 17 + 11' 45 46 47 9.60641 .60645 .60648 .60652 .40402 .40406 .40410 .40413 9.60870 .60874 .60878 .60882 .40817 .40620 .40634 .40637 9.61099 .61103 .61107 .61110 .40831 .40835 .40838 .40842 9.61327 .61330 .61334 .61338 .41046 .41049 .41053 .41056 9.61553 .61557 .61561 .61565 .41280 .41264 .41267 .41371 16 15 14 13 + 13' 49 ' 50 51 ■ 9.60656 .60660 .60664 .60668 .40417 .40420 .40424 .40427 9.60886 .60890 .60893 .60897 .40831 .40835 .40838 .40843 9.61114 .61118 .61122 .61126 .40845 .40849 .40853 .40856 9.61342 .61346 .61349 .61353 .41060 .41063 .41067 .41071 9.61568 .61572 .61576 .61580 .41375 .41278 .41382 .41285 12 11 10 9 + 13' 53 54 55 9.60671 .60675 .60679 .60683 .40431 .40434 .40438 .40442 9.60901 .60905 .60909 .60912 .40845 .40649 .40652 .40656 9.61129 .61133 .61137 .61141 .40880 .40863 .40887 .40870 9.61357 .61361 .61364 .61368 .41074 .41078 .41082 .41085 9.61583 .61587 .61591 .61595 .41289 .41293 .41298 .41300 8 7 6 5 4 3 2 1 + 14' 57 ■' 55 59 9.60687 .60691 .60694 .60698 .40445 .40449 .40453 .40456 9.60916 .60920 .60924 .60928 .40660 .40683 .40867 .40670 9.61145 .61148 .61152 .61156 .40874 i .40878 .40881 .40885 9.61372 .61376 .61380 .61383 .41089 .41092 .41096 .41099 9.61598 .61602 .61606 .61610 .41303 .41307 .41310 .41314 + 15' 9.60702 .40460 9.60931 .40674 9.61160 .40888 9.61387 .41103 9.61614 .41318 18^ 44"" 1 ISh 43m 18h 42^ 1 18h 4im 18h 40^ 1 Page 108] TABLE IV. Haversines. s Sh 20m 80° (K 5h 2im 80° 15' 5h 22m 80° 30' 5h 23m 80° 45' 5h 24^ 81° 0' s Log. Hav Nat. Hav Log. Hav. Nat. Hav Log. Hav Nat. Hav Log. Hav Nat. Hav Log. Hav Nat. Hav. 1 2 3 9.61614 .61617 .61621 .61625 .41318 .41331 .41335 .41338 9.61839 .61843 .61846 .61850 .41533 .41536 .41540 .41543 9.62063 .62067 .62071 .62074 .41748 .41751 .41755 .41758 9.62287 .62290 .62294 .62298 .41963 .41966 .41970 .41974 9.62509 .62513 .62516 .62520 .43178 .43183 .43185 .43189 60 59 58 57 + r 5 6 7 9.61629 .61632 .61636 .61640 .41333 .41335 .41339 .41343 9.61854 .61858 .61861 .61865 .41547 .41550 .41554 .41558 9.62078 .62082 .62086 .62089 .41763 .41766 .41769 .41773 9.62301 .62305 .62309 .62313 .41977 .41981 .41984 .41988 9.62524 .62527 .62531 .62535 .43193 .43196 .43300 .43303 56 55 54 53 52 51 50 49 48 47 46 45 + 2' 9 10 11 9.61644 .61647 .61651 .61655 .41346 .41350 .41353 .41357 9.61869 .61873 .61876 .61880 .41661 .41565 .41568 .41573 9.62093 .62097 .62100 .62104 .41776 .41780 .41783 .41787 9.62316 .62320 .62324 .62327 .41993 .41995 .41999 .43003 9.62538 .62542 .62546 .62550 .43307 .43311 .43314 .43218 + 3^ 13 14 15 9.61659 .61662 .61666 .61670 .41361 .41364 .41368 .413?! 9.61884 .61888 .61891 .61895 .41576 .41579 .41583 .41586 9.62108 .62112 .62115 .62119 9.62123 .62127 .62130 .62134 .41791 .41794 .41798 ,41801 9.62331 .62335 .62338 .62342 .43006 .43010 .43013 .43017 9.62553 .62557 .62561 .62564 .43231 .43335 .43339 .43333 + 4' 17 18 19 9.61674 .61677 .61681 .61685 .41375 .41378 .41383 .41386 9.61899 .61903 .61906 .61910 .41590 .41593 .41597 .41601 .41805 .41809 .41813 .41816 9.62346 .62350 .62353 .62357 .43030 .43034 .43037 .43031 9.62568 .62572 .62575 .62579 .43336 .43339 .43343 .43347 44 43 42 41 + 5^ 21 22 23 9.61689 .61692 .61696 .61700 .41389 .41393 .41396 .41400 9.61914 .61917 .61921 .61925 .41604 .41608 .41611 .41615 9.62138 .62141 .62145 .62149 .41819 .41833 .41837 .41830 9.62361 .62364 .62368 .62372 .43035 .43038 .43043 .43045 .43049 .43053 .43056 .43060 9.62583 .62586 .62590 .62594 .43350 .43354 .43357 .43361 40 39 38 37 + 6' 25 26 27 9.61704 .61708 .61711 .61715 .41404 .41407 .41411 .41414 9.61929 .61932 .61936 .61940 .41619 .41633 .41626 .41639 9.62153 .62156 .62160 .62164 .41834 .41837 .41841 .41844 9.62376 .62379 .62383 .62387 9.62598 .62601 .62605 .62609 .43364 .43268 .42272 .43375 36 35 34 33 + r 29 30 31 9.61719 .61723 .61726 .61780 .41418 .41431 .41435 .41439 9.61944 .61947 .61951 .61955 .41633 .41636 .41640 .41644 9.62168 .62171 .62175 .62179 .41848 .41853 .41855 .41859 9.62390 .62394 .62398 .62402 .43063 .43067 .43071 .43074 9.62612 .62616 .62620 .62623 .43379 .43383 .43386 .42290 32 31 SO 29 + 8^ 33 34 35 9.61734 .61738 .61741 .61745 .41433 .41436 .41439 .41443 9.61959 .61962 .61966 .61970 .41647 .41651 .41654 .41658 9.62182 .62186 .62190 .62194 .41863 .41866 .41870 .41873 9.62405 .62409 .62413 .62416 .43078 .43081 .43085 .43089 9.62627 .62631 .62634 .62638 .43393 .43397 .43309 .43304 28 27 26 25 + 9^ 37 38 39 9.61749 .61753 .61756 .61760 .4144^ .41450 .41454 .41457 9.61974 .61977 .61981 .61985 .41663 .41665 .41669 .41673 9.62197 .62201 .62205 .62208 .41877 .41880 .41884 .41888 9.62420 .62424 .62427 .62431 .43093 .43096 .43099 .43103 9.62642 .62646 .62649 .62653 .43308 .43311 .43315 .43318 24 23 22 21 + W 41 42 43 9.61764 .61768 .61771 .61775 .41461 .41464 .41468 .41473 9.61989 .61992 .61996 .62000 .41676 .41679 .41683 .41687 9.62212 .62216 .62220 .62223 .41891 .41895 .41898 .41903 9.62435 .62439 .62442 .62446 .43106 .43110 .43114 .43117 9.62657 .62660 .62664 .62668 .43333 .43336 ,43339 .43333 20 19 18 17 + ir 45 46 47 9.61779 .61783 .61786 .61790 .41475 .41479 .41483 .41486 9.62003 .62007 .62011 .62015 .41690 .41694 .41697 .41701 9.62227 .62231 .62234 .62238 .41905 .41909 .41913 .41916 9.62450 .62453 .62457 .62461 .43131 .43134 .43138 .43133 9.62671 .62675 .62679 .62682 .43336 .43340 .43344 .43347 16 15 14 13 + VA" 49 50 51 9.61794 .61798 .61801 .61805 .41490 .41493 .41497 .41500 9.62018 .62022 .62026 .62030 .41705 .41708 .41713 .41715 9.62242 .62246 .62249 .62253 .41930 .41933 .41937 .41931 9.62464 .62468 .62472 .62476 .43135 .43139 .43143 .43146 9.626S6 .62690 .62693 .62697 .43351 .43354 .43358 .43361 12 11 10 9 + l3^ 53 54 55 9.61809 .61813 .61816 .61820 .41504 .41507 .41511 .41515 9.62033 .62037 .62041 .62045 .41719 .41733 .41736 .41730 9.62257 .62261 .62264 .62268 .41934 .41938 .41941 .41945 9.62479 .62483 .62487 .62490 .43150 .43153 .43157 .43160 9.62701 .62704 .62708 .62712 .43365 .43369 .43373 .43376 8 7 6 5 + 14' 57 58 59 9.61824 .61828 .61831 .61835 .41518 .41533 .41535 .41539 9.62048 .62052 .62056 .62059 .41733 .41737 .41740 .41744 9.62272 .62275 .62279 .62283 .41949 .41953 .41956 .41959 9.62494 .62498 .62501 .62505 .43164 .43168 .43171 .43175 9.62716 .62719 .62723 .62727 .43379 .43383 .43387 .43390 4 3 2 1 + W 9.61839 .41533 9.62063 .41748 9,62287 .41963 9.62509 .43178 9.62730 .43394 18h39m ' 1 IS^SSm 1 18h 37m 1 ISft S6m 18fi S5m 1 TABLE IV. [Page 109 Haversinea. s 5ft f 5m 81° 15' 5h 26m 81° 30' 5h ojm 81° 45' 5h 2ST^ 82° 0' 5h 29m 82° 15' s Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav Nat. Hav. 1 2 S 9.62730 .62734 .62738 .62741 .42394 .42397 .42401 .42405 9.62951 .62954 .62958 .62962 .42610 .42613 .42617 .42620 9.63170 .63174 .63177 .63181 .42825 .42839 .42833 .42836 9.63389 .63392 .63396 .63399 .43041 .43045 .43049 .43052 9.63606 .63610 .63613 .63617 .43257 .43261 .43265 .43268 60 59 58 57 + V 5 6 7 9.62745 .62749 .62752 .62756 .42408 .42412 .42415 .42419 9.62965 .62969 .62973 .62976 .42624 .42628 .42631 .42635 9.63185 .63188 .63192 .63196 .42840 .42843 .42847 .42851 9.63403 .63407 .63410 .63414 .43056 .43059 .43063 .43067 9.63621 .63624 .63628 .63631 .43272 .43275 .43279 .43283 56 55 54 53 + V 9 10 11 9.62760 .62763 .62767 .62771 .42423 .42426 .42430 .42433 9.62980 .62984 .62987 .62991 .42638 .42642 .42645 .42649 9.63199 .63203 .63207 .63210 .42854 .42858 .42861 .42865 9.63418 .63421 .63425 .63429 .43070 .43074 .43077 .43081 9.63635 .63639 .63642 .63646 .43286 .43290 .43293 .43297 52 51 50 49 + 3' 13 14 15 9.62774 .62778 .62782 .62785 .42437 .42441 .42444 .42448 9.62995 .62998 .63002 .63006 .42653 .42656 .42660 .42663 9.63214 .63218 .63221 .63225 .42869 .42872 .42876 .42879 9.63432 .63436 .63439 .63443 .43085 .43988 .43092 .43095 9.63649 .63653 .63657 .63660 .43301 .43304 .43308 .43312 48 47 46 45 + 4' 17 18 19 9.62789 .62793 .62796 .62800 .42451 .42455 .42459 .42462 9.63009 .63013 .63017 .63020 .42667 .42671 .42674 .42678 9.63228 .63232 .63236 .63239 .42883 .42887 .42890 .42894 9.63447 .63450 .63454 .63458 .43099 .43103 .43106 .43110 9.63664 .63668 .63671 .63675 .43315 .43319 .43322 .43326 44 43 42 41 + 5' 21 22 23 9.62804 .62808 .62811 .62815 .42466 .42469 .42473 .42477 9.63024 .63028 .63031 .63035 .42681 .42685 .42689 .42692 9.63243 .63247 .63250 .63254 .42897 .42901 .42905 .42908 9.63461 .63465 .63468 .63472 .43113 .43117 .43121 .43124 9.63678 .63682 .63686 .63689 .43330 .43333 .43337 .43340 40 39 38 37 36 35 34 33 32 31 30 29 + 6' 25 26 27 9.62819 .62822 .62826 .62830 .42480 .42484 .42487 .42491 9.63039 .63042 .63046 .63050 .42696 .42699 .42703 .42707 9.63258 .63261 .63265 .63269 .42912 .42915 .42919 .42923 9.63476 .63479 .63483 .63487 .43128 .43131 .43135 .43139 9.63693 .63696 .63700 .63704 .43344 .43348 .43351 .43355 + r 29 30 31 9.62833 .62837 .62841 .62844 .42494 .42498 .42502 .42505 9.63063 .63057 .63061 .63064 .42710 .42714 .42717 .42721 9.63272 .63276 .63279 .63283 .42926 .42930 .42933 .42937 9.63490 .63494 .63497 .63501 .43142 .43146 .43149 .43153 9.63707 .63711 .63714 .63718 .43358 .43362 .43366 .43369 + 8' 33 34 35 9.62848 .62852 .62855 .62859 .42509 .42512 .42516 .42520 9.63068 .63071 .63075 .63079 .42725 .42728 .42732 .42735 9.63287 .63290 .63294 .63298 .42941 .42944 .42948 .42951 9.63505 .63508 .63512 .63516 .43157 .43160 .43164 .43167 9.63722 .63725 .63729 .63733 .43373 .43376 .43380 .43384 28 27 26 25 + 9' 37 38 39 9.62863 .62866 .62870 .62874 .42523 .42527 .42530 .42534 9.63082 .63086 .63090 .63093 .42739 .42743 .42746 .42750 9.63301 .63305 .63309 .63312 .42955 .42959 .42962 .42966 9.63519 .63523 .63526 .63530 .43171 .43175 .43178 .43182 9.63736 .63740 .63743 .63747 .43387 .43391 .43394 .43398 24 23 22 Ti + W 41 42 43 9.62877 .62881 .62885 .62888 .42538 .42541 .42545 .42548 9.63097 .63101 .63104 .63108 .42753 .42757 .42761 .42764 9.63316 .63320 .63323 .63327 .42969 .42973 .42977 .42980 9.63534 .63537 .63541 .63545 .43185 .43189 .43193 .43196 9.63751 .63754 .63758 .63761 .43402 .43405 .43409 .43412 20 19 18 17 16 15 14 13 + 11' 45 46 47 9.62892 .62896 .62899 .62903 .42552 .42556 .42559 .42563 9.63112 .63115 .63119 .63123 .427«8 .42771 .42775 .42779 9.63330 .63334 .63338 .63341 .42984 .42987 .42991 .42995 9.63548 .63552 .63555 .63559 .43200 .43203 .43207 .43211 9.63765 .63769 .63772 .63776 .43416 .43420 .43423 .43427 + ir 49 50 51 9.62907 .62910 .62914 .62918 .42566 .42570 .42574 .42577 9.63126 .63130 .63134 .63137 .42782 .42786 .42789 .42793 9.63345 .63349 .63352 .63356 .42998 .43002 .43005 .43009 9.63563 .63566 .63570 .63574 .43214 .43218 .43221 .43225 9.63779 .63783 .63787 .63790 .43430 .43434 .43438 .43441 12 11 10 9 8 7 6 5 + 13' 53 54 55 9.62921 .62925 .62929 .62932 .42581 .42584 .42588 .42592 9.63141 .63145 .63148 .63152 .42797 .42800 .42804 .42807 9.63360 .63363 .63367 .63370 .43013 .43016 .43020 .43023 9.63577 .63581 .63584 .63588 .43229 .43232 .43236 .43239 9.63794 .63797 .63801 .63805 .43445 .43448 .43453 .43456 + U' 57 58 59 9.62936 .62940 .62943 .62947 .42595 .42599 .42602 .42606 9.63156 .63159 .63163 .63166 .42811 .42815 .42818 .42822 9.63374 .63378 .63381 .63385 .43027 .43031 .43034 .43038 9.63592 .63595 .63599 .63602 .43243 .43247 .43250 .43254 9.63808 .63812 .63815 .63819 .43459 .43463 .43466 .43470 4 3 2 1 + 15' 9.62951 .42610 9,63170 .42825 9.63389 .43041 9.63606 .43257 9.63823 .43474 18^ 34"^ 18^ 33m 18h 32m. 1 18^ Sim 18^ SOm 1 Page 110] TABLE IV. Haversines. s 5A 30^ 82° 30^ 5hSim 82° 45^ Sh 32m 83° 0^ 5h 33m 83° 15^ 5'iJ4™83°3r 1 s Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav 1 2 S 9.63823 .63826 .63830 .63833 .43474 .43477 .43481 .43485 9.64038 .64042 .64046 .64049 .43690 .43694 .43697 .43701 9.64253 .64256 .64260 .64264 .43907 .43910 .43914 .43917 9.64467 .64470 .64474 .64477 .44123 .44127 .44130 .44134 9.64679 .64683 .64686 .64690 .44340 .44343 .44347 .44351 60 59 58 57 + r 5 6 7 9.63837 .63841 .63844 .63848 .43488 .43493 .43495 .43499 9.64053 .64056 .64060 .64063 .43704 .43708 .43712 .43715 9.64267 .64271 .64274 .64278 .43921 .43925 .43928 .43933 9.64481 .64484 .64488 .64492 .44138 .44141 .44145 .44148 9.64694 .64697 .64701 .64704 .44354 .44358 .44362 .44365 56 55 54 53 + r 9 10 11 9.63851 .63855 .63859 .63862 .43503 .43506 .43510 .43513 9.64067 .64071 .64074 .64078 .43719 .43723 .43726 .43730 9.64281 .64285 .64289 .64292 .43935 .43939 .43943 .43946 9.64495 .64499 .64502 .64506 .44152 .44156 .44159 .44163 9.64708 .64711 .64715 .64718 .44369 .44372 .44376 .44380 52 51 50 49 + 3^ 13 14 15 9.63866 .63869 .63873 .63877 .43517 .43521 .43534 .43538 9.64081 .64085 .64088 .64092 .43733 .43737 .43741 .43744 9.64296 .64299 .64303 .64306 .43950 .43953 .43957 .43961 9.64509 .64513 .64516 .64520 .44166 .44170 .44174 .44177 9.64722 .64725 .64729 .64732 .44383 .44387 .44390 .44394 48 47 46 45 + *' 17 18 19 9.63880 .63884 .63887 .63891 .43531 .43535 .43539 .43543 9.64096 .64099 .64102 .64106 .43748 .43751 .43755 .43759 9.64310 .64314 .64317 .64321 .43964 .43968 .43973 .43975 9.64523 .64527 .64531 .64534 .44181 .44185 .44188 .44192 9.64736 .64740 .64743 .64747 .44398 .44401 .44405 .44408 44 43 42 41 40 39 38 37 36 35 34 33 + 5' 21 22 23 9.63895 .63898 .63902 .63905 .43546 .43549 .43553 .43557 9.64110 .64113 .64117 .64121 .43762 .43766 .43769 .43773 9.64324 .64328 .64331 .64335 .43979 .43982 .43986 .43990 9.64538 .64541 .64545 .64548 .44195 .44199 .44203 .44306 9.64750 .64754 .64757 .64761 .44413 .44416 .44419 .44433 + 6' 25 26 27 9.63909 .63913 .63916 .63920 .43560 .43564 .43567 .43571 9.64124 .64128 .64131 .64135 .43777 .43780 .43784 .43787 9.64339 .64342 .64346 .64349 .43993 .43997 .44000 .44004 9.64552 .64555 .64559 .64563 .44310 .44313 .44217 .44221 9.64764 .64768 .64771 .64775 .44427 .44430 .44434 .44437 + r 29 30 31 9.63923 .63927 .63931 .63934 .43575 .43578 .43583 .43585 9.64139 .64142 .64146 .64149 .43791 .43795 .43798 .43802 9.64353 .64356 .64360 .64363 .44008 .44011 .44015 .44018 9.64566 .64570 .64573 .64577 .44234 .44338 .44331 .44335 9.64778 .64782 .64785 .64789 .44441 .44445 .44448 .44452 32 31 30 29 + 8^ 33 34 35 9.63938 .63941 .63945 .63949 .43589 .43593 .43596 .43600 9.64153 .64156 .64160 .64164 .43805 .43809 .43813 .43816 9.64367 .64371 .64374 .64378 .44022 .44026 .44029 .44033 9.64580 .64584 .64587 .64591 .44239 .44242 .44246 .44250 9.64793 .64796 .64800 .64803 .44455 .44459 .44463 .44466 28 27 26 25 + 9^ 37 38 39 9.63952 .63956 .63959 .63963 .43603 .43607 .43611 .43614 9.64167 .64171 .64174 .64178 .43830 .43834 .43827 .43831 9.64381 .64385 .64388 .64392 .44036 .44040 .44044 .44047 9.64594 .64598 .64602 .64605 .44253 .44257 .44260 .44264 9.64807 .64810 .64814 .64817 .44470 .44474 .44477 .44481 24 23 22: 21 + W 41 42 43 9.63966 .63970 .63974 .63977 .43618 .43633 .43635 .43639 9.64181 .64185 .64189 .64192 .43834 .43838 .43842 .43845 9.64396 .64399 .64403 .64406 .44051 .44055 .44058 .44062 9.64609 .64612 .64616 .64619 .44268 .44271 .44275 .44378 9.64821 .64824 .64828 .64831 .44484 .44488 .44492 .44495 20 19 18 17 + ir 45 46 47 9.63981 .63984 .63988 .63992 .43633 .43636 .43640 .43643 9.64196 .64199 .64203 .64206 .43849 .43852 .43856 .43860 9.64410 .64413 .64417 .64420 .44065 .44069 .44073 .44076 9.64623 .64626 .64630 .64633 .44282 .44286 .44389 .44293 9.64835 .64838 .64842 .64845 .44499 .44502 .44506 .44510 16 15 14 13 12 11 10 9 + n' 49 50 51 9.63995 .63999 .64002 .64006 .43647 .43650 .43654 .43658 9.64210 .64214 .64217 .64221 .43863 .43867 .43870 .43874 9.64424 .64428 .64431 .64435 .44080 .44083 .44087 .44091 9.64637 .64640 .64644 .64648 .44296 .44300 .44304 .44307 9.64849 .64852 .64856 .64860 .44513 .44517 .44521 .44524 + ir 5S 54 55 9.64010 .64013 .64017 .64020 .43661 .43665 .43668 .43672 9.64224 .64228 .64231 .64235 .43878 .43881 .43885 .43888 9.64438 .64442 .64445 .64449 .44094 .44098 .44101 .44105 9.64651 .64655 .64658 .64662 .44311 .44315 .44318 .44322 9.64863 .64867 .64870 .64874 .44538 .44531 .44535 .44539 8 7 6 5 + 1¥ 57 58 59 9.64024 .64028 .64031 .64035 .43676 .43679 .43683 .43686 9.64239 .64242 .64246 .64249 .43892 .43896 .43899 .43903 9.64452 .64456 .64460 .64463 .44109 .44112 .44116 .44120 9.64665 .64669 .64672 .64676 .44325 .44329 .44333 .44336 9.64877 .64881 .64884 .64888 .44543 .44546 .44549 .44553 4 3 S 1 + 15' 9.64038 .43690 9.64253 .43907 9.64467 .44123 9.64679 .44340 9.64891 .44557 18h 29m 18h 28^ 1811 27m 18^ 26m i5ft 25m TABLE IV. Havereinea. [Page 111 s 5^ 35m 83° 45' SJi 36m 84° 0' 5h sjm 84° 15' 5h 38m 84° 30^ 5hS9m 84° 45' s Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. 1 2 3 9.64891 .64895 .64898 .64902 .44557 .44560 .44564 .44568 9.65102 .65106 .65109 .65113 .44774 .44777 .44781 .44784 9.65312 .65316 .65319 .65323 .44991 .44994 .44998 .45001 9.65521 .65525 .65528 .65532 .45308 .45311 .45315 .45319 9.65729 .65733 .65736 .65740 .45435 .45439 .45433 .45436 60 59 58 57 + r 5 6 7 9.64905 .64909 .64912 .64916 .44571 .44575 .44578 .44583 9.65116 -.65120 .65123 .65127 .44788 .44793 .44795 .44799 9.65326 .65330 .65333 .65337 .45005 .45009 .45013 .45016 9.65535 .65539 .65542 .65546 .45333 .45336 .45339 .45333 9.65743 .65747 .65750 .65754 .45439 .45443 .45447 .45450 56 55 54 53 + It' 9 10 11 9.64919 .64923 .64926 .64930 .44586 .44589 .44593 .44596 9.65130 .65134 .65137 .65141 .44803 .44806 .44810 .44813 9.65340 .65344 .65347 .65351 .45030 .45033 .45037 .45030 9.65549 .65553 .65556 .65559 .45337 .45340 .45344 .45348 9.65757 .65761 .65764 .65767 .45454 .45458 .45461 .45465 52 51 50 49 + y IS 14 15 9.64934 .64937 .64941 .64944 .44600 .44604 .44607 .44611 9.65144 .65148 .65151 .65155 .44817 .44831 .44834 .44838 9.65354 .65358 .65361 .65365 .45034 .45038 .45041 .45045 9.65563 .65566 .65570 .65573 .45351 .45335 .45358 .45363 9.65771 .65774 .65778 .65781 .45468 .45473 .45476 .45479 48 47 46 45 + i' 17 IS 19 9.64948 .64951 .64955 .64958 .44614 .44618 .44633 .44635 9.65158 .65162 .65165 .65169 .44831 .44835 .44839 .44843 9.65368 .65372 .65375 .65378 .45048 .45053 .45056 .45059 9.65577 .65580 .65584 .65587 .45366 .45369 .45373 .45376 9.65785 .65788 .65792 .65795 .45483 .45486 .45490 .45494 U 43 42 41 40 39 38 37 + 5' 21 22 23 9.64962 .64965 .64969 .64972 .44639 .44633 .44636 .44640 9.65172 .65176 .65179 .65183 .44846 .44850 .44853 .44857 9.65382 .65385 .65389 .65392 .45063 .45067 .45070 .45074 9.65591 .65594 .65598 .65601 .45380 .45384 .45387 .45391 9.65799 .65802 .65806 .65809 .45497 .45501 .45505 .45508 + 6' 25 26 27 9.64976 .64979 .64983 .64986 .44643 .44647 .44651 .44654 9.65186 .65190 .65193 .65197 .44880 .44864 .44868 .44871 9.65396 .65399 .65403 .65406 .45077 .45081 .45085 .45088 9.65605 .65608 .65612 .65615 .45395 .45398 .45303 .45305 9.65812 .65816 .65819 .65823 .4.5513 .45515 .45519 .45533 36 35 34 33 + r 29 30 31 9.64990 .64993 .64997 .65000 .44658 .44661 .44665 .44669 9.65200 .65204 .65207 .65211 .44875 .44878 .44883 .44886 9.65410 .65413 .65417 .65421 .45093 .45096 .45099 .45103 9.65619 .65622 .65625 .65629 .45309 .45313 .45316 .45330 9.65826 .65830 .65833 .65837 .45536 .45530 .45534 .45537 32 31 30 29 + 8' 33 34 85 9.65004 .65007 .65011 .65014 .44673 .44676 .44680 .44683 9.65214 .65218 .65221 .65225 .44889 .44893 .44897 .44900 9.65424 .65427 .65431 .65434 .45106 .45110 .45114 .45117 9.65632 .65636 .65639 .65643 .45334 .45337 .45331 .45334 9.65840 .65844 .65847 .65850 .45541 .45544 .45548 .45553 28 27 26 25 + r 37 38 39 9.65018 .65021 .65025 .65028 .44687 .44690 .44694 .44698 9.65228 .65232 .65235 .65239 .44904 .44907 .44911 .44915 9.65438 .65441 .65445 .65448 .45131 .45134 .45138 .45133 9.65646 .65650 .65653 .65657 .45338 .45343 .45345 .45349 9.65854 .65857 .65861 .65864 .45555 .45559 .45563 .45566 24 23 22 21 + 1(K 41 42 43 9.65032 .65035 .65039 .65043 .44701 .44705 .44708 .44713 9.65242 .65246 .65249 .65253 .44918 .44933 .44935 .44939 9.65452 .65455 .65459 .65462 .45135 .45139 .45143 .45146 9.65660 .65664 .65667 .65671 .45353 .45356 .45360 .45363 9.65868 .65871 .65875 .65878 .45570 .45573 .45577 .45581 20 19 18 17 16 15 14 IS + 11' 45 46 47 9.65046 .65050 .65053 .65057 .44716 .44719 .44733 .44737 9.65256 .65260 .65263 .65267 .44933 .44936 .44940 .44944 9.65466 .65469 .65473 .65476 .45150 .45153 .45157 .45161 9.65674 .65677 .65681 .65684 .45367 .45371 .45374 .45378 9.65881 .65885 .65888 .65892 .45584 .45588 .45593 .45595 + n' 49 50 51 9.65060 .65064 .65067 .65071 .44730 .44734 .44737 .44741 9.65270 .65274 .65277 .65281 .44947 .44951 .44954 .44958 9.65480 .65483 .65486 .65490 .45164 .45168 .45173 .45175 9.65688 .65691 .65695 .65698 .45381 .45385 .45389 .45393 9.65895 .65899 .65902 .65906 .45599 .45603 .45606 .45610 12 11 10 9 + 13' 53 54 55 9.65074 .65078 .65081 .65085 .44745 .44748 .44753 .44755 9.65284 .65288 .65291 .65295 .44963 .44965 .44969 .44973 9.65493 .65497 .65500 .65504 .45179 .45183 .45186 .45190 9.65702 .65705 .65709 .65712 .45396 .45400 .45403 .45407 9.65909 .65913 .65916 .65919 .45613 .45617 .45630 .45634 8 7 6 5 + W 57 58 59 9.65088 .65092 .65095 .65099 .44759 .44763 .44766 .44770 9.65298 .65302 .65305 .65309 .44976 .44980 .44983 .44987 9.65507 .65511 .65514 .65518 .45193 .45197 .45300 .45304 9.65716 .65719 .65722 .65726 .45410 .45414 .45418 .45431 9.65923 .65926 .65930 .65933 .45638 .45631 .45635 .45639 4 3 2 1 + 15' 9.65102 .44774 9.65312 .44991 9.65521 .45308 9.65729 .45435 9.65937 .45643 18J^ 24'^ ISh 23^ 18^ 22m ISh 21m 18h 20m 1 Page 112] TABLE IV. Haversines. s 5h40m 85° 0' 5h 41^ 85° 15' 5h42m 85° 30' 5h43m 85° 45' 5h44m 86° 0' 3 Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. 1 s 3 9.65937 .65940 .65944 .65947 .45642 .4564C .45649 .45653 9.66143 .66146 .66150 .66153 .45860 .45863 .45867 .45870 9.66348 .66352 .66355 .66359 .46077 .46081 .46084 .46088 9.66553 .66556 .66560 .66563 .46295 .46298 .46302 .46305 9.66757 .66760 .66763 .66767 .46512 .46516 .46519 .46523 60 59 58 57 + r 5 6 7 9.65950 .65954 .65957 .65961 .45657 .45660 .45664 .4566S 9.66157 .66160 .66164 .66167 .45874 .45878 .45881 .45885 9.66362 .66366 .66369 .66372 .46092 .46095 .46099 .46102 9.66567 .66570 .66573 .66577 .46309 .46313 .46316 .46320 9.66770 .66774 .66777 .66780 .46527 .46530 .46534 .46538 56 55 54 53 + r 9 10 11 9.65964 .65968 .65971 .65975 .45671 .45675 .45678 .45682 9.06170 .66174 .66177 .66181 .45889 .45892 .45896 .45899 9.66376 .66379 .66383 .66386 .46106 .46110 .46113 .46117 9.66580 .66584 .66587 .66590 .46324 .46327 .46331 .46334 9.66784 .66787 .66791 .66794 .46541 .46545 .46548 .46552 52 51 50 49 + 3' 13 14 15 9.65978 .65981 .65985 .65988 .45686 .45689 .45693 .45697 9.66184 .66188 .66191 .66194 .45903 .45907 .45910 .45914 9.66389 .66393 .66396 .66400 .46121 .46124 .46128 .46131 9.66594 .66597 .66601 .66604 .46338 .46342 .46345 .46349 9.66797 .66801 .66804 .66807 .46556 .46559 .46563 .46567 48 47 46 45 + 4' 17 18 19 9.65992 .65995 .65999 .66002 .45700 .45704 .45707 .45711 9.66198 .66201 .66205 .66208 .45918 .45921 .45925 .45928 9.66403 .66407 .66410 .66413 .46135 .46139 .46142 .46146 9.66607 .66611 .66614 .66618 .46353 .46356 .46360 .46363 9.66811 .66814 .66818 .66821 .46570 .46574 .46577 .46581 44 43 42 41 + y 21 22 23 9.66006 .66009 .66012 .66016 .45715 .45718 .45723 .45726 9.66212 .66215 .66218 .66222 .4593!? .45936 .45939 .45943 9.66417 .66420 .66424 .66427 .46150 .46153 .46157 .46161 9.66621 .66624 .66628 .66631 .46367 .46371 .46374 .46378 9.66824 .66828 .66831 .66835 .46585 .46588 .46592 .46596 40 39 38 37 + 6' 25 26 27 9.66019 .66023 .66026 .66030 .45729 .45733 .45736 .45740 9.66225 .66229 .66232 .66236 .45947 .45950 .45954 .45957 9.66430 .66434 .66437 .66441 .46164 .46168 .46171 ,46175 9.66635 .66638 .66641 .66645 .46382 .46385 .46389 .46392 9.66838 .66841 .66845 .66848 .46599 .46603 .46606 .46610 36 35 34 33 + r 29 30 31 9.66033 .66037 .66040 .66043 .45744 .45747 .45751 .45755 9.66239 .66242 .66246 .66249 .45961 .45965 .45968 .45972 9.66444 .66447 .66451 .66454 .46179 .46182 .46186 .46189 9.66648 .66652 .66655 .66658 .46396 .46400 .46403 .46407 9.66851 .66855 .66858 .66862 .46614 .46617 .46621 .46625 32 31 30 29 + 8' 33 34 35 9.66047 .66050 .66054 .66057 .45758 .45762 .45765 .45769 9.66253 .66256 .66260 .66263 .45976 .45979 .45983 .45986 9.66458 .66461 .66464 .66468 .46193 .46197 .46200 .46204 9.66662 .66665 .66669 .66672 .46411 .46414 .46418 .46421 9.66865 .66868 .66872 .66875 .46628 .46632 .46636 .46639 28 27 26 25 + 9' 37 38 39 9.66061 .66064 .66067 .66071 .45773 .45776 .45780 .45783 9.66266 .66270 .66273 .66277 .45990 .45994 .45997 .46001 9.66471 .66475 .66478 .66482 .46208 .46211 .46215 .46318 9.66675 .66679 .66682 .66685 .46425 .46429 .46432 .46436 9.66878 .66882 .66885 .66889 .46643 .46646 .46650 .46654 24 23 22 21 + w 41 42 43 9.66074 .66078 .66081 .66085 .45787 .45791 .45794 .45798 9.66280 .66284 .66287 .66290 .46005 .46008 .46012 .46015 9.66485 .66488 .66492 .66495 .46332 .46226 .46339 .46333 9.66689 .66692 .66696 .66699 .46440 .46443 .46447 .46451 9.66892 .66895 .66899 .66902 .46657 .46661 .46665 .46668 20 19 18 17 + 11' 45 46 47 9.66088 .66092 .66095 .66098 .45802 .45805 .45809 .45812 9.66294 .60297 .66301 .66304 .46019 .46023 .46026 .46030 9.66499 .66502 .66505 .66509 .46337 .46340 .46344 .46347 9.66702 .66706 .66709 .66713 .46454 .46458 .46461 .46465 9.66905 .66909 .66912 .66916 .46672 .46675 .46679 .46683 16 15 14 13 + 13' 49 50 51 9.66102 .66105 .66109 .66112 .45816 .45820 .45823 .45827 9.66307 .66311 .66314 .66318 .46034 .46037 .46041 .46044 9.66512 .66516 .66519 .66522 .46351 .46355 .46358 .46363 9.66716 .66719 .66723 .66726 .46469 .46472 .46476 .46480 9.66919 .66922 .66926 .66929 .46686 .46690 .46694 .46697 12 11 10 9 + 13' 53 54 55 9.66116 .66119 .66122 .66126 .45831 .45834 .45838 .45841 9.66321 .66325 .66328 .66331 .46048 .46053 .46055 .46059 9.66526 .66529 .66533 .66536 .46366 .46369 .46373 .46376 9.66730 .66733 .06736 .66740 .46483 .46487 .46490 .46494 9.66932 .66936 .66939 .66943 .46701 .46704 .46708 .46712 8 7 6 5 + 14' 57 58 59 9.66129 .66133 .66136 .66140 .45845 .45849 .45852 .45856 9.66335 .66338 .66342 .66345 .46063 .46066 .46070 .46073 9.66539 .66543 .66546 .66550 .46380 .46284 .46287 .46291 9.66743 .66747 .66750 .66753 .46498 .46501 .46505 .46509 9.66946 .66949 .66953 .66956 .46715 .46719 .46723 .46726 4 S 2 1 + 15' 9.66143 .45860 9.66348 .46077 9.66553 .46295 9.66757 .46512 9.66959 .46730 ISh igm ISn 18m ISh 17m IShiem 18^ 15m TABLE IV. Haversinea. [Page 113 s 5fc^TO 86° 15' 5h 46^ 86° 30' 5h47m 86° 45' 5ft 45TO 87° 0' 5ft 49TO 87° 15' 3 60 59 58 57 Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. 1 2 S 9.66959 .66963 .66966 .66970 .46730 .46733 .46737 .46741 9.67161 .67165 .67168 .67]71 .46948 .46951 .46955 .46958 9.67362 .67366 .67369 .67372 .47165 .47169 .47173 .47176 9.67562 .67566 .67569 .67572 .47383 .47387 .47390 .47394 9.67762 .67765 .67768 .67772 .47601 .47605 .47608 .47613 + r 5 6 7 9.66973 .66976 .66980 .66983 .46744 .46748 .46753 .46755 9.67175 .67178 .67181 .67185 .46963 .46966 .46969 .46973 9.67376 .67379 .67382 .67386 .47180 .47184 .47187 .47191 9.67576 .67579 .67582 .67586 .47398 .47401 .47405 .47409 9.67775 .67778 .67782 .67785 .47616 .47619 .47633 .47637 56 55 54 53 + 2' 9 10 11 9.66986 .66990 .66993 .66997 .46759 .46763 .46766 .46770 9.67188 .67192 .67195 .67198 .46977 .46980 .46984 .46987 9.67389 .67392 .67396 .67399 .47194 .47198 .47303 .47305 9.67589 .67592 .67596 .67599 .47413 .47416 .47430 .47433 9.67788 .67792 .67795 .67798 .47630 .47634 .47637 .47641 52 51 50 49 + 3' 13 14 15 9.67000 .67003 .67007 .67010 .46773 .46777 .46781 .46784 9.67202 .67205 .67208 .67212 .46991 .46995 .46998 .47003 9.67402 .67406 .67409 .67412 .47309 .47313 .47316 .47330 9.67602 .67606 .67609 .67612 .47437 .47430 .47434 .47438 9.67801 .67805 .67808 .67811 .47645 .47648 .47653 .47656 48 47 46 45 U 43 42 41 + 4' n 18 19 9.67013 .67017 .67020 .67023 .46788 .46793 .46795 .46799 9.67215 .67218 .67222 .67225 .47006 .47009 .47013 .47017 9.67416 .67419 .67422 .67426 .47333 .47327 .47231 .47234 9.67616 .67619 .67622 .67626 .47441 .47445 .47449 .47453 9.67815 .67818 .67821 .67825 .47659 .47663 .47666 .47670 + 5' 21 22 23 9.67027 .67030 .67034 .67037 .46803 .46806 .46810 .46813 9.67228 .67232 .67235 .67238 .47030 .47034 .47037 .47031 9.67429 .67432 .67436 .67439 .47338 .47343 .47345 .47349 9.67629 .67632 .67636 .67639 .47456 .47459 .47483 .47467 9.67828 .67831 .67835 .67838 .47674 .47677 .47681 .47685 40 39 38 37 + 6' 25 26 27 9.67040 .67044 .67047 .67050 .46817 .46831 .46834 .46838 9.67242 .67245 .67249 .67252 .47035 .47038 .47043 .47046 9.67443 .67446 .67449 .67452 .47353 .47256 .47260 .47263 9.67642 .67646 .67649 .67652 .47470 .47474 .47478 .47481 9.67841 .67844 .67848 .67851 .47688 .47693 .47696 .47699 36 35 34 33 + r 29 30 31 9.67054 .67057 .67060 .67064 .46831 .46835 .46839 .46843 9.67255 .67259 .67262 .67265 .47049 .47053 .47056 .47060 9.67456 .67459 .67462 .67466 .47367 .47371 .47274 .47278 9.67656 .67659 .67662 .67666 .47485 .47489 .47493 .47496 9.67854 .67858 .67861 .67864 .47703 .47706 .47710 .47714 32 31 30 29 28 27 26 25 + 8' S3 34 35 9.67067 .67071 .67074 .67077 .46846 .46850 .46853 .46857 9.67269 .67272 .67275 .67279 .47064 .47067 .47071 .47075 9.67469 .67472 .67476 .67479 .47283 .47285 .47289 .47292 9.67669 .67672 .67675 .67679 .47499 .47503 .47507 .47510 9.67868 .67871 .67874 .67878 .47717 .47731 .47725 .47728 + 9^ 37 38 39 9.67081 .67084 .67087 .67091 .46860 .46864 .46868 .46871 9.67282 .67285 .67289 .67292 .47078 .47083 .47086 .47089 9.67483 .67486 .67489 .67493 .47296 .47300 .47303 .47307 9.67682 .67685 .67689 .67692 .47514 .47518 .47531 .47525 9.67881 .67884 .67887 .67891 .47733 .47735 .47739 .47743 24 23 22 21 + W 41 42 43 9.67094 .67097 .67101 .67104 .46875 .46879 .46883 .46886 9.67295 .67299 .67302 .67305 .47093 .47096 .47100 .47104 9.67496 .67499 .67503 .67506 .47311 .47314 .47318 .47321 9.67695 .67699 .67702 .67705 .47528 .47533 .47536 .47539 9.67894 .67897 .67901 .67904 .47746 .47750 .47754 .47757 20 19 18 17 + 11' 45 46 47 9.67108 .67111 .67114 .67118 .46890 .46893 .46897 .46900 9.67309 .67312 .67315 .67319 .47107 .47111 .47115 .47118 9.67509 .67512 .67516 .67519 .47325 .47329 .47332 .47336 9.67709 .67712 .67715 .67719 .47543 .47547 .47550 .47554 9.67907 .67911 .67914 .67917 .47761 .47765 .47768 .47773 16 15 14 13 + 13' 49 50 51 9.67121 .67124 .67128 .67131 .46904 .46908 .46911 .46915 9.67322 .67326 .67329 .67332 .47133 .47125 .47139 .47133 9.67522 .67526 .67529 .67532 .47340 .47343 .47347 .47351 9.67722 .67725 .67729 .67732 .47558 .47561 .47565 .47568 9.67920 .67924 .67927 .67930 .47775 .47779 .47783 .47786 12 11 10 9 8 7 6 5 + 13' 53 54 55 9.67134 .67138 .67141 .67145 .46919 .46933 .46936 .46929 9.67336 .67339 .67342 .67346 ,47136 .47140 .47144 .47147 9.67536 .67539 .67542 .67546 .47354 .47358 .47361 .47365 9.67735 .67738 .67742 .67745 .47573 .47576 .47579 .47583 9.67934 .67937 .67940 .67944 .47790 .47794 .47797 .47801 + 14' 57 58 59 9.67148 .67151 .67155 .67158 .46933 .46937 .46940 .46944 9.67349 .67352 .67356 .67359 .47151 .47155 .47158 .47163 9.67549 .67552 .67556 .67559 .47369 .47373 .47376 .47380 9.67748 .67752 .67755 .67758 .47587 .47590 .47594 .47597 9.67947 .67950 .67953 .67957 .47805 .47808 .47813 ,47815 4 3 2 1 + 15' 9.67161 .46948 9.67362 .47165 9.67562 .47383 9.67762 .47601 9.67960 .47819 jtSh i^»i 18h 13m ISfe 12m ISh lira IShlOra 55901°— IS- Page 114] TABLE IV. Haversines. s 5ft 50^ 87° W 5h 5im 87° 45' 5A 52^ 88° 0' 5A 53m 88° 15' 5h 54'^ 88° 30' Log. Hav Nat. Hav Log. Hav Nat. Hav Log. Hav Nat. Hav Log. Hav Nat. Hav Log. Hav Nat. Hav E 1 2 3 9.67960 .67963 .67967 .67970 .47819 .47833 .47826 .47830 9.68158 .68161 .68164 .68167 .48037 .48041 .48044 .48048 9.68354 .68358 .68361 .68364 .48255 .48259 .48262 .48266 9.68550 .68553 .68557 .68560 .48473 .48477 .48480 .48484 9.68745 .68748 .68751 .68755 .48691 .48695 .48698 .48702 60 59 58 57 + r 5 6 7 9.67973 .67977 .67980 .67983 .47834 .47837 .47841 .47844 9.68171 .68174 .68177 .68181 .48052 .48055 .48059 .48062 9.68367 .68371 .68374 .68377 .48269 .48273 .48277 .48280 9.68563 .68566 .68570 .68573 .48488 .48491 .48495 .48499 9.68758 .68761 .68764 .68768 .48706 .48709 .48713 .48717 56 55 54 53 + 2^ 9 10 11 9.67986 .67990 .67993 .67996 .47848 .47852 .47855 .47859 9.68184 .68187 .68190 .68194 .48066 .48070 .48073 .48077 9.68380 .68384 .68387 .68390 .48284 .48288 .48291 .48295 9.68576 .68579 .68583 .68586 .48502 .48506 .48509 .48513 9.68771 .68774 .68777 .68781 .48720 .48724 .48728 .48731 52 51 50 49 + 3' 13 14 15 9.68000 .68003 .68006 .68010 .47863 .47866 .47870 .47874 9.68197 .68200 .68204 .68207 .48081 .48084 .48088 .48092 9.68393 .68397 .68400 .68403 .48299 .48302 .48306 .48310 9.68589 .68592 .68596 .68599 .48517 .48520 .48534 .48538 9.68784 .68787 .68790 .68794 .48735 .48738 .48742 .48746 48 47 46 45 + 4' 17 18 19 9.68013 .68016 .68019 .68023 .47877 .47881 .47884 .47888 9.68210 .68213 .68217 .68220 .48095 .48099 .48102 .48106 9.68407 .68410 .68413 .68416 .48313 .48317 .48320 .48324 9.68602 .68605 .68609 .68612 .48531 .48535 .48538 .48543 9.68797 .68800 .68803 .68806 .48749 .48753 .48757 .48760 44 43 42 41 + 5' 21 22 23 9.68026 .68029 .68033 .68036 .47892 .47895 .47899 .47903 9.68223 .68227 .68230 .68233 .48110 .48113 .48117 .48121 9.68420 .68423 .68426 .68429 .48338 .48331 .48335 .48339 9.68615 .68618 .68622 .68625 .48546 .48549 .48553 .48557 9.68810 .68813 .68816 .68320 .48764 .48767 .48771 .48775 40 39 38 37 + 6' 25 26 27 9.68039 .68042 .68046 .68049 .47906 .47910 .47913 .47917 9.68236 .68240 .68243 .68246 .48124 .48128 .48131 .48135 9.68433 .68436 .68439 .68442 .48342 .48346 .48350 .48353 9.68628 .68631 .68635 .68638 .48560 .48564 .48568 .48571 9.68823 .68826 .68829 .68832 .48778 .48782 .48786 .48789 36 35 34 33 + r 29 30 31 9.68052 .68056 .68059 .68062 .47921 .47924 .47928 .47932 9.68249 .68253 .68256 .68259 .48139 .48142 .48146 .48150 9.68446 .68449 .68452 .68456 .48357 .48360 .48364 .48368 9.68641 .68644 .68648 .68651 .48575 .48578 .48582 .48586 9.68836 .68839 .68842 .68845 .48793 .48797 .48800 .48804 32 31 30 -29 + 8' 33 34 35 9.68066 .68069 .68072 .68075 .47935 .47939 .47943 .47946 9.68263 .68266 .68269 .68272 .48153 .48157 .48161 .48164 9.68459 .68462 .68465 .68469 .48371 .48375 .48379 .48382 9.68654 .68657 .68661 .68664 .48589 .48593 .48597 .48600 9.68849 .68852 .68855 .68858 .48807 .48811 .48815 .48818 28 27 26 25 + 9' 37 38 39 9.68079 .68082 .68085 .68089 .47950 .47953 .47957 .47961 9.68276 .68279 .68282 .68286 .48168 .48171 .48175 .48179 9.68472 .68475 .68478 .68482 .48386 .48389 .48393 .48397 9.68667 .68670 .68674 .68677 .48604 .48608 .48611 .48615 9.68862 .68865 .68868 .68871 .48822 .48826 .48839 .48833 24 23 \ 22 21 + W 41 42 43 9.68092 .68095 .68098 .68102 .47964 .47968 .47972 .47975 9.68289 .68292 .68295 .68299 .48182 .48186 .48190 .48193 9.68485 .68488 .68491 .68495 .48400 .48404 .48408 .48411 9.68680 .68683 .68687 .68690 .48618 .48622 .48626 .48629 9.68875 .68878 .68881 .68884 .48837 .48840 .48844 .48847 20 19 18 17 + ir 45 46 47 9.68105 .68108 .68112 .68115 .47979 .47983 .47986 .47990 9.68302 .68305 .68308 .68312 .48197 .48201 .48204 .48208 9.68498 .68501 .68504 .68508 .48415 .48419 .48422 .48426 9.68693 .68696 .68700 .68703 .48633 .48637 .48640 .48644 9.68887 .68891 .68894 .68897 .48851 .48855 .48858 .48863 16 15 14 13 + n' 49 50 51 9.68118 .68121 .68125 .68128 .47993 .47997 .48001 .48004 9.68315 .68318 .68322 .68325 .48311 .48215 .48219 .48222 9.68511 .68514 .68517 .68521 .48439 .48433 .48437 .48440 9.68706 .68709 .68713 .68716 .48648 .48651 .48655 .48658 9.68900 .68904 .68907 .68910 .48866 .48869 .48873 .48877 12 11 10 9 + 13' 53 54 55 9.68131 .68135 .68138 .68141 .48008 .48012 .48015 .48019 9.68328 .68331 .68335 .68338 .48336 .48230 .48233 .48237 9.68524 .68527 .68531 .68534 .48444 .48448 .48451 .48455 9.68719 .68722 .68726 .68729 .48663 .48666 .48669 .48673 9.68913 .68917 .68920 .68923 .48880 .48884 .48887 .48891 8 7 6 5 + W 57 58 59 9.68144 .68148 .68151 .68154 .48022 .48026 .48030 .48033 9.68341 .68344 .68348 .68351 .48241 .48244 .48248 .48251 9.68537 .68540 .68544 .68547 .48459 .48462 .48466 .48469 9.68732 .68735 .68739 .68742 .48677 .48680 .48684 .46688 9.68926 .68929 .68933 .68936 .48895 .48898 .48903 .48906 4 3 2 ' + 16' 9.68158 .48037 9.68354 .48255 9.68550 .48473 9.68745 .48691 9.68939 .48909 — Ign 9m 1 IShgm 1 ISh 7m 1 IShem ISJi 5m 1 TABLE IV. [Page 116 Haversines. s 5^ 55m 88° 45^ 5h 56m 89° 0^ 5^ 57m 89° 15' 5h 58m 89° 30^ 5h 59m 89° 45' s 60 59 58 57 Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. 1 2 9.68939 .68942 .68946 .68949 .48909 .48913 .48917 .48920 9.69132 .69136 .69139 .69142 .49127 .49131 .49135 .49138 9.69325 .69328 .69331 .69334 .49346 .49349 .49353 .49356 9.69516 .69520 .69523 .69526 .49564 .49567 .49671 .49575 9.69707 .69710 .69713 .69717 .49782 .49785 .49789 .49793 + r 5 6 7 9.68952 .68955 .68958 .68962 .48924 .48927 .48931 .48935 9.69145 .69148 .69152 .69155 .49143 .49146 .49149 .49153 9.69338 .69341 .69344 .69347 .49360 .49364 .49367 .49371 9.69529 .69532 .69535 .69539 .49578 .49583 .49585 .49589 9.69720 .69723 .69726 ,69729 .49796 .49800 .49804 .49807 56 55 54 53 + 2^ 9 10 11 9.68965 .68968 .68971 .68975 .48938 .48943 .48946 .48949 9.69158 .69161 .69164 .69168 .49156 .49160 .49164 .49167 9.69350 .69354 .69357 .69360 .49375 .49378 .49383 .49386 9.69542 .69545 .69548 .69551 .49593 .49596 .49600 .49604 9.69732 .69736 .69739 .69742 .49811 .49815 .49818 .49833 52 51 50 49 + 3^ IS 14 15 9.68978 .68981 .68984 .68988 .48953 .48957 .48960 .48964 9.69171 .69174 .69177 .69181 .49171 .49175 .49178 .49183 9.69363 .69366 .69370 .69373 .49389 .49393 .49396 .49400 9.69555 .69558 .69561 .69564 .49607 .49611 .49615 .49618 9.69745 .69748 .69751 .69755 .49835 .49839 .49833 .49836 48 47 46 45 44 43 42 41 40 39 38 37 -r 4' 17 IS 19 9.68991 .68994 .68997 .69000 .48967 .48971 .48975 .48978 9.69184 .69187 .69190 .69193 .49188 .49189 .49193 .49196 9.69376 .69379 .69382 .69386 .49404 .49407 .49411 .49415 9.69567 .69570 .69574 .69577 .49633 .49635 .49639 .49633 9.69758 .69761 .69764 .69767 .49840 .49844 .49847 .49851 + 5^ 21 22 23 9.69004 .69007 .69010 .69013 .48983 .48986 .48989 .48993 9.69197 .69200 .69203 .69206 .49300 .49204 .49307 .49311 9.69389 .69392 .69395 .69398 .49418 .49433 .49436 .49439 9.69580 .69583 .69586 .69590 .49636 .49640 .49644 .49647 9.69770 .69774 .69777 .69780 .49855 .49858 .49863 .49865 + 6^ 25 26 27 9.69017 .69020 .69023 .69026 .48997 .49000 .49004 .49007 9.69209 .69213 .69216 .69219 .49315 .49318 .49323 .49336 9.69402 .69405 .69408 .69411 .49433 .49436 .49440 .49444 9.69593 .69596 .69599 .69602 .49651 .49655 .49658 .49662 9.69783 .69786 .69789 .69793 .49869 .49873 .49876 .49880 36 35 34 33 + r 29 30 31 9.69029 .69033 .69036 .69039 .49011 .49015 .49018 .49023 9.69222 .69225 .69229 .69232 .49339 .49333 .49336 .49340 9.69414 .69417 .69421 .69424 .49447 .49451 .49455 .49458 9.69605 .69609 .69612 .69615 .49665 .49669 .49673 .49676 9.69796 .69799 .69802 .69805 .49884 .49887 .49891 .49895 32 31 30 29 + 8^ 33 34 35 9.69042 .69046 .69049 .69052 .49026 .49039 .49033 .49036 9.69235 .69238 .69242 .69245 .49344 .49347 .49351 .49355 9.69427 .69430 .69433 .69437 .49463 .49465 .49469 .49473 9.69618 .69621 .69625 .69628 .49680 .49684 .49687 .49691 9.69808 .69812 .69815 .69818 .49898 .49903 .49905 .49909 28 27 26 25 + ^ 37 38 39 9.69055 .69058 .69062 .69065 .49040 .49044 .49047 .49051 9.69248 .69251 .69254 .69258 .49358 .49363 .49366 .49369 9.69440 .69443 .69446 .69449 .49476 .49480 .49484 .49487 9.69631 .69634 .69637 .69640 .49695 .49698 .49703 .49705 9.69821 .69824 .69827 .69831 .49913 .49916 .49930 .48934 24 23 22 21 + W 41 42 43 9.69068 .69071 .69074 .69078 .49055 .49058 .49062 .49066 9.69261 .69264 .69267 .69270 .49373 .49376 .49380 .49384 9.69453 .69456 .69459 .69462 .49491 .49495 .49498 .49503 9.69644 .69647 .69650 .69653 .49709 .49713 .49716 .49730 9.69834 .69837 .69840 .69843 .49937 .49931 .49935 .49938 20 19 18 17 + 11^ 45 46 47 9.69081 .69084 .69087 .69091 .49069 .49073 .49076 .49080 9.69274 .69277 .69280 .69283 .49387 .49391 .49395 .49398 9.69465 .69469 .69472 .69475 .49506 .49509 .49513 .49516 9.69656 .69659 .69663 .69666 .49734 .49737 .49731 .49735 9.69846 .69850 .69853 .69856 .49943 .49945 .49949 .49953 16 15 14 13 + 12' 49 50 51 9.69094 .69097 .69100 .69103 .49084 .49087 .49091 .49095 9.69286 .69290 .69293 .69296 .49303 .49306 .49309 .49313 9.69478 .69481 .69484 .69488 .49530 .49534 .49537 .49531 9.69669 1 .49738 .69672 .49743 .69675 .49745 .69678 .49749 9.69859 .69862 .69865 .69869 .49956 .49960 .49964 .49967 12 11 10 9 + 13^ 53 54 55 9.69107 .69110 .69113 .69116 .49098 .49103 .49106 .49109 9.69299 .69302 .69306 .69309 .43316 .49320 .49334 .49337 9.69491 .69494 .69497 .69500 .49535 .49538 .49543 .49545 9.69682 .69685 .69688 .69691 .49753 .49756 .49760 .49764 9.69872 .69875 .69878 .69881 .49971 .49975 .49978 .49983 8 7 6 5 + W 57 58 59 9.69120 .69123 .69126 .69129 .49113 .49116 .49120 .49134 9.69312 .69315 .69318 .69322 .49331 .49335 .49338 .49343 9.69504 .69507 .69510 .69513 .49549 .49553 .49556 .49560 9.69694 .69698 .69701 .69704 .49767 .49771 .49775 .49778 9.69884 .69888 .69891 .69894 .49985 .49989 .49993 .49997 4 3 2 '1 + ijy 9.69132 .49127 9.69325 .49346 9.69516 .49564 9.69707 .49783 9.69897 .50000 Igh^m 28h 3m 18h 2m IShim IShQm Page 116] tablp: iv. Havereinea. s 6ft Om 90° (K 1 6ft im 90° 15' 6ft 2^ 90° ar 1 6ft Sm 90° 45^ 6ft 4^ 91° C 1 8 Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. 1 2 S 9.69897 .69900 .69903 .69906 ^0000 o50004 .50007 .50011 9.70086 .70089 .70092 .70096 .50218 .50222 .50225 .50229 9.70274 .70277 .70281 .70284 .50436 .50440 .50444 .50447 9.70462 .70465 .70468 .70471 .50654 .50658 .50662 .50665 9.70648 .70652 .70655 .70658 .50873 .50876 .50880 .50884 60 59 58 57 + r 5 6 7 9.69910 .69913 .69916 .69919 .50015 .50018 .50032 .50025 9.70099 .70102 .70105 .70108 .50233 .50236 .50240 .50244 9.70287 .70290 .70293 .70296 .50451 .50455 .50458 .50462 9.70474 .70477 .70480 .70484 .50669 .50673 .50676 .50680 9.70661 .70664 .70667 .70670 .50887 .50891 .50894 .50898 66 55 54 53 + 2' 9 10 11 9.69922 .69925 .69929 .69932 .50029 .50033 .50036 .50010 9.70111 .70114 .70118 .70121 .50247 .50251 .50255 .50258 9.70299 .70303 .70306 .70309 .50465 .50469 .50473 .50476 9.70487 .70490 .70493 .70496 .50684 .50687 .50691 .50694 9.70673 .70676 .70679 .70683 .50902 .50905 .50909 .50913 52 51 50 49 + 3' 13 u 15 9.69935 .69938 .69941 .69944 .50044 .50047 .50051 .50055 9.70124 .70127 .70130 .70133 .50262 .50265 .50269 .50273 9.70312 .70315 .70318 .70321 .50480 .50484 .50487 .50491 9.70499 .70502 .70505 .70509 .50698 .50702 .50705 .50709 9.70686 .70689 .70692 .70695 .50916 .50920 .50924 .50927 48 47 46 45 + 4^ 17 18 19 9.69948 .69951 .69954 .69957 .50058 .50062 .50065 .50069 9.70136 .70140 .70143 .70146 .50276 .50280 .50284 .50287 9.70324 .70328 .70331 .70334 .50495 .50498 .50502 .50505 9.70512 .70515 .70518 .70521 .50713 .50716 .50720 .50734 9.70698 .70701 .70704 .70707 .50931 .50934 .50938 .50942 44 43 42 41 + 5^ 21 22 23 9.69960 .69963 .69966 .69970 .50073 .50076 .50080 .50084 9.70149 .70152 .70155 .70158 .50291 .50295 .50298 .50302 9.70337 .70340 .70343 .70346 .50509 .50513 .50516 .50520 9.70524 .70527 .70530 .70533 .50737 ,50731 .50734 .50738 9.70710 .70714 .70717 .70720 .50945 .50949 .50953 .50956 40 39 38 37 + ^ 85 26 27 9.69973 .69976 .69979 .69982 .50087 .50091 .50095 .50098 9.70161 .70165 .70168 .70171 .50305 .50309 .50313 .50316 9.70349 .70353 .70356 .70359 .50524 .50527 .50531 .50534 9.70537 .70540 .70543 .70546 .50743 .50745 .50749 .50753 9.70723 .70726 .70729 .70732 .50960 .50964 .50967 .50971 36 35 34 33 32 31 30 29 + r 29 30 31 9.69985 .69988 .69992 .69995 .50102 .50105 .50109 .50113 9.70174 .70177 .70180 .70183 .50320 .50324 .50327 .50331 9.70362 .70365 .70368 .70371 .50538 .50542 .50545 .50549 9.70549 .70552 .70555 .70558 .50756 .50760 .50764 .50767 9.70735 .70738 .70741 .70745 .50974 .50978 .50982 .50985 + 8' 33 34 35 9.69998 .70001 .70004 .70007 .50116 .50120 .50124 .50127 9.70187 .70190 .70193 .70196 .50335 .50338 .50342 .50345 9.70374 .70378 .70381 .70384 .50553 .50556 .50560 .50564 9.70561 .70565 .70568 .70571 .50771 .50774 .50778 .50783 9.70748 .70751 .70754 .70757 .50989 .50993 .50996 .51000 28 27 26 25 24 23 22 21 20 19 18 17 + 9^ 57 38 39 9.70011 .70014 .70017 .70020 .50131 .50135 .50138 .50142 9.70199 .70202 .70205 .70209 .50349 .50353 .50356 .50360 9.70387 .70390 .70393 .70396 .50567 .50571 .50574 .50578 9.70574 .70577 .70580 .70583 .50785 .50789 .50793 .50796 9.70760 .70763 .70766 .70769 .51004 .51007 .51011 .51014 + W 41 42 43 9.70023 .70026 .70029 .70033 .50145 .50149 .50153 .50156 9.70212 .70215 .70218 .70221 .50364 .50367 .50371 .50375 9.70399 .70402 .70406 .70409 .50582 .50585 .50589 .50593 9.70586 .70589 .70593 .70596 .50800 .50804 .50807 .50811 9.70772 .70775 .70779 .70782 .51018 .51022 .51025 .51029 + 11^ 45 46 47 9.70036 .70039 .70042 .70045 .50160 .50164 .50167 .50171 9.70224 .70227 .70230 .70234 .50378 .50382 .50385 .50389 9.70412 .70415 .70418 .70421 .50596 .50600 .50604 .50607 9.70599 .70602 .70605 .70608 .50814 .50818 .50833 .50835 9.70785 .70788 .70791 .70794 .51033 .51036 .51040 .51043 16 15 14 13 + n' 49 50 51 9.70048 .70051 .70055 .70058 .50175 .50178 .50182 .50185 9.70237 .70240 .70243 .70246 .50393 .50396 .50400 .50404 9.70424 .70427 .70431 .70434 .50611 .50614 .50618 .50632 9.70611 .70614 .70617 .70620 .50829 .50833 .50836 .50840 9.70797 .70800 .70803 .70806 .51047 .51051 .51054 .51058 12 11 10 9 + 13^ 53 54 55 9.70061 .70064 .70067 .70070 .50189 .50193 .50196 .50200 9.70249 .70252 .70256 .70259 .50407 .50411 .50415 .50418 9.70437 .70440 .70443 .70446 .50625 .50629 .50633 .50636 9.70624 .70627 .70630 .70633 .50844 .50847 .50851 .50854 9.70809 .70813 .70816 .70819 .51062 .51065 .51069 .51073 8 7 6 5 + 14' 57 58 59 9.70074 .70077 .70080 .70083 .50204 .50207 .50211 .50215 9.70262 .70265 .70268 .70271 .50422 .50425 .50429 .50433 9.70449 .70452 .70456 .70459 .50640 .50644 .50647 .50651 9.70636 .70639 .70642 .70645 .50858 .50862 .50865 .50869 9.70822 .70825 .70828 .70831 .51076 .51080 .51083 .51087 4 3 2 1 + 15' 9.70086 .50218 9.70274 .50436 9.70462 .50654 9.70648 .50873 9.70834 .51091 i7h 69m i7A 58m i7ft 57m i7ft 56m i7ft 55m 1 TABLE IV. Haversines. [Page 117 s 6h 5m 91° W 6h 6m 91° 30^ eh 7TO 91° 45/ eh gm 92° 0^ eh 9m J3° 15^ s Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. 1 2 S 9.70834 .70837 .70840 .70843 .51091 .51094 .51098 .51103 9.71019 .71022 .71025 .71028 .51309 .51313 .51316 .51330 9.71203 .71206 .71210 .71213 .61537 .51531 .51534 .51538 9.71387 .71390 .71393 .71396 .51745 .51749 .51753 .51756 9.71569 .71572 .71575 .71579 .51963 .51967 .61970 .51974 60 59 58 57 + r 5 6 7 9.70847 .70850 .70853 .70856 .51105 .51109 .51113 .51116 9.71032 .71035 .71038 .71041 .51323 .51327 .51331 .51334 9.71216 .71219 .71222 .71225 .51541 .51545 .51549 .61553 9.71399 .71402 .71405 .71408 .51760 .51763 .51767 .51770 9.71582 .71585 .71588 .71591 .51978 .51981 .51985 .51988 56 55 54 53 + 2^ 9 10 11 9.70859 .70862 .70865 .70868 .51120 .51133 .51137 .51131 9.71044 .71047 .71050 .71053 .51338 .51343 .51345 .51349 9.71228 .71231 .71234 .71237 .61556 .61660 .61663 .51667 9.71411 .71414 .71417 .71420 .51774 .51778 .51781 .51785 9.71594 .71597 .71600 .71603 .51992 .51996 .61999 .63003 52 51 50 49 + 3- 13 14 15 9.70871 .70874 .70877 .70881 .51134 .51138 .51143 .51145 9.71056 .71059 .71062 .71065 .51353 .51356 .51360 .51363 9.71240 .71243 .71246 .71249 .61571 .51674 .51578 .51681 9.71423 .71426 .71430 .71433 .51789 .51793 .61796 .51799 9.71606 .71609 .71612 .71615 .63007 .63010 .52014 .52018 48 47 46 45 + 4^ 17 18 19 9.70884 .70887 .70890 .70893 .51149 .51153 .51156 .51160 9.71068 .71072 .71075 .71078 .51367 .51371 .51374 .51378 9.71252 .71255 .71259 .71262 .51585 .51589 .51593 .51596 9.71436 .71439 .71442 .71445 .51803 .61807 .51810 .61814 9.71618 .71621 .71624 .71627 .52021 .52025 .52028 .52032 44 43 42 41 40 39 38 37 + 5' 21 22 23 9.70896 .70899 .70902 .70905 .51163 .51167 .51171 .51174 9.71081 .71084 .71087 .71090 .51383 .51385 .51389 .51392 9.71265 .71268 .71271 .71274 .51600 .61603 .51607 .51611 9.71448 .71451 .71454 .71457 .61818 .61831 .61836 .51839 9.71630 .71633 .71636 .71639 .63036 .53039 .53043 .53047 + ^ 25 26 27 9.70908 .70911 .70914 .70918 .51178 .51183 .51185 .51189 9.71093 .71096 .71099 .71102 .51396 .51400 .51403 .51407 9.71277 .71280 .71283 .71286 .61614 .61618 .61631 .51625 9.71460 .71463 .71466 .71469 .51833 .61836 .61839 .61843 9.71642 .71645 .71648 .71651 .63050 .53054 .53057 .63061 36 35 34 33 + r 29 30 31 9.70921 .70924 .70927 .70930 .51193 .51198 .51300 .51303 9.71105 .71108 .71111 .71114 .51411 .51414 .51418 .51433 9.71289 .71292 .71295 .71298 .51629 .51633 .51636 .51640 9.71472 .71475 .71478 .71481 .51847 .51850 .51854 .51858 9.71654 .71657 .71660 .71663 .52065 .52068 .52072 .52076 32 31 30 29 + 8^ 33 34 35 9.70933 .70936 .70939 .70942 .51307 .51311 .51314 .51318 9.71118 .71121 .71124 .71127 .51425 .51429 .51432 .51436 9.71301 .71304 .71307 .71311 .61643 .51647 .51650 .51654 9.71484 .71487 .71490 .71493 .61861 .61866 .61869 .51873 9.71666 .71670 .71673 .71676 .62079 .62083 .52087 .52090 28 27 26 25 + 9" 37 38 39 9.70945 .70948 .70951 .70955 .51333 .51335 .51339 .51333 9.71130 .71133 .71136 .71139 .51440 .51443 .51447 .51451 9.71314 .71317 .71320 .71323 .51658 .51661 .61665 .61669 9.71496 .71500 .71503 .71506 .61876 .51879 .51883 .51887 9.71679 .71682 .71685 .71688 .62094 .62097 .62101 .62105 24 23 22 21 + ir 41 42 43 9.70958 .70961 .70964 .70967 .51336 .51340 .51243 .51247 9.71142 .71145 .71148 .71151 .51454 .51458 .51462 .51465 9.71326 .71329 .71332 .71335 .51673 .51676 .51680 .51683 9.71509 .71512 .71515 .71518 .61890 .61894 .51898 .51901 9.71691 .71694 .71697 .71700 .53108 .53113 .63116 .63119 20 19 18 17 + 11^ 45 46 47 9.70970 .70973 .70976 .70979 .51351 .51254 .51258 .51362 9.71154 .71157 .71161 .71164 .51469 .51472 .51476 .51480 9.71338 .71341 .71344 .71347 .61687 .61690 .51694 .51698 9.71521 .71524 .71527 .71530 .51905 .61908 .51913 .51916 9.71703 .71706 .71709 .71712 .53133 .52136 .53130 .53134 16 15 14 13 49 50 51 9.70982 .70985 .70988 .70992 .51365 .51369 .51373 .51376 9.71167 .71170 .71173 .71176 .51483 .51487 .51491 .51494 9.71350 .71353 .71356 .71359 .61701 .51705 .51709 .51713 9.71533 .71536 .71539 .71542 .51919 .51933 .51937 .51930 9.71715 :.71718 ;. 71721 .71724 .53137 .63141 .63145 .53148 12 11 10 9 + 13^ 53 54 55 9.70995 .70998 .71001 .71004 .51280 .51383 .51287 .51291 9.71179 .71182 .71185 .71188 .51498 .51501 .51505 .51508 9.71362 .71365 .71369 .71372 .61716 .51730 .51723 .51737 9.71545 .71548 .71551 .71554 .51934 .51938 .51941 .51946 9.71727 .71730 .71733 .71736 .63153 .63166 .53159 .53163 8 ' 7 6 5 + W 57 58 59 9.71007 .71010 .71013 .71016 .51294 .51298 .51303 .51305 9.71191 .71194 .71197 .71200 .51513 .51516 .51530 .51533 9.71375 .71378 .71381 .71384 .51730 .51734 .61738 .51741 9.71557 .71560 .71563 .71566 .51948 .51953 .51956 .51959 9.71739 .71742 .71745 .71748 .53166 .53170 .53174 .53177 4 3 2 1 4- 1^ 9.71019 .51309 9.71203 .61537 9.71387 .51745 9.71569 .61963 9.71751 .62181 17h 54m 17Ji 5Sm 17h 52m 17h sm 17h som 1 Page 118] TABLE IV. Haversinea. s 6ft lOm 92° sr 6h urn 93° 45/ 6h 12m 930 0' 6h 13m 93° 15' 6ft W^ 93° 30' 3 Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. 1 2 S 9.71751 .71754 .71757 .71760 .52181 .52185 .53188 .52192 9.71932 .71935 .71938 .71941 .52399 .52403 .52406 .52410 9.72112 .72115 .72118 .72121 .52617 .52620 .52624 .52628 9.72292 .72295 .72298 .72301 .52835 .52838 .52842 .52846 9.72471 .72474 .72476 .72479 .53052 .53056 .53060 .53063 60 59 58 57 + r 5 6 7 9.71763 .71766 .71769 .71772 .52196 .52199 .52203 .52206 9.71944 .71947 .71950 .71953 .52413 .52417 .52421 .52424 9.72124 .72127 .72130 .72133 .52631 .52635 .53639 .52643 9.72304 .72307 .72310 .72313 .53849 .53853 .52856 .52860 9.72482 .72485 .72488 .72491 .53067 .53071 ,53074 .53078 56 55 54 53 + r 9 10 11 9.71775 .71778 .71781 .71784 .62210 .52214 .52217 .52221 9.71956 .71959 .71962 .71965 .52428 .52433 .52435 .52439 9.72136 .72139 .72142 .72145 .52646 .52649 .52653 .52657 9.72316 .72319 .72322 .72325 .52864 .52867 .52871 .52875 9.72494 .72497 .72500 .72503 .53081 .53085 .53089 .53092 52 51 50 49 + 3' IS 14 15 9.71787 .71791 .71794 .71797 .52225 .52228 .52232 .52235 9.71968 .71971 .71974 .71977 .52443 .52446 .52450 .53453 9.72148 .72151 .72154 .72157 .52660 .52664 .53668 .53671 9.72328 .72331 .72334 .72337 .52878 .52882 .52885 .52889 9.72506 .72509 .72512 .72515 .53096 .53100 .53103 .53107 48 47 46 45 + 4' 17 18 19 9.71800 .71803 .71806 .71809 .52239 .52243 .52246 .52250 9.71980 .71983 .71986 .71989 .52457 .52461 .52464 .52468 9.72160 .72163 .72166 .72169 .53675 .52679 .52682 .52688 9.72340 .72343 .72346 .72349 .52893 .53896 .53900 .53904 9.72518 .72521 .72524 .72527 .53110 .53114 .53118 .53121 44 43 42 41 + 5' 21 22 23 9.71812 .71815 .71818 .71821 .52254 .52257 .52261 .52264 9 71992 .71995 .71998 .72001 .52472 .53475 .52479 .52482 9.72172 .72175 .72178 .72181 .52689 .52693 .52697 .52700 9.72352 .72354 .72357 .72360 .53907 .52911 .52915 .52918 9.72530 .72533 .72536 .72539 .53125 .53129 .53132 .53136 40 39 38 37 + 6' 25 26 27 9.71824 .71827 .71830 .71833 .52268 .52272 .52275 .52279 9.72004 .72007 .72010 .72013 .52486 .52490 .52493 .52497 9.72184 .72187 .72190 .72193 .52704 .52708 .53711 .53715 9.72363 .72366 .72369 .72372 .52922 .52925 .52929 .52933 9.72542 .72545 .72548 .72551 .53140 .53143 .53147 .53150 36 35 34 33 + r 29 30 31 9.71836 .71839 .71842 .71845 .52283 .52286 .52290 .52294 9.72016 .72019 .72022 .72025 .52501 .52504 .52508 .52511 9.72196 .72199 .72202 .72205 .52718 .52722 .52726 .53739 9.72375 .72378 .72381 .72384 .52936 .52940 .52944 .52947 9.72554 .72557 .72560 .72563 .53154 .53158 .53161 .53165 32 31 30 29 + 8' 33 34 35 9.71848 .71851 .71854 .71857 .52297 .52301 .52304 .52308 9.72028 .72031 .72034 .72037 .52515 .52519 .52522 .52526 9.72208 .72211 .72214 .72217 .53733 .53737 .53740 .52744 9.72387 .72390 .72393 .72396 .52951 .52954 .52958 .53963 9.72565 .72568 .72571 .72574 .53169 .53172 .53176 .53179 28 27 26 25 24 23 22 21 + ^ 37 38 • 39 9.71860 .71863 .71866 .71869 .52312 .52315 .52319 .52323 9.72040 .72043 .72046 .72049 .52530 .52533 .52537 .52541 9.72220 .72223 .72226 .72229 .52748 .52751 .52755 .52758 9.72399 .72402 .72405 .72408 .53965 .53969 .53973 .53976 9.72577 .72580 .72583 .72586 .53183 .53187 .53190 .53194 + W 41 42 45 9.71872 .71875 .71878 .71881 .52326 .52330 .52334 .52337 9.72052 .72055 .72058 .72061 .52544 .52548 .52551 .52555 9.72232 .72235 .72238 .72241 .53762 .52766 .52769 .52773 9.72411 .72414 .72417 .72420 .53980 .53983 .52987 .52991 9.72589 .72592 .72595 .72598 .53198 .53201 .53205 .53208 20 19 IS 17 + IV 45 4S 47 9.71884 .71887 .71890 .71893 .52341 .52344 .52348 .52352 9.72064 .72067 .72070 .72073 .52559 .52562 .52566 .52570 9.72244 .72247 .72250 .72253 .52776 .52780 .53784 .53787 9.72423 .72426 .72429 .72432 .52994 .52998 .53002 .53005 9.72601 .72604 .72607 .72610 .53212 .53216 .53219 .53223 16 15 14 13 + 12' 49 50 51 9.71896 .71899 .71902 .71905 .52355 .52359 .52363 .52366 9.72076 .72079 .72082 .72085 .52573 .52577 .53580 .53584 9.72256 .72259 .72262 .72265 .53791 .53795 .53798 .53802 9.72435 .72438 .72441 .72444 .53009 .53013 .53016 .53020 9.72613 .72616 .72619 .72622 .53227 .53230 .53234 .63238 12 11 10 9 + 13' 53 54 55 9.71908 .71911 .71914 .71917 .52370 .52373 .52377 .52381 9.72088 .72091 .72094 .72097 .53588 .53591 .53595 .53599 9.722G8 ,72271 .72274 .72277 .52806 .53809 .53813 .53816 9.72447 .72450 .72453 .72456 .53033 .53037 .53031 .53034 9.72625 .72628 .72631 .72634 .53241 .53245 .53248 .53262 8 7 6 5 + 14' 57 58 59 9.71920 .71923 .71926 .71929 .52384 .52388 .52392 .52395 9.72100 .72103 .72106 .72119 .53603 .53606 .53610 .53613 9.72280 .72283 .72286 .72289 .52820 .52824 .52827 .52831 9.72459 .72462 .72465 .72468 .53038 .53042 .53045 .53049 9.72637 .72640 .72642 .72645 .55256 .53269 .63263 .63267 4 S 2 1 + 15' 9.71932 .52399 9.72112 .52617 9.72292 .52835 9.72471 .53052 9.72648 .53370 17h49m 17^48^ IJh 47m 17h46m 17^ 45m TABLE IV. [Page 119 Haversines. s 6ft lo^n 93° 45' eh 16m 94° (y eh 17m 940 15/ eh ism 94° sr eh 19m 94° 45 3 Log. Hav. Nat. Hav Log. Hav. Nat. Hav Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav 1 2 3 9.72648 .72651 .72654 .72657 .53270 .53374 .53377 .53381 9.72825 .72828 .72831 .72834 .53488 .53491 .53495 .53499 9.73002 .73005 .73008 .73011 .53705 .53709 .53713 .53716 9.73177 .73180 .73183 .73186 .53923 .53927 .53930 .53934 9.73352 .73355 .73358 .73361 .54140 .54144 .54148 .54151 60 59 58 57 5 6 7 9.72660 .72663 .72666 .72669 .53385 .53388 .53393 .53396 9.72837 .72840 .72843 .72846 .53502 .53506 .53510 .53513 9.73014 .73016 .73019 .73022 .53730 .53724 .53727 .53731 9.73189 .73192 .73195 .73198 .53937 .53941 .53945 .53948 9.73364 .73367 .73370 .73373 .54155 .54159 .54163 .54166 56 55 54 53 1 + 3' . 9 10 11 9.72672 .72675 .72678 .72681 .53399 .53303 .53306 .53310 9.72849 .72852 .72855 .72858 .53517 .53520 .53524 .53528 9.73025 .73028 .73031 .73034 .53734 .53738 .53742 .53745 9.73201 .73204 .73207 .73209 .53952 .53956 .53959 .53963 9.73375 .73378 .73381 .73384 .54169 .54173 .54177 .54180 52 51 50 49 + 3' 13 14 15 9.72684 .72687 .72690 .72693 .53314 .53317 .53331 .53335 9.72861. .72864 .72867 .72870 .53531 .53535 .53539 .53542 9.73037 .73040 .73043 .73046 .53749 .53753 .53756 .53760 9.73212 .73215 .73218 .73221 .53966 .53970 .53974 .53977 9.73387 .73390 .73393 .73396 .54184 .54188 .54191 .54195 48 47 46 45 44 43 42 41 + r 17 18 19 9.72696 .72699 .72702 .72705 .53328 .53333 .53335 .53339 9.72873 .72876 .72878 .72881 .53546 .53549 .53553 .53557 9.73049, .73052 .73055 .73057 .53763 .53767 .53771 .53774 9.73224 .73227 .73230 .73233 .53981 .53985 .53988 .53992 9.73399 .73402 .73404 .73407 .54198 .54202 .54306 .54209 + 5' 21 22 23 9.72708 .72710 .72713 .72716 .53343 .53346 .53350 .53354 9.72884 .72887 .72890 .72893 .53560 .53564 .53568 .53571 9.73060 .73063 .73066 .73069 .53778 .53782 .53785 .53789 9.73236 .73239 .73242 .73244 .53995 .53999 .54003 .54006 9.73410 .73413 .73416 .73419 .54313 .54317 .54330 .54334 40 39 38 37 + 6' 25 26 27 9.72719 .72722 .72725 .72728 .53357 .53361 .53364 .53368 9.72896 .72899 .72902 .72905 .53575 .53579 .53582 .53586 9.73072 .73075 .75078 .73081 .53792 .53796 .53800 .53803 9.73247 .73250 .73253 .73256 .54010 .54014 .54017 .54021 9.73422 .73425 .73428 .73431 .54337 .54331 .54335 .54338 36 35 34 33 32 31 30 29 + r 29 30 31 9.72731 .72734 .72737 .72740 .53373 .53375 ..53379 .53383 9.72«08 .72911 .72914 .72917 .53589 .53593 .53597 .53600 9.73084 .73087 .73090 .73093 .53807 .53811 .53814 .53818 9.73259 .73262 .73265 .73268 .54024 .54038 .54033 .54035 9.73433 .73436 .73439 .73442 .54242 .54245 .54249 .54253 + 8' 33 34 35 9.72743 .72746 .72749 .72752 .53386 .53390 .53394 .53397 9.72920 .72923 .72926 .72928 .53604 .53608 .53611 .53615 9.73096 .73098 .73101 .73104 .53821 .53825 .53829 .53832 9.73271 .73274 .73277 .73280 .54039 .54043 .54046 .54050 9.73445 .73448 .73451 .73454 .54256 .54260 .54264 .54267 28 27 26 25 + 9" 37 38 39 9.72755 .72758 .72761 .72764 .53401 .53404 .53408 .53413 9.72931 .72934 .72937 .72940 .53618 .53622 .53626 .53629 9.73107 .73110 .73113 .73116 .53836 .53840 .53843 .53847 9.73282 .73285 .73288 .73291 .54053 .54057 .54061 .54064 9.73457 .73460 .73462 .73465 .54271 .54274 .54378 .54282 24 23 22 21 41 42 43 9.72767 .72770 .72772 .72775 .53415 .53419 .53433 .53436 9.72943 .72946 .72949 .72952 .53633 .53637 .53640 .53644 9.73119 .73122 .73125 .73128 .53850 .53854 .53858 .53861 9.73294 .73297 .73300 .73303 .54068 .54072 .54075 .54079 9.73468 .73471 .73474 .73477 .54285 .54289 .54393 .54296 20 19 18 17 45 46 47 9.72778 .72781 .72784 .72787 .53430 .53433 .53437 .53441 9.72955 .72958 .72961 .72964 .53647 .53651 .53655 .53658 9.73131 .73134 .73136 .73139 .53865 .53869 .53872 .53876 9.73306 .73309 .73311 .73314 .54082 .54086 .54090 .54093 9.73480 .73483 .73486 .73489 .54300 .54303 .54307 .54311 16 15 14 13 + 13' 49 50 51 9.72790 .72793 .72796 .72799 .53444 .53448 .53453 .53455 9.72967 .72970 .72972 .72975 .53663 .53666 .53669 .53673 9.73142 .73145 .73148 .73151 .53879 .53883 .53887 .53890 9.73317 .73320 .73323 .73326 .54097 .54101 .54104 .54108 9.73491 .73494 .73497 .73500 .54314 .54318 .54322 .54325 12 11 10 9 + 13' 53 54 55 9.72802 .72805 .72808 .72811 .53459 .53463 .53466 .53470 9.72978 .72981 .72984 .72987 .53676 .53680 .53684 .53687 9.73154 .73157 .73160 .73163 .53894 .53898 .53901 .53905 9.73329 .73332 .73335 .73338 .54111 .54115 .54119 .54122 9.73503 .73506 .73509 .73512 .54329 .54332 .54336 .54340 8 7 6 5 + 14' 57 58 59 9.72814 .72817 .72820 .72823 .53473 .53477 .53481 .53484 9.72990 .72993 .72996 .72999 .53691 .53695 .53698 .53703 .53705 9.73166 .73169 .73172 .73174 .53908 .53912 .53916 .53919 9.73341 .73343 .73346 .73349 .54126 .54130 .54133 .54137 9.73515 .73517 .73520 .73523 .54343 .54347 .54351 .54354 4 3 2 1 + 15' 9.72825 .53488 9.73002 9.73177 .53923 9.73352 .54140 9.73526 .54358 17^ 44'^ 1 17h 43m 1 17h 42m 1 17h 41m 17h 40m 1 Page 120] TABLE IV. Haversines. s Qh 20m 95° 0' 6h 21m 95° 15' Qh 22""<' 95° 30' 6h 23m 95° 45' gh 24^ 96° r s 60 59 58 57 Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. 1 2 3 9.73526 .73529 .73532 .73535 .54358 .54361 .543G5 .54369 9.73699 .73702 .73705 .73708 .54575 .54579 .54583 .54586 9.73872 .73875 .73878 .73881 .54793 .54796 .54800 .54803 9.74044 .74047 .74049 .74052 .55009 .55013 .55017 .55030 9.74215 .74218 .74220 .74223 .55226 .55330 .55334 .56337 + r 5 6 7 9.73538 .73541 .73544 .73546 .54373 .54376 .54380 .54383 9.73711 .73714 .73717 .73720 .54590 .54593 .54597 .54600 9.73883 .73886 .73889 .73892 .54807 .54810 .54814 .54818 9.74055 .74058 .74061 .74064 .55024 .55038 .55031 .55035 9.74226 .74229 .74232 .74235 .55241 .55245 .55248 .65252 56 55 54 53 + a' 9 10 11 9.73549 .73552 .73555 .73558 .54387 .54390 .54394 .54398 9.73722 .73725 .73728 .73731 .54604 .54608 .54611 .54615 9.73895 .73898 .73901 .73903 .54821 .54825 .54828 .54832 9.74067 .74069 .74072 .74075 .55038 .55043 .55046 .55049 9.74237 .74240 .74243 .74246 .55255 .55259 .55263 .55266 52 51 50 49 + 3' 13 14 15 9.73561 .73564 .73567 .73570 .54401 .54405 .54409 .54412 9.73734 .73737 .73740 .73743 .54619 .54633 .54636 .54639 9.73906 .73909 .73912 .73915 .54836 .54839 .54843 .54847 9.74078 .74081 .74084 .74087 .55053 .55056 .55060 .55064 9.74249 .74252 .74254 .74257 .66270 .65273 .55377 .55381 48 47 46 45 + 4' 17 18 19 9.73572 .73575 .73578 .73581 .54416 .54419 .54433 .54437 9.73746 .73748 .73751 .73754 .54633 .54637 .54640 .54644 9.73918 .73921 .73924 .73926 .54850 .54854 .54857 .54861 9.74089 .74092 .74095 .74098 .55067 .55071 .55075 .55078 9.74260 .74263 .74266 .74269 .55384 .55388 .65393 .65295 44 43 42 41 + 5^ 21 22 23 9.73584 .73587 .73590 .73593 .54430 .54434 .54437 .54441 9.73757 .73760 .73763 .73766 .54647 .54651 .54655 .54658 9.73929 .73932 .73935 .73938 .54865 .54868 .54872 .54876 9.74101 .74104 .74106 .74109 .55083 .55085 .55089 .55093 9.74272 .74274 .74277 .74280 .55399 .65303 .55306 .55310 40 39 38 37 + 6' 25 26 27 9.73596 .73598 .73601 .73604 .54445 .54448 .54453 .54456 9.73769 .73771 .73774 .73777 .54663 .54666 .54669 .54673 9.73941 .73944 .73946 .73949 .54879 .54883 .54886 .54890 9.74112 .74115 .74118 .74121 .55096 .55100 .55103 .55107 9.74283 .74286 .74289 .74291 .55313 .55317 .66330 .65324 36 35 34 33 + r 29 30 31 9.73607 .73610 .73613 .73616 .54459 .54463 .54466 .54470 9.73780 .73783 .73786 .73789 .54676 .54680 .54684 .54687 9.73952 .73955 .73958 .73961 .54894 .54897 .54901 .54904 9.74124 .74126 .74129 .74132 .55111 .55114 .65118 .55133 9.74294 .74297 .74300 .74303 .55328 .65331 .55335 .55339 32 31 30 29 + 8^ 33 34 35 9.73619 .73622 .73624 .73627 .54474 .54477 .54481 .54485 9.73792 .73794 .73797 .73800 .54691 .54695 .54698 .54703 9.73964 .73967 .73969 .73972 .54908 .54912 .54915 .54919 9.74135 .74138 .74141 .74144 .55125 .55129 .55132 .65136 9.74306 .74308 .74311 .74314 .55342 .55346 .55349 .55353 28 27 26 25 + 9^ 37 38 39 9.73630 .73633 .73636 .73639 .54488 .54493 .54495 .54499 9.73803 .73806 .73809 .73812 .54705 .54709 .54713 .54716 9.73975 .73978 .73981 .73984 .54923 .54936 .51930 .51933 9.74146 .74149 .74152 .74155 .55140 .55143 .55147 .65150 9.74317 .74320 .74323 .74325 .55357 .55360 .55364 .55367 24 23 22 Tl + 10' 41 42 4S 9.73642 .73645 .73648 .73650 .54503 .54506 .54510 .54514 9.73815 .73817 .73820 .73823 .54730 .54724 .54737 .54731 9.73987 .73989 .73992 .73995 .54937 .54941 .54944 .54948 9.74158 .74161 .74163 .74166 .55154 .55158 .55161 .55165 9.74328 .74331 .74334 .74337 .55371 .65375 .55378 .56382 20 19 18 17 + 11^ 45 46 47 9.73653 .73656 .73659 .73662 .54517 .54531 .54534 .54538 9.73826 .73829 .73832 .73835 .54734 .54738 .54743 .54745 9.73998 .74001 .74004 .74007 .54953 .54955 .54959 .54963 9.74169 .74172 .74175 .74178 .65169 .65172 .55176 .55179 9.74340 .74342 .74345 .74348 .55386 .65389 .65393 .55396 16 15 14 13 12 11 10 9 + ir 49 50 51 9.73665 .73668 .73671 .73674 .54533 .54535 .54539 .54543 9.73838 .73840 .73843 .73846 .54749 .54753 .54756 .54760 9.74009 .74012 .74015 .74018 .54966 .54970 .54973 .54977 9.74181 .74183 .74186 .74189 .55183 .55187 .55190 .55194 9.74351 .74354 .74357 .74359 .55400 .55404 .55407 .55411 + 13' 53 54 55 9.73676 .73679 .73682 .73685 .54546 .54550 .54553 .54557 9.73849 .73852 .73855 .73858 .54763 .54767 .54771 .54774 9.74021 .74024 .74027 .74029 .54980 .54984 .54988 .54991 9.74192 .74195 .74198 .74200 .55197 .55201 .65205 .55208 9.74362 .74365 .74368 .74371 .55414 .55418 .55422 .65425 8 1 6 5 + 1¥ 57 58 59 9.73688 .73691 .73694 .73697 .54561 .54564 .54668 .54571 9.73860 .73863 .73866 .73869 .54778 .54781 .54785 .54789 9.74032 .74035 .74038 .74041 .54995 .54999 .55003 .55006 9.74203 .74206 74209 .74212 .55212 .55216 .66219 .65223 9.74374 .74376 .74379 .74382 .55429 .55433 .66436 .55440 4 3 2 "1 + IS' 9.73699 .54575 9.73872 .54793 9.74044 .55009 9.74215 .55326 9.74385 .55443 _ 17 fi 39m nhssm nu 37m 17^ 36m i7ft SS-m TABLE IV. Haversines. [Page 121 s 6h 25m 96° 15' 6ft 26m 96° 30' 6h 27m 96° 45' 6ft 28m 97° Q' Oh ogm 97° 15' s Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. 1 2 3 9.74385 .74388 .74391 .74393 .55443 .55447 .55451 .55454 9.74554 .74557 .74560 .74563 .55660 .55664 ,55667 .55671 9.74723 .74726 .74729 .74732 .55877 .55880 .55884 .55888 9.74891 .74894 .74897 .74900 .56093 .56097 .56101 .56104 9.75059 .75061 .75004 .75067 .56310 .56314 .56317 .56321 60 59 58 57 + r 5 6 7 9.7439(3 .74399 .74402 .74405 .55458 .55461 .55465 .55469 9.74566 .74569 .74571 .74574 .55675 .55678 .55683 .55685 9.74734 .74737 .74740 .74743 .55891 .55895 .55899 .55903 9.74902 .74905 .74908 .74911 .56108 .56113 .56115 .56119 9.75070 .75072 .75075 .75078 .56324 .56328 .56332 .56335 56 55 54 53 + r 9 10 11 9.74408 .74410 .74413 .74416 .55473 .55476 .55479 .55483 9.74577 .74580 .74583 .74585 .55689 .55693 .55696 .55700 9.74746 .74748 .74751 .74754 .55906 .55909 .55913 .55917 9.74914 .74916 .74919 .74922 .56133 .56136 .56130 .56133 9.75081 .75084 .75086 .75089 .56339 .56343 .56346 .56350 52 51 50 49 + 3' 13 14 15 9.74419 .74422 .74425 .74427 .55487 .55490 .55494 .55498 9.74588 .74591 .74594 .74597 .55704 .55707 .55711 .55714 9.74757 .74760 .74762 .74765 .55920 .55924 .55927 .55931 9.74925 .74928 .74930 .74933 .56137 .56140 .56144 .56147 9.75092 .75095 .75097 .75100 .56353 .56357 .56360 .56364 .56368 .56371 .56375 .56378 Jy8 47 46 45 44 43 42 41 40 39 38 37 36 35 34 33 + i' 17 18 19 9.74430 .74433 .74436 .74439 .55501 .55505 .55508 .55513 9.74600 .74602 .74605 .74603 .55718 .55723 .55725 .55729 9.74768 .74771 .74774 .74776 .55935 .55938 .55943 .55945 9.74936 .74939 .74941 .74944 .56151 .56155 .56158 .56162 9.75103 .75106 .75109 .75111 + 5' 21 22 23 9.74442 .74444 .74447 .74450 .55516 .55519 .55523 .55526 9.74611 .74614 .74616 .74619 .55733 .55736 .55740 .55743 9.74779 .74782 .74785 .74788 .55949 .55953 .55956 .55960 9.74947 .74950 .74953 .74955 .56166 .56169 .56173 .56176 9.75114 .75117 .75120 .75122 .56383 .56386 .56389 .56393 .56397 .56400 .56404 .56407 + 6' 25 26 27 9.74453 .74456 .74458 .74461 .55530 .55534 .55537 .55541 9.74622 .74625 .74628 .74630 .55747 .55750 .55754 .55758 9.74791 .74793 .74796 .74799 .55964 .55967 .55971 .55974 9.74958 .74961 .74964 .74967 .56180 .56184 .56187 .56191 9.75125 .75128 .75131 .75134 + r 29 SO 31 9.74464 .74467 .74470 .74473 .55545 .55548 .55553 .55555 9.74633 .74636 .74639 .74642 .55761 .55765 .55769 .55773 9.74802 .74805 .74807 .74810 .55978 .55983 .55985 .55989 9.74969 .74972 .74975 .74978 .56195 .56198 .56203 .56305 9.75136 .75139 .75142 .75145 .56411 .56415 .56418 .56423 32 3^1 30 29 + 8' 33 34 35 9.74475 .74478 .74481 .74484 .55559 .55563 .55566 .55570 9.74645 .74647 .74650 .74653 .55776 .55779 .55783 .55787 9.74813 .74816 .74819 .74821 .55993 .55996 .56000 .56003 9.74981 .74983 .74986 .74989 .56309 .56313 .56316 .56330 9.75147 .75150 .75153 .75156 .56435 .56439 .56433 .56436 28 27 26 25 + 9' 37 38 39 9.74487 .74490 .74492 .74495 .55573 .55577 .55581 .55584 9.74656 .74659 .74661 .74664 .55790 .55794 .55797 .55801 9.74824 .74827 .74830 .74833 .56007 .56010 .56014 .56018 9.74992 .74994 .74997 .75000 .56333 .56337 .56331 .56334 9.75159 .75161 .75104 .75107 .56440 .56443 .56447 .56451 24 23 22 21 20 19 18 17 + W 41 42 43 9.74498 .74501 .74504 .74506 .55588 .55592 .55595 .55599 9.74667 .74670 .74673 .74675 .55805 .55808 .55813 .55815 -9.74835 .74838 .74841 .74844 .56031 .56035 .56039 .56033 9.75003 .75006 .75008 .75011 .56338 .56241 .56245 .56349 9.75170 .75172 .75175 .75178 .56454 .56458 .56461 .56465 + 11^ 45 46 47 9.74509 .74512 .74515 .74518 .55603 .55606 .55610 .55613 9.74678 .74681 .74684 .74687 .55819 .55833 .55836 .55830 9.74846 .74849 .74852 .74855 .56036 .56039 .56043 .56047 9.75014 .75017 .75020 .75022 .56353 .56256 .56259 .56263 9.75181 .75183 .75186 .75189 .56469 .56473 .56476 .56479 16 15 14 13 12 11 10 9 + ir 49 50 51 9.74521 .74523 .74526 .74529 .55617 .55630 .55634 .55638 9.74690 .74692 .74695 .74698 .55834 .55837 .55841 .55844 9.74858 .74860 .74863 .74866 .56050 .56054 .56057 .56061 9.75025 .75028 .75031 .75033 .56367 .56370 .56374 .56377 9.75192 .75195 .75197 .75200 .56483 .56487 .56490 .56494 + 13' 53 54 55 9.74532 .74535 .74538 .74540 .55631 .55635 .55638 .55643 9.74701 .74704 .74706 .74709 .55848 .55853 .55855 .55859 9.74869 .74872 .74874 .74877 .56065 .56068 .56073 .56075 9.75036 .75039 .75042 .75045 .56381 .56385 .56388 .56393 9.75203 .75206 .75208 .75211 .56497 .56501 .56505 .56508 8 7 6 5 4 3 2 1 > 14' 57 58 59 9.74543 .74546 .74549 .74552 .55646 .55649 .55653 .55657 9.74712 .74715 .74718 .74720 .55863 .55866 .55870 .55873 9.74880 .74883 .74886 .74888 .56079 .56083 .56086 .56090 9.75047 .75050 .75053 .75056 .56296 .56299 .56303 .56306 9.75214 .75217 .75220 .75222 .56513 .56516 .56519 .56533 + 15' 9.74554 .55660 9.74723 .55877 9.74891 .56093 9.75059 .56310 9.75225 .56536 17h 34"^ l^h ssm 17h32m 17h Sim 17h 30m Page 122] TABLE IV. Havereinea. s 6h som 97° 3(K en Sim 97° 45' 6h 32m 98° 0' 6h 33m 98° 15' eh 34m 98° 30' s Log. Hav. Nat. Hav. Log. Hav Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. 1 2 5 9.75225 .75228 .75231 .75233 .56536 .56530 .56534 .56537 9.75391 .75394 .75396 .75399 .56743 .56746 .56750 .56753 9.75556 .75559 .75561 .75564 .56959 .56963 .56966 .56969 9.75720 .75723 .75726 .75729 .57175 .57178 .57183 .57185 9.75884 .75887 .75889 .75892 .57390 .57394 .57398 .57401 60 59 58 57 + V 5 6 7 9.75236 .75239 .75242 .75244 .56541 .56544 .56548 .56553 9.75402 .75405 .75407 .75410 .56757 .56761 .56764 .56768 9.75507 .75570 .75572 .75575 .56973 .56977 .56980 .56984 9.75731 .75734 .75737 .75739 .57189 .57193 .57196 .57300 9.75895 .75898 .75900 .75903 .57405 .67408 .57413 .57416 56 55 54 53 + V 9 10 11 9.75247 .75250 .75253 .75256 .56555 .56559 .56563 .56566 9.75413 .75416 .75418 .75421 .56771 .56775 .56779 .56783 9.75578 .75581 .75583 .75586 .56987 .56991 .56994 .56998 9.75742 .75745 .75748 .75750 .57303 .57307 .57311 .57314 9.75906 .75908 .75911 .75914 .57419 .57433 .57436 .57430 52 51 50 49 + r 13 14 15 9.75258 .75261 .75264 .75267 .56570 .56573 .56577 .56580 9.75424 .75427 .75429 .75432 .56786 .56789 .56793 .56797 9.75589 .75592 .75594 .75597 .57003 .57005 .57009 .57013 9.75753 .75756 .75759 .75761 .57318 .57331 .57335 .57339 9.75917 .75919 .75922 .75925 .57434 .57437 .57441 .57444 48 47 46 45 n 18 19 9.75269 .75272 .75275 .75278 .56584 .56588 .56591 .56595 9.75435 .75438 .75440 .75443 .56800 .56804 .56807 .56811 9.75600 .75603 .75605 .75608 .57016 .57030 .57033 .57037 9.75764 .75767 .75770 .75772 .57333 .57336 ^7339 .57343 9.75927 .75930 .75933 .75936 .57448 .57453 .57455 .57459 U 43 42 41 + 5' 21 22 23 9.75280 .75283 .75286 .75289 .56598 .56603 .56606 .56609 9.75446 .75449 .75452 .75454 .56815 .56818 .56833 .56835 9.75611 .75614 .75616 .75619 .57031 .57034 .57038 .57041 9.75775 .75778 .75780 .75783 .57347 .57350 .57354 .57357 9.75938 .75941 .75944 .75947 .57463 .57466 .57470 .57473 40 39 38 37 + ^ 25 26 27 9.75291 .75294 .75297 .75300 .56613 .56616 .56630 .56634 9.75457 .75460 .75463 .75465 .56839 .56833 .56836 .56840 9.75622 .75625 .75627 .75630 .57045 .57049 .57053 .57056 9.75786 .75789 .75791 .75794 .57361 .57365 .57368 .57373 9.75949 .75952 .75955 .75957 .57477 .57480 .57484 .57488 36 36 34 33 + r 29 30 31 9.75303 .75305 .75308 .75311 .56637 .56631 .56634 .5663S 9.75468 .75471 .75474 .75476 .56843 .56847 .56851 .56854 9.75633 .75636 .75638 .75641 .57059 .57063 .57067 .57070 9.75797 .75800 .75802 .75805 .57375 .57379 .57383 .57386 9.75960 .75963 .75966 .75968 .57491 .57495 .57498 .57503 32 31 30 29 + S' 33 34 35 9.75314 .75316 .75319 .75322 .56643 .56645 .56649 .56653 9.75479 .75482 .75485 .75487 .56858 .56861 .56865 .56869 9.75644 .75646 .75649 .75652 .57074 .57077 .57081 .57085 9.75808 .75810 .75813 .75816 .57390 .57393 .57397 .57301 9.75971 .75974 .75976 .75979 .57506 .57509 .57513 .57516 28 27 26 25 + ^ 37 38 39 9.75325 .75327 .75330 .75333 .56656 .56660 .56663 .56667 9.75490 .75493 .75496 .75498 .56873 .56876 .56879 .56883 9.75655 .75657 .75660 .75663 .57088 .57093 .57095 .57099 9.75819 .75821 .75824 .75827 .57304 .57308 .57311 .57315 9.75982 .75985 .75987 .75990 .57530 .57534 .57537 .57531 24 23 22 21 + W 41 42 43 9.75336 .75338 .75341 .75344 .56670 .56674 .56678 .56681 9.75501 .75504 .75507 .75509 .56887 .56890 .56894 .56897 9.75666 .75668 .75671 .75674 .57103 .57106 .57110 .57114 9.75830 .75832 .75835 .75838 .57318 .57333 .57336 .57339 9.75993 .75995 .75935 .76001 .57534 .57538 .57541 .57545 20 19 18 17 + 11' 45 46 47 9.75347 .75350 .75352 .75355 .56685 .56689 .56693 .56696 9.75512 .75515 .75518 .75520 .56901 .56905 .56908 .56913 9.75677 .75679 .75682 .75685 .57117 .57131 .57134 .57138 9.75840 .75843 .75846 .75849 .57333 .57337 .57340 .57344 9.76004 .76006 .76009 .76012 .57549 .57553 .57556 .57559 16 15 14 13 + n' 49 50 51 9.75358 .75361 .75363 .75366 .56699 .56703 .56707 .56710 9.75523 .75526 .75529 .75531 .56915 .56919 .56933 .56936 9.75688 .75690 .75693 .75696 .57131 .57135 .57139 .57143 9.75851 .75854 .75857 .75859 .57347 .57351 .57355 .57358 9.76014 .76017 .76020 .76023 .57563 .57567 .57570 .57574 12 11 10 9 + 13' 53 54 55 9.75369 .75372 .75374 .75377 .56714 .56717 .56731 .56735 9.75534 .75537 .75540 .75542 .56930 .56933 .56937 .56941 9.75698 .75701 .75704 .75707 .57146 .57149 .57153 .57157 9.75862 .75865 .75868 .75870 .57363 .57365 .57369 .57373 9.76025 .76028 .76031 .76033 .57577 .57581 .57585 .57588 8 7 6 5 + W 57 58 59 9.75380 .75383 .75385 .75388 .56738 .56733 .56735 .56739 9.75545 .75548 .75550 .75553 .56944 .56948 .56951 .56955 9.75709 .75712 .75715 .75718 .57160 .57164 .57167 .57171 9.75873 .75876 .75879 .75881 .57376 .57380 .57383 .57387 9.76036 .76039 .76041 .76044 .57593 .57595 .57599 .57603 4 S 2 1 + 15' 9.75391 .56743 9.75556 .56959 9.75720 .57175 9.75884 .57390 9.76047 .57606 17h29m 1 17^ 28m 17h gym 17h ?6m 17h 25m 1 TABLE IV. [Page 123 Haversines. s 6ft S5m 98° 45' 6h 36m 990 0' 6h ,37m 990 15' 6ft 38m 990 30' 6ft S9m 99° 45' s Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. 1 2 3 9.76047 .76050 .76052 .76055 .57606 .57610 .57613 .57617 9.76209 .76212 .76215 .76217 .57833 .57835 .57839 .57833 9.76371 .76373 .76376 .76379 .58037 .58041 .58044 .58048 9.76531 .76534 .76537 .76539 .58353 .58356 .58360 .58363 9.76691 .76694 .76697 .76699 .58467 .58471 .58475 .58478 60 59 58 57 + r 5 6 7 9.76058 .76060 .76063 .76066 .57631 .57634 .57638 .57631 9.76220 .76223 .76225 .76228 .57836 .57840 .57843 .57847 9.76381 .76384 .76387 .76389 .58051 .58055 .58059 .58063 9.76542 .76545 .76547 .76550 .58367 .58370 .58374 .58377 9.76702 .76705 .76707 .76710 .58483 .58486 .68489 .58493 56 55 54 53 9 10 11 9.76069 .76071 .76074 .76077 .57635 .57639 .57643 .57646 9.76231 .76233 .76236 .76239 .57850 .57854 .57858 .57861 9.76392 .76395 .76397 .76400 .58066 .58069 .58073 .58077 9.76553 .76555 ,76558 .76561 .58381 .58385 .58388 .58393 9.76713 .76715 .76718 .76721 .58496 .58500 .58503 .58507 52 51 50 49 48 47 46 45 + 3' IS 14 15 9.76079 .76082 .76085 .76088 .57649 .57653 .57656 .57660 9.76241 .76244 .76247 .76250 .57865 .57868 .57873 .57876 9.76403 .76405 .76408 .76411 .58080 .58084 .58087 .58091 9.76563 .76566 .76569 .76571 .58395 .58399 .58303 .58306 9.76723 .76726 .76729 .76731 .58510 .58614 .58618 .58531 + 4' 17 18 19 9.76090 .76093 .76096 .76098 .57661 .57667 .57671 .57675 9.76252 .76255 .76258 .76260 .57879 .57883 .57886 .57890 9.76414 .76416 .76419 .76422 .58095 .58098 .58103 .58105 9.76574 .76577 .76579 .76582 .58310 .58313 .58317 .58331 9.76734 .76737 .76739 .76742 .58535 .58538 .58533 .58636 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 + 5' 21 22 23 9.76101 .76104 .76106 .76109 .57678 .57683 .57685 .57689 9.76263 .76266 .76268 .76271 .57894 .57897 .57901 .57904 9.76424 .76427 .76430 .76432 .58109 .58113 .58116 .58130 9.76585 .76587 .76590 .76593 .58334 .58338 .58331 .58335 9.76745 .76747 .76750 .76753 .58639 .68643 .68646 .68550 + 6' 25 26 27 9.76112 .76115 .76117 .76120 .57693 .57696 .57700 .57703 9.76274 .76276 .76279 .76282 .57908 .57911 .57915 .57919 9.76435 .76438 .76440 .76443 .58133 .58137 .58130 .58134 9.76595 .76598 .76601 .76603 .58338 .58343 .58346 .58349 9.76755 .76758 .76761 .76763 .68663 .68657 .58561 .68664 .68668 .58671 .58575 .68579 + r 29 30 31 9.76123 .76125 .76128 .76131 .57707 .57710 .57714 .57718 9.76285 .76287 .76290 .76293 .57933 .57936 .57939 .57933 9.76446 .76448 .76451 .76454 .58138 .58141 .58145 .58148 9.76606 .76609 .76611 .76614 .58353 .58356 .58360 .58364 9.76766 .76769 .76771 .76774 + 8' 33 34 35 9.76134 .76136 .76139 .76142 .57731 .57735 .57738 .57733 9.76296 .76298 .76301 .76303 .57937 .57940 .57944 .57947 9.76456 .76459 .76462 .76464 .58153 .58156 .58159 .58163 9.76617 .76619 .76622 .76625 .58367 .58371 .58374 .58378 9.76777 .76779 .76782 .76784 .68683 .68586 .58589 .58595 + r 37 9-38 39 9.76144 .76147 .76150 .76152 .57736 .57739 .57743 .57746 9.76306 .76309 .76311 .76314 .57951 .57955 .57958 .57963 9.76467 .76470 .76473 .76475 .58166 .58170 .58173 .58177 9.76627 .76630 .76633 .76635 .58381 .58385 .58389 .58393 9.76787 .76790 .76792 .76795 .68696 .68600 .58604 .58607 24 23 22 21 + W 41 42 43 9.76155 .76158 .76161 .76163 .57750 .57753 .57757 .57761 9.76317 .76320 .76322 .76325 .57965 .57969 .57973 .57976 9.76478 .76481 .76483 .76486 .58181 .58184 .58188 .58191 9.76638 .76641 .76643 .76646 .58396 .58399 .58403 .58407 9.76798 .76800 .76803 .76806 .58611 .58614 .58618 .68633 20 19 18 17 + 11^ 45 46 47 9.76166 .76169 .76171 .76174 .57764 .57768 .57771 .57775 9.76328 .76330 .76333 .76336 .57980 .57983 .57987 .57990 9.76489 .76491 .76494 .76497 .58195 .58199 .58303 .58306 9.76649 .76651 .76654 .76657 .58410 .58414 .58417 .58431 9.76808 .76811 .76814 .76816 .68635 .58639 .68633 .68636 16 15 14 13 12 11 10 9 8 7 6 5 + n' 49 50 51 9.76177 .76179 .76182 .76185 .57779 .57783 .57786 .57789 9.76338 .76341 .76344 .76346 .57994 .57998 .58001 .58005 9.76499 .76502 .76505 .76507 .58309 .58313 .58317 .58330 9.76659 .76662 .76665 .76667 .58434 .58438 .58433 .58435 9.76819 .76822 .76824 .76827 .58639 .68643 .58647 .68650 + 13' 53 54 55 9.76188 .76190 .76193 .76196 .57793 .57797 .57800 .57804 9.76349 .76352 .76354 .76357 .68008 .58013 .58016 .58019 9.76510 .76513 .76515 .76518 .58334 .58337 .58331 .58334 9.76670 .76673 .76675 .76678 .58439 .58443 .58446 .58450 9.76830 .76832 .76835 .76838 .68654 .58667 .68661 .58665 + W 57 58 59 9.76198 .76201 .76204 .76206 .57807 .57811 .57815 .57818 9.76360 .76363 .76365 .76368 .58033 .58036 .58030 .58034 9.76521 .76523 .76526 .76529 .58338 .58343 .58345 .58349 9.76681 .76683 .76686 .76689 .58453 .58457 .58460 .58464 9.76840 .76843 .76845 .76848 .58668 .58671 .68675 .58679 4 3 2 1 + 15' 9.76209 .57833 9.76371 .58037 9.76531 .58353 9.76691 .58467 9.76851 .58683 nn 24m 1 17h 23m 1 17h 22^ 1 17h 21m 1 17h 20m 1 Page 124] TABLE IV. Haversinea. 3 6h 40m 100° r 6^41^ 100° 15' 6h42m 100° sr 6h 4Sm 100° 45' 6k 44m 101° 0' s Log. Hav Nat. Hav Log. Hav Nat. Hav Log. Hav Nat. Hav Log. Hav Nat. Hav Log. Hav Nat. Hav 9.76851 .58683 9.77009 .58897 9.77167 .59112 9.77325 .59336 9.77481 .59540 60 1 .76853 .58686 .77012 .58901 .77170 .59115 .77327 .59330 .77484 .59544 59 2 .76856 .58690 .77015 .58904 .77173 .59119 .77330 .59333 .77480 .59548 58 S .76859 .58693 .77017 .58908 .77175 .59122 .77333 .59337 .77489 .59551 57 + r 9.76861 .58697 9.77020 .58911 9.77178 .59126 9.77335 .59340 9.77492 .59555 56 5 .76864 .58700 .77023 .58915 .77181 .59130 .77338 .59344 .77494 .59558 55 6 .76867 .58704 .77025 .58919 .77183 .59133 .77340 .59348 .77497 .59563 54 7 .76869 .58707 .77028 .58923 .77186 .59137 .77343 .59351 .77499 .59565 53 + r 9.76872 .58711 9.77031 .58926 9.77188 .59140 9.77346 .59355 9.77502 .59569 52 9 .76875 .58714 .77033 .58939 .77191 .59144 .77348 .59358 .77505 .59573 51 10 .76877 .58718 .77036 .58933 .77194 .59148 .77351 .59363 .77507 .59576 50 11 .76880 .58732 .77038 .58937 .77196 .59151 .77353 .59365 .77510 .59580 49 + 3^ 9.76883 .58735 9.77041 .58940 9.77199 .59155 9.77356 .59369 9.77512 .59583 48 13 .76885 .58739 .77044 .58944 .77202 .59158 .77359 .59373 .77515 .59587 47 14 .76888 .58733 .77046 .58947 .77204 .59162 .77361 .59376 .77518 .59590 46 15 .76891 .58736 .77049 .58951 .77207 .59165 .77364 .59380 .77520 .59594 45 + 4^ 9.76893 .58740 9.77052 .58954 9.77209 .59169 9.77366 .59383 9.77523 .59598 U 17 .76896 .58743 .77054 .58858 .77212 .59173 .77369 .59387 .77525 .59601 43 18 .76898 .58747 .77057 .58963 .77215 .59176 .77372 .59391 .77528 .59605 42 19 .76901 .58750 .77060 .58965 .77217 .59180 .77374 .59394 .77531 .59608 41 + 5^ 9.76904 .58754 9.77062 .58969 9.77220 .59183 9.77377 .59398 9.77533 .59613 40 21 .76906 .58758 .77065 .58972 .77223 .59187 .77380 .59401 .77536 .59615 39 22 .76909 .58761 .77067 .58976 .77225 .59190 .77382 .59405 .77538 .59619 38 23 .76912 .58765 .77070 .58979 .77228 .59194 .77385 .59408 .77541 .59633 37 + 6^ 9.76914 .58768 9.77073 .58983 9.77230 .59198 9.77387 .69413 9.77544 .59636 36 25 .76917 .58773 .77075 .58987 .77233 .59201 .77390 .59416 .77546 .59630 35 26 .76920 .58776 .77078 .58990 .77236 .59205 1 .77393 .59419 .77549 .59633 34 27 .76922 .58779 .77081 .58994 .77238 .59208 .77395 .59433 .77551 .59637 33 + r 9.76925 .58783 9.77083 .58997 9.77241 .59212 9.77398 .59436 9.77554 .59640 32 29 .76928 .58780 .77086 .59001 .77243 .59215 .77400 .59430 .77557 .59644 31 30 .76930 .58730 .77089 .59005 .77246 .59219 .77403 .59433 .77559 .59648 30 31 .76933 .58793 .77091 .59008 .77249 .59223 .77406 .59437 .77562 .59651 29 + 8' 9.76936 .58797 9.77094 .59013 9.77251 .59236 9.77408 .59440 9.77564 .59655 28 33 .76938 .58801 .77096 .59015 .77254 .59230 .77411 .59444 .77567 .59658 27 34 .76941 .58804 .77099 .59019 .77257 .59233 .77413 .59448 .77570 .59663 26 35 .76943 .58808 .77102 .59033 .77259 .59237 .77416 .59451 .77572 .59665 25 + 9" 9.76946 .58811 9.77104 .59036 9.77262 .59240 9.77419 .59455 9.77575 .59669 24 37 .76949 .58815 .77107 .59030 .77264 .59244 .77421 .59458 .77577 .59672 23 38 .76951 .58818 .77110 .59033 .77267 .59248 .77424 .59463 .77580 .59676 22 39 .76954 .58823 .77112 .59037 .77270 .59251 .77427 .59465 .77583 .59680 21 + W 9.76957 .58836 9.77115 .59040 9.77272 .59255 9.77429 .59469 9.77585 .59683 20 41 .76959 .58839 .77117 .59044 .77275 .59358 .77432 .59473 .77588 .59687 19 42 .76962 .58833 .77120 .59047 .77278 .59363 .77434 .59476 .77590 .59690 18 43 .76965 .58836 .77123 .59051 .77280 .59265 .77437 .59480 .77593 .59694 17 + ir 9.76967 .58840 9.77125 .59055 9.77283 .59269 9.77440 .59483 9.77596 .59697 16 45 .76970 .58843 .77128 .59058 .77285 .59273 .77442 .59487 .77598 .59701 15 46 .76972 .58847 .77131 .59063 .77288 .59376 .77445 .59490 .77601 .59705 14 47 .76975 .58851 .77133 .59065 .77291 .59380 .77447 .59494 .77603 .59708 13 + 12' 9.76978 .58854 9.77136 .59069 9.77293 .59383 9.77450 .59498 9.77606 .59712 12 49 .76980 .58858 .77139 .59073 .77296 .59387 .77453 .59501 .77609 .59715 11 50 .76983 .58861 .77141 .59076 .77298 .59390 .77455 .59505 .77611 .59719 10 51 .76986 .58865 .77144 .59080 .77301 .59394 .77458 .59508 .77614 .59722 9 + 13' 9.76988 .58869 9.77146 .59083 9.77304 .59298 9.77460 .59513 9.77616 .59726 8 53 .76991 .58873 .77149 .59087 .77306 .59301 .77463 .59515 .77619 .59730 7 54 .76994 .58876 .77152 .59090 .77309 .59305 .77466 .59519 .77622 .59733 6 55 .76996 .58879 .77154 .59094 .77312 .59308 .77468 .59533 .77624 .59737 5 + 14' 9.76999 .58883 9.77157 .59097 9.77314 .59312 9.77471 .59536 9.77627 .59740 4 57 .77002 .58886 .77160 .59101 .77317 .59315 .77473 .59530 .77629 .59744 8 58 .77004 .58890 .77162 .59105 .77319 .59319 .77476 .59533 .77632 .59747 2 59 .77007 .58894 .77165 .59108 .77322 .59323 .77479 .59537 .77634 .59751 1 + 15' 9.77009 .58897 9.77167 1 .59113 9.77325 .59336 9.77481 .59540 9.77637 .59755 i7h 19m 1 17h igm 1 17h 17m 1 17k i&m 1 17h 15m 1 TABLE I y. [Pa^e 125 Haversinea. s 6ft ^m 101° 15' 6ft 46^ 101° sr 6h 47m 101° 45' 6ft 4Sm 103° 0' 6ft 49m 103° 15' 3 Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. 1 2 3 9.77637 .77640 .77642 .77645 .59755 .59758 .59763 .59765 9.77792 .77795 .77797 .77800 .59968 .59973 .59976 .59979 9.77947 .77949 .77952 .77954 .60183 .60185 .60189 .60193 9.78101 .78103 .78106 .78108 .60396 .60399 .60403 .60406 9.78254 .78256 .78259 .78261 .60609 .60613 .60616 .60630 60 59 58 57 + r 5 6 7 9.77647 .77650 .77653 .77655 .59769 .59773 .59776 .59779 9.77803 .77805 .77808 .77810 .59983 .59986 .59990 .59993 9.77957 .77960 .77962 .77965 .60196 .60300 .60303 .60307 9.78111 .78113 .78116 .78118 .60410 .60414 .60417 .60430 9.78264 .78266 .78269 .78271 .60633 .60637 .60630 .60634 56 55 54 53 + y 9 10 11 9.77658 .77660 .77663 .77666 .59783 .59787 .59790 .59794 9.77813 .77815 .77818 .77821 .59997 .60000 .60004 .60008 9.77967 .77970 .77972 .77975 .60311 .60314 .60318 .60331 9.78121 .78124 .78126 .78129 .60434 .60438 .60431 .60435 9.78274 .78277 .78279 .78282 .60637 .60641 .60644 .60648 52 51 50 49 + 3' 13 14 15 9.77668 .77671 .77673 .77676 .59797 .59801 .59S01 .59808 9.77823 .77826 .77828 .77831 .60011 .60015 .60018 .60033 9.77978 .77980 .77983 .77985 .60335 .60338 .60333 .60335 9.78131 .78134 .78136 .78139 .60438 .60443 .60445 .60449 9.78284 .78287 .78289 .78292 .60653 .60655 .60659 .60663 48 47 46 45 + 4' 17 18 19 9.77679 .77681 .77684 .77686 .59813 .59815 .59819 .59833 9.77834 .77836 .77839 .77841 .60035 .60039 .60033 .60036 9.77988 .77990 .77993 .77996 .60339 .60343 .60346 .60350 9.78141 .78144 .78147 .78149 .60453 .60456 .60460 .60463 9.78294 .78297 .78299 .78302 .60666 .60669 .60673 .60676 44 4S 42 41 + 5' 21 22 23 9.77689 .77691 .77694 .77697 .59836 .59839 .59833 .59837 9.77844 .77846 .77849 .77852 .60040 .60043 .60047 .60050 9.77998 .78001 .78003 .78006 .60353 .60357 .60360 .60364 9.78152 .78154 .78157 .78159 .60467 .69470 .60474 .60477 9.78305 .78307 .78310 .78312 .60680 .60684 .60687 ,60691 40 39 38 37 + 6' 25 26 27 9.77699 .77702 .77704 .77707 .59840 .59844 .59847 .59851 9.77854 .77857 .77859 .77862 .60054 .60057 .60061 .60065 9.78008 .78011 .78013 .78016 .60368 .60371 .60375 .60378 9.78162 .78164 .78167 .78170 .60481 .60484 .60488 .60493 9.78315 .78317 .78320 .78322 .60694 .60698 .60701 .60705 36 35 34 33 + r 29 30 31 9.77710 .77712 .77715 .77717 .59854 .59858 .59861 .59865 9.77864 .77867 .77870 .77872 .60068 .60073 .60075 .60079 9.78019 .78021 .78024 .78026 .60383 .60385 .60389 .60393 9.78172 .78175 .78177 .78180 .60495 .60499 .60503 .60506 9.78325 .78327 .78330 .78332 .60708 .60713 .60715 ,60719 32 31 30 29 + 8' 33 34 35 9.77720 .77723 .77725 .77728 .59869 .59873 .59876 .59879 9.77875 .77877 .77880 .77882 .60083 .60086 .60090 .60093 9.78029 .78031 .78034 .78037 .60396 .60300 .60303 .60307 9.78182 .78185 .78187 .78190 .60509 .60513 .00516 .60530 9.78335 .78338 .78340 .78343 ,60733 ,60736 ,60730 .60733 28 27 26 25 + ^ 37 38 39 9.77730 .77733 .77735 .77738 .59883 .59886 .59890 ,59894 9.77885 .77888 .77890 .77893 .60097 .60100 .60104 .60107 9.78039 .78042 .78044 .78047 .60310 .60314 .60317 .60331 9.78192 .78195 .78198 .78200 .60534 .60537 .60531 .60534 9.78345 .78348 .78350 .78353 .60737 .60740 ,60744 ,60747 24 23 22 21 + W 41 42 43 9.77741 .77743 .77746 .77748 .59897 .59901 .59904 .59908 9.77895 .77898 .77900 .77903 .60111 .60114 .60118 .60133 9.78049 .78052 .78054 .78057 .60334 .60338 .60333 .60335 9.78203 .78205 .78208 .78210 .60538 .60541 .60545 .60548 9.78355 .78358 .78360 .78363 .60751 .60755 ,60758 ,60763 20 19 18 17 + 11^ 45 46 47 9.77751 .77754 .77756 .77759 .59911 .59915 .59919 .59933 9.77906 .77908 .77911 .77913 .60135 .60139 .60133 .60136 9.78060 .78062 .78065 .78067 .60339 .60343 .60346 .60349 9.78213 .78215 .78218 .78221 .60553 .60556 ,60559 .60563 9.78365 .78368 .78371 .78373 .60765 .60769 ,60773 ,60776 16 15 14 13 + 13' 49 50 51 9.77761 .77764 .77766 .77769 .59936 .59939 .59933 .59936 9.77916 .77918 .77921 .77924 .60139 .60143 .60146 .60150 9.78070 .78072 .78075 .78077 .60353 .60356 .60360 .60364 9.78223 .78226 .78228 .78231 .60566 .69579 .60573 .60577 9.78376 .78378 .78381 .78383 .60779 .60783 .60786 .60790 12 11 10 9 + 13' 53 54 55 9.77772 .77774 .77777 .77779 .59940 .59943 .59947 .59951 9.77926 .77929 .77931 .77934 .60154 .60157 .60161 .60164 9.78080 .78083 .78085 .78088 .60367 .60371 .60374 .60378 9.78233 .78236 .78238 .78241 .60580 .60584 .60588 .60591 9.78386 .78388 .78391 .78393 .60794 .60797 .60801 .60804 8 7 6 5 + W 57 58 59 9.77782 .77785 .77787 .77790 .59954 .59958 .59961 .59965 9.77936 .77939 .77942 .77944 .60168 .60171 .60175 .60179 9.78090 .78093 .78095 .78098 .60381 .60385 .60388 .60393 9.78243 .78246 .78249 .78251 .60595 .60598 .60603 .60605 9.78396 .78398 .78401 .78404 .60808 .60811 .60815 .60818 4 S 2 1 + 15' 9.77792 .59968 9.77947 .60183 9.78101 .60396 9.78254 .60609 9.78406 .69833 i7h 14m 17h 13m 17h ipn J?7ft lim 17h iom Page 126] TABLE lY. Havereines. s 6h oOm 102° 3(K 6^ 5im 102° 45' 6h S2m 103° 0' 6h 5Sm 103° 15' 6h 54^ 103° 30' s 60 59 58 57 56 55 54 53 52 51 50 49 Log. Hav. Nat. Hav. Hav.Log. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. 1 2 ~3 9.78406 .78409 .78411 .78414 .60822 .60825 .60829 .60833 9.78558 .78560 .78563 .78565 .61035 .61038 .61042 .61046 9.78709 .78711 .78714 .78716 .61248 .61251 .61255 .61258 9.78859 .78862 .78864 .78867 .61460 .61464 .61467 .61471 9.79009 .79011 .79014 .79016 .61672 .61676 .61679 .61683 + r 5 6 7 9.78416 .78419 .78421 .78424 .60836 .60840 .60843 .60847 9.78568 .78570 .78573 .78575 .61049 .61053 .61056 .61060 9.78719 .78721 .78724 .78726 .61262 .61265 .61269 .61272 9.78869 .78872 .78874 .78877 .61474 .61478 .61481 .61485 9.79019 .79021 .79024 .79026 .61686 .61690 .61693 .61697 .61701 .61704 .61708 .61711 + r 9 10 11 9.78426 .78429 .78431 .78434 .60850 .60854 .60857 .60861 9.78578 .78581 .78583 .78586 .61063 .61067 .61070 .61074 9.78729 .78731 .78734 .78737 .61276 .61279 .61283 .61287 9.78879 .78882 .78884 .78887 .61488 .61492 .61495 .61499 9.79029 .79031 .79034 .79036 + 3' 13 U 15 9.78436 .78439 .78442 .78444 .60865 .60868 .60872 .60875 9.78588 .78591 .78593 .78596 .61077 .61081 .61085 .61088 9.78739 .78742 .78744 .78747 .61290 .61294 .61297 .61301 9.78889 .78892 .78894 .78897 .61502 .61506 .61510 .61513 9.79039 .79041 .79044 .79046 .61715 .61718 .61722 .61725 48 47 46 45 44 43 42 41 + 4^ 17 18 19 9.78447 .78449 .78452 .78454 .60879 .60882 .60886 .60889 9.78598 .78601 .78603 .78606 .61092 .61095 .61099 .61102 9.78749 .78752 .78754 .78757 .61304 .61308 .61311 .61315 9.78899 .78902 .78904 .78907 .61517 .61520 .61524 .61527 9.79049 .79051 .79054 .79056 .61729 .61732 .61736 .61739 + 6' 21 22 23 9.78457 .78459 .78462 .78464 .60893 .60897 .60900 .60904 9.78608 .78611 .78613 .78616 .61106 .61109 .61113 .61116 9.78759 .78762 .78764 .78767 .61318 .61322 .61325 .61329 9.78909 .78912 .78914 .78917 .61531 .61534 .61538 .61541 9.79059 .79061 .79064 .79066 .61743 .61747 .61750 .61754 40 39 38 37 + 6^ 25 26 27 9.78467 .78469 .78472 .78474 .60907 .60911 .60914 .60918 9.78618 .78621 .78023 .78626 .61120 .61124 .61127 .61131 9.78769 .78772 .78774 .78777 .61333 .61336 .61340 .61343 9.78919 .78922 .78924 .78927 .61545 .6154S .61552 .61556 9.79069 .79071 .79074 .79076 .61757 .61761 .61764 .61768 36 35 34 33 + r 30 31 9.78477 .78479 .78482 .78485 .60921 .60925 .60928 .60932 9.78628 .78631 .78633 .78636 .61134 .61138 .61141 .61145 9.78779 .78782 .78784 .78787 .61347 .61350 .61354 .61357 9.78929 .78932 .78934 .78937 .61559 .61563 .61566 .61570 9.79079 .79081 .79084 .79086 .61771 .61775 .61778 .61782 32 31 30 29 + 8^ 33 34 35 9.78487 .78490 .78492 .78495 .60938 .60939 .60943 .60946 9.78638 .78641 .78643 .78646 .61148 .61152 .61155 .61159 9.78789 .78792 .78794 .78797 .61361 .61364 .61368 .61372 9.78939 .78942 .78944 .78947 .61573 .61577 .61580 .61584 9.79089 .79091 .79094 .79096 .61785 .61789 .61792 .61796 28 27 26 25 24 23 22 Tl + 9^ 37 38 39 9.78497 .78500 .78502 .78505 .60950 .60953 .60957 .60960 9.78649 .78651 .78654 .78656 .61163 .61166 .61170 .61173 9.78799 .78802 .78804 .78807 .61375 .61379 .61382 .61386 9.78949 .78952 .78954 .78957 .61587 .61691 .61594 .61598 9.79099 .79101 .79103 .79106 .61800 .61803 .61807 .61810 + W 41 42 43 9.78507 .78510 .78512 .78515 .60964 .60967 .60971 .60975 9.78659 .78661 .78664 .78666 .61177 .61180 .61184 .61187 9.78809 .78812 .78814 .78817 .61389 .61393 .61396 .61400 9.78959 .78962 .78964 .78967 .61602 .61605 .61609 .61612 9.79108 .79111 .79113 .79116 .61814 .61817 .61821 .61824 20 19 18 17 16 15 14 13 12 11 10 9 + 11^ 45 46 47 9.78517 .78520 .78522 .78525 .60978 .60982 .60985 .60989 9.78669 .78671 .78674 .78676 .61191 .61194 .61198 .61201 9.78819 .78822 .78824 .78827 .61403 .61407 .61410 .61414 9.78969 .78972 .78974 .78977 .61616 .61619 .61623 .61626 9.79118 .79121 .79123 .79126 .61828 .61831 .61835 .61838 + !%' 49 50 51 9.78528 .78530 .78533 .78535 .60992 .60996 .60999 .61003 9.78679 .78681 .78684 .78686 .61205 .61209 .61212 .61216 9.78829 .78832 .78834 .78837 .61418 .61421 .61425 .61428 9.78979 .78982 .78984 .78987 .61630 .61633 .61637 .61640 9.79128 .79131 .79133 .79136 .61842 .61845 .61849 .61853 + 13' 53 54 55 9.78538 .78540 .78543 .78545 .61007 .61010 .61014 .61017 9.78689 .78691 .78694 .78696 .61219 .61223 .61226 .61230 9.78839 .78842 .78844 .78847 .61432 .61435 .61439 .61442 9.78989 .78992 .78994 .78997 .61644 .61648 .61651 .61655 9.79138 .79141 .79143 .79146 .61856 .61860 .61863 .61867 8 7 6 5 4 3 1 + W 57 58 59 9.78548 .78550 .78553 .78555 .61021 .61024 .61028 .61032 9.78699 .78701 .78704 .78706 .61233 .61237 .61240 .61244 9.78849 .78852 .78854 .78857 .61446 .61449 .61453 .61456 9.78999 .79002 .79004 .79007 .61658 .61662 .61665 .61669 9.79148 .79151 .79153 .79156 .61870 .61874 .61877 .61881 + 15' 9.78558 .61035 9.78709 .6124S 9.78859 .61460 9.79009 .61672 9.79158 .61884 irhQm 17 h gm 17h jm 1 i7h em ]7h gm TABLE IV. Haversines. [Page 127 s 61 55m 103° 45' 6h 56m 104° 0' 6h 57m 104° 15' eh 58m 104° 30' 6^1 59>n 104° 45' 1 s Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. 1 2 3 9.79158 .79161 .79163 .79165 .61884 .61888 .61891 .61895 9.79306 .79309 .79311 .79314 .62096 .62100 .63103 .62107 9.79454 .79457 .79459 .79462 .63308 .63311 .63315 .63318 9.79601 .79604 .79600 .79609 .63519 .63533 .63536 .63530 9.79748 .79750 .79752 .79755 .63730 .63734 .63737 .63741 60 59 oS 57 56 55 54 53 52 51 50 49 48 47 46 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 + V 5 6 7 9.79168 .79170 .79173 .79175 .61898 .61903 .61905 .61909 9.79316 .79319 .79321 .79324 .63110 .63114 .63117 .63131 9.79464 .79466 .79469 .79471 .63333 .63335 .63339 .63332 .63336 .63339 .62343 .62346 9.79G11 .79613 .79616 .79618 .63533 .63537 .63540 .63544 9.79757 .79760 .79762 .79765 .62744 .62748 .63751 .63755 + 2' 9 10 11 9.79178 .79180 .79183 .79185 .61913 .61916 .61920 .61923 9.79326 .79329 .79331 .79334 .63134 .63138 .63131 .63135 9.79474 .79476 .79479 .79481 9.79621 .79623 .79626 .79628 .63547 .63551 .63554 .63558 9.79767 .79770 .79772 .79774 .63758 .63763 .63765 .63769 + 3' 13 14 15 9.79188 .79190 .79193 .79195 .61937 .61930 .61934 .61937 9.79336 .79339 .79341 .79343 .63138 .63142 .62145 .62149 .62153 .63156 .63160 .63163 9.79484 .79486 .79489 .79491 .63350 .63353 .63357 .63361 9.79631 .79633 .79635 .79038 .63561 .63565 .62568 .63573 9.79777 .79779 .79782 .79784 .63773 .62776 .62779 .62783 17 18 19 9.79198 .79200 .79203 .79205 .61941 .61944 .61948 .61951 9.79346 .79348 .79351 .79353 9.79493 .79496 .79498 .79501 .63364 .63368 .63371 .63375 .63378 .63383 .62385 .63389 9.79640 .79643 .79645 .79648 9.79650 .79653 .79655 .79657 .63575 .63579 .63582 .62586 9.79787 .79789 .79791 .79794 .62786 .62790 .62793 .62797 + 5' 21 22 23 9.79208 .79210 .79213 .79215 .61955 .61958 .61962 .61966 9.79356 .79358 .79361 .79363 .63167 .62170 .62174 .62177 9.79503 .79506 .79508 .79511 .62589 .62593 .62596 .62600 9.79796 .79799 .79801 .79804 .63800 .63804 .63807 .63811 + 6' 25 26 27 9.79217 .79220 .79222 .79225 .61969 .61973 .61976 .61980 9.79366 .79368 .79371 .79373 .62181 .63184 .62188 .62191 9.79513 .79516 .79518 .79520 .63393 .63396 .63399 .63403 9.79660 .79662 .79665 .79667 .62603 .62607 .62611 .62614 9.79806 .79808 .79811 .79813 .63814 .63818 .63833 .63835 + r 29 30 31 9.79227 .79230 .79232 .79235 .61983 .61987 .61990 .61994 9.79376 .79378 .79380 .79383 .62195 .63198 .63302 .63305 9.79523 .79525 .79528 .79530 .63406 .63410 .63413 .63417 9.79670 .79672 .79674 .79677 .62618 .62621 .63625 .62628 9.79816 .79818 .79821 .79823 .63839 .63833 .63836 .63839 + 8' 33 34 35 9.79237 .79240 .79242 .79245 .61997 .63001 .62004 .62008 9.79385 .79388 .79390 .79393 .63309 .63313 .63316 .63330 9.79533 .79535 .79538 .79540 .63430 .63434 .63427 .62431 9.79679 .79682 .79684 .79687 .62633 .63635 .63639 .63643 9.79825 .79828 .79830 .79833 .63843 .63846 .63850 .63853 28 27 26 25 + 9' 37 38 39 9.79247 .79250 .79252 .79255 .62011 .62015 .62018 .62022 9.79395 .79398 .79400 .79403 .63333 .63337 .63330 .63334 9.79542 .79545 .79547 .79550 .62434 .62438 .62442 .62445 9.79689 .79692 .79694 .79696 .63646 .63649 .63653 .62656 9.79835 .79838 .79840 .79842 .63857 .62860 .62864 .62867 24 23 22 21 + 10' 41 42 43 9.79257 .79260 .79262 .79264 .62036 .62029 .62033 .62036 9.79405 .79407 .79410 .79412 .62237 .62241 .62344 .63348 9.79552 .79555 .79557 .79560 .63449 .63453 .63456 .63459 9.79699 .79701 .79704 .79706 .62660 .62663 .62667 .62670 9.79845 .79847 .79850 .79852 .62871 .82874 .63878 .63881 .62885 .62888 .63892 .62895 29 19 IS 17 16 15 14 IS + 11' 45 46 47 9.79267 .79269 .79272 .79274 .63040 .62043 .62047 .62050 9.79415 .79417 .79420 .79422 .63351 .62255 .62258 .63363 9.79562 .79565 .79567 .79569 .63463 .63466 .63470 .62473 9.79709 .79711 .79714 .79716 .62674 .62677 .62681 .62684 9.79855 .79857 .79859 .79862 + 12' 49 50 51 9.79277 .79279 .79282 .79284 .63054 .62057 .62061 .62064 9.79425 .79427 .79430 .79432 .63365 .62269 .62272 .62276 9.79572 .79574 .79577 .79579 .62477 .62480 .62484 .63487 9.79718 .79721 .79723 .79726 .62688 .62691 .62695 .63698 9.79864 .79867 .79869 .79872 .62899 .62902 .63906 .63909 12 11 10 9 + 13' 53 54 55 9.79287 .79289 .79292 .79294 .62068 .62071 .62075 .62078 9.79434 .79437 .79439 .79442 .62279 .62283 .62287 .62290 9.79582 .79584 .79587 .79589 .63491 .63494 .63498 .62501 9.79728 .79731 .79733 .79735 .63703 .63706 .63709 .63713 9.79874 .79876 .79879 .79881 .63913 .62916 .63930 .63933 8 7 6 5 + 14' 57 58 59 9.79297 .79299 .79301 .79304 .62082 .62086 .62089 .62093 9.79444 .79447 .79449 .79452 .62294 .62297 .62301 .63304 9.79591 .79594 .79596 .79599 .63505 .63508 .63513 .63515 9.79738 .79740 .79743 .79745 .63716 .62730 .62723 .63737 9.79884 .79886 .79888 .79891 .63937 .63930 .63934 .63937 4 3 2 1 + 15' 9.79306 .62096 9.79454 .63308 9.79601 .63519 9.79748 .63730 9.79893 .62941 171 pn 17h Sm 17^ 2m nil im 17h Om Page 128] TABLE IV. Haversines. s 7ft0ml05^(K 1 7h im 105° 15' Ih 2m 105° 30' r'i 5wi 105° 45' 1 lh4mlOQ°(/ 1 s Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. 9.79893 .63941 9.80038 .63153 9.80183 .63363 9.80327 .63573 9.80470 .63783 60 1 .79896 .639M .80041 .63155 .80185 .63365 .80329 .63576 .80472 .63785 59 2 .79898 .63948 .80043 .63159 .80188 .63369 .80331 .63579 .80474 .63789 58 3 .79901 .63951 .80046 .63163 .80190 .63373 .80334 .63583 .80477 .63793 51 + 1' 9.79903 .63955 9.80048 .63166 9.80192 .63376 9.80336 .63586 9.80479 .63796 56 5 .79905 .63958 .80050 .63169 .80195 .63379 .80339 | .63590 .80482 .63799 55 6 .79908 .63963 .80053 .63173 .80197 .63383 .80341 .63593 .80484 .63803 54 7 .79910 .63965 .80055 .63176 .80200 .63386 .80343 .63597 .80486 .63806 53 + 2' 9.79913 .63969 9.80058 .63180 9.80202 .63390 9.80346 .63600 9.80489 .63810 52 9. .79915 .63973 .80060 .63183 .80204 .63393 .80348 .63604 .80491 .63813 51 10 .79918 .63976 .80063 .63187 .80207 .63397 .80351 .63607 .80494 .63817 50 11 .79920 .63980 .80065 .63190 .80209 .63400 .80353 .63611 .80496 .63830 49 48 + y 9.79922 .63983 9.80067 .63194 9.80212 .63404 9.80355 .63614 9.80498 .63834 IS .79925 .63987 .80070 .63197 .80214 .63407 .80358 .63618 .80501 .63837 41 14 .79927 .63990 .80072 .63301 .80216 .63411 .80360 .63631 .80503 .63831 46 15 .79930 .63994 .80075 .63304 .80219 .63414 .80362 .63635 .80505 .63834 45 + i' 9.79932 .63997 9.80077 .63308 9.80221 .63418 9.80365 .63638 9.80508 .63838 44 n .79935 .63001 .80079 .63311 .80224 .63431 .80367 .63633 .80510 .63841 43 18 .79937 .63004 .80082 .63315 .80226 .63435 .80370 .63635 .80513 .63845 42 19 .79939 .63008 .80084 .63318 .80228 .63438 .80372 .63639 .80515 .63848 41 + 5' 9.79942 .63011 9.80087 .63333 9.80231 .63433 9.80374 .63643 9.80517 .63853 40 21 .79944 .63015 .80089 .63335 .80233 .63435 .80377 .63646 .80520 .63855 39 22 .79947 .63018 .80091 .63339 .80236 .63439 .80379 .63649 .80522 .63859 38 23 .79949 .63033 .80094 .63333 .80238 .63443 .80382 .63653 .80524 .63863 31 36 + 6' 9.79951 .63035 9.80096 .63336 9.80240 .63446 9.80384 .63656 9.80527 .63866 25 .79954 .63039 .80099 .63339 .80243 .63450 .80386 .63660 .80529 .63869 35 26 .79956 .63033 .80101 .63343 .80245 .63453 .80389 .63663 .80532 .63873 34 21 .79959 .63036 .80103 .63346 .80248 .63457 .80391 .63666 .80534 .63876 33 + r 9.79961 .63039 9.80106 .63350 9.80250 .63460 9.80393 .63670 9.80536 .63880 32 29 .79964 .63043 .80108 .63353 .80252 .63464 .80396 .63673 .80539 .63883 31 30 .79966 .63046 .80111 .63357 .80255 .63467 .80398 .63677 .80541 .63887 30 31 .79968 .63050 .80113 .63360 .80257 .63471 .80401 .63680 .80543 .63890 29 + 8^ 9.79971 .63053 9.80116 .63364 9.80260 .63474 9.80403 .63684 9.80546 .63894 28 33 .79973 .63057 .80118 .63367 .80262 .63478 .80405 .63687 .80548 .63897 21 34 .79976 .63060 .80120 .63371 .80264 .63481 .80408 .63691 .80551 .63901 26 35 .79978 .63064 .80123 .63374 .80267 .63485 .80410 .63694 .80553 .63904 25 + 9' 9.79980 .63067 9.80125 .63378 9.80269 .63488 9.80413 .63698 9.80555 .63908 24 31 .79983 .63071 .80128 .63381 .80272 .63493 .80415 .63701 .80558 .83911 23 38 .79985 .63074 .80130 .63385 .80274 .63495 .80417 .63705 .80560 .63915 22 39 .79988 .63078 .80132 .63388 .80276 .63499 .80420 .63708 .80562 .63918 21 + W 9.79990 .63081 9.80135 .63393 9.80279 .63503 9.80422 .63713 9.80565 .63933 20 41 .79993 .63085 .80137 .63395 .80281 .63506 .80424 .63715 .80567 .63935 19 42 .79995 .63088 .80140 .63399 .80284 .63509 .80427 .63719 .80570 .63939 18 43 .79997 .63093 .80142 .63303 .80286 .63513 .80429 .63733 .80572 .63933 11 + 11' 9.80000 .63095 9.80144 .63306 9.80288 .63516 9.80432 .63736 9.80574 .63936 16 45 .80002 .63099 .80147 .63309 .80291 .63530 .80434 .63739 .80577 .63939 15 46 .80005 .63103 .80149 .63313 .80293 .63533 .80436 .63733 .80579 .63943 14 41 .80007 .63106 .80152 .63316 .80296 .63537 .80439 .63736 .80581 .63946 13 + 13' 9.80009 .63109 9.80154 .63330 9.80298 .63530 9.80441 .63740 9.80584 .63950 12 49 .80012 .63113! .80156 .63333 .80300 .63534 .80444 .63743 .80586 .63953 11 50 .80014 .63116 .80159 .63337 .80303 .63537 .80446 .63747 .80589 .63957 10 51 .80017 .63130 .80161 .63330 .80305 .63541 .80448 .63750 .80591 .63960 9 + 13^ 9.80019 .63133 9.80164 .63334 9.80307 .63544 9.80451 .63754 9.80593 .63964 8 53 .80022 .63137 .80166 .63337 .80310 .63548 .80453 .63757 .80596 .63967 1 54 .80024 .63131 .80168 .63341 .80312 .63551 .80455 .63761 .80598 .63971 6 55 .80026 .63134 .80171 .63344 .80315 .63555 .80458 .63764 .80600 .63974 5 + W 9.80029 .63138 9.80173 .63348 9.80317 .63558 9.80460 .63768 9.80603 .63977 4 51 .80031 .63143 .80176 .63351 .80319 .63563 .80463 .63771 .80605 .63981 3 58 .80034 .63145 .80178 .63355 .80322 .63565 .80465 .63775 .80607 .63984 2 59 .80036 .63148 .80180 .63358 .80324 .63569 .80467 .63778 .80610 .63988 1 + 15' 9.80038 .63153 9.80183 .63363 9.80327 .63573 9.80470 .63783 9.80612 .63991 16h 59m 16h 58m j I6fi 57771 16h 56m 16h 55m TABLE IV. Haversines. [Page 129 7h sm 106° 15' 7h em 106° W 7h 7m 106° 45'' 7ft sm 107° 0' 7h 9m 107° 15' 3 Log. Hav. Nat. Hav Log. Hav Nat. Hav Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav 1 2 S 9.80612 .80615 .80617 .80619 .63991 .63995 .63998 .64002 9.80754 .80756 .80759 .80761 .64201 .64204 .64208 .64211 9.80895 .80898 .80900 .80902 .64410 .64413 .64417 .&1420 9.81036 .81038 .81040 .81043 .64619 .64622 .64626 .64629 9.81176 .81178 .81180 .81183 .64827 .64831 .64834 .64838 60 59 58 57 + r 5 6 7 9.80622 .80624 .80626 .80629 .64005 .64009 .64012 .64016 9.80763 .80766 .80768 .80771 .64215 .64218 .64222 .64225 9.80905 .80907 .80909 .80912 .64424 .64427 .64431 .64434 9.81045 .81047 .81050 .81052 .64632 .64636 .64639 .64643 9.81185 .81187 .81190 .81192 .64841 ,64844 .64848 .64851 56 55 54 53 52 51 50 49 + r 9 10 11 9.80631 .80634 .80636 .80638 .64019 .64023 .64026 .64030 9.80773 .80775 .80778 .80780 .64229 .64232 .64236 .64239 9.80914 .80916 .80919 .80921 .64438 .64441 .64445 .64448 9.81054 .81057 .81059 .81061 .64646 .64650 .64653 .64657 9.81194 .81197 .81199 .81201 .64855 .64858 .64862 .64865 + 3' 13 14 15 9.80641 .80643 .80645 .80648 .64033 .64037 .64040 .64044 9.80782 .80785 .80787 .80789 .64343 .64246 .64250 .64253 9.80923 .80926 .80928 .80930 .64452 .64455 .64459 .64462 9.81064 .81066 .81068 .81071 .64660 .64664 .64667 .64671 9.81204 .81206 .81208 .81211 .64869 .64872 .64876 .64879 48 47 46 45 44 43 42 41 + 4' 17 18 19 9.80650 .80652 .80655 .80657 .64047 .64051 .64054 .64058 9.80792 .80794 .80706 .80799 .64257 .64260 .64264 .64267 9.80933 .80935 .80937 .80940 .64466 .64469 .64472 .64476 .81073 .81075 .81078 .81080 .64674 .64678 .64681 .64685 9.81213 .81215 .81217 .81220 .64883 .64886 .64890 .64893 + 5" 21 22 23 9.80660 .80662 .80664 .80667 .64061 .64065 .64068 .64072 9.80801 .80804 .80806 .80808 .64270 .64274 .64277 .64281 9.80942 .80944 .80947 .80949 .64479 .64483 .64486 .64490 9.81082 .81085 .81087 .81089 .64688 .64692 .64695 .64699 9.81222 .81224 .81227 .81229 .64897 .64900 .64903 .64907 40 39 38 37 + 6' 25 26 27 9.80669 .80671 .80674 .80676 .64075 .64079 .64082 .64086 9.80811 .80813 .80815 .80818 .64284 .64288 .64291 .64295 9.80952 .80954 .80956 .80959 .64493 .64497 .64500 .64504 9.81092 .81094 .81096 .81099 .64702 .64705 .64709 .64712 9.81231 .81234 .81236 .81238 .64910 .64914 .64917 .64921 36 35 34 S3 + r 29 30 31 9.80678 .80681 .80683 .80686 .64089 .64093 .64096 .64100 9.80820 .80822 .80825 .80827 .64298 .64302 .64305 .64309 9.80961 .80963 .80966 .80968 .64507 .64511 .64514 .64518 9.81101 .81103 .81106 .81108 .64716 .64719 .64723 .64726 9.81241 .81243 .81245 .81248 .64924 .64928 .64931 .64935 32 31 30 29 28 27 26 25 + 8^ 33 34 35 9.80688 .80690 .80693 .80695 .64103 .64107 .64110 .64114 9.80829 .80832 .80834 .80836 .64312 .64316 .64319 .64323 9.80970 .80973 .80975 .80977 .64521 .64525 .64528 .64532 9.81110 .81113 .81115 .81117 .64730 .64733 .64737 .64740 9.81250 .81252 .81255 .81257 .64938 .61942 .64945 .64949 + 9" 37 38 39 9.80697 .80700 .80702 .80704 .64117 .64121 .64124 .64128 9.80839 .80841 .80844 .80846 .64326 .64330 .64333 .64337 9.80980 .80982 .80984 .80987 .64535 .64539 .64542 .64546 9.81120 .81122 .81124 .81127 .64744 .64747 .64751 .64754 9.81259 .81262 .81264 .81266 .64952 .64956 .64959 .64962 24 23 22 21 + W 41 42 43 9.80707 .80709 .80712 .80714 .64131 .64135 .64138 .64142 9.80848 .80851 .80853 .80855 .64340 .64344 .64347 .64351 9.80989 .80991 .80994 .80996 .64549 .64552 .64556 .64559 9.81129 .81131 .81134 .81136 .64758 .64761 .64765 .64768 9.81269 .81271 .81273 .81276 .64966 .64969 .64973 .64976 20 19 18 17 + ir 45 46 47 9.80716 .80719 .80721 .80723 .64145 .64148 .64152 .64155 9.80858 .80860 .80862 .80865 .64354 .64358 .64361 .64365 9.80998 .81001 .81003 .81005 .64563 .64566 .64570 .64573 9.81138 .81141 .81143 .81145 .64772 .64775 .64778 .64782 9.81278 .81280 .81282 .81285 .64980 .64983 .64987 .64990 16 15 14 IS + ir 49 50 51 9.80726 .80728 .80730 .80733 .64159 .64162 .64166 .64169 9.80867 .80869 .80872 .80874 .64368 .64372 .64375 .64378 9.81008 .81010 .81012 .81015 .G4577 .64580 .64584 .64587 9.81148 .81150 .81152 .81155 .64785 .64789 .64792 .64796 9.81287 .81289 .81292 .81294 .64994 .64997 .65001 .65004 12 11 10 9 + W 53 54 55 9.80735 .80738 .80740 .80742 .64173 .64176 .64180 .64183 9.80876 .80879 .80881 .80883 .64382 .64385 .64389 .64392 9.81017 .81019 .81022 .81024 .64591 .64594 .64598 .64601 9.81157 .81159 .81162 .81164 .64799 .64803 .64806 .64810 9.81296 .81299 .81301 .81303 .65008 .65011 .65014 .65018 8 7 6 5 + W 57 58 59 9.80745 .80747 .80749 .80752 .64187 .64190 .64194 .64197 9.80886 .80888 .80891 .80893 .64396 .64399 .64403 .64406 9.81026 .81029 .81031 .81033 .64605 .64608 .64612 .64615 9.81166 .81169 .81171 .81173 .64813 .64817 .64820 .64824 9.81306 .81308 .81310 .81313 .65021 .65025 .65028 .65032 4 3 2 1 + W 9.80754 .64201 9.80895 .64410 9.81036 .64619 9.81176 .64827 9.81315 .65035 16^. S4m 16^ 53m 16h 5^771 16h 5im 1 16h 50m 1 55901°- Page 130] TABLE IV. Haversinea. 8 7A lOm 107° 30' 7h iim 107° 45' 7h 12m 108° 0' 7h 13m 108° 15' 7h 14m 108° W 8 Log. nav Nat. Hav Log. Hav. Nat. Hav Log. Hav Nat. Hav. Log. Hav. Nat. Hav. Log. Hav Nat. Hav. 1 2 3 9.81315 .81317 .81320 .81322 .65035 .65039 .65042 .65046 9.81454 .81456 .81458 .81460 .65243 .65247 .65250 .65254 9.81592 .81594 .81596 .81598 .65451 .65454 .65458 .65461 9.81729 .81731 .81733 .81736 .65658 .65662 .65665 .65668 9.81866 .81868 .81870 .81872 .65865 .65869 .65872 .65876 60 59 58 57 + r 5 6 7 9.81324 .81326 .81329 .81331 .65049 .65053 .65056 .65060 9.81463 .81465 .81467 .81470 .65257 .65261 .65264 .65267 9.81601 .81603 .81605 .81608 .65465 .65468 .65472 .65475 9.81738 .81740 .81743 .81745 .65672 .65675 .65679 .65682 9.81875 .81877 .81879 .81882 .65879 .65882 .65886 .65889 56 55 54 53 + r 9 10 11 9.81333 .81336 .81338 .81340 .65063 .65066 .65070 .65073 9.81472 .81474 .81477 .81479 .65271 .65274 .65278 .65281 9.81610 .81612 .81614 .81617 .65479 .65482 .65485 .65489 9.81747 .81749 .81752 .81754 .65686 .65689 .65693 .65696 9.81884 .81886 .81888 .81891 .65893 .65896 .65900 .65903 52 51 50 49 + 3' 13 14 15 9.81343 .81345 .81347 .81350 .65077 .65080 .65084 .65087 9.81481 .81483 .81486 .81488 .65285 .65288 .65292 .65295 9.81619 .81621 .81624 .81626 .65492 .65496 .65499 .65503 9.81756 .81759 .81761 .81763 .65700 .65703 .65707 .65710 9.81893 .81895 .81897 .81900 .65907 .65910 .65914 .65917 48 47 46 45 44 43 42 41 + i' 17 18 19 9.81352 .81354 .81357 .81359 .65091 .65094 .65098 .65101 9.81490 .81493 .81495 .81497 .65299 .65302 .65306 .65309 9.81628 .81631 .81633 .81635 .65506 .65510 .65513 .65516 9.81765 .81768 .81770 .81772 .65713 .65717 .65720 .65724 9.81902 .81904 .81907 .81909 .65920 .65924 .65927 .65931 -f 5' 21 22 23 9.81361 .81364 .81366 .81368 .65105 .65108 .65112 .65115 9.81500 .81502 .81505 .81507 .65312 .65316 .65319 .65323 9.81637 .81640 .81642 .81644 .65520 .65523 .65527 .65530 9.81775 .81777 .81779 .81781 .65727 .65731 .65734 .65738 9.81911 .81913 .81916 .81918 .65934 .65938 .65941 .65944 40 39 38 37 + 6' 25 26 27 9.81370 .81373 .81375 .81377 .65118 .65122 .65125 .65129 9.81509 .81511 .81513 .81516 .65326 .65330 .65333 .65337 9.81647 .81649 .81651 .81653 .65534 .65537 .65541 .65544 9.81784 .81786 .81788 .81791 .65741 .65744 .65748 .65751 9.81920 .81922 .81925 .81927 .65948 .65951 .65955 .65958 36 35 34 S3 S2 31 SO 29 28 27 26 25 24 23 22 21 + r 29 30 31 9.81380 .81382 .81384 .81387 .65132 .65136 .65139 .65143 9.81518 .81520 .81523 .81525 .65340 .65344 .65347 .65351 9.81656 .81658 .81660 .81663 .65548 .65551 .65555 .65558 9.81793 .81795 .81797 .81800 .65755 .65758 .65762 .65765 9.81929 .81931 .81934 .81936 .65962 .65965 .65969 .65972 + 8' 33 34 35 9.81389 .81391 .81394 .81396 .65146 .65150 .65153 .65157 9.81527 .81530 .81532 .81534 .65354 .65357 .65361 .65364 9.81665 .81667 .81669 .81672 .65561 .65565 .65568 .65572 9.81802 .81804 .81806 .81809 .65769 .65772 .65776 .65779 9.81938 .81941 .81943 .81945 .65976 .65979 .65982 .65986 + 9' 37 38 39 9.81398 .81400 .81403 .81405 .65160 .65164 .65167 .65171 9.81536 .81539 .81541 .81543 .6536S .65372 .65375 .65378 9.81674 .81676 .81679 .81681 .65575 .65579 .65582 .65586 9.81811 .81813 .81816 .81818 .65782 .65786 .65789 .65793 9.81947 .81950 .81952 .81954 .65989 .65993 .65996 .66000 + W 41 42 43 9.81407 .81410 .81412 .81414 .65174 .65177 .65181 .65184 9.81546 .81548 .81550 .81552 .65382 .65385 .65389 .65392 9.81683 .81685 .81688 .81690 .65589 .65593 .65596 .65599 9.81820 .81822 .81825 .81827 .65796 .65800 .65803 .65807 9.81956 .81959 .81961 .81963 .66003 .66006 .66010 .66013 20 19 18 17 + 11' 45 46 47 9.81417 .81419 .81421 .81424 .65188 .65191 .65195 .65198 9.81555 .81557 .81559 .81562 .65396 .65399 .65402 .65406 9.81692 .81695 .81697 .81699 .65603 .65606 .65610 .65613 .81829 .81832 .81834 .81836 .65810 .65813 .65817 .65820 9.81965 .81968 .81970 .81972 .66017 .66020 .66024 .66027 16 15 14 13 + 12' 49 50 51 9.81426 .81428 .81430 .81433 .65202 .65205 .65209 .65212 9.81564 .81566 .81569 .81571 .65409 .65413 .65416 .65420 9.81701 .81704 .81706 .81708 .65617 .65620 .65624 .65627 9.81838 .81841 .81843 .81845 .65824 .65827 .65831 .65834 9.81975 .81977 .81979 .81981 .66031 .66034 .66038 .66041 12 11 10 9 + 13' 53 54 55 9.81435 .81437 .81440 .81442 .65216 .65219 .65222 .65226 9.81573 .81575 .81578 .81580 .65423 .65427 .65430 .65434 9.81711 .81713 .81715 .81717 .65630 .65634 .65637 .65641 9.81847 .81850 .81852 .81854 .65838 .65841 .65845 .65848 9.81984 .81986 .81988 .81990 .66044 .66048 .66051 .66055 8 7 6 5 4 3 2 1 + 14' 57 58 59 9.81444 .81447 .81449 .81451 .65229 .65233 .65236 .65240 9.81582 .81585 .81587 .81589 .65437 .65440 .65444 .65447 9.81720 .81722 .81724 .81727 .65644 .55648 .65651 .65655 9.81857 .81859 .81861 .81863 .65851 .65855 .65858 .65862 9.81993 .81995 .81997 .81999 .66058 .66062 .66065 .66068 + 15' 9.81454 .65243 9.81592 .65451 9.81729 .65658 9.81866 .65865 9.82002 .66072 16h 49^ 16^ 48m 1 16h 47m 1 16h 46^ 1 ifih 45771 TABLE IV. [Page 131 Haversines. s 7h 15m 108° 45' 7h 16m 109° 0' 7h 17m 109° 15' 7A 18m 109° 3^ 7h 19m 109° 4^ 1 s Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. 1 2 3 9.82002 .82004 .82006 .82009 .66073 .66075 .66079 .66082 9.82137 .82139 .82142 .82144 .66278 .66282 .66385 .66289 9.82272 .82274 .82277 .82279 .66485 .66488 .66491 .66495 9.82406 .82409 .82411 .82413 .66690 .66694 .66697 .66701 9.82540 .82542 .82544 .82547 .66896 .66899 .66903 .66906 60 59 58 57 + r 5 6 7 9.82011 .82013 .82015 .82018 .66086 .66089 .66093 .66096 9.82146 .82148 .82151 .82153 .66293 .66396 .66299 .66302 9.82281 .82283 .82286 .82288 .66498 .66502 .66505 .66508 9.82415 .82417 .82420 .82422 .66704 .66707 .66711 .66714 9.82549 .82551 .82553 .82555 .66910 .66913 .66916 .66920 56 55 54 53 52 51 50 49 + 2^ 9 10 11 9.82020 .82022 .82024 .82027 .66100 .66103 .66106 .66110 9.82155 .82157 .82160 .82162 .66306 .66309 .66313 .66316 9.82290 .82292 .82294 .82297 .66512 .66515 .66519 .66522 9.82424 .82426 .82429 .82431 .66718 .66731 .66735 .66738 9.82558 .82560 .82562 .82564 .66923 .66927 .66930 .66933 + 3' IS 14 15 9.82029 .82031 .82033 .82036 .66113 .66117 .66120 .66134 9.82164 .82166 .82169 .82171 .66320 .66333 .66327 .66330 9.82299 .82301 .82303 .82306 .66526 .66529 .66533 .66536 9.82433 .82435 .82438 .82440 .66731 .66735 .66738 .66742 9.82567 .82569 .82571 .82573 .66937 .66940 .66944 .66947 48 47 46 45 44 43 42 41 + 4' 17 18 19 9.82038 .82040 .82042 .82045 .66137 .66130 .66134 .66137 9.82173 .82175 .82178 .82180 .66333 .66337 .66340 .66344 9.82308 .82310 .82312 .82315 .66539 .66543 .66546 .66550 9.82442 .82444 .82446 .82449 .66745 .66749 .66752 .66755 9.82575 .82578 .82580 .82582 .66951 .66954 .66957 .66961 4- 5' 21 22 23 9.82047 .82049 .82051 .82054 .66141 .66144 .66148 .66151 9.82182 .82184 .82187 .82189 .66347 .66351 .66354 .66357 9.82317 .82319 .82321 .82324 .66553 .66557 .66560 .66563 9.82451 .82453 .82455 .82458 .66759 .66762 .66766 .66769 9.82584 .82587 .82589 .82591 .66964 .66968 .66971 .66975 40 39 38 37 + 6^ 25 26 27 9.82056 .82058 .82061 .82063 .66155 .66158 .66161 .66165 9.82191 .82193 .82196 .82198 .66361 .66364 .66368 .66371 9.82326 .82328 .82330 .82333 .66567 .66570 .66574 .66577 9.82460 .82462 .82464 .82467 .66773 .66776 .66779 .66783 9.82593 .82595 .82598 .82600 .66978 .66981 .66985 .66988 36 35 34 33 + r 29 SO 31 9.82065 .82067 .82070 .82072 .66168 .66173 .66175 .66179 9.82200 .82202 .82205 .82207 .66375 .66378 .66382 .66385 9.82335 .82337 .82339 .82341 .66581 .66584 .66587 .66591 9.82469 .82471 .82473 .82475 .66786 .66790 .66793 .66797 9.82602 .82604 .82606 .82609 .66992 .66995 .66998 .67002 .67005 .67009 .67012 .67016 32 31 30 29 28 27 26 25 + 8' 33 34 35 9.82074 .82076 .82079 .82081 .66183 .66186 .66189 .66193 9.82209 .82211 .82214 .82216 .66388 .66392 .66395 .66399 9.82344 .82346 .82348 .82350 .66594 .66598 .66601 .66605 9.82478 .82480 .82482 .82484 .66800 .66803 .66807 .66810 9.82611 .82613 .82615 .82618 + ^ 37 38 39 9.82083 .82085 .82088 .82090 .66196 .66199 .66303 .66306 9.82218 .82220 .82223 .82225 .66402 .66406 .66409 .66412 9.82353 .82355 .82357 .82359 .66608 .66611 .66615 .66618 9.82487 .82489 .82491 .82493 .66814 .66817 .66821 .66824 9.82620 .82622 .82624 .82627 .67019 .67022 .67036 .67029 24 23 22 21 + w 41 42 43 9.82092 .82094 .82097 .82099 .66310 .68313 .66317 .66330 9.82227 .82229 .82232 .82234 .66416 .66419 .66423 .66426 9.82362 .82364 .82366 .82368 .66622 .66625 .66629 .66632 9.82495 .82498 .82500 .82502 .66827 .66831 .66834 .66838 9.82629 .82631 .82633 .82635 .67033 .67036 .67039 .67043 20 19 18 17 16 15 14 13 + ir 45 46 47 9.82101 .82103 .82106 .82108 .66333 .66337 .66330 .66334 9.82236 .82238 .82241 .82243 .66430 .66433 .66436 .66440 9.82371 .82373 .82375 .82377 .66635 .66639 .66642 .66646 9.82504 .82507 .82509 .82511 .66841 .66844 .66848 .66851 9.82638 .82640 .82642 .82644 .67046 .67050 .67053 .67057 + ir 49 50 51 9.82110 .82112 .82115 .82117 .66337 .66341 .66344 .66347 9.82245 .82247 .82250 .82252 .66443 .66447 .66450 .66454 9.82380 .82382 .82384 .82386 .66649 .66653 .66656 .66659 9.82513 .82515 .82518 .82520 .66855 .66858 .66863 .66865 9.82646 .82649 .82651 .82653 .67060 .67063 .67067 .67070 12 11 10 9 + 13' 53 54 65 9.82119 .82121 .82124 .82126 .66351 .66354 .66358 .66361 9.82254 .82256 .82259 .82261 .66457 .66460 .66464 .66467 9.82388 .82391 .82393 .82395 .66663 .66666 .66670 .66673 9.82522 .82524 .82527 .82529 .66868 .66872 .06875 .66879 9.82655 .82657 .82660 .82662 .67074 .67077 .67081 .67084 8 7 6 5 + W 57 68 59 9.82128 .82130 .82133 .82135 .66265 .66368 .66372 .66275 9.82263 .82265 .82268 .82270 .66471 .66474 .66478 .66481 9.82397 .82400 .82402 .82404 .66677 .66680 .66683 .66687 9.82531 .82533 .82535 .82538 .G6882 .G6886 .66889 .66892 9.82664 .82666 .82668 .82671 .67087 .67091 .67094 .67098 4 3 2 i + 15' 9.82137 .66378 9.82272 .66485 9.82406 .66690 9.82540 .66896 9.82673 .67101 16h44m 16^4Sm 16h 42m 16h 4im 16h40m Page 132] TABLE IV. Haversines. s 7ft 20m 110° 0' 7A 21^ 110° 15' 7A 22^ 110° 30' 7ft 23m 110° 45' 7ft 24'^ 111° 0' 3 Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav Nat. Hav. Log. Hav. Nat. Hav. 1 2 3 9.82673 .82675 .82677 .82680 .67101 .67104 .67108 .67111 9.82805 .82807 ,82810 .82812 .67306 .67309 .67313 .67316 9.82937 .82939 .82941 .82944 .67510 .67514 .67517 .67521 9.83068 .83070 .83073 .83075 .67715 .67718 .67721 .67725 9.83199 .83201 .83203 .83205 .67918 .67922 .67925 .67929 60 59 58 57 + 1' 5 6 7 9.82682 .82684 .82686 .82688 .67115 .67118 .67123 .67125 9.82814 .82816 .82818 .82821 .67320 .67323 .67326 .67330 9.82946 .82948 .82950 .82952 .67524 .67527 .67531 .67534 9.83077 .83079 .83081 .83083 .67728 .67732 .67735 .67738 9.83207 .83210 .83212 .83214 .67932 .67935 .67939 .67942 56 55 54 53 + V 9 10 11 9.82691 .82693 .82695 .82697 .67128 .67132 .67135 .67139 9.82823 .82825 .82827 .82829 .67333 .67337 .67340 .67343 9.82955 .82957 .82959 .82961 .67538 .67541 .67544 .67548 9.83086 .83088 .83090 .83092 .67743 .67745 .67749 .67753 9.83216 .83218 .83220 .83223 .67946 .67949 .67952 .67956 52 51 50 49 48 47 46 45 44 43 42 41 + 3' 13 14 15 9.82699 .82702 .82704 .82706 .67142 .67145 .67149 .67152 9.82832 .82834 .82836 .82838 .67347 .67350 .67354 .67357 9.82963 .82966 .82968 .82970 .67551 .67555 .67558 .67561 9.83094 .83097 .83099 .83101 .67755 .67759 .67762 .67766 9.83225 .83227 .83229 .83231 .67959 .67963 .67966 .67989 + 4' 19 9.82708 .82710 .82713 .82715 .67156 .67159 .67163 .67166 9.82840 .82843 .82845 .82847 .67360 .67364 .67367 .67371 9.82972 .82974 .82976 .82979 .67565 .67568 .67572 .67575 9.83103 .83105 .83107 .83110 .67769 .67772 .67776 .67779 9.83233 .83236 .83238 .83240 .67973 .67976 .67979 .67983 + 5' ;?5 9.82717 .82719 .82722 .82724 .67169 .67173 .67176 .67180 9.82849 .82851 .82854 .82856 .67374 .67377 .67381 .67384 9.82981 .82983 .82985 .82987 .67578 .67583 .67585 .67589 9.83112 .83114 .83116 .83118 .67783 .67786 .67789 .67793 9.83242 .83244 .83246 .83249 .67986 .67990 .67993 .67996 40 39 38 37 + 6' 25 26 21 9.82726 .82728 .82730 .82733 .67183 .67186 .67190 .67193 9.82858 .82860 .82862 .82865 .67388 .67391 .67395 .67398 9.82990 .82992 .82994 .82996 .67592 .67595 .67599 .67602 9.83120 .83123 .83125 .83127 .67796 .67800 .67803 .67806 9.83251 .83253 .83255 .83257 .68000 .68003 .68007 .68010 36 35 34 S3 + r 29 30 31 9.82735 .82737 .82739 .82741 .67197 .67200 .67203 .67207 9.82867 .82869 .82871 .82873 .67401 .67405 .67408 .67412 9.82998 .83001 .83003 .83005 .67606 .67609 .67613 .67616 9.83129 .83131 .83134 .83136 .67810 .67813 .67817 .67820 9.83259 .83262 .83264 .83266 .68013 .68017 .68020 .68034 32 31 30 29 + 8' 33 34 35 9.82744 .82746 .82748 .82750 .67210 .67214 .67217 .67221 9.82876 .82878 .82880 .82882 .67415 .67418 .67422 .67425 9.83007 .83009 .83011 .83014 .67619 .67623 .67636 .67630 9.83138 .83140 .83142 .83144 .67823 .67837 .67830 .67834 9.83268 .83270 .83272 .83275 .68027 .68030 .68034 .68037 28 27 26 25 24 23 22 21 + 9^ 31 38 39 9.82752 .82755 .82757 .82759 .67224 .67227 .67231 .67234 9.82884 .82887 .82889 .82891 .67429 .67432 .67435 .67439 9.83016 .83018 .83020 .83022 .67633 .67636 .67640 .67643 9.83147 .83149 .83151 .83153 .67837 .67840 .67844 .67847 9.83277 .83279 .83281 .83283 .68041 .68044 .68047 .68051 + W 41 42 43 9.82761 .82763 .82766 .82768 .67238 .67241 .67244 .67248 9.82893 .82895 .82898 .82900 .67442 .67446 .67449 .67452 9.83025 .83027 .83029 .83031 .67647 .67650 .67653 .67657 9.83155 .83157 .83160 .83162 .67850 .67854 .67857 .67861 9.83285 .83288 .83290 .83292 .68054 .68058 .68061 .68064 20 19 18 17 + 11' 45 46 41 9.82770 .82772 .82774 .82777 .67251 .67355 .67258 .67261 9.82902 .82904 .82906 .82909 .67456 .67459 .67463 .67466 9.83033 .83035 .83038 .83040 .67660 .67664 .67667 .67670 9.83164 .83166 .83168 .83170 .67864 .67868 .67871 .67874 9.83294 .83296 .83298 .83301 .68068 .68071 .68074 .68078 16 15 14 13 + 12' 49 50 51 9.82779 .82781 .82783 .82785 .67265 .67268 .67272 .67275 9.82911 .82913 .82915 .82917 .67469 .67473 .67476 .67480 9.83042 .83044 .83046 .83049 .67674 .67677 .67681 .67684 9.83173 .83175 .83177 .83179 .67878 .67881 .67884 .67888 9.83303 .83305 .83307 .83309 .68081 .68085 .68088 .68091 12 11 10 9 + 13' 53 54 55 9.82788 .82790 .82792 .82794 .67279 .67282 .67285 .67289 9.82920 .82922 .82924 .82926 .67483 .67487 .67490 .67493 9.83051 .83053 .83055 .83057 .67687 .67691 .67694 .67698 9.83181 .83184 .83186 .83188 .67891 .67895 .67898 .67901 9.83311 .83314 .83316 .83318 .68095 .68098 .68103 .68105 8 7 6 5 + U' 51 58 59 9.82796 .82799 .82801 .82803 .67392 .67296 .67299 .67302 9.82928 .82930 .82933 .82935 .67497 .67500 .67504 .67507 9.83059 .83062 .83064 .83066 .67701 .67704 .67708 .67711 9.83190 .83192 .83194 .83197 .67905 .67908 .67913 .67915 9.83320 .83322 .83324 .83327 .68108 .68112 .68115 .68119 4 3 2 1 + 15' 9.82805 .67306 9.82937 .67510 9.83068 .67715 9.83199 .67918 9.83329 .68122 16h S9m 16^ 38m 1 16h 37m 1 IG^Serr^ j 16^35^ | TABLE IV. [Page 133 Haversines. s 7ft 25m 111° 15' 7ft 26rn 111° 30' 7ft 27m 111° 45' 1 7ft ggm 112° C 7ft 29m 112° 15' s Log. nav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. 1 2 3 9.83329 .83331 .83333 .83335 .68133 .68135 .68129 .68133 9.83458 .83460 .83462 .83464 .68335 .68328 .68332 .68335 9.83587 .83589 .83591 .83593 .68538 .68531 .68535 .68538 9.83715 .83717 .83719 .83721 .68730 .68734 .68737 .68740 9.83842 .83844 .83847 .83849 .68933 .68936 .68939 .68943 60 59 58 57 56 65 54 53 52 51 50 49 + r 5 6 7 9.83337 .83339 .83342 .83344 .68135 .68139 .68143 .68146 9.83467 .83469 .83471 .83473 .68339 .68343 .68345 .68349 9.83595 .83597 .83600 .83602 .68541 .68545 .68548 .68552 9.83723 .83725 .83728 .83730 .68744 .68747 .68751 .68754 9.83851 .83853 .83855 .83857 .68946 .68949 .68953 .68956 + V 9 10 11 9.83346 .83348 .83350 .83352 .68149 .68153 .68156 .68159 9.83475 .83477 .83480 .83482 .68353 .68356 .68359 .68362 9.83604 .83606 .83608 .83610 .68555 .68558 .68562 .68565 9.83732 .83734 .83736 .83738 .68757 .68761 .68764 .68767 9.83859 .83861 .83864 .83866 .68959 .68963 .68966 .68969 + 3' IS 14 15 9.83355 .83357 .83359 .83361 .68163 .68166 .68169 .68173 9.83484 .83486 .83488 .83490 .68366 .68369 .68372 .68376 9.83612 .83615 .83617 .83619 .68568 .68572 .68575 .68579 9.83740 .83743 .83745 .83747 .68771 .68774 .68778 .68781 9.83868 .83870 .83872 .83874 .68973 .68976 .68980 .68983 48 47 46 45 44 43 42 41 40 39 38 37 + 4' 17 18 19 9.83363 .83365 .83368 .83370 .68176 .68180 .68183 .68186 9.83492 .83495 .83497 .83499 .68379 .68383 .68386 .68389 9.83621 .83623 .83625 .83627 .68583 .68585 .68589 .68593 9.83749 .83751 .83753 .83755 .68784 .68788 .68791 .68794 9.83876 .83878 .83881 .83883 .68986 .68990 .68993 .68996 + 5' 21 22 23 9.83372 .83374 .83376 .83378 .68190 .68193 .68196 .68200 9.83501 .83503 .83505 .83507 .68393 .68396 .68399 .68403 9.83630 .83632 .83634 .83636 .68595 .68599 .68603 .68606 9.83757 .83760 .83762 .83764 .68798 .68801 .68804 .68808 9.83885 .83887 .83889 .83891 .69000 .69003 .69006 .69010 + 6' 25 26 27 9.83380 .83383 .83385 .83387 .68303 .68307 .68210 .68313 9.83510 .83512 .83514 .83516 .68406 .68410 .68413 .68416 9.83638 . .83640 .83642 .83644 .68609 .68612 .68616 .68619 9.83766 .83768 .83770 .83772 .68811 .68815 .68818 .68831 9.83893 .83895 .83897 .83900 .69013 .69017 .69030 .69033 36 35 34 33 + r 29 30 31 9.83389 .83391 .83393 .83396 .68217 .68220 .68224 .68227 9.83518 .83520 .83522 .83525 .68420 .68423 .68427 .68430 9.83647 .83649 .83651 .83653 .68632 .68626 .68629 .68633 9.83774 .83777 .83779 .83781 .68835 .68828 .68831 .68835 9.83902 .83904 .83906 .83908 ,69037 .69030 .69033 .69037 32 31 30 29 + 8^ 33 34 35 9.83398 .83400 .83402 .83404 .68330 .68334 .68337 .68240 9.83527 .83529 .83531 .83533 .68433 .68437 .68440 .68443 9.83655 .83657 .83659 .83662 .68636 .68639 .68643 .68646 9.83783 .83785 .83787 .83789 .68838 .68843 .68845 .68848 9.83910 .83912 .83914 .83916 .69040 .69044 .69047 .69050 28 27 26 25 + 9' 37 38 39 9.83406 .83409 .83411 .83413 .68244 .68247 .68251 .68254 9.83535 .83537 .83540 .83542 .68447 .68450 .68454 .68457 9.83664 .83666 .83668 .83670 .68649 .68653 .68656 .68660 9.83791 .83794 .83796 .83798 .68853 .68855 .68858 .68863 9.83919 .83921 .83923 .83925 .69054 .69057 .69060 .69064 24 23 22 21 41 42 43 9.83415 .83417 .83419 .83421 .68257 .68261 .68264 .68268 9.83544 .83546 .83548 .83550 .68460 .68464 .68467 .68470 9.83672 .83674 .83676 .83679 .68663 .68666 .68670 .68673 9.83800 .83802 .83804 .83806 .68865 .68869 .68872 .68875 9.83927 .83929 .83931 .83933 .69067 .69070 .69074 .69077 20 19 18 17 45 46 47 9.83424 .83426 .83428 .83430 .68271 .68374 .68278 .68281 9.83552 .83555 .83557 .83559 .68474 .68477 .68481 .68484 9.83681 .83683 .83685 .83687 .68676 .68680 .68683 .68687 9.83808 .83811 .83813 .83815 .68879 .68882 .68885 .68889 9.83935 .83938 .83940 .83942 .69080 .69084 .69087 .69091 16 15 14 13 + ir 49 50 51 9.83432 .83434 .83436 .83439 .68284 .68288 .68291 .68295 9.83561 .83563 .83565 .83567 .68487 .68491 .68494 .68497 9.83689 .83691 .83694 .83696 .68690 .68693 .68697 .68700 9.83817 .83819 .83821 .83823 .68892 .68895 .68899 .68902 9.83944 .83946 .83948 .83950 .69094 .69097 .69101 .69104 12 11 10 9 + 13^ 53 54 55 9.83441 .83443 .83445 .83447 .68398 .68301 .68305 .68308 9.83570 .83572 .83574 .83576 .68501 .68504 .68508 .68511 9.83698 .83700 .83702 .83704 .68703 .68707 .68710 .68713 9.83825 .83828 .83830 .83832 .68906 .68909 .68912 .68916 9.83952 .83955 .83957 .83959 .69107 .69111 .69114 .69117 8 7 6 5 + W 57 58 59 9.83449 .83452 .83454 .83456 .68313 .68315 .68318 .68333 9.83578 .83580 .83582 .83585 .68515 .68518 .68521 .68525 9.83706 .83708 .83711 .83713' .68717 .68720 .68724 .68727 .68730 9.83834 .83836 .83838 .83840 .68919 .68923 .68936 .68939 9.83961 .83963 .83965 .83967 .69121 .69134 .69137 .69131 4 3 2 1 _ + 15^ 9.83458 .68335 9.83587 .68528 9.83715 9.83842 .68933 9.83969 .69134 16^ 34'^ 16^ 33m 16h 32^ ^6ft Sim le^som Page 134] TABLE IV. Haversinee. s 7ft ^aw 112° 30' 7h. Sim 113° 45^ | 7h 32^ 113° C | 7h 33m 113° 15' 7ft S4m 113° 30' | s Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. 1 2 3 9.83969 .83971 .83974 .83976 .69134 .69138 .69141 .69144 9.84096 .84098 .84100 .84102 .69336 .69339 .69343 .69346 9.84221 .84223 .84226 .84228 .69537 .69540 .69543 .69547 9.84346 .84349 .84351 .84353 .69737 .69741 .69744 .69747 9.84471 .84473 .84475 .84477 .69937 .69941 .69944 .69947 60 59 58 57 + r 5 6 7 9.83978 .83980 .83982 .83984 .69148 .69151 ,69154 .69158 9.84104 .84106 .84108 .84110 .69349 .69353 .69356 .69359 9.84230 .84232 .84234 .84236 .69550 .69553 .69557 .69560 9.84355 .84357 .84359 .84361 .69751 .69754 .69757 .69761 9.84479 .84481 .84483 .84485 .69951 .69954 .69957 .69961 56 55 54 53 + 3' 9 10 11 9.83986 .83988 .83990 .83992 .69161 .69164 .69168 .69171 9.84112 .84114 .84117 .84119 .69363 .69366 .69369 .69373 9.84238 .84240 .84242 .84244 .69563 .69567 .69570 .69573 9.84363 .84365 .84367 .84369 .69764 .69767 .69771 .69774 9.84488 .84490 .84492 .84494 .69964 .69967 .69971 .69974 52 51 50 49 + 3' 13 14 15 9.83995 .83997 .83999 .84001 .69174 .69178 .69181 .69185 9.84121 .84123 .84125 .84127 .69376 .69379 .69383 .69386 9.84246 .84248 .84251 .84253 .69577 .69580 .69583 .69587 9.84371 .84373 .84376 .84378 .69777 .69781 .69784 .69787 9.84496 .84498 .84500 .84502 .69977 .69981 .69984 .69987 48 47 46 45 + 4' 17 18 19 9.84003 .84005 .84007 .84009 .69188 .69191 .69195 .69198 9.84129 .84131 .84133 .84135 .69389 .69393 .69396 .69399 9.84255 .84257 .84259 .84261 .69590 .69593 .69597 .69600 9.84380 .84382 .84384 .84386 .69791 .69794 .69797 .69801 9.84504 .84506 .84508 .84510 .69991 .69994 .69997 .70001 44 43 42 41 + 5' 21 22 2S 9.84011 .84014 .84016 .84018 .69301 .69305 .69308 .69311 9.84138 .84140 .84142 .84144 .69403 .69406 .69409 .69413 9.84263 .84265 .84267 .84269 .69803 .69607 .69610 .69614 9.84388 .84390 .84392 .84394 .69804 .69807 .69811 .69814 9.84512 .84514 .84517 .84519 .70004 .70007 .70011 .70014 40 39 38 37 + 6' 25 26 27 9.84020 .84022 .84024 .84026 .69315 .69318 .69331 .69335 9.84146 .84148 .84150 .84152 .69416 .69419 .69433 .69436 9.84271 . .84274 .84276 .84278 .69617 .69630 .69634 .69637 9.84396 .84398 .84400 .84403 .69817 .69831 .69834 .69837 9.84521 .84523 .84525 .84527 .70017 .70031 .70034 .70037 36 35 34 33 + r 29 SO 31 9.84028 .84030 .84033 .84035 .69338 .69333 .69335 .69338 9.84154 .84156 .84159 .84161 .69439 .69433 .69436 .69439 9.84280 .84282 .84284 .84286 .69630 .69634 .69637 .69640 9.84405 .84407 .84409 .84411 .69831 .69834 .69837 .69841 9.84529 .84531 .84533 .84535 .70031 .70034 .70037 .70041 32 31 30 29 + 8' S3 34 35 9.84037 .84039 .84041 .84043 .69343 .69345 .69348 .69353 9.84163 .84165 .84167 .84169 .69443 .69446 .69450 .69453 9.84288 .84290 .84292 .84294 .69644 .69647 .69650 .69654 9.84413 .84415 .84417 .84419 .69844 .69847 .69851 .69854 9.84537 .84539 .84541 .84543 .70044 .70047 .70051 .70054 28 27 26 25 + 9^ 37 38 39 9.84045 .84047 .84049 .84051 .69355 .69358 .69363 .69365 9.84171 .84173 .84175 .84177 .69456 .69460 .69463 .69466 9.84296 .84299 .84301 .84303 .69657 .69660 .69664 .69667 9.84421 .84423 .84425 .84427 .69857 .69861 .69864 .69867 9.84545 .84547 .84550 .84552 .70057 .70061 .70064 .70067 24 23 22 21 20 19 18 17 + W 41 42 4S 9.84054 .84056 .84058 .84060 .69368 .69373 .69375 .69379 9.84179 .84182 .84184 .84186 .69470 .69473 .69476 .69480 9.84305 .84307 .84309 .84311 .69670 .69674 .69677 .69680 9.84430 .84432 .84434 .84436 .69871 .69874 .69877 .69881 9.84554 .84556 .84558 .84560 .70071 .70074 .70077 .70081 + 11^ 46 47 9.84062 .84064 .84066 .84068 .69383 .69385 .69389 .69393 9.84188 .84190 .84192 .84194 .69483 .69486 .69490 .69493 9.84313 .84315 .84317 .84319 .69684 .69687 .69690 .69694 9.84438 .84440 .84442 .84444 .69884 .69887 .69891 .69894 9.84562 .84564 .84566 .84568 .70084 .70087 .70091 .70094 16 15 14 IS + ir 49 50 51 9.84070 .84072 .84075 .84077 .69395 .69399 .69303 .69305 9.84196 .84198 .84200 .84203 .69496 .69500 .69503 .69506 9.84321 .84324 .84326 .84328 .69697 .69700 .69704 .69707 9.84446 .84448 .84450 .84452 .69897 .69901 .69904 .69907 9.84570 .84572 .84574 .84576 .70097 .70101 .70104 .70107 12 11 10 9 8 7 6 5 + 13' 53 54 55 9.84079 .84081 .84083 .84085 .69309 .69313 .69315 .69319 9.84205 .84207 .84209 .84211 .69510 .69513 .69516 .69530 9.84330 .84332 .84334 .84336 .69710 .69714 .69717 .69730 9.84454 .84456 .84459 .84461 .69911 .69914 .69917 .69931 9.84578 .84581 .84583 .84585 .70111 .70114 .70117 .70131 + 14' 57 55 59 9.84087 .84089 .84091 .84093 .69333 .69336 .69339 .69333 9.84213 .84215 .84217 .84219 .69533 .69527 .69530 .69533 9.84.338 .84340 .84342 .84344 .69734 .69737 .69731 .69734 9.84463 .84465 .84467 .84469 .69934 .69937 .69931 .69934 9.84587 .84589 .84591 .84593 .70134 .70137 .70131 .70134 4 S 2 1 + 15' 9.84096 .69336 9.84221 .69537 9.84346 .69737 9.84471 .69937 9.84595 .70137 ifift 29m IQh 2Sm 16h 27m 16ft 26m 16fi 25m TABLE IV. Havereines. [Page 136 s Jh 35m 113° 45' 7h sem 114° 6' 7h S7m 114° 15^ 7h SS-m 114° 30' 7h 39m 114° 45' 1 s Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. 1 2 3 9.84595 .84597 .84599 .84601 .70137 .70141 .70144 .70147 9.84718 .84720 .84722 .84724 .70337 .70340 .70343 .70347 9.84841 .84843 .84845 .84847 .70536 .70539 .70543 .70546 9.84903 .84965 .84967 .84969 .70735 .70738 .70741 .70745 9.85085 .85087 .85089 .85091 .70933 .70936 .70940 .70943 60 59 58 57 + r 5 6 7 9.84603 .84605 .84607 .84609 .70151 .70154 .70157 .70161 9.84726 .84729 .84731 .84733 .70350 .70353 .70357 .70360 9.84849 .84851 .84853 .84855 .70549 .70553 .70556 .70559 9.84971 .84973 .84975 .84977 .70748 .70751 .70755 .70758 9.85093 .85095 .85097 .85099 .70946 .70950 .70953 .70956 56 55 54 53 + 2' 9 10 11 9.84611 .84613 .84616 .84618 .70164 .70167 .70171 .70174 9.84735 .84737 .84739 .84741 .70363 .70367 .70370 .70373 9.84857 .84859 .84861 .84863 .70562 .70566 .70569 .70572 9.84979 .84982 .84984 .84986 .70761 .70764 .70768 .70771 9.85101 .85103 .85105 .85107 .70959 .70963 .70966 .70969 52 51 50 49 + 3' 13 14 15 9.84620 .84622 .84624 .84626 .70177 .70181 .70184 .70187 9.84743 .84745 .84747 .84749 .70377 .70380 .70383 .70387 9.84866 .84868 ■ .84870 .84872 .70576 .70579 .70582 .70586 9.84988 .84990 .84992 .84994 .70774 .70778 .70781 .70784 9.85109 .85111 .85113 .85115 .70973 .70976 .70979 .70983 48 47 46 45 44 43 42 41 40 39 38 37 + 4^ 17 18 19 9.84628 .84630 .84632 .84634 .70191 .70194 .70197 .70201 9.84751 .84753 .84755 .84757 .70390 .70393 .70397 .70400 9.84874 .84876 .84878 ,84880 .70589 .70592 .70596 .70599 9.84996 .84998 .85000 .85002 .70788 .70791 .70794 .70798 9.85117 .85119 .85121 .85123 .70986 .70989 .70992 .70996 + 5^ 21 22 23 9.84636 .84638 .84640 .84642 .70304 .70207 .70211 .70214 9.84759 .84761 .84763 .84765 .70403 .70407 .70410 .70413 9.84882 .84884 .84886 .84888 .70602 .70606 .70609 .70612 9.85004 .85006 .85008 .85010 .70801 .70804 .70807 .70811 9.85125 .85127 .85129 .85131 .70999 .71002 .71006 .71009 + 6^ 25 26 27 9.84644 .84646 .84648 .84651 .70217 .70221 .70224 .70227 9.84767 .84770 .84772 .84774 .70417 .70420 .70423 .70426 9.84890 .84892 .84894 .84896 .70615 .70619 .70622 .70625 9.85012 .85014 .85016 .85018 .70814 .70817 .70821 .70824 9.85133 .85135 .85137 .85139 .71012 .71016 .71019 .71022 36 35 34 S3 + r 29 30 31 9.84653 .84655 .84657 .84659 .70230 .70234 .70237 .70240 9.84776 .84778 .84780 .84782 .70430 .70433 .70436 .70440 9.84898 .84900 .84902 .84904 .70629 .70632 .70635 .70639 9.85020 .85022 .85024 .85026 .70827 .70831 .70834 .70837 9.85141 .85143 .85145 .85147 .71025 .71029 .71032 .71035 32 31 30 29 + 8^ 33 34 35 9.84661 .84663 .84665 .84667 .70244 .70247 .70250 .70254 9.84784 .84786 .84788 .84790 .70443 .70446 .70450 .70453 9.84906 .84908 .84910 .84912 .70642 .70645 .70649 .70652 9.85028 .85030 .85032 .85034 .70840 .70844 .70847 .70850 9.85149 .85151 .85153 .85155 .71039 .71042 .71045 .71049 28 27 26 25 + 9' 37 38 39 9.84669 .84671 .84673 .84675 .70257 .70260 .70264 .70267 9.84792 .84794 .84796 .84798 .70456 .70460 .70463 .70466 9.84914 .84916 .84919 .84921 .70655 .70659 .70662 .70665 9.85036 .85038 .85040 .85042 .70854 .70857 .70860 .70864 9.85158 .85160 .85162 .85164 .71052 .71055 .71058 .71062 24 23 22 Ti + W 41 42 43 9.84677 .84679 .84681 .84683 .70270 .70274 .70277 .70280 9.84800 .84802 .84804 .84806 .70470 .70473 .70476 .70480 9.84923 .84925 .84927 .84929 .70668 .70672 .70675 .70678 9.85044 .85046 .85048 .85050 .70867 .70870 .70874 .70877 9.85166 .85168 .85170 .85172 .71065 .71068 .71072 .71075 20 19 18 17 + 11^ 45 46 47 9.84685 .84688 .84690 .84692 .70284 .70287 .70290 .70294 9.84808 .84810 .84812 .84815 .70^83 .70486 .70490 .70493 9.84931 .84933 .84935 .84937 .70682 .70685 .70688 .70692 9.85052 .85054 .85057 .85059 .70880 .70884 .70887 .70890 9.85174 .85176 .85178 .85180 .71078 .71082 .71085 .71088 16 15 14 13 + n' 49 50 51 9.84694 .84696 .84698 .84700 .70297 .70300 .70304 .70307 9.84817 .84819 .84821 .84823 .70496 .70499 .70503 .70506 9.84939 .84941 .84943 .84945 .70695 .70698 .70702 .70705 9.85061 .85063 .85065 .85067 .70893 .70897 .70900 .70903 9.85182 .85184 .85186 .85188 .71091 .71095 .71098 .71101 12 11 10 9 + 13^ 53 54 55 9.84702 .84704 .84706 .84708 .70310 .70314 .703W .70320 9.84825 .84827 .84829 .84831 .70509 .70513 .70516 .70519 9.84947 .84949 .84951 .84953 .70708 .70712 .70715 .70718 9.85069 .85071 .85073 .85075 .70907 .70910 .70913 .70916 9.85190 .85192 .85, 94 .85196 .71105 .71108 .71111 .71114 8 7 6 5 + lif 57 58 59 9.84710 .84712 .84714 .84716 .70324 .70327 .70330 .70333 9.84833 .84835 .84837 .84839 .70523 .70526 .70529 .70533 9.84955 .84957 .84959 .84961 .70721 .70725 .70729 .70731 9.85077 .85079 .85081 .85083 .70920 .70923 .70926 .70930 9.85198 .85200 .85202 .85204 .71118 .71121 .71124 .71128 4 S 2 1 + W 9.84718 .70337 9.84841 .70536 9.84963 .70735 9.85085 .70933 9.85206 .71131 JffiA 24m 16h 23^ 16^ 22m 16^ 21m 16^ 20m Page 136] TABLE IV. Haversines. s 7h 40m 115° 0' 7A 4im 115° 15/ 7A 42m 115° 30' 7h 43m 115° 45' 7h 44m 116° 0' E Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. 1 2 S 9.85206 .85208 .85210 .85212 .71131 .71134 .71138 .71141 9.85326 .85328 .85330 .85332 .71328 .71332 .71335 .71338 9.85446 .85448 .85450 .85452 .71526 .71529 .71532 .71535 9.85565 .85567 .85569 .85571 .71722 .71726 .71729 .71732 9.85684 .85686 .85688 .85690 .71919 .71922 .71925 .71928 60 59 58 57 + r 5 6 7 9.85214 .85216 .85218 .85220 .71144 .71147 .71151 .71154 9.85334 .85336 .85338 .85340 .71342 .71345 .71348 .71351 9.85454 .85456 .85458 .85460 .71539 .71542 .71545 .71549 9.85573 .85575 .85577 .85579 .71735 .71739 .71742 .71745 9.85692 .85694 .85696 .85698 .71932 .71935 .71938 .71941 56 55 54 53 + 3' 9 10 11 9.85222 .85224 .85226 .85228 .71157 .71161 .71164 .71167 9.85342 .85344 .85346 .85348 .71355 .71358 .71361 .71365 9.85462 .85464 .85466 .85468 .71552 .71555 .71558 .71562 9.85581 .85583 .85585 .85587 .71748 .71752 .71755 .71758 9.85700 .85702 .85704 .85706 .71945 .71948 .71951 .71955 52 51 50 49 + 3' 13 14 15 9.85230 .85232 .85234 .85236 .71170 .71174 .71177 .71180 9.85350 .85352 .85354 .85356 .71368 .71371 .71374 .71378 9.85470 .85472 .85474 .85476 .71565 .71568 .71571 .71575 9.85589 .85591 .85593 .85595 .71762 .71765 .71768 .71771 9.85708 .85710 .85712 .85714 .71958 .71961 .71964 .71968 48 47 46 45 + 4^ 17 18 19 9.85238 .85240 .85242 .85244 .71184 .71187 .71190 .71194 9.85358 .85360 .85362 .85364 .71381 .71384 .71388 .71391 9.85478 .85480 .85482 .85484 .71578 .71581 .71585 .71588 9.85597 .85599 .85601 .85603 .71775 .71778 .71781 .71784 9.85716 .85718 .85720 .85722 .71971 .71974 .71977 .71981 44 43 42 41 + 5' 21 22 23 9.85246 .85248 .85250 .85252 .71197 .71200 .71203 .71207 9.85366 .85368 .85370 .85372 .71394 .71397 .71401 .71404 9.85486 .85488 .85490 .85492 .71591 .71594 .71598 .71601 9.85605 .85607 .85609 .85611 .71788 .71791 .71794 .71798 9.85724 .85726 .85727 .85729 .71984 .71987 .71990 .71994 40 39 38 37 + 6' 25 26 27 9.85254 .85256 .85258 .85260 .71210 .71213 .71217 .71220 9.85374 .85376 .85378 .85380 .71407 .71411 .71414 .71417 9.85494 .85496 .85498 .85500 .71604 .71608 .71611 .71614 9.85613 .85615 .85617 .85619 .71801 .71804 .71807 .71811 9.85731 .85733 .85735 .85737 .71997 .72000 .72003 .72007 36 35 34 33 + r 29 SO SI 9.85262 .85264 .85266 .85268 .71223 .71226 .71230 .71233 9.85382 .85384 .85386 .85388 .71420 .71424 .71427 .71430 9.85502 .85504 .85506 .85508 .71617 .71621 .71624 .71627 9.85621 .85623 .85625 .85627 .71814 .71817 .71820 .71824 9.85739 .85741 .85743 .85745 .72010 .72013 .72017 .72020 32 31 30 29 + S' S3 34 35 9.85270 .85272 .85274 .85276 .71236 .71240 .71243 .71246 9.85390 .85392 .85394 .85396 .71434 .71437 .71440 .71443 9.85510 .85512 .85514 .85516 .71631 .71634 .71637 .71640 9.85629 .85631 .85633 .85635 .71827 .71830 .71834 .71837 9.85747 .85749 .85751 .85753 .72023 .72026 .72030 .72033 28 27 26 25 + 9' 37 S8 39 9.85278 .85280 .85282 .85284 .71249 .71253 .71256 .71259 9.85398 .85400 .85402 .85404 .71447 .71450 .71453 .71456 9.85518 .85520 .85522 .85524 .71644 .71647 .71650 .71653 9.85637 .85639 .85641 .85643 .71840 .71843 .71847 .71850 9.85755 .85757 .85759 .85761 .72036 .72039 .72043 .72046 24 23 22 21 + 10' 41 42 43 9.85286 .85288 .85290 .85292 .71263 .71266 .71269 .71273 9.85406 .85408 .85410 .85412 .71460 .71463 .71466 .71470 9.85526 .85528 .85530 .85532 .71657 .71660 .71663 .71667 9.85645 .85647 .85649 .85651 .71853 .71856 .71860 .71863 9.85763 .85765 .85767 .85769 .72049 .72052 .72056 .72059 20 19 18 17 + ir 45 46 47 9.85294 .85296 .85298 .85300 .71276 .71279 .71282 .71286 9.85414 .85416 .85418 .85420 .71473 .71476 .71480 .71483 9.85534 .85536 .85538 .85540 .71670 .71673 .71676 .71680 9.85653 .85654 .85656 .85658 .71866 .71870 .71873 .71876 9.85771 .85773 .85775 .85777 .72062 .72066 .72069 .72072 16 15 14 13 12 11 10 9 8 7 6 5 + n' 49 50 51 9.85302 .85304 .85306 .85308 .71289 .71292 .71296 .71299 9.85422 .85424 .85426 .85428 .71486 .71489 .71493 .71496 9.85542 .85544 .85546 .85548 .71683 .71686 .71690 .71693 9.85660 .85662 .85664 .85666 .71879 .71883 .71886 .71889 9.85779 .85781 .85783 .85785 .72075 .72079 .72082 .72085 + 13' 53 54 55 9.85310 .85312 .85314 .85316 .71302 .71305 .71309 .71312 9.85430 .85432 .85434 .85436 .71499 .71503 .71506 .71509 9.85550 .85552 .85554 .85555 .71696 .71699 .71703 .71706 9.85668 .85670 .85672 .85674 .71892 .71896 .71899 .71902 9.85787 .85788 .85790 .85792 .72088 .72092 .72095 .72098 + ir 67 58 59 9.85318 .85320 .85322 .85324 .71315 .71319 .71322 .71325 9.85438 .85440 .85442 .85444 .71512 .71516 .71519 .71522 9.85557 .85559 .85561 .85563 .71709 .71712 .71716 .71719 9.85676 .85678 .85680 .85682 .71905 .71909 .71912 .71915 9.85794 .85796 .85798 .85800 .72101 .72105 .72108 .72111 4 3 2 1 + 15' 9.85326 .71328 9.85446 .71526 9.85565 .71722 9.85684 .71919 9.85802 .72114 16^ 19m len 18m 16h nm, 16h 16m 1 16h 15m 1 TABLP] IV. Haversinea. [Page 137 B S 7A 45m 116° 15' 7A 46™ 116° 30' 1 7ft AT^ 116° 45' inj^sm 117°©' 7h 49m 117° 15' 1 s Log. Hav. Nat. Hav. Log. Hav. Nat. nav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. 1 2 3 9.85802 .85804 .85806 .85808 .73114 .72118 .72121 .73124 9.85920 .85922 .85924 .85926 .73310 .73313 .73316 .72320 9.86037 .86039 .86041 .86043 .72505 .72508 .72511 .72515 9.86153 .86155 .86157 .86159 .73700 .73703 .73706 .73709 9.86269 .86271 .86273 .86275 .73894 .73897 .73900 .72903 60 59 58 57 + r 5 6 7 9.85810 .85812 .85814 .85816 .72127 .73131 .73134 .73137 9.85928 .85930 .85931 .85933 .72323 .73326 .73329 .72333 9.86045 .86046 .86048 .86050 .72518 .72521 .72524 .72528 9.86161 .86163 .86165 .86167 .73712 .72716 .72719 .72722 9.86277 .86279 .86281 .86282 .72907 .72910 .72913 .72916 56 55 54 53 + 3' 9 10 11 9.85818 .85820 .85822 .85824 .72141 .73144 .73147 .73150 9.85935 .85937 .85939 .85941 .72336 .73339 .73342 .72346 9.86052 .86054 .86056 .86058 .72531 .72534 .73537 .73541 9.86169 .86171 .86173 .86174 .72735 .73739 .73733 .73735 9.86284 .86286 .86288 .86290 .73920 .72923 .72926 .72929 52 51 50 49 + 3- 13 14 15 9.85826 .85828 .85830 .85832 .73154 .73157 .73160 .73163 9.85943 .85945 .85947 .85949 .72349 .72352 .72355 .72359 9.86060 .86062 .86064 .86066 .73544 .73547 .73550 .73554 9.86176 .86178 .86180 .86182 .73738 .72742 .72745 .72748 9.86292 .86294 .86296 .86298 .72932 .73936 .73939 .73943 48 47 46 45 + 4^ 17 18 19 9.85834 .85836 .85838 .85840 .73167 .73170 .73173 .73176 9.85951 .85953 .85955 .85957 .72362 .72365 .73368 .73373 9.86068 .86070 .86072 .86074 .73557 .73560 .73563 .735G7 9.86184 .86186 .86188 .86190 .72751 .72755 .73758 .73761 9.86300 .86302 .86304 .86306 .73945 .73949 .73953 .73955 44 43 42 41 + 5^ 23 9.85841 .85843 .85845 .85847 .73180 .73183 .72186 .73189 9.85959 .85961 .85963 .85965 .73375 .73378 .72381 .72385 9.86076 .86078 .86080 .86081 .73570 .73573 .73576 .73580 9.86192 .86194 .86196 .86198 .73764 .72768 .72771 .72774 9.86307 .86309 .86311 .86313 .73958 .73963 .73965 .73968 40 39 38 37 + 6^ 25 26 27 9.85849 .85851 .85853 .85855 .72193 .72196 .72199 .72202 9.85967 .85969 .85971 .85972 .72388 .72391 .72394 .72398 9.86083 .86085 .86087 .86089 .73583 .73586 .72589 .73593 9.86200 .86201 .86203 .86205 .72777 .72780 .72784 .73787 9.86315 .86317 .86319 .86321 .72971 .72974 .73978 .73981 36 35 34 33 + r 29 30 31 9.85857 .85859 .85861 .85863 .72206 .72209 .72213 .73315 9.85974 .85976 .85978 .85980 .72401 .72404 .72407 .72411 9.86091 .86093 .86095 .86097 .72596 .72599 .72603 .73606 9.86207 .86209 .86211 .86213 .73790 .73793 .73797 .73800 9.86323 .86325 .86327 .86329 .73984 .73987 .73991 .73994 32 31 30 29 + 8' S3 34 35 9.85865 .85867 .85869 .85871 .73219 .72222 .73335 .73339 9.85982 .85984 .85986 .85988 .72414 .72417 .72420 .72424 9.86099 .86101 .86103 .86105 .73609 .73613 .73615 .73618 9.86215 .86217 .86219 .86221 .73803 .73806 .73810 .73813 9.86331 .86332 .86334 .86336 .72997 .73000 .73004 .73007 28 27 26 25 24 23 22 21 20 19 IS 17 16 15 14 13 + r 37 38 39 9.85873 .85875 .85877 .85879 .73333 .73335 .73338 .73243 9.85990 .85992 .85994 .85996 .72427 .73430 .73433 .73437 9.86107 .86109 .86111 .86112 .73633 .73635 .73628 .73631 9.86223 .86225 .86227 .86229 .73816 .73819 .73833 .73836 9.86338 .86340 .86342 .86344 .73010 .73013 .73016 .73020 + 1(K 41 ■ 42 43 9.85881 .85883 .85885 .85887 .72245 .72248 .72251 .72355 9.85998 .86000 .86002 .86004 .73440 .73443 .72446 .73450 9.86114 .86116 .86118 .86120 .73635 .73638 .73641 .73644 9.86230 .86232 .86234 .86236 .73839 .73833 .73835 .73839 9.86346 .86348 .86350 .86352 .73023 .73026 .73029 73033 + 11' 46 47 9.85888 .85890 .85892 .85894 .72358 .73361 .72264 .72268 9.8G006 .86008 .86010 .86011 .73453 .73456 .73459 .72463 9.86122 .86124 .86126 .86128 .73648 .72651 .72654 .72657 9.86238 .86240 .86242 .86244 .73843 .73845 .73848 .73853 9.86354 .86355 .86357 .86359 .73036 .73039 .73042 .73046 + ir 50 51 9.85896 .85898 .85900 .85902 .72271 .73374 .73277 .72381 9.86013 .86015 .86017 .86019 .72466 .72469 .72473 72476 9.86130 .86132 .86134 .86136 .73661 .73664 .73667 .72670 9.86246 .86248 .86250 .86252 .73855 .73858 .73861 .73865 9.86361 .86363 .86365 .86367 .73049 .73052 .73055 .73058 12 11 10 9 + 13^ 54 55 9.85904 .85906 .85908 .85910 .72384 .72287 .72290 .72394 9.86021 .86023 .86025 .86027 .72479 .72482 .72485 .72489 9.86138 .86140 .86142 .86143 .72674 .72677 .73680 .73683 9.86254 .86256 .86257 .86259 .73868 .73871 .73874 .73878 9.86369 .86371 .86373 .86375 .73062 .73065 .73068 .73071 8 7 6 5 + 14' 57 58 59 9.85912 .85914 .85916 .85918 .73397 .73300 .73303 72307 9.86029 .86031 .86033 .86035 .73492 .72495 .72498 .72502 9.86145 .86147 .86149 .86151 .73687 .73690 .73693 .73696 9.86261 .86263 .86265 .86267 .73881 .72884 .72887 .72890 9.86377 .86379 .86380 .86382 .73076 .73078 .73081 .73084 4 3 2 i + 15' 9.85920 .72310 9.86037 .72505 9.86153 .73700 9.86269 .72894 9.86384 .73087 16h 14m 16h urn 16^ 12m 16^ Jim lehiom Page 138] TABLE lY. Havereines. £ 7h sm 117° W 1 7A 5m 117° 45' 7* 5m 118° (K 7ft 5Sm 118° 15' 7A 54^ 118° 30' s Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav .Nat. Hav Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. 1 S 9.86384 .86386 .86388 .86390 .73087 .73091 .73094 .73097 9.86499 .86501 .86503 .86505 .73281 .73284 .73287 .73290 9.86613 .86615 .86617 .86619 .73474 .73477 .73480 73483 9.86727 .86729 .86730 .86732 .73666 .73669 .73673 .73676 9.86840 .86842 .86843 .86845 .73858 .73861 .73864 .73868 60 59 58 57 56 55 54 53 6 6 7 9.86392 .86394 .86396 .86398 .73100 .73104 .73107 .73110 9.86507 .86509 .86510 .86512 .73294 .73297 .73300 .73303 9.86621 .86623 .86625 .86626 .73486 .73490 .73493 .73496 9.86734 .86736 .86738 .86740 .73679 .73682 .73685 .73688 9.86847 .86849 .86851 .86853 .73871 .73874 .73877 .73880 + ^ 9 10 11 9.86400 .86401 .86403 .86405 .73113 .73116 .73130 .73123 9.86514 .86516 .86518 .86520 .73306 .73310 .73313 .73316 9.86628 .86630 .86632 .86654 .73499 .73502 .73506 .73509 9.86742 .86744 .86746 .86747 .73692 .73695 .73698 .73701 9.86855 .86857 .86859 .86860 .73884 .73887 .73890 .73893 52 51 50 49 + 3' IS 14 15 9.86407 .86409 .86411 .86413 .73126 .73129 .73133 .73136 9.86522 .86524 .86526 .86528 .73319 .73333 .73336 .73329 9.86636 .86638 .86640 .86642 .73512 .73515 .73519 .73522 9.86749 .86751 .86753 .86755 .73704 .73708 .73711 .73714 9.86862 .86864 .86866 .86868 .73896 .73899 .73903 .73906 48 47 46 45 U 43 42 41 + 4' 17 18 19 9.86415 .86417 .86419 .86421 .73139 .73142 .73145 .73149 9.86529 .86531 .86533 .86535 .73332 .73335 .73339 .73342 9.86643 .86645 .86647 .86649 .73525 .73528 .73531 .73535 9.86757 .86759 .86761 .86763 .73717 .73720 .73734 .73737 9.86870 .86872 .86874 .86875 .73909 .73912 .73915 .73919 + ^ 21 22 23 9.86423 .86424 .86426 .86428 .73152 .73155 .73158 .73162 9.86537 .86539 .86541 .86543 .73345 .73348 .73351 .73355 9.86651 .86653 .86655 .86657 .73538 .73541 .73544 .73547 9.86764 .86766 .86768 .86770 .73730 .73733 .73736 .73740 9.86877 .86879 .86881 .86883 .73933 .73935 .73938 .73931 40 39 38 37 36 35 34 33 + 6' 25 26 27 9.86430 .86432 .86434 .86436 .73165 .73168 .73171 .73174 9.86545 .86547 .86569 .86550 .73358 .73361 .73364 .73368 9.86659 .86661 .86662 .86664 .73551 .73554 .73557 .73560 9.86772 .86774 .86776 .86778 .73743 .73746 .73749 .73752 9.86885 .86887 .86889 .86890 .73935 .73938 .73941 .73944 + r 29 SO SI 9.86438 .86440 .86442 .86444 .73178 .73181 .73184 .73187 9.86552 .86554 .86556 .86558 .73371 .73374 .73377 .73380 9.86666 .86668 .86670 .86672 .73563 .73567 .73570 .73573 9.86780 .86781 .86783 .86785 .73756 .73759 73763 .73765 9.86892 .86894 .86896 .86898 .73947 .73951 .73954 .73957 32 31 30 29 H- 8' 33 34 35 9.86446 .86447 .86449 .86451 .73191 .73194 .73197 .73200 9.86560 .86562 .86564 .86566 .73384 .73387 .73390 .73393 9.86674 .86676 .86678 .86679 .73576 .73579 .73583 .73586 9.86787 .86789 .86791 .86793 .73768 .73773 .73775 .73778 9.86900 .86902 .86904 .86905 .73960 .73963 .73967 .73970 28 27 26 25 24 23 22 21 20 19 18 17 + ^ 37 38 39 9.86453 .86455 .86457 .86459 .73303 .73207 .73310 .73313 9.86568 .86569 .86571 .86573 .73396 .73400 .73403 .73406 9.86681 .86683 .86685 .86687 .73589 .73593 .73595 .73599 9.86795 .86796 .86798 .86800 .73781 .73784 .73788 .73791 9.86907 .86909 .86911 .86913 .73973 .73976 .73979 .73982 + W 41 42 43 9.86461 .86463 .86465 .86467 .73216 .73230 .73333 .73336 9.86575 .86577 .86579 .86581 .73409 .73413 .73416 .73419 9.86689 .86691 .86693 .86695 .73602 .73605 .73608 .73611 9.86802 .86804 .86806 .86808 .73794 .73797 .73800 .73804 9.86915 .86917 .86919 .86920 .73986 .73989 .73992 .73995 4S 46 47 9.86468 .86470 .86472 .86474 .73229 .73232 .73236 .73239 9.86583 .86585 .86587 .86588 .73423 .73435 .73439 .73433 9.86696 .86698 .86700 .86702 .73615 .73618 .73621 .73624 9.86810 .86812 .86813 .86815 .73807 .73810 .73813 .73816 9.86922 .86924 .86926 .86928 .73998 .74002 .74005 .74008 16 15 14 13 12 11 10 9 8 7 6 5 4 S 2 1 + 13' 49 50 51 9.86476 .86478 .86480 .86482 .73242 .73245 .73249 .73252 9.86590 .86592 .86594 .86596 .73435 .73438 .73441 .73445 9.86704 .86706 .86708 .86710 .73628 .73631 .73634 .73637 9.86817 .86819 .86821 .86823 .73820 .73823 .73826 .73829 9.86930 .86932 .86933 .86935 .74011 .74014 .74018 .74031 .74034 .74037 .74030 .74033 5S 54 55 9.86484 .86486 .86488 .86489 .73256 .73258 .73261 .73265 9.86598 .86600 .86602 .86604 .73448 .73451 .73454 .73458 9.86712 .86713 .86715 .86717 .73640 .73644 .73647 .73650 9.86825 .86827 .86828 .86830 .73832 .73836 .73839 .73842 9.86937 .86939 .86941 .86943 57 59 9.86491 .86493 .86495 .86497 .73268 .73271 .73274 .73278 9.86606 .86607 .86609 .86611 .73461 .73464 .73467 .73470 9.86719 .86721 .86723 .86725 .73653 .73656 .73660 .73663 9.86832 .86834 .86836 .86838 .73845 .73848 .73852 .73855 9.86945 .86947 .86948 .86950 .74037 .74040 .74043 .74046 + W 9.86499 .73281 9.86613 .73474 9.86727 .73666 9.86840 .73858 9.86952 .74049 ifiApm lehgm 16^ Tm ifi/igTn 26ft 5'" TABLE ly. [Page 139 Haversines. s 7h 55m 118° 45' 7^56^119°©' 1 7h 57m 1190 15/ 7h 58m 1190 30^ | 7h 59m 119° 45' 1 Log. nav. Nat. nav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. s 1 2 3 9.86952 .86954 .86956 .86958 .74049 .74063 .74056 .74059 9.87064 .87066 .87068 .87070 .74340 .74344 .74247 .74350 9.87175 .87177 .87179 .87181 .74431 .74434 .74437 .74441 9.87286 .87288 .87290 .87292 .74621 .74624 .74628 .74631 9.87396 .87398 .87400 .87402 .74811 .74814 .74817 .74820 60 59 58 57 + r 5 6 7 9.86960 .86962 .86963 .86965 .74063 .74065 .74069 .74073 9.87072 .87073 .87075 .87077 .74353 .74356 .74260 .74263 9.87183 .87185 .87187 .87188 .74444 .74447 .74450 .74453 9.87294 .87295 .87297 .87299 .74634 .74637 .74640 .74643 9.87404 .87406 .87407 .87409 .74823 .74827 .74830 .74833 56 55 54 53 + V 9 10 11 9.86967 .86989 .86971 .86973 .74075 .74078 .74081 .74084 9.87079 .87081 .87083 .87085 .74366 .74269 .74373 .74375 9.87190 .87192 .87194 .87196 .74456 .74460 .74463 .74466 9.87301 .87303 .87305 .87306 .74646 .74650 .74653 .74656 9.87411 .87413 .87415 .87417 .74836 .74839 .74843 .74846 52 51 50 49 + 3' 13 14 15 9.86975 .86977 .86978 .86980 .74088 .74091 .74094 .74097 9.87086 .87088 .87090 .87092 .74379 .74282 .74285 .74288 9.87198 .87199 .87201 .87203 .74469 .74473 .74475 .74479 9.87308 .87310 .87312 .87314 .74659 .74662 .74665 .74669 9.87418 .87420 .87422 .87424 .74849 .74852 .74855 .74858 48 47 46 45 44 43 42 41 + *' 17 18 19 9.86982 .86984 .86986 .86988 .74100 .74104 .74107 .74110 9.87094 .87096 .87098 .87100 .74291 .74294 .74298 .74301 9.87205 .87207 .87209 .87211 .74483 .74485 .74488 .74491 9.87316 .87318 .87319 .87321 .74672 .74675 .74678 .74681 9.87426 .87428 .87429 .87431 .74861 .74864 .74868 74871 + 5^ 21 22 23 9.86990 .86991 .&e993 .74113 .74116 .74130 .74133 9.87101 .87103 .87105 .87107 .74304 .74307 .74310 .74314 9.87212 .87214 .87216 .87218 .74494 .74498 .74501 .74504 9.87323 .87325 .87327 .87329 .74684 .74688 .74691 .74694 9.87433 .87435 .87437 .87439 .74874 .74877 .74880 .74883 40 39 38 37 + 6' 25 26 21 9.86997 .86999 .87001 .87003 .74136 .74139 .74133 .74135 9.87109 .87111 .87112 .87114 .74317 .74320 .74323 .74326 9.87220 .87222 .87224 .87225 .74507 .74510 .74514 .74517 9.87330 .87332 .87334 .87336 .74697 .74700 .74703 .74707 9.87440 .87442 .87444 .87446 .74887 .74890 .74893 .74896 36 35 34 33 32 31 30 29 + r 29 30 31 9.87004 .87006 .87008 .87010 .74139 .74143 .74145 .74148 9.87116 .87118 .87120 .87122 .74329 .74333 .74336 .74339 9.87227 .87229 .87231 .87233 .74530 .74533 .74536 .74539 9.87338 .87340 .87341 .87343 .74710 .74713 .74716 .74719 9.87448 .87450 .87451 .87453 .74899 .74903 .74905 .74908 + 8' 33 34 35 9.87012 .87014 .87016 .87018 .74151 .74155 .74158 .74161 9.87124 .87125 .87127 .87129 .74342 .74345 .74349 .74352 9.87235 .87236 .87238 .87240 .74533 .74536 .74539 .74543 9.87345 .87347 .87349 .87351 .74722 .74726 .74729 .74732 9.87455 .87457 .87459 .87460 .74913 .74915 .74918 .74931 28 27 26 25 + 9^ 37 38 39 9.87019 .87021 .87023 .87025 .74164 .74167 .74170 .74174 9.87131 .87133 .87135 .87137 .74355 .74358 .74361 .74364 9.87242 .87244 .87246 .87248 .74545 .74548 .74553 .74555 9.87352 .87354 .87356 .87358 .74735 .74738 .74741 .74744 9.87462 .87464 .87466 .87468 .74924 .74928 .74931 .74934 24 23 22 21 + w 41 42 43 9.87027 .87029 .87031 .87032 .74177 .74180 .74183 .74186 9.87138 .87140 .87142 .87144 .74368 .74371 .74374 .74377 9.87249 .87251 .87253 .87255 .74558 .74561 .74564 .74567 9.87360 .87362 .87363 .87365 .74748 .74751 .74754 .74757 9.87470 .87471 .87473 .87475 .74937 .74940 .74943 .74946 20 19 18 17 + 11' 45 46 47 9.87034 .87036 .87038 .87040 .74190 .74193 .74196 .74199 9.87146 .87148 .87149 .87151 .74380 .74383 .74387 .74390 9.87257 .87259 .87260 .87262 .74571 .74574 .74577 .74580 9.87367 .87369 .87371 .87373 .74760 .74763 .74767 .74770 9.87477 .87479 .87481 .87482 .74950 .74953 .74956 .74959 16 15 14 13 + IV 49 50 51 9.87042 .87044 .87045 .87047 .74203 .74305 .74309 .74213 9.87153 .87155 .87157 .87159 .74393 .74396 .74399 .74402 9.87264 .87266 .87268 .87270 .74583 .74586 .74590 .74593 9.87374 .87376 .87378 .87380 .74773 .74776 .74779 .74782 9.87484 .87486 .87488 .87490 .74962 .74965 .74969 .74972 12 11 10 9 + 13^ 53 54 55 9.87049 .87051 .87053 .87055 .74315 .74318 .74231 .74335 9.87161 .87162 .87164 .87166 .74406 .74409 .74412 .74415 9.87271 .87273 .87275 .87277 .74596 .74599 .74603 .74605 9.87382 .87384 .87385 .87387 .74786 .74789 .74792 .74795 9.87492 .87493 .87495 .87497 .74975 .74978 .74981 .74984 8 7 6 5 + W 57 58 59 9.87057 .87059 .87060 .87062 .74328 .74331 .74334 .74337 9.87168 .87170 .87172 .87174 .74418 .74423 .74435 .74438 9.87279 .87281 .87283 .87284 .74609 .74612 .74615 .74618 9.87389 .87391 .87393 .87395 .74798 .74801 .74805 .74808 9.87499 .87501 .87502 .87504 .74987 .74991 .74994 .74997 4 S 2 1 + W 9.87064 .74340 9.87175 .74431 9.87286 .74621 9.87396 .74811 9.87506 .75000 16h4m iShsm 16h 2m 1 ig/i im 16^0^ Page 140] TABLE IV. | Haversines. 1 s : 8h Om 120° r 8h 2-m 120° 30^ 8h 4m 121° r 8h 6m 121° 30' 5ft 5m 133° O' 1 3 Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. 9.87506 0.75000 9.87724 0.75377 9.87939 0.75752 9.88153 0.76125 9.88364 0.76496 60 2 .87510 .75006 .87727 .75383 .87943 .75758 .88156 .76131 .88367 .76502 58 4+ 1 .87513 .75013 .87731 .75389 .87947 .75764 .88160 .76137 .88371 .76508 56 6 .87517 .75019 .87735 .75396 .87950 .75771 .88163 .76144 .88374 .76514 54 5+ 2 9.87521 0.75025 9.87738 0.75402 9.87954 0.75777 9.88167 0.76150 9.88378 0.76521 52 10 .87524 .75032 .87742 .75408 .87957 .75783 .88170 .76156 .88381 .76527 50 12+ 3 .87528 .75038 .87745 .75415 .87961 .75789 .88174 .76162 .88385 .76533 48 14 .87532 .75044 .87749 .75421 .87964 .75795 .88177 .76168 .88388 .76539 46 16+ 4 9.87535 0.75050 9.87753 0.75427 9.87968 0.75802 9.88181 0.76175 9.88392 0.76545 44 18 .87539 .75057 .87756 .75433 .87971 .75808 .88185 .76181 .88395 .76551 42 20+ 6 .87543 .75063 .87760 .75440 .87975 .75814 .88188 .76187 .88399 .76558 40 £^ .87546 .75069 .87764 .75446 .87979 .75820 .88192 .76193 .88402 .76564 38 24+ 6 9.87550 0.75075 9.87767 0.75452 9.87982 0.75827 9.88195 0.76199 9.88406 0.76570 36 ;g6 .87553 .75082 .87771 .75458 .87986 .75833 .88199 .76205 .88409 .76576 34 ;?5+ 7 .87557 .75088 .87774 .75465 .87989 .75839 .88202 .76313 .88413 .76583 32 SO .87561 .75094 .87778 .75471 .87993 .75845 .88206 .76318 .88416 .76588 30 32+ 8 9.87564 0.75101 9.87782 0.75477 9.87996 0.75853 9.88209 0.76224 9.88420 0.76595 28 .54 .87568 .75107 .87785 .75483 .88000 .75858 .88213 .76230 .88423 .76601 26 .3(5+ 9 .87572 .75113 .87789 .75490 .88004 .75864 .88216 .76236 .88427 .76607 24 .55 .87575 .75120 .87792 .75496 .88007 .75870 .88220 .76243 .88430 .76613 22 40+10 9.87579 0.75126 9.87796 0.75502 9.88011 0.75876 9.88223 0.76249 9.88434 0.76619 20 42 .87583 .75132 .87800 .75508 .88014 .75883 .88227 .76255 .88437 .76625 18 u+n .87586 .75138 .87803 .75515 .88018 .75889 .88230 .76261 .88441 .76632 16 46 .87590 .75145 .87807 .75521 .88021 .75895 .88234 .76267 .88444 .76638 14 48+1% 9.87593 0.75151 9.87810 0.75527 9.88025 0.75901 9.88237 0.76274 9.88448 0.76644 12 50 .87597 .75157 .87814 .75533 .88029 .75908 .88241 .76280 .88451 .76650 10 52+n .87601 .75164 .87818 .75540 .88032 .75914 .88244 .76286 .88455 .76656 8 54 .87604 .75170 .87821 .75546 .88036 .75920 .88248 .76292 .88458 .76662 6 56+U 9.87608 0.75176 9.87825 0.75552 9.88039 0.75926 9.88252 0.76298 9.88462 0.76668 4 58 9.87612 0.75182 9.87828 0.75558 9.88043 0.75932 9.88255 0.76305 9.88465 0.76675 2 15^ 59m I5I1 57m 15h 55m 15h 53m 15J>- 5im B ' 0+15 8h im 120° 0" 9,h^rn 130° 30' 8h 5m 131° 0' 8h 7m 121° 30' 8h 9m 133° O' s 60 9.87615 0.75189 9.87832 0.75565 9.88046 0.75939 9.88259 0.76311 9.88469 0.76681 2 .87619 .75195 .87835 .75571 .88050 .75945 .88262 .76317 .88472 .76687 58 4+16 .87623 .75201 .87839 .75577 .88053 .75951 .88266 .76323 .88476 .76693 56 6 .87626 .75208 .87843 .75583 .88057 .75957 .88269 .76329 .88479 .76699 54 5+17 9.87630 0.75214 9.87846 0.75590 9.88061 0.759G4 9.88273 0.76335 9.88483 0.76705 52 10 .87633 .75220 .87850 .75596 .88064 .75970 .88276 .76342 .88486 .76711 50 12+1% .87637 .75226 .87853 .75602 .88068 .75976 .88280 .76348 .88490 .76718? 48 14 .87641 .75233 .87857 .75608 .88071 .75982 .88283 .76354 .88493 .76724 46 16+19 9.87644 0.75239 9.87861 0.75615 9.88075 0.75988 9.88287 0.76360 9.88496 0.76730 44 18 .87648 .75245 .87864 .75621 .88078 .75995 .88290 .76366 .88500 .76736 42 fO+20 .87652 .75251 .87868 .75637 .88082 .76001 .88294 .76373 .88503 .76742 40 22 .87655 .75258 .87871 .75633 .88085 .76007 .88297 .76379 .88507 .76748 38 24+n 9.87659 0.75264 9.87875 0.75640 9.88089 0.76013 9.88301 0.76385 9.88510 0.76754 36 26 .87662 .75270 .87879 .75646 .88092 .76019 .88304 .76391 .88514 .76761 34 28+%% .87666 .75277 .87882 .75652 .88096 .76026 .88308 .76397 .88517 .76767 32 30 .87670 .75283 .87886 .75658 .88100 .76033 .88311 .76403 .88521 .76773 30 32+%Z 9.87673 0.75289 9.87889 0.75665 9.88103 0.76038 9.88315 0.76410 9.88524 0.76779 28 34 .87677 .75295 .87893 .75671 .88107 .76044 .88318 .76416 .88528 .76785 26 36+U .87680 .75302 .87896 .75677 .88110 .76050 .88322 .76423 .88531 .76791 24 38 .87684 .75308 .87900 .75683 .88114 .76057 .88325 .76438 .88535 .76797 0.76804 22 20 40+%5 9.87688 0.75314 9.87904 0.75690 9.88117 0.76063 9.88329 0.76434 9.88528 42 .87691 .75321 .87907 .75696 .88121 .76069 .88332 .76440 .88542 .76810 18 44+%6 .87695 .75337 .87911 .75702 .88124 .76075 .88336 .76447 .88545 .76816 16 46 .87699 .75333 .87914 .75708 .88128 .76082 .88339 .76453 .88549 .76823 14 48+%l 9.87702 0.75339 9.87918 0.75714 9.88131 0.76088 9.88343 0.76459 9.88552 0.76828 12 50 .87706 .75346 .87921 .75721 .88135 .76094 .88346 .76465 .88556 .76834 10 52+28 .87709 .75352 .87925 .75727 .88139 .76100 .88350 .76471 .88559 .76840 8 54 .87713 .75358 .87929 .75733 .88142 .76106 .88353 .76477 .88562 .76847 6 56+29 9.87717 0.75364 9.87932 0.75739 9.88146 0.76113 9.88357 0.76484 9.88566 0.76853 4 58 .87720 .75371 .87936 .75746 .88149 .76119 .88360 .76490 .88569 .76859 2 60+30 9.87724 0.75377 9.87939 0.75752 9.88153 0.76125 9.88364 0.76496 9.88573 0.76865 15^ 58m 15h sem 15h 54m 15^ 52m 1 15h 50m TABLE ly. [Page 141 Haversinea. s ' ^'^iO™ 122° 30^ 8^ 12m 123° 0' 8h 14m 1330 30/ 8h 16m 134° o' 8h 18^ 124° 30^ s Log. Ilav Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. 9.88573 0.76865 9.8S7S0 0.77232 9.88984 0.77597 9.89187 0.77960 9.89387 0.78320 60 ^ .88576 .76871 .88783 .77238 .88988 .77603 .89190 .77966 .89391 .78326 58 4+ 1 .88580 .76877 .88787 .77244 .88991 .77609 .89194 .77972 .89394 .78332 56 6 .88583 .76883 .88790 .77250 .88995 .77615 .89197 .77978 .89397 .78338 54 S+ 3 9.88587 0.76890 9.88793 0.77256 9.88998 0.77621 9.89200 0.77984 9.89400 0.78344 59. 10 .88590 .76896 .88797 .77262 .89001 .77627 .89204 .77990 .89404 .78350 50 12+ 3 .88594 .76902 .88800 .77269 .89005 .77633 .89207 .77996 .89407 .78356 48 14 .88597 .76908 .88804 .77275 .89008 .77639 .89210 .78002 .89411 .78362 46 16+ 4 9.88600 0.76914 9.88807 0.77281 9.89012 0.77645 9.89214 0.78008 9.89414 0.78368 44 18 .88604 .76920 .88811 .77287 .89015 .77651 .89217 .78014 .89417 .78374 42 20+ 5 .88607 .76926 .88814 .77293 .89018 .77657 .89221 .78020 .89421 .78380 40 22 .88611 .76932 .88817 .77299 .89022' .77664 .89224 .78026 .89424 .78386 38 24+ 6 9.88614 .076939 9.88821 0.77305 9.89025 0.77670 9.89227 0.78032 9.89427 0.78392 36 26 .88618 .76945 .88824 .77311 .89028 .77676 .89231 .78038 .89431 .78398 34 28+ 7 .88621 .76951 .88828 .77317 .89032 .77682 .89234 .78044 .89434 .78404 32 SO .88625 .76957 .88831 .77323 .89035 .77688 .89237 .78050 .89437 .78410 30 S2+ 8 9.88628 0.76963 9.88835 0.77329 9.89039 0.77694 9.89241 0.78056 9.89441 0.78416 28 5-^ .88632 .76969 .88838 .77336 .89042 .77700 .89244 .78062 .89444 .78422 26 56+ 9 .88635 .76975 .88841 .77342 .89045 .77706 .89247 .78068 .89447 .78428 24 38 .88639 .76981 .88845 .77348 .89049 .77712 .89251 .78074 .89450 .78434 22 40+10 9.88642 0.76988 .9.88848 0.77354 9.89052 0.77718 9.89254 0.78080 9.89454 0.78440 20 42 .88645 .76994 .88852 .77360 .89056 .77724 .89257 .78086 .89457 .78448 18 u+n .88649 .77000 .88855 .77366 .89059 .77730 .89261 .78092 .89460 .78452 16 46 .88652 .77006 .88858 .77372 .89062 .77736 .89264 .78098 .89464 .78458 14 48+Vi 9.88656 0.77012 9.88862 0.77378 9.89066 0.77742 9.89267 0.78104 9.89467 0.78464 12 50 .88659 .77018 .88865 .77384 .89069 .77748 .89271 .78110 .89470 .78470 10 5f+13 .88663 .77024 .88869 .77390 .89072 .77754 .89274 .78116 .89474 .78476 8 54 .88666 .77030 .88872 .77396 .89076 .77760 .89277 .78122 .89477 .78482 6 56+14 9.88670 0.77036 9.88876 0.77403 9.89079 0.77766 9.89281 0.78128 9.89480 0.78488 4 55 9.88673 0.77043 9.88879 0.77409 9.89083 0.77772 9.89284 0.78134 .9.89484 0.78494 2 15T^ 49m 15^ 47m 15h4Sm 15h43m i5h 41m B ' 0+15 8h lim 133° 3(y 8h ism 133° iy 8h 15m 133° 3(K 8h 17m 124° (K 8h 19m 124° 3(K 8 9.88677 0.77049 9.88882 0.77415 9.89086 0.77779 9.89287 0.78140 9.89487 0.78500 60 2 .88680 .77055 .88886 .77412 .89089 .77785 .89291 .78146 .89490 .78506 58 4+16 .88683 .77061 .88889 .77427 .89093 .77791 .89294 .78152 .89493 .78512 56 6 .88687 .77067 .88893 .77433 .89096 .77797 .89298 .78158 .89497 .78518 54 8+11 9.88690 0.77073 9.88896 0.77439 9.89099 0.77803 9.89301 0.78164 9.89500 0.78524 52 10 .88694 .77079 .88899 .77445 .89102 .77809 .89304 .78170 .89503 .78530 50 12+lS .88697 .77085 .88903 .77451 .89106 .77815 .89308 .78176 .89507 .78536 48 14 .88701 .77092 .88906 .77457 .89110 .77821 .89311 .78182 .89510 .78542 46 16+19 9.88704 0.77098 9.88910 0.77463 9.89113 0.77827 9.89314 0.78188 9.89513 0.78548 U 18 .88708 .77104 .88913 .77469 .89116 .77833 .89318 .78194 .89517 .78554 42 20+20 .88711 .77110 .88916 .77475 .89120 .77839 .89321 .78200 .89520 .78560 40 22 .88714 .77116 .88920 .77482 .89123 .77845 .89324 .78206 .89523 .78566 38 24+21 9.88718 0.77122 9.88923 0.77488 9.89126 0.77851 9.89328 0.78212 9.89527 0.78572 36 26 .88721 .77128 .88927 .77494 .89130 .77857 .89331 .78218 .89530 .78577 34 28+22 .88725 .77134 .88930 .77500 .89133 .77863 .89334 .78224 .89533 .78583 32 SO .88728 .77140 .88933 .77506 .89137 .77869 .89338 .78230 .89536 .78589 30 S2+2S 9.88732 0.77147 9.88937 0.77512 9.89140 0.77875 9.89341 0.78236 9.89540 0.78595 28 S4 .88735 .77153 .88940 .77518 .89143 .77881 .89344 .78242 .89543 .78601 26 S6+2i: .88739 .77159 .88944 .77524 .89147 .77887 .89348 .78248 .89546 .78607 24 S8 .88742 .77165 .88947 .77530 .89150 .77893 .89351 .78254 .89550 .78613 22 20 40+25 9.88745 0.77171 9.88950 0.77536 9.89153 0.77899 9.89354 0.78260 9.89553 0.78619 42 .88749 .77177 .88954 .77542 .89157 .77905 .89358 .78266 .89556 .78625 18 44+26 .88752 .77183 .88957 .77548 .89160 .77911 .89361 .78272 .89559 .78531 16 46 .88756 .77189 .88961 .77554 .89163 .77917 .89364 .78278 .89563 .78637 14 45+27 9.88759 0.77195 9.88964 0.77560 9.89167 0.77923 9.89368 0.78284 9.89566 0.78643 12 50 .88763 .77201 .88967 .77567 .89170 .77929 .89371 .78290 .89569 .78649 10 52+2S .88766 .77208 .88971 .77573 .89174 .77936 .89374 .78296 .89573 .78655 8 54 .88769 .77214 .88974 .77579 .89177 .77942 .89378 .78302 .89576 .78661 6 56+29 9.88773 0.77220 9.88978 0.77585 9.89180 0.77948 9.89381 0.78308 9.89579 0.78667 4 58 .88776 .77226 .88981 .77591 .89184 .77954 .89384 .78314 .89583 .78673 2 60+30 9.88780 0.77232 9.88984 0.77597 9.89187 0.77960 9.89387 0.78320 9.89586 0.78679 15h4Srn 1 15h 46^ 1 15h 44m 1 J5h 42m 1 15h 40m 1 Page 142] TABLE IV. | Saversines, • 8 ;. ' 8h 20m 125° r 8^^ 22m 135° 30' 8h 24'^ 126° 0' 8h 26m 126° 30' 8h 28m 1370 (/ 3 Log. Hav Nat. Hav Log. Hav Nat. Hav Log. Hav Nat. Hav Log. Hav Nat. Hav Log. Hav Nat. Hav 9.89586 0.78679 9.89782 0.79035 9.89976 0.79389 9.90168 0.79741 9.90358 O.S0091 60 '2 .89589 .78685 .89785 .79041 .89979 .79395 .90171 .79747 .90361 .80097 58 4+ 1 .89592 .78691 .89789 .79047 .89983 .79401 .90175 .79753 .90365 .80103 56 6 .89596 .78697 .89792 .79053 .89986 .79407 .90178 .79759 .90368 .80108 54 52 8+ 2 9.89599 0.78703 9.89795 0.79059 9.89989 0.79413 9.90181 0.79765 9.90371 0.80114 10 .89602 .78709 .89798 .79065 .89992 .79419 .90184 .79770 .90374 .80120 50 12+ 3 .89606 .78715 .89802 .79071 .89995 .79425 .90187 .79776 .90377 .80126 48 U .89609 .78721 .89805 .79077 .89999 .79430 .90191 .79783 .90380 .80131 46 16-\- i 9.89612 1 0.78726 9.89808 0.79082 9.90002 0.79436 9.90194 0.79788 9.90383 0.80137 44 18 .89615 .78732 .89811 .79088 .90005 .79442 .90197 .79794 .90387 .80143 42 20-{- 5 .89619 .78738 .89815 .79094 .90008 .79448 .90200 .78800 .90390 .80149 40 22 .89622 .78744 .89818 .79100 .90012 .79454 .90203 .79805 .90393 .80155 38 24+ 6 9.89625 0.78750 9.89821 0.79106 9.90015 0.79460 9.90206 0.79811 9.90396 0.80160 36 26 .89628 .78756 .89824 .79112 .90018 .79466 .90210 .79817 .90399 .80166 34 28+ 7 .89632 .78762 .89828 .79118 .90021 .79471 .90213 .79833 .90402 .80172 32 SO .89635 .78768 .89831 .79124 .90024 .79477 .90216 .79839 .90405 .80178 SO 32+ 8 9.89638 0.78774 9.89834 0.79130 9.90028 0.79483 9.90219 0.79835 9.90409 0.80184 28 34 .89642 .78780 .89837 .79136 .90031 .79489 .90222 .79840 .90412 .80189 26 36+ 9 .89645 .78786 .89840 .79143 .90034 .79495 .90225 .70846 .90415 .80195 24 38 .89648 .78792 .89844 .79148 .90037 .79501 .90229 .79853 .90418 .80201 22 40+10 9.89651 0.78798 9.89847 0.79153 9.90040 0.79507 9.90232 0.79858 9.90421 0.80307 20 42 .89655 .78804 .89850 .79159 .90044 .79513 .90235 .79864 .90425 .80313 18 44+11 .89658 .78810 .89853 .79165 .90047 .79519 .90238 .79870 .90428 .80318 16 46 .89661 .78816 .89857 .79171 .90050 .79524 .90241 .79875 .90431 .80334 14 48+lZ 9.89665 0.78822 9.89860 0.79177 9.90053 0.79530 9.90244 0.79881 9.90434 0.80330 12 50 .89668 .78828 .89863 .79183 .90056 .79536 .90248 .79887 .90437 .80336 10 52+li .89671 .78834 .89866 .79189 .90060 .79542 .90251 .79899 .90440 .80343 8 54 .89674 .78839 .89870 .79195 .90063 .79548 .90254 .79893 .90443 .80347 6 56+11 9.89678 0.78845 9.89873 0.79201 9.90066 0.79554 9.90257 0.79905 9.90446 0.80353 4 58 9.89681 0.78851 9.89876 0.79207 9.90069 0.79560 9.90260 0.79910 .9.90449 0.80359 2 15h 39m [ 15Ji37m j l5h 35^ 15h SSm 15h Sim 8^' 0+15 8h 21m 125° 0^ gn 23m 125° 30' 5ft 25^ 126° 0' 8h 27m 126° 3r 8h 29m 137° 0' s 60 9.89684 0.78857 9.89879 0.79212 .9.90072 0.79565 9.90264 0.79916 9.90452 0.80^5 2 .89687 .78863 .89883 .79218 .90076 .79571 .90267 .79922 .90456 .80270 58 •4+16 .89691 .78869 .89886 .79224 .90079 .79577 .90270 .79928 .90459 .80376 56 6 .89694 .78875 .89889 .79230 .90082 .79583 .90273 .79934 .90462 .80282 54 8+1-1 9.89697 0.78881 9.89892 0.79236 9.90085 0.79589 9.90276 0.79940 9.90465 0.80288 52 10 .89701 .78887 .89896 .79243 .90088 .79595 .90279 .79945 .90468 .80294 50 12+1% .89704 .78893 .89899 .79348 .90092 .79601 .90282 .79951 .90471 .80299 48 14 .89707 .78899 .89902 .79354 .90095 .79607 .90286 .79957 .90475 .80305 46 16+19 9.89710 0.78905 9.89905 0.79260 9.90098 0.79612 9.902S9 0.79963 9.90478 0.80311 44 18 .89714 .78911 .89908 .79266 .90101 .79618 .90292 .79969 .90481 .80317 42 20+30 .89717 .78917 .89912 .79271 .90104 .79624 .90295 .79974 .90484 .80323 40 22 .89720 .78923 .89915 .79277 .90108 .79630 .90298 .79980 .90487 .80328 38 24+21 9.89723 0.78928 9.89918 0.79383 9.90111 0.79636 9.90301 0.79986 9.90490 0.80334 36 26 .89727 .78934 .89921 .79289 .90114 .79642 .90305 .79992 .90493 .80340 34 28+22 .89730 .78940 .89925 .79295 .90117 .79648 .90308 .79998 .90496 .80346 32 SO .89733 .78946 .89928 .79301 .90120 .79653 .90311 .80004 .90499 .80351 30 32+23 9.89736 0.78952 9.89931 0.79307 9.90124 0.79659 9.90314 0.80009 9.90503 0.80357 28 34 .89740 .78958 .89934 .79313 .90127 .79665 .90317 .80015 .90506 .80363 26 36+21 .89743 .78964 .89938 .79319 .90130 .79671 .90320 .80021 .90509 .80369 24 38 .89746 .78970 .89941 .79325 .90133 .79677 .90324 .80027 .90512 .80375 22 40+15 9.89749 0.78976 9.89944 0.79330 9.90136 0.79683 9.90327 0.80033 9.90515 0.80380 20 42 .89753 .78982 .89947 .79336 .90140 .79688 .90330 .80038 .90518 .80386 18 U+2^ .89756 .78988 .89950 .79342 .90143 .79694 .90333 .80044 .90521 .80392 16 46 .89759 .78994 .89954 .79348 .90146 .79700 .90336 .80050 .90524 .80398 14 48+21 9.89763 0.79000 .9.89957 0.79354 9.90149 0.79706 9.90339 0.80056 9.90527 0.80403 12 50 .89766 .79006 .89960 .79360 .90152 .79712 .90342 .80062 .90531 .80409 10 52+2S .89769 .79011 .89963 .79366 .90356 .79718 .90346 .80068 .90534 .80415 8 54 .89772 .79017 .89966 .79372 .90159 .79724 .90349 .80073 .90537 .80421 6 56+39 9.89776 0.79023 9.89970 0.79377 9.90162 0.79729 9.90352 0.80079 9.90540 0.80427 4 55 .89779 .79029 .89973 .79383 .90165 .79735 .90355 .80085 .90543 .80433 2 60+30 9.89782 0.79035 9.89976 0.79389 9.90168 0.79741 9.90358 0.80091 9.90546 0.80438 i5A 38m 1 15^ 36m 1 15^ 34m 1 15f^ S2m 1 ISf^SOm TABLE IV. [Page 143 Haversinea. s ; 8h SOm 127° 30' Sh 32m 128° 0' 8h 34m 128° 30' 8h 36m 129° 0' 8h 38m 129° W a Log. Hav. Nat. Hav. Log. Ilav. Nat. Hav. Log. Ilav. Nat. nav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. 2 4+1 6 9.90546 .90549 .90552 .90556 0.80438 .80444 .80450 .80455 9.90732 .90735 .90738 .90741 0.80783 .80789 .80795 .80800 9.90916 .90919 .90922 .90925 0.81126 .81131 .81137 .81143 9.91098 .91101 .91104 .91107 0.81466 .81472 .81477 .81483 9.91277 .91280 .91283 .91286 0.81804 .81810 .81815 .81821 60 58 56 54 S+ 2 10 12+ 3 14 16+ 4 18 20+ 6 22 9.90559 .90562 .90565 .90568 9.90571 .90574 .90577 .90580 0.80461 .80467 .80473 .80478 0.80484 .80490 .80496 .80503 9.90744 .90747 .90751 .90754 9.90757 .90760 .90763 .90766 0.80806 .80812 .80817 .80823 0.80829 .80835 .80840 .80846 9.90928 .90931 .90934 .90937 9.90940 .90943 .90946 .90949 0.81148 .81154 .81160 .81165 0.81171 .81177 .81183 .81188 9.91110 .91113 .91110 .91119 9.91122 .91125 .91128 ■ .91131 0.81489 .81494 .81500 .81506 0.81511 .81517 .81523 .81528 9.91289 .91292 .91295 .91298 9.91301 .91304 .91307 .91310 0.81826 .81832 .81838 .81843 0.81849 .81854 .81860 .81866 52 50 48 46 44 42 40 38 24+ 6 26 28+ 7 SO 32+ 8 34 36+ 9 38 9.90584 .90587 .90590 .90593 9.90596 .90599 .90602 .90605 0.80507 .80513 .80519 .80525 0.80530 .80536 .80542 .89548 9.90769 .90772 .90775 .90778 9.90781 .90784 .90787 .90790 0.80852 .80858 .80863 .80869 0.80875 .80880 .80886 .80892 9.90952 .90955 .90958 .90962 9.90965 .90968 .90971 .90974 0.81194 .81200 .81205 .81211 0.81217 .81222 .81228 .81234 9.91134 .91137 .91140 .91143 9.91146 .91149 .91152 .91155 0.81534 .81539 .81545 .81551 0.81556 .81562 .81568 .81573 9.91313 .91316 .91319 .91322 9.91325 .91328 .91331 .91334 0.81871 .81877 .81882 .81888 0.81894 .81899 .81905 .81910 36 34 32 30 28 26 24 22 40+U 42 44+11 46 48+12 50 5f+13 54 9.90608 .90611 .90615 .90618 9.90621 .90624 .90627 .90630 0.80553 .80559 .80565 .80571 0.80576 .80582 .80588 .80594 9.90794 .90797 .90800 .90803 9.90806 .90809 .90812 .90815 0.80898 .80903 .80909 .80915 0.80920 .80926 .80932 .80938 9.90977 .90980 .90983 .90986 9.90989 .90992 .90995 .90998 0.81239 .81245 .81251 .81256 0.81262 .81268 .81273 .81279 9.91158 .91161 .91164 .91167 9.91170 .91173 .91176 .91179 0.81579 .81585 .81590 .81596 0.81601 .81607 .81613 .81618 9.91337 .91340 .91343 .91346 9.91349 .91352 .91355 .91358 0.81916 .81922 .81927 .81933 0.81938 .81944 .81950 .81955 20 18 16 14 12 10 8 6 56+U 58 9.90633 9.90636 0.80599 0.80605 9.90818 9.90821 0.80943 0.80949 9.91001 9.91004 0.81285 0.81291 9.91182 9.91185 0.81624 0.81630 9.91361 9.91364 0.81961 0.81966 4 2 15^ 29m 15h 27m 15h 25m 15h 23m 15h 21m s ' 0+15 2 4+1% 6 8h Sim 127° 3(K Sh 33m 128° r 8h 35m 128° 30^ Sh 37m 129° 0' 8h 39m 139° scK s 60 58 56 54 9.90639 .90642 .90646 .90646 0.80611 .80617 .80622 .80628 9.90824 .90827 .90830 .90833 0.80955 .80960 .80966 .80972 9.91007 .91010 .91013 .91016 0.81296 .81302 .81308 .81313 9.91188 .91191 .91194 .91197 0.81635 .81641 .81647 .81652 9.91367 .91369 .91372 .91375 0.81972 .81978 .81983 .81989 8+n 10 12+18 14 16+19 18 20+20 22 9.90652 .90655 .90658 .90661 9.90664 .90667 .90670 .90673 0.80634 .80640 .80645 .80651 0.80657 .80663 .80668 .80674 9.90836 .90840 .90843 .90846 9.90849 .90852 .90855 .90858 0.80978 .80983 .80989 .80995 0.81000 .81006 .81012 .81017 9.91019 .91022 .91025 .91028 9.91031 .91034 .91037 .91040 0.81319 .81325 .81330 .81336 0.81342 .81347 .81353 .81359 9.91200 .91203 .91206 .91209 9.91212 .91215 .91218 .91221 0.81658 .81663 .81669 .81675 0.81680 .81686 .81692 .81697 9.91378 .91381 .91384 .91387 9.91390 .91393 .91396 .91399 0.81994 .82000 .82005 .82011 0.82017 .82022 .82028 .82033 52 50 48 46 U 42 40 38 24+21 26 28+22 SO 32+2Z 34 36+24: 38 9.90676 .90680 .90683 .90686 9.90689 .90692 .90695 .90698 0.80680 .80686 .80691 .80697 0.80703 .80709 .80714 .80720 9.90861 .90864 .90867 .90870 9.90873 .90876 .90879 .90882 0.81023 .81029 .81035 .81040 0.81046 .81052 .81057 .81063 9.91043 .91046 .91049 .91052 9.91055 .91058 .91061 .91064 0.81364 .81370 .81376 .81381 0.81387 .81392 .81398 .81404 9.91224 .91227 .91230 .91233 9.91236 .91239 .91242 .91245 0.81703 .81708 .81714 .81720 0.81725 .81731 .81737 .81742 9.91402 .91405 .91408 .91411 9.91414 .91417 .91420 .91423 0.82039 .82045 .82050 .82056 0.82061 .82067 .82072 .82078 36 34 32 30 28 26 24 22 40+25 42 U+2Q 46 48+27 50 52+2S 54 9.90701 .90704 .90707 .90710 9.90714 .90717 .90720 .90723 0.80726 .80731 .80737 .80743 0.80749 .80754 .80760 .80766 9.90885 .90888 .90892 .90895 9.90898 .90901 .90904 .90907 0.81068 .81074 .81080 .81086 0.81092 .81097 .81103 .81109 9.91067 .91071 .91074 .91077 9.91080 .91083 .91086 .91089 0.81409 .81415 .81421 .81426 0.81432 .81438 .81443 .81449 9.91248 .91251 .91254 .91257 9.91260 .91263 .91265 .91268 0.81748 .81753 .81759 .81765 0.81770 .81776 .81781 .81787 9.91426 .91429 .91432 .91435 9.91437 .91440 .91443 .91446 0.82084 .82089 .82095 .82100 0.82106 .82112 .82U7 .82123 20 18 16 14 12 10 8 6 56+29 58 60+30 9.90726 .90729 9.90732 0.80772 .80777 0.80783 9.90910 .90913 9.90916 0.81114 .81120 0.81126 9.91092 .91095 9.91098 0.81455 .81460 0.81466 9.91271 .91274 9.91277 0.81793 .81798 0.81804 9.91449 .91452 9.91455 0.82128 .82134 0.82139 4 2 15h 28m 15h 26m 15h 24m 15h 22m 15h20m Page 144] TABLE IV. | Haversines. 1 s ' 5^40^ 130° 0^ 8fi 42^ 130° 3r 5ft U^ 131° O' 8h 46m 131° 3(K 5ft45'nl32°r 1 s Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. 9.91455 0.83139 9.91631 0.82472 9.91805 0.83803 9.91976 0.83131 9.92146 0.83457 60 .91458 .83145 .91634 .83478 .91807' .83808 .91979 .83136 .92149 .83462 58 4+ 1 .91461 .82151 .91637 .83483 .91810 .83814 .91982 .83142 .92152 .83467 56 6 .91464 .83156 .91640 .83489 .91813 .83819 .91985 .83147 .92154 .83473 54 8+ 2 9.91467 0.82163 9.91643 0.83495 9.91816 0.83835 9.91988 0.83153 9.92157 0.83478 52 10 .91470 .83167 .91645 .83500 .91819 .83830 .91991 .83158 .92160 .83484 50 12+ 4 .91473 .83173 .91648 .83506 .91822 .83836 .91993 .83164 .92163 .83489 48 14 .91476 .83178 .91651 .83511 .91825 .83841 .91996 .83169 .92166 .83494 46 16+ 4 9.91479 0.83184 9.91654 0.83517 9.91828 0.83847 9.91999 0.83175 9.92169 0.83500 44 18 .91482 .83189 .91657 .83533 .91830 .83853 .92002 .83180 .92171 .83505 42 20+ 5 .91485 .83195 .91660 .83538 .91833 .83858 .92005 .83185 .92174 .83511 40 22 .91488 .83300 .91663 .83533 .91836 .83863 .92008 .83191 .92177 .83516 38 24+ 6 9.91490 0.83306 9.91666 0.83539 9.91839 0.83869 9.92010 0.83196 9.92180 0.83521 36 26 .91493 .83313 .91669 .83544 .91842 .83874 .92013 .83303 .92183 .83527 34 28+ 7 .91496 .83317 .91672 .83550 .91845 .83880 .92016 .83307 .92185 .83533 32 SO .91499 .83233 .91674 .83555 .91848 .83885 .92019 .83313 .92188 .83538 30 S2+ 8 9.91502 0.83338 9.91677 0.83561 9.91851 0.83891 9.92022 0.83318 9.92191 0.83543 28 34 .91505 .83334 .91680 .82566 .91853 .83896 .92025 .83334 .92194 .83548 26 36+ 9 .91508 .83340 .91683 .82572 .91856 .82902 .92027 .83339 .92197 .83554 24 38 .91511 .83345 .91686 .83577 .91859 .82907 .92030 .83334 .92199 .83559 22 4^+10 9.91514 0.82251 9.91689 0.83583 9.91862 0.82913 9.92033 0.83340 9.92202 0.83564 20 4^ .91517 .83356 .91692 .83588 .91865 .83918 .92036 .83345 .92205 .83570 18 ■^+11 .91520 .83363 .91695 .83594 .91868 .83934 .92039 .83351 .92208 .83575 16 46 .91523 .83367 .91698 .83599 .91871 .83939 .92042 .83356 .92211 .83581 14 48+n 9.91526 0.83373 9.91701 0.83605 9.91874 0.83934 9.92044 0.83363 9.92213 0.83586 12 50 .91529 .83378 .91703 .82610 .91876 .83940 .92047 .83367 .92216 .83591 10 5^+13 .91532 .83384 .91706 .83616 .91879 .83945 .92050 .83373 .92219 .83597 8 54 .91534 .83390 .91709 .83631 .91882 .83951 .92053 .83278 .92222 .83602 6 56+14 9.91537 0.83395 9.91712 0.83637 9.91885 0.83956 9.92056 0.83383 9.92225 0.83608 4 58 9.91540 0.83301 9.91715 0.83632 9.91888 0.83963 9.92059 0.83389 9.92227 0.83613 2 15h 19m 15h 17m 15^ 15m 15Ji 13m 15h 11m s ' 0+15 8h 41m 130° 0^ Sh 43m 130° 30^ 8h 45m 131° 0' 8h 47m 131° 30: 8h 49m 132° r s 60 9.91543 0.83306 9.91718 0.83638 9.91891 0.83967 9.92061 0.83394 9.92230 0.83618 2 .91546 .83313 .91721 .83644 .91894 .83973 .92064 .83300 .92233 .83634 58 4+16 .91549 .83317 .91724 .83649 .91896 .83978 .92067 .83305 .92236 .83639 56 6 .91552 .83333 .91727 .83655 .91899 .83984 .92070 .83310 .92239 .83635 54 5+17 9.91555 0.83338 9.91730 0.83860 9.91902 0.83989 9.92073 0.83316 9.92241 0.83640 52 iO .91558 .83334 .91732 .83666 .91905 .83995 .92076 .83331 .92244 .83645 50 J^+18 .91561 .83339 .91735 .83671 .91908 .83000 .92078 .83327 .92247 .83651 48 14 .91564 .83345 .91738 .83677 .91911 .83006 .92081 .83332 .92250 .83656 46 16+19 9.91567 0.83351 9.91741 0.83683 9.91914 0.83011 9.92084 0.83337 9.92253 0.83661 U 18 .91570 .83356 .91744 .83688 .91916 .83016 .92087 .83343 .92255 .83667 42 fO+20 .91573 .83363 .91747 .83693 .91919 .83033 .92090 .83348 .92258 .83673 40 22 .91575 .83367 .91750 .83699 .91922 .83037 0.83033 .92093 .83354 .92261 .83678 38 24+91 9.91578 0.83373 9.91753 0.83704 9.91925 9.92095 0.83359 9.92264 0.83683 36 26 .91581 .83378 .91756 .83710 .91928 .83038 .92098 .83365 .92266 .83688 34 28+2^ .91584 .83384 .91758 .83715 .91931 .83044 .92101 .83370 .92269 .83694 32 SO .91587 .83389 .91761 .83731 .91934 .83049 .92104 .83375 .92272 .83699 SO 32+2S 9.91590 0.83395 9.91764 0.83736 9.91936 0.83055 9.92107 0.83381 9.92275 0.83704 28 34 .91593 .83400 .91767 .83733 .91939 .83060 .92109 .83386 .92278 .83710 26 56+24 .91596 .83406 .91770 .83737 .91942 .83066 .92112 .83392 .§2280 .83715 24 38 .91599 .83413 .91773 .83743 .91945 .83071 .92115 .83397 .92283 .83730 22 20 40+25 9.91602 0.83417 9.91776 0.83748 9.91948 0.83077 9.92118 0.83402 9.92286 0.83736 42 .91605 .83433 .91779 .83754 .91951 .83083 .92121 .83408 .92289 .83731 18 44+26 .91608 .83438 .91782 .83759 .91954 .83087 .92124 .83413 .92292 .83737 16 46 .91610 .83434 .91784 .83765 .91956 .83093 .92126 .83419 .92294 .83743 14 4^+27 9.91613 0.83439 9.91787 0.83770 9.91959 0.83098 9.92129 0.83424 9.92297 0.83747 12 50 .91616 .83445 .91790 .83776 .91962 .83104 .92132 .83430 .92300 .83753 10 5^+28 .91619 .83450 .91793 .83781 .91965 .83109 .92135 .83435 .92303 .83758 8 54 .91622 .83456 .91796 .83786 0.83793 .91968 .83115 .92138 .83440 .92305 .83763 6 56+29 9.91625 0.83461 9.91799 9.91971 0.83130 9.92140 0.83446 9.92308 0.83769 4 55 .91628 .82467 .91802 .83797 .91973 .83126 .92143 .83451 .92311 .83774 2 60+30 9.91631 0.82473 9.91805 0.83803 9.91976 0.83131 9.92146 0.83457 9.92314 0.83780 15hl8m 15h 16m 15h 14m 15^ 12m 15h lom TABLE IV. [Page 145 Havereines. s ' 8h 50m 133° 30' | Sh 52"* 133° 0' Sfi 54^ 133° 30' 1 5ft56"H34°0' 1 8h 58m 134° 30^ s 60 58 56 54 Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. 2 4+1 6 9.92314 .92317 .92319 .92322 0.83780 .83785 .83790 .83796 9.92480 .92482 .92485 .92488 0.84100 .84105 .84111 .84116 9.92643 .92646 .92649 .92652 0.84418 .84433 .84438 .84434 9.92805 .92808 .92811 .92813 0.84733 .84738 .84743 .84749 9.92965 .92968 .92970 .92973 0.85045 .85051 .85056 .85061 8+ 2 10 12+ 3 14 16+ 4 18 20+ 5 22 9.92325 .92328 .92330 .92333 9.92336 .92339 .92342 .92344 0.83801 .83806 .83813 .83817 0.83833 .83838 .83833 .83838 9.92491 .92493 .92496 .92499 9.92502 .92504 .92507 .92510 0.84131 .84137 .84133 .84137 0.84143 .84148 .84153 .84158 9.92654 .92657 .92660 .92662 9 92665 .92668 .92670 .92673 0.84439 .84444 .84449 .84455 0.84460 .84465 .84470 .84476 9.92816 .92819 .92821 .92824 9.92827 .92829 .92832 .92835 0.84754 .84759 .84764 .84770 0.84775 .84780 .84785 .84790 9.92975 .92978 .92981 .92984 9.92986 .92989 .92992 .92994 0.85066 .85071 .85077 .85083 0.85087 .85093 .85097 .85103 52 50 48 46 U 42 40 38 36 34 32 30 28 26 24 22 24+ 6 26 28+ 7 30 32+ 8 34 36+ 9 38 9.92347 .92350 .92353 .92355 9.92358 .92361 .92364 .92366 0.83844 .83849 .83855 .83860 0.83865 .83871 .83876 .83881 9.92512 .92515 .92518 .92521 9.92523 .92526 .92529 .92532 0.84164 .84169 .84174 .84180 0.84185 .84190 .84196 .84301 9.92676 .92679 .92681 .92684 9.92687 .92689 .92692 .92695 0.84481 .84486 .84493 .84497 0.84503 .84507 .84513 .84518 9.92837 .92840 .92843 .92845 9.92848 .92851 .92853 .92856 0.84796 .84801 .84806 .84811 0.84817 .84833 .84837 .84833 9.92997 .93001 .93002 .93005 9.93007 .93010 .93013 .93015 0.85108 .85113 .85118 .85133 0.85138 .85134 .85139 .85144 40+10 42 44+n 46 48+12 50 52+lZ 54 9.92369 .92372 .92375 .92378 9.92380 .92383 .92386 .92389 0.83887 .83893 .83897 .83903 0.83908 .83913 .83919 .83934 9.92534 .92537 .92540 .92543 9.92545 .92548 .92551 .92554 0.84306 .84311 .84317 .84333 0.84337 .84333 .84338 .84343 9.92698 .92700 .92703 .92706 9.92708 .92711 .92714 .92716 0.84533 .84538 .84534 .84539 0.84544 .84549 .84555 .84560 9.92859 .92861 .92864 .92867 9.92869 .92872 .92875 .92877 0.84837 .84843 .84848 .84853 0.84858 .84863 .84869 .84874 9.93018 .93021 .93023 .93026 9.93029 .93031 .93034 .93036 0.85149 .85154 .85159 .85165 0.85170 .85175 .85180 .85185 20 18 16 14 12 10 8 6 56+14 58 9.92391 9.92394 0.83939 0.83935 9.92556 9.92559 0.84349 0.84354 9.92719 9.92722 0.84565 0.84570 9.92880 9.92883 0.84879 0.84884 9.93039 9.93042 0.85190 0.85196 4 2 IShgm IShTm 15h 5m 15^ 3™- Uhim B ' 8h 5im 132° 30'' 8h 53m 133° O' 8h 55m 133° 30^ 8h 57m 134° r 8h 59m 134° 30' B 0+15 2 4+ie 6 9.92397 .92400 .92402 .92405 0.83940 .83945 .83951 .83956 9.92562 .92564 .92567 .92570 0.84359 .84364 .84370 .84375 9.92725 .92727 .92730 .92733 0.84576 .84581 .84586 .84591 9.92885 .92888 .92891 .92893 0.84890 .84895 .84900 .84905 9.93044 .93047 .93050 .93052 0.85301 .85306 .85311 .85316 60 58 56 54 52 50 48 46 44 42 40 38 36 34 32 SO 28 26 24 22 8+n 10 12+lS 14 16+19 18 20+m 22 9.92408 .92411 .92413 .92416 9.92419 .92422 .92425 .92427 0.83961 .83967 .83973 .83977 0.83983 .83988 .83993 .83999 9.92573 .92575 .92578 .92581 9.92584 .92586 .92589 .92592 0.84380 .84386 .84391 .84396 0.84303 .84307 .84313 .84317 9.92735 .92738 .92741 .92743 9.92746 .92749 .92751 .92754 0.84597 .84603 .84607 .84612 0.84618 .84633 .84638 .84633 9.92896 .92899 .92901 .92904 9.92907 .92909 .92912 .92915 0.84910 .84916 .84931 .84936 0.84931 .84936 .84943 .84947 9.93055 .93057 .93060 .93063 9.93065 .93068 .93071 .93073 0.85331 .85337 .85333 .85337 0.85343 .85347 .85353 .85358 0.85363 .85368 .85373 .85378 0.85283 .85388 .85394 .85399 24+21 26 28+22 30 32+2Z 34 ' 56+34 38 9.92430 .92433 .92436 .92438 9.92441 .92444 .92447 .92449 0.84004 .84009 .84015 .84030 0.84035 .84031 .84036 .84041 9.92594 .92597 .92600 .92603 9.92605 .92608 .92611 .92613 0.84333 .84338 .84333 .84339 0.84344 .84349 .84354 .84360 9.92757 .92760 .92762 .92765 9.92768 .92770 .92773 .92776 0.84639 .84644 .84619 .84654 0.84660 .84665 .84670 .84675 9.92917 .92920 .92923 .92925 9.92928 .92931 .92933 .92936 0.84963 .84957 .84963 .84968 0.84973 .84978 .84983 .84988 9.93076 .93079 .93081 .93084 9.93086 .93089 .93092 .93094 40+25 42 U+26 46 48+2:7 50 52+2S 54 9.92452 .92455 .92458 .92460 9.92463 .92466 .92469 .92471 0.84047 .84053 .84057 .84063 0.84068 .84073 .84079 .84084 9.92616 .92619 .92622 .92624 9.92627 .92630 .92633 .92635 9.92638 .92641 9.92643 0.84365 .84370 .84376 .84381 0.84386 .84391 .84397 .84403 9.92778 .92781 .92784 .92786 9.92789 .92792 .92794 .92797 0.84681 .84686 .84691 .84696 0.84703 .84707 .84713 .84717 9.92939 .92941 .92944 .92947 9.92949 .92952 .92955 .92957 0.84994 .84999 .85004 .85009 0.85014 .85030 .85035 .85030 9.93097 .93100 .93102 .93105 9.93107 .93110 .93113 .93115 0.85304 .85309 .85314 .85319 0.85334 .85330 .85335 .85340 0.85345 .85350 0.85355 20 18 16 14 12 10 8 6 4 2 56+29 58 60+30 9.92474 .92477 9.92480 0.84089 .84095 0.84100 0.84407 .84413 0.84418 9.92800 .92802 9.92805 0.84733 .84738 0.84733 9.92960 .92962 9.92965 0.85035 .85040 0.85045 9.93118 .93120 9.93123 15Ti'8m 15hem 15^ 4m I5h2m . 15^ Om 55901°— 18- -10 Page 146] TABLE IV. Haversines. s ' 9A 0^ 135° 5ft 4'" 136° 9A 8m 137° 9h 12m 138° Shiem 139° 1 Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. s 9.93123 0.85355 9.93433 0.85967 9.93736 0.86568 9.94030 0.87157 9.94318 0.87735 60 4 1 .93128 .85366 .93438 .85977 .93741 .86578 .94035 .87167 .94322 .87745 56 8 H .93134 .85376 .93443 .85987 .93746 .86588 .94040 .87177 .94327 .87755 62 12 3 .93139 .85386 .93448 .85997 .93751 .86597 .94045 .87186 .94332 .87764 48 16 4 9.93144 0.85396 9.93454 0.86007 9.93755 0.86607 9.94050 0.87196 9.94336 0.87774 U 20 5 .93149 .85407 .93459 .86017 .93760 .86617 .94055 .87206 .94341 .87783 40 U 6 .93154 .85417 .93464 .86028 .93765 .86627 .94059 .87216 .94346 .87793 36 28 7 .93160 .85427 .93469 .86038 .93770 .86637 .94064 .87225 .94351 .87802 32 S2 8 9.93165 0.85438 9.93474 0.86048 9.93775 0.86647 9.94069 0.87235 9.94355 0.87812 28 36 9 .93170 .85448 .93479 .86058 .93780 .86657 .94074 .87245 .94360 .87821 24 40 10 .93175 .85458 .93484 .86068 .93785 .86667 .94079 .87254 .94365 .87831 20 44 11 .93181 .85468 .93489 .86078 .93790 .86677 .94084 .87264 .94369 .87840 16 4S 13 9.93186 0.85479 9.93494 0.86088 9.93795 0.86686 9.94088 0.87274 9.94374 0.87850 12 55 13 .93191 .85489 .93499 .86098 .93800 .86696 .94093 .87283 .94379 .87859 8 56 U 9.93196 0.85499 9.93504 0.86108 9.93805 0.86706 9.94098 0.87293 9.94383 0.87869 4 14h 59m 14h 55m 14k Sim 14h 47m 14h 43m s ' gh im 135° ghsm 136° gh gm 137° gh ism 138° gh 17m 139° s 15 9.93201 0.85509 9.93509 0.86118 9.93810 0.86716 9.94103 0.87303 9.94388 0.87878 60 4 16 .93207 .85520 .93515 .86128 .93815 .86726 .94108 .87313 .94393 .87888 66 5 17 .93212 .85530 .93520 .86138 .93820 .86736 .94112 .87322 .94398 .87897 52 12 18 .93217 .85540 .93525 .86148 .93825 .86746 .94117 .87332 .94402 .87907 48 16 19 9.93222 0.85550 9.93530 0.86158 9.93830 0.86756 9.94122 0.87342 9.94407 0.87916 44 ;?0 20 .93227 .85560 .93535 .86168 .93835 .86765 .94127 .87351 .94412 .87926 40 24 n .93232 .85571 .93540 .86178 .93840 .86775 .94132 .87361 .94416 .87935 36 28 22 .93238 .85581 .93545 .86189 .93845 .86785 .94137 .87371 .94421 .87945 32 32 23 9.93243 0.85591 9.93550 0.86199 9.93849 0.86795 9.94141 0.87380 9.94426 0.87954 28 56 24 .93248 .85601 .93555 .86209 .93854 .86805 .94146 .87390 .94430 .87964 24 40 25 .93253 .85612 .93560 .86219 .93859 .86815 .94151 .87400 .94435 .87973 20 44 26 .93258 .85622 .93565 .86229 .93864 .86825 .94156 .87409 .94440 .87983 16 45 27 9.93264 0.85632 9.93570 0.86239 9.93869 0.86834 9.94161 0.87419 9.94444 0.87992 12 62 28 .93269 .85642 .93575 .86249 .93874 .86844 .94165 .87428 .94449 .88001 8 56 29 9.93274 0.85652 9.93580 0.86259 9.93879 0.86854 9.94170 0.87438 9.94454 0.88011 4 14h 58m 14h 54m 14h 5om 14h 46m 14h 40m s ' 9k pn 135° 9h6m 136° gh 10m 137° 9h 14m 138° gh 18m 139° s 30 9.93279 0.85663 9.93585 0.86269 9.93884 0.86864 9.94175 0.87448 9.94458 0.88020 60 4 31 .93284 .85673 .93590 .86279 .93889 .86874 .94180 .87457 .94463 .88030 56 5 32 .93289 .85683 .93595 .86289 .93894 .86884 .94184 .87467 .94468 .88039 52 12 33 .93295 .85693 .93600 .86299 .93899 .86893 .94189 .87477 .94472 .88049 48 i6 34 9.93300 0.85703 9.93605 0.86309 9.93904 0.86903 9.94194 0.87486 9.94477 0.88058 44 20 35 .93305 .85713 .93611 .86319 .93908 .86913 .94199 .87496 .94482 .88068 40 f4 36 .93310 .85724 .93616 .86329 .93913 .86923 .94204 .87505 .94486 .88077 36 28 37 .93315 .85734 .93621 .86339 .93918 .86933 .94208 .87515 .94491 .88086 32 55 38 9.93320 0.85744 9.93626 0.86349 9.93923 0.86942 9.94213 0.87525 9.94496 0.8S996 28 56 39 .93326 .85754 .93631 .86359 .93928 .86952 .94218 .87534 .94500 .88105 24 40 40 .93331 .85764 .93636 .86369 .93933 .86962 .94223 .87544 .94505 .88115 20 44 41 .93336 .85774 .93641 .86379 .93938 .86972 .94227 .87554 .94509 .88124 16 48 42 9.93341 0.85785 9.93646 0.86389 9.93943 0.86982 9.94232 0.87563 9.94514 0.88133 12 55 43 .93346 .85795 .93651 .86399 .93948 .86991 .94237 .87573 .94519 .88143 8 56 44 9.93351 0.85805 9.93656 0.86409 9.93952 0.87001 9.94242 0.87582 9.94523 0.88152 4 14>i 57m 14h 53m 14^ 49m ^ 14h45m 14h 41m 1 s ' 9h 3m 135° 9h im 136° gh 11m 137° 9^ 15m 138° gkigm 139° | s 45 9.93356 0.85815 9.93661 0.86419 9.93957 0.87011 9.94246 0.87592 9.94528 0.88162 60 4 46 .93362 .85825 .93666 .86429 .93962 .87021 .94251 .87602 .94533 .88171 56 5 47 .93367 .85835 .93671 .86438 .93967 .87030 .94256 .87611 .94537 .88180 52 15 48 .93372 .85846 .93676 .86448 .93972 .87040 .94261 .87621 .94542 .88190 48 16 49 9.93377 0.85856 9.93681 0.86458 9.93977 0.87050 9.942G5 0.87630 9.94546 0.88199 U 50 50 .93382 .85866 .93686 .86468 .93982 .87060 .94270 .87640 .94551 .88309 40 54 51 .93387 .85876 .93691 .86478 .93987 .87070 .94275 .87649 .94556 .88218 36 55 53 .93392 .85886 .93696 .86488 .93991 .87079 .94280 .87659 .94560 .88227 32 55 53 9.93397 0.85896 9.93701 0.86498 9.93996 0.87089 9.94284 0.87669 9.94565 0.88237 28 36 54 .93403 .85906 .93706 .86508. .94001 .87099 .94289 .87678 .94570 .88246 24 40 65 .93408 .85916 .93711 .86518 .94006 .87109 .94294 .87688 .94574 .88255 20 U 56 .93413 .85926 .93716 .86528 .94011 .87118 .94299 .87697 .94579 .88265 16 45 57 9.93418 0.85937 9.93721 0.86538 9.94016 0.87128 9.94303 0.87707 9.94583 0.88274 12 55 58 .93423 .85947 .93726 .86548 .94021 .87138 .^4308 .87716 .94588 .88284 8 66 59 .93428 .85957 .93731 .86558 .94026 .87148 .94313 .87726 .94593 .88293 4 60 60 9.93433 0.85967 9.93736 0.86568 9.94030 0.87157 9.94318 0.87735 9.94597 0.88302 14h 56m 1411 52m 1 14^ 48m Uh 44m 1 14h 40m 1 TABLE IV. [Page 147 Havereines. s ' 9h 20!m 140° 9A 24^ 141° gh 28m 142° gh S2m 143° gh S6m 144° s 60 Log. Hav Nat. Hav Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Ilav. Log. Hav. Nat. Hav. 9.94597 0.88302 9.94869 0.88857 9.95134 0.89401 9.95391 0.89932 9.95641 0.90451 4 1 .94602 .88312 .94874 .88866 .95138 .89409 .95396 .89941 .95645 .90459 56 8 2 .94606 .88321 .94878 .88876 .95143 .89418 .95400 .89949 .95649 .90468 52 12 3 .94611 .88330 .94883 .88885 .95147 .89427 .95404 .89958 .95654 .90476 48 16 4 9.94616 0.88340 9.94887 0.88894 9.95151 0.89436 9.95408 0.89967 9.95658 0.90485 44 20 5 .94620 .88349 .94892 .88903 .95156 .89445 .95412 .89976 .95662 .90494 40 24 6 .94625 .88358 .94896 .88912 .95160 .89454 .95417 .89984 .95666 .90502 36 28 7 .94629 .88368 .94901 .88921 .95164 .89463 .95421 .89993 .95670 .90511 32 5:? 8 9.94634 0.88377 9.94905 0.88930 9.95169 0.89472 9.95425 0.90002 9.95674 0.90519 28 S6 9 .94638 .88386 .94909 .88940 .95173 .89481 .95429 .90010 .95678 .90528 24 40 10 .94643 .88396 .94914 .88949 .95177 .89490 .95433 .90019 .95682 .90537 20 ^ 11 .94648 .88405 .94918 .88958 .95182 .89499 .95438 .90028 .95686 .90545 16 48 n 9.94652 0.88414 9.94923 0.88967 9.95186 0.89508 9.95442 0.90037 9.95690 0.90553 12 52 13 .94657 .88423 .94927 .88976 .95190 .89517 .95446 .90045 .95694 .90562 8 56 14 9.94661 0.88433 9.94932 0.88985 9.95195 0.89526 9.95450 0.90054 9.95699 0.90570 4 14h sm 14^ 35m 14h Sim 14h 27m 14h 23m s ' 15 gh 2im 140° gh 25^ 141° gh 29m 142° 9^ 33m 143° gh Sim 144° s 60 9.94666 0.88442 9.94936 0.88994 9.95199 0.89534 9.95454 0.90063 9.95703 0.90579 4 16 .94670 .88451 .94941 .89003 .95203 .89543 .95459 .90071 .97507 .90588 56 5 17 .94675 .88461 .94945 .89012 .95208 .89552 .95463 .90080 .95711 .90596 52 12 18 .94680 .88470 .94950 .89022 .95212 .89561 .95467 .90089 .95715 .90604 48 i6 19 9.94684 0.88479 9.94954 0.89031 9.95216 0.89570 9.95471 0.90097 9.95719 0.90613 44 fO 20 .94689 .88489 .94958 .89040 .95221 .89579 .95475 .90106 .95723 .90621 40 f^ 21 .94693 .88498 .94963 .89049 .95225 .89588 .95480 .90115 .95727 .90630 36 f5 22 .94698 .88507 .94967 .89058 .95229 .89597 .95484 .90124 .95731 .90638 32 S2 23 9.94702 0.88516 9.94972 0.89067 0.95234 0.89606 9.95488 0.90132 9.95735 0.90647 28 56 24 .94707 .88526 .94976 .89076 .95238 .89614 .95492 .90141 .95739 .90655 24 40 25 .94711 .88535 .94981 .89085 .95242 .89623 .95496 .90150 .95743 .90664 20 44 26 .94716 .88544 .94985 .89094 .95246 .89632 .95501 .90158 .95747 .90672 16 4^ 27 9.94721 0.88553 9.94989 0.89103 9.95251 0.89641 9.95505 0.90167 9.95751 0.90680 12 52 28 .94725 .88563 .94994 .89112 .95255 .89650 .95509 .90176 .95755 .90689 8 56 29 9.94730 0.88572 9.94998 0.89121 9.95259 0.89659 9.95513 0.90184 9.95759 0.90697 4 Uh S8m Wh 34'^ 14^ 30m 14^ 26m 14h 22m s ' 30 gh 22Tn 140° gh 26m 141° 9h SOm 142° gh S4m 1430 gh sgm 144° s 60 9.94734 0.88581 9.95003 0.89130 9.95264 0.89668 9.95517 0.90193 9.95763 0.90706 4 31 .94739 .88590 .95007 .89139 .95268 .89677 .95521 .90201 .95768 .90714 56 8 32 .94743 .88600 .95011 .89149 .95272 .89685 .95526 .90210 .95772 .90723 52 1^ 33 .94748 .88609 .95016 .89158 .95276 .89694 .95530 .90219 .95776 .90731 48 i6 34 9.94752 0.88618 9.95020 0.89167 9.95281 0.89703 9.95534 0.90227 9.95780 0.90740 U 20 35 .94757 .88627 .95025 .89176 .95285 .89712 .95538 .90236 .95784 .90748 40 f4 36 .94761 .88637 .95029 .89185 .95289 .89721 .95542 .90245 .95788 .90756 36 28 37 .94766 .88646 .95033 .89194 .95294 .89730 .95546 .90253 .95792 .90765 32 5:2 38 9.94770 0.88655 9.95038 0.89203 9.95298 0.89738 9.95550 0.90262 9.95796 0.90773 28 56 39 .94774 .88664 .95042 .89212 .95302 .89747 .95555 .90271 .95800 .90792 24 40 40 .94779 .88674 .95047 .89221 .95306 .89756 .95559 .90279 .95804 .90790 20 44 41 .94784 .88683 .95051 .89230 .95311 .89765 .95563 .90288 .95808 .90798 16 48 42 9.94788 0.88692 9.95055 0.89239 9.95315 0.89774 9.95567 0.90296 9.95812 0.90807 12 5:? 43 .94793 .88701 .95060 .89248 .95319 .89783 .95571 .90305 .95816 .90815 8 56 44 9.94797 0.88710 9.95064 0.89257 9.95323 0.89791 9.95575 0.90314 9.95820 0.90824 4 Uh Sim, 14h ssm 14''^ 29m 14h 25m 14^ 21m i s ' 45 gh2:pn U9° gh 27m 141° 9h Sim 1430 9h 35m 143° ghS9m 144° s 60 9.94802 0.88720 9.95069 0.89266 9.95328 0.89800 9.95579 0.90322 9.95824 0.90832 4 46 .94806 .88729 .95073 .89275 .95332 .89809 .95584 .90331 .95828 .90840 56 5 47 .94811 .88738 .95077 .89284 .95336 ■ .89818 .95588 .90339 .95832 .90849 52 if 48 .94815 .88747 .95082 .89293 .95340 .89827 .95592 .90348 .95836 .90857 48 16 49 9.94820 0.88756 9.95086 0.89302 9.75345 0.89835 9.95596 0.90357 9.95840 0.90866 44 fO 50 .94824 .88766 .95090 .89311 .95349 .89844 .95600 .90365 .95844 .90874 40 24 51 .94829 .88775 .95095 .89320 .95353 .89853 .95604 .90374 .95848 .90882 36 f5 52 .94833 .88784 .95099 .89329 .95357 .89862 .95608 .90382 .95852 .90891 32 5f 53 9.94838 0.88793 9.95104 0.89338 9.95362 0.89870 9.95613 0.90391 .9 95856 0.90899 28 36 54 .94842 .88802 .95108 .89347 .95366 .89879 .95617 .90399 .95860 .90907 24 40 55 .94847 .88811 .95112 .89356 .95370 .89888 .95621 .90408 .95864 .90916 20 U 56 .94851 .88821 .95117 .89365 .95374 .89897 .95625 .90417 .95868 .90924 16 4^ 67 9.94856 0.88830 9.95121 0.89374 9.95379 0.89906 9.95629 0.90425 9.95872 0.90933 12 5:2 58 .94860 .88839 .95125 .89383 .95383 .89914 .95633 .90434 .95876 .90941 8 56 59 .94865 .88848 .95130 .89392 .95387 .89923 .95637 .90442 .95880 .90949 4 60 60 9.94869 0.88857 9.95134 0.89401 9.95391 0.89932 9.95641 0.90451 9.95884 0.90958 14^ S6m 1 14^ S2m 1 14h 28m 1 14^ 24m 1 14h 20m 1 Page 148] TABLE IV. [ Haversines. 1 s ' 9A 40m 145° 9h, 44m 146° 9h 48m 1470 gh 52m 148° 9li5&n 149° s Log. Hav Nat. Hav Log. Hav Nat. Hav Log. Hav Nat. Hav Log. Hav Nat. Hav Log. Hav Nat. Hav 9.95884 0.90958 9.96119 0.91452 9.96347 0.91934 9.96568 0.92402 9.96782 0.92858 60 4 1 .95888 .90966 .96123 .91469 .96351 .91941 .96572 .92410 .96786 .92866 56 8 2 .95892 .90974 .96127 .91468 .96355 .91949 ,96576 .92418 .96789 .92873 52 12 3 .95896 .90983 .96131 .91476 .96359 .91957 .96579 .92426 .96793 .93881 48 16 4 9.95900 0.90991 9.96135 0.91484 9.96362 0.91965 9.96583 0.92433 9.96796 0.93888 44 20 5 .95904 .90999 .96139 .91493 .96366 .91973 .96586 .92441 .96800 .93896 40 24 6 .95908 .91008 .96142 .91501 .96370 .91981 .96590 .92449 .96803 .93903 36 28 ■? .95912 .91016 .96146 .91509 .96374 .91989 .96594 .92456 .96807 ,92911 32 82 8 9.95916 0.91034 9.96150 0.91517 9.96377 0.91997 9.96597 0.92464 9.96810 0.93918 28 36 9 .95920 .91033 .96154 .91525 .96381 .92005 .96601 .92472 .96814 .92926 24 40 10 .95924 .91041 .96158 .91533 .96385 .92013 .96604 .92479 .96817 .93933 20 44 li .95928 .91049 .96162 .91541 .96388 .92020 .96608 .93487 .96821 .93941 16 48 13 9.95932 0.91057 9.96165 0.91549 9.96392 0.92028 9.96612 0.92495 9.96824 0.92948 12 52 13 .95936 .91066 .96169 .91557 .96396 .92036 .96615 .93503 .96827 .92055 8 66 14 9.95939 0.91074. 9.96173 0.91565 9.96400 6.92044 9.96619 0.93510 9.96831 0.92963 4 14^ 19m 14h 15m 14h iim 14h7m Uhsm s 15 9h 4im 145° 9h 45m 146° 9h 49m 147° 9h 53m 148° 9h 57m 149° 3 60 9.95943 0.91082 9.96177 0.91574 9.96403 0.92052 9.96622 0.93518 9.96834 0.92970 4 16 .95947 .91091 .96181 .91582 .96407 .92060 .96626 .93535 .96837 .92978 56 8 17 .95951 .91099 .96185 .91590 .96411 .92068 .96630 .92533 .96841 .93985 52 12 18 .95955 .91107 .96188 .91598 .96412 .92076 .96633 .93541 .96845 .93993 48 16 19 9.95959 0.91115 9.96192 0.91606 9.96418 0.92083 9.96637 0.93548 9.96848 0.93000 44 20 20 .95963 .91124 .96196 .91614 .96422 .92091 .96640 .93556 .96852 .93007 40 24 21 .95967 .91132 .96200 .91622 .96426 .92099 .96644 .93563 .96855 .93015 36 28 22 .95971 .91140 .96204 .91630 .96429 .92107 .96648 .93571 .96859 .93032 32 32 23 9.95975 0.91149 9.96208 0.91638 9.96433 0.92115 9.96651 0.93579 9.96862 0.93030 28 36 24 .95979 .91157 .96211 .91646 .96437 .92123 .96655 .93586 .96866 .93037 24 40 25 .95983 .91165 .96215 .91654 .96440 .92130 .96658 .93594 .96869 .93045 20 44 26 .95987 .91173 .96219 ..91662 .96444 .92138 .96662 .93603 .96873 .93053 16 48 27 9.95991 0.91182 9.96223 0.91670 9.96448 0.93146 9.96665 0.93609 9.96876 0.93059 12 52 28 .95995 .91190 .96227 .91678 .96451 .93154 .96669 .93617 .96879 .93067 8 56 29 9.95999 0.91198 9.96230 0.91686 9.96455 0.93163 9.96673 0.92624 9.96883 0.93074 4 Uh Igm 1 Uh 14m 14h lom 14hem 14h 2m 8 30 9h42m 145° | 9h 46m 146° 9h 50m 147° 9h 54m 148° 9h 58m 149° s 60 9.96002 0.91206 9.96234 0.91694 9.96459 0.93170 9.96676 0.92632 9.96886 0.93081 4 31 .96006 .91215 .96238 .91702 .96462 .92177 .96680 .92640 .96890 .93089 56 8 32 .96010 .91223 .96242 .91710 .96466 .92185 .96683 .92647 .96894 .93096 52 12 33 .96014 .91231 .96246 .91718 .96470 .93193 .96687 .92655 .96897 .93104 48 16 34 9.96018 0.91239 9.96249 0.91726 9.96473 0.93301 9.96690 0.92662 9.96900 0.93111 44 20 35 .96022 .91247 .96253 .91734 .96477 .93309 .96994 .92670 .96904 .93118 40 24 36 .96026 .91256 .96257 .91742 .96481 .93316 .96697 .92678 .96907 .93136 36 28 37 .96030 .91264 .96261 .91750 .96484 .92224 .96701 .92685 .96910 .93133 32 32 38 9.96034 0.91272 9.96265 0.91758 9.96488 0.93333 9.96705 0.92693 9.96914 0.93140 28 36 39 .96038 .91280 .96268 .91766 .96492 .92240 .96708 .92700 .96917 .93148 24 40 40 .96042 .91289 .96272 .91774 .96495 .92248 .96712 .92708 .96921 .93155 20 U 41 .96046 .91297 .96276 .91782 .96499 .93355 .96715 .92715 .96924 .93163 16 48 42 9.96049 0.91305 9.96280 0.91790 9.96503 0.93263 9.96719 0.92723 9.96928 0.93170 12 52 43 .96053 .91313 .96283 .91798 .96506 .93371 .96722 .92731 .96931 .93177 8 66 44 9.96057 0.91321 9.96287 0.91806 9.96510 0.93379 9.96726 0.92738 9.96934 0.93184 4 14h J7m 1 14h ism 14^ 9m 14^ 5m 14^ im 1 s 45 9h43m 145° 9h47m 146° 9h 6m 147° 9h 55m 148° 9h59m 149° | s 60 9.96061 0.91329 9.96291 0.91814 9.96514 0.93386 9.96729 0.92746 9.96938 0.93193 4 46 .96065 .91338 .96295 .91822 .96517 .93394 .96733 .92753 .96941 .93199 66 8 47 .96069 .91346 .96299 .91830 .96521 .92302 .96736 .92761 .96945 .93306 62 12 48 .96073 .91354 .96302 .91838 .96525 .92310 .96740 .92768 .96948 .93314 48 16 49 9.96077 0.91362 9.96306 0.91846 9.96528 0.93317 9.96743 0.92776 9.96951 0.93221 44 20 50 .96081 .91370 .96310 .91854 .96532 .93335 .96747 .92783 .96955 .93228 40 24 51 .96084 .91379 .96314 .91862 .96536 .93333 .96750 .92791 .96958 .93236 36 28 52 .96088 .91387 .96317 .91870 .96539 .92341 .96754 .92798 .96962 .93243 32 32 53 9.96092 0.91395 9.96321 0.91878 9.96543 0.93348 9.96758 0.92806 9.96965 0.93250 28 36 54 .96096 .91403 .96325 .91886 .96547 .93356 .98761 .92813 .96968 .93258 24 40 55 .96100 .91411 .96329 .91894 .96550 .93364 .96765 .93831 .96972 .93365 20 44 56 .96104 .91419 .96332 .91902 .96554 .93373 .96768 .93828 .96975 .93272 16 48 57 9.96108 0.91427 9.96336 0.91910 9.96557 0.93379 9.96772 0.92836 9.96979 0.93279 12 52 58 .96112 .91436 .96340 .91918 .96561 .93387 .96775 .92843 .96982 .93287 8 50 59 .96115 .91444 .96344 .91926 .96565 .93394 .96779 .92851 .96985 .93294 4 60 60 9.96119 0.91452 9.96347 0.91934 9.96568 0.92402 9.96782 0.92858 9.96989 0.93301 14^ l&m 1 7^A 12m 1 14^ 8m 1 14h 4m 1 UhOm 1 J TABLE IV. [Page 149 Haversines. s ' 10ft Om 150° IQh 4m 151° IQh Sm 153° lOh 12m 163° lOh 16m 164° s Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. 9.96989 0.93301 9.97188 0.93731 9.97381 0.94147 9.97566 0.94550 9.97745 0.94940 60 4 1 .96992 .93309 .97192 .93738 .97384 .94154 .97569 .95557 .97748 .94946 56 8 2 .96996 .93316 .97195 .93745 .97387 .94161 .97572 .94564 .97751 .94953 52 12 3 .96999 .93323 .97198 .93753 .97390 .94168 .97575 .94570 .97754 .94959 48 16 4 9.97002 0.93330 9.97201 0.93759 9.97393 0.94175 9.97578 0.94577 9.97756 0.94965 44 20 5 .97006 .93338 .97205 .93766 .97397 .94181 .97581 .94583 .97759 .94973 40 24 6 .97009 .93345 .97208 .93773 .97400 .94188 .97584 .94590 .97762 .94978 36 28 7 .97012 .93353 .97211 .93780 .97403 .94195 .97587 .94596 .97765 .94984 32 32 8 9.97016 0.93359 9.97214 0.93787 9.97406 0.94303 9.97591 0.94603 9.97768 0.94991 28 S6 9 .97019 .93367 .97218 .93794 .97409 .94309 .97594 .94610 .97771 .94997 24 -W 10 .97022 .93374 .97221 .93801 .97412 .94315 .97597 .94616 .97774 .95003 20 ■^ 11 .97026 .93381 .97224 .93808 .97415 .94233 .97600 .94623 .97777 .95010 16 48 13 9.97029 0.93388 9.97227 0.93815 9.97418 0.94229 9.97603 0.94629 9.97780 0.95016 12 5:? 13 .97033 .93395 .97231 .93823 .97422 .94236 .97606 .94636 .97783 .95033 8 56 14 9.97036 0.93403 9.97234 0.93829 9.97425 0.94343 9.97609 0.94642 9.97785 0.95039 4 13^ 59m 13h 55m ISh Sim isn 47m 13h 43m s 15 IQh im 150° IQh 5m 151° IQh gm 1530 lOh 13m 153° lOh 17m 164° s 60 9.97039 0.93410 9.97237 0.93836 9.97428 0.94349 9.97612 0.94649 9.97788 0.95035 4 16 .97043 .93417 .97240 .93843 .97431 .94356 .97615 .94655 .97791 .95041 56 5 17 .97046 .93424 .97244 .93850 .97434 .94363 .97618 .94662 .97794 .95048 52 if 18 .97049 .93432 .97247 .93857 .97437 .94370 .97621 .94669 .97797 .95054 48 16 19 9.97052 0.93439 9.97250 0.93864 9.97440 0.94376 9.97624 0.94675 9.97800 0.95060 U fO 30 .97056 .93446 .97253 .93871 .97443 .94283 .97627 .94683 .97803 .95066 40 24 31 .97059 .93453 .97257 .93878 .97447 .94290 .97630 .94688 .97806 .95073 36 :?5 33 .97063 .93460 .97260 .93885 .97450 .94297 .97633 .94695 .97808 .95079 32 5f 33 9.97066 0.93468 9.97263 0.93893 9.97453 0.94303 9.97636 0.94701 9.97811 0.95085 28 36 34 .97069 .93475 .97266 .93899 .97456 .94310 .97639 .94708 .97814 .95093 24 -fO 35 .97073 .93483 .97269 .93906 .97459 .94317 .97642 .94714 .97817 .95098 20 44 36 .97076 .93489 .97273 .93913 .97462 .94324 .97645 .94731 .97820 .95104 16 45 37 9.97079 0.93496 9.97276 0.93920 9.97465 0.94330 9.97647 0.94727 9.97823 0.95111 12 5f 38 .97083 .93503 .97279 .93927 .97468 .94337 .97650 .94734 .97826 .95117 8 56 39 9.97086 0.93511 9.97282 0.93934 9.97471 0.94344 9.97653 0.94740 9.97829 0.95133 4 ISh 58m 13h 54m iSh 5om ISh 46m JSh 42m 30 lOh 2m 150° IQh 6m 151° ion 10m 153° IQh 14m 1530 ion ism 154° s 60 9.97089 0.93518 9.97285 0.93941 9.97474 0.94351 9.97656 0.94747 9.97831 0.95139 4 31 .97093 .93535 .97289 .93948 .97478 .94357 .97659 .94753 .97834 .95136 56 5 33 .97096 .93533 .97292 .93955 .97481 .94364 .97662 .94760 .97837 .95143 52 J?:? 33 .97099 .93539 .97295 .93963 .97484 .94371 .97665 .94766 .97840 .95148 48 16 34 9.97103 0.93546 9.97298 0.93969 9.97487 0.94377 9.97668 0.94773 9.97843 0.95154 U ;gO 35 .97106 .93554 .97301 .93976 .97490 .94384 .97671 .94779 .97846 .95161 40 24 36 .97109 .93561 .97305 .93983 .97493 .94391 .97674 .94786 .97849 .95167 36 :?5 37 .97113 .93568 .97308 .93989 .97496 .94397 .97677 .94*92 .97851 .95173 32 5:2 38 9.97116 0.93575 9.97311 0.93996 9.97499 0.94404 9.97680 0.94799 9.97854 0.95179 28 36 39 .97119 .93583 .97314 .94003 .97502 .94411 .97683 .94805 .97857 .95185 24 40 40 .97123 .93589 .97317 .94010 .97505 .94418 .97686 .94811 .97860 .95193 20 U 41 .97126 .93596 .97321 .94017 .97508 .94424 .97689 .94818 .97863 .95198 16 45 43 9.97129 0.93603 9.97324 0.94034 9.97511 0.94431 9.97692 0.94824 9.97866 0.95204 12 52 43 .97132 .93611 .97327 .94031 .97514 .94438 .97695 .94831 .97868 .95210 8 56 44 9.97136 0.93618 9.97330 0.94038 9.97518 0.94444 9.97698 0.94837 9.97871 0.95217 4 13h 57m ISh SSm 13^ 49m 13n45m 13h 41m s ' 45 IQh 3m 150° IQh Tm 151° lOh 11m 152° lOh 15m 153° ion 19m 1540 s 60 9.97139 0.93625 9.97333 0.94045 9.97521 0.94451 9.97701 0.94844 9.97874 0.95233 4 46 .97142 .93633 .97337 .94051 .97524 .94458 .97704 .94850 .97877 .95339 56 5 47 .97146 .93639 .97340 .94058 .97527 .94464 .97707 .94857 .97880 .95335 52 12 48 .97149 .93646 .97343 .94065 .97530 .94471 .97710 .94863 .97883 .95241 48 :?6 49 9.97152 0.93653 9.97346 0.94073 9.97533 0.94477 9.97713 0.94869 9.97885 0.95248 44 20 50 .97156 .93660 .97349 .94079 .97536 .94484 .97716 .94876 .97888 .95254 40 ^4 51 .97159 .93667 .97352 .94086 .97539 .94491 .97718 .94882 .97891 .95260 36 ;?5 53 .97162 .93674 .97356 .94093 .97542 .94497 .97721 .94889 .97894 .95266 32 32 53 9.97165 0.93683 9.97359 0.94099 9.97545 0.94504 9.97724 0.94895 9.97897 0.95272 28 56 54 .97169 .93689 .97362 .94106 .97548 .94511 .97727 .94901 .97899 .95378 24 40 55 .97172 .93696 .97365 .94113 .97551 .94517 .97730 .94908 .97902 .95385 20 44 56 .97175 .93703 .97368 .94120 .97554 .94524 .97733 .94914 .97905 .95391 16 45 57 9.97179 0.93710 9.97371 0.94127 9.97557 0.94531 9.97736 0.94921 9.97908 0,95297 12 52 58 .97182 .93717 .97575 .94134 .97560 .94537 .97739 .94927 .97911 .95303 8 56 59 .97185 .93734 .97378 .94141 .97563 .94544 .97742 .94933 .97914 .95309 4 60 60 9.97188 0.93731 9.97381 0.94147 9.97566 0.94550 9.97745 0.94940 9.97916 0.95315 ISh 56m 13h52m 13n48m 1 ISh 44m 1 isn 40m 1 Page 150] TABLE IV. Haversinea. s ' 10h20m 155° iO'i 24"^ 156° lOh 28m 1570 lOh S2m 168° lOh 36m 1590 3 60 Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. 0.96679 9.97916 0.95315 9.98081 0.95677 9.98239 0.96025 9.98389 0.96359 9.98533 4 1 .97919 .95322 .98084 .95683 .98241 .96031 .98392 .96365 .98536 .96684 56 8 2 .97922 .95328 .98086 .95689 .98244 .96037 .98394 .96370 .98538 .96689 52 12 3 .97925 .95334 .98089 .95695 .98246 .96042 .98397 .96376 .98540 .96695 48 16 4 9.97927 0.95340 9.98092 0.95701 9.98249 0.96048 9.98399 0.96381 9.98543 0.96700 44 20 5 .97930 .95346 .98094 .95707 .98251 .96054 .98402 .96386 .98545 .96705 40 24 6 .97933 .95352 .98097 .95713 .98254 .96059 .98404 .96392 .98547 .96710 36 28 7 .97936 .95358 .98100 .95719 .98256 .96065 .98406 .96397 .98550 .96715 32 S2 8 9.97939 0.95364 9.98102 0.95724 9.98259 0.96071 9.98409 0.96403 9.98552 0.96721 28 56 9 .97941 .95371 .98105 .95730 .98262 .96076 .98411 .96408 .98554 .96726 24 40 10 .97944 .95377 .98108 .95736 .98264 .96082 .98414 .96413 .98557 .96731 20 ■^ 11 .97947 .95383 .98110 .95742 .98267 .96088 .98416 .96419 .98559 .96736 16 ^ 13 9.97950 0.95389 9.98113 0.95748 9.98269 0.96093 9.98419 0.96424 9.98561 0.96741 12 52 13 .97953 .95395 .98116 .95754 .98272 .96099 .98421 .96430 .98564 .96746 8 56 14 9.97955 0.95401 9.98118 0.95760 9.98274 0.96104 9.98424 0.96435 9.98566 0.96752 4 ISh 39^ ISh 35m 13h 3im 13h 27m 13h 23m 8 ' 15 IQh 2im 155° 10^ 25m 156° 10h29m 157° IQh 33m 158° lOh sjm 1590 s 60 9.97958 0.95407 9.98121 0.95766 9.98277 0.96110 9.98426 0.96440 9.98568 0.96757 4 16 .97961 .95413 .98124 .95771 .98279 .96116 .98428 .96446 .98570 .96762 56 8 17 .97964 .95419 .98126 .95777 .98282 .96121 .98431 .96451 .98573 .96767 52 i;? 18 .97966 .95425 .98129 .95783 .98285 .96127 .98433 .96457 .98575 .96772 48 16 19 9.97969 0.95431 9.98132 0.95789 9.98287 0.96133 9.98436 0.96462 9.98577 0.96777 44 ;?0 20 .97972 .95438 .98134 .95795 .98290 .96138 .98438 .96467 .98580 .96782 40 ;g4 21 .97975 .95444 .98137 .95801 .98292 .96144 .98440 .96473 .98582 .96788 36 ;25 22 .97977 .95450 .98139 .95806 .98295 .96149 .98443 .96478 .98584 .96793 32 5? 23 9.97980 0.95456 9.98142 0.95812 9.98297 0.96155 9.98455 0.96483 9.98587 0.96798 28 S6 24 .97983 .95462 .98145 .95818 .98300 .96161 .98448 .96489 .98589 .96803 24 40 25 .97986 .95468 .98147 .95824 .98302 .96166 .98450 .96494 .98591 .96808 20 44 26 .97988 .95474 .98150 .95830 .98305 .96172 .98453 .96500 .98593 .96813 16 48 27 9.97991 0.95480 9.98153 0.95836 9.98307 0.96177 9.98455 0.96505 9.98596 0.96818 12 5^ 28 .97994 .95486 .98155 .95841 .98310 .96183 .98457 .96510 .98598 .96823 8 56 29 9.97997 0.95492 9.98158 0.95847 9.98312 0.96188 9.98460 0.96516 9.98600 0.96829 4 13^ 38^ 13h 34m 13^ 30m 13^ 26m 13h 22m 30 lOh 22m 155° IQh 26m 156° IQh 30m 157° IQh S4m 158° ion 38m 1590 3 60 9.97999 0.95498 9.98161 0.95853 9.98315 0.96194 9.98462 0.96521 9.98603 0.96834 4 31 .98002 .95504 .98163 .95859 .98317 .96200 .98465 .96526 .98605 .96839 56 5 32 .98005 .95510 .98166 .95865 .98320 .96205 .98467 .96532 .98607 .96844 52 12 33 .98008 .95516 .98168 .95870 .98322 .96211 .98469 .96537 .98609 .96849 48 16 34 9.98010 0.95522 9.98171 0.95876 9.98325 0.96216 9.98472 0.96542 9.98612 0.96854 U £0 35 .98013 .95528 .98174 .95882 .98327 .96222 .98474 .96547 .98614 .96859 40 ;?4 36 .98016 .95534 .98176 .95888 .98330 .96227 .98476 .96553 .98616 .96864 36 28 37 .98019 .95540 .98179 .95894 .98332 .96223 .98479 .96558 .98619 .96869 32 5;? 38 9.98021 0.95546 9.98182 0.95899 9.98335 0.96238 9.98481 0.96563 9.98621 0.96874 28 36 39 .98024 .95552 .98184 .95905 .98337 .96244 .98484 .96569 .98623 .96879 24 40 40 .98027 .95558 .98187 .95911 .98340 .96249 .98486 .96574 .98625 .96884 20 44 41 .98030 .95564 .98189 .95917 .98342 .96255 .98488 .96579 .98628 .96889 16 48 42 9.98032 0.95570 9.98192 0.95922 9.98345 0.96260 9.98491 0.96585 9.98630 0.96894 12 5« 43 .98035 .95576 .98195 .95928 .98347 .96266 .98493 .96590 .98632 .96899 8 56 44 9.98038 0.95582 9.98197 0.95934 9.98350 0.96272 9.98496 0.96595 9.98634 0.96905 4 ISh 37m 1 13h ssm I'Sh 29m 13h 25m i3h 21m s ' 45 10h2Sm 155° | iOh 27m 156° IQh 3im 157° IQh 35m 158° lOh 39m 159° s 60 9.98040 0.95588 9.98200 0.95940 9.98352 0.96277 9.98498 0.96600 9.98637 0.96910 4 46 .98043 .95594 .98202 .95945 .98355 .962S3 .98500 .96606 .98639 .96915 56 « 47 .98046 .95600 .98205 .95951 .98357 .96288 .98503 .96611 .98641 .96920 52 12 48 .98049 .95606 .98208 .95957 .98360 .96294 .98505 .96616 .98643 .96925 48 i6 49 9.98051 0.95612 9.98210 0.95962 9.98362 0.96299 9.98507 0.96621 9.98646 0.96930 44 fO 60 .98054 .95618 .98213 .95968 .98365 .96305 .98510 .96627 .98648 .96935 40 24 61 .98057 .95624 .98215 .95974 .98367 .96310 .98512 .96632 .98650 .96940 36 ;?5 62 .98059 .95630 .98218 .95980 .98370 .96315 .98514 .96637 .98652 .96945 32 32 63 9.98062 0.95636 9.98221 0.95985 9.98372 0.96321 9.98517 0.96642 9.98655 0.96950 28 56 54 .98065 .95642 .98223 .95991 .98375 .96326 .98519 .96648 .98657 .96955 24 40 55 .98067 .95648 .98226 .95997 .98377 .96332 .98521 .96653 .98659 .96960 20 U 56 .98070 .95654 .98228 .96002 .98379 .96337 .98524 .96658 .98661 .96965 16 45 57 9.980F3 0.95660 9.98231 0.96008 9.98382 0.96343 9.98526 0.96663 9.98664 0.96970 12 52 58 .98076 .95665 .98233 .96014 .98384 .96348 .98529 .96669 .98666 .96975 8 56 59 .98078 .95671 .98236 .96020 .98387 .96354 .98531 .96674 .98668 .96980 4 60 60 9.98081 0.95677 9.98239 0.96025 9.98389 0.96359 9.98533 0.96679 9.98670 1 0.96985 13^ 36^ 1 13h 32m 13h 28m 1 13h24m 1 13h2am \ TABLE IV. IPage 151 HavereineB. 3 '. IQh 40m 160° lOh 44m 161° lOh 48^ 163° lOh 52rn 163° 10h56m 164° s Log. Hav. Nat. Hav. 0.96986 Log. llav. Nat. llav. Log. Hav. Nat. Uav. Log. llav.| Nat. llav. Log. Hav. 9.99151 Nat. Uav. "9798670" '9^98861 0.97376 9.98924 0.97553 9.99041 0.97815 0.98063 60 4 1 .98673 .96990 .98803 .97381 .98926 .97557 .99043 .97819 .99152 .98067 56 s 2 .98675 .96995 .98805 .97385 .98928 .97562 .99044 .97834 .99154 .98071 52 12 3 .98677 .97000 .98807 .97390 .98930 .97566 .99046 .97838 .99156 .98075 48 16 4 9.98679 0.97005 9.98809 0.97395 9.98932 0.97571 9.99048 0.97833 9.99158 0.98079 44 20 5 .98681 .97009 .98811 .97300 .98934 .97575 .99050 .97836 .99159 .98083 40 24 6 .98684 .97014 .98813 .97304 .98936 .97580 .99052 .97841 .99161 .98087 36 28 7 .98686 .97019 .98815 .97309 .98938 .97584 .99054 .97845 .99163 .98091 3i 32 S 9.98688 0.97024 9.98817 0.97314 9.98940 0.97589 9.99056 0.97849 9.99165 0.98095 28 36 9 .98690 .97029 .98819 .97318 .98942 .97593 .99058 .97853 .99166 .98099 24 40 10 .98692 .97034 .98822 .97333 .98944 .97598 .99059 .97858 .99168 .98103 20 U 11 .98695 .97039 .98824 .97338 .98946 .97603 .99061 .97862 .99170 .98107 16 48 13 9.98697 0.97044 9.98826 0.97332 9.98948 0.97606 9.99063 0.97866 9.99172 0.98111 12 52 13 .98699 .97049 .98828 .97337 .98950 .97611 .99065 .97870 .99173 .98115 8 56 14 9.98701 0.97054 9.98830 0.97342 9.98952 0.97615 9.99067 0.97874 9.99175 0.98119 4 ISh 19m 13h urn 23h 11m 13h7m 13h sm 1 s ' lOh 41m 160° lOh 45m 161° IQh 49m 163° lOh 53m 163° lOh 37m 164° s 15 9.98703 0.97059 9.98832 0.97347 9.98954 0.97630 9.99069 0.97879 9.99177 0.98133 60 4 16 .98706 .97064 .98834 .97351 .98956 .97634 .99071 .97883 .99179 .98137 56 8 17 .98708 .97069 .98836 .97356 .98958 .97639 .99072 .97887 .99180 .98131 52 12 18 .98710 .97074 .98838 .97361 .98960 .97633 .99074 .97891 .99182 .98135 48 16 19 9.98712 0.97078 9.98840 0.97365 9.98962 0.97637 9.99076 0.97895 9.99184 0.98139 U 20 20 .98714 .97083 .98842 .97370 .98964 .97643 .99078 .97899 .99186 .98143 40 24 21 .98717 .97088 .98845 .97374 .98966 .97646 .99080 .97904 .99187 .98146 36 28 22 .98719 .97093 .98847 .97379 .98968 .97651 .99082 .97908 .99189 .98150 32 32 23 9.98721 0.97098 9.98849 0.97384 9.98970 0.97655 9.99084 0.97912 9.99191 0.98154 28 36 24 .98723 .97103 .98851 .97388 .98971 .97660 .99085 .97916 .99193 .98158 24 40 25 .98725 .97108 .98853 .97393 .98973 .97664 .99087 .97920 .99194 .98163 20 44 26 .98728 .97113 .98855 .97398 .98975 .97668 .99089 .97924 .99196 .98166 16 48 27 9.98730 0.97117 9.98857 0.97402 9.98977 0.97673 9.99091 0.97929 9.99198 0.98170 12 52 28 .98732 .97132 .98859 .97407 .98979 .97677 .99093 .97933 .99200 .98174 8 56 29 9.98734 0.97127 9.98861 0.97413 9.98981 0.97681 9.99095 0.97937 9.99201 0.98178 4 1 ISh ism ISh 14m ISh 10m IShem 13h 2m 1 s ' lOh 42m 160° lOh 46m 161° IQh 50rn 163° lOh 54^ 163° 10^ 58^ 164° s 30 9.98736 0.97132 9.98863 0.97416 9.98983 0.97686 9.99096 0.97941 9.99203 0.98182 60 4 31 .98738 .97137 .98865 .97431 .98985 .97690 .99098 .97945 .99205 .98185 56 8 32 .98741 .97142 .98867 .97425 .98987 .97695 .99100 .97949 .99206 .98189 52 12 33 .98743 .97147 .98869 .97430 .98989 .97699 .99102 .97953 .99208 .98193 48 16 34 9.98745 0.97151 9.98871 0.97435 9.98991 0.97703 9.99104 0.97957 9.99210 0.98197 44 20 35 .98747 .97156 .98873 .97439 .98993 .97708 .99106 .97962 .99212 .98301 40 24 36 .98749 .97161 .98875 .97444 .98995 .97713 .99107 .97966 .99213 .98305 36 28 37 .98751 .97166 .98877 .97448 .98997 .97716 .99109 .97970 .99215 .98309 32 32 38 9.98754 0.97171 9.98880 0.97453 9.98999 0.97731 9.99111 0.97974 9.99217 0.98313 28 36 39 .98756 .97176 .98882 .97458 .99001 .97735 .99113 .97978 .99218 .98316 24 40 40 .98758 .97180 .98884 .97463 .99003 .97739 .99115 .97982 .99220 .98330 20 44 41 .98760 .97185 .98886 .97467 .99004 .97734 .99116 .97986 .99222 .98324 16 48 42 9.98762 0.97190 9.98888 0.97471 9.99006 0.97738 9.99118 0.97990 9.99223 0.98338 12 52 43 .98764 .97195 .98890 .97476 .99008 .97743 .99120 .97994 .99225 .98333 8 56 44 9.98766 0.97200 9.98892 0.97480 9.99010 0.97747 9.99122 0.97998 9.99227 0.98336 4 1 23h 17m ISh 13m IShgm ISh 5m ISh im 1 s '1 lOh 43m 160° IQh 47m 161° IQh 5im 162° IQh 55m 163° IQh 59m 164° 1 a 45 9.98769 0.97304 9.98894 0.97485 9.99012 0.97751 9.99124 0.98002 9.99229 0.98339 60 4 46 .98771 .97209 .98896 .97490 .99014 .97755 .99126 .98007 .99230 .98343 56 8 47 .98773 .97314 .98898 .97494 .99016 .97760 .99127 .98011 .99232 .98347 52 12 48 .98775 .97319 .98900 .97499 .99018 .97764 .99129 .98015 .99234 .98351 48 16 49 9.98777 0.97334 9.98902 0.97503 9.99020 0.97768 9.99131 0.98019 9.99235 0.98355 U 20 50 98779 .97338 .98904 .97508 .99022 .97773 .99133 .98023 .99237 .98358 40 24 51 .98781 .97333 .98906 .97513 .99024 .97777 .99135 .98037 .99239 .98363 36 28 52 .98784 .97338 .98908 .97517 .99026 .97781 .99136 .98031 .99240 .98366 32 32 53 9.98786 0.97343 9.98910 0.97531 9.99027 0.97785 9.99138 0.98035 9.99242 0.98370 28 36 54 .98788 .97347 .98912 .97536 .99029 .97790 .99140 .98039 .99244 .98374 24 40 55 .98790 .97353 .98914 .97530 .99031 .97794 .99142 .98043 .99245 .98377 20 U 56 .98792 .97357 .98916 .97535 .99033 .97798 .99143 .98047 .99247 .98381 16 48 57 9.98794 0.97363 9.98918 0.97539 9.99035 0.97803 9.99145 0.98051 9.99249 0.98385 12 52 58 .98796 .97366 .98920 .97544 .99037 .97807 .99147 .98055 .99250 .98389 8 56 59 .98798 .97371 .98922 .97548 .99039 .97811 .99149 .98059 .99252 .98393 4 60 60 9.98801 0.97376 9.98924 0.97553 9.99041 0.97815 9.99151 0.98063 9.99254 0.98396 1 ISh l&n 1 ISh 12m 1 ISh gm 1 ISh 4m 1 ISh am ^ Page 162] TABLE IV. Haversinee. s ' llh am 165° llh 4m 166° llh 8m 167° llh 12m 168° llh 16m 169° s Log. Hav. Nat. Hav, Lor. llav. Nat. Uav. Log. Ilav. Nat. Hav. Ix)g. Hav. Nat. Hav. Log. Uav. Nat. Hav. 9.99254 0.98296 9.99350 0.98515 9.99440 0.98719 9.99523 0.98907 9.99599 0.99081 ~60 4 1 .99255 .98300 .99352 .98518 .99441 .98722 .99524 .98910 .99600 .99084 56 8 % .99257 .98304 .99353 .98522 .99443 .98725 .99526 .98913 .99602 .99087 52 12 3 .99259 .98308 .99355 .98525 .99444 .98728 .99527 .98916 .99603 .99090 48 16 4 9.99260 0.98311 9.99356 0.98529 9.99446 0.98732 9.99528 0.98919 9.99604 0.99092 44 20 5 .99262 .98315 .99358 .98532 .99447 .98735 .99529 .98922 .99605 .99095 40 24 6 .99264 .98319 .99359 .98536 .99448 .98738 .99531 .98925 .99606 .99098 36 28 7 .99265 .98323 .99361 .98539 .99450 .98741 .99532 .98928 .99608 .99101 32 S2 8 9.99267 0.98326 9.99362 0.98543 9.99451 0.98745 9.99533 0.98931 9.99609 0.99103 28 S6 9 .99269 .98330 .99364 .98546 .99453 .98748 .99535 .98934 .99610 .99106 24 -^0 10 .99270 .98334 .99366 .98550 .99454 .98751 .99536 .98937 .99611 .99109 20 ■f^ 11 .99272 .98337 .99367 .98553 .99456 .98754 .99537 .98940 .99612 .99112 16 48 n 9.99274 0.98341 9.99369 0.98557 9.99457 0.98757 9.99539 0.98943 9.99614 0.99114 12 52 13 .99275 .98345 .99370 .98560 .99458 .98761 .99540 .98946 .99615 .99117 8 56 14 9.99277 0.98349 9.99372 0.98564 9.99460 0.98764 9.99541 0.98949 9.99616 0.99120 4 12h 59m 12h 55m 12h 5im Ijh 47m 12h43m s ' llfi m _ 165° llh 5m 166° llh 9m 167° llh 13m 168° llh 17m 169° s 15 9.99278 0.98352 9.99373 0.98567 9.99461 0.98767 9.99543 0.98952 9.99617 0.99123 60 4 16 .99280 .98356 .99375 .98571 .99463 .98770 .99544 .98955 .99618 .99125 56 5 17 .99282 .98360 .99376 .98574 .99464 .98774 .99545 .98958 .99620 .99128 52 12 18 .99283 .98363 .99378 .98577 .99465 .98777 .99546 .98961 .99621 .99131 48 ^6 19 9.99285 0.98367 9.99379 0.98581 9.99467 0.98780 9.99548 0.98964 9.99622 0.99133 44 ;?0 20 .99287 .98371 .99381 .98584 .99468 .98783 .99549 .98967 .99623 .99136 40 f-; 21 .99288 .98374 .99382 .98588 .99470 .98786 .99550 .98970 .99624 .99139 36 £<§ 22 .99290 .98378 .99384 .98591 .99471 .98789 .99552 .98973 .99626 .99141 32 S2 23 9.99291 0.98382 9.99385 0.98595 9.99472 0.98793 9.99553 0.98976 9.99627 0.99144 28 56 24 .99293 .98385 .99387 .98598 .99474 .98796 .99554 .98979 .99628 .99147 24 ^ 25 .99295 .98389 .99388 .98601 .99475 .98799 .99555 .98982 .99629 .99149 20 U 26 .99296 .98393 .99390 .98605 .99477 .98802 .99557 .98985 .99630 .99152 16 ^ 27 9.99298 0.98396 9.99391 0.98608 9.99478 0.98805 9.99558 0.98987 9.99631 0.99155 12 52 28 .99300 .98400 .99393 .98611 .99479 .98809 .99559 .98990 .99633 .99157 8 56 29 9.99301 0.98404 9.99394 0.98615 9.99481 0.98812 9.99561 0.98993 9.99634 0.99160 4 12^ 58m 12h 54m 12h SQm- 12h 46m 12h 42m s ' llh 2m 165° llh 6m 166° llh lom 167° llh 14m 168° llh 18m 169° 1 s | 30 9.99303 0.98407 9.99396 0.98619 9.99482 0.98815 9.99562 0.98996 9.99635 0.99163 60 4 31 .99304 .98411 .99397 .98622 .99484 .98818 .99563 .98999 .99636 .99165 56 \ 8 32 .99306 .98415 .99399 .98625 .99485 .98821 .99564 .99002 .99637 .99168 52 J;? 33 .99308 .98418 .99400 .98629 .99486 .98824 .99566 .99005 .99638 .99171 48 ^6 34 9.99309 0.98422 9.99402 0.98632 9.99488 0.98827 9.99567 0.99008 9.99639 0.99173 U 20 35 .99311 .98426 .99403 .98635 .99489 .98830 .99568 .99011 .99641 .99176 40 ^4 36 .99312 .98429 .99405 .98639 .99490 .98834 .99569 .99014 .99642 .99179 36 28 37 .99314 .98433 .99406 .98642 .99492 .98837 .99571 .99016 .99643 .99181 32 5^ 38 9.99316 0.98436 9.99408 0.98646 9.99493 0.98840 9.99572 0.99019 9.99644 0.99184 28 56 39 .99317 .98440 .99409 .98649 .99495 .98843 .99573 .99022 .99645 .99186 24 40 40 .99319 .98444 .99411 .98652 .99496 .98846 .99575 .99025 .99646 .99189 20 -f^ 41 .99320 .98447 .99412 .98656 .99497 .98849 .99576 .99028 .99648 .99192 16 48 42 9.99322 0.98451 9.99414 0.98659 9.99499 0.98852 9.99577 0.99031 9.99649 0.99194 12 5£ 43 .99324 .98454 .99415 .98662 .99500 .98855 .99578 .99034 .99650 .99197 8 56 44 9.99325 0.98458 9.99417 0.98666 9.99501 0.98858 9.99580 0.99036 9.99651 0.99199 4 12h 57m 12h 53m 12h 49m 12h 45m 12h 41m s ' llh sm 165° llh 7m 166° llh 11m 167° llh 15m 168° llh 19m 169° s 45 9.99327 0.98462 9.99418 0.98669 9.99503 0.98862 9.99581 0.99039 9.99652 0.99202 60 4 46 .99328 .98465 .99420 .98672 .99504 .98865 .99582 .99042 .99653 .99205 56 5 47 .99330 .98469 .99421 .98676 .99505 .98868 .99583 .99045 .99654 .99207 52 i^ 48 .99331 .98472 .99422 .98679 .99507 .98871 .99584 .99048 .99655 .99210 48 16 49 9.99333 0.98476 9.99424 0.98682 9.99508 0.98874 9.99586 0.99051 9.99657 0.99212 44 go 50 .99335 .98479 .99425 .98686 .99510 .98877 .99587 .99053 99658 .99215 40 24 51 .99336 .98483 .99427 .98689 .99511 .98880 .99588 .99056 .99659 .99217 36 ;g5 52 .99338 .98487 .99429 .98692 .99512 .98883 .99589 .99059 .99660 .99220 32 5;? 53 9.99339 0.98490 9.99430 0.98696 9.99514 0.98886 9.99591 0.99062 9.99661 0.99223 28 S6 54 .99341 .98494 .99431 .98699 .99515 .98889 .99592 .99065 .99662 .99225 24 ^ 56 .99342 .98497 .99433 .98702 .99516 .98892 .99593 .99067 .99663 .99228 20 U 56 .99344 .98501 .99434 .98705 .99518 .98895 .99594 .99070 .99664 .99230 16 ^ 57 9.99345 0.98504 9.99436 0.98709 9.99519 0.98898 9.99596 0.99073 9.99666 0.99233 12 5:? 58 .99347 .98508 .99437 .98712 .99520 .98901 .99597 .99076 .99667 .99235 8 56 59 .99349 .98511 .99438 .98715 .99522 .98904 .99598 .99079 .99668 .99238 4 60 60 9.99350 0.98515 9.99440 0.98719 9.99523 0.98907 9.99599 0.99081 9.99669 0.99240 12^ 56m 12h 52m 1 12h 48m 1 12h 44m 1 12h 40m 1 TABLE IV. [Page 153 Haversines. s llh20>n 170° 1 llh24^ 171° I llh 28m 172° [ llhS2m 173° [ llhS6m 174° j s Log. Hav. Nat. Ilav. Log. Ilav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. 9.99669 0.99340 9.99732 0.99384 9.99788 0.99513 9.99838 0.99627 9.99881 0.99726 60 4 1 .99670 .99343 .99733 .99387 .99789 .99515 .99839 .99629 .99882 .99728 56 8 2 .99671 .99345 .99734 .99389 .99790 .99517 .99839 .99631 .99882 .99729 52 12 3 .99672 .99348 .99735 .99391 .99791 .99519 .99840 .99633 .99883 .99731 48 16 4 9.99673 0.99350 9.99736 0.99393 9.99792 0.99531 9.99841 0.99634 9.99884 0.99732 U 20 S .99674 .99353 .99737 .99396 .99793 .99533 .99842 .99636 .99884 .99734 40 24 6 .99675 .99355 .99738 .99398 .99793 .99535 .99842 .99638 .99885 .99735 36 28 7 .99677 .99358 .99739 .99400 .99794 .99537 .99843 .99640 .99885 .99737 32 S2 8 9.99678 0.99360 9.99740 0.99403 9.99795 0.99539 9.99844 0.99641 9.99886 0.99738 28 S6 9 .99679 .99363 .99741 .99405 .99796 .99531 .99845 .99643 .99887 .99740 24 40 10 .99680 .99365 .99742 .99407 .99797 .99533 .99845 .99645 .99887 .99741 20 U 11 .99681 .99368 .99743 .99409 .99798 .99535 .99846 .99647 .99888 .99743 16 48 13 9.99682 0.99370 9.99744 0.99411 9.99799 0.99537 9.99847 0.99648 9.99889 0.99744 12 52 13 .99683 .99373 .99745 .99414 .99800 .99539 .99848 .99650 .99889 .99746 8 56 14 9.99684 0.99375 9.99746 0.99416 9.99800 0.99541 9.99848 0.99652 9.99890 0.99747 4 12h 39m \ 12h S5m 1 12h 3im 1 12h27m' \ 12h 23m 1 . ■ 1 llh2im 170° 1 llh25in 171° 1 llh 29m 173° 1 llh 33m 173° 1 llh 37m 174° 1 s 15 9.99685 0.99378 9.99747 0.99418 9.99801 0.99543 9.99849 0.99653 9.9*691 0.99748 60 4 16 .99686 .99380 .99748 .99430 .99802 .99545 .99850 .99655 .99891 .99750 56 8 17 .99687 .99383 .99748 .99433 .99803 .99547 .99851 .99657 .99892 .99751 52 12 18 .99688 .99385 .99749 .99435 .99804 .99549 .99851 .99659 .99893 .99753 48 16 19 9.99690 0.99388 9.99750 0.99427 9.99805 0.99551 9.99852 0.99660 9.99893 0.99754 44 20 20 .99691 .99390 .99751 .99439 .99805 .99553 .99853 .99662 .99894 .99756 40 24 31 .99692 .99393 .99752 .99431 .99806 .99555 .99854 .99664 .99894 .99757 36 28 33 .99693 .99395 .99753 .99433 .99807 .99557 .99854 .99665 .99895 .99759 32 S2 33 9.99694 0.99397 9.99754 0.99436 9.99808 0.99559 9.99855 0.99667 9.99896 0.99760 28 36 34 .99695 .99300 .99755 .99438 .99809 .99561 .99856 .99669 .99896 .99761 24 40 35 .99696 .99303 .99756 .99440 .99810 .99563 .99857 .99670 .99897 .99763 20 U 36 .99697 .99305 .99757 .99443 .99811 .99565 .99857 .99672 .99897 .99674 16 48 37 9.99698 0.99307 9.99758 0.99444 9.99811 0.99567 9.99858 0.99674 9.99898 0.99766 12 52 28 .99699 .99309 .99759 .99446 .99812 .99568 .99859 .99675 .99899 .99767 8 56 29 9.99700 0.99313 9.99760 0.99449 9.99813 0.99570 9.99859 0.99677 9.99899 0.99768 4 121 SS^- 12^34'^ >" 12h 30m 12h 26m 12h 22m s -1 llh22m 170° llh26m 171° llhsom 173° llh 34m 173° llh 38m 174° 3 30 9.99701 0.99314 9.99761 0.99451 9.99814 0.99572 9.99860 0.99679 9.99900 0.99770 60 4 31 .99702 .99317 .99762 .99453 .99815 .99574 .99861 .99680 .99901 .99771 56 8 32 .99703 .99319 .99763 .99455 .99815 .99576 .99862 .99682 .99901 .99773 52 12 33 .99704 .99331 .99764 .99457 .99816 .99578 .99862 .99684 .99902 .99774 48 16 34 9.99705 0.99334 9.99765 0.99459 9.99817 0.99580 9.99863 0.99685 9.99902 0.99775 44 20 35 .99706 .99336 .99766 .99461 .99818 .99583 .99864 .99687 .99903 .99777 40 24 36 .99707 .99339 .99766 .99464 .99819 .99584 .99864 .99688 .99904 .99778 36 28 37 .99708 .99331 .99767 .99466 .99820 .99585 .99865 .99890 .99904 .99780 32 32 38 9.99710 0.99333 9.99768 0.99468 9.99820 0.99587 9.99866 0.99692 9.99905 0.99781 28 36 39 .99711 .99336 .99769 .99470 .99821 .99589 .99867 .99693 .99905 .99782 24 40 40 .99712 .99338 .99770 .99473 .99822 .99591 .99867 .99695 .99906 .99784 20 44 41 .99713 .99340 .99771 .99474 .99823 .99593 .99868 .99696 .99906 .99785 16 48 42 9.99714 0.99343 9.99772 0.99476 9.99824 0.99595 9.99869 0.99698 9.99907 0.99786 12 52 43 .99715 .99345 .99773 .99478 .99824 .99597 .99869 .99700 .99908 .99788 8 56 44 9.99716 0.99347 9.99774 0.99480 9.99825 0.99598 9.99870 0.99701 9.99908 0.99789 4 12h S7m 12h 33m 12h 29m 12h 25m 12h 21m s ' llh23m 170° llh 27m 171° llh Sim 173° llhssm 173° llh 39m 174° a 45 9.99717 0.99350 9.99774 0.99483 9.99826 0.99600 9.99871 0.99703 9.99909 0.99790 60 4 46 .99718 .99353 .99775 .99485 .99827 .99603 .99871 .99704 .99909 .99793 56 8 47 .99719 .99354 .99776 .99487 .99828 .99604 .99872 .99706 .99910 .99793 52 12 48 .99720 .99357 .99777 .99489 .99828 .99606 .99873 .99708 .99911 .99794 48 16 49 9.99721 0.99359 9.99778 0.99491 9.99829 0.99608 9.99874 0.99709 9.99911 0.99796 U . 20 50 .99722 .99361 .99779 .99493 .99830 .99609 .99874 .99711 .99912 .99797 40 24 51 .99723 .99364 .99780 .99495 .99831 .99611 .99875 .99712 .99912 .99798 36 28 52 .99724 .99366 .99781 .99497 .99832 .99613 .99876 .99714 .99913 ,99799 32 32 53 9.99725 0.99368 9.99782 0.99499 9.99832 0.99615 9.99876 0.99715 9.99913 0.99801 28 36 54 .99726 .99371 .99783 .99501 .99833 .99617 .99877 .99717 .99914 ,99802 24 40 55 .99727 .99373 .99784 .99503 .99834 .99618 .99878 .99719 .99915 .99803 20 44 56 .99728 .99375 .99785 .99505 .99835 .99630 .99878 .99720 .99915 .99805 16 48 57 9.99729 0.99378 9.99786 0.99507 9.99836 0.99623 9.99879 0.99722 9.99916 0,99806 12 52 58 .99730 .99380 .99786 .99509 .99836 .99624 .99880 .99723 ,99916 .99807 8 56 59 .99731 .99383 .99787 .99511 .99837 .99626 .99880 .99725 .99917 .9S808 4 60 60 9.99732 0.99384 9.99788 0.99513 9.99838 0.99627 9.99881 0.99726 9.99917 0.99810 12^36^ if ft 32m 12h 28m 12h 24"^ 12h20'n Page 154] TABLE IV. Havereines. 3 ' llh 40m 175° llh 44m 176° llh 48m 1770 llh 52m 178° llh 56m 179° | s 60 Log. Hav. Nat. Hav J Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. Log. Hav. Nat. Hav. 9.99917 0.99810 9.99947 0.99878 9.99970 0.99931 9.99987 0.99970 9.99997 0.99992 4 1 .99918 .99811 .99948 .99879 .99971 .99933 .99987 .99971 .99997 .99993 56 8 2 .99918 .99812 .99948 .99880 .99971 .99933 .99987 .99971 .99997 .99993 52 12 3 .99919 .99814 .99948 .99881 .99971 .99934 .99987 .99971 .99997 .99993 48 16 4 9.99919 0.99815 9.99949 0.99883 9.99972 0.99934 9.99988 0.99972 9.99997 0.99994 44 20 5 .99920 .99816 .99949 .99883 .99972 .99935 .99988 .99972 .99997 .99994 40 24 6 .99921 .99817 .99950 .99884 .99972 .99936 .99988 .99973 .99997 .99994 36 28 7 .99921 .99819 .99950 .99885 .99973 .99937 .99988 .99973 .99997 .99994 32 5f 8 9.99922 0.99820 9.99951 0.99886 9.99973 0.99937 9.99988 0.99973 9.99998 0.99994 28 36 9 .99922 .99831 .99951 .99887 .99973 .99938 .99989 .99974 .99998 .99995 24 40 10 .99923 .99822 .99951 .99888 .99973 .99939 .99989 .99974 .99998 .99995 20 ■44 11 .99923 .99823 .99952 .99889 .99974 .99940 .99989 .99975 .99998 .99995 16 48 12 9.99924 0.99835 9.99952 0.99890 9.99974 0.99940 9.99989 0.99975 9.99998 0.99995 12 5^ 13 .99924 .99836 .99953 .99891 .99974 .99941 .99989 .99976 .99998 .99995 8 56 14 9.99925 0.99837 9.99953 0.99893 9.99975 0.99943 9.99990 0.99976 9.99998 0.99996 4 12h 19m 12h 15m 12h lim 12h7m 12h3m s ' llh 4im 175° llh 45m 176° llh 49m 177 llh 53m 178° llh 57m 179° s 15 9.99925- f 0.99838 9.99953 0.99893 9.99975 0.99943 9.99990 0.99977 9.99998 0.99996 60 4 16 .99926 .99839 .99954 .99894 .99975 .99943 .99990 .99977 .99998 .99996 56 5 17 .99926 .99831 .99954 .99895 .99976 .99944 .99990 .99978 .99998 .99996 52 12 18 .99927 .99833 .99954 .99896 .99976 .99944 .99990 .99978 .99998 .99996 48 i6 19 9.99927 0.99833 9.99955 0.99897 9.99976 0.99945 9.99991 0.99978 9.99998 0.99996 44 fO 20 .99928 .99834 .99955 .99898 .99976 .99946 .99991 .99979 .99999 .99997 40 24 21 .99928 .99835 .99956 .99899 .99977 .99947 .99991 .99979 .99999 .99997 36 f5 22 .99929 .99837 .99956 .99900 .99977 .99947 .99991 .99980 .99999 .99997 32 32 23 9.99929 0.99838 9.99957 0.99900 9.99977 0.99948 9.99991 0.99980 9.99999 0.99997 28 56 24 .99930 .99839 .99957 .99901 .99978 .99949 .99992 .99981 .99999 .99997 24 40 25 .99931 .99840 .99958 .99903 .99978 .99949 .99992 .99981 .99999 .99997 20 44 26 .99931 .99841 .99958 .99903 .99978 .99950 .99992 .99981 .99999 .99998 16 45 27 9.99932 0.99842 9.99958 0.99904 9.99978 0.99950 9.99992 0.99982 9.99999 0.99998 12 52 28 .99932 .99844 .99959 .99905 .99979 .99951 .99992 .99982 .99999 .99998 8 56 29 9.99933 0.99845 9.99959 0.99906 9.99979 0.99953 9.99992 0.99982 9.99999 0.99998 4 i2h ism 12h 14m 12h lOm 1 12h 6m 12h2m s ' llh 42m 175° llh 46m 176° llh 5am 177° llh 54m 178° llh 58m 179° a 30 9.99933 0.99846 9.99959 0.99907 9.99979 0.99953 9.99993 0.99983 9.99999 0.99998 60 4 31 .99934 .99847 .99960 .99908 .99980 .99953 .99993 .99983 .99999 .99998 56 8 32 .99934 .99848 .99960 .99909 .99980 .99954 .99993 .99984 .99999 .99998 52 if 33 .99935 .99849 .99961 .99909 .99980 .99954 .99993 .99984 .99999 .99998 48 i6 34 9.99935 0.99850 9.99961 0.99910 9.99980 0.99955 9.99993 0.99984 9.99999 0.99999 44 20 35 .99935 .99851 .99961 .99911 .99981 .99956 .99993 .99985 .99999 .99999 40 ;g4 86 .99936 .99853 .99962 .99912 .99981 .99956 .99994 .99985 9.99999 .99999 36 28 37 .99936 .99854 .99962 .99913 .99981 .99957 .99994 .99985 0.00000 .99999 32 5:? 38 9.99937 0.99855 9.99963 0.99914 9.99981 0.99957 9.99994 0.99986 0.00000 0.99999 28 56 39 .99937 .99856 .99963 .99915 .99982 .99958 .99994 .99986 .00000 .99999 24 40 40 .99938 .99857 .99963 .99915 .99982 .99959 .99994 .99986 .00000 .99999 20 44 41 .99938 .99858 .99964 .99916 .99982 .99959 .99994 .99987 .00000 .99999 16 48 42 9.99939 0.99859 9.99964 0.99917 9.99983 0.99960 9.99994 0.99987 0.00000 0.99999 12 5:2 43 .99939 .99860 .99964 .99918 .99983 .99960 .99995 .99987 .00000 .99999 8 56 44 9.99940 0.99861 9.99965 0.99919 9.99983 0.99961 9.99995 0.99988 0.00000 0.99999 4 12h 17m 12h 13m 12h9m 12h5m 12h im s ' llh 43m 175° llh 47m 170° llhsim 177° llh 55m 178° llh 59m 179° s 45 9.99940 0.99863 9.99965 0.99930 9.99983 0.99961 9.99995 0.99988 0.00000 1.00000 60 4 46 .99941 .99864 .99965 .99930 .99983 .99962 .99995 .99988 .00000 .00000 56 ,5 47 .99941 .99865 .99966 .99931 .99984 .99963 .99995 .99989 .00000 .00000 52 J?f 48 .99942 .99866 .99966 .99933 .99984 .99963 .99995 .99989 .00000 .00000 48 16 49 9.99942 0.99867 9.99966 0.99933 9.99984 0.99964 9.99995 0.99989 0.00000 1.00000 44 fO 50 .99943 .99868 .99967 .99934 .99984 .99964 .99996 .99990 .00000 .00000 40 24 51 .99943 .99869 .99967 .99934 .99985 .99965 .99996 .99990 .00000 .00000 36 f5 52 .99943 .99870 .99968 .99935 .99985 .99965 .99996 .99990 .00000 .00000 32 ■Sf 53 9.99944 0.99871 9.99968 0.99936 9.99985 0.99966 9.99996 0.99991 0.00000 1.00000 28 36 54 .99944 .9987% .99968 .99937 .99985 .99966 .99996 .99991 .00000 .00000 24 40 55 .99945 .99873 .99969 .99928 .99986 .99967 .99996 .99991 .00000 .00000 20 44 56 .99945 .99874 .99969 .99938 .99986 .99967 .99996 .99991 .00000 .00000 16 45 57 9.99946 0.99875 9.99969 0.99939 9.99986 0.99968 9.99996 0.99992 0.00000 1.00000 12 52 58 .99946 .99876 .99970 .99930 .99986 .99969 .99996 .99993 .00000 .00000 8 56 59 .99947 .99877 .99970 .99931 .99987 .99969 .99997 .99993 .00000 .00000 4 60 60 9.99947 0.99878 9.99970 0.99931 9.99987 0.99970 9.99997 0.99992 0.00000 1.00000 12h 16m 1 12h 12m 1 12h gm 1 12h 4m 1 12h&m 1 TO FIND THE HOUR ANGLE CROSSING THE PRIME VERTICAL Mark the latitude on the latitude scale at the left-hand boundary and, with a pair of compasses, take out the horizontal distance from that point to the curve whose number represents the declination, 7\ppiy this distance to the scale of hour angles, and the re- sulting reading, taken in the same manner as the divisions and propor- tional parts are read from the ordinary diagonal scale of equal parts, will be the hour angle of crossing the prime vertical. ILLUSTRATION From the second example at the be« ginning of this book — L, the latitude=S.34°10' d, the declination =S. 16° 36 The i'me of dashes (a b) indicates the horizontal distance from (a), the point on the latitude scale marking the lati- tude 34° 10' to (b), the point between the declination curve 16° -and the dec- lination curve 17° marking the declina- tion 16° 36'. The distance (a b), being applied to the scale of hour angles, gives the reading 4" 16"" as the value of the hour angle of crossing the prime vertical. n \\ \\ Hoiir Angles < m¥? h=w=M « WWW I0» «»- io» C » 1 ' i h »*• k» •• 55901°— 18. (To face page 156.) TABLE V FOR FINDING THE AZIMUTH RULE. Take out the tabulated number corresponding to the ^iven declination and hour-angle, then find this number again in that declination column which has at its head a value equal to the altitude, and, in the hour-angle column, opposite to the number thus found again in the declination column, will be the required azimuth. MARKING THE AZIMUTH. The azimuth found from the table is always marked east (E.) or west (W.) according as the observed body is to the eastward or westward of the meridian of the observer. If the latitude and decUnation are of different name the azimuth is marked from the pole of opposite name to the latitude. If the latitude and declination are of the same name and the latitude is less than the declination, the azimuth is marked from the pole of the same name as the latitude. If the latitude and declination are of the same name and the latitude is greater than the declination, the azimuth is marked from the pole of the same name as the latitude when the hour-angle is greater than the hour-angle of crossing the prime vertical, and from the pole of opposite name when the hour-angle is less than the hour-angle of crossing the prime vertical. The hour-angle of crossing the prime vertical may be found from the diagram facing this page. ILLUSTRATION. From the first example worked at the beginning of this book — d, the decltnation=S. 21° 19'. t, the hour-angle=3A 30"» 11*. h, the calculated altitude=17° 53'. Take out the tabulated number corresponding to the declination 21° 19' and the hour-angle 3^ 30'", which is 9.86885. Then in that declination column which has at its head a value equal to the altitude, 17° 53' or, to the nearest degree, 18°, find the number 9.86885 again, and opposite to it in the hour-angle column will be 51°, which is the azimuth reckoned from the south pole toward the eastward, S. 51° E. 155 Page 156] TABLE V. The Finding of the Azimuth. 3-2 S83§£32 01>00(NCO C4 C^l CSicO CO O'TOOC^ CO -T- -f< 1" >0 >0 O-f ooc^ o O OO 1-1 i-( O-)"00CVl CO CM CM ocot^ooo» O— KNCO-r 1/5 CO r~ ooo g?5i5ss; ssfiss O— ■CMCO'*" CO CO CO CO CO lOOt^OCO CO CO CO CO CO O -H CM CO nfi "O ■^ 11** "tl -"tl -^ "^ o • r-t 0) © h — OO 2390G 54002 71600 84078 93750 01043 08309 1407G 19153 23687 27780 31608 34929 38088 41020 43754 46314 48718 60984 53125 55163 57078 58908 60651 62315 63904 65425 66881 68277 69617 70904 72141 73331 74476 75579 76642 77G0G 78654 79007 80527 81414 82271 83098 83897 84669 00 00 00 00 OOO OO o OOOOO OOOOO o o o o o o o o o o OOOOO OOOOO o>a3a>o>a>o> 1 b o to — 00 23947 54043 71G41 84119 93791 01084 0S350 14117 19194 23728 27821 31549 34970 38129 41061 43795 40355 48769 51025 53166 55194 57119 58949 60092 62356 G3945 65466 66922 68318 69658 70945 72182 73372 74617 75020 70G83 77707 78695 79048 805G8 81455 82312 83139 83938 84710 00 00 oooo 00 OOO o o O O f^ o OOOOO OOOOO o o o o o OS o o o o o o o o o OOOOOO 1 b "5 — OO 239SG 54082 71080 84158 93830 01723 0S389 14150 19233 23767 27860 31588 35009 381G8 41100 43834 40394 48798 510G4 63205 55233 67168 58988 60731 62395 63984 65605 66961 68357 69G97 70984 72221 734 U 74566 75059 70722 77746 78734 79687 80007 81494 82351 83178 83977 84749 00 00 00 00 ooc3>ai050 o o o o o OOOOO aa^aia^a OOOOO OOOOO o o o o o aa>a>ao> ■ 1 °-5 — OO 24020 54116 71714 84192 93864 01707 08423 14190 192G7 23801 27894 31022 35043 38202 41134 43868 46428 48832 51098 53239 552G7 57192 59022 60765 62429 64018 65539 60995 68391 69731 71018 72255 73445 74590 76093 90766 77780 787C8 79721 80641 81528 82385 83212 84011 84783 00 00 00 CO 00 OOOO OOOOO OOOOO o ooo o OOOOO o o o o o OOOOO OOOOOO 1 § ^ — 00 24062 64148 71740 84224 9389G 01789 08455 14222 19299 23833 27920 31054 35076 38234 411GG 43900 464G0 48804 51130 53271 55299 67224 59064 G0797 62461 64050 65571 67027 68423 69763 71050 72287 73477 74G22 75725 70788 77812 78800 79753 80G73 81560 82417 83244 84043 84815 00 oooo 00 00 o o o o OOOOO o o ooo o o o o o O O OO o o o o o o o o o o o o o ^ ^ o o 1 b o — OO 24080 54176 71774 84252 93924 01817 08483 14250 19327 23801 27954 31G82 35103 38262 41194 43928 4G488 48892 61168 63299 65327 57252 59082 60825 62489 G4078 G5699 67055 68451 69791 71078 72315 73605 74650 75763 70816 77840 78828 79781 80701 81588 82445 83272 84071 84843 00 00 00 00 C30 O O O OS o oooo OOOOO o o o o o OOO o o OOOOO o ooo o o o ooo o 1 — CO 24105 54201 71799 84277 93949 01842 08508 14275 19352 23886 27979 31707 36128 38287 41219 43963 40513 48917 61183 63324 55352 67277 69107 60850 62514 64103 65624 67080 68476 09816 71103 72340 73530 74675 75778 7G841 77865 78853 7980G 80726 81613 82470 83297 84096 84868 00 00 00 00 CO 002 05 05 OOOOO o o o o o o o o o o O O O O OS OOOOO o o o o o OS o o o o o 1 1 — OO 24 120 54222 71820 84298 93970 01803 08529 1429G 19373 23907 28000 31728 35149 38308 41240 43974 40634 48938 61204 53345 56373 57298 59128 60871 62625 64124 06645 67101 68497 69837 71124 72361 73651 74696 75799 70862 77886 78874 79827 80747 81034 82491 83318 84117 84889 oooo 00 00 OOOOOO OOOOO OOOO o OOOOO o o o o o OOOOO o o o o o O O O O O O 1 b — OO 24145 64241 71839 84317 93989 01882 08548 14315 19392 2392G 28019 31747 35168 38327 41269 43993 40653 48957 51223 53364 55392 57317 59147 60890 62554 64143 65664 671 20 68516 69856 71143 72380 73570 74715 75818 7G8S1 77905 78893 7984G 807G6 81063 82510 83337 84136 84908 00 00 00 00 OOOOOO o o o o o o o o o o o o o o o OOOOO o o o o o o o o o o o o o o o o 1 — 00 24160 54266 71854 84332 94004 01897 08563 14330 19407 23941 28034 31762 35183 38342 41274 44008 46568 48972 51238 53379 55407 67332 69162 60905 62569 64158 66679 67135 68531 69871 71158 72395 73585 74730 76833 70896 77920 78908 79861 80781 81008 82526 83362 84151 84923 00 00 00 00 OOOOOO o o o o o o o o o o a o o o o o o o o o OOOOO o o o o o o oooo o 1 — OO 24171 542G7 718G6 84343 94015 01908 08574 14341 19418 23952 28045 31773 35194 38353 41285 44019 46679 48983 61249 53390 65418 67343 69173 60916 62580 64109 05690 67146 68542 69882 71169 72406 73596 74741 75844 70907 77931 78919 79872 80792 81079 82530 83303 84162 84934 00 00 00 00 OOOOOO O OOO o o o o o o OS OOO o OOOOO OOOOO o ooo o OOOOOO 1 — OO 24179 64275 71873 84351 94023 01916 08682 14349 19426 23960 28053 31781 35202 38361 41293 44027 46587 48991 51257 53398 65426 57351 59181 60924 62588 64177 66098 67154 68550 69890 71177 72414 73604 74749 75862 70915 77939 78927 79880 80800 81087 82544 83371 84170 84942 00 00 00 00 00 o o o o o o ocs o o ooo o o o o o o OOOOO o o o o o OOOOO oaaxxaa^ —00 24184 54280 71878 84366 94028 01921 08587 14354 19431 23965 28058 31786 35207 38366 41298 44032 46592 48996 51262 53403 55431 57356 59186 60929 62593 64182 65703 67159 68565 69895 71182 72419 73009 74764 76857 70920 77944 78932 79885 80805 81092 82549 8337G 84176 84947 00 00 00 00 00 OOO o OOOOO OOOOO OOOOO OOOOO o o o o o OOOOO ...... o — OO 24186 64282 71880 84368 94030 01923 08699 14356 19433 23907 28060 31788 35209 383G8 41300 44034 46594 48998 51204 53405 56133 57358 59188 60931 62695 64184 65705 67161 68557 69S97 71184 72421 73611 74766 75859 70922 77946 78934 79887 80807 81694 82551 83378 84177 84949 00 00 oooo ooo OO o OOOOO o o o o o OOOOO OOOOO OOOOO o o o o o o o o o o o Hour < o Oi-clNCO-Tji «5 CO l^ 00 O O-HNCO'*" W3COt~000 sssgss sssss CO CO CO CO CO toot- ooo CO CO CO CO CO O i-H CO CO Tf* to ^ ^ 1^ ^ ^ -^ tH 1-1 1-1 i-( t-t l-< 1-1 1-< 1-1 1-1 S^cscoco s^^ss o-f ooe^ico ooo i-irt O 't'OOCM o CM CM Oi CO CO O-fOC CMCO O-^ GO CM CO Soort-H CM C« CM CM CM CMCqCMC^CM O -^ OOCM OO Tf -^ -^fi to to o TABLE V. The Finding of the Azimuth. Page 157] "I c o -!r 00 c-1 CO S OOO— I-H »< CO CO CO CO CO O-rP 00 cs CO CSCS csco CO CO CO CO CO CO O -^ OOCS CO •^ -<}♦ -v to to CO CO CO CO CO o -«f 00 csco OOO— ( ^ O -^OOC^CO (MC^ CO COCO ■^ T}1 ..^ T^ «t4 O -0 "O o lO »0 »0 «0 to CO . lOCOf^OO OS o^cqco-»i» to to to to to to CO t^ OOO to to to to to o^csco-^ OCOO CO CO lOO r^oo Oi o — < coco -^ t^ t^ t^ t- 1- LO CO t^ OC o> 1- 1- 1- 1^ w o^csco-^ 00 00 00 00 00 to CD r^ OO OS o 00 00 00 00 00 o> a .2 .2 'o <» Q 9.84669 9.85413 9. 86133 9. 86827 9. 87498 9.88145 9. 88770 9. 89373 9. 89955 9.90516 9.91056 9.91577 9.92079 9. 92562 9.93027 9.93473 9.93902 9.94313 9.94708 9.95086 9. 95448 9.95793 9. 96123 9.96437 9.96735 9.97019 9. 97287 9.97541 9. 97780 9.98004 9.98214 9.9S410 9. 98592 9.98760 9.98915 9.99055 9. 99182 9.99295 9. 99395 9.99481 9.99554 9.99614 9.99660 9.99694 9.99713 9.99720 « 9.84710 9.85454 9.8G174 9.86868 9. 87639 9.88186 9.88811 9.89414 9. 89996 9. 90557 9.91097 9.91618 9.92120 9.92603 9.93068 9.93514 9. 93943 9. 94354 9.94749 9.95127 9.95489 9.95834 9. 96164 9. 96478 9.96776 9.97060 9. 97328 9. 97582 9.97821 9. 98045 9.98255 9.98451 9.98633 9. 98801 9. 98956 9.99096 9.99223 9. 99336 9. 994.36 9. 99522 9.99595 9.99655 9. 99701 9.99735 9. 99754 9.99761 b w 9. 84749 9.85493 9.86213 9. 86907 9. 87578 9. 88225 9.88850 9. 89453 9.90035 9.90596 9.91136 9.91657 9.92159 9. 92642 9.93107 9.93553 9.93982 9.91393 9.94788 9. 95166 9.95528 9. 95873 9.96203 9.96517 9.96815 9.97099 9. 97367 9. 97621 9. 97860 9.98084 9.98294 9. 9S490 9. 98672 9.98840 9.98995 9. 99135 9. 99262 9. 99375 9. 99475 9.99561 9.99634 9. 99694 9. 99740 9. 99774 9. 99793 9.99800 9.84783 9. 85527 9.86247 9.86941 9.87612 9.88259 9. 88884 9. 89487 9.90069 9.90630 9.91170 9. 91691 9. 92193 9. 92676 9.93141 9.93587 9.94016 9.94427 9. 94822 9.95200 9.95562 9.95907 9. 96237 9.96551 9.96849 9.97133 9.97401 9.97655 9. 97894 9.98118 9. 98328 9.98524 9.98706 9. 98874 9.99029 9.99169 9.99296 9. 99409 9. 99509 9.99595 9.99668 9. 99728 9.99774 9. 99808 9.99827 9.99834 b 9.84815 9. 85559 9. 86279 9. 86973 9. 87644 9.88291 9. 88916 9.89519 9.90101 9. 90662 9.91202 9.91723 9.92225 9.92708 9.93173 9.93619 9.94048 9.94459 9.94854 9.95232 9.95594 9.95939 9.96269 9.96583 9.96881 9.97165 9. 97433 9.97687 9. 97926 9.98150 9.98360 9.98556 9. 98738 9. 98906 9.99001 9.99201 9.99328 9.99441 9.99541 9.99627 9.99700 9.99760 9.99806 9.99840 9. 99859 9.99866 1 84843 85587 86307 87001 87672 88319 88944 89547 90129 90690 91230 91751 92253 92736 93201 93647 94076 94487 94882 95260 95622 95967 96297 96611 96909 97193 97461 97715 97954 98178 98388 98584 98766 98934 99089 99966 69966 69166 95866 62266 99728 99788 99834 99868 99887 99894 O OOOO o o o o o O OO o o o o o o o 0>0.C6C»0> O OOO o o o o o o O O O O O O O O OOO © CO ?5 9.84868 9.85612 9.86332 9.87026 9.87697 9. 88344 9.88969 9.89572 9. 90154 9.90715 9.91255 9.91776 9.92278 9.92761 9.9322C 9.93672 9.94101 9.94512 9. 94907 9.95285 9.95647 9.95992 9.96322 9.96636 9.96934 9.97218 9.97486 9.97740 9.97979 9.98203 9.98413 9.98609 9.98791 9. 98959 9.99114 9.99254 9.99381 9. 99494 9.99594 9. 99680 9.99753 9.99813 9. 99859 9.99893 9.99912 9.99919 1 « 9.84889 9.85633 9.86353 9. 87047 9. 87718 9.88365 9. 88990 9.89593 9.90175 9.90736 9.91276 9.91797, 9.92299 9. 92782 9.93247 9.93693 9.94122 9.94533 9.94928 9.95306 9.95668 9.96013 9.96343 9.96657 9.96955 9.97239 9. 97507 9.97761 9.98000 9. 98224 9.98434 9. 9S630 9.98812 9. 98980 9. 99135 9.99275 9. 99402 9.99515 9. 99615 9.99701 9.99774 9. 99834 9. 99880 9. 99914 9. 99933 9. 99940 b 9.84908 9.85652 9.86372 9. 87066 9.87737 9.88384 9. 89009 9.89612 9.90194 9.90755 9.91295 9.91816 9.92318 9. 92801 9.93266 9..93712 9.94141 9.94552 9. 94947 9.95325 9.95687 9. 96032 9.98362 9. 96676 9. 96974 9.97258 9.97526 9. 97780 9.98019 9.98243 9.98453 9. 98649 9.98831 9.98999 9.99154 9.99294 9.99421 9. 99534 9.99634 9.99720 9.99793 9.99853 9.99899 9. 99933 9.99952 9.99959 1 9.84923 9.85667 9. 80387 9. 87081 9.87752 9. 88399 9. 89024 9.89627 9. 90209 9.90770 9.91310 9.91831 9.92333 9.92816 9.93281 9.93727 9.94156 9.94567 9.94962 9.95340 9.95702 9. 96047 9.96377 9. 96691 9.96989 9.97273 9.97541 9.97795 9.98034 9. 98258 9.98458 9. 98664 9.98846 9. 99014 9.99169 9.99309 9.99436 9. 99549 9. 99649 9. 99735 9.99808 9.99868 9. 99914 9. 99948 9.99967 9.99974 1-1 9.84934 9.85678 9. 86398 9. 87092 9. 87763 9.88410 9. 89035 9.89638 9.90220 9.90781 9.91321 9. 91842 9. 92344 9.92827 9.93292 9.93738 9.94167 9.94578 9.94973 9.95351 9.95713 9. 96058 9.96388 9. 96702 9.97000 9.97284 9.97552 9.97806 9.98045 9.98269 9.98479 9.98675 9.98857 9.99025 9.99180 9.99320 9.99447 9.99560 9. 99660 9. 99746 9.99819 9. 99879 9. 99925 9.99959 9.99978 9.99985 1 1-1 9. 84942 9.85686 9. 86406 9.87100 9. 87771 9. 88418 9.89043 9. 89646 9.90228 9.90789 9.91329 9.91850 9. 92352 9.92835 9.93300 9.93746 9.94175 9.94586 9.94981 9.95359 9.95721 9.96066 9.96396 9.96710 9.97008 9.97292 9.97560 9.97814 9. 98053 9.98277 9.98487 9.98683 9.98865 9.99033 9.99188 9.99328 9.99455 9.99568 9. 99668 9.99754 9.99827 9. 99887 9.99933 9. 99967 9.99986 9.99993 1 O 9.84947 9.85691 9.80411 9. 87105 9.87776 9.88423 9.89048 9.89651 9.90233 9.90794 9.91334 9.91855 9.92357 9.92840 9.93305 9.93751 9.94180 9.94591 9.94986 9.95364 9.95726 9.96071 9.96401 9.96715 9.97013 9.97297 9. 97505 9.97819 9. 98058 9. 98282 9.98492 9.98688 9.98870 9.99038 9.99193 9.99333 9.99460 9. 99573 9.99673 9.99759 9.99832 9.99892 9. 99938 9.99972 9. 99991 9. 99998 o 9. 84949 9. 85693 9.86413 9.87107 9.87778 9.88425 9.89050 9. 89653 9. 90235 9. 90796 9.91336 9.91857 9.92359 9.92S42 9.93307 9.93753 9.94182 9.94593 9. 94988 9. 95366 9.95728 9.96073 9. 96403 9.96717 9.97015 9.97299 9.97567 9.97821 9.98060 9.98284 9.98494 9.98690 9. 98872 9.99040 9.99195 9.99335 9.99462 9. 99575 9. 99675 9. 99761 9.99834 9. 99894 9.99940 9.99974 9. 99993 10.00000 S-2 a toco t^COO -«' -9< -^ ■<»< -sr to CO t^ 00 o lO to to to to O — 1 Cl CO- lO eOh.. 00 Ci CO CO CO =00 O-i coc^ -r t- 1- 1^ t- 1~ O -^ CO CO -^ 00 00 OCOO OC to CO r* OOO o 00 00 CO 00 00 o S 3 < s^' ^ 2! SS "^^ =^ «> OOO— 1 i-( ^ CO coco CO CO O-^COC^co C«C^ CSCOCO CO CO CO CO CO O Tf 00 CS CO ■V-^ '^ to to CO CO CO CO CO O-9<00IMc0 OOOrt-1 ■^ -^ -^ -^ TJ« O-^OOlMO O^CICO'^ »OCOb-0OOl O'-^CflC icoi^ooos Oi-HC^eo-^ »r>or>-oooj C^CSC-JMC^ C^CSCSCICS COCOMCCCQ COMCOCOCO OOOOCCOO OOOOdOaO 0> A O) o> o 03 O O) 0& O 0^0 05 0^ Od Od O O) OS 03 O O O O O O Oi Oi Oi O O) 0> O) 0> Oi OaO^O^OdOdOb CDC^OQO OC205COPO r*oc _ ) CO O CO 005- t^-^i-li-HO 05(N':D^t>- t^ -^ 1-* 00 h* Ci Id lO lO *0 lO JCJ'ifOO COCIOiOOJ OlOOOt^C^J -^COCSi-Hi-tOO o ss 00O'-'(NC0 ^ lO ^ t " <£! o ^ t^r*t^ t r-t^t>-t^t- OOOOOOOO OOOsOJOiOi OOSOiOiOi O O 03 O^ Od O) 03 O Oi C^ O Oi G^ O^ C) O^ O^ 03 OS O) 0> OiOiOiO^Oi ycococ I wot OSMOOiOC^ CO 1-1 t^ CO 00 OOOi-l'-t OOOOOOOO OOOiOOiOS CDOS t^OOb- OOt^OCN 00 Oi-<^ CO'*** CO t^ -^ t>- (M (M coco CO O O) o> O^ O) c<> »o r- o "5 »0»QTtlC0O M tH :5 C6 S -^co-^o^o fH OC-IOOt^ 1>>COOOC^ CO CO CD to ^ "^ ,-HO^cor- gcoio cwr-iiccoo ^coot^toe t^'«* O Oi Oi Oi OiOi Oi Oi OiOiOi Oi OiCi Oi O^Oi I N*ot^co OOOOOOOO lOOO"^ i-< 00 C^i-(00iC(N cs 1-H r^ lo ) lOOOCq O»0C0i^ ■*t*oo6o OOSOCOCl C^OiOt^OiC»0 Oit^»-tOiO t^eocScot^ Ocoooooi O) 0> O) Oi o or^i^t>-t>- t>-t*t>.t S o r^ 00 S 5 OOt^ *CCO*-* OS OS OS O) Oi OS OS OS OS OS OS OS 0> 02 a OS coos r-^io t^Or^ooos t>- 1-- !>• r^ r- OS OS OS OS OS >oot6"*N toooOc OS OS OS 09 OS O^ 1-4 t^lO CO (v, ^ ^ OS giOcDC^cO I C^iOt^OO iCOO'i^^OO cor5osot^ CO »H r-- CO 00 OSOO— IT-H 3 1-1 lOt CO r* 1— I -^ r^ csjc^cococo »0 OS OS CO OS CO oc- OO -, , - - COi-lt^COOO cot^^-^t^ OSOOi-l*-l C^CNJCOCOCO StP^OO^ CO OS OS CO r^Ttios CO CO uocooooo^H w5Tf*io^Hr^ b* ""jf »H 1-1 o osc^co^t-^- ^~ -^ i-i oo f^ ca QCOOOOCO OS00OC0»O OS00-< *~ -~ " (M-^COOOQ t-tCOiOcOt^ UD ut LO U3 O cOcOcOcOcO OS Oi— I CO -^ lO O - (£> t^ t^ r* t>, i>.t^t^t^t-, »0 i--l>- coco^coco ^^ooSti^ lOCOt^OOOS S^^c^c^co OOcOOS OSCOCOQOS— t — OS Tl« CO lO •-< ^ CO •-* OOOSOSOSOS OSOSAOSOS OSOSOOSOS OSOSOSAO^ OSOSOSOSOS OSOSOSOSOS OSOSOSOSOS OS^CSOb^O^ COCflOOO . ooot- J h- 00^ 00 OCOOSCOCO lO ^ oi-^ lO lO ■^--tooos CO i-ioo coco OS OO^i-t 00 OS OS OS OS 500OS 00 O^-^OO** 0& OS OS OS OS OS OS OS OS OS lO CO CO 00 1-1 OS OS GO t^ "^ . OS (M — * r* OS OS ^o OS OS OS OS OS OS Oi OS OS O OCi i-tr-icco > l>.O0 -rf OS lOoo^vHao 3 CO CO r>- OS icososcoos Qoocococo ooaoco00CS»OQ r^iOC^Qi-l J CO CO <— • ^ CO '-' CO ^ OS Cl»Ot^00 OsOO'-H'-t OOCXiodoO OOOSOSOSOS OOOCOCOCO OOSOCDC5 ^<5SPS5^ C^iOCO'l^CO vocsoscoos ...^_ _.- T^coooo-^ r-ocDt>-co ooococoo r^iooococo COI^-^OOO ~ — ~r K — COf^ ^ -^ 00 CS CQ cococo OsOwOSOSOS OSOSOSOSOS OSOSOSOSOS OSOSOSOSOS OSOSOSOSOS lO 00 oca 'i* CSSOCSCO'^ COt^I>-l>t- O O CO CO lO lOcO t^OOOS i>-i> t^r- 1^ OS 09 OS OS OS C^ OS CD CO CI ^ 00 O CS »0 'O CM ■*t< CO CS o oo cp 00 00 00 CO 00 CO OS OS a OS OS OS r^OOOOsoO Ot^-^OOtJ* iOCOOOOOfH lO^iC— It* t^^i-(f-HCO OSCSCD^b- t--'^*-<00t*^ OOOOOC^OO CSiO'-t-— lOO Cli0t--0"5 1-HOCSOQr* i-«Q'*COt^ t--TjJcOioQ C'X)0 lO-^csoooS cot^i-i^oo 1— (cocDooo co'f5t-ooo cscoococo osooico-^ *oot*ooos Qri?!3C5!?93! cscscococo ^rti-<3*'^u5 *r5ou^io35 cococococo cot-r^t-t- l^i^t^t^r- oooooooOoOoo OOOOOOOO OOOSOsO^OS OSOSOSOSOS OSOSOSOSOS OSOSOSOSOS OSOSOSOSOS OSOSOSOSOS OSOSOSOSOS OSOSOsOiOSOs 5 w) 0'-t Tjt TT -^ -^ -^ Oi-cno>oo> OS OS OS OS Cs OS OS OS OS OS OS OS 05 OS Oi OS OS OS OS OS Cs OS CS OS OS osososososos 1 n 84008 84812 85532 86226 80897 87544 88109 88772 89354 89915 90455 90970 91478 91901 92420 92872 93301 93712 94107 94485 94847 95192 95522 95830 90134 96418 90080 90940 97179 97403 97013 97809 97991 98159 98314 98454 98581 98094 98794 98880 98953 99013 99059 99093 99112 99119 03 05 0J0105 Cs OS OS OS Cs 0> OS Cs C3S OS OS OS OS OS OS ooifficno OS OS OS Cs Cs 03002 05 OS OS Cs OS OS OS OS OS cs cs 1 b o 1-1 84144 84888 85008 80302 80973 87020 88245 88848 89430 89991 90531 91052 91554 92037 92502 92948 93377 93788 94183 94561 94923 95208 95598 95912 90210 96494 96702 97016 97255 97479 97689 97885 98007 98235 98390 98530 98057 98770 98870 98950 99029 99089 99135 99109 99188 99195 03 0>0S0>0> OSCVCIOO: OS OS OS OS Cs Cs O CS O Cs CS CS OS OS OS OOOOOl OS CS OS OS OS OS OS O OS OS C; OS C3S CS OS OS 1 b CO © T-l 84216 84960 85680 80374 87045 87692 88317 88920 89502 90003 90003 91124 91026 92109 92574 93020 93449 93860 94255 94633 94995 953'10 95070 95984 90282 90506 96834 97088 97327 97551 97701 97957 98139 98307 98402 98002 98729 98842 98942 99028 99101 99101 99207 99241 99200 99207 OS OS OS O CTS OOOTOCR OS CS CS CS Cs CS OS Cs Cs OS OS Cs CS OS Cs OS Cs OS Cs Cs CS Cs OS CS Cs 02 O C: 05 05 Osososososos 1 b o o 84284 85028 85748 86442 87113 87700 88385 88988 89570 90131 90671 91193 91694 92177 92642 93088 93517 93928 94323 94701 95003 95408 95738 90052 96350 96634 96902 97156 97395 97619 97829 98025 98207 98375 98530 98070 98797 98910 99010 99096 99109 99229 99275 99309 99328 99335 OS OS OS OS OS OS OS OS OS OS cno:.0>0i0 OS CS Cs Cs OS OS CS C; CS CS Cs CS OS OS Cs OS CS OS OS Cs OS OS OS OS OS C< Cs OS OS OS OS 1 b n 84349 85093 85813 80507 87178 87825 88450 89053 89035 90190 90736 91257 91759 92242 92707 93153 93582 93993 94388 94766 95128 95473 95803 96117 96415 96699 96967 97221 97400 97084 97894 980S0 98272 98440 98595 98735 98862 98975 99075 99161 99234 99294 99340 99374 99393 99400 OS 05 CS O OS o> o cv o o 0> OiOiOi Cs OS OS OS OS CS cs OS OS OS OS OS OS OS Cs OS Cs OS Cs CS OS Cs Cs OS OS OS OS OS OS OS cs 1 b o c 84411 85155 85875 86509 87240 87887 88512 89115 89097 90258 90798 91319 91821 92304 92709 93215 93644 94055 94450 94828 95190 95535 95865 90179 90477 96761 97029 97283 97522 97746 97956 98152 98334 98502 98657 98797 98924 99037 99137 99223 99290 99356 99102 99436 99455 99462 OS O CS CS OS OS OS OS OS CS OS OS OS OS OS Cs Cs OS OS OS OS OS OS CS OS OaCDCnO Cs CS CS Cs OS Cs OS OS CS OS OsCsOsCSOsO 1 b 05 84469 85213 &5933 80627 87298 87945 88570 89173 89755 90316 90850 91377 91879 92302 92827 93273 93702 94113 94508 94886 95248 95593 95923 96237 96535 96819 97087 97341 97580 97804 98014 98210 98392 98560 98715 98855 98982 99095 99195 99281 99354 99414 99460 99494 99513 99520 O OS OS Cs OS OS OS OS OS OS O CS OS OS CS OS CS CS OS OS OS OS O Cs O o=o>ao=o= OS OS OS O; OS Oi 05 o Oi ro OS OS CS CS Cs C 1 b o 00 84524 85208 85988 80082 87353 88000 88625 89228 89810 90371 90911 91432 91934 92417 92882 93328 93757 94108 945C>3 94941 95303 95648 95978 90292 90590 96874 97142 97396 97635 97859 98069 98205 98447 98615 98770 98910 99037 99150 99250 99330 99409 99409 99515 99549 99508 99575 OS OS a OS OS OS OS OS 0> OS OS O^ OS OS 0> OS OS OS OS OS OS OS OS OS cs OS OS OS OS OS OS OS OS OS OS OS OS OS OS OS Oi Oi Oi crt cTi Ci 1 b w 84570 85320 86040 80734 87405 88052 88077 89280 89802 90423 90903 91484 91980 92469 92934 93380 93809 94220 94015 94993 95355 95700 90030 90344 90042 96926 97194 97448 97687 97911 98121 98317 98499 98667 98822 98902 99089 99202 99302 99388 99401 99521 99507 99001 99020 99027 esojooJOJ OS Oi OS OSOl OS OS OS OS OS OS OS OS OS o OOSOS OS OS OS OS OS OS OS Cs OS CS OS OS o c C-. o o C^ OSCSCR Oi 1 b o 84624 853(i8 86088 80782 87453 88100 88725 89328 89910 90471 91011 91532 92034 92517 92982 93428 93857 94208 94603 95041 95403 95748 90078 90392 96090 96974 97242 97496 97735 97959 98169 98305 98547 98715 98870 99010 99137 99250 99350 99436 99509 99509 99615 99049 99608 99675 O) a OS OS OS OS OS OS OS OS OS OS OS OS OS OS OS OS OS OS OS OS OS OS Cs OJOlOOiOi a a: a a a: Ol 05 Ci cs o a: o> ci 01 0-- 1 b CO 84669 85413 80133 80827 87498 88145 88770 89373 89955 90510 91056 91577 92079 925(i2 93027 93473 93902 94313 94708 95086 95448 95793 90123 90437 96735 97019 97287 97541 97780 98004 98214 98410 98592 98700 98915 99055 99182 99295 99395 99481 99554 99614 99660 99694 99713 99720 OJOcaoo CSOS OS OS OS O^ Oi 0> Oi C^ OS OS CS OS OS 03 0^ O^ Oi 05CS OS OS OS OC5 05 0JO O CSOS CsOi OS CS OS c:s CT- c?j li B 1 Of csco-* to to to to to lO »0 "5 lO o S3SS3 S :oo coo O^HCS CO-* O-^CS CO-* 0000000600 OTOOOOOOOO OS ~ O -r » M --3 Sooo — -. o-*oocso CSCSCSCOCO O-5>00(NO 8S§£22 C^» C^ (>» CO CO o-^oocs o M- TT M- to to O-^OOCVUO OOO— -^ CS^CSCOCO O-^oocso ■*r -* 'tr to to Page 160] TABLE V. The Finding of the Azimuth. 5-2 w5 OOOi-Hi-i CSiMC ?C^!£> OM*00«O 0->t to ^h- OOOl O^ ( CO CO CO CO CO lOOt^OOOS Oi-HMC 1-H b-Xf^CO CD I - CO 1^ I C^ lOcO 00 06060606 ^OO-^^ 00 C^ if^CO -^ CO o o> c^ -^ o 1-no ai iM 10 CS C5 C^ CO CO O O O 03 o> CO "lO C<) CO 0> -n" CD Oi c^ o f- -r O T CO CO (Xi 1^ O CO CO .-H -r CD 00 O (M -ti CO QO CO -r -f M" rj« 10 lO »0 lO »o o^ o oi O) O) O) 93 o^ o OCSOCON CO^-H -rO'^ OcD— i 10 CO CO CO CO CO Oi pi Qi Oi Oi WOiCOCO rH CO --^ 1-0 -^ a> __ COCOCOOrH ^.-Hec-r>o r- CO Oi <-« c^ 01 "O OOCD 04 0> 0> 03 O Od 0> 0>OiOi Oi Oi Oi ost*»o t^ o ^ 2 5 S 1 C CO lO .^^\Of-H COC^^r-CO cOOcOCOCO t^ O CN 10 03 coco 1-H 1006 iCS CO CO CO " 00 00 0> Oi O Oi Oi 0> Oi Oi Oi Oi OiOi Oi 0 00 t^ O CN 10 <* 05 O 01 I^ OcO -f to QO 10 if5 »^6 10 O) o^ o o^ o> Cl—lC^OO-t^ CO iO r^ (M w 1— ( t- d r- 1— I 0--< CO n- CO = S8gKg5 1 00 Si 1^25 coos CO"-* -^ C^O0i-l OiO CO -t" 10 CO t^ '^ •-< 00 lO ^J* CO 1^ CO --• -^r -r T-H Sc^ —* (^ r- io 01 00 --H M t- t-- CO 00 00 00 05 d 01 o 01 Oi N OOcOtJ* 00l-t-»O 00 01 lO o r-H r-H Oi "M I C^ iO CO 00 06060606 «0 OS ift C^ OS CO CO ft OS CO cs t- _ O 00 O CO CO t- -^ OS O 1r-« >o OS (M CO O "^ COOO'tO ,-t OS CO OS CS CO OSCSO'-Hi-H C^ CS OS O) OS OS OS OS 't "^ t-* _ ?4 >0 ofo (N »-< ^ 000 CO ^H CO »Q CDOO lO »0 lO 10 »o OS OS OS OS OS O •-< CO '^ -O) CO '^ •:_ CO CO CO CO CO OS OS OS OS OS COOt^ t^CM OS og^ o»o lO CO W CO '^ t^OOO*-'Co CNi c^ r-. 1-H o T CO r— r- OCN -r»0 I-OSOrH (N CO CO r^ t- t— OS OS OS OS OS OCOI^»0 00 00 -r CO »C O CD r- I'- t— r- CO -^ 10 CD r- t--r* r- t- t— OS OS OS OS OS COiOCSOsOOO csrwt--: — CO 10 CO- CO OS O"- CS r-l t— OS 01 t CO 10 CO .-H 01 1- t— I— 00 00 CO 00 OS OS OS OS OS OS oo-*tS^o 9?^c3os?5 I C^ 10 CO GO C^iOt-HOOtO OSC<»Oi-<0 Ncocooco r- CO CO 01 1-- o o CO o i-H ■n' r^ CO -^ o OSOO'OC^CO OSOt-'— ICO CSOSiOOiCS r-- OS OS OS OS OS OS OS O^ OS OS OSOCOOOS 1-H ■^ CO OS C^ 1-H OS t- CO ■^ CO I-H 00 coos O1-H (NC^ i- i>- 00 00 00 00 OS OS OS OS O OS COC^IOOO I C^ 10 CO CO 06060606 I-H OS 06 -^ W OS OOscO -^ '^ OS OS O •-< -H M oi -r CD c<» ^ CO OS CO CO '^CO-'J* iOCO0000i-t COCiuOiO C^ „ _- . CO O CO O CO -T* f - OS CJ Tf h- OS 00 00 OS OS OS ososososos OS OS OS OS OS 10 »o idO »o OS OS OS OS OS »C -^ lO »-H t— 10 Tt* CON <-< CO N r- c^ CD O N COIOCO CO CO CO CO CO I— OS O^ (N OS OS OS OS OS • CO CO coco t- t— l— OS OS OS OS OS OSNCO'^t- 1-H 00 o cb -^ OS OS O Os c» CO -^ CD CO t- t- I— t— 1~» r- OS d OS OS OS t— ■»?• 1-H 00 r- OS CD »C ^ CO coo 00 r- CO -^ N o 000s Or-t NCO t-t- 00000000 OS OS OS OS OS OS ocorfN SCO LO »0 CO co-t OiO , NNOCq W O t- 00 'h-COOt- 1-H -t* N CO N M'OOOONOO 5OSCDCOO ■^C0cO00'«t« " "■ — ' — i-HN05coto "n'Nr-i-H- OSOOi-ii-l INNCOCO co-^-^-^Tp t~- OCOCO o *0 CO »0 CO r-H » CD OS CO CO OS N "^ t- OS »-H CO »0 t 00000000 OOOSOSOSOS ososososos OSOSOSOSOS 10 iC lO lO lO OS OS OS OS OS OsoOOSiOi-t *-<00i0U5O COCOC COLOt—COCO t- lO OS OO CO CO OS c t-- CO CO CO t— O CO "^ t^ OS O O »■ ONCOlOCO OOOSO1-HN -^vOC CO CO ^ CO o CO CO t-- t— t— t— r^ I 1-H 00 lO N i-# CO 00 CO N^ 10 M OS 00 t- »0 CO 1-H QO OS O 1-H d CO t- t* 000000 00 ososososos ososososos ososososos OS OS OS OS OS OS OOTf (N 8t-- coco -n* -Tj^lO-HCO , (NC^OlM I Nor-oo 06060606 '^ »— COOl^ co N CO CD r— . OS OS OS OS OS coco O 00 1-H rf O CO '-' f^ 1-H C^ N N^H '^r lioco t- 00 1-H OOiON^cO OS t— CO CD CO CO O^oOco-T-N OS OS O .-H N CO t-t- 00000000 OS OS OS OS OS OS I N*0 t-00 1-H '^ot-'n* N t-H 00 *f lO »0 lO »C W3 OS OS OS OS OS cp»iO CON 00 00 t- OS 10 Tp OS 10 o »0 OS ON -1- IC CO O CO CD CO O OS OS OS O OS OOlONNr- OS OS OS OS OS Oco r— »« CO lO »-t CO N t- - — )e^ N CO CO CO < ■^ o CO r- ou OS OS OS 0> OS OOiQNOSOOO OS 00 T* CO CO -^ »-H ocb t— 10 CO OS O Q—* N CO t- 00 00 kjO X 00 OS OS OS o) OS o:> OCD-^N Y NNON 06060606 ■»*(— COOb- N 1-H 00 U-? N iQ ^ OCCOS Nor- Nt- OSOOi-Hi-H 00 OS OS OS OS 1-H-^NCON '^OOOONOO Ost-NN S to CO OCO ■-j< lO N t— 00 NcO OcO CO NNCOCOCO OS OS OS OS OS OS N cO OS lO r- tQ o -^ t— OSN 10 t- OS CO ^ "^ '':J' ^ CfS N *0 CON 000s coco 'Tf' 1-H CO u5 I— 01 lO >0 to lO^O d OS OS OS OS ososososos OS coos liO 1-H 00 t- OS lO 10 OcDi-H O O 1-H N'T »0 t- CO CD O CO CO OS OS OS OS Os th ooio»r;o OS t-1-H 0»0 MO^i-H N coco t- t- t- OS d OS OS O) eOcDOOOi-H 1-H CO »C N 1-H CO iO 1-H TT N 00 O QO "»?' r- r- -^ CO'q"*'^CO COi-HOCOCp'^ ■Tj< 10 CO t— 00 OS O -H 1-H N CO t-t-t-t-l— t-0000000000 O OS O) d CS OS OS OS OS OS o> OCD-^N 00 t^ t-iO 8r- co'fos NNON I Nior- GO ON r- GO 06060606 •^ t— coot- N — ( 00 to N CO to 1-H 01 o NO t-NoO OSOOi-Hr-H 00 OS OS OS OS ^H-^NCON -^COOONOO Ost-NNtO cOtOcOOcO OS N 00 OS to OS C^ to CO N OS O 01 1— »0 ,,^^_,, _-., .- _- i-H-7OCOCD <7SNtOt-Os OS00OS»O»-l CO t-CSVOiO 1-H t-NI—i-H r-tN"^tOr- CO CD CD CO CO ososososos Ososososos Ososososos Ososososos 1-H OOiO^OO OS t— 1-H OiO ■rr r- ONco 00 OS 1-H NCO CD CD t— r- 1— OS OS OS OS OS O CO ■^ t— t— "^ -5" N^H OS r-io OSQi-Hi-HNcO t— 0000000006 OS P) OS O) O^ OS OS 0> OS OS OS CO -4 N N O t— CO CO OSOO--Hr-4 00 OS OS OS OS OCOi-HN»-4 »o -f t- OS to INCOCOCO OS OS OS OS OS CDN tOt— o rr '^^ 'tj*'^ lO OS OS OS OS o> 00 co^^ -^ GO »-H If* t- 1-H i-hN^hosI- N '^CO t— OS iO to to to to OS OS OS OS OS 00 t— 00 M* o t- CD CO TT' 'ft* CO OS -^ OS CO I-H N -^ to t— CO CO CO CO CO OS OS OS OS OS . Tt* -f O) NiOOSt-O CO OS N CO to COOS ^ c5 CO CO CO t- t- I— OS OS O OS OS Ot--^^ ON OS t— CO CD «© CO to '^ CO1-H ^ t- OSQ^H-Hi-H l^^ Nto O-'I'OOMcOO TABLE V. The Finding of the Azimuth. [Page 161 s^ O M* OQ C^ CO O f OO C^ CO 0^*00 0^(0 O "f 00 C^ eO C^ C^WCOCC OOO^-i^ cscsc^coeo "^OOC^tO O-^OOM^D O-*00C^tD 0"^QOC<«DO f-«riOiO 000»-«i-t C^C^CSCOCO Tf'^'«ri0«30 »0 - OO Oi O »-< W CO ^J' jcpr-ooo or-*c:?M:T "255!::?e55 Pr^?'?^;*' ''^fot~£?«' S:^S25S:7; ^JS^SS^S to LQ to O us lO^^O^ CO CO O CO to - r- -1-- 1^ t^t^ OQCCQOWCC 00 00 00 00 00 O:) oocSttjJ^h tC)OOoor»M CO^OOlOC^ OO^OtCtN c5coc*?'*«io up CD r- 1— oo OOOOOOCOOO 0000000000 Od 03 03 03 C^ Od Od Od O) Od 00 00 00 OdO> »-i to O ^ 00 T-i ^ cs 04 05 o^ o> o> a o> Od O O) o o^ 0> Od O) o o% 03 0)0)0^ ■^C^COiOCS CO OiO Oi •-< O iO t^ »0 O C4 C-* O t - CO Oi ^H CO ^J* ^ lO CO '^ '£i CO O 03 O Oi o> 0> 03 0> Od 09 ot^oo to t- 05 ^ .-H CT> l-oOOi-H.-t CO CO r- I- r>- 0> 03 Ob O) O^ Od O^ Od O) Od O^O^iO ^00 u? CO C^ t^ O 04 CO ^COCO -T ^ *^ r— r- t— t- r- l- o O o o o O) 9d O O) O^ O COOO'^iO C4r^OP4CO »-icocCr*"^ Oi»-»CSO:0 0006060006 Od 0& Od O^ 03 O^ 0% 03 O) O) C. *9* 05 "^ 00 00 O Oi o o 00 00 00 o>o> Cd 0> O) O) o OOiOuo CO CS --r cc ^ CO CO i^ — < »c oi .-H --« CS O* ?4 Oi C^ OS 03 o^ U3pO^C4 Qi * r- CT' 00 CJCC OS CSlO CO CO CO ■^ ■^ 0> Od 03 OS OS OS OS OS OS OS OS OS OS cs Os ^OS04 04 00 00? -^ '^ (N 3COCOCOCO cDr*»t^f^r OS Cs OS cs OS OsOSCsCsOs cscsOsCsOs Cs CS A OS Os cs OS ^ OS cs ObO>cs OS cs ,-(,-( r^ .-• o t— O too -^ CD CD •rr ^T* lO lO lO to cs OS OS OS cs OS Cs cs cs Cs cs OS - 00 o o t^ M- 00 o < _ coco f-H 00 ' (MCO -^ '?" "^ 00 00 00 00 00 OS OS cs cs cs i-HcOCS'-'C^ c*« -^ -^ CO '— ^H r~-co OS CO CO t^ r- ut^ 00 00000000 OS cs OS OS cs C4cO"ti OOCO OS C CO cs CO »0 »0 CO o - OtoOtOO OS cs O O -— I OS cs Cs OS OS "^ 00 cs CO O .-H-^ C4 CSCO O OS OS OS cs cs cs OS OS cs ■^ososccn-' 10 CO r-- CO o ocooocO'-t C4 CO OS *-< •— < OS CO '—"O 00 OS 00 CD CO cs -^r^O-^t^ 0S04»OI-0S i-HCO»OI--CO COCO-n"-^-^ "^tOiOtOiO CDCOCOOCO OS OS OS OS OS cs cs OS OS OS OS ^ ^ OS OS cs cs OS cs ^ OS cs OS cs Cs cs cs OS cs ^ i-(oo»-H-H r* CO wi) I^ t- us 0'-- 1-- r- OS OS OS cs cs cs OS cs cs Cs O OCOOCSCD CO OS CO I- 00 OS to uo CD ^ CD CO t-- t^ t— r- t^ t— OS cs cs cs CS cs cs Cs OS cs OS Cs o-*"^oacs r*^H CO (Ncs r^ to 04 OS us cs OS cs Cs cs r--ooOco 00 to I-^ CO CO C4 __, ^HCO-HCDi-t O r^ cC cc OS OS O O •— « """"-'" oooocscscs OS cs cs cs OS -m i^- t- us 1-1 C^ 00 '^ OCO ) 00 00 00 OS Cs Cs cs ^ t^O --H 000 to O TP 00 1-H 1-H C^ (M C» CO cs cs OS OS OS cs cs OS Cs cs - O00C41-HUS us-^eOr-tco CSC4COCO (MOO-^COO i-l ^ OS CO »-< --' »-ieocooo.-< couscoooo lOtOUStOCD COCOCOCOI^ Cs OS OS OS OS cs cs cs OS ^ cs OS OS OS OS cs cs cs OS Oi I ^ 00 CO . _>C4CO "" to 00 C4 to CO CO -^ "^ T' cs OS cs OS OS OS OS Cs cs OS 5 cs OS 00 to <-! CO OS i-t « t^ i-H -^Ji us to coococoos CO -^ -^ TT -^ OS Cs OS OS OS O CSCS OS OS i-40SCOC»lcO cOC^-^Nh- rrOcOOC*4 COCOi-HOOcO csusr-ocs -^f CO cc OS 1— I »0'0»OCOCO cpcpcOcDt Cs ^ OS OS OS Cs OS OS Cs OS cs Cs OS OS OS Cs cs ^ OS Cs t^-* t^t^ CO r*Oi-ti-to C4 rj' to CO t- t^ t^ t^ t^ t^ OS OS cs O OS OS c; cscs OS coco C4 CO us 04 t* CO 00 1-1 CO ^ t^OOC )ooosos cs OS OS OS OS OS cs OS OS cs Cs OS o scocot^oo us o CO us CO CO f- cs ^ t— ::ust^cOCO 00 1-H ,— I OS to OS '-<'—« O CO 3 r- -^ t-H 00 "^ .-H t^ cs 00 CO OS 'S^ OS CO ^co■'TU5lO CO r* r* 00 00 ososoO'-h DCOQCOOOO 0000000000 OCOOCSOSCS Cs cs OS OS OS OS cs Cs OS OS cs OS cs cs Cs CO cs CO 00 CO 1— t 'T to 'S" cs 00 CSCDO "^ — 1 cs C-1 CO CO OS cs OS OS Cs OS OS OS Cs Cs oococot^us csr^i-iO'^ oococor^r- tocsoccs-^ i-^ ^^ -^ r- o CO CO OOr-l CO ,. . fto tOtOuscOcO OS OS OS C^ cs OS OS Cs OS OS OS Cs O OS OS OS Cs OS OS OS ■^O C^O to tOtOCO ous tOI^OS^ cs CO CO CO I— t^ OS OS OS OS OS OS OS OS cs OS us CSUS lOr-t CSCS cocoes CO us CO t^ CO OS OS Cs OS o^ cs OS OS OS cs '<*' Tf O '^ CO o OSUS oco to o OOOSOOO CD i>. r^ 00 00 00 00 Cs OS OS OS cs cs OS OS Cs OS Cs cs e*s r- 1>- <-! cs Cs-rf*i^a>o CSCOOOOOUS CSC4CSOr- »-iOOtoCSCs us cs CO ^J* OS cocOTTtous cor~-i>-oooo OOOOOOCOOO 0000000000 OS OS Cs OS OS OS OS OS OS cs O^COCOi-l 1— I coco*-* CO to Ous O M* c:s o o ^ .-H 00 OS OS OS Cs OS OS OS cs OS t^cor^c<»o CSUS coco TP OS CO t^ '—t us ^CS CSCOCO OS OS Cs OS OS cs I-^l^.-i OS O -^ t^ OS 00 OS C^ us CO 1-1 CO -^ -^ "^ us OS cs OS OS OS OS OS OS cs OS CO •-» us -!j' 00 to to to CO CO OS cs Cs OS OS OS Cs OS OS cs 00 Tf o -^os COCCOCSCO COCDt^ t- I^ OS OS OS OS ^ cs Cs OS cs Cs OS cO csos us oco '«r 3* CO to CO r^ coos OS OS cs OS OS CO 00-^ 00 r- V CO 00 00 CO 00 CO OS cs OS Cs cs OS OS OS <^ OS OS OS cs cs OS OS OS coi^r^^cs cor- OS OS CO C4CSCO CO O 00 06 00 00 00 oco ro^ CO i^ CO cs to o CO r- t^ 00 OS 00 00 00 00 CO OS cs ^ cs cs OS cs cs OS OS O—iCOcO— I cs -rj"^ cs OS OsO O^ «-H 00 cs OS c:s OS OS ^ OS OS Cs t-cOI^CSO CO CO r- r- to O "TT CO C4 CO cs CSCS CO CO Cs OS OS OS Cs OS OS OS Cs OS cs t^r^ 1-H cs 1-4 to CO O OS ococo o cs ^ OS OS OS cS OS OS cs OS cs to to CO CO CD OS OS OS cs OS OS OS OS OS OS 00 -^ CO -^ cs t^ r^ to CI t^ r^ OS .-I CO ■n' cc CO 1^ r^ I-- cs OS OS cs ^ OS Cs cs OS A OS CO OS OS us rH -r to us "^ CO r- 00 cs O r^ r^ r- 1^ 00 cs OS OS OS o Cs OS Cs cs Cs 00 00 -^ 00 b- -rr ^H i>- cs to r* CO 1-H rH cs cs cs cs 00 00 00 00 00 00 OS cs OS ^ OS Cs OS cs cs cs Cs Cs >■* -^00 o " 000 OS CO ?O00-^i-t Sotootooo 03 cs OS OS OS CO i-t '^^ to I-- .-I Tf< Tf CSOO COtTOcD ^ CO r^ 00 00 OS CO 00 CO CO 00 cs OS OS OS OS r-* 000 CO 00 cs M* to CO OS r~ cs r^ oi CD OsOOi-t i-( CO OS OS cs OS cs OS OS OS OS ^^ to OS CO r^ cs cs 04C0C0 OS OS OS OS OS cs -^ ■-1' CO CD O CO cs .— I to . ._, OSUSi— iiOt^ — i-t-^t-^i-tTj* cOOSCStPCO OOOC4"^US ^ COOSOO ■ — ^- ,-t TJ» , _ ^ tous OS OS OS OS OS OS OS Cs OS Oi to us o CO CO CO t^ r- (^ r- t^r-r^cooo coco O O OS OS OS CS OS OS OS OS OS Cs Cs OS OS cs OS ^ ^ ^ coco COCO cs cs to CO CD to ^ oooso »-^ ■^r^r^co 00 cs OS cs cs Cs OS OS OS OS OS ^Sc 1 1—110 "* 1-t )COCOOOOS I CO CO CO CO J 0600 CO CO OS OS OS OS OS cs OS OS OS OS Cs OS cor-r^— *C4 M" oooot^ ■^ .-H OS CO cs S'^ TP US ^ OC' 00 00 00 Cs ^ cs OS Cs cs Tj« t^ OS O ^ -^^csos OS us i-H h- cs cor- 00 00 OS 00 CO 00 00 00 cs ^ OS OS OS O i-t CO CO ^ CO us »0 CO O 00 CO 00 CO 00 OSOO ^ .— I 'CO 00 06 OS OS OS OS cs OS A cs OS r- :0 r- cs O ■^ r- CO 00 CD C^cOO'^ CO cs CSCOCO CO cs OS OS cs Cs cst-r-^C5 CSCDOS'-H O cs us CO cs us -^ rji ^ to to OS OS cs OS o OS cs cs cs Cs CO -— t us -^ 00 OS CO —» to I— to CD CD O CD OS OS OS OS OS OS OS OS OS OS CO Tf CO -^ cs CO 00 yD CO 00 OS >-( CO us to o r-- t— r- t-- OS Cs OS Cs O o ^ A cs ^ 00 cso-H cs r-- t— CO 00 00 OS cs OS cs cs cs cs OS cs ^ 00 00'* 00 r- ■ Cs O OS OS OS ^ cs cs Cs Cs Cs cs cor-r-^cs -^oooor- tOCSOt-CO OS OS OS OS Cs OS Tt* t^ OS o ^^ ^escs oco C4 00 CO t- r- 00 00 OS CO GO coco CO cs ^ OS OS Cs Or-4CO CO ^ CO us to CO O OS o o ^ .-< OC Cs cs OS OS OS OS OS OS OS r* CO r- cs o - ^ OS CO ^ to '* 00 ■rrr— oococo cscoosi-ho oscOi-itot— -_ -, CO t^ 1— < us OS CO CO OS CO CO cc i-H ■TP :o 00 O CS ■- -^ "" ^- — — 10 to to CO to CO CO 1— I— r OS OS ^ OS OS OS cs cs OS OS OS cs OS cs OS ^ OS OS OS cs OSCSOSOSCS OS cs O cs OS OS OS OS O Cs OS Cs cs O Od cs CO OS OS to cs to CD CO us osc5^ csco I> 00 00 00 CO cs OS OS cs OS ^ ^ Oi Oi Oi 00 00 Tf 00 I-- -^ cs 00 CO CO 00 OS "^ -■»' to to to us 00 00 CO 00 CO 00 c^ OS cs OS cs Cs OS cs OS OS OS OS cD CO 1— ' t^ ^f ^H OS OS OS cs cs to Oco us CD 1-t '*?•'* cs 00 COS-* r-r-oO^CS 0000000000 OS OS OS OS OS '^ I-- OS cs t- cs rr ■* COCS O us O 10 OS O O «—<•-< -H OS cs Oi cs Cs OS OS OS OS ^ CO cs ^? 00 -^ ■* t- cor- to -f OOCSCO o cs cs CO CO -* Cs Cs cs OS Cs OS OS CS cs OS CO CO CO r- us csr-^O'*' -^ocsous »ocsu:>usi-i -^-^om-coo 00tO«-itoI-- COOOCOCOCO 04totOcOtO CSCOCOCDOOOS CSCStoi— OS •— tCOUSr—CO Oi-hCSCO-* tOtOtOCDcDcO lOcococDco r-r-r-r-r-- oooooooooo oooooocococo OS Cs Cs OS OS OS cs OS OS Oi OS cscs OS OS cs OS OS OS OS cs OSCSOSOSCS OSOSl^OSCS cs ^ OS OS OS OSOSOSOSCSOS 04 CO CO O ^H cor-cs©-* I^ ^ ^ CO _ oooooooooo 05 OS OS OS OS _ _ 00 CO -X) 00 OS CsOscO Ococo^t- cs 00 '^ o us r- r- CO OS OS oooooooooo cs OS cs OS Cd OS O Ol to O i-< -^ <* cs O — OS Cs Cs A Cs •H CO toooo ^H lOODO cs us 00 1-1 1- - Cs cs OS Cs c& OS O OS OS OS CO to O rr CO Oco tooc o ■'usioto cOcOCOcOI— OS OS OS OS OS "- to cs r- i-i-vusus-* .-H r OS OS cs cs OS I- CO <0 CO 00 ' - ■ to csr- 'CD 00 OS r^ r- r- t- t^ OS cs OS OS OS OS cs OS O OS 00 us 00 CO" ^H CSC OS OS ^ ^ cs OS OS cs ^ OS t^ r-co t^coc OS C& OS O OS OS OS cs cs OS OS OS wususOSO CSCOOQt^tO oous cs OSCO CO TT us to to 0600000000 cs OS OS Cs OS r>-csusr-oo oscscsoco 64 0StO^CO oooooooooo 00 cs^^ -»■ cs Ocsco ^ r- csr-c^r-r-i 00^ ^cs OS OS OS OS Cs to ** us O CO cs to CO CO CO CO CD-* 00 cs csco coco •* O US us OS r— O -#r-oo cr> CO OS c^ us c OS OS OS cs OS OS OS Cs OS Cs »-l CSCOCS CO t- CO OS CO to « 10 us to CD CO CO to t OS OS OS OS OS CO cS'^c* ro- coco Tj" ^H CD CO us r— OS o i^ r- 1- r- 00 OS OS OS OS cs OS Cs OS OS Cs r- ■* t- 1- CO oco ^r rr" CO cs CO ■* to CO CO 00 00 CO CO ^ o 9 cs ^ cs 9 OS Cs OS 8 CO C4 CO uses CO •— I "* cor- ^- t-cocooo 00 00 00 00 CO CO 00 OS OS Oi OS 0> OS Cs OS OS OS OS OS OSCSOSOSCS csoscscsos oscscscs^ OS Cs OS Cs OS I! to cor- 00 00 OS O rH < uscOt— 000s Oi-tCSCO- lOustOUSto loustousto (©cocOCOcO '^cOcOcOcO us CO r— 00 OS o -^ cs CO -^ uscor— ooos o»-*csco-* i-r-(^r-t- r-t-r-r-t- >COt-OOCSO OOOOOOCOOO cooooocooooa ecf oocsto «=000'-t»-i •«ico O'^OOC^cp O">^- coot Oit^t^ OlOlt— 0» 0>t--COC)'»« 06000606 o6o6o^o^ai CO ■* >-< lOt- CJi CO t^ O CO i-H W(NCOCO CO O X- O CO O n* OCO CD O 01 >-H T*< O CO CO -^ -^ •?« ^ Oi 0> Oi O) r^ 01 c^ »o 05 OOOfN '^ CO *r »o »o »o "O O) O) 0> O) Oi 01 »o o »o o> t-CJ>i-i 0> 0> Od O) too r^ CM 1 1-- 01 ■-* ir^coo icoco t-- 0> 03 Od 0> O) »o CO r^ CO o i-o 00 N o CO cmoo^mO"5 cm - 1^ t- !•- 00 O) A O) 0> Ok OaO I--00 0>0i O) Oi 0> O) . cOeoSo ^ r- qO -f ^ »-< ■^ CO t- 00 O) i^r^coooo »o rr r-i o a> 9? tr zrS?'^ I^ O CO CO 01 00000000 oocoaia>ai O CO CJJCO i-HOJ CM coco 05 CO CO t^ CO ^ ^- 500»0 00— (lOCOO CO CO O CO *^ gr^OOSog ^^OCMCMO> ' t-- t^ (^ C^ t^ t^ (^ t^ CO O) O^ O) o> o 0)0^03 0)0 O) OS 0> O 0> 0)0)0103 0)01 "**-i O) t-- ^ o »n .-H (M CM CO CO O) Oi O) o^ o^ CONOCO o> CO CO« rHlO ■^010 StO O) O) O) O) o> COC^COOiiO irjCMOlOS"^ 0)0^0^0) 0> 0)0)0)0)0) »0 W 0>cpiO b- cocM r^oo t »0 -^CM f-< ^C CO t^ 00 oiox ^- 1* t^ r- t^ c ^0)0)0^0)0) 00000000 00000)0)0) 0)0)0)0)0) CM CO OQcO — '>0>OC0 . . _)^0)W r^ o>^ ^ 1^ CO CO ^ ^ ^ r^ioooco COCO^OOO 0)-H CO 10 CO < lO »0 lO I O) O) O) O) O) t'- CO b* CO O) O) c 0)00 O Cp iC 0)C §COO' •-I CO ' coCM-i«cooo oo5»ooi5t r-oooQooi^ t^iOTftcSc ^HCMco-^io ot^ooox: cocococot* t-r-t-^t^t^ t^t^t^ 0)0)0)0)0 0)0)0)0)0) 0)0)0)0^0)0) j CM CO O) -^ »-l C 00000000 00000)0)0) OCOrHCMrH )^O0C^^ CM ^ CM CO CO O) O ^ O) O) COt^t*^r^ t^Ocot-co co^ooco S2j -^ lOiO ic 10 O) O) O) O) O) 0)0)0 0) o coo* t>. CM CO So ^CO -^ CO CO CO CO O 0)0 o CO CO CO CO t^ CM»0Ot*O Ob*"^«-HC o) 000 o ^CM rJ*i5io jcOCMiOiOCM 5 t^CO ■* CM o >t-.oooo»-< -t>-t^t^oooo o o o 00 o o 000 o 000 O O) rjCMCM I CM»0 oeoococo t^CO^ o t^ cooo -H'S CM CM 05 CO CO o o o o o O-^-^OQ^ *0 CM 00 CM 35 t^OCM lO h- gCO»0 TjJ i-H ^H CO 10 t-- ^ lO »o »o o o 0000 5r+< W5 ^ t* iCM ^00 3 3* d) -^ t^ )CO00t^CM CM CO ^tO CO 00000 t^'^ "-too t^o SCO O <-H .-t 00 O t^ Cp ^ r-H t^ t^ t^ |s- 00 CO o 000 o o 00000000 ooooooo> o o o o o 8 00 00 00 CO *ococMr- , 00000 1 CM 10 cooo COCOCMOCO CO C^ 0*0 CO ^coor^oo 3«-H Tt* t^< lOOcD ^o-^co o o o o o OOcO'-t'-l'^ OCO COOCO oooo^*^oco 0)«-. 0. 00 00 00000 000000 oOT4-cqo i^-^J* TfCM t'-oo -^ o 00000 CM io CO 00 CMiOr-iOOO OCMQt-*0 OOOOi-'O CNCM»Ot^CO lO'^^OO tococoi>o OOO'-'t-i c5cMc5coco 0000000 Oi 0> f^ Oi Oi o o o o o r* ift o Q CO . „D O 1-^ Ti* _^ -^ CO »c t- o 000 o I CO CO CO CO o o o o o O OCO CO 00 »0 "*J« 00 t^ 1-H St^Of-tCO t>-c ■ coco c 00000 riiSJOS*^^ ocococ CM OPOO "^ r*ooo>oQ ^^ o o o o o o o o o o o ^sss:2 _(«5^Hi-*oo oi^co r^o o^ )iO*0 o o o o o 10 r^ 00 CMco*o toco CO CO CO O O O A -^^-^ 00 00 CO 1-HOCOC^ t- SO) »-«CO Tj< r»oo^H CO COCOt^b* ooco*-"^ ^i-Horno^co r*cocp»co rMi->a?oocD lococp^o »o-b.t>.t^l:^ t* t^ t^ 00 00 00 o o o o o o o 0000 00000)00 00000 00000 o o o o o S-i^ Q ooco iAiO-<^ CM OrHt^?^ ^^OO-H CM »0 CO 00 00^t>.-f .-H ICC 00000000 0000000 o 000 o S«3*0»0 «5 OO) o o o coc to 00 1^ cS t^OCM ^-CO coooooi-t f'.OTjtC^iO iOCMOcO»Ot* t-r--00O0t^ cO»OTt*CMOOO CqcO-^^OCO b- 00 O O "-H »-i t>-t^t*t*r* c- 1- 1>- 00 00 00 00000 000000 w t-iOCO SM^OOCO I CM 10 CD 00 06060606 •o 00 -+> ' 3 coo t ococ I 00 CM lOCO -^CO 0000000 00000 •o 00 coo coo COOCM 00 -H CO cooo CO ^ ■^ ^ ^ S 00 CO CO ^ '^COCM iO»OtOtO fOOOCOCM CM O 50 ^ »-H001t^l>. «-»OCONt^ CO «-H h» .-* 10 O) ^H ^ (p t>- t^ O^CM-^iO CPOOOO-^ w> 10 CO o CO CO ooor-t>- Ok o o o o 00000 00000 '^ t----«OCM t^ CO CO ^ O CMCO-^iOO t^OOOO^r-i 00 o > , . o o o o o SOCO CM Tt< O O) O CO 00 t^ t?5 CO — 10 CM 10 CO 00 06060606 O CM 00 »0 CM 00 00 -^ ^ o »-HOi£2'-*cO 000 ^i-* 0606 0)0)0 00000 coco O h- CO 00 ^ *0 <-t CO CO O 000 t^»0 CO i-« t>.Q0OO r-lCM t^ t^t^oooooo 000000 W5 SCOO b-COOO 1-1000 CO -^ CM OOQOOO «-H CM t^t^t^OOOOOO o<-HCMcO'* *oot^ooo o^c^eo-^ >ocot^ooo Sc 3 Tji lOcQI^QOO) O'-'CMCO^ lO CD t>- 00 O O ^ CM CO -^ t iCM CMCMCMCMW CO CO CO CO CO CO CO CO CO CO -^ tJ« rt* 'tt* -^ - S' 'S Zt 92 ^ '^ O'iJOOCMco O'^OOCMcO O^00C*J*0 Q-^OOCMcO O^OOCMcD O^OOCMcO O'tOONcO Q'^OOCMCOO OOOi^r-H ^CMCMCOCO 1«'*-**0«0 OOOr-t?-* S^CMCMCOCO ^■^-0 000»-lr-l C^OIC^COCO ^•^■<*"OtOO TABLE V. The Finding of the Azimuth. [Page 163 SO3<00C (■- 1^ r* t- 1-^ lOOt^OOO o^^c^c iO O t^ 00 CI C t^ OOGOOOOOQO OOOOCOC ^05 05 00 ■* I— I »o t- r^ '^r CO o r- -^ i-^ O'-H --< C^ CO OO 00 CO 00 CO •-< CO a> --< CI t-- -^ O io 1-H CO -^ lO lO CO OOOOOOOOOO 03 03 C> O) C^ C: G) O O) G> M COOOOCO 0- O OiO) •^ OlOCO-H O CO -O ^ OO O " 03 o lO CO r- CO O coco OOCS irt CO a> rH -^ CO C^ C^ CO CO CO O) O^ 0> O) o^ 1-H CO <-H .-« 1^ O Q CO O CT) CO o> O) o> o> o> o O O 0> Oi o o> ooMC^cor- '*^05C^'«fir5 locooo^co c^r-ic»r*»o r-(N(Mco^ oj ■«»» o »o (N r^osooo-^ cooO':7>o Oco-^coi-i ■ "■ riC'Mt--CO Oi-Hi-HMCQ CO'^iOiOCO OOOOOOOOOO oo 00 "^ O CO OO CO t-^ «-! O 05 00000000 OOOOOOOOC 050100Q T-* r-t 1-1 (N C^ OOOOOlO^ OOSOiOiO 00 CO O OJ CO -^JWI'-OCO Cl CO CO CO CO C3 03 o> O^ O) CO Ol •— ' O) O) Oi O) 03 O^O^O^O) G^OO^O^ O) Od Cs O) O) Od O 0> O) G> O) O O^ O^ O^ O) CO CD -— « C-» CO ■>rr lO lO o o Oi Oi CI O Oi O O 03 O Ci CO CO CI CO M CI w TP CO c^ --t* -t' S-^ Tp lO lO *o lO lO O lO »o O^ o o o o o Ci C) 03 O^ Ol o t^cvi ■* CO CD CO ■^ »-( CO io o <-< c^ (^^ CO 00 00 OG 00 00 C3 C) C3 C) O CO 00 rH CO -^ -^lor^o^ wSr-oocow cococor-co rHr-eociiO 0*0000 TT -rP lO W5 CO t— r-cOCOCi OOOOOOOOOO OOOOOOOOOO O O G3 O^ O 03 O) 0> O O 1— I o*-< cO-^ OOi-H CS ^ Oi Tt< C5 CO r--o OlClOOi-4 OOOO OS CI Oi CO f-t i-H lOCO lOOCO -^ -^ '^CO^^ "^ !>• T-H rH(N(NCS| 030^00 r^in ciooc^ CJ C7> -"J* DO >-l O CI lO t' o CO CO CO CO '* o CI d o c^ 0> C) O) OS o CJOOO OOCO CI <-" oo CI CI ^ CO i-^ o coococoo cqwcoci^oo COCTiOOCO OCtCOOCICI O'-'CO'*^''^ lOcOOt-l-t- lOOiOifSiO iOiO»0'OiO»0 O O O O CS OS OS Cs O CS Cs Cs OS CS CS Cs C3 CS Cs Cs OS OS t-Hiomcso t^cnot^oo oocs^^-^cs ift'^j^ioooo ujOSr-^OOO diOOCOCs COUOCOM'O »OC005C:.cO ooiocooco cocsiQi-Hco cir*c»r-c» coo-^coc) o---r^cococs osooO'-« OOOOCOCOOO OOOOOOOOOO OOOOOOOOOO oocsososos O lO IOCS t^ St^Ol-H 1-1 OS CO CO cs 1-t .-iC) dd Cs cs cs Cs Cs - •MOicOClcO _..,.. t^OF-Hi-i OcOCJCOCO cscst^-^ C4"^l-OS.-l — — CO CO r.-D CO -5* C) cs cs OS OS OS cs OS cs cs Cs cs cs Cs cs cs cs cs cs OS Cs OS cs Cs cs Cs Cs OS cs Cs cs cs OS Cs ^ CO CI "^ CI t^ cscs t^-^ O CO O t— OS O ■«tj< -^ -r -^ to cs Cs OS cs cs cs OS Cs cs cs t^«^t^r^co ococicoiocj OS Cs cs cs cs cs Cs OS cs cs cs cs Cs Cs cs OS Cs cs cs Cs A cs dcOcDO'-' OOcOCOcOCi cjcocooo^o csc5c- CO CO O CO -^ ■«< CO o co i-< "^ CO tr '«)<»OCDr^CO CSCSOQQO lO "0 O lO lO lOiOCDCOCDCp Cs cs OS cs cs OS cs cs OS Cs OS cs cs cs cs cs Cs OS OS OS OS cs ® 2 P 2 2^1 OS CO cot- 00 coco lO-^'-^ »-( OS CD CO o »-« •— I CI CO -^ OOOOOOOOOO Cs OS Cs cs OS »OOCO lOcO CD C) OS !>• CO 00 00 00 00 00 Cs OS cs OS Cs CDt^OsMt^ CONCOQOCO • cs cs CO "^ CSC 100*00^0 _- - t--»ooo6osos CsOO»Hi-< OOOOOOOOOO cs OS OS OS Cs CI CD 00 o OS Cs cs cs d cs cs OS OS CO CO OS CI rHC^WCICO 0> Cs C> Cs 09 CSt^i-t O'*!* SOcDOCl OOOCO^O CO CO '«»< -^ ■»»< OS CsCS Cs cs o OS cs cs OS cs cs cs o cs COCO^H^CO t— cs r-( d -«J< OS cs OS cs OS cs cs OS Cs o r^o»-< <-< o lO lO lO lO c OS OS cs cs OS cs Cs OS OS OS OS CI CDCOO--* lO CS.-t I-) QO COOOOiO.-" i-HdCICQ'^ OOOOOOOOOO OS Cs Oi cs Cs 00 CO CD 00 OS d w5 lo CO cs CO Tf QcO»M ■^ to coco r- OOOOOOOOOO CsQCIiOO CO CD CO -^1—1 t>-C4 t^CI t^ t^OO 00 cs OS cs cs Cs OS cs OOOOOOOOOO OS Cs cs OS o epiOCO^HCS ^HcOcOOOO C*©'^ kOCOCSOSCD »-* lo OS CO r~- t-t-^cO'-''" OOO^i-t ^ ^. OS cs cs OS cs •-* Ot>»dc OS cs cs OS cs OS o OS o^ cs OS OS Oi cs Oi 00*00000'* r-t^cor*coco cocDt^r— CD CO cs ««3' r- OS Q t^COCSO'-' C^CICOCOCO^ lO to to CD CO O CD CD CD CO CO OS cs cs cs OS OS OS cs O cs OS cs cs cs cs OS OS cs Cs OS OS OS OS Cs Cs cs OS cs cs OS cs Cs ,-tioiocso r-c^tor^oo cocsi-«'^cs 1-t to t^ CO ** CO i-< 1— I cs >0 cs —* CI O CD to CJ OS CD CO cs CO d t- CO 00 ■* OS "* 00 r-tddCO'* -^tOcDOt-- t~-oooooscs OOOOOOOOOO OOOOOOOOOO OOOOOOOOOO to ■* tOOOO »M TT lOtOC* CO t-- 1-t to cs QO*-* — *i-( 0& A OS OS c^ cs cs cs cs cs cs cs cs cs Cs o cs cs d cs OS cs OS Cs cs o toto c> r^ OCOCOt^t^ d CD OS CI to o OS cs cs o i-iOPOCICO COCi coci ■* OOi-HCOcDOO CO '«r 'rr "<5"* cs OS OS cs OS OS OS OS OS cs to»ocooto csdcocod cs o CI TT CO r* cooi-(dco co to tO to tO lO tO CD CO CD cp CO cs cs cs cs cs OS cs OS cs OS OS COCJCOiOCJ tOOCO »o o TT to to to to cs cs OS OS Cs OS cs cs cs cs cs cs OS OS OS OS Cs OS cs cs OS COO O"* to CDi-H fOCJ O CO Tt< ^H CO '•r »-l d coco-^ OOOOOOOOOO cs OS cs Cs OS c^r-OCJco co-*cocsTj» ^ CD r* to .— I tor-»t^tod f-H r- CO cs to otootoo lO tO O CO t~- ^ CO cs cs o OOOOOOOOOO ooooooooos cs OS cs OS OS OS OS cs cs Cs OCsO tOCO 1-^ Csi-t OOO •^oocor-O oo^<-«ci cs cs OS cs OS OS OS Cs cs OS »ooO'-< 1-H tOcDcocD r-r^ cD CD CD CO CO CD OS Cs cs OS OS Cs OS Cs cs OS Cs o OS Cs cs Cs Cs t^ .-* i-< to CD — *COOO t^'*'* OO^Od CiCO ^ CJCO CO ■'3' 00 oooo oooo cs OS Cs cs Cs COOC'-'CO'* -^tOt^OtO csi-tdOcD odd^^r* OS Cs OS cs Cs cs cs cs cs Cs d toco toco COO"* OOd OS cs OS OS OS cs OS cs OS Cs o^^»-^ioco i>.tooood doooooc cs ■^ t^ 00 oo CO CO CO d to CD to ■* o c iOOSCJiOOO f-4-*CDCS'-t cotor^csc cs cs Cs cs OS COOCOCOCS ddOOdi-HC oco«*«-rd o o o ■* CD c C^ CO ■* to O t-t-tfSfyicrif cOcOcDcOcD cOcOc cs Cs OS cs OS OS cs cs OS Cs OS cs OS OS OS OS OS OS Cs cs Cs cs cs cs OS Cs Cs OS Cs Cs OS Cs -* CO cod CO cOOd d cs OS r-- ■* --H t-- i-idco^;^ 00 00 CO 00 00 OS cs OS OS cs otoc^o-^ 1-td-* OOOOOOOOOO OS cs OS cs Cs to t^ t^ tOCi COCOCOCOCO t— f-H ooooo oc h>.00CO-H _ CsO O 00 t^,-HOOCO cs cs c& Cs cs COCQoOdO cs OS OS OS cs cs cs cs cs Cs cs cs Cs OS cs cs cs Cs cs OS Tj« d CO toes »-« CO CO r- OS CO to 00 O d TT ■'J^ "* lO tO OS OS cs OS cs OS OS cs Cs OS C5tOr>.tOO QI>-OOCO CsCliOCSOOtO ..-£ . -rc^ TjtOtOoOO^ c> d o o O I- c6 Q d CO - lO to CO CO CO Ci OS C> OS Cs OS cs OS cs OS OS _5cococor^t^ OS cs OS Cs Cs cs OS oo Cs OS O Cs OS cs OS Cs cs OS Cs OS Cs Cs OOddcOr* ■^OSd-^tO tOcOOOc*^ d^ndr^-to t^ddcO* GOcOOCscO OtOr-cDCO OOO^CStO CS—^-hOcO .-i -«*» lO * d CO CO cD t>-. I>- lO d CO <-" * ^COtOdCS tQdOOCOCS -^OtOO-* CSCOt^^iO 5<3dtOCOr-t '^t^CsCI-* •* o to o ■* cs CO r- ■— < to ^>,^-. » - ^ -- — — - - CO OS CSO O O*-? F-fd d - - -. OOOOOOOOOO COOOOOCOOO cooooocsos oscscscscs oscscscscs oscsoscscs OsCsososo^ OS OS OS d OS oscscscscs OS cs cs d OS oscscscscs oscscscscs CO cs ^-1 Cs I" to f CO cs to CO «?0^ CO to tO CD CO cD OS OS cs Cs cs oscscscscs oscscscscs ■^14 i-< ■**« -^ O OSd COCOCJ ■* cD r- CO OS cs cs OS OS OS coddco t- ■f osi-( o r^ d cs t^-*** O ddCO* tO OOOOOOOOOO OS cs Oi cs OS Tfcsd^to lococo-^co di-idr-»o gSggSS rHi-(,-ldd SiOtO"*C ^ CO'^C oscscscscs cs cs cs OS d cs OS Cs OS a cs cs OS d Cs t^-ddco* d r»0'-' --H OcOlwOcO CO CO CO ^T' " toes 00 »o CD ca t-- o d CO d CO CO * * * r* t-- 1^ r- r- 1>- OsCS OS cs OS OS S-" tocDr^coos o .-< d CO * Oi-tdco* to'or^cocs 0-HC1CO* tocor— oocs tocDr>-coos Oi-tdco* to'or^cocs tOtOtOtOtO zO 'X>iO ^ '^ cDcOcOcDcO J CO ■* »OcO t t^t^t^t--t^ OOCOOOCOOO OOOOOOOOOOOS ■O'*00dc0 O-*00dCD O- gooO'-t'-^ dddcoco ■*■ 'codcD o*oodco 0"*codO O'*oocico O'*aodco ooO"-**-" dC«C4coco ■^ ■««< ■*r to to oooi-ii-t dddcoco ^OOCICD O^iCOdcDO Page 164] TABLE V. The Finding of the Azimuth. 'ooc^--o o-^ooe^co 8SS22 S; 5C^ O O-^OOMCO 300»-«^ cswc 0-^0* CO CC CO CO CO J cor^QO oi o^hc I CC -V LO ? t- 00 -* c 00 GO 00 OO CO CO C? OS CD coc^ catoco O lO »-• C30 00C5OO«-« i-t CM CV» C^ CO CO 030CO OlO 1-HOOO coo 0>-HCO CO CO CO ^' '^ 00 CO^^- §CO CD 0>C 00OS'-<« 00 r^ 00 ■'?< O OOOOCDCD r-lt^COt-»-H lOCDOO C3>i-H 0*0 »0 "3 CD Ot^'»*< Tt< Oi CD OOCD O J "-fs o> r* o 5 65 -*< CO o> ■ o o^ o^ Oi Oi Oi Oi Oi a ^C^» -^ i?5 CD t-- CD CD OOCD OS 0> OS OS OS »-H -»»^ 00 CD OS ocDoor-c^ t-^ r^ r— t- ^» OC OsOtMCM CD CD t^ t>. t^ OS OS OS OS OS OSCO COOOS<-' ■V CO OS CM <— I OS o lO CO CM o r^ CO'T OcDt^ t- r^ r* t^ !>. t^ r^ OS OS OS OS OS o^ Sosr* >o "2 LOCO r-. o o CO o O CD CD CO -H 00 OSOO»-1 00060606 06000SOSOS -^r t^ 10 "^- >o ■^ CO CD 00 -^f O'-iOOCM'V r--. 1-t TT 00 -— I i-iNC. .-( .-H 10 r-* r-» T-H t>- i^ -Tfi CO'-I CD OCO -rj< r- OS C^ 'J' CO CO CO ^ ^^^ OS OS OS OS OS C. CD cD cD CD O OS OS OS OS OS 5 OlCOi-H ■<»< ■rj' •-« C 00 OS <-< CM C^ CO -^ 10 CD t CD CD l> l^ !>. OS O^ OS OS C3S CO OS r^ 10 8 OS 00 CO CD -(j'lO'-tO I i-C^CDt^ 06060606 r^ OcDcoO CO CO OS CD -^ CO CM 00 CD r^ I-- 10 •— t^ CM OOOSOO'-t o6o6os^os ■^ r* yj CD U3 i-HC-< CO "^ »o CD 00 iOtO*OCDO O CD CO CD CD OS OS OS OS OS OS OS OS OS OS CO OSCOi-HTf* CD 5i IQ '^ CJS ^CMCMCM ^ C:sO>-i CM CO CD t* t^ l^ t^ OS OS OS OS OS r^ r^ r^ r* t^ t^ OS OS OS O OS OS 00-^C^O 8r-(i-li— I OS 1^00 "^00 I ^-vcDt^ 06060606 10 -^ '-' 00 ps t-tOCMt-Cvj 000s oo»-< OsC^ OS OS TTilO _- t^ 1-1 10 OOi-t OsOi^TT O TT 10 CO r-- C7S 00 00 OS OS OS 1-1 0^04 CM CO OS OS OS Cs OS C^COCDOCD CO CD C^ CO OS -' -,r-tlQt ■OC<^' CO CO ■^ "^ "^ OS OS OS OS OS t* U5 O O CO t^cOt^COOS COCDC3SCMCO CMi-iCOOSOO OsOsOOr-TP .-H t— CM CD o cDOOOCM^ Or^CSOCM TfTTiiOOlO tOOiOCDCD OS OS OS OS OS OS OS OS OS OS OS CO CO CO CO W .-* 10 "^ CO '*' r^ Oil— I CM CO -^ 10 t- 00 CO cD CO CD cD OS OS OS OS OS i-H'-r OOOOS CO -rf Tji "^ ■-»' OSO^ CM CO CD r* i>- 1^ r^ O OS OS OS OS OSCOCO OOS'- CO C^ 06 ^ O OC' CO CM o cs r^ --r- ■^ lO '-D C^ 1-- OC' r* i>- r^ r* t^ t^ O A OS d d c^ os»oeoi-i cococ^^co .cococOf-H ooi-^-^oco ^ - - rococo--' i-i i^ 10 CM coco 00OsOO<-l V t^ 00 10 00 I .-H Tji CD t^ 00000000 OOOOOSOSOS oco^c^r* (Mi-f-V CDCM O. OOlO CSi-H r* fh lo coCM ^CM CM CM CO OS OS OS cs OS CO t^r^ -H t^ to 00"^»O J^ tQ I^ OCM »0 OS OS OS Cs OS 00 CD »W r-H <<»< 10 00 1-t ''9' 00 ^H ^ ^ OSCD t^ Os^ CM tt< "^ -^ ic 10 lO X t^OO M* o ■^ coo— ' .-I oj CS ""CT" cs CO OS cs OS OS OS lO CO r* CD & O 1-1 CO O 3-^ coI-- CO CD CD CD CO cs OS OS OS OS c<» o est-* o — ^ r^ csoc -^ CD CD CO CO cD OsOt-i CM CO O !>. t^ l>- l^ OS c: d OS OS CD "V OCO CO O UO "^ CO ^H cs 1^ TP to o r^ t— 00 t-* r- 1* t^ r* r^ OS d OS OS OS cs CDC^OOO '^ cri m i^r\ on O 00 lO CO ■■ 0000*000 ooocMogco OOOSOO»H T-HCSIC^CMCO t^OCDOCO CM OOCSCM lOOO OCMiO 00000000 00 00 OS cs OS cs cs OS cs cs cs cs cs Cs OS O CO CO 00 I-" t-OCMOO CO -^ CO •-* OS r^ OS 1— < CO -^ ^3< -^lOOlO cs OS OS OS OS STf 10 »-< t^ Of^COCM S<-» CD •-< to 00 OSi-iC^ 1000 CD O OS OS OS OS cs t^TP»-l»-( CO CO lO cs OOCM 00 1—1 CO O f^ CO O CD r- 00 CD CD CD CD CD OSW CO^JT* M OS— fOlO OOOOCSOiQO C3SO«- cs cs cs OS OS coc>-t^t^r- CS OS OS Cs Cs »-H -^ cor* 06060606 C« O 1-r 00 10 — ^or^co—t CM 1-1 r^ - 00 CD CM OOCSOO^ 06 06 OS OS OS OSC«Ot-<0 OOCO OOCMiO C^C 1-tC^CMCMCO Cs OS OS OS OS CO •-« t^ 00 -^ TT c- GO CO CD CD CD CD OS cs cs OS OS OS d OS cs cs — c-^r oocDos '^ OC^r-H CD o--*^^ o 0—1 CM CO '- r* i>- £>- 1^ OS OS OS OS cs ^o cor^oc OS r^ooo^c .»^^^w-« -^^,,_w.- OOCMCDOSC, — - _- -- --, -, -™, |^'.r*t^t^r* i>. i> t^ r* r>. t 06060606 COOO^OSCS CSOdOSOSOs CDC»000 OfOOSCDCO t^r^t^'iji c^i-tt^'^rCM ''OcDCMt^ Tr*coost^on SOOOOO OOCOCIGOC » OSCO C ., .:)OcoL, OS OS Os OS OS OS to OiO OS COOOO^N to to CO CD CD OS OS OS OS OS OOt^— t OtJ< CM 10 00 O^ ■^ to CD 00 C3S CO CO CO CD O OS OS OS OS cs oswco-^r^ t^rt<^QOt>-oa ScO*^ to CD O f- 06 OS cs OS cs Cs Cs OS Cs OS Cs OS OS — (-^ CD ro- coco ff? OS CD CM-HOOtTCJ o o »o cs Cs Cs cs cs 00t*00Tj«O 00 1* OSOO ^Hr-wr* «-( r^ coOf-^ CO to to CD CD CD OS cs OS OS Cs O I>- TJ< •**' OS O^OOSt^O est-— tO-^ tO—fCOCMOO Tj«r-ocMco M' 10 o o '^ "^ O ^* CO OS ~ ^ CD CD O CO CD i>- 1> t- 1^ r- 81— Tt*^ OCM ootp I— r— -^ TT CM 1-t est— to O CD t— I— OC OS CO COC^ CSCO CM»-t00-?'CS 00 t- CO 1-1 CM 00 CD CO CS'^ OOOSOO^ 0606 ^00 Sco^^^ OOOOCO OOCMOOCO r-t C^CMCOCO OS cs cs OS OS cot— r— — ( r- C3SCM CO CstO 000 CO I— o CD C30 1-1 CO CD OS Oi cs OS cs 00 CD^^^H Tj* CSCMOOOCM — iCM -^ est— , OOOCMCOto t— 000 TP o trs o O Cs Cs Cs OS OS 00 t— OOM* o 00 t— OS O O CO OS TT 01 CO t— 00 O 1— 1 CO O to CO O CO Ob»Tj< -^ OS Ost— — « O-^ CO OS CM -^ O Tp O t^ 00 OS CO CD CD CD CD OS OS OS OS OS CM o csr— o t— t- 1- 1- 1- OS OS A OS OS ■V 000 CO t— t— CDtP ) 1-tCSOOCO 00— tt-'TPi-i OOOOt— CD T-li-Ht--rj«CM tO-^ft- OSO ocsoco-^ oor— — *co Os*X)COCS'»9< oocoooco OOCSOO— I i- O'-hcim'^ uocor-ooo o— iwcom* w5cDt*ooo> Ot-HMco'*!* »ocor»»ooo> ■^r "*■<**"«*• -^ <— ' "-* c^ n -T" «--3 ^o r^ uu u* s,^ ^-^ t^ c^j t- uj <4_i »^ wu as iOO*OW5^ iOiO»OiO»0 0«0«O^CO CO «-H rH cc io <>» o r* CO t— 00 O Ci O 03 0> OS O) o CO CO CO 00 a> O Oi o^ o> o^ 3 CO 00 00 Oi O 0> O) Ci JOOOOOOC O O O O) O) COiOOOCO''*' CO O t^ I ' CO Ci O .-H C» CO Oi C2 O O) o O Oi 0> Oi o> o O Oi Od O^ 0> O) '-H lO 1^ Ci O Oi CO »0 -n* l CD cp r^QO OS Ci Q t>-r^r^t^oo b- C^ »C 1^ CO CO oi or^ CO (M 00-^ OCO t-H --I (>) COCO 00 00 CO 00 00 O O Od Oi o COOS^-^ OS I-- OiOOO -^ i-(COC50rH ^ GO 00 06 CO C5C^ COCOO OS O 03 O) O) "ifiooo ~ "3COO Oi 03 o^ 000000 coco — (^COMCO COCS-^iMt--. t^r*4t^t^co J) cooes »-H TT CD Q>i-* OOQO^ 01 05 oi 0> OS 03 OS O) OS O io ^Mt*. CD r* t-- 00 00 CO C^C^CS(MCS(N OS Oi Oi OS OS Oj O) O) 03 Cs OS O) OS O) OS O^ O^ OS Os Os Os OS 03 0> O) OS Cs t^t^r^oodo O Od OS OS OS 00 xcocooo 03 OS 0> O) OS COTt^cOCl-^ ^H COCOf-tCO ■<** OS Ti* 01 CO OS OS O) OS OS OOiOiCcO CO 10 r^ CO ■*»« OOCS COQ Tp CD r^ 1^ 00 00 00000000 CO O^ OS OS 0> OS > 10 00 •^cs co-^oot^i-t rHr>-osr^cs csoscsc^co r^-^ 01 CO CO CO CD CO f-H CO OS OS Od 02 OS r^ CO "'J' .-Hi »o t^ 01 1-1 C-l »-H t-4 .-H * t^ CO 00 OS OS OS OS OS e*i t^Qc<»co COiOCO"* O t— CO CS »0 i-H ^ CSC3 CO '^ 00 00 00 0000 OS OS OS OS OS CO -^ CD OSM« rft CD CO T?< .-* CO r-< CD .-H CD "^ O ^O CD CD 00 00 00 00 0(5 CD CO O OS I-* CO 00 OS OS OS OS OS O OS Q »C CO CDCOO C~ ■ O-V OSC r- r^ t^ &j uu 00 00 00 00 00 OS OS OS OS OS ^ c^ w 00 CO 00 OS OS OS OS OS OS OS CD -'J'oor^-H St^ OS OS OS OS OS i-(icw3oso t^(N"5t^oo 000s— <-*ros 00CStJ«CO.-I iOOOOOCDfM COOOOSt^CO -iCSOScOCO OSkOi-4l-^CO oocooocoqp OOOsOSO<-H 1-HC^ICOCO-^ t^r»i^cooo Qooocoooco ^o6(»Sc ^ OS OS OS OS OS OS OS OS OS OS OS OS OS OS lO-^iOOCO OO^C^CNCTS t^ r— 00 00 GO CO 00 00 CO CO OS OS OS OS OS io»o OS r- CO Qco -^ -^ (N CO 0)o 00 o*-*— * — * ^ OS OS OS OS OS OS OS OS OS OS (M C^Ot^CS O CS TP 10 t— 0*4 (N C^ CI (N cp OSOO OS oB OS F-* CI ?» (MCSCO coco CO CD Cfl CD O N COC*4 t— OCS CO CO CO coco CO CO OS OS OS OS OS OSOsososos Os OS os Os os Os OS OS OS OS OS OS OS OS OS OS OS SCOCDOrH ■^ CD CD 00 r- -ff .— 1 00 10 000s 00^^ t^ t^oocooo OS OS OS OS OS CO CO CD 00 OS t-QOGO-^ 1-1 00-^ OS 10 CS- lOCSI t^i-i CO Oeo»Oooo ,-, i-H 1-1 ,-1 C- CO i^ CD CO ."CSOS-^ OOi-tCNJCS'-t OO'^OSW-^iO (rrcor-os ocqco-**»o locotot^r-i-- 1 W CS CS (N CO CO CO CO CO CO CO CO CO CO Tf S OS OS OS OS OSOSOSOSOS OS OS OS OS OS OS Os Os OS Os OS Os Os OS OS OS Os OS Os Os Os Os OS CO CO r^ 00 t-( CD CO r— -Tj* oscD coor^ COOSO <-i ^H r*r>-oooooo OS Os OS OS OS 10 oco^oco coi^ OS (M CS O CO 3S 0606 OsNr>- CO 00 CO CO cs eoc^cooocD 00COC0t--t C<»»Ocp»OCO OS-^ft^OOG -i-H lAqsco CDC OSOSOSOSOS OS OS OS OS OS OS OS OS OS OS OSOSOSOSOS OS t^.-H O -^ CD CO OS CO 10 Os Os OS OS Os Os Os OS OS OS ''J'QC^OiO CO CO -n* ^ CO ■^ COCrf>Oi-i csc^cscoco OS OS OS OS OS OS OS OS Os OS OCOtP ■»r CO CO -^J* 10 CO t^ OS OS OS OS Os OS OS OS Os Os ■3* -^ o-^ coo g CD f-< •**' CD r^ 00 00 OS Ob OS OS CO CO CO CO CO CO Os Os OS OS Os Os OS OS OS OS OS OS i-tiouioso CO t^ OS 00 CD »-l CO t O CS OS OSOS Q .-t i-( t^t^OOCOCO OS 9 OS OS OS Ococo^r^ CO CS 00-^ OS CJ coco-^ -f 00 00 00 00 CO OS OS OS OS OS OOOS^M^^ 1-1 CO -^CS 00 lOCDiOO"^ 10 CD CD r-- r^ QOOOOOOOOO OS OS OS OS OS cocDr-t-^-^ .-41000010s OS CO r^ »-( 10 OS cs lO CO i-( 1-H OlCONCO GO '-»-(0'^ ■^t^OOt— »0 1-ICOOSOO OOW5r-l»Or— •— < «0 OS CO t^ .— t TT r^ 1— « Tj* CDC3SCS*^CD 9559^'^'=^ 000^^ i-tr-*e^CM(N OOCOOOOOCO OSOSOSOSOS OSOSOSOSOS 000!M-«J^iO - cococococo cococo-* OS OS OS OS OS OS OS OS Os Os C7S OS OS OS OS OSOSOSOSOS OS OS OS OS Os OS OS OS OS OS M« '^O'rt" coo (NOOCOCOOOOfc C^ C^ CO CO CO CO OS OS OS OS OS OS OS OS OS OS OS OS 10 «»< Tf TT ^J» OS Os OS OS OS OS OS OS OS OS OS OS W^cOO-H -«j«00OOt^ I>- -^ CO OS lO OSO-^^CM 1-1 -T* rpCS 00 CO 00 ^o »o CO CO Tfi IQ up QOOOOOOOOO >C^iftO CDiCcDi-iCS S lO CO o -^ t^ 00 00 o S 1— I CD r-4 »o CJS CO r- 1— I oocoososo 00 00 00 00 25 OS OS OS OS OS 0000000006 OS Os Os OS OS — (COCOOCO CO cOOS,-t o ggi-iiooo OS OS OS OS OS I^COlOCOCO OCOcOOOO CS "^ CD cococococo COCOCOCOCO -5* OS OS Os OS OS Os OS Os Os Os i-HC^ co-^ 10 '^p -rj* ^ -r Tf< OS OS Os Os OS OS OS OS OS OS t— r^ cor^ CD CO CS 00 CO CD CO OS CO CD r- r- r- 1^ OS OS OS OS OS OS OS OS OS Os OS Os OS OS Os OS OS Os OS OS Os Os OSOSOSOSOS OSOSOSOSOS r^ ,-H .-(lO CO COOOO^CD OsQ ^ CO CO OS OS OS Os OS CO TP Tji in iO CO 00 CO 00 00 OS OS Os OS Os '^lOh-OiO c^ -v^ CO 00 CO CD CD r^ r^ og QOOOOOOOOO Os OS Os OS OS _ . 1-1 Oi-t"©-* coos rpt— OOt-iO " — 5; i-H 10 OS CO OS Os OS OS Os CDi-Hi-tiDCO ^HCpOsOO rrOcor^O O •-« '-H .-4 c^ OS OS OS OS OS OS OS OS OS OS CcDOOCp.-« 3COOCO CO "*** »D ^00^ — t^ 5 O CD O 01 CD ^CDO-V 10 CO CVI CO CO CO CO CO 510 iO"0iO»O>Ofc SOS OS OS OS OS OS OS OS OS ^ OS OS OS OS Os OS Os OS OS OS Os Os OS ^ OS OS OS OS 5- lOcDt-^OOOS O'-iClCO'^ iO:Dh-GOOS ■^■^"^ iO»OiO*00 I0*0»0i0t0 ScDcOCDcD COCO^COCO CO CDC OCOI^OOOS o—^coco-^ »ocot^ooos l,t,.l^t-»t^ I- 1' t^ l^ t- SS! g-* COCA'S) 00.-^—. c< w c^ CO sc -^r -^ -^ »« o Page 166] TABLE V. The Finding of the Azimuth. •OTOOMCO O-^OOC^tO O^»<00C^CO 0**CCC^«0 O'-»«00CSCO O^-OOC^^O O-g-COC'^O o-^ooc^«o o-^ccc^cco gOOOi-Hi-i CSC^CMCOrO •>9"^'*»00 OOO^^ C^CSCSCOCO -^-^-^iC^O OOOi— rH MCSWCOCO -^t^-^tCiOO • O ^ W CO »0(Ot^ooa> o 1-H cs cc "* w:i 0*-tWCOM< IC«DI>»00Oi 0«-co r^ocoooo q-^'^oO'**" cococoo oor^cooco .— i,— «coiOi-i low-^'^'-< C^COQi-^ OQ?«0"^"^ 0'-*CCCS-^ ^Oi^QfO - -^-- coot^fooo cor-Q-^r^ ocoioooo OOcSOiOO »-<^^C^CS COCOCOCO'iJ* O^ ^ O) o> ^ sOiOO ccodod 03oi O^ O^ O) O) Od lOcOQOoo-^ ic^ic^r^ t^-0 lO^cOOcD OS 03 0% 0> O) 0)0)0^0)0 Ob 0> O) 0% Oi 0> Oi Q? Oi i O ^ Oi O) O) O^ O Oi O OS o> 00.-H CN CO CO St" COCOi-H . COCO«-< CO 00 CO CO 00 -»r r* CO or* OOt^-^— iCO COC^ Oi ' " So OiCiOO 00 00 00 03 Cs .-H t^ CO 00 CO t •- M'OOOOe^OO Osr-NNU? OSOQOSlrt^H i-iOO»0'0 COOQOO^H i-tOOU5C«t-iCO »O00'riC»-i lOOO-HTpOO T}«COO>— 0 O OO lO LO "t to o OS OS OS OS OS Sr^'«j«Tj<^ c^ioost^o ot^'S' cor-coo 1— it-c3soo-^ S -^ O CO CO »O00OO4'rr ii0iOiOiQ»O -^COOIOCC OsOC-^CO-T;" lOcQt^OO— — iCCO OS OS OS OS OS ■^ coc - o ^ c cococo t*t^i^t^r^t>. OS OS OS OS OS OS OS OS OS OS OS .CO(NCNO r^i^coooo t>-OcOfOO r-t-- CO ooo OS CO lO coco CO I—" OO ^ ^ 00 OS OS O O CO 00 00 OS OS Tj« t>- lO to lO i-hOCOiO^-h osor^.-^ CO COOO^ UOQO ■^ 00 "* 't?' >— « C^ CS »-0 OS c^ 1— I CO CO 00 .-H OS OSOSOSOs OsOSOsOsOS OsCSOSOSOs OS OS OS OS OS -^-HOOOOCO CO OS CO 1-t ■«?• ■n* CO O O o QcOosooco oOi-Hco'Ct-- oooooboQoo OS'-^CJCO-T' lOcOt^OOOi lO CO CO CO CO CO CO CO CO cO 5 -q; CsC4 C4 ® - CO "* CO «-• 00 ?-^M co-^ -* - 1— r- r* !-■ r>- OS OS OS OS OS OS i-^t^iOco U5c0'*»-^oo c^i-Oco-^co 8C*« .-H ^ OS COOo OS OS OS OS OS Tj« h-»HOsc C^OscOcO.-( CO •-" iC "^ OS ^ TT cooo Os Qr-CSCO-* _ ^ CO ^ CO CO CO CO CO CO t* OS OS OS OS OS OS OS OS OS OS stood CON -00 OsO i-H ^cs co- • CO-V 1-t - I CO -rr 10 OS OS OS OS OS OS ^fQooco 00 -H r* *»*« iM BOQOsr- TT-^j'Or^io t— OOCOOO lO-^^OOOS I rH -tj* CO l~* OOOSCSOO 06060606 oocooocso sr^cD ?csioo 5cs 10 oo ^ .-i^hCSCS cs OS OS OS OS OS 05^ CO CO CO CO ^' Oi OS OS OS OS CO lO r^- OS 1-t -rr rp -(T -^ U3 O OS OS OS OS CON CO OS 10 »-t OCS i^ t^ ^^ 1^ C^ CO O CO ^^ cor- OS lO o to to 10 Cs OS OS OS OS lONOsosTf* t^o-^rNto iON05coi/^r>- f-HOCONt* t^-^cOuOO ^C^-*iO COt^COOSO ^ CS CO CO ■'J' »o cococococo cocococot^ t*i-»t>-r»i^r>- OS OS OS OS OS OS OS OS OS OS OS OS OS OS OS OS CO 00 00 OS OS COOO^O -SCO OS OS CO SC/) COt^Q CS TT t-- <3S N CO CO CO CO ^ OS OS OS OS OS »-t 01 M* 'I' t>- ON 10 OON ?5ci^osi- --cOOO t^ CO C^ -v -^ <—• i-H CM CO -"MO ® r* t^ r>. t^ r* t^ OS OS OS OS O' OS ,. - COOS»ON»S COcO'^tO-*' N'-««-'OS COtONOSCO OOSN- ~ NOOCO'^t* 8. r- 1>- OS Od OS O OS O) ' lO to CO to 06060606 OS CO cot- CO CO CO CO "^t* '^ 00 00 OS OS OS OS OS OS OS OS 'T'N t^t^O §COiO 00 CO o 01 1^ to t^OOON Tt« -^ Tj« to to OS OS OS Oi OS -«*« c0"*O CO CS 00 O CO to i-( r* CO r* <-• '^ >o r^ CO o 10 to tO tO CO OS OS ^ OS OS CO CO O O to CJi GO N 1-H to ■* I-^ O N CO ^H N '^ tOCO CO coco coco OS A OS OS OS OOr-iOCOcO to C* TT CO 00 '(T lO to lO ■* r-oo CSO1-1 CO CO cot- r* CO coor- CO CO o OS to r— 1-. ■»»■ ■rr N >-H OS r— lO N CO-* -^ toco t— r>- 1- r- 1— t- O OS OS ^ OS CS §COCO^ CO CO CO I ^ ** CO l^ t-Q CO coo CO ^ TT ^H OS 00 1^ r-i C^3 N tOcOOcO— « oocsoo»-« 06 06 OS OS OS ■* r>- to CO t to OS CO r— o — <-^NNCO OS OS OS OS OS r-,-H^io w to OS to t^N »-( 00 -^ 00 .-* CO to CO O 00 CO CO CO"*"* OS OS OS OS OS N OiOiOoO CO OS <-< -g* 00 NNNOt-- _ tot— OS«-tN Tf CO OS OS OS OS OS N <-HN 00"* trt"*CO^ ^ to O "* , _ t— OSQ to lO to to "io OS OS OS OS OS "*^ooooco CO 01 CO w '* tO'*I-=C"-' .-Ht-OOs-* t— o N "* CO r— t— 00 r- 1-- «— < CO "* to CO t— QO OS O •— t cCcOcocOcO cOcOcOt— t— OOSOSOSOS OSOSOSOSOS t-COi-tOS OS OS <^ CO 8 N COOS'* CO CO CO CO I 1-1 "* cot— o6o6o6Q6 »H ■* o r--* "*cOOcO'* ^H Ot~^ ■* O 00 »— t OS O OS r— r— OS N t— O rH 00 CO ■* o O CO r- o -^NNN CO OS OS OS OS OS —* to to o to ■-r .-H t-^ .-< CO COcO00r-< CO CO"* OsOsN ,-H ■* CO OS"* 10 to ■* N O to r- OS 1-H CO OS OS OS OS OS f— N OON CO •* -^ 1^ C: O lO tO to to cO OS OS OSO Cs So CON CO N to r— 00 CM CO ■* to CO CO CO CO coco OCO r- to 00 f- CO 'O ^ OS OS qQOcs t— ?: O .-( ,— ( CO o t— t— r— 00 to N O 00 O »-i QCDOC X3 3 OS 00 o " ^HNNN CO O o O OS OS cor- t— ^ t 00 CO —4 r-^"* ,-( r- CO I- .-< kOCOC^O'-« 10 to to to CO OS o o o o 8r- -* ■* o OON— (to to t- C5 N CO N CO io O t— to O CO CO CO OS O O OS o N to O t-O O N ■* CO OS -gjiOtOtO"* <» OC5 — (N O OS OS OS o Ot-"*,— ON i-» OS to 00 00 "0 "* N i-H est- to CO "f to to CO r— t— t— t— t-t— r- OS Oid OS o o tOOr-000 O^hNCO"* iOcOt-000 O^HC 3-f. tOcOI^OOO O— ICMCO"* lOcOr^OOOS O— lNCO"*tO )N CMNNNN COCOCOCOCO COCOCOCOCO ^ -^ -^^ -i^ -^ "* •Q-*0ONCO O'VOONCO O^OONCO Q" gOOOi-H^ NNNCOCO "*"*'*iOtO OC lOONCO 0"*CONCO O-^OON CMNCMOOCO 5SS g "(fgoMco o^ooNco OOf-Hi-l CMCSC4C0C0 0"*ooeM CO o -r*t^t-t- i^t^tN.t«Fw Sbccoooooo ooo5aooocio25 * ^ QO >CD<0 O O) ^ Oi o 03 0^05 03 o> CO "^ CO —I 65cOO"^ S9S5?!2'^"^ osr-wo-<** -rfowoio w5C^io>Ct-i i^c^jocoyp -^ »-^ h* i-H (vj -T^-TiM^fcrr «5^ OS O^ 5 t^-^-i-H OS Qi OS 9 OS OS OS OS Cs OS OS OS OS OS OS OS OS OS OS <^» t>- IN- .-I OS CO^^lO'TfOO 00 00 M »o t^ — "^ — »0 iQ SSK^:^ 2?4:ss? g:28ss -'"OS'-H-t'O OOOC^COIO 'OOOOSOi— < toi^t^r- i^ogoooDog ooSOoooscs 00000000 OOOOO0C«OO OOOOOOOOOO 00 00 OS OS O OS OS OS OS OS OS Cs OS OS OS OS OS OS OS OS OS OS OS Cs OS OS cs cs OS OS oooocacnc 00 ^ ^ OJ t.- 00 00 00 00 00 OS OS OS OS cs OS Cs o cs OS cs cs ^t< t^ ^ oo 0000 00 00 Cs cs OS Oi Cs t>- r^ M t* cp ec '^ lib 10 o ^ 'C OS CS CS Cs Cs CT cpQO'^ic CSr^QWcO co-^'£OSM! OS^cpiOC^ r^-CSOOO-** OOQQOO"? ooco^o^- c2®SPr5t; oioocot^cs '<*-r-t-»oooo 0000000000 OS OS OS OS OS OS OS OS OS cs cs cs OS cs OS t- .-H Ub cs CO CO -rj* -^ -^ o 00 00 00 00 00 OS OS cs OS OS 000000c OS OS OS O^ Cs cs cictocscsoo »-i^t^^ot>- 5£S 3^ =5 r::^ 99 "^ oqoc^cso 00 •** 00 cs -n* -^ scs -Tfcooocsr- 1 cSTfo »o CD r— CO oioooo»-i 1-icS'^r^cs cooQ® r — ' — 25?5oo-« 00 OS CSC QC-HCSCSO CS"^ oocs o CO -^-^ 10 to 00 0000 00 00 300 0QCSQ lO 3 -O CO t^ 00 00000000 cs CO lO cs CSiOl^uOO QwSps.-* cscsor>-co cocD w5 OS »ooooci r^r--. 00 00 Cs OS OS cs cs OS OS OS OS OS CS OS OS OS OS OOOOOOOOOO OS OS OS OS c^ iCSt^OCSCO ^^i-(?5cscs OS cs % OS OS en OS OS OS Cs OS OS co^ cocs ^ ^c^csco^ »0 CO CO l>- 00 OS A OS OS OS COOO'-tCOTt* '^U^b-O'O '^Sr^io^H icr«.r*cDCs CsiOi— ir^CO OOCOOQCOOO OOOSOO1-I i-tCSCSCOCO i>.r^oooooo OOOOOOOOOO OS CS OS O OS Cs OS OS OS OS cs OS cs Cs OS O OS 03 OS OS CSOOQCOCO o cs CO »f5 t^ OS Cs o> o cs OOOOOOOOOO O^ OS cs O^ OS COOCOCOCS C^CSOOCS— 100 »ooooosr^ lO "M 10 OS .-H ^H OS Cs OS cs OS cs cs cs cs OS 'O 0> O^ CO "^ r-- ■^ ^ osio OCO t^t^ 00 O O) OS OS Cs -h-XjOS^hCS CSCOiOOOCO CS'^'-tCOCs CO»OiOCOO csoo4!Oto T-H CO 1-H CO »-< CSOSQ^H^ cs M CO CO '^J* r»r>-ODsooo 0000000000 CS OS OS Cs OS OSOSOSCSCS »6CSCOb-.»-t lOOO^iOOO -gj-^iCiOcO cocot^txt^ OOOOOOOOOO OOOOOOOOOO *CCOt-C -i-Oi-ii scoc - :)ooc ooooc Cs cs OS cs cs cs cs OS OS OS Cs OS OS OS OS soDcpcrS^ co^b»r^io dscsososos OOQOO OOOOOOOOOO oScfccKos cs^csosos cscscscsos cs OS OS OS OS a£ OOcOOCScp CO cs CO r*" 00 OS S'X" t^ r>- r^ t^ OOQOO CS OS OS Os OS Od "^CSCfl-^iO »OcO0Qi-4cO OSiifsOtO OC■ CO CO "^ OS ^ CS CO csoOi-^^H csc^coeo-^ r^oooooooo OOOOOOOOOO OS OS Cs cs Cs OSOSOSCSCS cs Cs OS A OS oo«cscot>- ^H CO OOt^ -9* CO r^ 00 00 cs*-* 1^06 OOOOOOOOOO OS cs o cs OS oocoogseo coas^^a)'' cococsc^io CO »o Tt< o c CO"OOOi-HCO L??I^CS»-tC 00 CO 05 '^ -~ '^ 'ytuo cc_,, M^CSf uy oy uu 03 03 oSOSCSC OOOOOOOOOO OOOOOOC OSOSOSCSCS cs OS cs Cs OS OS Cs cs OS OS cocoococso^ ~" 188 S CS Os CS Cs CS OS cs Cs Os cs in OS OS CO '^ oOcs -^ -f ^ csor--^'-' CO t^ 1^ 00 OS cs cs cs OS Os »-*'XJOS^HCS CSCOIOOO -^ — — I^OSOSt^ > w cs -=^ — — ■■ 00 t--co t^ OS c ■ ---^c_ _ _ - - CO CO ^ '^ 00000000 OOOOOOOOOO OS OS OS OS cs cs OS OS O) cs OSOOCsC^CS M*OCSfO>-* ©CO 161 00— iCSCSO o »o osco r^ oooooiSoo 0000000606 Os OS OS OS Cs cs OS OS OS OS ^co^-coo Ocpoocoi-t -^ ^Oiocscs co^or^co r>. iOS^^COcp OOOC^COiO CO 00 cs Cs O OS OS OS cs OS OS .oo>— 1>— tr- oocoocsco r>»os<-— < 6) CO "Op-C&OO r-tCSCSCOCOCO scsoscscs csosososcscs scsCsosos csosososcscs oocscscpi^ '^CSi-HOI^ io?^0 r- CO CO I^ 00 QO OS -^CSCS-^iO »J5:O00'-*cp cs^cs»o»c CSTftiOCOOS CO>OiOrttO »OOOOSOOcO Q'OlCSOOCO c6rj4CS^OS COI^'-<»OOS SO'-H'-tCS ^coco-^n? ioiocococo OOOOOOOOOO OOOOOOOOOO OOOOOOOOOO OS OS O A OS OS OS OS Cs OS OS OS OS OS cs ^>.cscscoM* CO CO O CO CO 00 00c cs OS Cs OS OS S OS OS OS OS OS OS OS OS OS coco csco cs ^ CO O^ CO t^ cs OS "^ Tt* 10 iC »0 lO 3u5r* coco 5»ocs cscp Cs OS cs OS OS csr^p^fo co'^coca^ S J^ ^ o i-t csOiOOco 1— it^CS: Qp— .r^ •ocsoO'-t'^ O tJ* h- O CO CD cs •-• Tt' to oooboocscs oosopo OOOOOOOOOO O000CS^C3S O cs Oft OS Cs OS OS OS OS OS O^^-HrH ^ ^H ^ ^ O CO CO CSCSCOCOCS CiiO0SC0»O»O CO 00 cs O -— « I— I CS C^ CO CO CO ^^^e-t>-t^oo a Ob OS OS Os 00 CO to 00 p O: P C^ »C O CSifSiQCOOS McOcP'**'-" OcoCSooco o-^ro^cs i-H^CSCSCO ^'^'^^»^ OOOOOOOOOO OOOOOOOOOO Od OS OS OS OS OS cs Cs OS o CD »0 -O i-t OS ■-poo OS OS CO 5 r- ^ toes _5 -o t^ 1^ r>- 0000000000 OS OS OS OS Cs OS OS OS Os Os r-cs»ocooo OS Os OS OS OS OS OS OS cs cs ^lOoocc^ i^r^cot^coco i2iS?^fcS cocs-* gbO UO tOt^QOOs ■^ ■^ -^^ -^ Tfi iO»OW3u^»0 C^CO-^ lOcOt^OOCn O'-tCScO;*' »OCDh-.OOOS Oi-tCSCO"^ »OcOt^00CS Oi-tCS ss r^ootra *_?•— n,^c^j"^ "j'ijr-uuoa tJ*-»cNCT*T' ujcor>-ooos ^i-^CScO'^ *ftcD»»*Of)a5tf5 tOioo ocDcococo ococococo r»t^r*t^t^ t^r>.t>-t>.t>- oooooooow oooooooooocB S8SS2S SSSSS? S5!^S8 SSSas SSSfSSg S;3:$S3§ SSS2S SSI?S?3^ S?S£?3i8 Page 168] TABLE V. The Finding of the Azimuth. 9-2 C O ^ 00 (M CO SOOOrt-H .sjo O -rOO(MCO iMIMNCOeo O -"K 00 M CO .-r^-^-io-o O O O •-* f-* O 't'OOOlcD NC^C<»COCO O M" 00 (MCO "9" ..r -.I* lo to o -j«ao CM CO OOOrHrH CM o-^ooo»m C^MiMCOra O -"TOOIMCOO CO O Ort C>«CO-1< locpr^ooos Oj-tcsco-j* lOCOt^OOOS O-^CMCO-O' C^«.coos (MC^C^OJM OrHCMCO-^ COCO CO CO CO «0 CO 1^00 OS CO OO CO CO CO 0^(MCO -n-o a o Q b —00 08752 38848 56446 68924 78596 86489 93155 98922 03999 08533 12626 16354 19775 22934 25866 28600 31160 33564 35830 37971 39999 41924 43754 45497 47161 48750 50271 51727 53123 54463 55750 56987 58177 69322 60425 61488 62612 63500 64453 65373 66260 67117 67944 68743 69516 00 00 00 00 00 00 00 00 OS OS OS OS 0>^ OS Os Oft OS Os Oi OS OS ^ OS OS OS OS OS OS OS OS OS OS OS OS OS 0> OS OS OSOSOSOSOSOS I b o —00 09135 39231 56829 69307 78979 86872 93538 99305 04382 08916 13009 16737 20158 23317 26249 28983 31543 33947 36213 38354 40382 42307 44137 45880 47544 49133 50654 52110 63506 64846 56133 57370 58560 59706 60808 61871 62895 63883 64836 65756 66643 67500 68327 69126 69898 00 00 00 00 00 00 00 00 OS OS OS Os Os Os OS OS OS OS OS OS Os Os OS Os OS OS Os OS Os OS OS OS OS OS OS OS Os OS Os oso>*sososo> 1 © M —CO 8.09510 8.39606 8.57204 8.69682 8.79354 8. 87247 8.93913 8.99680 9.04757 9.09291 9. 13384 9. 17112 9.20533 9.23692 9.26624 9.29358 9.31918 9.34322 9.36588 9.38729 9. 40757 9.42682 9.44612 9.46255 9.47919 9.49508 9.51029 9.52485 9.53881 9.55221 9.56508 9.57746 9. 58935 9.60080 9.61183 9.62246 9.63270 9.64258 9.65211 9.66131 9.67018 9.67876 9.68702 9.69501 9.70273 -co 09879 39975 57573 70051 79723 87616 94282 00049 05126 09660 13753 17481 20902 24061 26993 29727 32287 34691 36957 39098 41126 43051 44881 46624 48288 49877 51398 52854 54250 55590 56877 68114 59304 60449 61652 62616 63639 64627 65580 66500 67387 68244 69071 69870 70642 00 00 00 00 00 00 00 OS OS OS Os Os OS OS OS OS OS 9 Os OS OS OS OS OS Os OS Os OS Os OS OS Oi Os Os Os Os Os Os Os OS OS OS OS 0> OS 1 b M OS —00 10242 40338 57936 70414 80086 87979 94645 00412 05489 10023 14116 17844 21265 24424 27356 30090 32650 35064 37320 39461 41489 43414 46244 46987 48661 50240 51761 63217 64613 55953 57240 58477 59667 60812 61915 62978 64002 64990 65943 66863 67750 68607 69434 70233 71005 00 00 00 00 OO 00 00 OS OS 0> OS OS Os OS OS OS O) Os Os OS ^ Os Os OS OS ^ OS Os o^ O OS OS OS OS Os OS OS OS OS OSOSOSOSOSOS 1 —00 10599 40696 68293 70771 80443 88336 95002 00769 05846 10380 14473 18201 21622 24781 27713 30447 33007 36411 37677 39818 41846 43771 45601 47344 49008 60597 62118 53574 54970 66310 57597 58834 60024 61169 62272 63335 64359 65347 66300 67220 68107 68964 69791 70590 71362 CO 00 00 00 00 00 00 OS OS OS OS OS OS o> OS OS OS Os Os Os Os Os OS Os OS OS OS OS OS OS OS OS OS OS Os Os OS Os OS Os Os OS Os Os OS 1 b « N —CO 10949 41046 58643 71121 80793 88686 95352 01119 06196 10730 14823 18551 21972 25131 28063 30797 33357 36761 38027 40168 42196 44121 45951 47694 49358 50947 62468 53924 56320 56660 57947 69184 60374 61519 62622 63685 64709 65697 66650 67570 68457 69314 70141 70940 71712 00 00 00 00 00 OO 00 OS OS Os OS Os OS Os OS OS OS OS OS OS OS Os OS OS Os OS OS Os Os OS OS OS OS OS OS OS OS Os Os OSOSOSOSOSOS 1 —00 11293 41389 68987 71465 81137 89030 96696 01463 06540 11074 15167 18895 22316 25475 28407 31141 33701 36105 38371 40512 42540 44465 46295 48038 49702 51291 52812 54268 56664 57004 58291 59528 60718 61863 62966 64029 65053 66041 66994 67914 68801 69658 70485 71284 72056 oooooooo 00 00 CO OS OS OS OS OS OS OS ^ OS OS OS OS Os OS OS Os OS OS Ofc OS OS OS OS ^ Os Os Os OS Os ^ Os Os OS OS Os Os Os Os 1 b w —00 8.11632 8. 41728 8.69326 8.71804 8.81476 8.89369 8.96035 9.01802 9.06879 9.11413 9. 15606 9. 19234 9.22655 9.25814 9.28746 9. 31480 9. 34040 9.36444 9.38710 9.408.51 9.42879 9.44804 9.46634 9. 48377 9.50041 9.51630 9.53151 9. 54607 9.66003 9.57343 9.68630 9.59867 9.61057 9.62202 9.63305 9. 64368 9.65392 9.66380 9.67333 9.68253 9.69140 9.69997 9.70824 9. 71623 9. 72395 1 — OO 11964 42060 69658 72136 81808 89701 96367 02134 07211 11746 15838 19566 22987 26146 29078 31812 34372 36776 39042 41183 43211 45136 46966 48709 50373 61962 53483 54939 56336 57675 58962 60199 61389 62534 63637 64700 65724 66712 67666 68585 69472 70329 71156 71955 72727 oooooooo 00 00 00 OS OS OS OS OS ^ Os OOS OsOSOS Os OS OS OS OS OS OS Os Os OS OS 0> OS OS OS OSOS^^OS OSOSOSOSOSOS 1 § 1 —CO 12291 42387 59985 72463 82135 90028 96694 02461 07538 12072 16166 19893 23314 26473 29405 32139 34699 37103 39369 41510 43538 45463 47293 49036 50700 52289 53810 55266 66662 68002 59289 60526 61716 62861 63964 65027 66051 67039 67992 68912 69799 70656 71483 72282 73054 oooooooo 00 00 00 OS OS OS Os ^ Os Os Os OS Os Os A OS Os OS Os Os OS Os Os OS Os OS OS OS OS OS OS OS OS Os Os OS OS Os OS Os OS 1 © —00 8.12611 8.42707 8.60305 8.72783 8.82455 8.90348 8.97014 9.02781 9.07858 9. 12392 9.16485 9.20213 9.23634 9.26793 9.29726 9.32459 9. 35019 9.37423 9.39689 9.41830 9.43858 9.45783 9. 47613 9.49.356 9.51020 9.52609 9.54130 9. 55586 9.56982 9.68322 9. 59609 9.60846 9.62036 9.63181 9.64284 9.65347 9.66371 9.67359 9.68312 9.69232 9.70119 9.70976 9.71803 9.72602 9. 73374 05 M —00 12927 43023 60621 73099 82771 90664 97330 03097 08174 12708 16801 20529 23950 27109 30041 32775 35335 37739 40005 42146 44174 46099 47929 49672 51336 52926 54446 55902 57298 58638 59926 61162 62352 63497 64600 65663 66687 67675 68628 69548 70435 71292 72119 72918 73690 00 00 00 00 OO 00 00 05 0> OS Oi o> Os Os 0>0) OS OS OS OS OS OS OS OS OS OS OS Os OS OS OS OS OS OS Os OS Os Os OS OSOSOSOSOSOS 1 b o 05 M 80*£Z 08609 2888* 98281 oo- 83080 90973 97639 03406 08483 13017 17110 20838 24259 27418 30350 33084 36644 38048 40314 42455 44483 46408 48238 49981 61646 53234 54756 56211 57607 58947 60234 61471 62G61 63806 64909 65972 66996 67984 68937 69857 70744 71601 72428 73227 73999 oooooo 00 00 00 00 OS OS OS OS ^ OS Oi OS OS OS OS OS OS OS 0> OS OS OS OS os^ Os OiOiOiOiOi OS OS OS OS OS OS OS OS 0> O^ Ok 1' ill 3 • Oi-icMco-r •O CO t>- 00 OS OrHNCO-S- to CD t^ 00 OS SSS?5S to CO I^OOOS o5 CM CM CM CM OrHCMCO-^ CO CO CO CO CO lO CO t* 00 OS O rH CM 00 ■*»* to TT -^ --f -* -"J"^ r-t rHrH rH rH K O -K 00 IM CO «=000-H-^ O-^-OOlMCO (MMCMeoco O->J<00i- t^r* 03 OsO^OdO^ ScO CV) ^ OS ^ - coco t 03 01 O) OS OS CSQOOS-'KN Os ^ O ^ 0> ^^'^^^^ *^Wf^^O OtOCO'-Of-H ^HOQ*-^»-tt> OOCOOOSCD OSCrStOGCOO COCOCOC^.O CDiOWOO OC-t-^t^r^ t^t>-t--'t^t^ r-t^t^t^^ OS OS OS OS OS OS OS ^ OS OS OS OS OS OS OS t-ONCOt* r- c*l lo CO :0 CO O CO -^ OS SoO OOQO 00 OS OS OS OS OS OOCOO<^ M -t" f-t t^ O CO (M 4C r- O (>» (N cs c^ .-o ro 000000 0000 OS OS OS OS OS ^SJr^j?"^ -w; 1-t -t; -rr o oocooscowos ■n-coc^O^rr a)w(N«.-i cySTCCCM-w-^ fCOGOCD.-* (N-^iOCOt-- t-CCOOOldsOS 0000000000 ooooooSoo coSS^oSoB OS OS OS OS OS OS OS OS OS OS OSOSOSOSOSOS cc^*^*1^^^^ os-^t^os j;:-^ CO coo C^ O t^ TP 1— I o^^c^co OS OS O^ OS OS b* CO OS "0 1-t CO Tj« ''J' to CD OS OS OS OS OS O-^ eocO «-t t-CDt^C^Q _- r^o-^^OT cDi-hcD'-hO OUOQSCO--D COr^b-OOOO OS OS OS Q o b-b-b-t^t-- b-t^t^OOOO OS OS OS O) OS OS OS OS OS OS (Nt^t-r^CS _, r-< ^ C^ -!00 OCOOQCO>-H FH00i-H^Ht>. O O CD O OS CO QCOn'^rCM 00CMiOt~^t>- iJOCMr^r-i-^ iOttCMOSi-O OSi— icOCO'— • osioosco-^o ^^coo^ f^rirct^o cocooo»-Hco ior-a>ocM co»ocDb-oo ooososooo OSQO'— '•— • i-^CMCMCMCO COCOCO-^"^ "^^r-^Ln'^^ iOiQt.'SiOiO inioocococo b-00 00 0000 0000000000 ooooooobyj 0000000600 ooooooo6g«5 OOCCOOOOCCOO OSOSOSOSOS OSOSOSOSOs OS OS OS OS OS OS OS Os OS OS OSOSO^OSOS OSOSOSOSOSOS C^COCOO^ OOcO^OOOOS OiOCMtOp CO'-iOOiO'-' 00Tt«O«0?5 t^CMt^CMb-. ^CMCMCO-^ ----- . t^ b- b* t>- 1^ OS OS OS OS OS JCD«D'^< Tt«0«OC . "TP lo CO CO r— t^ b- t^ t-^b- OS OS OS OS OS b*AO < . t^CMl 00 00 OS OS OS OS OS OS OS CDiO«O^HOs 1-(CDCOOOO COOSOC^ - CMQ*t< cot* t-* 00 CO t^ OS r- OS CM ■^ CO CO CO ■*»< "»r ■^ oiSoooooOo) OS OS OS OS OS OS 03 OS OS OS OS OS OS OS OS b* CO "5 CO CO TOOoSoD 06 OS OS OS OS OS 00 10 00 00 -"J* -^ t—00 00 b- t^QOOSO ^ io>o »o coco CO 00 00 00 00 OS OS OS OS OS t^ b- CO t^ COb- F- 1 >.-trHCM 500 00 00 OS OS OS OS OS »-< cOOO 00 CM O -^ COb- CO COOOCM TP O COiOOOO ^ Tp Tf« tP lO 00 00 00 00 00 b>.COiO COCO O 10 CO Q »0 CM -^ CD 00 OS u5 10 iO »0 10 OOOOCOOOCO 00 00 *r b"b-cob-cDco OS S coco C^ O CM CO Tt< lO CD CO CO CO CO CO 00 00 00 00 OS uo o CO 10 CO »0 CO b- b- b^ t'- CD cO CD CO CO CO 00 00 00 00 00 00 OSOSOSOSOS OSOSOSOSOS OS OS OS OS O OSOSOSOSOs OSOSOSOSOSOS 000 lO CM OC CMCM CO-^'^ CM b-OCM CO CO lO CO ■<»" o 10 1-1 r^ coos *0 O CO I^ b- b-b-t^b-t-. OS OS OS OS OS rcOosTP OOsOioeo Tf CD CO ^ji ^H *r 0» ■^ OS f COOOOSOSQ b^b-b~ b-« CDM'OO b-^H Ob^ CM CD OS Tj- CO OS .— f CO Tj< tp ■-r 40 lO OOOOCOOOCO ^b-Ost^CM CMOSC^CMCO ^wb,r-i<: OOsb-'J'O ^rcoooooco ■^Otooc CD b- OS i-H CO ■•?• «0 C sss OOCO 00 00 OOOCQO OSOSOSOSOs OSOSOSOSOS OS OS OS ^ OS OS OS OS OS OS OSOSOSOSOs OSOSOSOSOs O CO CD ':D CO CO CD cO b- b- b- b- b- — -^ 00 00 00 CO GO 00 OS OS OS OS OS OS OSCOUJiJ^ J4 CO ^H 00 10 CM CM CO CO •9' lO i-< CD Oi ^ CM b^ OS ^ 00 tP 00 ■^ O CD CM »o CD b- r ~ CM CO in 00 CO COOQOQiO b- CO 00 CM t^ OS 00 01 -^ CM OS C^ CO CO"-! 00 00 00 00 00 ooooooSS ■^ 1-f cooco b-OCM 10 b- otSooSoo b-I>-t^b-b-. b^b-b-C OS ^ OS OS OS OS OS OS ^ OS O^ OS OS OS OS OSOSOSOSOS OS OS OS OS OS OOOOCO*-H •r CO 1-H 30 ■'^ OS — < CO T CO SCO CO CD CD 00 00 00 00 OS OS OS OS OS ^oOTMwb- OOOCMCMO t^OSOi-iCM CDcD b- b- r* 00 00 00 00 00 OS OS ^ OS OS O O coo OS CD 00 -r cco5 eoTj< CM CO CO -^ rp "«^ b- ir^ b- b- b- b^ OOOOCOOOCO 00 OS OS OS OS OS OS CM b- OS S in b^Tp-^OOu^ CM CO -^ TT O b-r^b-b*b- 00 00 --ICO ■^ SCMco-^r- 00 -^ o in coco b-C OS OS OS OS OS I 00 -t** c _)CO b-C b»b-.b-b-b>- OS OS OS OS OS tt uD b»0 in ■i-i COCOM 00 t^b-w 00 00 OS OS OS O^ OS *H O 1-" CO Tf CO CO b- CO ■^ 0000000000 OS OS OS OS OS COi-t ^4lOCO b-in 0"5000SOs b^ Tj< in 00 1-* TP t- CO CO ^ '^ ^ CO 00 00 00 00 OS OS OS OS OS Sin in lO CD OCD 0000 0600 0000 CM 00000 CO b-coin -^ b- cm-^ CO 00 OS - - coco CD 00 00 00 COOCOCOOS CM CM 00 CM T-( 00 t-H TT in in CO »-i b^ i-( in t— t- »-< CM CO -^ in CD CO b- b^ b- b- b- b- b- b- b^ b- b- b- b- b» b- 0000000000 000000000000 OSOSOSOSOs OSOSOSOSOS OSOSOSOSOs OSOSOSOSOSOS o b- in CM 00 CO CO "^ in in b- b- b- b* t^ OSOSOSOSOS OSOSOSOSOs OOOOO-^ rHCfl'frt-.CM CO in in ■^ o tp CD CO ■^ <— ' CO b' CO CO' oCcmo 00 00 00 S3 !S 3 1-1 in GO <— < i*« CO OS •— • CO coco CO ^ -n; ■^ lO in in in c 0000 oooooboooo 000000c OSOSOSOSOS OS OS OS OS OS OSOSOSOSOs OS in b» in o OS Cs t^ Tp O lO t- OS 1— t CO CO CO CO b- b- 000000 00 00 OS OS OS OS OS ? CD OSi^iOOSOOiD Tp in CO b- 00 5 CO CO ^ -TP b- C . b- b- b- b* C OS OS OS OS OS 000000060666 OS OS (^ ^ OS OS ,-. __._ -J-ft^CM GOb-OOCO*-- b*»-^cocoQ int^b-coc^ cooooococo b-o^-^os inc;scM-r CO^OOiDCM OO-VQCOCM b-CMb-CMI-^ r-fcDO'^t* ^htj<00^ OS OS in OS 00 in in ^ 00s ^ CM CO ■v ■*?< in CD b-b-b-.b^b» OS OS OS o ^ o mcoo^ OO-rr QCOCM cot^ooooos - ,™^ „ b*t^t"-b^b- i-o5oooooo OSOSOs^OS OSOSOSOSOs ^OSOSOsOs OSOSOSOSOS OSOSOSOSOS OSOSOSOSOs OSOSOSOSOs OSOSOSOSOSOS ^ osmb-mo ot-»oo n- 00 O 1-t 1— « OS CO C^ CO GO o o _,__-- ,,- , -^. CM-rb- OSi— iW-^CO b-OOOi-'. ,.., CMCMcococo Tp'W''^intn intncococo cob-t>-b-t^ r-b-cccooo 0000 OOOCOOOOCO 0000000600 0606000000 00000000 'GO OOOOOCOOOO COOO eo'tf'inino b*b- _ __ t^b-b-t^b- l^b*b-b-t^ CO^^-^* CD t CO OS OS b- S t- 00 O CO 00 OSOSOSOSOs OSOSOSOSOs 00 00 00 00 00 OS OS OS OS OS ■V CO -^ 35 t^ OSCM COCiO ^ (N coco -»* 0000000000 OS OS OS OS OS OS ■^ '»J»00 CO CO *-*•»»« 10 in ■^ CO 1-H -itf b- M? t lO lO lO 00 00 00 06 od OS OS OS OS OS oooCM^m in-^cO'-^co ocoi^ooo CO CO coco b- 00 00 00 00 00 OS OS OS OS OS coco^ooco CM ^r CD b* OS b^b- b-i^r^ 00 00 00 00 GO OS OS OS OS OS owococM io»0'-'in'«j"-< b^OrH^O b-COOO^CO-Tfi SCM CO -n* "? in CO CO b- b» b« OOCOOOQQ CQOOCOOOOOOO 0000060000 060000000000 OSOSOSOSOS OSOSOSOSOSOS CO "^ in CO CD b-b-t^b-r- O OS OS OS OS ^ 9 OS OS OS OSOSOSOSOS OSOSOSOSOS OSOSOSOSOs OS b-^o f f ^r--i-i CO COCO 00--^ CO CDCDCD b^b^: 00 00 QO 00 GO OS OS OS OS OS ■^ O CM O »0 in b-CSOCM t^r^b-ooGO OOOOCOOOCO OS A OS OS OS ooi-hw^.-^ ooM'S^s'in co»ncDb-co ooososooo QQCdOOOOOO 06000Q^030> 06CO000600 55 00 00 CO 00 38 OSOSOSOSOS OSOSOSOSOSOS a- lOCOb-OOOs Oi-lCMCO'i* lOCDb^OOOS O'-'CMCO'^ 'ncDb-OOOs O-HCMC0*t< ifSCOt— coos O'-HCM So -V 00 CM CO OOO--^^ *ctco --- ._- --_ _ -.- ._- --,. ., , ^. ..,,„,- mcDt^ooosc ininioioin loiooioin cococococo cdcocdcox; t*b-b-t^t^ t^b-i^i'-b^ oooooooooc ooooooooooc s^ OOCMc© 0"*'»CMcD O-^OOCMcO O'<^Q0CMe0 O'a»00CMc0 CMCOCO ^r^ViOiO 000«^«-i CMO*CICQCO ■^'«»^>0»0 ScM QOCMcO O-^OOCMcOC Page 170] TABLE V. The Finding of the Azimuth. N*^ ^^^^^ ^^^^^ CSCSC4C4C1 C^C^WCiCN CO CO CO CO « CO CO CO CO CO -^f TP -^ -i--'-ieo t^OOCOirfO OO'-H'-Hi-t odoOOOOO 0606060606 OsOsOiOiOi : COCOQCO I oco«oco '^OOQOC^OO CO CD M CO 05 CJI Oi »0 Oi g S S (N C5 CO Od C> O^ O Ci coo$5C^sP CO CO c^^ 00 CJ ■^ CO QC Oi CO CO CO CO CO O) 03 Od 03 o^ COCOOOO.M ,-lC < CO "0 CO r- cc 00 00 00 ^-cp■^eo'— ic > r-« cn CO -^ lo CO r- og oio»-hcscoc .._.^.j' .i._.Te._.Ti IOCOCOCO• St^ ,-t Tf r^ iCOiOiCOOS OOOCOCOCO rH ■<** o *-i r- c^-^r-orp 1--. -'^ C* Ocp C6 OS CD w *-i ^ r^ lO CO O w ,-. CS CO -^t" CD O CD CO CO CO OS OS OS OS OS OS COOSh*»C b-OCOCOO .b-COCO"^ ,-H^t^-w-C' io»-tr^N OsocpfNC ■n"i>uOCOiO t>- iM ^-t 10 1-H C^OiO»000 C^-^C^lOO'^ 't'^HOOOOCO co^eoi-t-^ 3* -h 00 iC "r co O^Pt-*CSu5 00W0000»O OS^-^I^i-i 00t-^OS'*-«P OOI^OOl'^ ''pQcOCSt--. OSCCCOCOCDCO , 00a»cDC>c5 — tOs'^OOi-t C^COOIOOO -^OiOOt r^oco*rcD b-OOOOOOt;^ cOiOtCNOOO , ^, ^ _ ^ co»- lO^iO^CD COCDCDCOCDCO OSOSOSOSOS OSOSOSOSO-O: coost^ws 8 0000c CO 0>OcD»-i I OCOiOCD 06060606 t^OcDCOO SKS2S -00 00 CiO odoioooco ■«1- t^ IC OcD cOCOcDcOcDcD OSOsOSOSOS OSOSOSOSOS OSOSOS^OS CSOSOSOsOS OsO^OSOsOS OSOsOSOSOS OSOSOSOsOsOS 8-«*cocO'-i oor^-^i-iQO lOiOCOiO kCCOOSUOO locooco t^oooooso 06060606 060606060s CQ^ '«t*cpC^ O>C0O-*cD ^ OS CO CD OS OS OS oT cs ci -^00 00 eg 00 CI lOb- oc^ C^ (N wcoco OS OS OS OS OS CO CO CO ■^'-1 Ti CD OOOC< CO CO CO Tp "^ OS OS OS OS OS ttiOOOSiO*-* ^CO^i— f t-H 00 -n* OS -n* 00 CO "0 CD 00 OS 10 CO »^ cot::; »-< -n" CD 00 O 1— ' C» CO ■^ CD »o ^ »o o 10 OS OS OS OS OS OS OS OS OS OS CO CD O 00 .-( T-H r- o 00 -v r^ 0001 O^^ lO W5 O CO CO OS OS OS OS OS 1-H OOW^C^i-iCO CD "*** O CO CO O ocsooco^ ^ C5 M CO '^ i--^ CD CD CO CO CD CO CD OS 9 C^ OS OS OS S5i! 8QO»— I— 10 CS'-'OQiOC^ 00OS»«Q t^cOC^Oi-t ,LO»OCOCO OCOO«>-^ OCOiO CD 06060606 i:^ ooosc 060606060s CDICOOOCO 10 OS CO CD O OS OS OS OS OS "^00002300 OS cs 000s 10 osr^ CJcoos c OOiCO o osr--i-i oio irti 00 1-H CO 'S' .-I cs -^ lOcp »0 iC >Jt UD 10 OSOSOSOSOS OSOSOSOSOS ?^P25ri ^OQiocs^co JO(»Cp iC ic lO CD O OS OS OS OS OS CO CD CD CC CD CO OS OS OS OS OS OS xco-^O"^ V CO CO 'i' CD I OCOOCD 06060606 COOMOCSOS iO •^»-i OOiO CO "T" O CDi— t t^ 00 OS OS o 06 06 06 06 OS CScOCS ^Cft •<** .-c r^ ,-1 CO ^-tOS^ -^b- sts; COcD-^iO-^ CDOO gOOi-H cocs 1— ( OS CO ■^ - - . . . CDOCOr^O COCDOQ^-* o ^ r-t »-i cs CSCSCSCO OsOsOSOsos OsOSOSOsOs OS OS OS OS Os CO iOr*o>'-- cs CS1-1 -^ cooQ Qcoior-oo ^CO-^»Ccp OS OS Os Os Os ilOOOCSOCO CO O t-* "^ CO »'5 00"^^*cp'-* cocst^oOt-- OSOOOQ OsoOcOiOCOO t'-ClOT-HC^ c^co-^^coi^ lOiCcOcDcO cDcDcOcOcD^ OS Os OSOSOS OSOSOSOSOS OS 5 CO O 00 t— -^ I OCOU^cO 06060606 »-t -^ o 00 t— 'Tp 10 TpT-H _ _ CO "T* 1-1 CO i-" r^ooososo 06 06 06 06 OS S 2:n 00»-o OS Os OS OS cs ocot-»coo i-H t^ OS 00 CO 000s Oi-* ^ ■ 10 10 CO b- I OS t^ » . _ , JiO CO t CO CD CO CO CD CO Os OS Os Os Os Os' ■*OOOCD 00 »-< b- ''f 1-t iO0CCPb»CD >iO-pcs ososujcso cocsi55r^co icsooco crsoooco-^ osot^i-ico [oco^co r^obososo 0'-''-"'-'Cs 06060606 060606060s' OSOSOSOSOS OOCSCSCDCS TP r-^ OS »-« ^ CSCSC<)COCO ^C0«0^ 3CSIOOS - COi-t 00 DOCS CO CO cs coos 10 CD to t>- C^ W iC 1-t CD ^H »0 »0 t— CC- O ^H OSOSOSOSOS OOSOSOsO TP Tp TP lC*0 OS OS cs OS OS 1.0 cs OS OS -^ CD to oor^ cs OO*-" co»o t^ cs f i-O CO t-- O 10 lO »S W3 h- O-'^^CSiO cs Os^^ OiO Os Os Os Os Os cs OS Os Os Os iC cs OS CO wt l~» b- CD r-l -"f M" 1-t r^ CO 10 CO —K OS CO t* lO CD r^ r- CD CD CO CO CD CD O OS OS Cs OS OS "^ Ooo CO CD CO IQ CO JiOcDCSl— I OcO"J =D 06 06 c^ 06 00»-lt--^P^ »O00«Db-CO OOCSCSCOCS OOCDcOtM '-PCOCDOO'^ *^ .^ ^ ^ •^coO5i>.0Q CO -^p t-t to r^ r^u5T-tr*cs i^i-«kOoOT-i I-OOOSOSO O— i'-<»-0 O >0 OS 10 t^ OS O-H Os OS OS Cs Os iOCSOsOS*^ t'-O'^CStO 1-^cOOsooco ■ "~ -.pcsto locsoscoior^ CO o cs f-H CD 00 I— cs i-o to cs Csc^cocooi r-o ^ S? IjOsoso Or-tt-i' 06060606 060606&60S OSO>OSOSCS CD OO-* O cpOCDCD ^ CS«COCO CO OS cs OS OS OS t-^cs»oos OS Osos h» -^ i-^ OS T-*eo 10 CO cO "* ^ ^ OS cs OS Os cs ^o^t-co coor-*r>.cs lOoocsoco cotor^cscs to>oooi--cs csoor-io^ »-t b- cs r- »-« -^t— o&.- O-^QOO*'^ O'^00N<£'O uiot^oooi o^NfO'^ lOcor^coos o^c^eo'^ »cor^ooo5 o«-ic«i iOiOiOiQiO (DCOO^DO cotootoo t^b-r*t^t-- t^t^r*' ' 0000000000 oooooooooocB os'<*|r^<3iO ooS-^f-g*--! ioo5cio«;c _ ■ r- 00 Oi o> CO CO o -^ o O^fOcO f^ oi Oi r^ ^ ^ t^ CO t^ c^ c O ^ 'O Oi CO . 03 0> O) Od ^ O) C^ O^ O^ Oi O) 03 0> O) O) (3> 0> Oi Oi Oi t^ i^ t^ 1^ r- 03 0> 03 0> Od CO ^^»0 "*00 (N u5 t- ex (N CD CO O CO 1"^ * CD -^ 0> Oi CD C 1 O t^ 5i O Oi c 5 0> CD C^ t-- O CM CO ? CD t>- CO OO ^ a> Ci boo 00 00 CO CO OD CO I- r- 1^- 1^ t' t^ O) Oi Oi Oi 0> O) 0> O^ 0% 91 CO^HOOiO^^ OO'^QcOfN ■^iciocor-. b-oba&CBO OCDOCDCO COCDCOCOt^ Oi Oi o 03 c^ a o o> Od o^ o •-< • . _ r* t^ r^ r* t^ lO t- 1— »o c^ 00 r* 00 CO --I en O) OS Oi o> COOO ooc^ o 'J* oo*-" coco iO ^ "O CD cD t-^ t- 1^ t* t^ 03 O^ OS O) o^ I>- O: CS -^ CD CO o r-t^;^ b- t- t^ £-- t-» 03 OS O) OS OS 8tot— LOO or^oocD OS— *CN-. t^ t^ r^ O OOs OS 0> OS OOO"^^ C^t^ONCO Cfi'^^Q>'ri* OOsO»CCO lO O Q "^ CS cD "^ 00 b- i-H »-< f^ OS h* N C^ OS C*4 W OO i-t »-l r^ t-H o r- COOCOCSCD i-HCO-^C^OO C^'^'^CSIO -«t*cp00t^»0 i-(CO^OO OO^OO-rt^t^ OOt^^OC^OO C^I-^cOCp^ (NQ0-tcp csi^cst-i-H cdothooc^ oosoicoct) 1— i-rr^Oi'-' coior^cso oi— t-t^t^t^t^ r^t^t--t^t>- i>-i:^t^i>t>. t^t^i-t^t^-t^ O^OsGSO^OS O^OsOS OS OS OS OS Os OS OS OS OS OS OS OS OS O) Oi OS OS OS 0> OS OS OS OS O) OS OS 0> OS OS OS OS OS OS OS OS OS Cs OS Cs ^ Os O d CO -^ CO 1-t t-H CS -^'- t^ 00 oooo -t^t^t^ t^t-^t-t^t^ rP'^lNOS'^ OOrH^CSr-H .t-I^ CO"*COOS"^ ^ CO CD "* ^ ^^ O -H CDi— I C^l C^ CO CO "^ O OSQ »OCO CO ooo OS r^ lO os'^ r^i-H ■^ -J« lO lO CO OS Os Os Os OS OS osososos OSOSOSOS Os »o o o ■«** N CD ■<** QO t>- T-t O t^ CS O OS 1-H CO CD OOO 00 00 00 GO OS ^^i^^c ■^fO-^OOC — it>-Ost^C4 cooooo gssss CO CD CD CD CD CO !>• t-- t-- t* Eroso o-HcocDi-H h-tor^NC cocor^-ooc Os^^< •O -H CO O 113 c5 coco ■* -^ cs t-r>.i-4 0s CO C^ lO t^ CD OSCO CO C3SM CD t^ t^ t^ 00 CO -^lO-^ 00 »0 C^l t>- i-i CO -5*0 IlO OOOCO* , OO 00 OS OS OS OS^OOO GOOOOOOOOO oooooooooooo O OS OS OS OS OS O^ OS OS OS OsOsOSOsOs OS Os OS OS Os Os Os Os Oi O^ Os Os Os OS OS Os -^^^Z to-*. OO-H-HC^ Of-HCOCD^ COiOiOCO O OiOOiOO CO CO 'T ^3* "O t^t— t^t^t- ^ b* 00 00 CD 4!ooc^ coo iO "O CD CO r^ c*< fN. h* ,-( gs cO'-*iO'*oo (NCOOSi-hO OSCOr-tlOt^ '^t-OTt*!^ osi-«CS t^»-te0C0O »Ot^l:^cDCS i>.r^o6o>os c>.-«^c^6» CDCDOCOCO t^t^t-t^t^ I ^ Tf< lO OS 00 OS"*** cs h-0^i-t0> -t^t^r* t^t^r^t^t^ ^ OS Os CO ^^ lO OSCS Tj" -^ OO — I lO GC 1-1 l^OOOOOO OS lOCOt^tOO csos-^oo—i ■^ CD OS wl* Os OS OS o o OCDOOCD^H i-H CO i-l 1-1 b- OOCOOOSO CSWOCDCS CDOOOOOQ cpwSoX^CS CO00g5»-ICO '^LOt^OOOO OSOO— "•-<<-( ooo.-«^H 1-H ^ 1-H ^ 1-H •-t CS c5 cs CS cs OCOOCOOOOO GOOOOOOOOO OOOOOOOOOOOO Os Os OS ^ 0> Os OS OS OS OS Cs OS OS 0> Os Cs OS Os OS Os O OS OS OS OS cs OS Cs OS OS OS OS OS OS OS o S'Tj'-^coCs ■^ CD IOCS lO cs ^ CD CO i^coooroo cDi-t^cDt^ r-QOoo-^ ScDCS I>.CO 1-HC iN-i>t^t--r- I*- OOO CO 00 QQO<-Hasio CC-^CSCOOQ O CO ^co ^^ St^i-H lO OS Osrf-*OOCD OQOCSwiO »0 ^ CO w O SiOi-tlO ^T-4 OOOOOOCSOs OsOOC t^ 00 00 00 00 cs OS OS ^ OS o OS ^ OS od OS OS OS OS cs cs CS OS OS OS '^-fCSCS'* d5i-icsc5-^ 00"^OSCS>,-_ O cs ■^ lO t>- 00 O 1-H cs CO CO M< "^ lO to lO ^^^^^ T-HCSC^CSCS CSCS«CSCSCS OOOOGOOOOO 0O0CX)00OO OOOOOOOOOOOO O^ Os OS Cs Cs Cs cs O Os OS OS OS OS Cs OS OS t^i-Hi-* lOcO -H cDoo r--^ OS ^ CO o f-* r^oooso o COCOCO b* t^ O OS OS OS OS COOO'-'CO'^ -HCSC^COCO ■^ lO t^O lO o CS cs 1-H t^ ) cocoes 3i-(i-HiOfO tN.iOOS00CS _S'*^r^ooco cDcoooc^'O COOCOCOOs C»»Oi>.OCS ^lOuocD cor^r^r>.oo oooscsdsos ooo^^i-t ,-h^i-h^cs )0>CO . _ __ ___.r>.oo r^t^t^i^t^ r-t^i--t— t^ t* t-" !>• t- t-" i->- 1^ t^ r- 1- oooooooooo 3000CO COOCOCOCS cs cs OO cs r-^ 00 _ S-^OCO OCOTHTt^CS C^ zn C^ ^^ a-i CC-. rJ-OiO -csoo»o 3*CSC)-H 5cD Cs OS cs OS OS Os OS OS OS OS OS »-tO^CO"* »-|iOOSCOt " " " -ooc. O »w 1-H lO CO O »0 000 cs ■!*' »o »o CD CO t— b^r>.oooo OS cs cs c r- t^t^ooco Os Cs OS Os Os I^iOCSOOCS t^-^OSCO O OOOOOOOOOO Cs OS Cs OS Cs CSOOOOOCO COOCOCOOS CSCSOON^CO I^COiOi-Ht^ ^-^UtiiOCO i-Ht^^iOl^t^ ooocs-^io t>-oooso^ cscscocococo ^cscscscs cscs^coeo eococococ»co oooooooooo oooooooooo OOOOOOOOOOOO Os Os cs OS Cs Cs Os Cs C7s OS OS OS OS OS OS Cs -S^-c o-^-^coc: CD— -i-*r>-r»t^ t--.t>.t'-i>i>- '^Ot-' OS '■*<'<** OO CD OOOCS-HiO csosososos osososcsos ososcscsos cs OS OS OS OS r^ooooos oscso _ . . , CO^HCO OCOCOCDCS lOiOi-fuO-^-H o»oooosas opt^o-^co r-t>-»ocsr^ r~t -rf* io lo -^ «-Ht^csiot-.oo lOOOi-H-^t- OCOCDOOQ CS-^cDOOOs .-t CS CO -f lO O cD t^ t^ t^ r- OO ^H i-< 1-H 1-H o5 CSCSCSCSCS cococococo cocococococo OOCO OOOOOOOOOO oooooooooo OOOOOOOOOO OOOOOOOOOOOO OS OS CSOSOSOSOS OS Cs OS ^ OS OS OS OS OS OS OS cs OS OS OS OS CDOQ-* lO Oil b- OS OO u-r> »-HQOiO OSOSO COcDt^t^t^ Os cs OS Cs Os CSt^OCSCO CO'^CDOS'** OCS CO »-< t^ - , . _ COCSOO -^ Ci O 1-H 1-H cs CO CO Tf Tt< Ci cs Cs OS cs OS Os OS OS OS O OSO »oco CO »0 t^ CD -^ cs CO t^«-< »0 t— 00 00 OS OS cs OS Os OS Cs CD ''fOOt^-H t^ -^t OS CO CO 'f r-cscs -^ i-Hh*c>r*cs cscscscsoo t^ CD -J< i-t (^ 1-H CO 'O lO CO COCOOCSCO iOCDl^COCS cscscococo cococococo oooooooooo oooooooooo osososcsos csosososos csosososos OS Cs OS OS OS lOOO-^CS O tOGO CS04 CSCSiooO i-H C3sOOO.-t Ir^ 00 00 00 OO ,-H^t^^or^ 1-H r- 1-H lo i^ t^ OOOOOOOOOOOO cs OS Cs OS OS OS osooos'* cs i-H rt" lO O CO St^-H lo d 00 OS OS OS lO CO t^ CD O o CO 00 cs »o OO ^CO COGO *-tCSCSCSCS OOOOOOOOOO OSOsOsOSOs OSOSOSCSOS OSCSCSOSOS OSOSOSCSOS OS OS OS OS Cs OS locoh-oocs o^csco O^HCSCO-^ lOcp lO^^U^iO to iO :S3§2S 8 h»ooos o^^csM-^ lOcoh-ooos o-^cseo-* lOcor-^ooos o^hcsco;^ lOcor^ooos lO iO lO CD CD CO CO CD CD CD CD CD CO -*OOCSCO OfOOCS cscscoco -^ -^ ■^ lO g S3S22 CSC^(NcOCO N -JS O -»> 00 N !0 -t^t^r^ oooooooooo oooooooooo g o-^otc ?5cscsc O -^ 00 cs CPQ ^ -4* 1^ i0»00 Page 172] TABLE V. The Finding of the Azimuth. w5 S o -i> 00 e^ -^ g'S'OONCD OO-H-l )MC4C0CO o-^oocqo o-j-ooNo Q-*ooc^to oi>ooe<>co< 52S § OfHCsec^ «3cDt^Q0Oi o.-HNe^'f W5cot'-ooa> Oi- o> o> o> C^(MC^ coco 0> O) 0> O) G3 O CT> 1-1 t^ CD SCOOOiO OOi-iiOCOcO JOiCOC^CD COCOiO-^CTi . 05 CS -^ IQ CO I"- I"- 1-^ CO 2S coooco>o OiOiOiOiOi OiOiOi aOi • coco *.-< TO -^ lO lO CO »0 lO lO O lO ^ O) O) O) O Od o^ r^co*-< o> V coo rr* CO r>^ 00 CO 00 lO TT •-« t'- WJ SCO or* CO ■n" I-" CO ■— I O I^ 00 00 c» 0600060606 OiOOO<-> 00 G3 O O) O) 1— I U51O <3i»^ C^lCilHr-JCO r-.-^ o-^ CO Oi O) 0> O) O) co-Tf as iff-c ooooi^ coc trj i^ 05 1— I c c5cs ICJC^OOCO 0> CS 0> O O) 0»0 cp W 00 1— I oc^oo^- ira O 00 C5 O CO CO CO CO '^ O) O^ O Oi C^ CO -^ CO t-- O O) C3 O O cioa>o«-HC^ Tj< -^ iO W3 1/5 0% O OS o o^ oo»oc^giooo CS »-« Oit>- U5 CO 00-^ (NO 800000 (N CO 01 CO . t- ^- -r r— I ocs-^io l>^ 06 06 06 C^iC— 'OOiO IQ Tt< 1-H t^ 10 <© OICO CO -^ r^ rr --H t^ cq Ot^ 00 00 OS 0606060606 OiC^Oi-H Q 00 CO ^H CO 03 OSOCOC^CO 01000^ 00 OS O) OS OS C«coco0!:0 eqwj »-< ojoo CO oco ocs ■^ t^ OiC^ -^ OS OS OS OS OS »-- 10 O O CO cocoO(Nco *or--ooO'-< f -r coiM coco 0(N - , C^ CM CO CO CO OS OS OS OS OS co(Nr-' ut. r-- r- ■ coco < O OS OS OS ^ oscocococo »-t*^00OO Tjt -^ »0 lO to ^H O-fCO t OIC^ Tf CD t^ CI TT io CO r- OSCO CO QOS-H 00 r^ fcO ■n' "-H OS CO "^ 10 CO r^ r^ kO to IQ to «0 lO ^ OS OS OS OS OS OS OS OS OS OS O) OS OS OS OS t^ CO -^ OS .-I '^ O t^ ' r-»oc^r^ CO CO r- CO 00 OS 00 --< OS 001 ) CO -^ t^ r^ OS O-Hi-t^-HO rfiOCOr-OO 0*->C^COTt< ■■^■^■Tf'-f"^ tOtOtOtO^O OS O) OS OS CS OS OS a OS OS «OCO ot^coco OS 00 -V CD CO CO OS 00 r^ to CO <-< -ji io cor^ coos lO to to to to to OS OS OS OS OS Oi SOSOCO^ . 00 OS CO OS I oawrto CO OS to C^ OS 00 t^ ^T* i-< 00 I'- CD CO 1-1 i-< 00 CD CO OS -^ ot^ 00000s 0606060606 CO CO M' 10 ■*** Cvq^Tl«COC^ t^OOto OS--« OOC^OOSCO OSOOO— 4 CO 00-^ o CO 00 -H CO CO CO OS OS OS OS OS OS OS OS OS ^^ OS ^ ^ t^ CO OOi-H -n* 00 i-< — t ^ OS CO cooe^coto (N CO CO CO CO OS OS OS OS OS t-( o^t^co iQ -^ CO— < i-< CO OS "g* OS CO t-^CO 0—» O OS -^ CO OS •-( CO 10 CO :d r^ CO CO '^tor^cocS o»-«c^co'3' •^ -v ■^ "^ ^f to to to to to s Ot^-^ CO to 5 to Oco coo >-^#o^H os^- >cp^- 0000 OS OS OS OS OS O^ OS OS OS OS OS OS OS OS OS o^ Sgstoco <-H Os Os 0>t^ TJ* tO—l O . OSOTt^ OS os(MTrto cocodosco -n^cOOCD-^ cocq oscot^ St^oOooos 0606060606 00 t-- o c^i 00 C- to CO 8oot^ t^ to »o cocs r^ . 00000 I oco '^r CO tQco-qo»-<'>3* t^t-»00C?SOS OOO^Ht-( 0606060606 OSOSOJOSOS 01 5* 00 OS to CD ■3' OSCO CO t^oc^tot^ OS OS Od OS OS OSi-< COtO t^ W CO CO CO CO OS OS OS OS OS SOSOcOW t^ O to to OS to •— t to OS OOOfNCO^ W OS CO CD —I OS r- — I Oto ^J« -V •* lO to OS Os OS Os OS OS OS Os Os Os tO«-<"* ^ 00 c^ CO coco c* CSCO n* to CO 10 to to to to Od OS Os Os OS C^^ OS cocoes ■»}' 10 to to to CO CO OS OS OS OS OS OS oo^c^o « 00000 I OCO"* CD 00 00 00 00 W to •-< CO to 000 1— I CO t^ t>» 00 OS Os 0606060606 cscs o-^ o 00 00 ■-< CO OS OS OS Os Os OS C^COCOOCD C^tOi-i^CO M OTtO OSi-H COOCOtf? 00 OS O OS OS o> CO CO CO CO CO Os OS OS OS OS r^ CO t^ CO OS 1-1 o — iOO*OtOO COOOCC— 4 — (COiOC^— ICO CO — ( to "* OS OS 10 00 CO CO •* CO 00 —I — < 00 00— (COtOCO t— OOOOCOOO t— CP-*C0— 100 000— iCqcO "*tOCDt— 00 OSO— IC3COCO ■*?' lO to »0 to to to *0 to to loiwCDcDcDcD OS OS ^ OS OS OSOSOSOSOS OS OS A OS OS OS 9* Of-IC^lM-n' »O5Dt^00Oi O^C^M-- )2;ociMo o-weodco ottoocn ir3«ot^00O5 o-^N«'* 1P;S~2S NNwe^cq M«c<>c^c>i cococococo s «D i^ 00 o> O^HC^eo-^iO _, _^ ^^OOWO O-'J'OOWO O-^OOCSO O-^00.Co 000-H.-1 nnc^coco -^t-^ttioio ooo^-h ojsr'>r So 9.66758 9.67502 9.58222 9.68916 9.59587 9.60234 9.60859 9.61462 9. 62044 9.62605 9.63145 9.63666 9.64168 9.64651 9.65118 9. 65562 9. G5991 9. 66402 9. 66797 9.67175 9.87537 9. 67882 9. 68212 9.68526 9.88824 ,9.69108 9.69376 9. 69630 9.69869 9.70093 9. 70303 9. 70499 9.70681 9. 70849 9. 71004 9.71144 9. 71271 9. 71384 9. 71484 9. 71570 9.71643 9.71703 9.71749 9.71783 9. 71802 9.71809 1 00 57370 58114 58834 59528 60199 60846 61471 62074 62656 63217 83757 84278 64780 65263 65728 66174 66603 87014 67409 67787 68149 68494 68824 69138 69436 69720 69988 70242 70481 70705 70915 71111 71293 71461 71618 71756 71883 71996 72096 72182 72255 72315 72361 72395 72414 72421 OS OS OS OS OS OS OS OS OS OS OS OS OS OS OS OS OS OS OS OS OiCROCnOi OS OS OS OS OS OS OS OS OS OS OS OS OS OS OS osososososos 1 05 •0 57971 58715 59436 60129 60800 61447 62072 62675 63257 63818 64358 64879 65381 65864 66329 66775 67204 67615 68010 68388 68750 69095 69425 69739 70037 70321 70589 70843 71082 71308 71516 71712 71894 72062 72217 72357 72484 72597 72697 72783 72856 72916 72982 72996 73015 73022 OS OS OS OS OS OS OS OS OS OS OS OS OS OS OS OS OS OS OS OS OS OS OS OS OS OS OS OS <3i OS OS OS OS Os Os OS OS OS OS OS OSOSOSOSOSOS 1 b o ^• "5 58560 59304 60024 60718 81389 62036 62861 83264 63846 64407 64947 66468 66970 66463 66918 67364 67793 68204 68699 68977 69339 69884 70014 70328 70626 70910 71178 71432 71671 71895 72105 72301 72483 72651 72806 72946 73073 73186 73286 73372 73445 73505 73551 73585 73604 73811 o>o.oo» OS OS OS OS OS OS OS O OS OS OS OS OS OS OS OS OS OS OS OS OstOs Os Os OS OS OS Os Os Os OS OS C3S O*.! Os OSOSOSOSOSOS 1 O CO >0 59138 59882 60602 61298 61967 62614 83239 63842 64424 64985 65525 68046 66548 67031 87496 67942 68371 68782 69177 69555 69917 70262 70592 70906 71204 71488 71756 72010 72249 72473 72683 72879 73061 73229 73384 73524 73851 73764 73864 73950 74023 74083 74129 74163 74182 74189 OOJOiCRO OS OS ^ OS OS OS OS OS OS OS OS OS OS OS ^ OS OS OS OS OS Os Os OS OS OS OS OS OS OS OS Os OS OS Os OS OSOSOSOSOSOS 1 59705 60449 61189 61863 62534 63181 63806 64409 64991 65552 68092 68613 67115 87698 68063 68509 68938 69349 69744 70122 70484 70829 71159 71473 71771 72065 72323 72577 72816 73040 73250 73446 73628 73796 73951 74091 74218 74331 74431 74517 74590 74650 74698 74730 74749 74756 OS OS OS OS OS OS OS OS OS OS OS OS OS OS OS OS OS OS OS OS Oj OS OS OS OS OS OS OS OS OS OS Os OS OS Os OS OS OS OS OS OSOSOSOSOSOS 1 b M »0 60262 61006 61726 82420 63091 63738 64363 64966 65548 66109 66649 67170 67672 68156 68620 69066 69495 69908 70301 70679 71041 71386 71716 72030 72328 72812 72880 73134 73373 73697 73807 74003 74185 74363 74508 74648 74775 74888 74988 76074 75147 75207 75253 75287 75308 75313 OS OS OS OS OS OS OS OS OS OS OS OS OS OS OS OS OS OS OS OS OS OS OS OS OS Os OS OS Os OS OS Os Os Os Os OS OS OS OS OS OS Os OS OS OS Os 1 b o lb 60808 61552 62272 62966 63637 64284 64909 65512 66094 66655 67195 67716 68218 68701 89166 69612 70041 70452 70847 71226 71587 71932 72262 72676 72874 73158 73426 73680 73919 74143 74363 74549 74731 74899 75054 75194 75321 76434 75534 75620 75693 75753 75799 75833 75862 75859 OS OS OS CS OS OS OS OS OS OS OS OS OS OS OS OS OS OS OS OS OS OS OS OS OS Os OS Os Os OS (SOioioao OS ^ A Os OS Os ^ Os Os OS OS 1 >0 61344 62088 62808 83502 64173 64820 65446 66048 66630 67191 67731 68252 68754 69237 69702 70148 70677 70988 71383 71761 72123 72468 72798 73112 73410 73694 73962 74216 74455 74879 74889 76085 76267 75435 76590 75730 75857 75970 76070 76156 76229 76289 76335 76369 76388 76395 OS ^ OS OS OS ^ OS OS OS OS OS OS OS OS OS O OS OS OS OS OS ^ OS OS OS Os OS Os OS Os Cs OS OS OS OS O^ OS OS OS OS OJ OJ O) 0-. C-. 1 15 61871 62815 63335 64029 64700 85347 65972 66575 67167 67718 68258 68779 69281 69764 70229 70675 71104 71615 71910 72288 72650 72996 73325 73639 73937 74221 74489 74743 74982 75206 75418 75612 76794 76962 78117 76257 76384 76497 78697 76683 78768 67818 76862 76896 76915 76922 Cl OS m Ol OS OS OS OS OS OS OS OS OS OS OS OS Os OS OS OS OS OS OS OS OS OS OS OS OS OS Os O OS Os Os OS OS OS OS Os OS OS Os OS OS Os 1 >0 62388 63132 63852 64546 05217 65864 66489 67092 67674 68235 68775 89296 69798 70281 70746 71192 71621 72032 72427 72805 73187 73612 73842 74166 74454 74738 75008 75260 76499 75723 75933 78129 76311 76479 76634 76774 76901 77014 77114 77200 77273 77333 77379 77413 77432 77439 OS OS OS OS OS OS OS OS OS OS OS OS OS OS OS OS OS OS OS OS OS OS OS OS OS Os OS Os OS OS OS OS Os OS OS OS OS O Os Os ...... b o 10 62895 63639 64359 65063 66724 66371 68996 67699 68181 68742 69282 69803 70305 70788 71263 71699 72128 72539 72934 73312 73674 74019 74349 74663 74961 75245 75513 75767 76006 76230 76440 76638 76818 76988 77141 77281 77408 77621 77621 77707 77780 77840 77886 77920 77939 77946 CSOOIOOJ OS OS OS OS OS OS OS OS OS OS OS OS OS OS OS OS OS OS OS OS Oi OS OS OS Os OS OS Os Os OS C?S Os OS Os OS ..,»., 1 63394 64138 64858 65652 66223 66870 87495 88098 68680 69241 69781 70302 70804 71287 71752 72198 72827 7303S 73433 73811 74173 74518 74848 76162 75460 75744 76012 78266 76505 76729 76939 77136 77317 77485 77640 77780 77907 78020 78120 78206 78279 78339 78385 78419 78438 78445 OS OS (^ OS OS OS OS OS OS OS OS OS OS OS OS OS OS ^ OS OS OS OS OS OS OS OOOOlOi Os OS OS OS OS OS Oi OS OS OS ....... 1 1 »0 63883 64627 65347 66041 68712 67369 67984 68587 69169 69730 70270 70791 71293 71776 72241 72687 73118 73527 73922 74300 74662 75007 75337 76651 75949 76233 78501 76756 76994 77218 77428 77624 77808 77974 78129 78269 78396 78509 78609 78895 78788 78828 78874 78908 78927 78934 OS A O OS OS OS OS ^ OS OS OS OS C7s OS OS OS OS OS OS Od OS OS OS OS OS Oi a Oi Si 03 OS Os Os OS o> OS Os OS OS Os Os OS Oi OS OS Os IHour i a [ - toco t-QO OS -*•*"*"*"* to to tO up to tOcO t-00 OS up tO to to to O^CMCO"* CO CO CO CO CO toco t^ 00 OS cococoSco SSE^Sg woo 00 00 CO tocor-00 oso ocoococooocB gSSSSS 0-* OOCM CO CM CM CM CO CO O^OOCMCO ■V* "* to to 8SS22 O"* 00 CM CO CM CM CM CO CO O-S-OOCSCO -^ -r -n* ta iTi 8S§2S O^OOCMCO CM CM CM CO CO O"* 00 CM coo •i«» "* ■* to to CO 3S-E"- Page 174] TABLE V. The Finding of the Azimuth. O-^igW o >'»ooeoo ssss o-^ or)e<»o c u^:Ot^C>0ai O^dcO"*?* lOOr-OOCi o^Mco-^ ^^^^^ ^^^^^ C4CSC4C4C4 CO CO CO CO CO I'^t^COOi O 1^ C^ CO ■«>« lO CO O -^ CO »0 00 -^ ^ 00 C5rH00lO23 o -t; ^ -^ c^ WD O t- t^ 00 Cfl u:> rt -* CO <0 M5 OO O CD in ^cooo^ 00 Oi C35 OO oooocoodo gOl 05C0 OS QCOC C^ 00 01W5 OC^L 00 o ^ lo 00 o o <: CO --O ^ 1-* CO O 00 c O) Oi 0> 0> 0> 0> 03 OS o> o OS Q CO N 01 1^ O lO lO r-l !-• CO I - 1-H c5c^csc^ CO OS 0& OS OS OS (N OS O CO -H Ci 1^ *-< O lO T* r- o c^ CO C^ CO iO CO t^ CO CO CO CO CO OS OS OS OS OS TPt^i-HOSN ■ C^ OS O CO C*^ "* iO'-<"^M00 OOO-^r^ [-"«»• oooso-— ic^ cO"^»0'0 OS OS OS OS OS OS OS OS OS OS lO 00 ococscoco . OOQOOOiO < »0 cO, -^ ,-t ^-« CO OSOOC^ 1-fijO cmooooi-i CO -V lO t-- CO CO CO CO CO CO oscvio-'fr- r- '^ i-H 00 1^ OS lOC^-^COCO OOStOt^t^TT" (NCOCOCOC^ C^OOSt--iOCO oso*-ie^co -^loiocoi-cc CO -n* Tp TT -er -.(r -^ -^ rr -n- -^ OS OS OS OS O O^ OS OS OS OS OS C^OOCO-'*' t>- ID O M* ' OD 00 CO 00 CO ^10 N OS 00 CO (N 00 COOO'^O'^ COO'< ^ lO '^ I-^ OS 10 — i-( C<) OSCOiO CO - C3S 1— ( CO lo f-4 -H CS CS CS| OS OS OS OS OS t-^ o^t^co 00 t^ OS tt -^ i^ CO 00 CO r^ 000 gs^ c^ WCS W CO CO CO ot^t— N 00 t^ O OSTj« OCO CD !>■ OS -^ lO CD t-- CO CO CO CO CO CO OS OS OS OS OS lOQOCqOcO coot^-vcoo "^ococm^ osoocococoro S^ i-< ^ O osoor^ioco— • 1— I c-1 CO -v ■^ 10 CO r^- GO OS OS OS 0% OS OS OS OS OS OS OS OS i-tr-irt CO OS OS CO OS I oo^co iO 00-* i-H 00 OS 00 iQ CO CO 00 CO CO OS ■'^ toco t^ t^ 00 0606060606 CVJt^CO'^CO lOOSCOCOOS OQOCOCOCD O OS Q CO C^ C^i-t-^COC^ lOOOTfiO'-* COOOrHTjiQO iO CO CD ^-> i-H — — ~ -.— C^OSiOCSC^ COCOCOi— 100 lOi-icO'-Hio cooO'-HcocD oooc. OS wv CD OS 03 OS OS OS Cfl 0»C >0 00 1— I -H OCO CD OS— « CO T* CO OS OS OS OS OS oosi-icoco ooscq CO 00 '- OCO— 4 coo OSONCOIO 01 CO CO CO CO )CO00Q— < C3 to cs r^ o O CO 00 1-^ CO CO CO CO CO CO CS CO -^ »0 CO o»— -^ ^OC^ lOCO OSCSJ C^J OS I^ COCO OSO—f O OS OS OS OS OSOSOSOSOS OS OS CS OS OS OS OS OS OS OS OS OSIQ CO — H -. -rf ^r -^ C^ g CO'^J' 0*0 I OSC*lC0*O t* 00 W 00 COCDC^OCO OC0^«— 4 CO t^r^ — < t- CO OSiO CD C^ 00-4 CO coco 00 00 00 OS OS O-H-4-4— I COOSWIO OS C^C^C^. IC^ COiOCpl^N C^OSi-HOiO (COCO CO OS OS OS OS OS t^ ON ■*»• CO CO r^ crso—tcs OS OS OS OS OS OS OS OS OS OS uo W OS cOiO I •^ -*■ I TT TT » 'NOOO I »o *o 10 OS OS OS OS OS OS r^ CO — 1 ■rr TT — I coio -^N 000 00 OS O -^ C< C^l I OS^ 06 06 06 ©M 000 w 0000 TT — • OS 10 "^ ^ OS OS C^ot-C^r- co t^r^ 00 00 0606060606 coost^oot^ oscocor>.co -^c^t^r^-o C^i-H-^COC^ lOOSiOiOC^ COOSi-H-roS »OCOCOt>-OS 00*0—14000 — — — . — N CO OCO CD OSOSOOO Soiio t- c:s OOOOOSOSOS OSOsOSOsOS OS OS OS OS OS •^ CO ■**• O CO »0 -^ CD C^ — t — I t- C^ t- — I — ( (N Tf 10 t^ CO CO CO COCO 0>0i OS OS OS COCO OOiO 00 ^»o coo — ( 00 O OS M* •CO OsO^ — « C^ CO Oi OS OS OS OS ^ _ < —< C^ CO ■^ lO *0 lO 10 10 ^ 0> OS Oi OS OS OCO'^C^ '^I^eOOT'- JN— *— OSO^C^CO COCOOOO— 4 S 10 00 CD C^ •^ •■* r5 *"* 10 cor- 00 OS i-< 00 "2 c^ — < CO -^ c^oO^ -^00 8^1-, COT' —4 O i-HOiroT lO 10 10 10 »o »o O) OS OS OS OS OS OS OS A OS OS OS OS OS OS OS CO osr-»o 8 CO I— r- 10 o^ r-c*^ ^ ^ ^ y^ I OsC^ -^ 10 r- OCO COO CSCN»OOiOCO CD r- 1— 00 00 t-oooooo oooooooooo cor- '^ 10 00 OSOSOOO 06 06 OS oi OS t- ^ — ( 10 «-" OS CO OS 01 o —t CO CD 00 —I OS OS OS OS OS Cv» O lO »0 00 OCOiOQCCS cocoes 000 N^CS^CO OS OS OS OS OS W ^ « 00 -^ OS 00 QiO 10 ■V O CO O Tf" c^ "^ »o r— 00 CO CO CO CO CO OS OS OS OS OS • O CO lO c S — lOJ CO" OS OS OS OS OS 10 CO r- 00 OS OS OS OS OS OS •^ —I 00 10 ^ CO O OS "^ r— t-- -^ t-tO'TCMOOO O ^ C^ CO ■'T "?• 40 lO 10 iC 10 ^o OS OS OS OS OS CS CO est— 10 COM Ol O 1 t-CCTT O CS c^ -»■ 10 t^ 060606 r- Ococo o r- t-co O CO iO ■*»*—< C^ CS ■^ C^ OS -r c7i O t— t- CO 00 0606060606 -rr r- »0 CO »o — t O CO »o — < iO CD COt^ CS 'Tj' 00 C^ »0 GO CscsOO O 00 00 OS 0> OS CS OiO iO 00 10 CO O CO t- -- -, -. -. OS CS OS t~— "^ — f-TPt— OS— t cool— CS— ( r- — < — < lo — • 00 10 —< 10 00 OS OS OS OS OS CS — I CS CO -^ -^j-— looooeo cooco— "-^ •'I'COiOOO -TCOcOiOO OCOCSQOCO — ir-cst— — ( -n't— CS— tco -"T-^rTf-^Tj' CO -^ CO t— CS o — < CS -^ lO CO r- 00 CS o OS OS OS OS OS OS OSOSOSOS OSOSOSOSOS OS OS OS OS OS rr — 4 00 lo '^r CO 10 "-. CI CS OS OS OS OS OS est— CSCSUO 00 — I '^ r- ^H 10 CD 10 CO —I "(T coco OC^ CSCSCSCOCO OS OS OS OS OS OS Cs OS OS O i CO -^ »o '«7' -«i' -^r "^ ^r r-oocso-H OS OS OS OS OS •-fOOuoCS ^ CO OS t- CO CO CO CO osoor-*o CO — I — < CS CO "^ 10 CO lO 10 *o 10 »o 10 OS OS OS OS OS OS CJSCSCOiOCS SCO CS CO -^ t-CO — 'CS 10 CO OCO —t cot— 00 OC OS 0606060606 >r-.cot - . JL 10 CSC oosc 00 CO OS OS OS t- O CS ^ - - —J too— J )Cor- o OOSOO— < 01 CO cor- CO O'?' OOt- ^ 0O"T 00 O CO lO 00 O CO —1 -lueses SCOOOiO OC— HiOCOC _ _SCSCOCSCO CDCOiO-^C TTOsiOOiCO t— OCS-rio ' " " OS OS OS OS OS O CS — I t- CD — ' CTSiO OiCO « 1^ t— 00 O CO CO CO CO "V ^^ ^^ -^ -^T "^3* OSOSOSOSOS OS^OSOSOS r- 00 CS o — < -co 00 D OC'iO 1 cir- SiOCO SiOiO OS OS O OS OS OS — ' O CO c o 10 CO— ' cir- cs CO -^ »o 10 CO to lO 10 fcO lO 10 »OCOt-00OS O— ICSC loor-cocs o^csco- iocot-oo<3* o^csco-^ C*CSCSCSCS CSCSCSCSCS COCOCOCOCO COCOCOCOCO - OT-(e^(ro-^ u-icor^(«^-isf-» fc0»O4OiO4o ioioou^o ocococcco C00050CO tit-i>:t^i^ tiStCt-^ SooSSS 3Sooo?S§ -<*« oe 00 c*! CO ■ Ol o ■^ C^ OS CO »0 lO CO O O C^ 00 00 ^^ CM -^ -^ C^ OS O :0 (N GO CO i-*^O»(MC0 lO O lO »o »o OS C^ 9 O) O^ .-iC^Tft^^ OOt-OOCO^H lO lO lO »0 lO 0% OS 0> OS OS mo lo CD CO r- r- t^ ^ OS OS OS OS coooooc^^o C^co OS ^ — « SCO OS CO CO 00 00 OS OS lOiO lO to "O ^ OS ^ O) o> -J^OiOOS OiOt-iOO OS CO i-H iCI - OOi-l TTCOOO osoo o o O CD CO O O 0> OS OS OS Os O CM -rf CD l^ O t- O O CD CO to I- i^ lO OSO ^ CMCO i-H CM CM c^ cs CO CO CO CD CO OS OS OS O) OS OS OS lO O 00 to nl Tl "^ ""^ ■"" i-H CM CM CM C^ CMCM CM 00 CO CO C/J OS CD CD CO CO CO CO OS OiOs OS OS oi CO O 00 to -H OOOSOSO ^ -^ Tf -^ to to O Od OS OS OS tp O CO to CO Cm to to CO OS oo -^OcD ^ rH C^COCO -^ »o to to to to CO t^ OS c*^ r^ CO»Q to M-O ^< O to CO CO CO 0< CO CO CO to 00 0> OO CO i-H to oa CO t^ lO o to »o to to to to to to OS 0> Oa OS OS OS OS OS OS OS OOCOCOt'-lO 0St»i-(O' C OS OS OS OS OS 00 OS -^ W CO CD r- 1- to ^00 OS OS »o to to to to OS 0> OS OS OS ^*« Oi OS CJ » OS C^ I OSOc ^H to cc c5o to CO '-D '^ CO OS OS OS OS OS »o cot* coo OO toO-^ r^ ■^r-ocM-v — t ^ C^l CM C^ CO CD CDO CO OS 0> OS OS OS O CDOOCO F-i 00 t-* to CI 00 CO ooooico CM CM CO CO CO qO CO CO CO CO OS OS OS O^ OS _( 00 —* *-M l^ C^I"^cDco ^ to CO t- 00 OS coco coco CO cO CO CO CO CD OS OS OS OS (Sb O Oco O OS CO CM CO CM CO t^ 00 OQ 1-1 ^ ,-1 ^ CD CO CD CO CD CO OS OS OS OS OS OS 2* xooc^co O "^ CO CO CO OS CD CO OI^ OsO^ C^ICM ■^ to tO to to OS OS OS OS OS OiO OOO ^^ 00 O O Ol to CO O CD •-* t'- co ■^ -^ to lO to to to to to OS OS OS OS OS OS •-< r-« OS CO CM 00 CO 1^ CM CD CO r* (^ CO to to *o to to OS OS OS OS OS cot- coco ^ oco -^"T CM t- 1-t to C?S CO 00 OS OS OS o lO to to to CO OS 0> OS OS OS coooooc^o CO CM to t- t- CPOCOCOOS CO CD CO CO CO OS OS OS OS OS '^ cacoioos to C^* !>■ i-< CO CM >o r- O 05 CM CM CM CO CO CO CD CO CO CO OS OS OS OS OS OSiO t-^ to TP TP CMOS ■«J«cD M OS COCO coco '^ CO O CD CO CO OS OS OS OS OS o r- o o CO OS -— I CO CO 1-H CM "^ to CD t'- CD CO CO CO CO OS OS OS OS OS OS OS to OS 00 to GO -?* OS CM T}. »o I— 00 OO OS OS OS Tj< -^ *t< -^ -t^ .^ CO CO CO CO CO CO OS OS OS OS OS OS COOOtPio C^t-OCQCO tOOCS'-HOO COtOcD-^O CO-TPi-HOC-^ t-^t— COOStO O^C^C^CO ——--- — lO to to to to OS OS OS OS OS 5 to to I toco CO TpcDOSTj* Tp coco TP .-t O to O to O r- t-oo ooos to to to to *o OS O OS OS OS OS OS OS OS OS to to CO coco OS OS OS OS OS 5 o o Tj* M coTjfoor-— ( SOO'-'CMCM Or-.C^COC3S -- ■-- 00.3. - r-4 — I CM CM CM COCOCOCOCO CO CD CD CO CJD OS OS OS OS OS CO CD CO CO CO OS OS OS OS OS <-- lO'OtOtOtO tOtoiOtOiOto CO CO CD CD CD CO CO CO CO CO CD OS OS OS 01 OS OS OS OS OS OS OS CM CO 00 ^ OS CO to to CM CO ■— t OOtO CM to to to to »o OS OS OS OS OS CO coo OC OS cDOs^ r-co 00 -VOCO CS TpiocDCO t- lOtO to to to OS OS OS OS OS OS O C^ to O I:-- O O 00 to t-" CO 00 CM t— I--. CO 00 OS OS to to to to to OS OS OS OS OS CD 10 CD »-' O OS C^ CO COO 1-c cp O M* 00 O O — < <— < i-H t-«cO CD O 00 t— I— < Tp o to i-t4O00 — (TJ« C<1 C^ CMCOCO CO CO CO O CO OS OS OS OS OS Tp r-< CD O CM CO CO 1— • 00 CO C^ O T3< CO t-- TP r-< CD O CM t- O CM to t- CO Tp TP Tp T?. CO CD CO CO O OS OS OS OS OS t-COiOCOCO COtOOOCO- I— CO t— CO CO O rH i-( O t— CO 00 1-H CO TP OS^COtpO I— OSOf-HCM CMCOCO- - .^ ■^lOtOtOiO tOtOcOCOcD COCDCOCOCDCD OS OS OS OS OS CD CD CO CO CD OS OS OS OS OS CO CO CO CO CO CO OS OS OS OS OS OS e^cDCDO'-' ^-(00 to CMOS N C^CO T?« TP COCOCOOOOS OSOC^tOO 00<-Hr-iOStO OSCMCMOI- lOCMOOCOOS -^OtOO^ to O CO t— t- 00 OS OS o o lOtOtOtOtO tOtOtOCOCO OS OS OS OS OS OS OS OS OS OS OS OS OS OS OS OS OS OS OS OS OS OS OS OS OS OS OS OS OS Os CO to CO <-< OS T-t "* to to M SCO 1— •-< to -H^CMCM t-icOcOOoO C^COCOCO TP . . - -, -, CD O CO O CO CO CD O CO CO TJ1 "^ Tp 10 to t— CO to CO 00 to to CO o to CD 000 CM CO to to CD CO CO CO CO CO CD CD - . __ CO to 00 00 T»< P to OS CMCO CO CM ^cocococo cor-h- ^-t'•^-. cO CD CO CO CO O 0> OS O) OS CO CO CO CO CD CD OS OS OS OS OS OS t- i-H -^ 10 O 1-H coco t- TP CO to C^ OS CO lO to to to to CO OC <-< CO Tj« OS^CMOO C^Os to <-• CD CD CO t- 00 00 lO to to to to Tf<40t-*0t0 P-lO'-HCOTp oc5c^^t^ c^tootoco CMt-C^t-f-H COOtTOOCM OSOsOO-^ ^HC^CMCMCO lOtOcOCOcO CO CD CD CO CO OS OS OS OS OS OS OS OS OS OS CD^-HiOCO OS TP t- 00 00 to OS CM to 00 CO CO '?' TT' T}< CD CD CO CD CO OS OS O OS OS t-ioosccc^ c^oooooco CD CO 00 CM to CO to TP O CO — ( Tjl o OS r-l COtOI--OSO tOtOtotOCO CDCOCOCOI-^ CO CD O CD CO CDCOCO^CO OS OS ^ OS OS OS OS OS OS OS 2 Oco CO OS CO -V TP C^ C* CO '^ to CD CO CO CO CD CD OS OS OS OS OS C^ C^ CO C^ 1-* 00 O CD O Tp CD CO t^ r- CO 00 CO 00 t— t— r- I- t^ t>- CO CD CO CO CO CD OS OS OS OS OS OS ooc^c^cor- O to r-cD -- to C^OSCD - . -- - --toco coco GO O »-< OS to OS CO CM r-- CO CO t-- 00 CO OS lOtOtOtOtO lOtOtOtOtO OB OS OS OS OS OS OS Oi OS OS to coco r-l CO OS-^r-iOcD 00 TP OS TPOO OSOO—t i-< to CD CD CO CO OS OS OS OS OS C-C^ OS 00 CD CO ~ CO tor- OS 00 CO 00 00 _. CD CD CO CO O OS OS OS OS OS OSOSOSOSOS CO 00 CO OS OSOSOSOSOS "^ -^ "^ ■" CD CO CD O CO CO OS CO t— OS OS I- t-^ CO CO 00 00 OS OS OS OS 01 OS CD CO CD CO CO CO OS OS OS OS OS OS COOOtPiO C^Jt-OC^CO OSTPcOtOCM t'-OSOOOTT TPC<10SOCO OSiOC^t-cO tocDcor-00 ooosoo^ tOtOtOtOtO lOtocOcDO CO ■^ CO OS Tp 00 O O c^ to 00 -T- 01 CO 00 f-H CM C^CO CO CD CD CO CO CO OS OS OSOSOS OSOSOSOSOS OSOSOsOsOS § OS o toco C^ Tf CO ^ CO r— — * to OS T?< -p lO to to CO CD CD CD CO OS OS OS OS OS tOOOTpCM t— CM to CD CO CMCO OS CM to CD CO CD I- r- CD CD CO CO CO GO '— ' CO CO 00 t>- ^y:) 00 (Xi 00 CO CO CO CO CO wr-OSt^CS CMOSCMCMOO — i^t— .-ico coTPM' OSOSOSOSOS OS O O O O OOO CO CD O CD CO CD t- t- t- t- ss< ^OSOSOSOS OSOSOSOSOS OSOSOSOSOS OSOSOSOSOS OS OS OS OS Os OS O — * CO CD ^ CM TP -r CI OS to O to O -r Cl CO CO -r Tj. CO CO CD CO O OS OS OsOSOs OSOSOSOSOS OSOsOsOsOs COt-t-^^C^ OSTPt-OsO COr-OSCTSCD O CO CO — CO »-t00toCMOS CD CM 00 TP C?S CO CO t- CC 00 OsOO^^ r- X) t- c^ o CO CD I- t- to OS CO t- -H 10 -P to to CO CD CO CO coco CO ^ OS OS OS OS 00 00 OS OS OS 00 TpcO TP OS r- r- to CM t- CD X) O CJ CO ososooo OS CO OS OS to CO CO CO CO CO CO CD t- OSOSOsOsOS OSOSOSOSOS OSOSOSOSOS 00 CO Tt< 00 t~* TP JH I; CM to t- GO O O t-H 1-H — I .-( r- r- 1-* t>- 1- 1— OS OS OS OS OS OS 00 CM C^ CO t- tOOCM-HOO r- to c<»os to CO t— 00 00 OS to to to to to OSOSOSOSOS OSOSOSOSOS Tp OS C^ •* to COOCD -^O CMGO TP O CD o o i-> ci ?5 CD CD CO oco »0 CD 00 1-H O -P CO CO to •— ' ^ O^cO ^ CO CO "^ TP lO OS OS OS OS OS CM -H CM t' to CD OS O OS t-- to to CD CD r- OS OS O) OS OS > TP CO CD OOSCO I CM O t- CO CO ^ O CD CO CD CD 0> OS OS OS OS CO OS OS OS OS C O OS GO '^ O CO "^ CO 00 o X) 00 r- Tjt o —I CMCO 'P 10 cDcococot- t-t-t-t-t— i>.t-»t-t-r- OSOSOSOSOS OSOSOSOSOS OSOSOSOSOS CO CO OS CO CM^ 0000 t- r- 1- 1— t— 1>- OS OS OSOS OS ^ w5 locor-ooos O'-HC^co^ tocot JOS O— S ooc-"-!— < e^weS :ooo c^ re O •^ 00 w < CO CO 'T -^ ^ >o t CSCOCO ■n«'^'^»0»0 Oi-HC^co*r iotrr>-ooOi o^^c^co*^ woeot^ooos o-^wco-^ ^-i rt T-< i-H ^.-ii-ii-i« e^MCscic^ p5e5e<>e^N cooocomeo eococococs ■»< -ir -?• ■«• M* O0Q«O t^ 00 CO 00 00 1-t t-- -f 1-t t>- t^ CO o oo i-> Q I-- lO »0 "V C< 00 ■«T Oi 0606000606 10 00 to b- 0 O O t'- CO coco t^ c^ -^ lo r- 00 "fCOO^O Or^-OiCO -f CO O ^ O O CO "^ r^ Ci S C^ CI CS c5 OiOi Oi Oi 0> C^ 0> Oi d Oi Oi Oi 0> Oi o^ ~5 r>. Oi CO CO »0 -^ C5 01 C4 0> Soooo cnoocoocoo r-cocio O-^c^co-riO C^C^JCSC^CO cocococococo OS O O^ O) O OS OS OS Cs O OS -t"C'-^ CO t^ocsi CO "«**b- coor>- ^ -^ C? CO 04 coMOr^ CO c4 CO o -r «o iC CO OS lO O »0^i CO to OS CO toe coco c I^OOOOOO OOOOOOOCOO 0000000000 s??gs?s »o O CO W ^'^ OSCSO 00 0606060s Ci OClC^iOO C<»iOO to cs o -n- <— < '* CO c/-^ o ci OS OS ^ OS O OSOOOSiC^H ^-(COiCUSO »c^toc^e CO t^ CO CO CO CO COCO OS OS OS 03 O OS »-tr*»cc5 8 OS CO 00 CO , r>. r* uO t^ I r- o Wco rococo :o iOQ-^^CO 3MOSCOCO ■* coos t^ 00 NiOCO'rf CO t^ COOSr-l t^ CO -^ •-< cor-» t- 1-1 »0 CO *-« r* 00 CO 00 OS 0606 060606 u^ OS OS CO OS OCOC7SOCO t^ -^ OS -^ CO ■^ r^ OS C* -n* OS OS OS o O CO CO 06 cs' OS OCsOcOC* O 00^^ CD CO 000 CO CO CO i-H CO tOOSCO ooogt— lOco _ -- — CO CO O C4 •*»« CO^-OSO»-< OO-H^-t^ rH<-Hi-lC4C4 OS ^ OS OS 0> OS OS OS OS OS C^OSCOCOi-l OCOro6o6o6 CO cocoes to CO lO C^ OC to OOSC^*^0 COCDC^COOS ;3; CO or- 00 QOOOCOOO obcococ oco::HCOCS OS O O lO OS O cs -^ CO 00 OS ■-' CO -^ in ^^^^^ 1-iCSCSCSCS OsOSOSOSOs 0SOSO3OSCS iCCS OscDiC t- S 25 lO C^ OS OS •**« t— O 1^ cs uo >o-rt-cD-^ ^^cooos CS^Ot— OS--4 cscscocs t-COCSOCS CO'T^tO cscscscoco COCOCOCOCO CO CO CO "^ -rr -^ OS ^ OS OS O OSOSOSOSOS CSCSOdOsOSCs OCO"^CS 8r-cDCO^ , ^Socs I oo^eo-r t^ CO 06 CO ^ Ot-*r ^ CO cs 00 CO t^ cs o CO c-1 ^* 10 CD CO t— t^ IQ ■*»* t— OS »0 cSeoOT CO cs CD O CO CO CO CO OS OS OS ooooooooco oococooooo OS cs -r t-Os OSOOOO CO OS OS OS o CSt-CSCSiO OS0GOSiCi-( CO»-H-^t-i— I t— tOOOTj-T cot-co-n'cs ootos'n'co T-«COO^-OS OCSCOIOCD OS OS OS OS Od cscscscscs OS ^ OS OS OS i-H 00 10 IC O 00 CO OOS "T 1-t -ri- 00 O 00 OS Oi-» CO CSCSCOCOCO cs OS OS O OS CO CO O OOr-l '^ OCO i-« t- 1-t CSCS CS-H 'If lOcO t-OO CO CO CO CO CO OS OS 0% OS OS ^ OOi^CS^CO OS t— coco coco OCSCOcO-^CS OS OS O^^CS CO CO CO 't* '^ M* "^ OS O O Od O^ OS ■^" (_J V^J 5i^ 81— t- CO 'V CO -^ 010 , coco rH CO OOf-iCO'^ co^ r-M^T-i 1-! — 4 r- -^ CS C4 ^ t- 10 CO CO ^H r^ CO 00 lOcOcO t— t— 0606060606 looocot: ^ iO Tf t— OS lO .-» csos CO 10 CO t-oij;t; OOCOOSOSOS 0606060606 OOCSCStOCS CC CS GO CO »0 *r cs r- ^ 2: OC0 40C0O OOOO*-" OS OS OS o o> CO'-'COCOOS COCSCOOSiO L^iCSOSOS-** OSCS-^t-t-l 001— OS'*?''^ Ont— CSf-ft-r*. iO CO lO CO »-< t— COOOCOt— CS-rcDOOQ ^^cO'TcOt- ^^^^C5 CSCSCSCSCS OSO— • csco cs CO CO CO CO OS 0% 0& 0& OS ^ OS OS OS OS Oi Cs OS OS OS t- O't'CS WD 'rf ,-^ CO C^ t- 0^T-<1-«0 iC cot— 00 OS CO CO CO CO CO OS ^ OS O Oft iC C^ cs to LO t- OS 00 CO CO CD CO OS 00 t— 10 CO 1-1 OS 0—4 cs co-^ ^ OS OS ^ OS O^ cocsoco Ococscoco irjutH-tCS OOSIOCSO >cscocs-rfi 1— I 01 CO -tr >£? 5^^^^ '^^cotcs I oO'-tcO'-r »o to CO t— t— r^ocoooo 0606060006 0606060606 r-ocoo^oo COcoiOj^-CO ^rM (JO C^ -rr •<-- cci-« i^cp CO CC OS Oi OS O -^ ^r CO-Tf t— O to tD CO CO ^ -^OOCO T-< -r 00 i-« OOOOi-t OS OS OS OS OS 10 CO 00 00^ t- OCS uo O •«T lO "^ cs O CO lO r- OS i-< l-« W WrHCS OS Cs ^ OS OS i0"*10t-< t cscscscscs OS ^ OS 0& OS ..^,-(^^ep OsCSCO"^t Si-« CScO "^ CO CO CO CO Cs OS OS OS OS cs 01 i-« O iO OS OS OOCS m to 00 OS OS CO CO CO CO CO OS OS OS OS OS t- -^ 1— t 00 t- OS r- to cs '^ ■*?- 1— I CO I— CO -^ cs o o 1-t cs CO ■-?• »o ■^ ■^ -^ ■f "«r ■^ OS OS O^ OS OS OS t-co«-<^ J^NOOCS 3 »o IOCS 10 I OOi-ICO-^ t^ 060606 CO «o cs OC tO OS oo^c5 CO '^r csos 10 O 10 to tot- 00 0606060606 OOi-hOsOCS OS CS»-H '•r OS coci t— 1-1 cs Soocs coos 00 OS OS o 0606060606 i-iiOiOCs»0 cocoes csos cs OnOOr-i cs •* t-ClCS OOOOi-t OS OS OS OS OS to-^ososcs coco 00 1—" CO coco cs ':^ 00 -^cOOOOi-i ^^ i-4C r— t— CO t— CC CS o — » CO CO CO -^ -v A OS OS OS Cs or--t^i-iocs OCcOCSiOuOCS »0 *r CO 1-1 OS t- CSCO-^iOiOcO CSOS CSOS OS OS cot- t- O— ^CScO'^WD COCOCOCOCO -^^^^fi^j*^* iO'^OOCStO O-^OOCSCO O"^00CSc0 O^-roOC^cO O-^OgCScO O'^OONcO 0"^COCSCO O'^COCSCO p.'O'^OOCStO o-^ feOOO— i-^ CSCi* -.fli ■<*< "^ *0 WD OOO^^^H C*C^CSCOCO •"TWDWD 000— **■ CSCSCSCOCO W5 TABLE V. The Finding of the Azimuth. [Page 177 O-^OOWCO O-VOOC^^cp O'S'COC^eO O -^ QO O CS-oooi o^wco"** wjor^oooi o-hc^mm* lo '^o r^ oo ct) < t^ -H --* »^ CO CO CO 1-H CO ^ 1-H o 1— I o •><»• coi-H^ioco r^ioaaoo Oi Oi 0> Oi Oi Oi Oi ■f-r-^ ^^^^^ ^^^^^ ^iO"^w^^>o iOiOlOiOi OSOlOiOlOi O:050S0id Oi Oi 0> Oi Oi OiOOiOiOiCi CO r- r>. 1-H M (N OicDCOO OCO t^COOi CO CO CO CO CO Oi O) 0> O) c^ Q0r-<^OlC Si-hcocOf-i r-cot^c^o c^^^-^-^': MC^Ot-* ,-H "«5« "3 »C CO ^COCDOOI CO-COi-HUO 0-^00(Ncp OiCOCDOiC "" CO CO -^ "^ »o ">*o CO ^ CO r^ ^- 1^ c ^ 03 A O) O) o> SoQ^COi 00 ■^ CO -^ a: --jiOCOOi" - -Oi ^CO " iO»OCOO^ ^ -i^CO'-- Oi Oi O'-' 0> 0> O O) 03 O) O^ ci to oi oi lO on oQ tP 00 f^ "^ OS -5«coioc^ t^OQoo-^ r-Sooooio o^csc^co CO CO CO CO 'ff Tf* "tJ* ^ ^^ Tj* 0> O) O^ OS O) C3 O) Oi O) o^ coc^cococD oococot^io oar-^HO-Tf Oi OJOOO ■^ ^ »o »o »o Oi Oi Oi Oi Oi C^COiO C^ lO »C •-« 'S' ^ O "* CO o •-• CN» Ci .-» GO ■*J' Ol C^ -v lO COOiOw ,-( Oi O^ Oi o^ SQOOOC^CO OU^QOOi-H f-l cq ■<»' r^ c^ C) 1-H »-( CO CO lO u? n* O -^ CO CO -^ i-H jcoio^H oo ODO»0&0'— < »— I CN CTJ C^ TT A 03 0> O) OS 03 03 O) 0> Oi O) O) O C> Oi aor>.coco-H lO 00 C>01 1^ i-H «0 OS CO t^ COOOGOMO CO t^QCM C^ fH -^ oo i-H ^ O Oi OS Q O ■^ Tt« ■fj' to *0 l-^CSCOQO OiQil'-'^O r— ajiMTP Oi Oi Oi 03 Or^QQ'O OSOiiOOiXiO ■^COOOOOcO COO>'^t--OiO r-00^Or-< C^ C^ CO CO CO -'T c^cscqcoco COCOCOCOCOCO lOiOtOiOiO »0»OiOiO*0*0 Oi OiOi OiOi Oi Oi Oi Oi Oi Oi SCOCOOi-H COCOCOOOO CO •-• 00 lO M OO-^OCOM OlOO«-HCS (MCO-^-'i'iO 0> O O) 0> O^ 0% OS 03 0> G) 50(MiOO cOtOcO^Os *-^c t^COiOCOOO OQ^C^CSIOi CO-SCOO-^ COOUOOi^ C^C^Ot ,-(cOO'3'I>' »-tiO00<-H-V h-OCN-^t^ 01»-(CO'0 to lO tO tC to to O^ O^ OS 0& OS OS OS OS OS OS OS 0> OsOsOs OsOsOsGSOs OS OS OS OS Os ^^SSSS^" i^i^cor-coco 0 to to »0 to to to to to 40 OS OS OS OS OS OS OS OS OS OS OS OsOC^iOO >tOCDi. lOS ^C ''cor^ r-cotoffoco ootocooo-- CO OS Q O OS t~- 1* CO r^ CO CO ooc^-^-^1— < tocoooSc^ coososr-"^ o6.-«c^mos coScot^-^t* co25'^oi«-< OS OS OS OS OS OS OS OS OS OS OS OS OS OS OS OS OS OS OS r.i-ii-HiocOio<-i CO^O^I^ COCOi-hCSCS Ot~^CSCOOS O <^ 00 '^ _ __ _ _ It^rC^t^ .-HtOOCOt^ f-H^OO»-*"^ t^OSOJ-^cO OsQC»<"^(S t— COOSO.-H C^eOCOCOTy^j" 5 OO OS OS O Q *-H 1— ifH C^ C^ iM CO CO CO CO tt tT "n" ■*** to to to to to to to CO CO CO CO CD CD CO eo ■* ■*.coco eoot^'<*«i-i CJCO CO"V to OS OS OS OS OS OS OS OS OS OS rH O^CO"^ ►-• -.J1 to -rr cs i-H to o> cor^ rH^^CSCS H-*i«iot5 iOtOtOiOtO OS OS OS OS OS OS OS OS OS OS CO *-« ^ tOCO ^ CO CD r^ t^ O-^ r^ Oco CO CO CO '^ '^ to to to *0 to OS OS OS OS OS r^toosoocs coos 1-f -q" S TP TT lO tQ to to to to tO to CJOOOOOCO OS 00 ^ CD -9« OS t^ t- to cs t-- r-* OS 1-H CO "T** cDcDr^r^r>- tO to to to to OS OS OS OS OS OS CO OS OS tO rH -V tfttO ■a* CDt^OO OSQ iO to to to to 0> OS OS OS OS 00 00 Tt* 00 r^ -rf« .-H t^ cs to r- CO .-« ^cs CS cs cs 00 00 op CO 00 CO lO tO tO tO to to OS OS OS OS OS OS r»^i-(toco COCOQ CSCD OS OS OS OS OS CO tOf-ti-c^ ^ cO'^c^ob COCSW-V OS r- 00 CO OS oa ■^ ■^ -^ -^ Tf OS OS OS OS OS '^ to r>- O to .-H O '-' CO Tp cs ■g* -^ CO OS -^ t— 00 r-- to SOtOQ-'J' OscOt~-i-HiO ^.-|?5CS CSCOCOM''* lOtOtOtOtO lOtOtOtOiO OS OS OS OS OS OS OS OS OS OS ^':i'-^^'^ ^*^'Si'^'^ c^ioooooco cooeocoos escsooM^c ■^ to to to CO to to to to to 0> ^ OS OS OS oo to 3r» tj cs ■T' to »o to to to to to to to to OS OS OS OS OS OS OS OS OS OS to to lO to to »o OS OS cs OS OS OS OS CO CO t^ 00 5 tOCDt^t-^ to r>- CO CO CO OS--ICS OCD '■s'^t^eoco CO OSOSO o TT '^■«r toto sr^osc^t'- cocscococo ^ ^c^csco to to to to to OS OS OS OS OS iO to 5 to to 0> OS OS OS OS 00 CO CO r^ to OS '«j' r^oooo r* .-» ^ t^o tO':DcDcpr^ to to to to to OS OS OS OS OS ost-» .-« o ■^ 0 lOCStOtO^ CD CO ^ CO to CO ^ -^ *-H CO O CO '<*' M* CO CO CO Ob .-H CO 00 00 OS OS ososososos lO to tO tb to to to to to to to to to to to OS OS OS OS OS OS OS OS OS OS OS OS 0> OS OS to toe OS OS OS OS OS OS to CO t-- do oo OS OS OS OS OS COCO ■^ "^ t^ tOt- 00 CDCS CO OS to ^ r^ OSOSC? -H f-i ■^ -^ to tO to OOOCS— cs ^ OS tooco-n*-^ csr^csr-*cs co.^tooscs ? _ CO CO •-» CO cs to O tC CO O M« t^ OS CO f^ -^ OS i-HCO—»CDQ tOOSCOr— — I tOCOf-HTft— OS OS OS Os Os - coc to to to to to OS OS OS OS OS cs O'^ cor^ " -^ OSC" " CO toe Osos <: to to to tO c; Os Os Os OS OS t>.COtOCOOO qOtOOOOO'^ 1-* t^ CO r* CD CO „ Oco-^-^co QcO-HT»«COt-- i-tcsco"^to OOt^r^t^b* CO CO CO CO CO CD CO CO CD CO ^ 0> Os OS OS Os OS OS OS OS Ol OS OS OS OS OS OS D to coo 0> OS Os Os OS oor^QQco^ ■«* t--00 00^ -^lO* ) r>- 1^ r^ )tOtO to Os OS OS Os C7S 0> OS Os OS OS OS -^ OS -t< OS cor* CO "* -^ to to cOcO lOtOtOtOtO to »o CScp^i-H^ Oi:D<-HtOr^ COgOSCOcp 00 ■-« ^ CD 00 GO TO 00 (^ ^ OS O O Q Q to tO tO to to to CO CD CO CD OS OS OS OS Os Os OS OS OS OS ^tOt^iOO Qt'-OOcp OSOStOOSOOtO * 00 CD CO OS COtQt*t-tO cs 00 CO CD oo OS OCS^^CDt— OSQ«-«MCO TH-^tO'OtotO ^r^r~t ^*~i — t^CSCSCS CSCSCSCSCSCS cDcDcOcDCO cDCDcOcOcO cDcDcOcOcDcO OS Os OS Os Os Os OS Os Os OS OS OS OS Os OS OS tOCDt*COOi O—iC-ICO"^ to to to to to tOcDI^OOOS O -H CS CO 'J' lO'^t-^CO iOLOtOtO>0 ^ CO CD CO CO COcDcDCO <5 o^csco" t^t^t^t>-t>- r-t^t toco t^ 00 OS OOOOOOOO 0000000000^ g8SS2S g 55901°— IJ CSCSCOCO '^ ■«!»''* to t" 8'^OOCSCD O'^QOCSCO O-^OOCSCp Q -a* 00 CS eO O ■V 00 CS CO O ■^ 00 CS cD O OOi~«^ CSCSCSCOCO -^-^-^tOtO OOOr-1— 1 ^CSCSCOeO -^'^"'^tOtOO T3 ® C3 $ 0! 7 », S saga '^ VI 1 3 O IS c O a> ^ 9 "A 9 ■^ ^ ft a o a o S o « an ^ 2 H .52 T) ft ■§ rl a> ^.n n t^ > "sSa ® f '^ ■^ 3 ,2~ 0) a) Bt; is 03 '^ Q A 5® «il :§a sis, -I 2 fj © cJ a) aj W O ® ® ® 5|£aaa S->S bSS Page 178] TABLE V. The Finding of the Azimuth. g M a5 gO-^OONcO O'^OOC^cD 0"^OON(0 O-^OOCflO OM'OOC^'CO _000'-H»-t C^C^WeOCO '^-. t^ t- CO U^ -V 10 c^ Oi cc >o r* CO CO CO CO CO r-i Ci^-- o 03 o Ci Ci o^ ■< t^ CO o r^ »-( " CSCOC^ TJ'OOOOC^OO 05t~»C^NiO OlOOCiiO»-H i-HCC»0»00 COcOOOOrH 1-tOOt ScOCSCOd COcOOiC^CO C^^-tCOCi^ CO-— iiO^^OS OiiOOOCOC^ -^c^c, -. iO'-<"?t^ OiOiOOl—^t" »-*t— C^COO ■^r--.a)'-"C< co-r^J*'?'-^ coC^OCit— ^r _^. -*_v_, oc^M* ot-*d^c^ c2"^»ot^oo ^0>-(wco "^lOcocor-oC' ' CNgO^.-«o6 ..-.-•^^i.- i-iOCSt^M f-»-HtO00.-H M^I— OC^^J* COOQOC^M' Ot-^OQC^ COM«tOt^00 |»oooo»-( wcO'^'^iO locococot-- t^t^oooooo ooooososoj osoioioo 00000 t-^r^o6o6 0606060606 0606060606 0606060606 0606060606 o6o6o6oo> cioiosoioi oiooJoJoi oooicioioi lO-^'-Hoooi »o^cot^a> ooiO'-<"? " -M f-»-HtO00.-H M^I— oc^ 8c» 03 ou cc CO -^o»o , CftOi t^ Oi »oooo«-t oscqooioM CO CO 0> CO '^ CS <-i 1^ *0 CO CR t^ CO Oi -^ C^ CO -^ "^ »o OS CO CO t^ CO Oi CO CO O CO CO O 1-H - ■<*«c^r^i^O M'cO'^Oco cocooo»o oo^-^uoeoo cocoor^ccoC' f-H -^ CO 03 ^tJ* O 05 •— ' r^ CO O Ci CO CN !0 Cp CO lO ^J* 05 *-« O CO QC 00 lO Cp CO 10 CO •-• 00 CO 05 CO t^ i-t CO CO 00 01 O ^H ,-H .— I O O O t— lO CO *-• ogOiN'^co t~-oioc^co iocoi~c»5o> 1— ic^co^rio cOcOt-^OOOiO OOOSCSOIOS OOiOOO 00000 ^^ r-( ,-H ^-( ^ ,-1 ^ — ( -^ F-i Cfl t^t^OOOO 0000000000 0000000000 OOOOOOOOOC 0000000000 000005050* 050>0i0S0i OSOl050lO> 03050505050 8u5'-<05t^ OC^OOioC^ cOOit^OOf^ OiCOcOt--CO 'S'C^t^r^O '^CO'«1'OCO cOCOOOiO 00^-iiocOCO cDCOOt^cOOO Q005t>- ■»J'n'Ot^»Q OOr-OCSOO i-H4Oi-(.-iq0 (M^QI^QiO ^^QC^OOt^ ^O'^T'cOt-^ t^'S'cOiOO CN'-^t^OOicO Ot-' t-OOOOOOOO Oi050>Oi05 05 O O O O O O O r-l r-t ^H i-H f-I i-l ,-t ,-| ^ ,-i C^^05 O5^05o5o5 o>oso5»oi c^^oiooioi 00 .-4 t-- ■^ rH lO CO CO t^ CO 00 d C^ CO C^ CO '-' CO CO 05 Oi05»OCSO COC^iOt>-CO cOOcOcOCO t--ocs»o^ CO c^eo OiQ »0 C^ Oi 05 *^ t^ O ^r C^ UO ic C^ OS CO I iOco'-< csc^cococs <— iO05t— loco ,csc>^oc^ c5oco(Mt^ c5coococo osc^'^t~-o> ^^coioo-o. oc>)-rr>ioco oooso^co 'fl<40cDt^oo osoo-^c5co |c005i-hC4 CO •*!*'* >0 10 COcOt^t^t^ t^OOOOOOOO 05 05 05 05 05 OOOOO O O <-< <-"-l ^h .-t -h ,-h ,-1 i-t cs c<» c^ cs c5 t>t>o6o6 0606060606 0606060606 0606060606 0606060606 05^050505 050505^05 05^05 03 05 05 05 05 05 0105 ocgooo oeoo5coco o^t^C4 oor^'S'C^c^ .--^"■^T-lTfJ CO-HOO-^OS |c005»-tC^ CO-^"^»OiO t>^t>^o6o6 0606060606 t^ 000 05 0Q CO 05C0O C^ cor- ^^lOoo cocor^r^r- 0606060606 .-HOO i-H CO _ 00 00 OC 00 05 0606060606 -«*< lOCOOO CO f-* C< CO 051-I M< 03 __ 1-1 oic^c^ot- CO »-H CO 10 1-- gs O 03 O cs CO Tfr t^-m-4 0C I ■( 00 005 -r-oot^- ^-_-,, io CO r^ 00 o o '-' N CO "^ *?■ 1-4 0C r^ O CO to »— • CO CO O — — ^ cs c 00 10 ^** Id »— < t* r^ -^ ^^ .— I CO 10 'T' CO e^ >— ' lO'^cot*'-' ■^OtoO'T* r^ o (N -^ CO C^-^iCr--O0 Q3— <(MCO'^ -. „. .. 00000 O-lfH,-)^ ,-lr-<^rHi-l C^ CS (N CS C^ W O5O5O50505 005030305 05 05 05 05 03 05 03 03 05 03^ coc^ooo ocoococo t>.ooo«oo o-^-^oo-^ OOOOOOiO COtNOOiOCO COCOOOOCO OCOOOiCD 'sr lO 1-H CO CO CS 00 CO t^ C^COOiOcO CO CO 00 C? lO 10 O CO »Q 10 CO 05 O O no 05 CO CO Ol C^ iC t^ O CS ■ '"^ - - 000000003 0606060606 CO CO 00 O CO _ c^co Y 10 O CO »Q 10 CO O O O no 05 |c005'-HCS C0'^' coioc^osco C^COOSCO OOSCOCO"^ OOOOiOOO OOiOC^ODCO CO OS «-< c^ CO 'no ic CO 00 00000000 ^-^c^coc? ooooc oocsi." ' 06 06060606 S^ C^ "^ o 000 c^-^ 00 cs »o OS c^» * 00 00 C^ 00 SC0CSC0 03 sOcooc^ S OOOCOiO 5 00 OS OS OS CO CO OS CS CO ososooo 05000510^-1 ^H00-• CO OS 05 CO 1— < lO ■^ OS COC^r^rHlO OSCS" OS iO O *r CO c^ u^ r* OS O r^gs^^c^co iocoi>-ooo t>-t^oooo 0000000000 0000000000 oooooocooo ooosooso 505 OS . _5 -r CO ... -gs^^c^co iocoi>-oo( O 05 OS O 05 O 05 05 05 OS COCOOOO»-i 1-1 00 IC Cfl 1— t CO 05 10 00 CO C^ TT" M 00 >—«.—' 00 i-<(NC^CSC^ »-iOOOr-iOC^ rH C^ CO 'f »0 CQ t^ t^ 00 05 O csc^c5o«c^ cic^c^csc^ro O OS OS O O 05 O OS 05 OS 05 OcD-»**w ■^t^coor^ i-< ' -^00 OOCl 00 OS CS 00 OS lO 00 CO 1-1 iC 00 r^ocoior- 00 05 05 OS 05 SOOSb-iO ^H OS 00 OS lO »-< T-H00C^>OO '*■ i-iOiQ O c^co 00 I^ 05 »0 uo 5 o cs CO ^o CO r- OS O i-( coco 000 -^ 10 ^ -^ c^ 00 "(J" o »o *o "^ CSCO -^IQCO <-« 00 iC C* -H CO O 00 TT h- r* --j^ T CS •-< OSt^iO r-ooosooi-t C^M^CSlCOfO -000000 0000000000 0000000000 0000000000 00O3O5OSOS 005050S05 OS005050 00500S05 03C5CS0050 ocO'it'c^ M^t^coor- i-< " c^-Oi-«co t^ 06 06 06 3C005lO»-< T-< 00 e^ IQ O i-f00C^<£> o-^ooc^tp Q3;goc^co 0"^COC»CO o-^ooc^cp o^qowto Q'^coe^to o-vcoc^cpo C^C^C^COCC TJ" -^ -itr O »0 OOOi-t»-t C^C^C^COCO -V^f^iOnO OOOi-Hi-t cSwc^coco -v^-^ioioo ssoco ^ i>-r^ 0'-*c*^co-^ »oor^oops I- 1>. r* I'- f^ tctor^oociO OO CC 00 00 00 o C^OSO^OdO OSOC^OO OOO^O^C: O O O^ Oi o ^tOCiC r^r>- ooc Od Od O Ci Oi c»oooooco cs-^ooooi i-tc^co-^^o 05-^ r* 050 lO 00 00 CO CO 2Spf " 03 C3 O^ O) o^ OtMCOCO^ CO CO 00 00 00 F^t^oooooo CO Q CO lO "^ Oi Oi Oi O O C4CS C^ COCO C^ O) O Od O O Oi OS o o^ COi-HlO-^ 00 COO>OO^H OOt-i co»ooo CO CO CO CO CO OS OS OS OS OS c^ « or^cM "** OS oso^osio 00 oo -n* 00 r^ -^ - -- 'OOCS «3C^C*001CO .- -- J^-HWN c^S-^-^io^^io 04C^C^C^C T* ooc^McOr* ^ ^cocoos COiO CO TT O O(N00-»J«Q CO-^ "^ lO CD O OS OS OS OS »OcO 00-H CD -rr O CO iC "-H lO O^O Q "5 5p t^ r-oooo OS OS OS OS OS ci^c^ t^iO 00 05 Oi _ _ OICSCS COCO OS OS CS OS CS SS 8 r^c^c^cD-^ - OOi-' C^l C^) C5 COOS CN COCO CO OS OS OS OS OS OOCDOOSCO Ot^ CO to OS OS OS OS OS OS CO OS 1—1 OS ■■ O^oo-'j'*: r- 00 o CS -- CO CO •fj' 'SJ "(J* COCOOSCOC^O> ■^ O'^OO oo OfH w^. lO C^ OS lO »-HC5 coco-^ CB OS OS OS OS -^ 05« ■<*• lO ■^ CO r^ lO •-< CSCC-^OcD liO lO CD t— r* c<»c5csc^c^ OS OS OS OS OS IC CO 00 ^ -x> lO t>- t^tocs — « cp— *co ^ OOOO OSOsO OICSC^CSCO CS OS OS OS CS CS^Nt>iQ f^Q-^O«0 oO*voo^H ^i* cscs coco lOOOCSiOOO o»c^ cococo COCOCOCOCO OS CS CS OS CS oocpocsco 1-1 oo-^r^O 1-t COCDOO .-< Tf -^ "* '^IQ CO CO CO CO CO OS OS CS OS CS i-< OOS CO lOtO -- 0<5> iO' - - _ CO CO CO CO CO CS CS OS Od OS IQ 00 OSC5 00 i-iC^CO'^iO CO CO CO cP cO COCOCOCOCO OS CS 03 OS OS CO CO escort OS S»-l lO OS <-* --* r^r-r-coco CO CO CO CD cO CO OS^CS QCD 1— t r^ -^ o ^ ■— < t>- ^H ,-* If5 CO COOO^HCO" 1-t^OOt- - - COOI^'^ 04CSCSC4cN| OS CS 9 CS OS a CS o OS CS OCS CS ^ I^ r^ csr^csco OSOOf-<^ cs co co co co cs os os cs os 1-t O-H Cprt* CS iO *X> "0 CO *-^ IOCS cor- es c-r- 1>. r^ OS OS OS CS CS >OCS' CO CO CO CO CO CS OS OS OS OS COOCO COOS OCOtT ^CS r- t^r- Soo CO CO CO CO CO OS OS OS CS CS CS CS 00 C<) *H oo O CO O"^ CO CO CS CS coco coco OOOO 00 00 OOOO CO CO CO CO CO CO OS OS CS OS OS OS OS CO cor* 00 Old r- CO CO 00 lO CS CI CD ■^ lO CO CO r* cscscscscs CS OS CS OS CS SOcOiOCO CS osiooy? OOCO OsO o C^CSWCOCO OS OS A CS OS coi>»cscs r* OSi-(i-i OCD i-i r- CS r* 1-t ^^ cscsco CO CO CO CO CO OS CS OS OS OS CO CS CO 00 CO .-I Trie* CS CPOtJ«00CS COCOCOCOCO OS OS OS OS OS 00 coco r*io 00 CO CD r^ r^ lO Cioi upoo COCOCOCOCO OS r» «— I o "* IOCS oocs ** ^^ *«a^ CO c- ^^ i> r- t^r^oo CO CO CO CO CO •QC )lOC 5ior 3 00 00 00 OS lOCSiOUi.-) ■^'^O'^COO Ca CS CO CO CS osioQcoioco i-iCOTfUOcD cpt-OOOOOOOO _ . _ OS CS CS CS OS OS CS OS CS CS OS CO CO CO CO CO CO CO CO CO CO CO rO CO CO CO CO OS CS CS OS OS ^ OS CS OS OS CS OS OS OS OS OS CS OS OS OS CS 3S OS OS OS CS 06 CO CO 1^00 socoiOcD cor-ocsr* t'-COCiiO c CsOO'-cCS CSCOC <0 •-* CD 1— ( CD CSCSCSCSCS CSCOCOCOCO COCOCOCOCO CO CS CO CO CD lO 00 OS 00 CD S-* COCS CO lO »0 CO cp CO CO CO CO CO CS O OS OS CS OS CS OS Cs OS OS OS OS OS Od OS OS OS OS OS CO CO cor- »o CS r*0 OfOt^ i^ (•* r- CO CO CO CO CO OS CS OS CO OS csr>.^^0'*' M'OcsolO iocs»oto^ ■^-^ott'coc OS CO CS CO 00 00 •000c CO CS'»f t^oso rH .-( CS CS CS CO CO CO CO CO CO CS CS Cs Cs CS Cs Cs OS Cs OS OS CS CS O CS cor-00 lOOcoiOQ OSCO__ -, COOOOCSCO COCO^ t^ ■S' r-ogcscso c<»c5cscsco r-< r- CO a> ■•sr ^.-tO^<^iO cscsor-cs cocsooos lor-ciocs co"*cot--r- CS cs cs CO CO COCOCOCOCO cscsosACs ososcsoscs 00 00 ■* CO »0 Tf cpCS t^ QCS CO 00 cs OS o oo CO CO CO M* -«r '^ OS cs OS OS OS OS >>_s§ 00«'^'*i-i CSOt-TT 1-H O-H 1-iCSCO CO CO CO CO CO OS OS OS cs cs CS-«ft^OsO O^HWcOi-i wo 00 00 CO CO r-oscsr*'* ■"-COOSlOi— * CPi-HCpi-CO'— < CO i-» CD •-« iOOS-^OOt-^ CSOSOO-H ^wCSCSCO coco-*"*-* ■* rr ^ -* ■v OS o Cs o cs ososcsoscs cqiN-t^^cs ■-o«- ^•csi-tOr- cs"*»ococs coiQioirC- cscO'*'— tr- TTOcpcsr- cooocoooco r-i-iioosco r- co-*iococo r-oooocsci oo^^cs cscococo-t * CO oo CO CO CO CO CO CO CO CO ^<^'T*»^<^' ■^Tfi^'*^ ^^ CD 1-1 1-1 lO CO o-vr-Q t^iOOSOOCS CSOOOOOCO COOCOCOCS CSCSOOCSi-lOO cscOf-iioco csooi^cocs cocor-r-io cocscor-osos csiocoocs ■*(OcoQ»-i cos;'^^^* ^oocsososcs OS cs OS OS OS cs cs OS cs cs OS OS OS cscs cscscscscs OSOSO OS cs OS o cs Cs OS OS A OS cs Cs OS OS OS OS OS cs OS cs cs cs cs r--H^ioco coo0i-0*0i0i0 lO lO *0 lO O cp cp CO CD CO 5cor-ooo> o— "CScorr locot^oocs o^hcsco-- scpcpcocp i^r-r-i>i- r-i>.r-r-t>- ooooooooc 5 00 00 00 00 c:s EQ'-S'OOCSCP f«; CO 8-*oocscp oo— 1^ S-^OOCSCP O-^OOCSCP O'^OOCSCPO OOt-i— I CSCSCSCOCO ■-r'*"*iO»00 Page 180] TABLE V. The Finding of the Azimuth. 5 hn i^s C^C^CiCOCQ O-^OOtNcO O'3'OOMO 0"^OOC*«0 O -^ OO OJ O O 'I* 00 C^ O 0^0001(0 O'«»*a0C^'©Q «9<'^'*3«iOO 0O0«-H^H 0«0*WMCO -^^-^tOO OOOrH^ C^ O* O i-« OJ CO "f O « f -* -^ 'J* J. O o CO o ■*j«r>»»0':o 00 00 -^ fH Oi •-H O t- U3 »0 ^ 2.COC5 .^^irj^ C^O»o»o95 (N.-lNOO'** lO 0> »o lO •-< '«r c ■^fHOOOOCO CDO>pO.-tTj» '^r^OOiO'^cp S-^j< i^ (£) r-< •rftro^^i coiaococgo _ C0iQt*0>OOrHOO0lQ0t-»0C0«-» ccOcc^ oics-«ri-^oi i-*c^»ot^05 oc^eo»ocD ooo>0-H6fl ^^loot^oo ooo>o<-- t^t^t^l— 1^ i>r-oooooooo OOOOOOOOOO 0000000000 OOOOOOOOOO OOCOOOOOOO OOQOOOOOOO OOOOOOOOOO OOGOOOOOOOOO ,ss? COcDOilOiO »0 ■^ t-J I'- »o O>00»Q CSPO lO COOcO <-• t^ 00 00 00 00 OCO ^ (N ^ Oioot-Hco 55 oo<^t- f-» iN to Oicor^ o c5 wcooo '^ OOOOOOOOOO COt^ t^ t-H I-^ .-^OCOOOOO C^lO'^COl'- •O'-HOO^ O0'-*CO»OCO "^COt'-OlO t-«CO^»OCO ^ cOtDcD^Dt^ t>-i>.t>-r^t>- t^r-t-QOOo OOOOOOOOOO OOOOOOOOOO OOOOOOOOOO (MO '- o> o>t^cooi _ t* -^J* 1-H '^ CO 05 t-- OO O>r-C0 0i -^ OSO<-<'-« (N t^ 00 00 00 00 coco -^o •»« CDOO 00 csco ,-40a<^-^t^ th o ^r t— CO _ -OiCOCD t^OOt^iOCO OiiOC ':OOi--H'^cO OOOCS-^CO t^Oi- ^« ■^ lO »o «o toco^coco cocot OOOOOOOOOO OOOOOOOOOO OOOOOOOOOO CO o^- 1^ c^ OO t- O 1^ -^ (MiOOO^ r-j lO CO l~- oO O i> t^t^r-00 OOOOOOOOOO »0 GOfNOCO -T OCOCS I' CNCOCOCO cs 1-tC^c -■- OOOOC Oi 00 CO CO coco i-< O Ol t; »0 CO 3 00 00 00 00 0^ OOOOOOOOOO oooooooooooo I CO CDOO O* OiC^OOuOC^ CD<3>O>00t^ OiC0C0r«00 .-Hi-it-TrC^ •OTri--OlU0 OQCSOOOOiO — — -—iO »QCDC0l--O> OO^DfHioOO ioo C^COOCOCD 0>(NtO^-0> O r- < »-* ^C. C>.t>-t*t>« OOOOOOOOOO OOOOOOOOOO OOOOOOOOOO OOOOOOOOOO OOOOOOOOOO CD fOOO to OO l^ --H O TT TT t-.0(NCO oooi-H (Meo t^ I"- OO 00 00 OOOOOOOOOO 00«-H toco CD ■<1« rHCO C^ t- -»si to*o uo 3; ■^ trt CD I- 00 OOOOOOOOOO CD coot* CDOO 0» OO "T CO CO CO CO (N r-f o> t* »n 0>0 -H i-i MCO 00 d o> o> O) o> OOOOOOOOOO OOOOOOOOOOOO ' »n lO CO t COCDOO< oco os^eo oc>»o ^o CO -^ •-< c>o oc>»o ( CO -^ •-< <_ _ to CO O to i-H Or-ic^c^eo OOOOOOOOOO r^ooooaoo SC0»O I^CO coco r^Oi to CO OO 00--^ t^OC^tOO Oi O 0> t^ »0 — - "JOi '^lO t^ooo t^ t^ r* t- 00 OOOOOOOOOO r-* -* <-H F-» CD cDOOiOOC^ OOOOOOOOOO ac^co ■«»< r* 10>'-»0 to pJ -rj« to »0 TT -oboo^ >ooooa>a> t-* -rs* y* 00 t~~ 0> t-- CO (M -»< -^ •-• CO c5 .-H oa (^ to "ICO -r rr tO CD OOOOOOOOOO OOOOOOOOOO 0> 0> Oi ^ Oi ^ 00 00 00 00 00 00 cq oocD ■«*« ft»oS?Mt^ Y oooocpoo I CO CO 00 o> CO q6 CO CO Tf to ^ 05r-( -^CDCM — ■<1' f-H to t* (NcOOiO* COOO-'T o to 05^0 to C^ CO « CftCOCO to OO O CO lO >0 to CD CO CO ,— I 0> rj* TP h- 1^ OS ^ CO »o CD CO t^ (^ t* t>.t^t*t^ OOOOOOOOOO OOOOOOOOOO OOOOOOOOOO OOOOOOOOOO »-i O '^ l>.CO to -^cOi-H ^ O) u^ O to 0> COOOO <-* C^ t- t^oooooo OOOOOOOOOO COO t- t* w c5io t^ Ol «-• TT to CD t^ 0> 00 00 00 00 00 OOOOOOOOOO lO 00C4OC0 •-H I>. O OJ "^l C^CSJCO C^ (N O -H cj CO "«r O) O O) o> o OOQOOOOOOO CO o t^ ■««• CO tn to CO cOlr^OOOi ^ 0> G> 0> 0> 0> OOOOOOOOOOOO 8tOtq»0"0 c*»o OOO toco TT ,-IOO^i-HCO 1-H ^cqcoco OOOOOOOOOO r-o ooojoo CO CO »0 t* CO i^O t^^ CO i''J'to*0 tocOCOcOCO tOCOOOQO i-< I^OCSiOO CO ■^ CO »-< OS O C*^ -^CD t OOOOOOOOOO OOOOOOOOOO t- r- 1^ t* t* OOOOOOOOOO to "^ lO »-« t- CD to t^CO « to 1-1 CO --I to Ol <-H Cq TT to |>.00 00 00 00 OOOOOOOOOO Is. ^ _^ ,^ CO OO 00 00 0>0i OOOOOOOOOO (M CO ^f to CO OOOOOOOOOO t^ ^1-1 00 t^ o> r^ CO CS ^r ^< rH t^COO CO ^o ^OiSoOO 00 00 00 Oi (3> O) 0> tOCOr-^ fi CO W CO t^ Y CO CO--? CO I -^ t- Oi o t^t^t^OO COCOC^OCO C0»0 C»«OOCD ''J'COOh-OO CO »-< oocooo 1-* c*< c^coco OC0»-HCSi-* OOiCM-'J'O -* -^IMCDOO CO t^ >-< ■^ t^ coc^t*<->r^ oocO'-*^'^ COCOSSCOO COCOOiC^CD OO 00 00 00 00 CO CD CD CO I^ 00 00 00 00 c/i OOOOOOOOOO 00t*00-^O (M i-(COO>Oi O CD I-* »0 0> O^COlQcDt^ OOOOOOOOOO OOOOOOOOOO CiO ^co 2< OO c> o>d O) (NtOOSt^O Oi to t^cocq fNCOCOCOCO to CD r- OO oi O) 9^0 0) OOOOOOOOOO Ot-"^r-«0 W ■»f C^ OO rl ^ OO C^ 1-H Oi 00 CO CO Ot^ -HCJCO^* OOOOOO 0> O d OS G> O) •-H -^ O t^ ■^ OQOto ,-(0> ^- CD CO 1-1 .1 tOCOOcD F^ 1-H OOi ts-00 to OS'-' ''< to OiCOCDO »-* to»o os*o «D OSJO to C3 COiOCOOCO CO "<*«0>01C^ <-< -^•i^Sftco to t^ OiO c^ t-t^t^oooo CD»OCD<>)00 to -^CD CO OS -^ OS CO ■rp to r* 00 O 00 OOOOOO OS OOtOC^C^lt- to ■^ oot* >-• CO OS •-" CO »o ^?1 TPtoco OS OS 0> OS o> t^OO »Q •-• 00 locsoioe o C0*0"- t^ d c — OOOOOOOOOO OOOOOOOOOO OOOOOOOOOO OOOOOOOOOO OOOOOOOlO* ooc>3oo OS OS OS OS 0> OS W -H 0)00 CO Y OOOOtOOO I TT t— 0»0 OS OS »0 C^ P> 00 to CO 00 OO-OO 00 00 -j^t^tOCDiO t-- ^H ,-( to «-t COC^tOt'-CO coocococo OsOt^'-'CO C^Ot^gjiM ^ to tO o «0 OOOOOOOOOO cocD t^ t-^r* W O to to 00 t^O c5iO OS CO ''J" CO i-< OO C^f-^CiOO** -^-HOOOOCO COOSCO^I* CO to t^ 03 C^ to -^CO T-t to CD to 00 t- C^ 00 >-< CO »o r- JCDI^OO OSO - .00 wOtO OO OO OS OS OO QOOOOOOSOS OlOSOSOlOS 050000 OOOOOOOOOO OOOOOOOOOO OOOOOOOOOO OOOSOSOSO) ^ >— « 00 to f CO t^co^ -^ '^—i r-COtOCOrnOJ ■^ O CD t* oOoo ocSoooo OS OS O 0> OS Ol 8§SSS CO <0 C-» Ol CO Soo»o ^ oa OacD -^ ^ O t^ ■^ O UD (MIMCO ■«< ■» OOOOOOOOOO CO C^l 'O t^ CO O^OOIM ^ o -^ t^ »-< "^ to *0 lO CD O OOOOOOOOOO CO t^ t*^ t- cos>0 3gcs t~ O OS.-tCO«3 CD r- 00 00 00 00 OOOOOOOOOO o6 o> 9 OS OS OOOOOOOOOO • O O f^ ^r •»** OS I C^ CD -"t* 00 t^ ■-» OS C^ 'W'CDOO to t- 00 ^ O OS OS OS Os o (N to ^ t^O (NOO O OStO OS OS O Os 0> .-H ?) -^ 3" to oooocS Or^ ■v <-hO OJ C- to t-" -^ ^ >-" ooooooooos o>o>o>o»a» o>o>o)0>osos t- 1- r- 00 POSCDCO t^OOOOiOO O- ^ C3(N3;co(N co< O rHOO (M -^ CO ( SS3S3 I TT t^ OS 00 00 OOOOOO to CO 00 00 1-H CD OS ^ -^ OS Tfi ^»i T?« (M OS ooooSoooo OOOOOOOOOO to ^J* to 1— « t- lO -^cOC^fH gp cs t^ CQ CD t^ -^ ^ ,-lCO to -^ 00 I^ 1-1 os^ooo r-«00Q^-^ OO 00 Oi OS OS OSWC r-«00C OSOSC ooSSo 0> OS OS OS OS CO to •-< CO CO Q 0Q(-*^ "^CiO ^c&0'-He^^co O O «-H .-I F-l rt OS OS OS OS OS OS lOObO ^ t-^t^o6o6 CD Ol to 04 OS OSOQ tO (NO> Os00*0 CO CO CO •-< 00 ^r OS C^Ot CO ■^ -* OOOOOOOOOO CO CP f lO -^ CO^tOt-CO OsQt^^M CO 00^ to 00 to »0 CO CO CD COQO ■^O coOcococo (NOiOOiM *-H -^ CO OO f-i !>• t>- t^ t- 00 OOOOOOOOOO OOOOOOOOOO »-( OS ■«(}' ^< ts- t^OS CSuo OS cococo^^ CO to t^ OSO ooooooooos OOOOOOOOOO CO to t^ OJ c^ to --«co 1-t "3 M 'Tjtto r-00 Oi OS 0> 0> OS coot^t-c« CD »0 00 t- Ol OO ^COtO t-- OsOOOO lOOOCflOCO oo^ososoo coot* fCOiO t* CO •-< ^ "T •-! ScO»O00-hOS rH c5 CO Tj» •*»< OOOOOOOOOO ooosososos o>osososos OSOSOSOIOSOS Tt< O 00 CD > OSOcO 1-t »qc00<0^ to 00 CO t* CO to 3 1* ^ »o to OS CO coo 00 5^03 CD C* 00 04 00 00 lO oooco<>c5 eotoooOco r*t*t*oooo *C4^CP5* St-OSOOl 00 00 OS OS t-t-0000 OOOOOOOOOO OOOOOOOOOO OOOOOOOOOO COC^COOSfcO 00 1- 01 2; 2" COO&J^^g OS OS 0> OS o 00 00 00 00 OS to c^gsos -*« oot-oos-v CD ^CSCOi oocsSS OS OS OS 0> OS t*0 Tfi(N to 0QC4 t* t* t^ CO r^QOChOi-H ooo^-i OS OS OS OS OS _ .... »OC^O>CDiOt* ^OQC^t* OSOOCOCDCOCO - - *^ — tOTpCOrHOlI-^ c5co^totoco OS OS OS OS OS OS Otmcmcot tocot»ooas o— toico-^ tocot^ooos o^HC^eO'* eO"* iocot^-ooos O^C^CO-^ tocOt-OOOS O'-^MCOfto COCOCOCOCO OOCOOOOOOO ^^^^r^-v KQ'^OOC^CO O-^OOCICO t=OOOi-»"-( .j lotor^coob Q— 4 OOOOOOOOOOO SQO-fkO wi^oc^eo cO'<»":o«'^ o^O"5co "JOQ-^w to-^oor-rH ^t^Ar^c^ c^oac^c^co i-«i-tt^-HQr- uSt^gjcc 000--JCSIO os^-ifftp •^coio'^cj ogC^^tr*^ iONi^.-t-«f io-vwoiio o&i-hcoc«3^h aiioa»co"5»o ^H06iOC5Oi u5«OOCCC3 ■3tO»OS"* "^ K tt '^ "^ 0OCiwb0O«-t "^'I^^N'*' (ioOO^HCO -^tOr^ODOl Soo»-t^H.-t Sa3;i2^ *SE;tx9S9S SS^SllJ ^^SSS2SS S23S3!^ SSiGiSif'Se $^«^i^t^ f-r^r^r^r^ r- oo oo oo oo oo OOObOOO OCOOOOOOOO OO^O^OCd Ca Ci 0> 03 O 0> O 0:> 03 O 0)03i?9^<^ Ob^O^OdO OaOaC^O^O ClC)030iO>Oi ooooooodoD ooodoocood cooooocccc ocioco<5cioci6 ccoocccooo ooo6o(5o6o6 0606060600 0606060606 060606060606 c^totoo--* ooeotoooc* OiQC^yjo i- wr-cst'-cs to*- itooics tooscotpoa c ^r-oooSoi oo^o»c^ eoco^-^fcc ocpyStpr^ t^r^oooooo Q?a'a>$>o oooo.-t ^^^rH»=i ^;^;s;i;iH^ 0000000000 Oi ^ 0>0i Oi Oi OS C5 Oi Oi 05 05 Oi OS Os OS 05 05 Cs O eft 05 Cft c& o ooooo ooooo oooooo 0606060606 0606060606 0606060606 GCCO060C06 0606060606 o6o6o6o6c5 oiosoioioi oJosoiOios ososoioiosol C*3 I'- cS Cs to coo (^ ■n' '-• iK O^ Od OS o 06060606 06 1-HO03--4CS ^H CO CO woo O^ OS 03 OS o> weo»oooco osooos-^w '»j'oscicoi-t w^-^cj" " " to r- 1-^ 00 0> OS Od ^ i-( »o^cor^ 00 00 00 00 00 00 00 00 05 OS 1-1 TP i^ rH Tp tpoac5"«rto ooooo ooooo OS OS OS OS OS SCOOOCP^H ^HOO-Hi-lt-. 50W" )wc«tpr^ '^posN'^io incooo^o JCOO^tO rHCO'^ClOO c4'f'3«CO^ ?0 tOiQ CO COI^i-' 10 OS 100 to to to OOOOO OS OS OS OS OS 00 CO cor- 10 OS -^t- 00 00 W tOOSCSiO I— t- 1— 0000 OOOOO OA OS OS OS OS ■^owou? §tO-^i-l<0 w^tot- 0000 OS OS OS OS OS »0 WiO »0'-t O CO -n- ^ CO oso^csco ■n' ^ o-^ coo O to t-i '•f tp t"- M* -r iC »0 >o »o OS OS OS OS OS OS OS OS OS OS OS >0 OS - i-H lO OS CO •^ ow o »o to to -^ 1—1 CO . - - o to "-H -"T cor )cO(- OOOOOSOiOiOi SiOiOcOtO cOtOtOtOtO eotOtO^Ocb OS OS OS ^ OS OS OS 03 OS OS OSOSOSOSOS OS OS OS OS ^ OsOSOSOSOS OS OS OS OS OS OS 53 XI to o -^ CO^ 00 "bW ■^ »0 OS wS 0000^ oso w>oo CO O OS t-- ' to «:> tO'-' OS OO^CM WOS »-< to O "^ t- *-t to to O 00 COOCO^ ^ ■•-ioO'-H OS OS OS ^ OS OSOSOSOSOS OS OS OS OS OS WO" icioiototo coF^r-^r^r~» OS OS OS O OS OS OS OS OS OS is lOcooo oO'Ooooo^ r— r-.cor-toco Ot^W tOOiOOOS cOWt-OWC- r-wr-c^S. T-tcoo-^t- 1— ivoo6*-H-^ r— oc5-^t* osi-ico'^to r— ooo»-t*-< wcoco-^Tr-n* o-H^HC^W coco'^'^-n' icio»ototo cob-r-*r— r~» r^oooooooo ooooososos osososososoj 0(^OsOsOS OSOSOSOSOS osososososo o-M* '«»' 000s "^co-^os t- 1-t '.^f 16 -v cs iO OS cot^ «— < w5 »o to CO r* OS'*"" OSOSOSOSOS OSOSOSOSO^ OSOS^OSOS OSOSOSOSOS i^r- 00 00 00 OS OS OS OS OS S W 00 W - oco»o c»o OS OS OS OS ►i5 "-I CO ^H CO 00 W '^ to "0 CO < w ■n' to c _ , oooo< W W(NC5C OS OSOSOsOb OsOsOSOsOS CD CO to to C« ^ tN CO COCS OOJ CO'*!^ OS OS OS OS OS cocoes OSiOOCOiOtD -CO'*!^ iOtor-r^r^t- iC lO i-i U5 -^ 1-t OS lO O CO iO to iO to r-r^r^ t- C* W C<» WCI w OS OS OS OS OS O^ tOOQ-^iO — ^ iooOh- M« OS tpcoor-- 00*O»-< -H Wt^O Wco ~S 1-H CS O tj- SOtOCNt Sooco c^ " 10 tot CSCOCOM"^ lOiOtOtOb- t— oooOooos <^ O loco 1000^31 w ^o CO OS ** r- 06 00 www w w w< ^»— OSl> w wowwgo OW^*"^ w CO -* »ocor- 5 fo CO CO CO I WW WW ^^t^^ot^ OSOOSOSCS OSOSOSOSOS OSOSOSOSOS OSOSOSOSOS OSOSOSOSOS OsOsOsosOs OSOSOSOSOS osososososos W tOtOO^ -HTuSr^t- 'n; O r* -^ *— ' 00 w,-t Wcoco OS OS O OS OS 00 coco 000s 00 1-1 T-t OilO 2j.-Hr- Woo * lO 10 to CO OS OS OS OS OS CO»(^COi-H OS T-t w w w w OS CO t, OS^OSOSOS OSOSOSOSOS pOOO _- ., —loot; r*i-H^t^o www WW OS OS OS OS OS w O'^cor- to CO 00 w -^ CO CO00«-iCO I— CO 10 CO 00 SuScoOw? t^OSi-H W ■^ ■»** -^ lO 10 w w wc5c5 OS OS OS OS OS 00 iC 00 00-^ OS wcoco w CO »o cor— op u5 uo »ra lO io www WW OS OS OS OS OS 00 OSOOOO 10 *JO CD to to CO W W W W W C-l CR OS OS 01 OS Oi >t-0> Wt^ CO WC >^rt oco ■ ^ OSOSOSOSOS OSOSOSOSOS ososos^os os^^osos ost^— *< M< O W OiO " ^co 0»0 ,, , , -, . - OS ^ W ir5>0»iOcpto cpotot^r- wwwww wwwww OSOSOSOSOS OS O OS OS OS vowoow-^ »oiocoow5 o w»ou:ii-t OS wcoco W CO o to t- 00 I- r— t- r- t- wwwww Tf*'*0-»ctor-oooi o-^wco-^ totor^ooos o^^wco- »o*o»o»o»J0 tctotctoto cototototo i^r— r— r^r^r^r* t^ 1 tor-oooso 0000000600 o6ooooo6ooo> g8Sg2£ SJ5S? ^ ■»»- -.f lO 'C 0- eg CO 013; ^Tf«0!»M04 4A ■«!}< I— 01 O Qi-«O0CN -^ 00 04>0 Oi04 r-<04o5 04CO Tj<0000O»O0 0>t-0»04iO OS0OOSU5-H CO^OOCC '^lO'^CMO oo^t^o^io oco^oco :oot^t^t>- t^r*t^t'-t' t-*t^t 000 001 -^ cS O CD CO S t'- t^l^t^t^t^ t>-t>-t^t^t a>^ i5icoco t^ t^ l^ t^ t- ^00004 -HCC OS b* eo ;o cp rt 00 t- «2 -r ^ Q ■^ to '^ (>• 00 01 ooooSoo I tP t^ Oi O O^COt^ CO 55*0 04 CJJ CS 1-H l^ ^ CO 00 03 04 00 CO CO O "^ 40 '^ COOOtt O 00 04 GO 00*0 ^04t-^ Tf 300 oco»o zo t^ r^ t^ t^ l- 1^ t^ t- rH o> ^ ^ r^ 10 coioco--* t* Oi'-fCOcO l^t'-OOOOOO t- 1^ t^ t-^ t-^ 00 t^ OiTT ■**• t- CO 00 cot- CD 00 0>^ C4 000000 0101 ecot^t-04 00 t— O Oi TT OCOCOt^ CTl "^ to CO t- 00 10 00 040CO -r o CO cs i^ O — ^r-«0 00000 00 00 00 00 00 CO o t-* -r CO »o 01 00 CO CO CO CO 01 00 I— *0 CO 1-^ -f IQ CO t- 00 Q? ocSooSo 00 00 00 00 00 00 ) 10 04 10 >00O^ :>oi 000 "M SOCDCOr-^ ^00 "^ OJ CO " 04 0*0 o O Olt-OOt- 'J' CO O 00 ■^ 00 Oi CD O 04 t^ l> t- (^ t- OS CO CO !•-• CO t— .— I o. r- Tf ^ Ol -^ QO<-i O^Tj^ t-OiOJ t^ t- !>- r- 00 I>^ t^ t'^ t-^ t^ -*'04t-l- O CO —i CO CO -H 04 CO . OOO-" "'f OiQ O-n- co»o 000 o> O^ O) 05 05 o t- CO O OJCO r^ oco -^ CO 00000 3 TJ4 lo o r- c t- 1^ t- 1^ t- l> t- 1- 1- 1- 00 WOO 00 00 OOOOrl 0606060606 CO CO o r^ CD 00 QQ t>- CO »0 »0 04 Oio --roiooo s« 000000000000 04»0 ^ QOiO 04 --^ooTr o5 00 t^CO rH -- JCOCOCO lOCOOCD ISOf-iOJ 00^^10*0=0 04 -O --D O CO t- »0 O O CO OiCNOOOltO 0104*0000^ OOOC ?3^ It-- o ^04 •-• o>- tOCO lOt- OiOCO I 05 05 o> 0> O) O O t^ t^ t^ t- t^ !> t- l-» I'- t>. t- t> t- 00 00 t- Ot-CO Oi CO t— 01 lO 'J* 00 Oi "^ O CO "Tj" to t^ ^ O 0000^ 0606060606 Oi CO CO CO 00 00 t- <-> O-r CD 0104 Tp lO ^C4 f *0 CO •-I -^ 000 01 r^ 00 oio<-» OiCOCOOO'-" OS 00 TT« 1-- CO -^ 10 -^ CO "-I 01 1— 04 CO "^ *o *o '© O4O4O4 04O5C4 0000000000 0000000000 000000000000 04»0 f-tOOiO 1-H o t- CO ^ coo^ooo t- 04 CO O O CO CO-H t-oo-^ •OCOQ004»0 _,-- locooco^o t-g>>--"t^t t- t- 00 00 00 t-iO ooco ^=.:: T 004^ CD •::;04O4 04 ^ 0^04 CO '^ CO CO CO CO CO CJiOcOQO*^ SI-CO^ »0 CO 01 CO CO -^o^ lO »0 3 l:^ 00 Ci CO CO CO CO COCO 00000000 00 00 00 00 00 00 00 TT 000 CO »0 JO "^ 04 i 00 00*0 00 00 ^H CO 'a* CiOl*004 O - 0>00*OCO'* OiOt . r-i00400CO t-.O4*OQi04 kocot-t^oo ooaaa>o>o )O304--D04 CO'-HOcOa> C004C0Oi»O I CO CO CO 04 C> »o 01 04 SCO 004*0 O r-( r-t »-t t-004*00l 0i0t^0404 CO TT CO "-H 00 *Q i-H CD i-H 10 t^O><-HC0»O cD00Oii-'O4 00 -H CO *0 t^ CO lO CO h-00 CO CO C CO^-t^t- t>-t*t--l^t>- t-t^t^t^OO 0000000000 0000000000 0000 0000 00 icococo 0606060606 t^O'^04iO 04 CJl^ 0*0 00 00 00 00 00 *0 04 OiCD*0 t- t-- CO *0 CO rH OJ Tf 10 CO t^ 00 00 060606060606 )04000 p )cococo * ?^t-04 COOICDCO t^OOOOiCO O'^'^OO-^ Oi04 ■V »0 O>0Q3!O4CO 0001CD004 — (Ol-^gOf- iO CO O CD <-• *oo3cor-o co»ooooc cj5r-oooooi o>oiOOi-H FHr-tr-ic4c QO rH COCOi-l 04 00 0^ 000 *0 t- 01 .-H CO CI 04 04 CO CO t— CD O 01 CO " t^ O CO 'T CD i-« CO -^ *0 CO r»t^000000 0000000000 OOOOOOOOOO OOOOCOOOOO 0000000000 01 03 CO- -0 04' -0000c I- 00 Oi <:_ ■^ ■»3» ■^ »o *o 0606060606 CO OC^i-^CO ' •00 00 op t- ■ oooiO-H r— ^ r-i 00 1— 05 CO t^eo*o»Q 04 g*Q ^04000 04CO'<3« *oo o *o *o *o *o *o *o 00 00 00 00 00 00 "* OOOCD *o*o -^ 04 Io4 040« OC0*0 CD OOrH r- '(t* ^ *0 00 CD t-O •O 04 *0 (^ CO *0 CD cot- Oi 04C0OC0C0 oo«-* •-< 1-t 00 M 04 CD 04 OOcOCOCO 00 CD^ 10 00 Oi04 »Ot- 0> F-t 04 04 C" — iC4 04 0606060606 eo^ coo 1: t^ O 04 *0 C 01 O OJ I- " S04C0Oi*O *0 t^04C4 »-<04"**or- 0606060606 *Q 04 0101 'T cD*O00t^04 ^ t— Oi r^ CO 00 0*004 CO Tj« TT *0 »0 ^ •^f »0 CD t- 00 *o *o *o *o )0 *0 04 0>CO*Ot^ I- CO ^ -^ ■* -H CO 04 •-< Oit- *0 OJQ-H 1-1 04C0 10 OCOOCO CO 060606060606 .e^t-t^r- OOOOOOOOOO OOOOOOOOOO OOOOOOOOOO OOOOOOOOOO iOOCOQQ 5co*o CO J »-H t- ■* »-* »0 00 O t— CO aS04 Oit-t- 00 CO 0)00 CO t— 00 o> 01 o 01^-^cD04 t^ CO -^ .-H *o t- 00 04 04004 SOliO *0 04 CO OCOO 1000 OCO 10 04 04 CO CO CO Sr-i O CD Oi 05 — < Tf" 00 t>-. t^ t- u? 04 r- oii-Hco o CO CO "^ f ^ C0 04COC5l*0 *0 O4a>0i-*J' 04 *0 t>- Olft " ~i o t- o: * *o '^ - M0*O*OtO 0606060606 t-- O ^ 04 *0 ^H 00 O 01 ■'T 04 04 CO 04 04 g^c4eo"^ CO CD CD CO S04 OS CD lO r- WJOCOCO O *0 ^Ot-OT 01 CO CO CO CO CD "O 06 06 06 06 06 oi t-t-t-t- t-t-r-t^OO OOOOOOOOOO OOOOOOOOXf OOOOOOOOOO OOOOOOOOOO OOOOOOOOOO 8 cot- CO 00 COCOr-icO '^ h-CO ot- OiOO O) O o ^ -t" 04 CO 04 CO04 »0(- CO ^■-| 04 CO 00 CO t- ^H ^r i- t- t- t- 00 00 '^tOC COt^f .-<^04 04O4 0606060c 06 O OS O CO' 04 OCOOOOO 00 00 CO C CO CO CO CO ^ 06 06060606 O>00C31*O rH SS: O^-fCDOOrH 04CO»OCDOO Tt--• 04 ^ OOQO*^ 0^04Coooco*o r-04^ OOOOOOOOOO 00 :H ^CO 04 01 co*o TT Tf«*0»0 »0 0606060606 »0 Tf< *o 04 WCOOSOO CO 04 (- —< *0 CDO0CT>r-^O4 *o *o *0 CO CO r-(t- ^---r ^ »-< CO 04^*0 ■^00 OOOOOOOOOO OOOOOOOOOO o t^ t- 1- r- 0606060606 - ■V «-t 00 !>■ 0> ?04 0000t- t- *o -^r Oj a> " 10 Ot-00 00 . t- t— l^ t- 1^ 060606060606 •^ t- lO o *o 040404eOCO CO" *0 OS*0*0 04 Tj* .-t r- f-H -rr 004 "**' t- o> 040*0 *0 00 O ^--H -V 00 *o»o *OCOO ^ CO 10 t- Oi *o *o *o *o *o 04 '-HO4 00Tt< to ^r CO r-t rH t-00000000 OOOOOOOOOO OOOOOOOOOO OOOOOOOOOO OOOOOOOOOO COCO t- t-i- 0606060606 O OlCO rH TT •-I t— O OS ■»»< 00^ 00 "»*' *0 CO t— CO t-^ t-. 1^ r^ r- 0606060606 S-H 00 *0 '*' '^^ *o Ococo O OS 00 1- *^ £f^ !:? 00 0SO^04C0 I- 1- 00 00 00 00 060606060c 06 O^-«04C0-n' lOCDC^OOOl 0^04CO-^ *0 CO r- 00 OS 0'-'C4 0404 04C 0^04CO'>' *OOt'-OQOS O^C4C0"^*O COCOCOCOCO COCOCOCOCO •^■^TT-'a'^'T* SSSSS32 c^c^cacoeo f ^r -^ o o oo-> -• C^CHCSCOCO -^ *r T >o »o o TABLE V. The Finding of the Azimuth. [Page 183 a5 •O-^OOMcO O'^GOJN':© O'^COMtO gOOO-HrH C^C^C^CCCO n'- O-^QOCNcO O-^XJC^If© O-^OOiNO • 00^ O'-tC^CO'f iO.00 00 00 t-^ t^ t^ t-^ r-^ "icoio Oi-^eoep^ c5 r 00 00 00 00 00 5 00 00 OO OO OO OO 00 oo r* t"- 1>. t^ t^ ■ t^t^i>. r-.i>.t^t^t^ 1-H ^O 00 O CT) GO f-H -^ CO O CT> O O O --( OO 05 Oi o> CS t^ t-^ t^ t^ r^ CO ^^ »o ^ 00 00 '<*•!© --r Oi 05 CO o o> in cccoof-Hco »oi--aj^c^ -^ tool-- 00 1— l^^HCItM csc^cscoco cocccococo O^O^O^dOs CSOSO)0^ O) O O) o> O Cs 00 00 ■<*« 00 r^ -rr <-l t^ (N »Q r- OO .OO ^ t^ t^ t^ t- r^ c^ t>- 1>. r>. t- 1^ t^ t>. OSOSOOOO CO CO "^ -r M« -n* 0> QS 0> OS 0> 0> t-^ t^ t>^ 1-1 1^ t>^ ro t' OS OS O ^ OOiO CO OSOO OS ■* iM ^^ to OOO o OSCSO OS c^ OSOOO i-H iQ CO r- aD C CC' lO o -^ t M'r-oiM' i-H ^ (M (M C OcOOOcOi^ 00 l^ lO ?^ OO COOO 0) 00 C^CO t' 00 OO^'-^-H^ C^ (N CS (N » OS t- r-- OO OO GO cc OOOOO o CO CO CO CO CO CO 00 00 00 00 00 GO ,-( U5 to OS O '-J' 00 O Cs t^ r* -f c^ 00 to CO t^ GO 00 OS W W iM CI CN 00 00 00 00 00 t^ fM CO t^ cc CS 00 -^ O iO O O ^ 01 c^ CO CO CO CO CO oooooooooo 00 OS ^H -f OS (M TT o CO OS ^ -o ^ o o CO CO -f -^ >o po CO CO coco 00 00 00 00 00 lO -^ »0 O 00 f r- OO 00 *o »0 OS CO t^ ^H lO lO CO CO r^ CO CO CO CO CO 00 00 060606 0»0i0 OS t-- ^ c 00 00 00 00 00 M -rf CO 06 OS OOOOO TT -^ TT -^ "«S* 06 06 06 06 06 CO CO WcO 10 (N c^ooco c ' cocot^ t C^ 00 CO CO 00 OS oooooooooo 000000000000 --* 10 'O OS O t'- C^ CO t CS OSCDCO C OCO CO <-t t-. OSOSO^C^ C^ CO CO - 00 0> 1— I '^ OS ■-H CO -?♦ cs 00 CO 1-* CO ^ 10 *0 '^ 10 O 00 CO CO l^ t-- tJ* O ^r 00 C^ CO O »0 ^ OS t-- .-( to 00 OS OS »0 lO to 10 lO —I OS CO (N CO 00 -^ O -^ CO lO CZ) --H CO lO 1-H f-H C^J CN CS 10 to lO »o »o oooooooooo oooooooooo ooooxococ oooooooooo oooooooooo oooooooooo , , . - ^ - .-< t^ C^ 10 t' 00 t^OS.-HCO-^ COI^oOOsO «-H^HC^CS- 00 00 GC OS to to to to to 0606 06 0606 CO O CO CO OS 050000 to CO CD CO CO oooooooooo . OscO to 00 to CM OS CO So .-4 to CO CO CO <-< t- CO OS L CD r* 00 00 OS o O -— ' CM c to to to to »0 CO O CO CO C 00 00 00 00 00 o r- OS c^ t^ -H CO CO C^ 00 CM t- CI (-—« CO CO f *** lO CD CD CO CD O 0606060606 CO CM CO 00 O 00 CO CO r^ to tocococor^ i>.f^ccoooo cOcOcOCDCD cOCOcOcDcO oooooooooo coooooxoo 05 r- f-t O ■**« r- -n" o "^ CO O OS OS OS o CO coco o t^ 06 06 0606 06 ■"^•O CMO to to CM 10 to »-* CM CO "* to CO 00 00 00 00 00 -i-j" ^}< O •^ CO o 1-H i^ CM to r* 00 i^ t-^ GO 00 00 a5 t^ t- 1^ t— ^^^-. o6o6 0606 06 06 r* 1-4^^ to CO ft CO 00 t- -^ »0 CM OS CO CO CO -^ ^r to CO CO CO CD cO CO 0606060606 CO 00 OS CO -^ OS^ ^ O CO OS CO CM 00 CO CO t— 00 00 OS CD CO CD cD CO 0606060606 -f lO t^ O 10 O CI CM rH t^ 05 "^O -*• 00 OSOO^i-f CO t— r— t^i^- 06 06060606 CM to CO to CO CO t* ^ to OS CM CM CO CO CO t^t^ t^ I^ t^ oooooooooo CO ^ f-H to C3S -^ r* 00 -- CM CO OS CM to "»r "V rf 10 to r- 1— t^ r- r- 0606060606 t-- to OS 00 CM CD CO 00 CM to . . _. 00 ^-H CO CO CO to to to CO CO CD CO t--. r^ r- r- 1^ t>- t* t>- t^ !>. oooooooooo oooooooooo SOcocoos CO •*»* "^ M OSO i-< CM CO r* 00 00 00 00 0606060606 CM CM 00 CM i-< 00 O CO O ^J" CO CO 00 00 OoS 00 S ooooocoooooo t^-H WtOCO O tor- CO CO coc5i^ -"T ^ 0>00<-iCM 00 00 OC' 00 00 Sooosco -?< O O Osto CM CO "^ "* to r^ r^ t- t^r^ 06 06 0606 06 "f lO t» O to OS ^F-^OcD CO CJ r- CM CD to to CD r— t^ t- t^ t^ r-r* CO 06 06 06 06 -H Oi-HCD TP .-( TT* to -^ C-l »-4 to osco r- 00 00 «) OS OS CD 1-H ^ 10 CO 00 CO CD t^ I-- S:2;jroco O O 1-H .-« 000000 00 00 oooooooooo r^to OS cc CM CO OS •-< 'J* CO r-l ^ CM CM CM 00 00 0000 00 0606 060606 M 00 O 00 CO S"^ CO OS to OCMCOtO CM CO CO CO CO 000000 00 00 0606060606 CO OCO CO OS OS CM coco —I cOOOOsOi-" OOOOOOGoS OOOOOOOOOO CM CM 00 CM -H 00 OS to O CO »o to •-« CM CM CO CO CO 00 00 00 woo 00 0606060606 06 cor^t-*^^ CM »-i to 1^ t^ -^ TP ^ OOiO CM ■*?< to to CD r— 0606060606 osM*r^osO O1— icocOt-1 00 -H r-i 01 CO O CM CM o r^ CO to •-< CO d 00 CO 00 CO *^ t^OOOsOSO O ^ »-i CM CM t^t^t^r^oo oooooooooo OOOOOOOOOO oooooooooo r- o t- CM o -H •»?' to to CO CM CO O '^ 00 CO CO *f f M* 00 000000 00 06 060606 06 oooooooooo CO --I to Tf 00 CO CO 00 CM M« r- o CM to t- co t-* t^ r* t^ 00 00 00 00 00 00 00 00 00 00 00 rj«cD -^ OS to »0 CO o to 01 <-» CO to CO t^OOCCOCOO oooooooooo 0606060606 OSCOOSOStO 0000-^OOt--*" OSCMCOCOCM OstOOCOtOCO t^0>O«-iCM CMcO-^'^Tf"'^ 00 00 OS OS OS OS OS OS OS OS OS OOOOOOOOOO 000000000000 oooooooooo 000000000000 OS CO CO r^ GO t-- CM ''T CO O 05 r- 'T .— I 00 00 oso »-*.-< r^ t^ 00 00 00 06 06 06 06 06 to O CO to CO to 00 00 CO c» •^ O CO dOO CMCO CO TT -ff 00 00 00 00 00 0606 0606 06 cOt-*OSC^r^ COCMCOODcO cOCOOOt-CO OO'-tCM.— iCS COOOCOCCCO r^CMCDOCO tOtOcOcDt- t-^OOOOOsOS 00 00 GO Xt 00 oooooooooo OOOOOOOOOO oooooooow GO CO CO t^ to to O CO -^ -^ OSOOOi-i 00 OS OS OS OS 0606060606 osr^ *-! o **« CMOS to OS I-H CO to ccoco -fl- -^O -^ CO o CO CJ I^ O CM CO 00 OS OS O O O D CO CO CO CO COCOCO- OC 00 00 00 00 00 00 00 00 00 00 CD O O -^ to O 10 t - CO CO r-4 00 to CM CS 00 00 obSoo 0606060606 CM r- O CI CO 00 O '-H OS *0 OS •-•■-< C7S CO ' CO OS »*« O OS o to to CM GO CO OS cor- t^ 00 GO 00 00 00 00 00 OSO O O ^H OO OS 0\0> OS «-H CO to *3' CM OS CO t^ '-' to ^H CM CM CO CO oooooooooo OOOOOOOOOO oooooooooo to O O *J^ CM 00 CO CD I^ t^ CO CM to OO1-H CO"^ -^ -^ to O OS OS OS 0i 0606 060606 CO **■ oor^ 1-t - -T t-^ -^ . - ■ OS CM -* to to tO CD CO to CM t-^ • — 1 CM ' - , J O c_ OS OS OS 0> OS 0606060606 »-i r- OS r-- CM to -rr" CM OS to coco O -^ CO o CO t- r^ t- OS OS OS OS OS oooooooooo CM OS CM CM 00 -•ro t-' 000s t— t^ t^ t^r-- OS 0> O OS Oi 0606060606 • 00 00 0000 OC tocor^ooos o^wco' lOcOt^oOOs O-hCMCJ" ■^r'^'^r-^'V tototototo tO*OtOtOtO (OcOcOcOCO COCOCOCDCD lOCOt^OOOS 0«-»CMCOM« lOCO^^0CO> O-HCM t- r- 1* t^ «^ 10 cor-^oooso r^t^r^ OOOOOOOOOO 00000000000s iO-l-OCCMcO O-^GOCMcO O-'TGOCMcD O-^COCMcO OtpooCMcD "OOOi-i^ CMCMCMCOCO 000^ --H CM CM CM CO CO 'OCCMcO O-^oOCMcO OM'OOCMcOO ' '^ tO to O O O •-< I-H CM CM CM CO CO TABLE VI ALTITUDE AND AZIMUTH TABLES FOR FACIUTATING THE DETERMINATION OF LINES OF POSITION AND GEOGRAPHICAL POSITION AT SEA 185 ALTITUDE AND. AZIMUTH TABLES. The results which have been reached by the foregoing proceedings may also be attained by the employment of the following tables, which are reprinted from the Sublication by Lieut. Radler de Aquino, BraziUan Navy, entitled "The 'Newest' Tavigation: Altitude and Azimuth Tables for Facilitating the Determination of Lines of Position and Geographical Position at Sea." These are spherical traverse tables which consist of the tabulation of the solu- tions of the right-angled spherical triangle, just as the plane traverse tables consist of the solutions of the right-angled plane triangle, and, by means of them, the astronomical triangle is solved by suitablv combining the tabulated values in relation to the two right-angled spherical triangles into which it may be decomposed by a perpendicular conceived to be passed from the observed celestial body at right angles to the celestial meridian of the observer. Presupposing a knowledge of the astronomical triangle, such as is imparted in the American Practical Navigator, the Erecepts for combining the various elements of the two right-angled triangles may e stated as depending upon where the point in the foot of the perpendicular falls on NS, the celestial meridian of the observer (see fig. 1). This is determined by the relative algebraic signs of L and d, by the relative values of L and h, and by whether t is greater or less than 6 hours or 90°. Accompanied by an outline of their deduc- tion, these precepts, four in number, are set forth herewith, reference being made to figures 1, 2, 3, and 4, respectively. (1) The point m can only fall between P and Z by the concurrence of the three conditions that d and L shall be of the same sign or name, that t shall be less than 90°, and that L shall be less than h. Hence (fig. 1) Z<90°; M = a + i8; and, putting Cfor90°-B, C = 90°-B = (90°-L)-(90°-6) = 6-L. 187 Page 188] ALTITUDE AND AZIMUTH TABLES. (2) The point m will fall between Z and Q when d and L are of the same name, if /<90° and L>&. Hence (fig. 2) Z>90°; M = a-/3; and C = 90°-B = (90°-6)- (90°-L)=L-6. (3) Tlie point m will fall between P and N when d and L are of the same name, if 90° (and then the tables must be entered with 180° -<, instead of t). Henc€ (fig. 3)Z<90°; M = /3-a; and C = 90°-B = (90°-L) + (90°-&) = 180°- (L + 6). ALTITUDE AND AZIMUTH TABLES. [Page 189 Fig. 4 (4) When d and L are of opposite sign or name, the point m will fall between (^, the equator, and P', the depressed pole, and reckoning from the depressed pole in order that the value of 90 — (^ shall remain within the range of the table, which is 90 ^^ in declination, by fig. 4 Z > 90° (from the elevated pole) ; M = a + /3; and C = 90° - B = (90 + L)-(90-6)=L + 6. SUMMARY. (1) d and L same name, <<90°, L<6, then C = &-L, Z<90°, and M = a + /3. (2) d and L same name, <<90°, L>6, then C = L-&, Z>90°, andM = a-/3. (3) (^ and L same name, i> 90° then C=180° - (L + 6), Z<90°, andM = /3-a. (4) d and L contrary names then C =L + &, Z > 90°, and M = a + /3. In the first two precepts the smaller of the quantities L and 6 is subtracted from the larger to get C, and in the last two they are added. In the third precept, when t is greater than 90°, their smn is greater than 90° and it is subtracted from 180°. When d and L are of contrary names their sum is always less than 90°. By a glance at the figm-es it wiU be seen that when Z is less than 90° in the precepts its value as given by the table is reckoned from the elevated pole to east or west according as the body is east or west of the meridian; and when greater than 90°, in like manner from the depressed pole. The position angle M may vary in value from 0° to 180°. In the first and fourth precepts a and /3 are added to find M ; and, in the second and third, the smaller is subtracted from the larger. The precepts will be referred to as occasion may arise. It is unnecessary to commit them to memory, as they will, with a httle use, become familiar. In order to avoid making the tables too voluminous, a, for the most part, is tab- ulated for every 30' only, and h and C for every 1° only. The double interpolating that this would seem to necessitate may be done away with by any one of the three methods which will be explained and illustrated in detail. In the descriptions of the methods about to be »iven and in the solution of the examples, the following abbreviations, almost all of \mich are in common use among Page 190] ALTITIDE AND AZIMUTH TABLES. American navigators, are employed to supplement the designations already used in the statement of the precepts and in the illustrative figures: a. m Ante meridian. La Latitude assumed. C. C Chronometer correction. Lp r Latitude by dead reckoning. C. T Chronometer time. L. A. noon Local apparent noon. C — W Chronometer minus watch. L. M. noon Local mean noon. Corr Correction. L. A. T Local apparent time. d Declination. L. M. T Local mean time. Dev. . ; Deviation. L. S. T Local sidereal time. Diff Difference. X Longitude. D. R Dead reckoning. Xa Longitude assumed. Eq. t Equation of time. . Xd. r Longitude by dead reckoning. .Altitude. p. m Post meridian. h^ Approximate altitude. p. s.c Per standard compass. hg Calculated altitude from K. A Right ascension. tables. R. A. M. S Right ascension of mean sun. ho Observed altitude (corrected), t Local hour angle. h^ Sextant altitude. ^a Assumed local hour angle. H. D Hourly difference. 4 Greenwich hour angle. I. C Index correction. |< Star or planet. FiKST METHOD. — Using an assumed position and simple interpolations. The usual procedure by the Saint Hilaire method of fixing a Une of position has been to determine the distance from the D. R. position to the line. The Une may be just as accurately fixed by determining its distance from any assumed position near the D. R. position. In the first two methods advantage is taken of this choice in position by assuming a position such as will give a value to a of an even half degree and to C a whole degree. The solution of the triangle by means of the tables is thus simplified by having tabulated values of a and C with which to work. The method of determining the assumed position appears in the description of the procedure which follows: Given d, Ld.e. and tj,,^^, to find h, Z, Xa, and La- Ent«r the tables from below with the nearest value of 5 as tabulated, and i^,^,, take out a to the nearest 30' . Reentering the tables from above with this a and with the given d, by a simple interpolation the corresponding values of 6 and t are obtained. These are exact values of a and h corresponding to the given d and an approximate t. Now, takhig this t as tj^ and combining it with the Iq (Greenwich hour angle) gives X^ near the D. R. position. Assuming this new longitude from which to plot the fine, proceed with the above values of a and 6. As previously explamed, b is combined with L to get C. C is only tabulated to whole degrees, so, in order to again avoid interpolating, assume as the latitude from which to plot the line the nearest value to the D. R. latitude that will, when combined with h, give C in whole degrees. Having for the assumed position exact tabulated values of a and C, take directly from the tables the corresponding values of h and Z. Comparing this he with the observed Ji, gives the altitude difference and the line is plotted from the assumed position for which Jic was obtained. Example 1. — A. M., December 30, 1916, sextant altitude of sun's lower limb is 23° 54', bearing south and east. W. T., 9^ 25'" 18«; C-W, 4*^ 58°^ 00^; C. C, + 3'"45«; height of eye, 37 feet; I. C, +2'.0; D. R. position, L. = 29° 11' N., X = 78° 29' W. Solve for fine of position. Solution in detail: See page 192 (Form 1). Enter all the given data in the proper g laces as indicated in the form. Start with the W. T. in line 1 and work down until r. M. T. with date is found in hne 5. From the Nautical Almanac enter, for December 30, G. M. T. 2**, the equation of time and decUnation with their proper signs on lines 4 and 11, respectively, and their respective hourly differences for the day with their signs on lines 1 and 8 (second col- umn). Correct the equation of time and declination for the difference in G.M.T. (27™), getting the corrected values in lines 5 and 12. Enter the equation of time in line 7. Applying it to the G. M. T. gives the G. H. A. in Line 12. This is immediately con- verted into arc and entered in both columns, line 14. Combine the G. H. A. with Xd.r. (lines 14 and 15, left-hand column) and obtain 9 ^^ i ^ t i i 1 ' O ! 1 t— 1 CO o CO CO eo o ^ ^ _ .a 1 ! J ^ o -^ CO IM eo CO CO 00 8 s O O .CI o lO OS Id CD eo i (M I-H 1 (M Q t 1 OoJPh D- 6' o [ J3 ea Time: 6. Beaiine: Long. D. B^ w w H ^ 1 fH iJ A^ M d o pt5 pi W d o : : >c d ^3 2 i $ ^ 1 X i , ^^ ^ K O lO lOI iffl, -"T »0 (M eo CO O CO O CO CO (M CO O CO 00 IM o »c ■<}' eo 00 CO CO o r- IM lO o o CC 1 1 1 1 1 1 '-'Pho §f^^ CO ( I i ] I^^P^ (M «^ ! 1 1 d W. T. C-W C. T. C. C G. M. T, s H' < 1 ! *^ 1 s w Ph' 6 d P5 d « ! ■ ds! fci 1^' .^ lO i iCi I' l-H 05 05 05 (M -^ O O eo o ^ w P4 i i > >-^ cc CO i—t I— 1 i^ 'z s ' IM IM 1 'o eo eo 00 •^ IM t- eo o ^. ■ S ■ ji (M ■ o 1 IM + IM lO r>- o eo o CO , ^^ V.S • \ 1 ! r-H 00 O td eoCCiM ^ 1 l^i d b Q o . H 1 H d ' . ^. ^ ^. c3 «■ ei « b 1 Q 1 ^ 1 d d d w P5 6 d « d J5 o ^6 o O n .« o' -4' .JS 72 ^J I— i CO CO t^ a. m. and .: 32^ < o ,_^ 1 (K i 1 i ! 1 1 l—t godPH 1 1 ( i •g « «!>•§ bio M S S O Eh' W W Eh' o - o s ii r r-H ^a ft CO o 1— ( O CO CO CO CO a O U3 rH o «o O CO O 00 CO o CO CO o> 00 t- t> b- iO f-H o o CO TJ< O CO CO CO CO CO CO 2 §3 C>1 + 00 o CO 1— I + 05 00 rH 1 + -fliO 1 lo C--i CO CO ■*' o ?d t^ 00 05 O rH fH i-H ci CO I— ( I-H fH I-H I-H 00 1-H OS 1-H § 1-H CO CO CO eo eo CO CO CO CO 55901= Page 194] ALTITUDE AND AZIMUTH TABLES. Example 3. — October 15, 1916, during a. m. twilight, the sextant altitude of Saturn, bearing S. and E., is 67° 29'; W. T., 5^ 50°> 22.5«; C-W, 2^ 15°» 10«; C. C, + !«• 15.5"; height of eye, 42 feet; I. C, -I'.S; D. R. position, L. 41° 45', X 32° 10' W. Solve for line of position. See page 193 (Form 1). Enter in the form all the given data and find the G.M.T. and date as before. Take from the Almanac and enter Satm'n's R. A. and d for G. M. noon 15th, the corrections for G. M. T. from Table IV of Almanac, the R. A. M. S. for G. M. noon 14th, and its correction for the G. M. T. Correct the R. A. and the d and enter the corrected R. A. in line 11. Nowwork down the form as in example 2 and find in line 16, ^d r =9° 01'. Enter Table VI from below with d = 20° 00^ and f = 9° 00', take out a = 8° 30' (nearest half degree). Reenter same table from above with a = 8° 30' and ^ = 20° 12'. 7 and by interpolating take out 6 = 20° 26'. 7 and t^ = 9° 03'. 9. Notice that this problem also comes under the second precept, so C = L-&. Taking L^=41° 26'.7, C; = 21° 00'. Turning agam to Table VI, where a = 8° 30' and C = 21° 00' take out Tic = 67° 25' and Z = 22° 38'. The altitude difference obtained as before is 4'. 3 from the body. Z as obtained is S 22° 18' E (greater than 90° and t is east) or body bears 157^°. The \j, is found as before and is 32° 12'.9 W. The assumed position then from which to plot the line is: La 41° 26'.7 N. X^ 32° 12'.9 W. The altitude difference is 4.3 miles away from the body bearing 157J° and the line of position is at right angles to the bearing. Second method. — Using an assumed position without interpolating. In this method a is found to the nearest half degree as in the first method. Now instead of entering with a and the given d and interpolating for h and t, enter with a and take out h and t as found opposite that tabulated value of d which is nearest to the given d. This tabulated value is taken out as the assumed d and marked d'. C is obtained by combining b and L in the usual way. As 6 in this method will be in whole degrees, L^ is taken as the nearest whole degree to L^.r. Now with a and C take out h' and Z' (approximate values of h and Z). The values of h' and Z' are in in error by an amount depending on the effect of Ad = d — d', the difference between the assumed and the true declination. The correction to Z', AZ, is always so small it may be neglected in practical work. The correction to h', Ah, is given by the formula: Ah = Ad cos M M, as previously shown, is a combination of a and /3. So when taking out b and t from the tables also take out the corresponding a; and likewise /3 when taking out h' and Z'. The manner in which a and /? must be combined to give M is shown in the precepts. To find the value of A^ per minute of declination, or its equivalent cos M, enter the second column of Table VII with 90° — M instead of Z' in the first column. The sign of A?^ is determined as follows : When M is less than 90°, Ah has the same sign as Ad; and for M greater than 90°, the opposite sign. The three examples worked out by the first method will now be used to illus- trate the second method. Example 1. — See page 196 (Form 2). The procedure is the same as in the first method, down to and including the determination of a. Now enter Table VI with a = 38° 30' and find d' = 23° 02' (the tabulated value nearest to the given d). Enter it in the form, line 12, and take out and enter the values of b, tj,, and a as found oppo- site d\ Now take La = 29° 00' (the nearest whole degree to Lp. r.). C is now obtained by combining b and L^ as before, and this gives = 59° 00'. With a = 38° 30' and = 59° 00', take out h', Z', and /3. As this example comes under the fourth precept, M = a + /3 = 140°.l, Ad = d-d' =8'.3. Entering the first column of Table VII with 90°-M = 90°- 140°.l =50°.l, cos M is found to be 0.77, and this multiplied by AcZ = 8'.3 gives 6'. 3 as the value of A^. ALTITUDE AND AZIMUTH TABLES. [Page 195 Referring to the i-ule given above for determining the sign of A/i, it is seen that as M is greater than 90°, and Ad is plus, A^ is minus. Applying A^ to h' gives he 23° 39'. 7. The altitude difference is 24'. 6. Neglecting AZ, the bearing of the body- is S 42° 52' E, or 137°. The londtude, X^, is found to be 78° 39'.8. The assumed position, then, from which to plot the line is: L, 29° 00' N K 78° 39 '.8 W The altitiide difference is 24.6 miles toward the body bearing 137°, and the line of position is at right angles to the bearing. Example 2. — See page 196 (Form 2). Entering Table VI from above with a = 9° 30', take out ^' = 12° 49'; also the corresponding t^, b, and a. L^ is taken as 35° 00'; then C=La-6 = 22° 00'. Now with a = 9° 30' and C = 22° 00', take out 7i', Z', and ^. By the precepts, M = a-/3 = 20° 00'. Ad = d-d' = -2Q'A. From Table VII, cos M is 0'.94; and hence AcZxcos M = A?i = 26.4x0.94 = 24'. 8. In this example, since M is less than 90°, Ah is minus like Ad. Applying Ah to h' gives Ac = 65° 43'. 2; and the altitude difference is 28'. 4 toward the body bearing S 24° 04' W, or 204°. The X^ is found to be 65° 22'.6 W. The assumed position, then, from which to plot the line is: L, 35° 00' N \j, 65° 22'.6 W The altitude difference is 28.4 miles toward the body bearing 204° and the line of position is at right angles to the bearing. Example S. — See page 197 (Form 2). Entering the tables from above with a = 8° 30', take out d' = 19° 46', also the corresponding tj,, h, and a. Take L^ = 42° 00', and combining it with h, gives C = 22° 00'. Now enter with a = 8° 30' and C = 22° 00' and take out /i',Z', and (8. By the precept, M = a- /3 = 16°.l. Ad = 26.7. FromTable VII cos M is 0.96; and hence Ad X cos M = AA = 26.7 X 0.96 = 25'. 7. Since M is less than 90°, Ah is plus like Ad. Applying Ah to h' gives i^c = 66° 54'. 7, and the altitude difference is 26.0 toward the body bearing S 21° 45' E, or 158°. The X^ is found to be 32°11'W. The assumed position, then, from which to plot the line is: L^ 42° 00' N Xa32° 11' W The altitude difference is 26.0 miles toward the body bearing 158°, and the line of position runs at right angles to the bearing. Third method. — Usmg the D. R. position. This method is the least desirable for the practical navigator in that it involves interpolating and also the correcting of the h and Z obtained. It is given here because the line is plotted from the D. R. position, and its use may be desirable when tD,^,—t is large, when the altitude difference is large, or when two or more lines of position are to be plotted simultaneously. The values of a and b are obtained by using tj^ instead of to. r. as in the first method. Then b is combined with Ld. r. to get C. C will seldom come out in whole degrees, so entering the tables with a and C it will be necessary to interpolate for A,' and Z'. Since the h' and Z' obtained are for L^. r. and tj,, they must now be corrected for the effect of ^d. r. — ^a? or ^^• The formulas are : . . ^h . , . . Ah T • rw, Ah = At X-^, 111 which -TT= ± cos L sm Z . AjZ = At X -Vt, in which -^ = — sin L. A,Z = AhX^, in which ^= -tan h' cot Z'. AZ = AiZ + A2Z. In Tables \1I and VIII are given the values of the coefficients -^» -vr» and -^t the arguments being the elements shown in the above formulas. Above the tables are Page 196] ALTITUDE AND AZIMUTH TABLES. 2'C bio S ^ 1=1 4^ 1 i J3 ^ ^ -" *- cr cr W Pc^ ' — H o ss S 00 00 o t-- t^ o ;o o 1 ^ 1 ISJ o < ^ < ^ 8 ill S o o ob iM S lO 00 «o Tt< lO IM 00 § 00 CO CO o eo § r-t O eo o 8 ■3 <1 ^ OS 00 ai O rf! . 05 H 1 ■a o Time: Bearii Long. w d 6 rt P5 ^ <1 o J -5 O e <5a s ■73 1 • 1 ' ! j V ! e o V J3 o 1 I ; 1 ..id ^^ Hd S ^ Q d d d CO H _ ^ i ^ * Q Date Obs. Lat. o o pi 6 -< ^ -^ \ al \ »^ 6 1 - ^ i. < ^ 1 ec o t^ r-t CO 1 r^ O t^ ■< ■ 1 (M o I— 1 "^ 1—1 1 CO (M 1 Ph a o 00 o § g O 05 ^ W ^ ^ o I-H A + + ■ ■ + ^ CO ] i-f O O 1 o CQ ^ '^ 00 1 00 C ^ o o F-H o o o i-t © I-H OJ d" c CO 05 CO CO © CO t-^ i-H «d w E a (M oo Tfl CO CO 00 t^ rH "^ ^ .£ o 00 a. m and .: 32 -=5 O 8 Ki "3 P5 ^ O Q 50 OoQp^ 6* & m CO PL| Time: 6. Bearing: Long. D. H. D. G. M. T. Corr. R. A. (E R. A. (E W d IH O <3 < ^^ ^ ^ 1 a oa S '■J g X ^ ^ W O w lO o lO o o . t- © W o lO 00 00 t- 00 CO 1^ «o oi o r-l O rH CO 00 Oi © 05 Ifi "^l CO (M rt i-H -^ Tf TjH r-H lO I-H CO O i-H O CO CO CO CO CO lO C^ B o O "3 1— t «o «o o ec o 00 C^ CO 00 t>. t^ CO CO lO f-l o o cc Tt< O CO (M CO CD CO CO CO eC3 ft) (M 00 o CO 05 00 1-H 05 t^ + (N I-H + ' 1 1 1 1 + ..die i , '-'Bo ^ 1 is c3 •-' -^ OJ ^ j Sra-* r-l JO' O o • 1 H d' < w ^ K » rS 3 %4 s ^ci d d 6 ^ i w rt 6 6 ei d ■< ,< ^ ee 1— i o O o O V < o «« ^ N eo ■* "3 » t>i 00 oi d 1— i I-H I-H CO I-H I-H I-H I-H I-H 00 I-H d C^J 1—1 CO CO CO CO CO CO CO ^ CO 00 Page 198] ALTITUDE AND AZIMUTH TABLES. also given the precepts for determining their signs. The correction AZ is generally negligible, unless A< is large. The same examples which were solved by the first and second methods will now be worked out to illustrate the third method. Example 1 . — See page 200 (Form 3) . The value of a is determined as before, and is 79* so* 40' 30" zo' 10* 78* 38° 30'. Now entering the tables with thisa Sindd = 23° 10'.3, take out6 = 30° ll'.3and <^ = 42°37'.4. 6 is combined with Ld R and gives C = 59° 22'. 3. Enter with a and C and by interpolating take out h' = 23° 29'.6 and Z' 42° 45'. Now A< = ^.e. - .j.... | .l.i .| .... |, ,.. | ..., | ,.,.[.. M| ..,,. 65* JEraxniile- 2 ??z -•35* -SOf -•40' -•30' d=l2° 22'.6, takeout&=12°33'.3 and<^ = 9° 44'. C = Li, « -& = 22° 04'.7. Enter with a and C and by interpolation find h' = 66° 03'.7 and Z' = 23° 59'. A< = + 11'.6. ALTITUDE AND AZIMUTH TABLES. Page 199] From Tables VII and VIII take out a7 ' aT' ^ Ah "^^*" their proper signs. The corrections A^, AjZ, and AjZ are obtained as explained in example 1 ; applying them to Ji' and Z' we find hc = e>5° 59'.9 and Z = 24° 25'. The altitude difference is 11'.7 toward the body bearing S 24° 25' W, or 20^°, and the line is plotted from the D. R. position. Example 5.— See page 201 (Form 3). Entering Table VI with a = 8° 30' and ^ = 20°12'.7,takeout6 = 20°26'.7and^A = 9°03'.9. C = Li, ^ -& = 21° 18'.3. Enter with a and C and by interpolating take out ^'=67° 07'.9 and Z' =22° 22'. A^ = — 2'. 9. From Tables VII and VIII take out ~^. > -~r, and -^ with their proper signs. The corrections A^, AjZ, and AjZ are obtained as before. Applying them to h' and Z' gives ^c = 67° 08'.7 and Z = 22° 15'. The altitude difference is 12.0 miles toward the body bearing S 22° 15' E, or 157f °, and the line is plotted from the D. R. position. The three lines of position, determined by the solutions of the three foregoing examples, are charted in the accompanying diagrams. The line of position from each example falls in the same place — as of course it should — whether laid down from Pi, P2, or p^, the respective points indicating the geographical positions from which the altitude differences are to be reckoned in the three solutions of each example by the three different methods. Page 200] ALTITUDE AND AZIMUTH TABLES. CO bcQ .. C . a e3 a • "•Do 3^ CD ?v ® _• • *J CO .tj> QOh-^ O P5 tf c^ o CO W d 6 "c •« to tn + I ! 1 1 ^^ ! o» t^ Ob _ i 1 «c rH Co eo OQ a 1 Decern ody: S '. R.: 2 H ^ H d ;-) < < o M K 1 i:^ 1 1- i i ^6 d d d O d C5 d <1 (S -h" c > 1 O rC O i-e :« < -g *S CO ^J 1 r-l c eo CM CM id CM CO CM CM S ALTITUDE AND AZIMUTH TABLES. [Page 201 m V a i o J3 1 i ^ ^ W < 43 1 -^ -^ tf & o* tcQ Eh w w Eh j:3 a 03 a Q S ^ -jj o W d 6 rt rt W d o a> O T3 •« «■ CS3 tJ -o Q to OJ S3 .9 » O >-iw eo'"*' iccot^oo o> c^ieo -^ici c\ / / / / / / - 30 0.00 I 0.00 90 90.0 I I I 30 .00 I .00 89 90.0 2 2 2 30 .00 2 .00 88 90.0 3 3 3 30 .00 3 .00 ^7 90.0 4 4 4 30 .00 4 .00 86 90.0 5 5 5 30 0.00 5 0.CX3 ?5 90.0 6 6 6 30 .00 6 .00 ^ 89.9 7 7 7 30 .00 7 .02 P 89.9 8 8 8 30 .00 8 .00 82 89.9 9 9 9 30 .02 9 .00 81 89.9 10 10 10 31 0.00 10 0.00 80 89.9 1 1 II II 31 .00 II .00 7§ 89.9 12 12 12 31 .00 12 .02 78 89.9 13 13 13 31 .00 13 2 .00 7? 89.9 14 14 14 31 .00 14 2 .CX5 76 89.9 IS 15 IS 31 0.00 15 2 0.00 75 89.9 16 16 16 31 .00 16 2 .02 74 89.9 17 17 17 31 .02 ^7 t 3 .00 73 89.8 18 18 18 32 .00 18 I 3 .00 72 89.8 19 19 19 32 .00 19 3 .02 71 89.8 20 20 20 32 0.00 20 4 0.00 70 89.8 21 21 21 32 .00 21 J 4 .02 69 89.8 22 22 22 32 .02 22 I 5 .00 68 89.3 23 23 23 33 .00 23 5 .02 P. 89.8 24 24 24 33 .00 24 6 .00 66 89.8 25 25 25 33 0.00 25 I 6 0.02 ^5 89.8 26 26 26 33 .02 26 7 .00 64 89.8 27 27 27 34 .00 27 7 .02 P 89.7 28 28 28 34 .00 28 8 .02 62 89.7 29 29 29 34 .02 29 9 .00 61 89.7 30 30 30 35 0.00 30 9 0.02 60 89.7 31 31 31 35 .CX3 31 10 .02 5S 89.7 32 32 32 35 .02 32 II .02 58 89.7 33 33 33 36 .00 33 12 .00 ^l 89.7 34 34 34 36 .02 34 12 .02 56 89.7 35 35 35 37 0.00 35 13 0.02 55 IH 36 Z^ 36 37 .02 36 ^ 14 .02 54 89.6 17 37 17 38 .00 37 15 .02 53 89.6 38 38 38 38 .02 38 16 .02 52 89.6 39 39 39 39 .00 39 17 .02 51 89.6 40 40 40 39 0.02 40 18 0.02 50 89.6 41 41 41 40 .00 41 19 •03 49 89.6 42 42 42 40 .02 42 21 .02 48 89.6 43 43 43 41 .02 43 . 1.02 22 .02 ^Z 89.5 44 44 44 42 .00 59 I 23 •03 46 89.5 45 45 45 42 44 59 25 45 89.5 a 6& 6 a 60^ b A a ^[ b _A_ a t A A 60' A 60' d = 0°0' d = 0°30' d = i°0' 00 114.6 57.29 [Page 203 \ = 0^0' a = 0<*30' a = rO' I \- \ f/ 60' \ t \ d 60' \ ' A \ d 6cy \ < A A A A^ \ A Z\ A \ A 2\ 60' ^ \ A Z\ 6c/ '^\ A o J / / / / / 45 45 45 42 0.02 44 59 I 25 0.02 45 89.5 46 46 46 43 .02 45 59 26 •03 44 895 47 47 47 44 .02 46 59 28 •03 43 895 48 48 48 45 .02 47 59 30 .02 42 89.4 49 49 49 46 .02 48 59 31 .03 41 89.4 50 50 ■;o 47 0.02 49 59 zz 0.03 40 89.4 51 51 51 48 .02 50 59 35 .03 39 89.4 52 52 52 49 .02 51 59 17 .05 38 89.4 53 53 53 50 .02 52 59 40 .03 37 89-3 54 54 54 51 .02 53 59 42 .05 36 89-3 55 55 55 52 0.03 54 59 45 0.03 35 893 56 56 56 54 .02 55 59 47 .05 34 893 57 57 57 55 •03 56 59 50 .05 33 89.2 58 58 58 57 .02 57 59 5J •05 32 89.2 59 59 59 58 •03 58 59 56 .07 31 89.2 60 60 60 I 0.03 59 59 2 0.07 30 89.1 61 61 61 2 •03 60 59 4 .07 29 89.1 62 62 62 4 •03 61 59 8 .07 28 89.1 63 63 63 6 .03 62 59 12 .08 27 89.0 64 64 64 8 .05 ^Z 59 17 .08 26 89.0 65 6=; 65 II 0.05 64 59 22 0.08 25 88.9 60 66 66 14 .05 65 59 27 .10 24 88.9 67 f7 67 17 .05 66 59 11 .12 23 88.8 68 68 68 20 .07 67 59 40 .12 22 88.8 69 69 69 24 .07 68 59 47 •'3 21 88.7 70 70 70 28 0.07 69 59 1.02 55 0.15 20 88.6 71 71 71 32 .08 70 58 3 4 •17 19 88.5 72 72 72 37 .10 71 58 M .18 18 88.5 73 73 73 43 .10 72 58 25 .20 17 88.4 74 74 74 49 .12 71 58 17 •23 16 88.3 75 75 75 1.02 56 0.13 74 58 51 0.28 15 88.1 76 76 59 2 4 •'5 75 58 4 8 ■30 14 88.0 77 77 76 59 13 .18 7^ 58 26 •37 13 87.8 78 78 77 59 24 .22 77 58 1.02 48 •43 12 87.6 79 79 78 59 17 7^ 57 5 14 II 87.4 80 80 79 59 53 79 57 . 44 10 87.2 81 81 80 59 3 12 80 57 1.02 6 22 g 86.8 82 82 81 59 35 81 56 7 9 8 86.4 ^^ 83 82 59 4 6 82 56 1.02 8 9 7 85^9 84 84 83 59 46 83 55 1.02 9 29 6 85.3 85 85 84 59 1.02 5 43 84 54 1.02 1 1 20 5 843 86 86 85 58 I 7 8 85 53 1.05 14 3 4 C2.9 87 87 86 58 1.03 9 28 86 50 1.07 18 27 3 80.S 88 88 87 56 1.05 14 2 87 46 1.22 26 34 2 76.0 89 89 88 53 1.62 26 34 88 35 2.40 45 I 634 90 90 89 30 QO 89 90 0.0 a 60' h a ^' h _A^ a ^'|i 6 A a t A A 60' A r 6c/ ^ = 0° 0' rf = 0°30' fZ = l°0' Page 204] 38.19 26 .64 32.90 \ a = r30' 0=2" (r a = 2° 30' t\' \' \ d 60' X i A \ d 60' X i _A V rf 60' \ * A A A h\ A Z\ 60' h\ A z\ 6(/ ft N^ ^ Z\ ex/ ^\ "X o / / / / / / Q O I 30 0.00 2 0.00 2 30 0.00 ^° 90.0 I I 30 .00 I .00 I 30 .00 89 90.0 2 2 30 .00 2 .00 2 30 .00 88 89.9 3 3 30 .00 3 .00 3 30 .00 l^ 89.9 4 4 30 .00 4 .00 4 30 .02 86 89.9 5 5 30 0.00 5 0.02 5 31 0.00 85 89.8 6 6 30 .02 6 I .00 6 31 .00 84 89.8 7 7 31 .00 7 I .00 7 31 .00 83 89.8 8 8 31 .00 8 I .00 8 1.02 31 .02 82 89.7 9 9 31 ,CX3 9 I .02 59 32 .00 81 89.7 10 10 31 0.02 10 2 0.00 9 59 32 0.02 80 89.6 1 1 II 32 .00 II 2 .02 10 59 33 .00 79 89.6 12 12 32 .00 12 3 .00 II 59 33 .02 78 89.6 13 13 32 .02 13 1.02 3 .02 12 59 34 .02 77 895 14 14 33 .00 59 4 .00 13 59 35 .00 76 89.5 15 IS 3Z 0.02 14 59 4 0.02 14 59 35 0.02 75 89.5 i6 16 34 .00 15 59 5 .00 15 59 36 .02 74 89.4 17 17 34 .02 16 59 5 .02 16 59 37 .02 73 89.4 i8 18 35 .00 17 59 6 .02 17 59 38 .02 72 89.4 19 19 35 .02 18 59 7 .02 18 59 39 .02 71 893 20 20 3f 0.00 19 59 8 0.02 19 59 40 0.02 70 893 21 21 3^ .02 20 59 9 .00 20 59 41 .02 69 89.2 22 22 1.02 37 .02 21 59 9 .02 21 59 42 .02 68 89.2 23 59 38 .02 22 59 10 .02 22 59 43 .02 67 89.2 24 23 59 39 .00 23 59 II .02 23 59 1.02 44 .02 66 89.1 25 24 59 39 0.02 24 59 12 0.02 24 58 45 0.03 65 89. z 26 25 59 40 .02 25 59 13 ■03 25 58 47 .02 64 89.0 27 26 59 41 .02 26 59 15 .02 26 58 48 •03 63 89.0 28 27 59 42 .02 27 59 16 .02 27 58 50 .02 62 88.9 29 28 59 43 .02 28 59 17 •03 28 58 51 .03 61 88.9 30 29 59 44 0.02 29 59 19 0.02 29 58 53 0.03 60 88.8 31 30 59 45 .02 30 59 20 .02 30 58 55 .03 59 88.8 32 31 59 46 .02 31 59 21 •03 31 58 57 .03 58 88.8 33 32 59 47 •03 32 59 23 •03 32 58 59 •03 57 88.7 34 ii 59 49 .02 33 59 25 .02 33 58 3 I .03 56 88.7 35 34 59 50 0.02 34 59 1.02 26 0.03 34 58 3 0.03 55 88.6 36 35 59 51 .03 35 58 28 •03 35 58 5 •05 54 ^•5 37 36 59 53 .02 36 58 30 .03 36 58 1.02 8 •03 53 88.5 38 37 59 54 •03 37 58 32 -03 37 57 10 •05 52 88.4 39 38 59 56 .02 38 58 34 .05 38 57 13 •05 51 88.4 40 39 59 57 0.03 39 58 37 0.03 39 57 16 0.05 50 88.3 41 40 59 59 .03 40 58 39 •03 40 57 19 .05 49 88.3 42 41 59 2 I •03 41 58 41 .05 41 57 22 •05 48 88.2 43 42 59 3 •03 42 58 44 •05 42 57 25 •05 47 88.1 44 43 59 5 •03 43 58 47 •05 43 57 28 .07 46 88.1 45 44 59 7 44 58 50 44 57 32 45 88.0 a 6c/ I ^_ a ^^ h A 60' a — h A a t A 6(/ A 60' A to' ^ = 1°80' tZ = 2°0' (? = 2"'30' 38.19 28.64 22.90 [Page 205 \b a = i° 30' a = 2'^0' a = 2° 30' \ \ * \rf 60' |\ i A \i 60' \« ■^ X d 60; X f A \ b\ * \ A Z \ 6(/ A \ A Z\ 60' a\^ a z\ 60' ^\ p\ o / / / / / / _o 45 44 59 2 7 0.03 44 58 2 50 0.05 44 57 I 3 32 0.07 45 88.0 46 45 59 9 .05 45 58 53 .05 45 57 1.02 36 .07 44 87.9 47 46 59 12 •03 46 58 56 .05 46 56 I 40 .07 43 87.9 48 47 59 14 .05 47 58 59 .07 47 56 I 44 .07 42 87.8 49 48 59 17 .05 48 58 3 3 .07 48 56 I 48 .08 41 87.7 50 49 59 20 0.05 49 58 1.02 7 0.07 49 56 I 53 0.08 40 87.6 51 50 59 1.02 23 .05 50 57 II .07 50 56 I 58 .08 39 87.5 '{2 51 58 26 •OS 51 57 15 .07 51 56 I 4 3 .10 38 87.4 53 52 58 29 .07 52 57 19 .08 52 56 I 9 .10 37 87.3 54 S3 58 33 .07 53 57 24 .08 53 56 1.02 15 .10 36 87.2 55 54 58 37 0.07 54 57 29 0.08 54 55 I 21 0.12 35 87.1 56 55 58 41 .07 55 57 34 .10 55 55 I 28 .12 34 87.0 57 56 58 45 .08 56 57 40 .10 56 55 I 35 • 13 33 86.9 58 57 58 50 .08 57 57 46 .12 57 55 I 43 • 13 32 86.8 59 58 58 55 ,08 58 57 1.02 53 .12 58 55 1.02 51 •15 31 86.7 6o 59 58 3 O.IO 59 56 4 0.12 59 54 I 5 0.15 30 86.5 6i 60 58 6 .10 60 56 7 • 13 60 54 I 9 •'7 29 86.4 62 61 58 12 .10 61 56 15 •'S 61 54 I 19 .18 28 86.2 63 62 58 18 .12 62 56 24 •15 62 54 1.02 30 .18 27 86.1 64 63 58 1.02 25 •13 63 56 33 •17 63 53 I 41 .22 26 85^9 65 64 57 33 0.13 64 56 1.02 43 0.18 64 53 I . 54 0.23 25 85.7 66 65 57 41 •15 65 55 54 .20 65 53 1.02 6 8 •2S 24 855 67 66 57 50 •17 66 55 5 6 .22 66 52 I 23 •27 23 853 68 67 57 4 .18 67 55 19 •2S 67 52 I 39 .30 22 85.1 69 68 57 11 .20 68 55 1.02 34 •27 68 52 1.02 57 •32 21 84.8 70 69 57 23 0.22 69 54 . 50 0.28 69 51 I 7 16 0.37 20 84.5 71 70 57 1.02 36 •25 70 54 6 7 •33 70 51 1.02 38 .42 19 84.2 72 71 56 51 •27 71 54 1.02 27 •37 71 50 1. 02 8 3 •4S 18 839 73 72 56 5 7 •32 72 53 49 .40 72 49 I 30 •SO 17 83.5 74 73 56 26 •35 73 53 1.02 7 13 •47 73 49 1.02 9 .58 16 83.1 75 74 56 1.02 . ^7 0.40 74 52 41 o^S3 74 48 1.02 35 0.65 IS 82.6 76 75 55 6 II •47 75 52 1.02 8 13 .62 75 47 1.02 10 14 •7S 14 82.0 77 76 55 1.02 39 •S3 76 51 1.02 50 .70 76 46 1.02 59 .88 13 81.4 78 77 54 7 II .63 77 50 1.02 9 32 •83 77 45 1.03 II 52 1.02 12 80.7 79 78 54 1.02 49 78 49 1.02 10 22 78 43 1.02 12 53 1.23 II 79.8 80 79 53 8 35 79 48 1.02 II 22 79 42 1.03 14 7 10 78.8 81 80 53 1.02 9 30 80 47 1.03 12 35 80 40 1.05 15 36 9 77.6 82 81 52 1.02 10 39 81 45 1.03 14 5 81 37 i.os 17 25 8 76.1 83 82 51 1.03 12 8 82 43 1.03 15 59 82 34 1.07 19 43 7 74.1 84 83 49 1.03 14 4 83 41 1.07 18 28 83 30 1.09 22 40 6 71.6 85 84 47 1.05 16 43 84 37 1.09 21 50 84 25 I. IS 26 37 5 68.3 86 85 44 1.09 20 35 ll- ^"^ 1. 15 26 36 85 17 1.22 32 3 4 63s 87 86 39 1. 18 26 35 86 24 1.30 33 43 86 6 1.43 39 50 3 56.3 88 87 30 '■43 36 53 87 10 1.67 45 I 48 2.00 51 22 2 45^0 89 88 12 3-33 56 19 46 4.29 63 27 87 18 5.00 68 13 I 26.6 90 30 90 88 90 30 90 0.0 a — 6 A a Cxy b A a 67 55 26 .07 37 53 4 •07 52 873 39 38 56 51 .07 38 55 30 .07 38 53 8 .08 51 87.2 40 39 56 55 0.05 39 55 1.02 34 0.07 39 53 13 0.08 50 87.1 41 40 56 58 .07 40 54 38 .07 40 53 1.02 18 .08 49 87.0 42 41 56 4 2 .07 41 54 42 .08 41 52 23 .08 48 86.9 43 42 56 1.02 6 .07 42 54 47 .08 42 52 28 .08 47 86.7 44 43 55 I 10 .07 43 54 52 .08 43 52 23 .10 46 86.6 45 44 55 14 44 54 57 44 52 39 45 86.5 a 60' h A a 6c/ I A a 60' 6 A a t ^ 60' A 6c/ A 6c/ d = 2.°0' d = Z°2Q' rf = 4°0' IS ».o8 16-35 14.30 [ Pag( i207 \ a = 3° 0' a=3 °30' a = 4° 0' ); \ * \ d 60' \^ A \ d 60' \ t A \^ 60' \ ^ A \ ^\ A \ A ^ 60' h\ A Z\ 60' A \ A z\ eo' A /5\ o 45 / 44 55 I / 4 14 0.08 / 44 54 1.02 / 4 57 0.08 / 44 52 1.02 / 5 39 0. 10 45 ^.s 46 45 55 I 19 .08 45 53 I 5 2 .08 45 51 I 45 .10 44 86.4 47 46 55 I 24 .08 46 53 I 7 .10 46 51 I 51 .12 43 86.3 48 47 55 I 29 .08 47 53 I 13 .10 47 51 1.02 . 58 .12 42 86.1 49 48 55 1.02 34 .10 48 S2 1.02 19 .12 48 50 I 6 5 •13 41 86.0 50 49 54 I 40 0. 10 49 52 I 26 0.12 49 50 I 13 0.13 40 85.8 51 50 54 I 46 .10 50 52 I Zi .12 50 50 1.02 21 • 13 39 85.7 52 51 54 I 52 .12 51 52 1.02 40 •13 51 49 I 29 •15 38 855 53 52 54 I 59 .12 52 51 I 48 •13 52 49 I 38 •15 37 85^4 54 53 54 1.02 5 6 .12 53 51 I 56 •»5 53 49 1.02 47 •17 36 85.2 55 54 53 I 13 0.13 54 51 1.02 6 S 0.15 54 48 I 57 0.18 35 85.0 56 55 53 I 21 •15 55 50 I 14 •»7 55 48 1.02 7 8 .18 34 84.8 57 56 53 1.02 30 •15 56 50 I 24 .18 56 47 I 19 .20 33 84.6 58 57 52 I 39 •17 57 50 1.02 35 .18 57 47 1.02 31 .22 32 84.4 59 58 52 I 49 •17 58 49 I 46 .20 58 46 I 44 •23 31 84.2 60 59 52 I 59 0.18 59 49 1.02 58 0.22 59 46 1.02 58 0.25 30 84.0 61 60 52 1.02 6 10 .20 60 48 I 7 II •23 60 45 1.02 8 13 •25 29 837 62 61 51 I 22 .22 61 48 1.02 25 •25 61 44 I 28 .28 28 83.S ^^ 62 51 1.02 35 .23 62 47 1 40 •27 62 44 1.02 45 •32 27 83^2 64 6z 50 I 49 •25 63 47 1.02 56 •3° 63 43 1.02 9 4 •33 26 82.9 65 64 50 1.02 7 4 0.27 64 46 I 8 14 0.32 64 42 1.02 24 ''•35 25 82.5 66 65 49 I 20 .30 65 46 1.02 33 ■35 65 41 1.02 45 .40 24 82.2 67 66 49 1.02 38 •33 66 45 1.02 54 •37 66 40 1.02 10 9 •42 23 81.8 68 67 48 I 58 •35 67 44 1.02 9 16 •42 67 39 1.02 34 •47 22 81.4 69 68 48 1.02 8 19 .40 68 43 1.02 41 •45 68 38 1.02 II 2 •52 21 81.0 70 69 47 1.02 43 0-43 69 42 1.02 10 8 0.50 69 37 1.02 33 0.57 20 80.5 71 70 46 I 9 § .48 70 41 1.02 38 •57 70 36 1. 02 12 7 .63 ^§ 79-9 72 71 46 1.02 38 •53 71 40 1.02 II 12 .62 71 35 1.03 45 .70 18 794 73 72 45 1.02 10 10 .60 72 39 1.02 49 .70 72 33 1.03 13 27 .78 ^l 78.7 74 73 44 1.02 46 .68 73 38 1.03 12 31 .78 73 31 1.03 14 14 .88 16 78.0 75 74 43 1.03 II 27 0.77 74 36 1.02 13 18 0.88 74 29 1.03 15 7 1. 00 15 77.2 76 75 41 1.02 12 13 .90 75 35 1.03 14 II 1.03 75 27 1.03 '^ I 1. 15 14 76.2 77 76 40 1.03 13 7 1.03 76 zz 1.05 15 13 1. 18 76 25 1.05 17 16 1-32 13 75-2 78 77 38 1.03 14 9 1.22 77 30 1.03 16 24 '•37 77 22 1.07 18 35 '•55 12 74.0 79 78 36 1.03 15 22 '•43 78 28 1.05 17 46 1.63 78 18 1.07 20 8 1.80 II 72.6 80 79 34 1.05 16 48 79 25 1.07 19 24 79 14 1.09 21 56 10 70.9 81 80 31 1.05 18 31 80 21 1.09 21 21 80 9 1.09 24 5 9 68.9 82 81 28 1.09 20 38 81 16 1.09 23 43 81 4 i^i3 26 41 8 66.5 83 82 23 1.09 23 16 82 II 1. 15 26 39 57 1. 18 29 51 7 63.6 84 83 18 I. IS 26 38 83 3 1. 18 30 20 82 48 1.25 33 47 6 599 85 84 10 1.20 31 I 54 1.28 35 4 83 36 ^•33 38 44 5 5SI 86 85 1-33 36 55 84 41 1-43 41 15 84 21 '•54 45 4 4 48.9 87 45 1-54 45 2 85 23 1. 71 49 27 85 1.88 53 II 3 40.6 88 86 24 2.31 56 20 0. 58 2.50 60 17 32 2.86 63 29 2 29.8 89 50 6.00 71 35 86 22 7^5o 74 4 53 8.57 75 59 I 16,0 90 2,7 90 30 90 86 90 0.0 a 6c/ h _A_ a 60' h A a ^' h A a t A 60' A 6c/ A 60' rf=3*(y d = Z °30' d = ^°0' Page 208] 12.71 "43 10.39 \ a = 4°30' a = 5"0' a = 5'' 30' \' \« \ i 60' \ * A \ I 1.02 30 .00 89 89.9 2 2 1.02 30 .00 2 1.02 .00 59 I 30 .00 88 89.8 3 59 30 .02 59 I .02 2 59 I 30 .02 ^7 89.7 4 3 59 31 .00 3 59 I I .00 3 59 I 31 .00 86 89.7 5 4 59 31 0.00 4 59 I I 0.02 4 59 1.02 31 0.02 85 89.6 6 5 59 31 .oz 5 59 1.02 2 .00 5 58 I 32 .00 84 895 7 6 5Q 32 .02 6 58 I 2 .02 6 58 I 32 .02 83 89.4 8 7 59 1.02 33 .00 7 58 I 3 .02 7 58 I 33 .02 82 893 9 8 58 IZ .02 8 58 I 4 .02 8 58 1.02 34 .02 81 89.2 10 9 58 34 0.02 9 58 i.oa 5 0.02 9 57 I 35 0.02 80 89.1 II 10 58 35 .02 10 57 I 6 .02 10 57 I 36 .02 79 89.0 12 II 58 l^ .02 II 57 I 7 .02 II 57 1.02 37 .03 78 fA 13 12 58 1.02 2,7 .02 12 57 I 8 .02 12 56 I 39 .02 77 88.8 14 13 57 38 .02 13 57 1.02 9 .02 13 56 I 40 .03 76 88-8 15 14 57 39 0.03 14 56 I 10 0.03 14 56 1.02 42 0.02 75 88.7 16 IS 57 41 .02 15 56 I 12 •03 IS 55 I 43 .03 74 88.6 17 16 57 42 •03 16 56 I 14 .02 16 55 I 45 .03 73 88.5 18 ^l 57 1.02 44 .02 17 56 1.02 15 .03 17 55 I 47 •03 72 88.4 19 18 56 45 •03 18 55 I 17 •03 18 55 1.02 49 .03 71 88.3 20 19 56 47 0.03 19 55 I 19 0.03 19 54 I SI 0.03 70 88.2 21 20 56 49 .03 20 55 I 21 .03 20 54 I 53 .05 69 88. 1 22 21 56 51 .03 21 55 1. 02 23 .05 21 54 1.02 56 .03 68 88.0 23 22 56 1.02 53 ■03 22 54 I 26 •03 22 53 I . 58 •05 67 V% 24 23 55 55 .05 23 54 I 28 .05 23 53 I 6 I •05 66 87.8 25 24 55 58 0.03 24 54 I 31 0.05 24 53 1.02 4 0.05 65 87.7 26 25 55 5 .05 25 54 1.02 34 .05 25 52 I 7 •05 64 87.6 27 26 55 1.02 3 .05 26 53 I 37 .05 26 52 I 10 .05 63 87.5 28 27 54 6 .05 27 53 I 40 .05 27 52 1.02 13 .07 62 87.3 29 28 54 9 .05 28 53 1.02 43 ■°5 28 51 I 17 •07 61 87.2 30 29 54 12 0.05 29 52 t 46 0.07 29 51 1.02 21 0.C7 60 87.1 31 30 54 1.02 15 .05 30 52 I 50 .05 30 50 I 25 •07 59 87.0 32 31 53 18 .07 31 52 I 53 ■°7 31 50 I 29 •07 58 86.9 33 32 53 22 •05 32 52 1.02 . 57 .07 32 50 1.02 33 .07 57 86.8 34 33 53 25 .07 33 51 I 6 I .08 33 49 I 37 .08 56 86.6 3| 34 53 1.02 29 0.07 34 51 I 6 0.07 34 49 I 42 0.08 55 86.5 36 35 52 33 .08 35 51 1.02 10 .08 35 49 1.02 47 .08 54 86.4 17 36 52 38 .07 l^ 50 I 15 .08 26 48 I 52 .10 53 86.2 38 17 52 1.02 42 .08 37 50 1.02 20 .08 37 48 1.02 58 .10 52 86.1 39 38 51 47 .08 38 49 I 25 .10 38 47 I 7 4 .10 51 86.0 40 39 51 52 0.08 39 49 I 31 O.IO 39 47 1.02 10 O.IO 50 85.8 41 40 51 1.02 . 57 .10 40 49 1.02 37 .10 40 46 I 16 .12 49 857 42 41 50 6 3 .10 41 48 I 43 .10 41 46 1.02 23 .12 48 8S5 43 42 50 9 .10 42 48 1.02 49 .12 42 45 I 30 .12 47 8S4 44 ^3 50 1.02 15 .10 43 47 I 56 .12 43 45 1.02 37 •13 46 85.2 45 44 49 21 44 47 7 3 44 44 45 45 85.0 a tc/\ & A a 60' b A a 60' 6 A a t ^ \ 6c/ A 60' A 6c/ f/ = 4°30' 1 d = 5 0' d = b '8(r I27I 11.43 1039 [Page 209 \ a = 4° 30' a = 5°0 a = 5° 30' \ \ * \ d 60^ \ < A \rf 60' i\ t A \<^ 60' \ t A \ ^\ h \^ A z\ 60' /t\ A z\ 60' A \ A z\ 6^ ^\ 0\ o / / / / / / „ 45 44 49 I 6 21 0.12 44 47 1.02 7 3 0.13 44 44 I 7 45 0.13 45 85.0 46 45 49 I 28 .12 45 46 I II ••3 45 44 1.02 53 •15 44 84.8 47 46 49 1.02 35 .12 46 46 1.02 19 •'3 46 43 1.02 8 2 •15 43 84.7 48 47 48 I 42 •13 47 45 I 27 •15 47 42 I II •17 42 84-5 49 48 48 1.02 50 •15 48 45 1.02 36 •'5 48 42 1.02 21 •'7 41 84-3 50 49 47 I 59 0.15 49 44 I 45 0.17 49 41 I 31 0.18 40 84.1 51 50 47 1.02 7 8 •15 50 44 1.02 „ 55 •17 50 41 1.02 42 .18 39 839 52 51 46 I 17 •17 51 43 I 8 5 .18 51 40 1.02 53 .20 38 83.6 53 52 46 1.02 27 .18 52 43 1.02 16 .20 52 39 1.02 9 5 .22 37 834 54 53 45 I 38 .18 53 42 1.02 28 .20 53 38 I 18 •23 36 83.2 55 54 45 1.02 . 49 0.20 54 41 I 40 0.22 54 38 1.02 32 0.23 35 82.9 56 55 44 I 8 I .20 55 41 1.02 53 •23 55 Z7 1.02 46 .27 34 82.6 57 56 44 1.02 13 .23 56 40 1.02 9 7 •25 56 36 1.02 10 2 •27 33 82.4 58 57 43 1.02 27 •25 57 39 1.02 22 •27 57 35 1.02 18 .28 32 82.1 59 58 42 I 42 •25 58 38 1.02 38 .30 58 34 1.02 35 •32 31 81.7 60 59 42 1.02 57 0.27 59 Z7 1.02 56 0.30 59 ZZ 1.02 54 ^•33 30 81.4 61 60 41 1.02 9 13 •30 60 36 1.02 ro 14 •32 60 32 1.03 II 14 •35 29 81. 1 62 61 40 1.02 31 •32 61 35 1.02 Zl •35 61 30 1.02 35 .38 28 80.7 f^ 62 39 1.02 50 •35 62 34 1.02 54 •38 62 29 1.02 58 .42 27 80.3 64 63 38 1.02 10 II •37 ^l ZZ 1.02 II 17 .42 63 28 1.03 12 23 •45 26 79-9 65 64 ^ 1.02 33 0.40 64 32 1.02 42 0-43 64 26 1.02 50 0.48 25 79-4 66 fl ^^ 1.02 57 •43 65 31 1.03 12 8 .48 65 25 1.03 13 19 •53 24 78.9 67 66 35 1.02 II 23 .48 66 29 1.02 37 •S3 66 23 1.03 51 •57 23 78.4 68 ^7 34 1.02 52 •52 67 28 1.03 13 9 •57 67 21 1-03 14 25 .62 22 77.8 69 68 IZ 1.03 12 23 •57 68 26 1.02 43 .63 68 19 1.03 15 2 .68 21 77.2 70 69 31 1.02 57 0.63 69 25 1.03 14 21 0.68 69 17 1.03 ^ 43 0.75 20 765 71 70 30 1.03 13 35 .70 70 23 1.05 15 2 ■71 70 15 1.05 16 28 •83 19 75-8 72 71 28 1.03 14 17 .78 71 20 1.03 48 .87 71 12 1.05 17 18 •93 18 75^0 73 72 26 1.03 15 4 .87 72 18 1.05 16 40 ■95 72 9 1.05 18 14 1.02 17 74.1 74 73 24 1.05 56 .98 71 IS 1.05 17 Z7 1.07 7Z 6 1.05 19 15 1. 15 16 73-1 75 74 21 1.05 16 55 1. 10 74 12 1.05 18 41 1.20 74 3 1.07 20 24 1.30 15 72.0 76 75 18 1.05 18 I 1.27 75 9 1.07 19 53 1-37 59 1.09 21 42 1.47 14 70.7 77 7^ 15 1.05 19 17 1-45 76 5 1.07 21 It; 1-57 75 54 1.09 23 10 1.68 13 693 78 77 12 1.07 20 44 1.68 77 I i.og 22 49 1.82 76 49 I. II 24 51 1.93 12 67.7 79 78 8 1.09 22 25 1.97 56 I. II 24 38 2.10 77 43 '•'3 26 47 2.23 II 659 80 79 3 I. II 24 23 78 50 1-13 26 44 78 36 1. 15 29 I 2.60 10 637 81 57 1-13 26 42 79 43 1. 18 29 13 79 28 1.20 31 37 9 61.2 82 80 50 1. 18 29 29 80 34 1.20 32 9 80 18 1.25 34 41 8 58.2 83 81 41 1.22 32 51 81 24 1.25 35 40 81 6 1.30 38 19 7 54^6 84 82 30 1.28 36 59 82 12 1.36 39 56 52 1^43 42 39 6 50.3 85 83 17 1-43 42 5 56 1.50 45 7 82 34 1.58 47 51 5 45-1 86 59 1.62 48 27 83 36 1.76 51 26 83 12 1.88 54 5 4 38.7 87 84 36 2.07 56 23 84 10 2.22 59 7 44 2.40 61 28 3 31-0 88 85 5 3-33 66 5 37 3-53 6?> 15 84 9 3-75 70 5 2 21.8 89 23 8.57 77 30 54 10. 78 43 25 12.0 79 44 I "•3 90 30 90 85 90 30 90 0.0 a 60' 6 A a 6c/ 6 A a 60' h A a t A 60' A 60' ^ 60' fZ = 4°S0' <^ = 5°0' d==5°2(y 55901°- Page 210] 95^4 8.777 8.144 \ a = 6 °0' a = 6 °30' a = 7° 0' \ \ ° \ o' 1 \ ^ ~ \(f 6& \ ^ A \ d 60' \ ^ A A A ^ \ A z\^ 60' A \ A Z\ 60' A \ A z\ 60' "^X / / / i 30 / / I 6 0.00 I 0.00 I 7 0.00 ?° 90.0 I I 1.02 .00 I 1.02 30 .00 I 1.02 .00 89 89.9 2 59 I .00 59 I 30 .02 59 I .02 88 89.8 3 2 59 I .02 2 59 1.02 31 .00 2 59 1.02 I .00 ^7 89.7 4 3 59 1.02 I .00 3 58 I 31 .00 3 58 I I .02 86 89^5 5 4 58 I I 0.02 4 58 I 31 0.02 4 58 1.02 2 0.00 !5 89.4 5 5 58 I 2 .02 5 58 1.02 32 .02 5 57 I 2 .02 ^ 89-3 7 6 58 1.02 ■ 3 .02 6 57 I 33 .02 6 57 1.02 3 .02 l^ 89.2 8 7 57 I 4 .02 7 57 I 34 .02 7 56 I 4 .02 82 89.1 9 8 57 I 5 .02 8 57 1. 02 35 .02 8 56 1.02 5 .02 81 89.0 10 9 57 1.02 6 0.02 9 56 I 3^ 0.02 9 55 I 6 0.03 80 88.9 1 1 10 56 I 7 .02 10 56 1.02 37 .03 10 55 I 8 .02 79 88.7 12 II 56 I 8 .02 II 55 I 39 .02 II 55 1.02 9 .03 78 83.6 13 12 56 1.02 9 •03 12 55 1.02 40 •03 12 54 I II •03 77 88. 5 14 13 55 I II ■03 13 54 I 42 •03 13 54 1.02 13 •03 76 88.4 15 14 55 I 13 0.02 14 54 I 44 0.03 14 53 I 15 0.03 75 88.3 16 15 55 1.02 14 •03 15 54 1.02 46 .03 15 53 1.02 17 .03 74 88.1 17 16 54 I 16 .03 16 53 I 48 •03 16 52 I 19 •03 73 88.0 18 17 54 I 18 .05 17 53 1.02 50 •03 17 52 1.02 21 .05 72 87.9 19 18 54 1.02 21 .03 18 52 I 52 .05 18 51 I 24 .05 71 87.8 20 19 53 I 23 0.03 19 52 I 55 0.03 19 51 1.02 27 0.05 70 87.6 21 20 53 1.02 25 .05 20 52 1.02 57 •05 20 50 I 30 .05 ^2 87.5 22 21 52 I 28 •05 21 51 I 7 •05 21 50 1.02 33 •OS 68 87.4 23 22 52 I 31 .05 22 51 1.02 3 .05 22 49 I 36 •OS 67 87.2 24 23 52 1.02 34 .05 23 50 I 6 .07 23 49 1.02 39 .07 66 87.1 25 24 51 I 37 0.05 24 50 1.02 10 0.05 24 48 I 43 0.07 ^5 87.0 26 25 51 1.02 40 .07 25 49 I 13 .07 25 48 1.02 47 •07 f4 86.8 27 26 50 I 44 .05 26 49 1.02 17 .07 26 47 1.02 51 .07 f3 86.7 28 27 qo I 47 .07 27 48 I 21 .07 27 46 I 55 .07 62 86.6 29 28 50 1.02 51 .07 28 48 1.02 25 .08 28 46 1.02 59 .08 61 86.4 30 29 49 I 55 0.07 29 47 I 30 0.07 29 45 I 8 4 0.08 60 86.3 SI 30 49 1.02 59 .08 30 47 1.02 34 .08 30 45 1.02 9 .08 5g 86.1 32 31 48 I 7 4 .08 31 46 I 39 .08 31 44 1.02 14 .10 58 86.0 33 32 48 1.02 9 .08 32 46 1.02 44 .08 32 43 I 20 .10 57 85.8 34 11 47 I 14 .08 33 45 I 49 .10 33 43 1.02 26 .10 56 85.6 35 34 47 1.02 19 0.08 34 45 1.02 55 O.IO 34 42 1.02 ^l O.IO 55 8S5 36 35 46 I 24 .10 35 44 1.02 8 I .10 35 41 I 38 .12 54 853 n 36 46 1.02 30 .10 36 43 I 7 .12 3^ 41 1.02 45 .12 53 8S1 38 2,7 45 I 36 .10 37 A3 1.02 14 .12 37 40 1.02 52 .12 52 f4-9 39 38 45 1.02 42 .12 38 42 1.02 21 .12 38 39 I 59 .12 51 84.8 40 39 44 I 49 0.12 39 41 I 28 0.12 39 39 1.02 9 6 0.13 SO 84.6 41 40 44 1.02 56 .12 40 41 1.02 35 •13 40 38 1.02 14 •15 4§ 48 84.4 42 41 43 1.02 8 3 • 13 41 40 1.02 43 •13 41 37 1.02 23 •15 84.2 43 42 42 I 1 1 • 13 42 39 I 51 •IS 42 36 1.02 32 •15 '^Z 84.0 44 43 42 1.02 19 •"3 43 39 1.02 9 •15 43 35 1.02 41 •17 46 83.8 45 44 41 27 44 38 9 44 34 51 45 83-5 a 60' 6 A a 60' h A a 60' h A a / A 60' A 60' A 60' d = i 3°0' rZ = e .° 30' d = TO' ^■^"" 9-514 8.777 8.144 [Page 211 \ a = 6°0' a = 6° 30' a^TQt ^ \ * \ rfj fo' W i A X d 60' \ t A \ d 60' \ t z\ A \ f\ * \i A 2\ 60' A \ A z \ 60' h \ A 60' /?\ o / ff ' / / , / % 45 44 41 I 8 27 0.15 44 38 1.02 9 9 0.17 44 34 I 9 51 0.17 45 83^5 46 45 41 1.02 36 •'7 45 37 1.02 19 •17 45 34 1.02 10 I .18 44 83.3 47 46 40 1.02 46 ••7 46 36 I 29 .18 46 33 1.02 12 .20 43 83.1 48 47 39 1.02 56 •17 47 36 1.02 40 .18 47 32 1.02 24 .20 42 82.8 49 48 38 I 9 6 .18 48 35 1.02 51 .20 48 31 1.02 36 .22 41 82.6 50 49 38 1.02 17 0.20 49 34 1.02 10 3 0.22 49 30 1.02 49 0.22 40 82.3 51 50 37 1.02 29 .20 50 33 1.02 16 .22 50 29 1.03 II 2 •25 3? 82.0 52 51 36 1.02 41 .22 51 32 1.02 29 •23 51 27 1.02 17 •25 3S 81.8 53 52 35 1.02 54 •23 52 31 1.02 43 .25 52 26 1.02 ^0 .27 37 81.S 54 53 34 1.02 10 8 •25 53 30 1.02 58 .27 53 25 1.02 48 .28 36 81.1 55 54 2>Z 1.02 23 0.27 54 29 1.03 II 14 0.28 54 24 1.03 12 5 0.30 35 80.8 56 55 32 1.02 39 .27 55 27 1.02 31 •30 55 22 1.02 23 .32 34 80.5 57 56 31 1.02 55 •30 56 26 1.02 49 •32 S6 21 1.03 42 •35 33 80.1 58 57 30 1.02 II 13 •32 57 25 1.02 12 8 •33 57 19 1.02 13 3 •37 32 79-7 59 58 29 1.02 32 •33 58 24 1.03 28 •37 58 18 1.03 25 .38 31 79-3 6o 59 28 1.03 52 0.37 59 22 1.02 50 0.38 59 16 '■03 48 0.42 30 78.9 6i 60 26 1.02 12 14 .38 60 21 1.03 13 ^^ .42 60 14 1.03 14 13 •43 29 78^5 62 61 25 1.03 Z7 .42 61 19 1.03 3S •45 61 12 1.03 39 .48 28 78.0 63 62 23 1.02 13 2 •45 62 17 1.03 14 5 .48 62 10 1.03 15 8 •52 27 77^5 64 63 22 1.03 29 .48 63 15 1.03 34 •52 63 8 1.03 39 •55 26 76.9 65 64 20 1.03 58 0.52 64 13 '•03 15 5 o^57 64 6 1.03 16 12 0.60 25 76.4 66 65 18 1.03 14 29 •57 65 11 1.03 39 .60 65 4 I. OS 48 .65 24 757 67 66 16 1.03 15 3 .62 66 9 1.05 16 15 .67 66 I 1.05 17 27 .70 23 75^1 68 67 14 1.03 40 .68 67 6 1.03 55 •72 58 i.os 18 9 •77 22 74^3 69 68 12 1.05 16 21 •73 68 4 1.05 17 38 .78 67 55 1.05 55 .83 21 73^6 70 69 9 1.05 17 5 0.82 69 I 1.05 18 25 0.87 68 52 1.07 19 45 0.92 20 72.7 71 70 6 1.05 54 .88 58 1.07 19 17 •95 69 48 1.07 20 40 1. 00 iq 71.8 72 71 3 1.05 18 47 .98 70 54 1.07 i 20 14 1.05 70 44 1.09 21 40 1. 12 18 70.8 73 72 1.07 19 46 1. 10 71 50 1.07 21 17 1. 17 71 39 1.09 22 47 1-23 17 69.7 74 56 1.07 20 52 1.23 72 46 1.09 22 27 1.30 72 34 1.09 24 I '•37 16 68.5 75 73 52 1.09 22 6 1.38 73 41 1.09 23 45 1.47 73 29 I. II 25 23 '•53 15 67.1 76 74 47 1.09 23 29 '•57 74 36 I. II 25 13 1.65 74- 23 ^■n 26 55 1.72 14 65^6 77 75 42 I. II 25 3 1.77 75 30 1. 13 26 52 1.85 75 16 1. 15 28 38 '•93 13 639 78 76 36 I-I3 26 49 2.03 76 23 1. 15 28 43 2.12 76 8 1. 18 30 34 2.20 12 62.0 79 77 29 1. 15 28 51 2-33 77 15 1.18 30 50 2.43 59 1.20 32 46 2.50 11 59^8 80 78 21 1. 18 31 II 2.72 78 6 1.22 33 16 2.80 77 49 I.2S 35 16 2.87 10 57^3 81 79 12 1.22 33 54 55 1.28 36 4 78 37 1.30 38 8 9 54^4 82 80 I 1.30 37 4 79 42 1.30 39 18 79 23 1.36 41 25 8 51^ I 83 47 1.36 40 47 80 28 1-43 43 4 80 7 1.50 45 13 7 47^3 84 81 31 1.46 45 9 81 10 1.58 47 28 47 1.62 49 36 6 42.9 85 82 12 ,.67 50 20 48 1.76 52 35 81 24 1.82 54 38 5 37-7 86 48 2.00 56 26 82 22 2.07 58 31 57 2.31 6o 24 4 31-7 87 83 18 2.61 63 32 51 2.86 65 20 82 23 3.00 66 55 3 24.8 88 41 4.29 71 38 83 12 4.62 72 58 43 4.62 74 8 2 17. 1 89 55 12.0 80 34 25 12.0 81 17 56 15.0 81 55 I 8.8 90 84 90 30 90 83 90 0.0 a 60' h A a 60' b A a 60' > b A a t A 60' A 60' A 60' J = 6*'0' d = &Z 0' d^TQ' Page 212] 7 50 7-"S 6.691 I a = 7° 30' a = 8 OQ, = 8 °30' \ \ * 6cy A A 60' A \ A z\ A 60' 60' A Z\ _A 60' A / / / R ' / % ' 1.02 7 30 0.00 1.02 8 0.00 1.02 8 30 0.00 90 90.0 I 59 I 30 .00 59 I .00 59 I 30 .00 89 89.9 2 I 59 1.02 30 .02 I 59 1.02 .02 I 59 1.02 30 .02 88 !9-7 3 4 2 58 I 31 .00 2 58 I I .00 2 58 1.02 31 .00 87 89.^ 3 58 1.02 31 .02 3 58 1.02 I .02 3 57 I 31 .02 86 89.4 g 4 57 1 32 0.00 4 57 1.02 2 0.02 4 57 1.02 32 0.02 !5 893 5 5 57 1.02 32 .02 5 56 I 3 .02 5 56 1.02 33 .02 l^ 89.2 7 6 56 I 33 .02 6 56 1.02 4 .02 6 55 I 34 .02 l^ 89.0 8 7 56 1.02 34 .02 7 55 I 5 .02 7 55 1.02 35 .02 82 88.9 9 8 55 I 35 •03 8 55 1.02 6 .02 8 54 1.02 36 .03 81 88,7 10 9 55 1.02 37 0.02 9 54 1.02 7 0.03 9 53 I 38 0.02 80 88.6 II 10 54 I 38 •03 10 53 I 9 .03 10 53 1.02 39 •03 79 88.5 12 II 54 1.02 40 .03 II 53 1.02 II .03 1 1 52 1.02 41 •03 78 88.3 13 12 53 I 42 •03 12 52 I 13 .03 12 51 I 43 •03 7? 88.2 14 13 S3 1.02 44 •°3 13 52 1.02 15 •03 13 51 1.02 45 .05 76 88.0 15 14 52 I 46 0.03 14 51 1.02 17 0.03 14 50 1.02 48 0.03 75 87.9 16 15 52 1.02 48 •03 15 50 I 19 •OS 15 49 1.02 50 .05 74 ^7-7 17 16 51 1.02 50 .05 16 50 1.02 22 .03 16 48 I 53 .05 73 87.6 18 17 50 I 53 •05 17 49 1.02 24 .05 17 48 1.02 56 •05 72 87.4 19 18 50 1.02 56 •OS 18 48 I 27 .05 18 47 1.02 59 •05 71 873 20 19 49 I 59 0.05 19 48 1.02 30 0.07 19 46 I 9 2 0.07 70 87.1 21 20 49 1.02 8 2 .05 20 47 1.02 34 .05 20 46 1.02 6 .05 69 86.9 22 21 48 I 5 .05 21 46 I 37 .07 21 45 1.02 9 .07 68 86.8 23 22 48 1.02 8 .07 22 46 1.02 41 .07 22 44 1.02 13 .07 67 86.6 24 23 47 1.02 12 •07 23 45 1.02 45 .07 23 43 1.02 17 .08 66 86.5 25 24 46 I 16 0.07 24 44 I 49 0.07 24 42 I 22 0.07 ^5 86.3 26 25 46 1.02 20 •07 25 44 1.02 53 .08 25 42 1.02 26 .08 64 86.1 27 26 45 1.02 24 .08 26 43 1.02 58 .08 26 41 1.02 3^ .08 ^3 ^5? 28 27 44 I 29 .08 27 42 1.02 9 3 .08 27 40 1.02 3^ .10 62 85.8 29 28 44 1.02 34 .08 28 41 I .08 28 39 1.02 42 .10 61 85.6 30 29 43 1.02 39 0.08 29 41 1.02 13 o.io 29 38 1.02 48 0.10 60 854 31 30 42 I 44 .08 30 40 1.02 19 .10 30 37 1.02 54 .10 5? 85.2 32 31 42 1.02 49 .10 31 39 1.02 25 .10 31 36 I 10 .10 58 85.0 33 32 41 1.02 55 .10 32 38 1.02 31 .10 32 36 1.02 6 .12 57 84.8 34 33 40 1.02 9 I .12 33 37 I 37 .12 33 35 1.02 13 .12 56 84.6 35 34 39 I 8 0.12 34 37 1.02 44 0.12 34 34 1.02 20 0.13 55 84.4 36 35 39 1.02 15 .12 35 36 1.02 51 •13 35 33 1.02 28 •13 54 84.2 1>7 36 38 1.02 22 .12 36 35 1.02 59 •13 3^ 32 1.02 36 •13 53 84.0 38 37 37 1.02 29 •13 37 34 1.02 10 7 •13 37 31 1. 02 44 •15 52 83.8 39 38 36 1.02 37 •13 3^ 33 1.02 15 •15 38 30 1.03 53 •15 51 835 40 39 35 I 45 0.15 39 32 1.02 24 0.15 39 28 1.02 II 2 0.17 50 83.3 41 40 35 1.02 54 •IS 40 31 1.02 33 •17 40 27 1.02 12 •17 4^ 83.1 42 41 34 1.02 10 3 •IS 41 30 1.02 43 •17 41 26 1.02 22 .18 48 82.9 43 42 33 1.02 12 • 17 42 29 1.02 S3 •17 42 25 1.02 33 .18 4Z 82.6 44 43 32 1.02 22 .18 43 28 1.02 II 3 .18 43 24 1.03 44 .20 46 82.3 45 44 3^ 33 44 27 14 44 22 56 45 82.1 a 60' h A a 60' 6 ^ a 60' & A a t A 60' A 60' A 60' d = ' rso' d = \ 5°0' d = l ;*'30' 7596 7- "5 6.691 [Page 213 46 47 48 49 50 51 52 53 54 56 57 58 59 60 61 62 63 64 65 66 67 68 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 90 a = 7° 30' 60' A 44 31 45 30 46 29 47 28 48 26 49 25 50 24 51 23 52 21 53 20 54 18 55 17 56 15 57 13 58 12 59 10 60 8 61 5 62 3 63 I 58 64 55 65 52 66 49 67 46 68 42 69 38 70 Zi 71 28 72 22 7Z 16 74 9 75 I 53 76 43 77 31 78 18 79 3 45 80 24 81 o 30 56 82 14 26 30 / 1.02 10 33 1.02 44 1.02 56 i-o.l II 8 1.02 21 1.02 35 1.02 49 1-03 12 4 1.02 20 1.03 Z7 1.02 56 1.03 13 15 1.03 35 1.02 57 1.03 14 20 1.03 45 1.05 15 12 1.03 40 1.03 16 10 1.05 43 i.or; 17 18 1.05 56 1.05 18 37 1.05 19 22 1.07 20 10 1.07 21 3 1.09 22 I 1.09 23 5 I. II 24 15 l.II 25 32 1-13 26 58 1. 15 28 33 1. 15 30 20 1.20 32 20 1.25 34 36 1.28 Z7 10 1-33 40 5 1-43 43 25 1.54 47 13 1.67 51 31 2.00 56 30 2.31 62 s 3-33 68 19 5.00 75 9 15.0 82 27 90 _A 60' .22 •23 0.23 ■25 •27 .28 •32 0.32 •33 •37 .38 .42 0.45 •47 .50 •55 .58 0.63 .68 •75 .80 0.97 1.07 1. 17 1.28 1^43 1.58 1.78 2.00 2.27 2.57 2.92 3^33 60' J A d = T 30' _A_ 60' a = 8°0' 60' A / / 44 27 1.02 II 14 45 26 1.03 26 46 24 1. 02 39 47 23 1.02 52 48 22 1.03 12 6 49 20 1.02 20 50 19 1.02 35 51 18 1-03 52 52 16 1.03 13 9 53 14 1.02 27 54 13 1.03 46 55 II 1.03 14 6 56 9 1.03 28 57 7 1.03 qi 58 5 1.03 15 16 59 3 1.03 42 60 I Ko-; 16 10 58 1.03 40 61 56 i.o:; 17 12 62 53 1.05 47 6Z 50 1.05 18 24 64 47 1.07 19 4 65 43 1.07 47 66 39 1.07 20 34 67 35 1.07 21 25 68 ^i 1.09 22 20 69 26 1.09 23 21 70 21 i.09 24 27 71 16 I. II 25 40 72 10 I-I3 27 I 7Z 3 1. 15 28 30 55 1.18 30 9 74 46 1. 18 32 75 37 1.22 34 4 76 26 1.28 36 23 77 13 1.30 38 59 59 1.40 41 56 78 42 1.46 45 17 79 23 1.58 49 4 80 I 1.76 53 22 35 2.07 58 12 81 4 2.<;o 6i 36 28 3^53 69 35 45 5-45 76 3 56 15.0 82 55 82 90 _A 60' ■23 •23 0.25 .28 .28 •30 •32 0^33 •37 •38 .42 •43 0.47 .50 •53 •58 .62 0.67 .72 .78 •85 .92 •35 1.48 1.65 .85 2.07 2.32 2.60 2.95 3-35 A I d = S° 0' _A^ 60' a = 8° 30' / / 44 22 1. 02 II 56 45 21 1.02 12 9 46 20 1.03 22 47 18 1.02 36 48 17 1.03 50 49 15 1.02 13 5 50 14 1.03 22 51 12 1.03 39 52 10 1.02 57 53 9 1.03 14 16 54 7 1.03 36 55 5 1.03 58 56 3 1.05 15 21 57 1.03 45 58 1.03 16 II 58 56 1.05 ^2 59 53 I. OS 17 8 60 50 1.05 39 61 47 1.05 18 13 62 44 1.05 50 63 41 1.07 19 29 64 37 1.07 20 1 1 65 33 1.07 56 66 29 1.07 21 45 67 25 1.09 22 38 68 20 1.09 23 36 69 15 I. II 24 39 70 9 I. II 25 48 71 3 ••13 27 4 56 1. 15 28 28 72 48 1. 15 30 73 40 1.20 31 42 74 30 1.20 33 36 75 20 1.2'; 35 43 76 8 1.30 38 4 54 ^•33 40 43 77 39 1-43 43 41 78 21 '•54 47 2 79 1.62 50 48 37 1.88 55 2 80 9 2.14 59 45 37 2.73 64 59 59 3^53 70 42 Si 16 5-45 76 51 27 20.0 83 20 30 90 6c/ •23 •23 •25 0.28 .28 •30 .32 •33 0.37 •38 .40 •43 •47 0.48 •52 •57 .62 .65 0.70 •75 •97 1.05 1. 15 1.27 1.40 ^•53 1.70 1.90 2.12 2.35 2.65 2.97 3^35 3^77 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 II 10 9 8 7 6 5 4 3 2 I 82.1 81.8 81.S 8i.2 80.9 80.6 80.2 79-9 795 79.2 78.8 78^3 77.9 77-4 77.0 76.4 75-9 753 74-7 74.1 73^4 72.6 71.8 71.0 70.1 69.1 68.0 66.8 65.5 64.1 62.6 60.8 58^9 56.8 54-4 51-7 48.7 453 41.4 37-1 32.2 26.7 20.0 14. 1 7-1 0.0 ^' 6 A I r/ = 8°30' 6c/ Page 214] 6.314 5976 5-671 \ = 9^0' a = 9 °30' a = 10''0' \ ^ \ * 1 ■ , 1 \ d 1 60' \ t A \ d 60' \. t A \ d 60' \ ^ A \ A A\T z\ 60' A \ A Z\ 60' ^\ A 2\ 60' c\ I3\ / / / / / / 1.02 9 0.00 1.02 9 30 0.00 1.02 10 0.00 90 90.0 I 59 I .00 59 1. 02 30 .00 59 1.02 .00 89 89.8 2 I =;o 1.02 .02 I 58 1.02 30 .02 I 58 1.02 .02 88 89.7 3 2 58 1.02 I .00 2 57 I 31 .00 2 57 1.02 I .00 ^7 895 4 3 57 1.02 I .02 3 57 1.02 31 .02 3 56 1.02 I .02 86 89-3 5 4 56 I 2 0.02 4 56 1.02 32 0.02 4 55 I 2 0.02 85 89.2 6 5 56 1.02 3 .02 5 55 1.02 33 .02 5 55 1.02 3 .02 84 89.0 7 6 55 1.02 4 .02 6 54 1.02 34 .02 6 54 1.02 4 •03 83 88.8 8 7 54 1.02 5 •03 I 53 I 35 •03 I 53 1.02 6 .02 82 88.7 9 8 53 I 7 .02 8 53 1.02 37 .03 8 52 1.02 7 .03 81 88.5 10 9 53 1.02 8 0.03 9 52 1.02 39 0.03 9 51 1.02 9 0.03 80 '38.3 II 10 52 1.02 10 •03 10 51 1.02 41 ..03 10 50 1.02 II •03 79 88.1 12 II 51 1.02 12 •03 II 50 1.02 43 •03 II 49 1.02 13 •03 78 83.0 13 12 50 1.02 14 .03 12 49 1.02 45 •03 12 48 1.02 15 .05 77 87.8 14 13 49 I 16 .05 13 48 1.02 47 .05 13 47 1.02 18 .05 76 87.6 15 14 49 1.02 19 0.03 14 47 1.02 50 0.05 14 46 1.02 21 0.05 75 87-S 16 15 48 1.02 21 .05 15 46 I 53 •05 15 45 1.02 24 .05 74 87-3 17 16 47 1.02 24 .05 16 46 1.02 56 .05 16 44 1.02 27 .05 73 87.1 18 17 46 1.02 27 .05 17 45 1. 02 59 .05 17 43 1.02 30 .07 72 86.9 19 18 45 I 30 .07 18 44 1.02 10 2 .07 18 42 1.02 34 .07 71 86.7 20 19 45 1.02 34 0.07 19 43 1.02 6 0.07 19 41 1.02 38 0.0/ 70 86.6 21 20 44 1.02 38 .07 20 42 1.02 10 .07 20 40 1.02 42 .07 69 86.4 22 21 43 1.02 42 .07 21 41 1.02 14 .07 21 39 1.02 46 .08 68 86.2 23 22 42 1.02 46 .07 22 40 1.02 18 .08 22 38 1.02 51 .08 67 86.0 24 23 41 1.02 50 .08 23 39 1.02 23 .08 23 37 1.02 56 .08 66 85.8 25 24 40 1.02 55 0.08 24 38 1.02 28 0.08 24 36 1.02 II I 0.08 65 85.6 26 25 39 1.02 10 .08 25 37 1.02 33 .08 25 35 1.03 6 .10 64 S5-4 27 26 38 I 5 .08 26 36 1.02 38 .10 26 33 1.02 12 .10 63 85.2 28 27 38 1.02 10 .10 27 35 1.02 44 .10 27 32 1.02 18 .10 62 85.0 29 28 37 1.02 16 .10 28 34 1. 02 50 .10 28 31 1.02 24 .12 61 84.8 30 29 36 1.02 22 O.IO 29 33 1.02 56 0.12 29 30 1.02 31 0.12 60 84.6 31 30 35 1.02 28 .12 30 32 1.02 II 3 .12 30 29 1.03 38 .12 5§ 84-3 32 31 34 1.02 35 .12 31 31 1.03 10 .12 31 27 1. 02 45 .12 58 84.1 33 32 33 1.02 42 .12 32 29 1.02 17 •13 32 26 1.02 52 •13 57 83-9 34 33 32 1.03 49 •13 33 28 1.02 25 •13 33 25 1.02 12 •'5 56 83.6 35 34 30 1.02 57 0.13 34 27 1.02 33 0.13 34 24 1.03 9 o.is 55 834 36 3 5 29 1.02 II 5- •13 35 26 1.02 41 •15 35 22 1.02 18 •15 54 83.2 37 36 28 1.02 13 •15 36 25 1.03 50 .15 36 21 1.03 27 •17 53 82.9 38 37 27 1.02 22 •15 37 23 1.02 59 •17 37 19 1.02 37 •17 52 82.7 39 38 26 1.02 31 •17 38 22 1.02 12 9 •17 38 18 1.03 47 .18 51 82.4 40 39 25 1.03 41 0.17 39 21 1.03 19 0.18 39 16 1.02 58 0.18 50 82.1 41 40 23 1.02 51 .18 40 19 1.02 30 .18 40 15 1.03 13 9 .20 4§ 81.8 42 41 22 1.02 12 2 .18 41 18 1.03 41 .20 41 13 1.02 21 .20 48 81.5 43 42 21 1.03 13 .20 42 16 1.02 53 .22 42 12 1.03 33 .22 47 81.3 44 43 19 1.02 25 .22 43 15 1.03 13 6 .22 43 10 1.03 46 .23 46 80.9 45 44 18 38 44 13 19 44 8 14 45 80.6 60' 6 A 60' h A 60' b A a a a a ^ A 60' A 60' A M d = 9°0' d = £ ° 30' d = i 0°0' 6 •314 $•976 5-671 [Page 215 \ a = 9° 0' a -9° 3b' a = 10"*0' V \' \^ 60' \ ' A \ d 60/ \ t A X d 6c/ \ t A A A /i \. A z\ 60' A \ A z\ 60' A\ A z\ CC/ ^\ A o / / / / / / ^ , 45 44 18 1.03 12 38 0.22 44 13 1.02 13 19 0.23 44 8 1.03 14 0.25 45 80.6 46 45 16 1.02 51 .23 45 12 1.03 Z3 •23 45 6 1.03 15 .25 44 80.3 47 46 15 1.03 13 5 •23 46 10 1.03 47 .25 46 4 1.03 30 •27 43 80.0 48 47 13 1.02 19 .25 47 8 1.03 14 2 •27 47 2 1.03 46 .28 42 79.6 49 48 12 1-03 34 .28 48 6 1.03 18 .28 48 1.03 15 3 .28 41 79^3 SO 49 10 1.03 51 0.2« 49 4 1.03 35 0.30 58 1.03 20 0.32 40 78.9 51 50 8 1.03 14 8 • 3^ 50 2 1.03 S3 •32 49 56 1-03 39 •33 39 78.S 52 51 6 1.03 26 •32 51 1.03 15 12 •33 50 54 1.03 . 59 •35 38 78.1 53 52 4 1.03 45 •33 5! 1.03 32 •35 51 52 1.05 16 20 •37 37 77.6 54 53 2 1.03 IS 5 •35 52 56 1.03 53 .38 52 49 1.03 42 .38 36 77.2 55 54 1.03 26 0.3S 53 54 1.05 16 16 0.40 53 47 1.05 17 5 0.42 35 76.7 5t) 5^ I.Oj 49 • 4c 54 51 1.03 40 •42 54 44 i.os 35 •43 34 76.2 57 55 56 1.05 16 n .43 55 49 1.05 17 5 •45 55 41 1.05 „ 56 •47 33 75-7 58 56 53 1.03 39 •45 56 46 1.05 32 ■47 56 38 i.os 18 24 •50 32 75-2 59 57 SI 1.05 17 6 •48 57 43 1.05 18 •50 57 35 I.os S4 •53 31 74-6 60 58 48 1.05 35 0.52 58 40 1.05 30 0-55 58 32 1.07 19 26 0.55 30 74.0 61 59 45 1.05 18 6 •55 59 37 1.07 19 3 •57 59 28 1.07 59 .60 29 73-4 6c 60 42 1.05 39 •58 60 33 1.05 17 .62 60 24 1.07 20 35 .65 28 72.8 63 61 39 1.05 19 14 .63 61 3c 1.07 20 14 .67 61 2C 1.07 21 14 .68 27 72.1 64 62 36 ..07 S2 .68 62 26 1.07 54 .70 62 16 1.07 55 •73 26 7i^3 65 63 32 1.07 20 33 0.73 63 22 1.07 21 36 0.77 63 12 i.og 22 39 0.7" 25 70-5 66 64 28 1.07 21 17 .78 64 18 1.09 22 22 .82 64 7 1.09 -3 26 .85 24 69^8 &7 65 24 1.09 22 4 .85 ^'5 13 1.09 23 II .88 65 2 I. II 24 17 .92 23 68.8 68 66 19 1.09 55 •93 66 8 I.I I 24 4 •97 56 I. II 25 12 I.OG 2 2 67.8 69 67 14 1.09 23 51 I. CO 67 2 I. II 25 2 1.03 66 50 I. II 26 12 1.07 21 66.7 70 68 9 I. II 24 51 i.c8 56 I. II 26 4 i^i3 67 44 I-I3 27 16 I. 17 20 65.6 71 69 3 I. II 25 56 I.2C 68 5c 1.13 27 12 1.23 68 37 1. 15 28 26 1.28 ^% 64.4 72 57 i-'3 27 8 1-32 69 43 1. 13 28 26 '.35 69 20 1. 15 29 43 1.38 18 63.1 73 70 50 1. 15 28 27 1-43 70 36 i.iS 29 47 1.48 70 21 r.i8 31 6 1.50 17 61.6 74 71 42 I. IS 29 53 1.58 71 27 1. 18 31 16 1.62 71 12 1.20 32 36 1.67 16 60. 1 75 72. 34 1.20 ^i 28 '•75 72 18 1.20 32 53 1.78 72 2 1.22 34 16 1.82 15 58.4 76 73 24 1.20 ^^^ 13 1.93 7i 8 1.22 34 40 1.98 51 1.21; 36 5 2.00 14 56.5 77 74 14 1. 21; 35 9 2.15 57 1.2S :^6 39 2.18 73 39 1.28 ^.^ 5 2.22 13 54-4 78 75 2 1.28 37 18 2.40 74 44 i.-^o 38 50 2.42 74 26 '•33 40 18 2.43 12 52.2 7'-^ 49 1.30 39 42 2.67 75 30 1.3^' 41 15 2.68 75 II 1.40 42 44 2.70 II 49-7 80 76 35 1.40 42 22 2.98 76 14 1.40 43 56 3.00 54 1.46 45 26 2.98 10 46.9 i^i 77 18 1.46 45 21 3-35 57 1.54 46 56 3-32 76 35 1.5S 48 25 3-30 9 43-8 82 59 1.58 48 42 3-72 77 36 1.62 50 15 3.68 77 13 ..67 51 43 3.63 8 tx 83 7^ 37 1. 71 52 25 78 13 1.76 53 56 4.08 49 1.88 55 21 3.98 7 'vl 79 12 1.94 56 35 47 2.00 58 I 78 21 2.07 59 20 6 325 85 43 2.31 61 II 79 17 2.40 62 29 50 2.50 &3 42 5 27.9 ?6 80 9 2-73 66 14 42 2.86 67 22 79 14 3.00 68 25 4 23.0 87 31 3-75 71 43 80 3 4.00 72 38 34 4.29 73 28 3 : 17.6 88 47 6. CO 77 34 18 6.67 78 13 48 6.67 78 48 2 ' 11.9 89 57 20.0 83 43 27 20.0 84 3 57 20.0 84 21 I 6.0 90 81 90 30 90 So 90 0.0 a 60' h A^ a 60' h A a '^ h A_ a / ^ 1 6n' A 1 (0' A r,c/ \ ■ f^-9"0' 1 fZ = 9°30' d = \0°0' Page 216] 5396 SMS 4-915 10 II 12 13 14 IS 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 a = 10** 30' A _A_ 60' / / 1.02 10 30 59 1.02 30 I 5« 1.02 30 2 57 1.02 31 3 56 1.02 32 4 55 1,02 32 5 54 1.02 33 53 1.02 35 7 52 1.02 36 « 51 1.02 38 9 50 1.02 40 10 49 1.02 42 II 48 1.02 44 12 47 1.02 46 13 46 1.02 49 14 45 1.02 52 15 44 1.03 55 16 42 1.02 58 17 41 1,02 II 2 18 40 1.02 6 19 39 1.02 10 20 38 1.02 14 21 37 1.02 18 22 36 1.03 23 23 34 1.02 28 24 33 1.02 33 25 32 1.02 39 26 31 1.03 45 27 29 1.02 51 28 28 1.02 58 29 27 1.02 12 5 30 26 1.03 12 31 24 1.02 20 32 23 1.03 28 33 21 1.02 36 34 20 1.03 45 35 i« 1.02 54 36 17 1.03 13 4 37 15 1.02 14 3« 14 1.03 25 39 12 1.03 36 40 10 1.02 48 41 9 1.03 14 42 7 1.03 13 43 5 1.03 27 44 3 41 0.00 .00 .02 .02 .00 0.02 •03 .02 •03 •03 0.03 •03 .03 .05 .05 0.05 .05 .07 .07 .07 0.07 .07 .08 .08 .08 a = ir 0' 6& A 6c/ •'3 • 13 • 13 •IS 0.15 .«7 •17 .18 .18 0.20 .20 .22 •23 •23 60' A b A_ 60' d = 10° sc / 1.02 59 1.02 I 58 1.02 2 57 1.02 3 56 r.03 4 54 1.02 5 53 1.02 6 52 1.02 7 51 1.02 8 SO 1. 02 9 49 1.02 10 48 1.02 II 47 1,03 12 45 1.02 13 44 1.02 14 43 1.02 15 42 1.02 16 41 1.03 17 39 1.02 18 38 1.02 19 37 1.02 20 36 1.02 21 35 1.03 22 33 1.02 23 32 1.02 24 31 1.03 25 29 1.02 26 28 1.02 27 27 1.03 28 25 1.02 29 24 1.03 30 22 1.02 31 21 1.03 32 19 1.02 33 18 1.03 34 16 1-03 3 5 14 1.02 36 13 1.03 37 II 1.03 38 9 1.03 39 7 1.03 40 5 1.03 41 3 1.03 42 I 1.03 59 1.03 43 57 10 12 14 17 20 23 26 29 33 37 41 46 51 56 12 I 6 12 18 25 32 39 47 55 13 3 12 21 31 41 51 14 2 14 27 40 53 15 7 22 60' A d = irO' 0.00 .00 .02 .02 .02 0.02 .02 .02 .03 .03 0.03 .03 .05 .05 .05 0.05 .05 .07 .07 .07 0.08 .08 .08 .12 .12 0.13 • 13 • 13 • 15 • 15 0.17 .17 .'7 .18 .20 0.22 .22 .22 •23 •25 a = 11° 30' A _A 60' A 60' / 1.02 59 1.02 I 58 1.03 2 56 1.02 3 55 1.02 4 54 1.02 5 53 1.02 6 52 1.03 7 50 1.02 8 49 1.02 9 48 1.02 10 47 1.03 II 45 1.02 12 44 1.02 13 43 1.02 14 42 1.03 15 40 1.02 16 39 1.02 17 38 1.03 18 36 1.02 19 35 1.02 20 34 1.03 21 32 1.02 22 31 1.03 23 29 1.02 24 28 1.03 25 26 1.02 26 25 1.03 27 23 1.02 28 22 1-03 29 20 1.02 30 19 1.03 31 17 1.03 32 15 1.02 33 14 1.03 34 12 1.03 35 10 1.03 36 8 1.03 37 6 1.03 38 4 1.03 39 2 1.03 40 1.03 58 1.03 41 56 1.03 42 54 1.03 43 52 11 30 30 30 31 32 33 34 35 37 38 40 42 45 48 51 54 57 12 I 5 9 13 18 23 28 33 39 45 52 59 13 6 13 21 29 38 47 57 14 7 18 29 40 52 15 5 19 33 48 16 3 0,00 .00 .02 .02 .03 .02 •03 0.03 .05 .05 .05 .05 0.05 .07 .07 .07 .07 0.08 .08 .10 o. 10 .12 .12 .12 0.13 • 13 0.17 .18 60' A ^ = 11" 30' A_ 60' 8q 88 86 §4 ^3 82 80 79 78 77 76 75 74 73 72 71 70 69 68 67 66 65 63 62 61 60 59 58 57 56 55 54 53 52 51 50 48 46 45 90.0 89.8 89.6 89.4 89.2 89.0 88.9 88.7 88.5 88.3 88.1 87.9 87.7 87-5 873 87.1 86.9 86.7 86.5 86.2 86.0 85.8 85.6 854 85.1 84.9 84.7 84-5 84.2 84.0 83-7 83.5 83.2 82.9 82.7 82.1 81.8 81.S 81.2 80.9 80.6 80.3 79-9 79-6 79.2 5-39^ 5-145 4-915 [Page 217 \ a = 10° 30' a = iro' a = 11° 30' \ V \ d 60' \ ^ A \rf 60' \ t A \rf 60' \ * A A A ^ \ A Z\ 60' A\ A z\ 60' A\ A z\ 6c/ ^\ o / / / / / p ' p 45 44 3 1.03 14 41 0.25 43 57 1.03 15 22 0.27 43 52 I.os 16 3 0.2S 45 79.2 46 45 I 1.03 56 .27 44 55 1.03 38 .28 44 49 1-03 20 .28 44 78.8 47 59 1.03 15 12 .28 45 53 1.03 55 .28 45 47 I.os 37 .30 43 78.4 48 46 57 1.05 29 .30 46 51 1.05 16 12 .30 46 44 1.03 55 .32 42 78.0 49 47 54 1.03 47 .30 47 48 1.03 30 .33 47 42 I.os 17 14 .33 41 77-6 50 48 52 1.03 16 5 0.33 48 46 I.os 50 0.33 48 39 I.os 34 0.3s 40 77.2 51 49 50 1.05 25 •33 49 43 1.05 17 10 •35 49 36 I.os 55 •37 39 76.7 52 50 47 1.03 45 .37 50 40 1.05 31 • 38 50 33 1.05 18 17 .40 38 76-3 53 51 45 1.05 17 7 .38 51 Z7 1.05 54 .40 51 30 1.05 ^\ •42 37 75-8 54 52 42 1.05 30 .40 52 34 I.os 18 18 .42 52 27 ..07 19 6 •43 36 75-3 55 53 39 1.05 54 0.43 53 31 I.os 43 0.45 53 23 1.05 32 0.47 35 74.8 56 54 Z^ i.os 18 20 •47 54 28 1.05 19 10 •48 54 20 1.07 20 .48 34 74.2 57 55 3^ 1.05 48 .48 55 25 1.07 39 .50 55 16 1.07 29 .52 33 73-6 58 56 30 I.os 19 17 .50 56 21 1.07 20 9 .53 56 12 1.07 21 •55 32 73-0 59 57 27 1.07 47 •55 57 17 1.07 41 .5/ 57 8 1.07 33 .58 31 72.4 60 58 23 1.07 20 20 o.<;8 58 13 1.07 21 15 0.60 58 4 1.09 22 8 0.63 30 71.7 61 59 19 1.07 55 • 63 59 9 1.07 51 •65 59 1.09 46 .67 29 71.0 62 60 15 1.07 21 33 •65 60 5 1.09 22 30 .68 59 54 1.09 23 26 .70 28 70-3 63 61 II 1.09 22 12 •72 61 1.09 23 II •73 60 49 1.09 24 8 •71 27 695 64 62 6 1.09 55 '77 55 1.09 55 .78 61 44 I. II 54 .80 26 68.6 65 63 I 1.09 23 41 0.82 62 50 I. II 24 42 0,8 s 62 38 I. II 25 42 0.87 25 ^2/1 66 56 I. II 24 30 .88 63 44 I. II 25 33 .90 63 32 I. II 26 34 .93 24 66.8 67 64 50 I. II 25 23 •95 64 38 I. II 26 27 .98 64 26 1. 13 27 30 1.00 23 65.8 68 65 44 I. II 26 20 1.02 65 32 1. 13 27 26 I.os 65 19 LIS 28 30 1.08 22 64.7 69 66 38 1-13 27 21 1. 10 66 25 LIS 28 29 1^13 66 II LIS 29 35 1. 17 21 63.6 70 ^7 31 1. 15 28 27 1.20 67 17 1. 15 29 37 1.22 67 3 1.18 30 45 1.25 20 62.3 71 68 23 1. 15 29 39 1.30 68 9 1. 18 30 50 1.33 . 54 1. 18 32 «-37 19 61.0 72 69 15 1. 18 30 57 1.42 69 1.20 32 10 1^45 68 45 1.22 33 22 '•47 18 59-6 11 70 6 1.20 32 22 1-5=; 50 1.20 33 37 i.S8 69 34 1.22 ^ 50 1.60 17 58.0 74 56 1.20 33 55 1.6S 70 40 1.25 35 12 1.72 70 23 1.25 36 26 1-73 16 56-4 75 71 46 1.25 35 36 1.85 71 28 1.25 36 55 1.87 71 II 1.30 38 10 1.90 15 54-5 72 34 1.28 ?>7 27 2.03 72 16 1.30 38 47 2.05 57 1.30 40 4 2.07 14 52.6 77 73 21 1-33 39 29 2.23 7Z 2 1-33 40 50 2.23 72 43 1.40 42 8 2.2s 13 50-4 78 74 6 1.36 41 43 2-45 47 1.40 43 4 2.47 73 26 1-43 44 23 2.45 12 48.1 79 50 1.43 44 10 2.70 74 30 1.46 45 32 2.68 74 8 i.So 46 50 2.68 II 45-5 80 75 32 1.50 46 52 2.97 75 II I.S8 48 13 2.95 48 i.S8 49 31 2.93 10 42.7 Si 7^ 12 ..58 49 50 3-27 49 1.62 51 10 3-23 75 26 1.71 52 27 3.18 9 39-7 82 50 1.76 53 6 3-57 76 26 1.82 54 24 3^52 76 I 1.82 55 38 3^45 8 3*5-4 83 77 24 1-94 56 40 3-92 59 2.00 57 55 3^82 34 2.07 59 5 3^73 7 32.8 84 55 2.14 60 35 4.23 77 29 2.22 61 44 4.12 77 3 2.40 62 49 4.00 6 28.8 85 78 23 2.61 64 49 56 2.73 65 SI 4.42 28 2^73 66 49 4.27 5 24.6 86 46 3.. 6 69 23 78 18 3^33 70 16 . 50 3-53 71 5 4-48 4 20.1 87 79 5 4.29 74 14 36 4.62 74 56 78 7 4.62 ^5 34 3 15-4 88 19 7.50 79 20 49 7.50 79 49 20 8.57 80 i6 2 10.4 89 27 20.0 84 37 57 20.0 84 52 27 20.0 85 6 I 5-2 90 30 90 79 90 30 90 0.0 a 60' h _^_ a 6c/ h A a ^' 6 A a t A 60' A 60' A 6c/ i = 10°30' ^ = 11° 0' (i-ll°30' Page 218] 4.705 4-5II 4332 \b a = 12° 0' a = lJ 2" 30' a = 13° 0' V \- A \ \ d ec/ \ * A \ d 60' \ t A X d 63 28 15 1.03 14 •13 28 II 1.03 47 ••5 61 S3. 2 30 29 17 I. 03 4^ 0.13 29 13 1.03 22 0.13 29 9 1.03 56 0.15 60 82.9 31 30 15 I. 03 56 •13 30 II 1.03 30 • IS 30 7 1.03 15 5 •'S 59 82.6 32 31 13 '• 03 14 4 •IS 31 9 1.03 39 •15 31 5 1.03 14 •17 58 82.3 33 32 II I. 02 13 •17 32 7 1.03 48 •'7 32 3 1.03 24 •17 57 82.0 34 33 10 '• 03 23 ••7 33 5 1.03 58 .18 33 I 1.03 34 •17 56 81.7 35 34 8 . 03 33 0.17 34 3 ••03 15 9 0.18 59 1.05 44 0.18 55 81.4 36 35 6 . 03 A3 .18 35 I 1.03 20 .18 34 56 1.03 55 .20 54 8i.i 37 36 4 '• 03 54 .20 59 1.03 31 .20 35 54 1.03 16 7 .22 53 80.7 38 37 2 I. 03 15 6 .20 36 57 1.03 43 .20 36 52 1.05 20 .22 52 80.4 39 38 .. OS 18 .22 37 55 1.05 55 .22 37 49 1.03 33 .22 51 80.1 40 57 '• 03 3' 0.22 38 52 1.03 16 8 0.23 38 47 1.05 46 0.23 50 79-7 41 39 55 '• 03 44 •23 39 50 1.05 22 •2S 39 44 1.05 17 .25 4Q 79-3 42 40 53 >• 03 . 58 •23 40 47 1.03 37 .25 40 41 1.03 15 .27 48 79.0 43 41 51 I. OS 16 12 •27 41 45 1.05 52 .27 41 39 1.05 31 .28 47 78.6 44 42 48 I. 03 28 .27 42 42 1.05 17 8 .28 42 36 1.05 48 .28 46 78.2 45 43 46 44 43 39 25 43 33 18 5 45 77^8 a '- 0' h A a 60' 6 A a 60' b A a / A 60' A 6c/ A 60' d = 1 2°0' a ' = 1^ J°30' d = i ro' B 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 7S 79 80 81 82 83 84 85 86 87 88 90 4-705 a = 12°0' 60' / / 43 4f^ 1.05 16 44 44 43 i.os 17 I 45 4'"' ••03 19 46 38 1.05 37 47 35 1.05 57 48 3- 1.05 18 18 40 29 1.05 40 50 26 1.07 19 3 51 22 1.05 27 52 19 1.07 53 53 15 1.07 20 20 54 11 1.07 49 55 7 1.07 21 19 56 3 1.07 51 59 1.09 22 26 57 54 1.09 23 2 58 40 1.09 41 59 44 I. II 24 22 60 ^S I. II 25 5 61 32 I. II 52 62 26 I. II 26 42 (13 20 1. 13 27 36 64 I T. LIS 28 33 65 5 LIS 29 34 57 I.18 30 40 66 48 L18 31 52 67 3Q 1.20 33 8 68 20 1.22 34 31 6q 18 i.2<; n6 I 70 6 1.28 37 38 S3 1.33 39 24 71 38 1.33 41 18 72 23 1.40 43 23 73 6 1.46 45 38 47 1-54 48 5 74 26 1.67 50 45 7S 2 1.71 53 39 37 I.Q4 56 47 76 8 2.14 60 10 36 2.40 63 49 77 I 2.86 67 42 22 3-7'; 71 50 38 5.00 76 10 50 7. so 80 41 58 30.0 85 18 78 90 0.28 .30 .30 •33 •35 0-37 .38 .40 •43 •45 0.48 .50 •53 .58 .60 0.65 .68 •72 •7? •83 0.90 •95 1.02 l.IO 1.20 t.27 1.3S 1.50 1.62 1.77 1.90 2.08 2.25 2.45 2.67 2.90 3-13 3^38 3^65 3^88 4.13 4.33 4-52 4.62 45" a = 12° 30' 60' A _A 6c/ 6c/ , — A fZ = 12°0' _A^ 6c/ 43 39 44 37 45 34 46 31 47 28 48 24 49 21 50 18 51 14 52 10 53 6 54 2 58 55 53 56 48 57 43 58 38 59 33 60 27 61 21 62 14 63 7 59 64 51 65 42 66 33 67 2^ 68 12 69 o 48 70 34 71 19 72 2 44 73 24 74 2 38 75 12 42 76 9 33 53 77 9 21 28 30 / '•03 17 25 L05 42 1.05 18 1.05 20 1.07 40 1.05 19 2 1.05 24 1.07 48 1.07 20 13 1.07 40 1.07 21 8 1.07 38 1.09 22 9 1.09 42 1.09 23 17 1.09 55 1.09 24 35 I.II 25 17 I. II 26 2 '•13 50 i^i3 27 41 1. 15 28 36 1. 15 29 34 1.18 30 37 L18 31 45 1.20 32 57 T.22 34 15 I. 25 35 39 1.25 37 10 1.30 38 49 '•33 40 35 1.40 42 30 ^•43 44 35 1.50 46 50 1.58 49 17 1.67 51 56 1.76 54 48 2.00 57 53 2.22 61 12 2.50 64 45 3.00 68 32 3^75 72 32 5.00 76 43 8.57 81 3 30.0 85 30 90 0.28 .30 .33 •33 •37 4332 a = 13°0' [Page 219 .40 .42 •45 •47 0.50 .52 •55 .58 .63 0.67 .70 •75 .80 .85 0.92 •97 1.05 1.13 1.20 1.30 1.40 1.52 1.65 1.77 1.92 2.08 2.25 2.4 s 2.65 2.87 3.08 3^32 3^55 3.78 4.00 4.18 4^33 4-45 4.50 43 33 44 30 45 27 46 24 47 20 0.37 48 17 49 13 50 9 51 5 52 I 57 53 53 54 48 55 43 56 38 57 33 58 27 59 21 60 15 61 8 62 I 53 63 45 64 3" 65 Cib 18 67 7 55 68 43 69 30 70 15 59 71 42 72 23 73 2 39 74 14 46 75 16 42 76 5 25 40 51 58 77 f^' 09 5^45 " 57 30.0 18 s 23 42 19 2 23 45 20 33 59 21 27 22 26 58 23 33 24 9 47 25 28 26 II 57 27 46 60' A ^=12° 30' — 6c/ 28 39 29 35 30 35 31 39 32 47 34 I 3 5 20 36 46 38 18 39 57 41 44 43 40 -]5 45 48 c 50 26 53 3 55 53 58 55 62 13 65 38 69 19 73 II 77 14 81 24 85 41 90 o 0.30 •32 •3? •35 •37 0.40 .40 •43 •47 .48 56 0.50 •53 .60 •63 0.68 •72 •77 .82 .88 0-93 LOO 1.07 LI3 1.23 1.32 ^•43 '•53 1.65 1.78 1.93 2.08 2.25 2-43 2.62 2.83 3^o3 3-25 3^47 3.68 3^87 4.05 4^i7 4.28 4.32 60' A 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 £1 10 9 I 5 4 3 I 2 I 77-S 77^4 76.9 765 76.0 755 75-0 74-5 74.0 734 72.8 72.2 71.6 70.9 70.2 695 6-7 67.9 67.0 66.1 65.1 64.1 63.0 61.8 60.6 59^3 57- 3 65 83.6 26 25 14 1.03 57 •13 25 10 T.03 30 .13 25 7 1.05 16 3 .13 64 i 83.3 27 26 12 1.03 15 5 •13 26 8 1.03 38 •13 26 4 1.03 II .13 63 83.0 28 27 10 1-03 13 •13 27 6 1.03 46 •15 27 2 1.03 19 .15 62 82.7 29 28 8 1.05 21 •15 28 4 1.05 55 •15 28 1.05 28 .'5 61 82.4 30 29 5 1.03 30 0.15 29 I 1.03 16 4 0.15 57 1.03 37 0.17 60 82.0 31 30 3 1.03 39 •15 59 1.03 13 .17 29 55 1.05 47 •17 5§ 81.7 32 31 I 1.03 48 •17 30 57 1.05 23 •'7 30 52 1.05 57 .18 58 81.4 33 59 1.05 58 .18 31 54 1.03 33 .18 31 49 1.03 17 8 .18 57 81. 1 34 32 56 1.03 16 9 .18 32 52 1.05 44 .20 32 47 1.05 19 .20 56 80.7 3| 33 54 1.05 20 0.20 33 49 1.05 56 0.20 33 44 1.05 31 0.22 55 80.4 36 34 51 1.03 32 .20 34 46 1.03 17 8 .20 34 41 1.05 44 .22 54 80.0 3^ 35 49 1.05 44 .22 35 44 1.05 20 .22 35 38 1.05 57 .22 53 79-7 38 36 46 1.03 57 .22 36 41 i.os 33 •23 36 35 1.05 18 10 • 23 52 79-3 39 37 44 1.05 17 10 •23 37 38 1.05 47 •25 37 32 1.05 24 •25 51 78.9 40 38 41 1.05 24 0.25 38 35 1.05 18 2 0.25 38 29 I.OS 39 0.27 SO 78.5 41 39 38 1.05 39 .25 39 32 1.05 17 •27 39 26 1.05 55 .27 ^l 78.1 42 40 35 1.05 54 •27 40 29 1.05 33 .28 40 23 1.07 19 II .28 48 77-7 43 41 32 1.05 18 10 .28 41 26 1.05 50 .28 41 19 1.05 28 .30 ^Z 77-3 44 42 29 1.05 27 .30 42 23 1.07 19 7 .30 42 16 1.07 46 •32 46 76.9 45 43 26 45 43 19 25 43 12 20 5 45 76.4 a 60' h A a 6& b A a 60' & A a t A ec A 6(y A 60' d=n r 30' d = U l°0' c Z=14°30' 4i6S 4. 01 1 3.867 [Page 221 K* a = 13° 30' a = 14^ 0' a = 14° 30' \ V \ Kd 60' \ < A \ d\ 60' \ t A \ d 60' \ t A A A:*\ A z\ 6c/ h \ A z\ ' 0' h\ A z\ 60' ^\ ^\ 45 / 43 26 1.05 / 18 45 0.32 43 19 1.05 / 19 25 0.33 / 43 12 1.07 / 20 5 0-33 45 7(?.4 4b 44 23 1.05 19 4 .33 44 16 1.07 45 •33 44 8 1.07 25 •35 44 75^9 47 45 20 1.07 24 •33 45 12 1.07 20 5 •35 45 4 1.07 46 •37 43 75-5 48 46 16 1.05 44 •37 46 8 1.07 26 •37 46 1.07 21 8 .38 42 7S0 49 47 13 1.07 20 6 •38 47 4 t.07 48 .40 56 1.07 31 .40 41 74-4 50 48 9 1.07 29 0.40 48 1.07 21 12 0.42 47 52 1.07 55 0.42 40 73^9 51- 49 5 1.07 53 .42 56 1.07 37 •43 48 48 1.09 22 20 •45 3i 73^4 52 50 I 1.07 21 18 .45 49 52 1.07 22 3 •45 49 43 I.oq 47 •47 38 72.8 53 57 1.07 45 •47 50 48 1.09 30 .48 50 38 1.09 23 15 .50 37 72.2 54 51 53 1.09 22 13 .50 51 43 1.09 59 •52 51 33 1.09 45 .52 36 71.6 55 52 48 1.09 43 0.52 52 38 1.09 23 30 0.53 52 28 1.09 24 16 ^•55 35 70.9 56 53 43 1.09 ^l 14 •55 53 33 1.09 24 2 •57 53 23 I. II 49 .58 34 70.3 57 54 38 1.09 47 .58 54 28 I. II 36 .60 54 17 I. II 25 24 .62 33 69.6 58 55 32> 1.09 24 22 •63 55 22 I. II 25 12 .63 55 II I. II 26 I .65 32 68.8 59 ^6 28 1. 11 25 .65 56 16 I. II 50 .67 56 5 I. II 40 .68 31 68.1 60 57 22 MI . 39 0.70 57 10 I.I I 26 30 0.72 59 1. 13 27 21 0-73 30 673 61 58 16 1-13 26 21 •73 58 4 '•'3 27 13 •77 57 52 1. 13 28 5 ■77 29 66.4 62 59 9 ••'3 27 5 .78 57 1. 13 59 .80 58 45 1. 15 51 .82 28 655 ^3 60 2 1. 13 52 •83 59 50 1. 15 28 47 .85 59 37 1. 15 29 40 .87 27 64.6 64 55 I-I3 28 42 .90 60 42 I. IS 29 38 .90 60 29 1. 18 30 32 •93 26 63.6 65 61 48 1. 15 29 36 0.95 61 34 1. 18 30 32 0.98 61 20 1. 18 31 28 0.98 25 62.6 60 62 40 1. 18 30 13 1.02 62 25 i.i8 31 31 1.03 62 1 1 1.20 32 27 1.05 24 61.5 67 63 31 1,18 31 34 1.08 ^J> 16 1. 18 32 33 1. 10 63 I 1.20 33 30 1.12 23 60.3 68 64 22 1.20 32 39 1. 17 64 7 1.22 33 39 1. 18 51 1.22 34 37 1.20 22 59^1 69 65 12 1.20 33 49 1.25 56 1.22 34 50 1.25 64 40 1.25 35 49 1.28 21 57.8 70 66 2 1.25 35 4 '•33 65 45 1.25 36 5 1-37 65 28 1.25 37 6 '•37 20 56^4 71 50 1.25 16 24 '•45 66 33 1.28 37 27 '•45 66 16 1.30 38 28 1.47 ^§ 54-9 72 67 3^ 1.28 37 51 1-55 67 20 1.28 38 54 1-55 67 2 1.30 39 56 '•57 18 53-3 73 68 25 1.30 39 24 1.65 68 7 '•33 40 27 1.68 48 ..36 41 30 1.68 17 5i^6 74 69 II 1.36 41 3 1.80 52 ..36 42 8 1.80 68 32 1.40 43 II 1.80 16 49.8 75 55 1.36 42 51 '•93 69 36| ••43 43 56 '•93 69 15 '•43 44 59 1.93 15 47^9 76 70 39 1-43 44 47 2.08 70 18 1.46 45 52 2.08 57 1.50 46 55 2.07 14 45-9 ^2 71 21 1.50 46 52 2.23 5§ '•54 47 57 2.23 70 37 '•54 48 59 2.22 13 43-7 78 72 I 1.58 49 6 2.42 71 38 1.58 50 II 2.40 71 16 ..67 51 12 ^•38 12 413 79 39 1.67 51 31 2.60 72 16 1. 71 52 35 2.57 52 1.71 53 35 ^•53 II 38.8 80 73 15 1.76 54 7 2.80 51 1.82 55 9 ^•75 72 27 1.88 56 7 2.72 10 36.1 81 49 1.88 56 55 2.98 73 24 1.94 57 54 2.93 59 2.00 58 50 2.88 9 33-2 82 74 21 2.14 59 54 3.18 55 2.14 60 50 3.12 73 29 2.22 61 43 3^o5 8 30^2 83 49 2.31 63 5 3^38 74 23 2.40 63 57 3^3° 56 2.50 64 46 3.22 7 26.9 84 75 15 2.73 66 28 3^58 48 2.86 67 15 3.48 74 20 2.86 67 59 3.38 6 235 85 H 3.16 70 3 3-75 75 9 3^33 70 44 3.63 41 3-53 71 22 3^53 5 19.9 86 r 5^ 4.00 73 48 3-90 27 4.29 74 22 3^78 58 4.29 74 54 3^67 4 16. 1 87 •j6 1 1 6.00 77 42 4-03 41 5-45 78 9 3.88 75 12 6.00 78 34 3^75 3 12.2 88 21 8.57 81 44 4.12 52 lO.O 82 2 3^97 22 1 0.0 82 19 3.82 2 8.2 89 28 30.0 85 51 4-15 58 30.0 86 4.00 28 30.0 86 8 3^87 I 4.1 90 30 90 7^ 90 30 90 0.0 a 60' h A a 60' 6 A a 6c/ b _A a t A 60' A fo' A 60' i = 13°30' rf = 14.»0' d = i4>°20' Page 222] 3 •732 3< 5o6 3487 \ a = 15°0' a = 15 30 a = 16° 0' \ ^ c\ \ * \ dj 6c/ \ < A \ d 60' 1 "X t _A_ \d 60' \ t A \ A A\^i A 2 \^ 60' h\ A Z \ 60' * \ A Z\ 22 1.07 53 0.23 33 16 1.07 28 0.23 33 10 1.07 21 3 0.2s 55 78.4 36 34 18 1.05 20 7 .23 34 12 1.07 42 .25 34 6 1.07 18 .25 54 78.0 },7 35 15 1.07 21 •25 n ^ 1.07 57 .25 35 2 1.07 ll> .27 53 77-6 38 36 II 1.07 36 .27 36 4 1.07 21 12 •27 58 1.09 49 .27 52 77.1 39 1,7 7 1.07 52 .28 37 1.07 28 .28 Z^ 53 1.07 22 5 .28 51 76.7 40 38 3 1.07 21 9 0.28 56 1.07 45 0.30 Z7 49 1.09 22 0.30 50 76.2 41 59 1.07 26 •30 38 52 1.09 22 3 .32 38 44 1.09 40 •32 49 75-7 42 39 55 1.09 44 •32 39 47 1.09 22 •32 39 39 1.09 59 •33 48 75-2 43 40 50 1.07 22 3 •33 40 42 1.07 41 •3'; 40 34 1.09 23 19 •35 47 74.7 44 41 46 1.09 23 •35 41 38 1.09 23 2 •35 41 29 1.09 40 •37 46 74.2 45 42 41 44 42 33 23 42 24 24 2 45 73.7 a 60' I A a 60' 6 A a 60' & A a ^ A 60' A 60' A 60' d = \i )°30' d = V 7°0' d = Vi ^°30' 3-378 3^27i 3.172 1 Page 225 \h a = 16" 3(X a = 17° 0' a = 17° 30' \ ^ V d 60' \ * ^ \ d 60' \ ' A \ d .60' \ t A \ b\ A \ A Z \ 60' A \ A z\ 60' A \ A z\ 6c/ c\ / / / / f / 45 42 41 1.09 22 44 0-37 42 33 1.09 23 23 0.37 42 24 1.09 24 2 0.38 45 73^7 46 43 36 1.09 23 6 .38 43 28 1.09 45 .40 43 19 1.09 25 .40 44 73-2 47 44 31 1.09 29 .40 44 23 1.09 24 9 .40 44 14 I. II 49 .42 43 72.6 48 45 26 1.09 53 .42 45 18 I.I I 33 •43 45 8 I.I I 25 14 •43 42 72.0 49 46 21 1.09 24 18 .43 46 12 I. II 59 •45 46 2 I.I I 40 •47 41 71.4 SO 47 16 I. II 44 0.47 47 6 I. II 25 26 0.48 56 I. II 26 8 0.48 40 70.8 SI 48 10 I. II 25 12 .50 48 I. II . 55 •5° 47 50 I. II 37 •50 32 70.1 52 49 4 1. 1 1 42 .50 54 I. II 26 2; •52 48 44 I-I3 27 7 •53 38 695 53 58 I. II 26 12 •55 49 48 1. 13 56 •55 49 37 1. 13 39 •57 37 68.8 54 50 52 I. II 45 •57 50 41 1.13 27 29 .58 50 30 1. 13 28 13 .58 36 68.1 55 51 46 1. 13 27 19 0.60 51 34 1. 13 28 4 0.60 51 23 1. 15 48 0.62 35 ^^1 56 S2 39 1. 13 55 .62 52 27 1. 13 40 .63 52 15 1. 15 29 25 .65 34 66.6 57 5? 32 1. 15 28 32 .67 53 20 1. 15 29 18 .68 53 7 1. 15 30 4 .68 33 65.8 58 54 24 1. 15 29 12 .70 54 12 1. 15 59 •72 59 1. 18 45 •72 32 64.9 59 55 16 1. 15 54 •75 55 4 1. 18 30 42 •75 54 50 1. 18 31 28 •77 31 64.1 60 56 8 I. IS 30 39 0.78 55 1. 18 31 27 0.78 55 41 1. 18 32 14 0.80 30 63.1 61 57 1. 18 31 26 .82 56 46 1.20 32 14 .83 56 32 1.20 33 2 .85 29 62.2 62 51 1.20 32 15 .87 57 36 1.20 33 4 .88 57 22 I.2Z 53 .90 28 61.2 63 58 41 1.20 33 7 •93 58 26 1.20 57 •93 58 II 1.22 34 47 •95 ^l 60.2 64 59 31 1.22 34 3 .98 59 16 1.22 34 53 1. 00 59 1.25 35 44 1. 00 26 59.1 65 60 20 1.22 35 2 1.03 60 5 1.25 35 53 1.05 48 1.25 36 44 1.05 25 57-9 66 61 9 1.25 36 4 1. 10 53 1.25 36 56 1. 12 60 36 1.28 37 47 1. 12 24 56-7 67 57 1.25 37 10 1. 17 61 41 1.28 38 3 1. 17 61 23 1.28 38 54 1. 18 23 55-4 68 62 45 1.28 38 20 1.25 62 28 1.30 39 13 1.25 62 10 '•33 40 5 1.25 22 54^1 69 63 32 '•33 39 35 1-32 &3 14 1^33 40 28 '•33 55 1.33 41 20 '•33 21 52.7 70 64 17 '•33 40 54 1.40 59 1.36 41 48 1.40 63 40 1.40 42 40 1.42 20 51-2 71 65 2 1.36 42 18 1.48 64 43 1.40 43 12 1.50 64 23 1.40 44 5 1.50 19 49-7 72 46 1.40 43 47 1.58 65 26 1-43 44 42 1.58 65 6 1.46 45 35 1.58 18 48.0 73 66 29 1.46 45 22 1.68 66 8 1.46 46 17 1.68 47 I. SO 47 10 ..67 'Z 46.3 74 (>7 10 1.50 47 3 1.80 49 1.50 47 58 1.78 66 27 ^•54 48 50 1.78 16 44.4 75 50 '•54 48 51 1.92 ^7 29 i.SS 49 45 1.90 67 6 1.62 50 37 1.88 15 425 76 68 29 1.62 50 46 2.02 68 7 1.67 51 39 2.00 43 ..67 52 30 2.00 14 40.5 77 69 6 1.67 52 47 2.15 43 1.71 53 39 2.13 68 19 1.76 54 30 2.10 13 38.3 78 42 1.82 54 56 2.28 69 18 1.88 55 47 2.25 53 1.88 56 36 2.22 12 36.0 79 70 15 1.88 57 13 2.40 50 '•94 58 2 2.37 69 25 2.00 58 49 2.35 II 33-6 80 47 2.07 59 37 2.55 70 21 2.07 60 24 2.50 55 2.14 61 10 2.45 10 3I-I 81 -I 16 2.22 62 10 2.67 50 2.31 62 54 2.62 70 23 2.31 63 37 2.57 9 28.4 82 43 2.50 64 50 2.80 71 16 2.61 65 31 2-75 49 2.61 66 II 2.68 8 25.7 83 "2 7 2.86 67 38 2.93 39 2.86 68 16 2.85 71 12 3.00 68 52 2.80 7 22.8 84 28 3.16 70 34 Z'OZ 72 3-33 71 7 2.97 32 3^53 71 40 2.88 6 19.8 85 47 4.00 73 36 3^15 18 4.00 74 5 3^07 49 4.00 74 33 2.98 5 16.7 86 73 2 vOO 76 45 3^23 33 5.00 77 9 3.«3 72 4 5-45 77 32 3-05 4 135 87 14 6.67 79 59 3-30 45 7.50 80 17 3.20 15 7.50 80 35 3.10 3 10.2 88 23 12.0 83 17 3-35 53 12.0 83 29 3^25 23 12.0 83 41 3^i5 2 6.8 89 28 30.0 86 38 3-37 58 30.0 86 44 3-27 28 30.0 86 50 3.17 I 3-4 90 30 90 72 90 30 90 0.0 a 60' 6 A a 60' 6 A a 60' 6 A a t A 60' A 60' A 6& ^ = 16*30' d^\T(y rf = 17°30' 55901°— IS- -15 Page 226] 3.078 2.989 2.904 V a = 18°0' Q = 18° 30' a = 19° 0' !( \ * A 60' A z\ 60' 60' A \ i 2\ A 60' 60' A JZ \^^ 60' ^\ ^, / / / / / / „ d 1.05 18 0.00 1.05 18 30 0.00 I.os 19 0.00 f. 90.0 I 57 1.05 .02 57 1.05 30 .C2 57 1.05 .02 89.7 2 I 54 1.05 I .00 I 54 1.05 31 .02 I 54 1.07 I .02 88 89.4 3 2 51 1.05 I .02 2 51 1.05 32 .02 2 50 I.os 2 .02 f7 89.0 4 3 48 I. OS 2 •03 3 48 1.05 33 .02 3 47 1.05 3 .02 86 88.7 5 4 45 1.05 4 0.03 4 45 1.07 34 0.03 4 44 1.07 A 0.03 85 88.4 6 5 42 1.05 6 •03 5 41 1.05 36 •03 5 40 1.05 6 .03 84 88.1 7 6 39 1.05 8 .03 6 38 1.05 38 •03 6 37 I.os 8 •03 ^3 87.8 8 7 36 1.05 10 •05 7 35 1.05 40 •05 ■ 7 34 1.07 10 .OS 82 87.4 9 8 33 1.05 13 .05 8 32 i.os 43 .05 8 30 I.os 13 .OS 81 87.1 10 9 30 1.05 16 0.05 9 29 1.05 46 0.05 9 27 I.os 16 0.07 80 86.8 1 1 10 27 1.05 19 .07 10 26 1.07 49 .07 10 24 1.07 20 .07 79 86.5 12 1 1 24 1.05 23 .07 II 22 1.05 53 .07 II 20 I.os 24 .07 78 86.1 13 12 21 1.05 27 .07 12 19 1.05 57 .07 12 17 1.07 28 .07 77 85.8 14 13 18 1.05 31 .08 13 16 1.07 19 I .08 13 13 I.os 32 .08 76 85-5 IS 14 15 1.05 36 o.oS 14 12 I.os 6 o.oS 14 10 1.07 37 0.08 75 85.1 10 15 12 1.05 41 .08 15 9 I.os II .10 15 6 I.os 42 .10 74 84.8 17 16 Q 1.05 46 .10 16 6 1.07 17 .10 16 3 1.07 48 .10 73 84-5 i8 17 6 1.07 52 . 10 17 2 I.OS 23 • lO 59 I.os 54 .12 72 84.1 19 18 2 1.05 58 .10 59 I.os 29 .12 17 56 1.07 20 I .12 71 83.S 20 59 1.05 19 4 0.12 18 56 1.07 36 0.12 18 52 1.07 8 0.12 70 83^4 21 19 56 1.07 1 1 • •3 19 52 1.05 43 •13 19 48 1.05 15 .12 69 83.1 22 20 52 1.05 19 • 13 20 49 1.07 51 •13 20 45 1.07 22 •13 68 82.7 23 21 49 1.07 27 .'3 21 45 1.07 59 .13 21 41 1.07 30 •IS 67 82.3 24 22 45 1.05 35 .13 22 41 1.05 20 7 .15 22 37 1.07 39 .15 66 82.0 25 ^3 42 1.07 43 0.15 23 38 1.07 16 o.is 23 33 1.07 48 0.17 65 81.6 20 24 38 1.05 52 ••7 24 34 1.07 25 .17 24 29 1.07 5^^ • 17 ^ 81.2 27 25 35 1.07 20 2 • 17 25 30 1.07 35 .'7 25 25 1.07 21 8 • 17 63 80.8 28 26 31 1.07 12 .iS 26 26 1.07 45 .18 26 21 1.07 18 .18 62 80.4 29 27 27 1.05 23 .iS 27 22 1.07 50 .18 27 17 1.07 29 .20 61 80.0 30 28 24 1.07 34 0.20 28 18 1.07 21 7 0.20 28 13 1.07 41 0.20 60 79.6 31 29 20 1.07 46 .20 29 14 1.07 19 .22 29 9 1.09 53 .22 59 79.2 32 30 16 1.07 58 .22 30 10 1.07 32 .22 30 4 1.07 22 6 .22 58 78.8 33 31 12 1.07 21 II .22 31 6 1.07 45 •23 31 1.09 19 .23 57 78.4 34 32 8 1.07 24 •23 32 2 1.09 59 • 23 55 1.07 33 •25 56 77-9 35 33 4 1.09 38 0.25 57 1.07 22 i'^ 0.25 32 51 1.09 48 0.25 55 77-5 3& 59 1.07 53 .25 33 53 1.09 28 •27 33 46 1.09 23 3 .27 54 77.0 37 34 55 1.09 22 8 .27 34 48 1.09 44 .28 34 41 1.09 19 .28 53 "6.6 38 35 50 1.07 24 .28 35 43 1.09 23 I .28 35 36 1.09 36 •30 52 76.1 39 36 46 1.09 41 •30 36 38 1.09 18 .30 36 31 1.09 54 •30 51 75- <5 40 37 41 1.09 59 0.32 37 33 1.09 36 0.32 37 26 I. II 24 12 0.33 50 '^H 41 38 36 1.09 23 18 •32 38 28 1.09 55 •32 38 20 1.09 3^ •33 '^2 74.6 42 39 31 1.09 37 •33 39 23 1.09 24 14 •35 39 15 I. II 52 •35 48 74.1 43 40 26 1.09 57 •35 40 18 I. II 35 .37 40 9 I. II 25 13 •37 47 73-5 44 41 21 1.09 24 18 .38 41 12 1.09 57 •37 41 3 I. II 35 .38 46 730 45 42 16 41 42 7 25 19 57 58 45 72.4 a 60' b _A a 60' h A a fio' b A a / A 60' A ! 60' A 60' d = i 8°0' f/ = 18"S0' d = 19° 0' 3.078 2.989 2.904 [Page 227 \ a = 18°0' a = 18° 30' a = 19° 0' \' \ * \ d 60' \ ^ A d 60' \ f A d 60' \ i A \ A h \ A z\ 6^' h \ A z\ 60' U \ A Z\ 60' A ^\ / / / / 1 / P 45 42 16 I. II 24 41 0.38 42 7 I. II 25 19 0.40 41 57 I. II 25 58 0.40 45 72.4 46 43 10 I. II 25 4 .40 43 I I.I I 43 .42 42 51 I. II 26 22 .42 44 71.8 47 44 4 I. II 28 •43 55 I. II 26 8 •43 43 45 I. II 47 •45 43 71.2 48 58 I. II 54 •45 44 49 1. 13 34 •45 44 39 '•13 27 14 •47 42 70.6 49 45 52 I. II 26 21 •47 45 42 1.13 27 I .48 45 32 1. 13 42 .48 41 69.9 50 46 46 i-'3 49 0.48 46 35 1.13 30 0.50 46 25 1.13 28 II 0.50 40 69-3 51 47 39 1-13 27 18 .52 47 28 JI.I3 28 .52 47 18 1. 15 41 •S3 39 68.6 52 48 32 i-'S . 49 •55 48 21 I.I3 31 .55 48 10 1. 15 29 13 •57 38 67.9 53 49 25 I-I3 28 22 •57 49 14 I. IS 29 4 .58 49 2 1.15 47 .58 37 67.2 54 50 18 1.15 56 ,60 50 6 1.15 39 .60 54 LIS 30 22 .62 36 66.4 55 51 10 1.15 29 32 0.63 58 1. 15 30 15 0.65 50 46 1.18 59 0,63 35 65.6 56 52 2 1. 15 30 10 .65 51 50 1,18 54 .67 51 37 1. 18 31 37 .68 34 64.8 57 54 1. 15 49 .70 52 41 1. 18 31 34 .70 52 28 1.20 32 18 •72 33 64.0 58 53 46 1. 18 31 31 •73 53 32 1. 18 32 16 •75 53 18 1.20 33 I •75 32 63-1 59 54 37 1.20 z^ 15 •77 54 23 1.20 11 I •77 54 8 1.20 46 .78 31 62.2 60 55 27 1.20 3Z I 0.82 55 13 1.22 47 0.83 58 1.22 34 33 0.83 30 61.2 61 56 17 1.20 50 .85 56 2 1.22 34 17 .87 55 47 1.22 35 23 .88 29 60.2 62 57 7 1.22 34 41 .90 51 1.22 ,>5 29 .90 56 36 1.25 36 16 .92 28 59-2 ^J 56 1.25 35 35 •97 57 40 1.2^ 1>^ 23 •97 57 24 1.28 37 11 .97 27 58.1 64 ^8 44 1.25 36 3Z 1. 00 58 28 1.28 7 7 21 1.02 58 1 1 1.28 38 9 1.02 26 57^0 65 59 32 r.28 17 11 1.07 59 15 1.28 38 22 1.07 58 1.30 39 10 1,08 25 55-8 66 60 19 1.28 38 17 '•IS 60 2 1.30 39 26 1. 13 59 44 1-30 40 15 i^i3 24 54^5 67 61 6 1.30 39 45 1. 18 48 '•33 40 34 1.20 60 30 '•33 41 23 1.20 23 53-2 68 52 1-33 40 56 1.27 61 33 1-33 41 46 1.27 61 15 1.40 42 35 1.27 22 51^9 69 62 37 1.36 42 12 1.33 62 18 1.40 43 2 1-33 58 1.40 43 51 1.33 21 50^4 70 63 21 1.40 43 32 1.40 63 I 1-43 44 22 1.42 62 41 1-43 45 II 1.42 20 48.9 71 64 4 1.46 44 56 1.50 43 1^43 45 47 1.50 63 23 1.46 46 36 1.50 19 47-3 72 45 1.46 46 26 1.58 64 25 1.50 47 17 1.57 64 4 '•54 48 6 '•57 18 45-7 73 6^ 26 1.50 48 I 1.68 65 5 '•54 48 51 1.67 43 1-58 49 40 1.65 17 43-9 74 66 6 ..58 49 42 1.77 44 1.62 50 31 1.77 65 21 1.62 51 19 1-75 16 42.1 75 44 1.67 51 28 1.87 66 21 1.67 52 17 1.85 58 1.71 53 4 1.85 15 40.2 76 67 20 1. 71 53 20 1.97 57 1.76 54 8 '•95 66 33 1.76 54 55 1-93 14 38.2 77 55 1.76 55 18 2.08 (^7 31 1.82 56 5 2.05 67 7 1.88 56 51 2.03 13 36.0 78 68 29 1.94 57 23 2.20 68 4 1.94 58 8 2.17 39 2.00 58 53 2.12 12 338 79 69 2.07 59 35 2.30 35 2.14 60 18 2.27 68 9 2.14 61 2.23 II 31-5 80 29 2.22 61 53 2.42 69 3 2.22 62 34 2.38 17 2.31 63 14 2.33 TO 29.1 81 56 2.40 64 18 2.52 30 2.50 64 57 2.47 69 3 2.50 65 34 2.43 9 26.5 82 70 21 2.61 66 49 2.62 54 2-73 67 25 2.57 27 2.86 6Z 2.52 8 23.9 83 44 3.16 69 26 2-73 70 16 3.16 69 59 2.67 48 3.16 70 31 2.60 7 21.2 84 71 3 3-S3 72 10 2.82 35 3^53 72 39 2.75 70 7 3^75 73 7 2.68 6 18.3 85 20 4.00 74 59 2.90 52 4.62 75 24 2.82 23 4.62 75 48 2.75 5 15-4 80 35 5-45 77 53 2.97 71 5 5^45 78 13 2.90 36 6.00 78 33 2.82 4 12.4 87 46 7.50 80 51 3.02 16 7.50 81 7 2.93 46 7.50 81 22 2.85 3 9.4 88 54 15.0 83 52 3^o5 24 15.0 84 3 2.q7 54 15.0 84 13 2.88 2 6.3 89 58 30.0 86 55 3.08 28 30.0 87 I 2. 98 58 30.0 87 6 2.90 I 3-1 90 / - 90 30 90 71 90 0.0 a 60' I A a 60' I A a 60' & A a t A 60' A 60' A 60' cZ = 18°0' cz=i8°3(r d = i9°0' Page 228] 2.824 2.748 2.67s 10 1 1 12 13 14 IS 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 36 37 38 39 40 41 42 43 44 45 a = 19*' 30' (O' A 6(/ o 57 53 50 46 4 43 5 39 6 36 7 32 8 29 9 25 10 22 11 18 12 15 13 II 14 7 15 4 16 o 56 17 52 18 48 19 45 20 41 21 37 22 33 23 29 24 25 25 20 26 16 27 12 28 7 29 3 58 30 54 31 49 32 44 33 39 34 34 35 29 36 23 37 18 38 12 39 6 40 o 54 41 48 / 1.05 19 30 0. 1.07 30 1.05 31 1.07 32 1.05 33 1.07 34 0, 1.05 30 1.07 38 1.05 41 1.07 44 1.05 47 0, 1.07 50 I. OS H 1.07 58 1.07 20 3 1.05 8 o.< 1.07 13 1.07 19 1.07 25 1.07 32 1.05 39 0. 1.07 46 1.07 54 1.07 21 2 1.07 II 1.07 20 0. 1.09 30 1.07 40 1.07 51 1.09 22 2 1.07 14 0. 1.09 27 1.07 40 1.09 H 1.09 23 8 1.09 23 0. 1.09 39 1.09 55 I. II 24 12 1.09 30 I. II 49 0. I. II 25 8 MI 29 MI 50 I. II 26 13 36 6(y A _A d = 19°20' a = 20''(y \d\6o' o o 56 1 53 2 49 3 46 4 42 5 38 6 35 7 31 8 27 9 23 10 20 11 16 12 12 13 8 14 5 15 I 57 16 53 17 49 18 45 19 41 20 37 21 32 22 28 23 24 24 20 25 15 26 II 27 6 28 2 57 29 52 30 47 31 42 32 37 33 32 34 26 35 21 36 15 37 9 38 3 57 39 51 40 45 41 39 20 o o I 2 3 4 6 8 1 1 14 17 21 25 29 34 39 44 50 56 21 3 10 18 26 34 43 53 22 3 13 24 36 48 23 I 14 28 42 57 24 13 30 48 25 6 25 45 26 6 27 50 27 14 A _A_ _A^ 60' a = 20** 30' 60' A X'! 60' / / 1.07 20 30 0. 56 1.07 30 , I 52 i.os 31 , 2 49 1.07 32 , 3 45 1.07 33 . 4 41 1.07 H o.( 5 37 1.07 3t .< 6 33 1.07 38 .( 7 29 I.os 41 .< 8 26 1.07 44 .( 9 22 1.07 47 0. 10 18 1.07 51 , II 14 1.07 55 . 12 10 1.07 21 . 13 6 1.07 5 . 14 2 1.07 10 0. 58 1.07 15 . 15 54 1.09 21 16 49 1.07 28 17 45 1.07 35 18 41 1.07 42 0. 19 37 1.09 5? . 20 32 1.07 5« 21 28 1.07 22 6 22 24 1.09 15 . 23 19 1.07 25 0. 24 15 1.09 ^1 . 25 10 1.09 46 . 26 5 1.09 57 .: 27 1.09 23 9 .: 55 1.09 21 0.: 28 50 1.09 34 29 45 1.09 48 30 40 1.09 24 2 .: 31 35 1.09 17 •^ 32 30 I. II 32 0. ; 33 24 1.09 48 34 19 MI 25 5 35 13 I. II 23 .' 36 7 I. II 42 37 I I. II 26 I 0,' 55 I. II 21 38 49 1.13 42 39 42 MI 27 5 40 36 '•13 28 ,t 41 29 52 A d = 20^2(y A_ 6(y 90 f7 86 |5 ^4 ^3 82 81 80 78 77 76 75 74 73 72 71 13 70 n 6q n 68 !■; 67 17 66 17 65 18 64 18 6,3 20 62 20 61 22 60 23 59 23 58 25 .57 25 5t> 27 ,SS 28 S4 53 52 51 50 49 48 47 46 45 \ 90.0 89.7 89-3 89.0 88.6 S-3 87.9 87.6 87.2 86.9 86.5 86.2 85.8 85.5 85.1 84.8 84.4 84.0 837 83.3 82.9 82.5 82.1 81.7 81.3 80.9 80.5 80.1 79.7 79-3 78.8 78.4 77-9 77-5 77.0 765 76.0 75-5 75-0 74-5 74-0 73-4 72.9 72.3 71.7 71. 1 2 824 2.748 8675 [ Pag b229 K a = 19° 30' a = 20°0' a = 20*'30' \1 V \ d 1 ^0' \* — d 6c/ \ i A \ d 6& \ < A A ^\ ^ \ ^ Z \ 60' h \ A z\ 6c/ h \ A z\ ac/ A n o , / / / / / ^ 45 41 48 I. II 26 36 0.42 41 39 i->3 27 14 0,42 41 29 '.«3 27 52 0.42 45 71.1 46 42 42 '•'3 27 I .42 42 32 I-I3 „ 39 •43 42 22 MS 28 17 •45 44 70^5 47 43 35 I-I3 26 •45 43 25 I-I3 28 5 •47 43 15 I.IS 44 •47 43 69.9 48 44 28 I-I3 53 .48 44 18 1. 15 33 •47 44 7 1. 15 29 12 .48 42 69.2 49 45 21 '•'3 28 22 .48 45 10 I.IS 29 I •50 59 1. 15 41 .50 41 68.5 SO 46 14 i.iS 51 0.52 46 2 I.IS 31 0^53 45 51 I.IS 30 II O.S3 40 67.8 51 47 6 1. 15 29 22 .53 54 I.IS 30 3 •55 46 43 1. 18 4^ •55 39 67.1 52 58 I.IS 54 •57 47 46 I.IS 36 •57 47 34 1. 18 31 16 .58 38 66.4 53 48 50 1. 15 30 28 .60 48 38 1. 18 31 10 .60 48 25 1. 18 51 .62 37 65.6 54 49 42 i.iS 31 4 .63 49 29 1. 18 46 .63 49 16 1. 18 32 28 .63 36 64.8 55 50 32, 1. 18 42 0,65 50 20 1.20 32 24 0.6s 50 7 1.20 33 ^ 0.67 35 64.0 56 51 24 1.20 32 21 .68 51 10 1.20 33 3 .70 ^l 1.22 46 .70 34 63.1 57 52 14 1.20 Z2> 2 •72 52 1.20 45 .73 51 46 1.22 34 28 •73 33 62.2 58 53 4 1.20 45 .77 50 1.22 34 29 •77 52 33 1.22 35 12 .78 32 ^•3 59 54 1.22 34 31 .80 53 39 1.22 35 15 .80 53 24 1.22 59 .80 31 60.3 60 54 43 1.22 35 19 0.83 54 28 I.2S 36 3 0.8 s 54 13 1. 25 36 47 0.85 30 59-3 61 55 32 1.25 36 9 .88 55 16 I.2S 54 .88 55 I 1.28 37 38 .90 29 58-3 62 56 20 1.25 37 2 .92 56 4 1.28 37 47 •93 48 1.30 38 32 •95 28 57^2 63 57 8 1.28 57 .98 51 1.28 38 43 .98 56 34 1.30 39 29 .98 27 56.1 64 55 1.30 38 56 1.03 57 38 1.30 39 42 1.03 57 20 1.30 40 28 1.03 26 55-0 65 58 41 1.30 39 58 1.08 58 24 1.33 40 44 1.08 58 6 1.36 41 30 1.08 25 53.7 66 59 27 1.33 41 3 I-I3 59 9 1.36 41 49 I.IS 50 1.36 42 35 1. 15 24 525 67 60 12 1.36 42 II 1.20 53 1.40 42 58 1.22 59 34 1.40 43 44 1.22 23 Si^i 68 56 1.40 43 23 1.27 60 36 1.40 44 II 1.27 60 17 1.43 44 57 1.27 22 49-7 69 61 39 1.43 44 39 '•35 61 19 1-43 45 27 '•33 59 1.46 46 13 '•33 21 48.3 70 62 21 1.46 46 1.40 62 I i.So 46 47 1.40 61 40 1.50 47 33 1.40 20 46.8 71 63 2 1.50 47 24 1.48 41 1.50 48 II 1.48 62 20 1.54 48 57 1.48 19 45-2 72 42 1-54 48 53 1-57 63 21 i.S8 49 40 '•57 59 1.62 50 26 1.55 18 43-5 73 64 21 1.58 50 27 ..65 S9 1.62 51 14 ,.63 63 36 1.67 51 59 1.62 ^I 41.8 74 59 1.67 52 6 1-73 64 36 1. 71 52 52 1.72 64 12 1. 71 53 36 1.70 16 40.0 75 65 35 1.76 53 50 1.83 65 II 1.76 54 35 1.80 47 1.76 55 18 1.80 15 38.1 66 9 1.82 55 40 1.92 45 1.82 56 23 1.90 65 21 1,88 ^l 1.87 14 36.1 77 42 1.88 57 35 2.00 66 18 2.00 58 17 1.98 53 2.00 58 58 '•95 13 34^o 78 67 14 2.07 59 35 2.10 48 2.07 60 16 2.07 66 23 2.14 60 55 2.05 12 31-9 79 43 2.14 61 41 2.20 67 17 2.22 62 20 i.17 51 2.31 62 58 2.12 II 29.6 80 68 II 2.40 ^3 53 2.28 44 2.40 64 30 2.2s 67 17 2,50 ^5 5 2.22 10 273 81 36 2.61 66 10 2.38 68 9 2.73 66 45 2^33 41 2^73 67 18 2.28 9 24.8 82 59 2.86 68 33 2.47 31 3.00 69 5 2.40 68 3 3.00 69 35 2^37 8 22.3 83 69 20 3-33 71 1 2-53 51 3-33 71 29 2.S0 23 3-33 71 57 2.43 7 19.7 84 38 3-75 73 33 2.62 69 9 3-75 73 59 2^55 41 4.00 74 23 2.50 6 17.1 65 54 4.62 76 10 2.68 25 5.00 76 32 2.62 56 5.00 76 53 2^55 5 14-3 86 70 7 6.00 78 51 2.75 27 6.00 79 9 2.67 69 8 6.67 79 26 2.60 4 11.6 87 17 8.57 81 36 2.77 47 8.S7 81 49 2.70 17 8^57 82 2 2.63 3 8.7 88 24 12.0 84 22 2.82 54 12.0 84 31 2.73 24 12.0 84 40 2.67 2 S8 89 29 60.0 87 II 2.82 59 60.0 87 15 2.75 29 60,0 87 20 2.67 I 2.9 90 30 90 70 90 30 90 0.0 a 6.i5 30 20 .52 44 36 i.iS 59 •52 44 24 1. 18 38 •52 41 67.1 50 45 40 1. 18 SI o^53 45 27 1. 18 31 30 0.55 45 15 1. 18 32 9 0.55 40 66.4 65.6 =)i 46 31 1. 18 31 23 •57 46 18 i.i8 32 3 •57 46 6 1.20 42 .58 39 52 47 22 1. 18 57 .58 47 9 1. 18 37 •58 5^ 1.20 33 17 .60 38 64.9 S3 48 13 1.20 32 32 .62 48 1.20 33 12 •63 47 46 1.20 53 .62 37 64.1 54 49 3 1.20 33 9 .65 50 1.22 50 .65 48 36 1.22 34 30 •67 36 63.2 55 53 1.20 48 0.67 49 39 1.22 34 29 0.68 49 25 1.22 35 10 0.68 35 62.4 ^t> 50 43 1.22 34 28 .72 50 28 1.22 35 10 •72 50 14 1.25 ^ 51 •72 34 61.S 57 51 32 1.22 35 II •73 51 17 1.22 , 53 •75 51 2 1. 25 36 34 •75 33 60.6 58 !;2 21 1.25 ^ 55 .78 52 6 1.25 36 38 .78 5° 1.25 37 19 .80 32 59-6 59 53 9 1.25 36 42 .82 54 1.28 37 25 .82 52 38 1.2S 38 7 .82 31 58.6 6o 57 1.28 37 31 0.S5 53 41 1.28 38 14 0.87 53 25 1.30 56 0.87 30 57-6 6i 54 44 1. 28 38 22 .90 54 28 1.30 39 6 .90 54 II 1.30 39 48 •92 29 56^5 62 55 31 1.30 39 16 •95 55 14 1.30 40 •95 57 1-33 40 43 •95 28 5S4 63 56 17 1.30 40 13 1. 00 56 1-33 57 1. 00 5 5 42 1. 31 41 40 1. 00 27 54^3 64 57 3 1.33 41 13 1.03 45 1.36 41 57 1.03 56 27 1.36 42 40 1.05 26 53^1 65 48 1.36 42 15 1. 10 57 29 1.40 42 59 1. 10 57 II 1.40 43 43 1. 10 25 5i^8 60 58 32 1.40 43 21 1. 1 5 58 12 1.40 44 5 1. 15 54 '•43 44 49 1. 1 5 24 50^5 67 59 15 1-43 44 30 1.20 •S5 ••43 45 14 1.20 58 36 1.46 45 58 1.20 23 49.2 68 57 1-4^1 45 42 1.27 59 37 1.46 46 26 1.27 59 17 1.50 47 10 1.27 22 47^8 60 60 39 1.50 46 58 1-33 60 18 1.50 47 42 1-33 57 '•54 48 26 1.32 21 46^3 70 61 19 1.54 48 18 1.40 . 58 ••54 49 2 1.40 60 36 1.58 49 45 1.38 20 44.8 71 58 1.^8 49 42 ••47 61 37 1.62 ^o 26 1-45 61 14 1.62 51 8 '•45 19 43^2 72 62 36 1.62 51 10 '•53 62 14 1.62 51 S3 '•53 SI 1.67 52 35 '•53 18 41.0 73 65 13 1.67 52 42 1.62 51 1. 71 53 25 1.60 62 27 1. 71 54 7 1.58 17 39-8 74 49 1.76 54 19 1.70 63 26 1.82 55 I 1.68 63 2 1.82 55 42 i.6s 16 38.0 75 64 23 1.82 56 I 1.77 59 1.82 56 42 ••75 . 35 1.88 57 21 ••73 15 36.2 76 56 1.94 57 47 1.85 64 32 2.00 58 27 1.82 64 7 2.00 59 5 1.80 14 34-2 77 65 27 2.00 59 38 '•93 65 2 2.07 60 16 1.90 . 37 2.14 60 53 1.88 13 32.2 78 .. 57 2.14 61 34 2.00 ^l 2.22 62 10 1. 98 65 5 2.22 62 46 '•95 12 30.1 79 66 25 2.40 63 34 2.10 58 2.40 64 9 2.07 32 2.50 64 43 2.02 II 27.9 80 50 2.50 65 40 2.17 66 23 2.61 66 13 2.12 56 2.61 66 44 2.10 10 25.7 81 67 14 2-73 67 SO 2.23 46 2-73 68 20 2.20 66 19 2.86 68 50 2.17 9 234 82 36 3.16 70 4 2.32 67 8 3-33 70 32 2.27 40 3-33 71 2.22 8 21.0 83 55 3-53 72 23 2.38 26 3-53 72 48 2.33 58 3-75 73 13 2.28 7 18.5 84 68 12 4.29 74 46 2-43 43 4.29 75 8 2.38 67 14 4.29 75 30 2^33 6 16.0 0^5 26 5.00 77 12 2.50 .0 57 5.00 77 31 2.43 28 5-45 77 SO 2-37 5 13-4 80 38 6.00 79 42 ^•53 68 9 6.67 79 57 2.48 39 6.67 80 12 2.42 4 10.8 87 48 ^.57 82 14 ^•57 18 8.57 82 26 2.50 48 S.57 82 37 2.45 3 8.1 88 55 15.0 84 48 2.60 25 15.0 84 56 2-53 55 15.0 85 4 2-47 2 5-4 89 59 60.0 87 24 2.60 29 60.0 87 28 2^53 59 60.0 87 32 2.47 I 2.7 90 69 90 c 30 90 68 90 0.0 a 6c/ b A a 60' b A a 60' b _A a t A 6c/ A 60' A 60' d = 2i°0' J = 21" 30' d = 22° 0' Page 232] 2414 2356 2.300 \ a = 22^ 30' a = 23°0' a = 23° 30' K \ * \<« 60' \ t A \ d M \ * _A \ d 6c/ X t A \ A A\ A Z\ 60' k\ 1 ^ 2\ 60' li\ A z\ 6C/ ^\ ^\ / / / / / / 1.09 22 30 0.00 1.09 23 0.00 1.09 23 30 0.00 90 90.0 I 55 1.07 30 .02 55 1.07 .02 55 1.09 30 .02 ^o2 89.6 2 I 51 1.09 31 .02 I 51 1.09 I .02 I 50 1.09 31 .02 88 ^l 3 2 46 1.07 32 .02 2 46 1.09 2 .02 2 45 1.09 32 .02 f7 88.8 4 3 42 I.J9 33 •03 3 41 1.09 3 •03 3 40 1.09 33 .03 86 88.4 5 4 37 1.07 35 0.03 4 36 1.09 5 0.03 4 35 1.09 35 0.03 85 88.0 6 5 33 1.09 37 .03 5 31 1.09 7 .03 5 30 1.09 37 .03 84 87.6 7 6 28 1.09 39 .05 6 26 1.07 9 •05 6 25 1.09 39 .05 f3 ll-^ 8 7 23 1.07 42 •05 7 22 1.09 12 •05 7 20 1.09 42 .07 82 86.9 9 8 19 1.09 45 .07 8 17 1.09 15 .07 8 15 1.09 46 .05 81 86.5 10 9 14 1.09 49 0.07 9 12 1.09 19 0.07 9 10 1.09 49 0.07 80 86.1 1 1 10 9 1.09 53 .07 10 7 1.09 23 .07 10 5 1.09 53 .08 79 8S7 12 II 4 1.07 57 .08 II 2 1.09 27 .08 II MI 58 .08 78 IH 13 12 1.09 23 2 .08 57 1.09 32 .10 54 1.09 24 3 .08 77 84.8 14 55 1.09 7 .10 12 52 1.09 38 .08 12 49 1.09 8 .10 76 84.4 IS 13 50 1.09 13 0. 10 13 47 1.09 43 0. 10 13 44 1.09 14 0. 10 75 84.0 16 14 45 1.09 19 .10 14 42 1.09 49 .12 14 39 I.II 20 .12 74 83.6 17 15 40 1.09 25 .12 15 37 1.09 56 .12 15 33 1.09 27 .12 73 83.2 18 16 35 1.09 32 .12 16 32 I.II 24 3 •13 16 28 I.II 34 .13 72 82.8 19 17 30 1.09 39 •13 17 26 1.09 11 • 13 17 22 1.09 42 •13 71 82.3 20 18 25 1.09 47 0.13 18 21 1.09 19 0.13 18 17 I.II 50 0-13 70 81.9 21 19 20 1.09 55 •IS 19 16 MI 27 •»5 19 II 1.09 58 •15 69 81.5 22 20 IS 1.09 24 4 •17 20 10 1.09 36 •15 20 6 I.II 25 7 •«7 68 81.0 23 21 10 I. II 14 •17 21 5 I.II 45 •17 21 I.II 17 • 17 67 80.6 24 22 4 1.09 24 •'7 59 1.09 55 .18 54 I.I I 27 .18 66 80.1 25 59 1.09 34 0.18 22 54 I.II 25 6 0.18 22 48 I.II 38 0.18 65 79-7 26 23 54 I. II 45 .18 23 48 I.II 17 .18 23 42 I.II 49 .20 64 79.2 27 24 48 I. II 56 .20 24 42 I.TI 28 .20 24 36 I.II 26 I .20 63 78.7 28 25 42 1.09 25 8 .22 25 36 MI 40 .22 25 30 I.II 13 .22 62 78.3 29 26 37 I. II 21 .22 26 30 I.II 53 .23 26 24 I.II 26 • 23 61 77-8 30 27 31 i.ii 34 0.23 27 24 I.II 26 7 0.23 27 18 M3 40 0.23 60 77^3 31 28 25 MI 48 .23 28 18 I.II 21 • 23 28 II MI 54 •25 5§ 76.8 32 29 19 I.II 26 2 ■25 29 12 I-I3 35 .27 29 ■; '•I3 27 9 .25 58 76.3 33 30 13 I.II 17 •27 30 5 I.I I 51 •27 58 '•i3 24 .27 5Z 75-8 34 31 7 I.13 33 .28 59 1. 13 27 7 .28 30 51 1. 13 40 .28 56 75-2 35 32 I.II SO 0.28 31 52 1. 13 24 0.28 31 44 1. 13 57 0.30 55 74-7 36 54 M3 27 7 .30 32 45 I-I3 41 • 30 32 37 '•i3 28 15 .32 54 74.2 1>7 Zl 47 I-I3 25 •32 33 38 '•n 59 .32 33 30 i^J3 34 • 32 53 73-6 38 34 40 1.13 „ 44 .33 34 31 1. 13 28 18 •33 34 23 1. 15 53 •35 52 730 39 35 33 1. 13 28 4 •33 35 24 1. 13 38 •35 35 15 '•15 29 14 •35 51 72.4 40 36 26 1. 13 24 0.35 36 17 1.15 59 0.37 3^ 7 1.15 35 0.37 50 71.8 41 37 19 1. 15 45 .38 37 9 I. IS 29 21 •38 59 1. 15 57 .38 4^ 71.2 42 38 II 1. 15 29 8 .40 38 I 1.15 44 .40 37 51 1. 15 30 20 .40 48 70.6 43 39 3 1. 15 32 .40 53 1. 15 30 8 •42 38 43 1. 18 44 .42 4Z 70.0 44 55 1.15 56 •43 39 45 1.15 33 •43 39 34 1.15 31 9 • 43 46 69.3 45 40 47 30 22 40 37 59 40 26 35 45 68.7 a 60' h ^ a 60^1 6 A_ a 60' 6 A a t ^ 6c/ A 1 60' A 6c/ d = 22° 30' I i = 2 S^'O' d = 25 l°30' 2.414 2.356 2-300 [Page 233 45 46 47 48 49 50 51 52 53 54 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 7i 72 73 74 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 = 22" 30' 6c/ A / / 40 47 1. 15 30 22 41 39 1. 15 48 42 31 1. 18 31 16 43 22 1. 18 45 44 13 1.20 32 16 45 3 1.20 48 53 1.20 iZ 21 46 43 1.20 56 47 23 1.22 34 32 48 22 1.22 35 10 49 II 1.25 . 50 59 1.25 36 32 50 47 1.25 37 15 51 35 1.28 38 I 52 22 1.30 48 53 8 1.30 39 38 54 1.30 40 31 54 40 1.36 41 25 55 24 i.S*^ 42 23 5b 8 1.40 43 23 51 1.40 44 26 57 34 1-43 45 31 58 16 1-50 46 40 5<3 1.50 47 52 59 36 1.54 49 8 60 15 1.62 50 27 52 1.62 51 50 61 29 1. 71 53 17 62 4 ..76 54 47 38 1.82 56 21 63 II 1.94 58 42 2.07 59 43 64 II 2.14 61 30 39 2.31 63 21 65 5 2.50 65 16 29 2.73 67 15 51 3.00 69 19 66 II 3-33 71 26 29 3-75 73 36 45 4.29 75 50 59 ';-4'; 78 7 67 10 6.67 80 26 19 lO.O 82 48 25 iS.o 85 II 29 60.0 87 35 30 90 63 71 81.9 20 18 12 1.09 21 o.is 18 8 1. 1 1 . 52 0.15 18 3 I. II 23 0.15 70 81.4 21 19 7 I.I I 30 •15 19 2 I. II 26 I •15 57 I.I I 32 •17 69 81.0 22 20 I I.I I 39 •17 56 I. II 10 •17 19 51 '•13 42 •17 68 80.5 23 55 I. II 49 •17 20 50 I-I3 20 .18 20 44 I. II 52 .18 67 80.0 24 21 49 I. II 59 .18 21 43 I. II 31 .18 21 38 1-13 27 3 ,18 66 79^5 25 22 43 I. II 26 10 o.iS 22 37 I. II 42 0.18 22 31 1. 1 1 14 0.18 65 79.1 20 23 37 1-13 21 .20 23 31 1. 13 53 .20 23 25 M3 25 .20 64 78.6 27 24 30 I. II 33 .22 24 24 1-13 27 5 .22 24 18 '•13 37 .22 63 78.1 28 25 24 '•'3 46 .22 25 17 I. II 18 .22 25 II 1. 13 50 •23 62 77.6 -9 26 17 I. II 59 •23 26 II i-'3 31 •23 26 4 '•i3 28 4 •23 61 77.1 30 27 II 1-13 27 13 0.23 -V 4 1-13 45 0.25 57 '•i3 18 0.25 60 76^5 .•;i 28 4 I-I3 27 .25 57 •••3 28 •25 27 50 1. 15 33 •25 59 76.0 ^2 57 i-'3 42 .27 28 50 1. 13 15 •27 28 42 1. 13 48 •27 58 75-5 33 29 50 1-13 58 •27 29 43 1. 15 31 .28 29 35 1. 15 29 4 .28 57 74-9 34 30 43 1-13 28 14 .28 30 35 '•13 48 .28 30 27 1.15 21 •33 56 74^4 35 3^ 36 1-13 31 0.30 31 28 1. 15 29 5 0.30 31 19 1. 15 39 0.32 55 73-8 so 32 29 1. 15 49 •32 32 20 1. 15 23 •33 32 II 1. 1 5 58 •32 54 73-2 37 33 21 1. 15 29 8 •33 33 12 1. 15 43 •33 33 3 i.iS 30 17 •33 53 72.6 38 34 13 1. 15 28 •35 34 4 1. 15 30 3 •35 55 1.15 37 •35 52 72.0 39 35 5 1. 15 49 •35 56 1. 15 24 .35 34 47 1. 18 58 • 37 51 71.4 40 . -"^^ 1. 15 30 10 0.37 35 48 1. 18 45 0.37 3 5 38 1. 18 31 20 0.38 50 70.8 41 36 49 I.I s 32 .40 36 39 1. 18 31 7 .40 36 29 1. 18 43 .40 49 70.2 42 37 41 1. 18 56 .40 37 30 1. 18 31 .42 37 20 1. 18 32 7 •40 48 69-5 43 38 32 1. 18 31 20 .42 38 21 i.iS 56 .42 38 II 1.20 31 •43 47 68.9 44 39 23 1. 18 45 •45 39 12 i,i8 32 21 •45 39 I 1.20 57 •45 46 68.2 45 40 14 32 12 40 3 48 51 33 24 45 67^S a 60' b A a Gey b A a 6(/ h A a t - A 60' A (& A 60' f/ = 24'*0' ti = 24°30' d = 25°0' 45 4b 47 48 49 50 51 ^2 =^3 54 55 50 57 SS 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 76 77 78 79 80 Si 82 83 85 86 87 88 89 90 2.246 a = 24°0' 40 14 41 5 55 42 4;-; 43 35 44 2S 45 14 46 3 51 47 39 27 14 I 47 33 52 18 53 2 46 54 29 ^5 II 53 56 34 57 14 53 58 31 59 8 44 60 19 53 61 25 56 62 26 54 63 20 44 64 7 28 47 65 3 18 31 41 49 55 59 66 o ■94 2.00 2.14 2-3' 2.';0 2,61 3.16 3-75 4.00 4.62 6.00 7.50 lO.O 15.0 60.0 12 39 8 38 34 10 33 43 35 17 36 30 37 9 49 38 32 39 16 40 2 50 41 41 42 34 43 29 44 27 45 27 46 30 47 35 48 44 49 5 5 51 10 52 28 53 49 55 14 36 42 58 14 59 50 61 29 63 12 64 58 66 48 68 42 70 39 72 39 74 42 76 47 78 55 81 6 83 18 85 31 87 45 00 o 60' a — 60' 0.4'; .48 .50 •53 •55 0.57 .60 .62 • 65 .67 0.72 •73 •77 .1=; ,iS •25 ,30 .35 ■42 .47 ■53 ,60 .6s •7~ ■77 .83 ,90 1.95 2.00 2.05 2.08 2.13 2.18 2.20 2.22 2.23 Co' ^ = 24°0' 2.194 = 24° 30' 6c/ / / 40 3 1.20 32 48 53 1.20 33 16 41 43 1.20 45 42 33 1.22 34 15 43 2J 1.22 47 44 II 1.22 35 20 45 1.22 , 55 49 1.25 ^6 31 46 37 1.25 37 8 47 25 1.28 47 48 12 1.30 -,8 28 58 1.30 39 II 49 44 1.30 55 50 30 '•33 40 42 51 15 1-33 41 30 52 ..36 42 21 44 1.40 43 14 53 27 1.4c 44 9 54 10 1^43 45 7 52 1.46 46 7 5 5 33 1.46 47 10 56 14 1. 54 48 15 53 '•54 49 24 57 32 1.62 50 35 58 9 1.62 51 49 46 1.67 53 7 59 22 1.76 54 28 56 1.82 55 52 60 29 iM 57 19 61 I 2.00 58 50 31 2.07 60 24 62 2.22 62 2 27 2^3I 63 44 53 2.50 65 29 63 17 2.73 67 17 39 2.86 69 9 64 3-33 71 3 18 3-53 73 I 35 4.29 75 2 49 4.62 77 5 65 2 6.00 79 10 12 7-5° 81 18 20 12.0 83 27 25 15.0 85 37 29 60.C S7 48 30 ';0 0.47 •48 .50 •53 •55 0.58 .60 .62 .6^ .6;s 0.72 •73 •78 .80 •85 .92 •97 .00 •05 .08 • I"; .18 •23 .30 •35 .40 •45 •52 .57 .63 .70 .7S .So •87 .90 •97 2.02 2.05 2.08 2,13 2.15 2.17 2.1S 2.20 60' A (? = 24°30' A_ 60' 2.14s o = 25°0' [Page 235 T A 60' / / 39 51 1.20 33 24 40 41 1.20 52 41 31 1.22 34 22 42 20 1.22 52 43 9 1.22 35 24 58 1.22 57 44 47 1. 25 36 32 45 3S 1.28 37 8 46 22 1.28 46 47 9 1.28 38 26 56 1.30 39 7 48 42 1.30 49 49 28 1.30 40 34 50 14 '•33 41 21 59 1.36 42 9 51 43 1.40 43 52 26 1.40 53 53 9 1.43 44 48 51 1.43 45 46 54 33 1.50 46 46 ss 13 1.50 -17 49 53 '•54 48 54 56 32 1.58 qo 2 57 10 1.62 51 13 47 ..67 52 27 58 23 1.71 53 44 ss 1.76 55 5 59 32 1.82 56 28 60 s 1.94 57 55 36 2.00 59 25 61 6 2.14 60 58 34 2.22 62 35 62 I 2.40 64 15 26 2.50 65 58 50 2^73 67 45 63 12 3.00 69 35 32 3-33 71 27 50 3-75 73 23 64 6 4.29 75 21 20 5.00 77 22 32 6.00 79 25 42 7.50 81 30 i;o 1 0.0 83 36 56 20.0 85 43 59 60.0 87 51 65 c 90 ^•4' .50 .50 .53 •55 0.58 .60 .63 .67 ,68 0.70 •75 .78 .80 •85 ,3^ 45 ■50 .55 ,62 ,67 .72 ,78 ■83 ,87 ■93 ■97 2.02 2.05 2.08 2. 10 2.12 2.13 2.15 60' A A^ 6(y d = 25° 0' 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 19 18 17 16 15 14 13 12 II 10 9 8 7 6 5 4 3 2 I 67^5 66.8 66.0 65^3 64-5 637 62.9 62.0 61.2 60.3 59-4 58.4 57^4 56^4 55-4 54^3 53-2 52.0 50-9 49.6 48.4 47.0 45-7 44^3 42.8 4i^3 39^7 38.1 36^4 34-7 329 31^0 29.1 27.1 25.1 23.0 20.9 18.7 16.S 14.2 I1.9 9.6 7.2 4.8 2.4 0.0 Page 236] 2 097 2050 2.006 I a = 25'' 30' = 26*' 0' = 26*30' ){ \ * 60' A A 60' 60' A Z\ A 60' 60' A A 60' A / I. II / 25 30 0.00 / I.II 26 0.00 / I.II 2^ 30 0.00 t 88 87 86 90.0 I 2 3 4 54 1 48 2 43 3 37 I. II 1.09 1. 1 1 I. II 30 31 32 33 .02 .02 .02 •03 54 1 48 2 42 3 36 I.II I.II I.II I.II I 2 3 .02 .02 .02 .03 54 1 47 2 41 3 35 i^i3 I.I I I.II 1. 13 30 31 32 33 .02 .02 .02 •03 89.6 89.1 88.7 88.2 5 6 7 8 9 4 31 5 25 6 19 7 13 8 7 I. II I. II I. II I.I I 35 37 40 43 47 0.03 .05 .05 .07 .07 4 30 5 23 6 17 I ^^ 8 5 1.13 I.II I.II I.II I.II 5 7 10 13 17 0.03 •05 •05 .07 .07 4 28 5 22 6 16 7 9 8 3 I.II I.II '•13 I.II 1. 13 35 37 40 43 47 0.03 •05 •05 .07 .07 |5 82 81 87.8 87.4 86.9 86.5 86.1 10 1 1 12 13 14 9 I 55 10 49 11 43 12 37 i.ii I. II I. II I.II I.II SI ^ 55 26 5 II 0.07 .08 .08 .10 .10 59 9 53 10 46 11 40 12 34 I.II 1^13 I.II I.II M3 21 25 30 35 41 0.07 .08 .08 .10 .10 56 9 50 10 43 11 37 12 30 I.II i^i3 I.II ■•13 I.II 12 0.08 .08 .08 .10 .10 80 79 78 76 85.6 85.1 847 842 83.8 17 18 19 13 31 14 24 15 18 16 12 17 5 1.13 I.II I.II 1. 13 I.II 17 24 31 46 0.12 .12 .12 .13 •15 13 27 14 21 15 14 16 8 17 I I.II 1. 13 I.II M3 1. 13 47 54 27 I 9 17 0.12 .12 • 13 •13 •15 13 24 14 17 15 10 '^ k 56 '•i3 '.13 1.13 1. 13 1.13 18 25 32 40 48 0.12 .12 •13 •13 •15 75 74 73 72 71 83.3 82.8 82.4 81.9 81.4 20 21 22 23 24 59 18 52 19 46 20 39 21 32 1. 13 I.II '•13 1. 13 1. 13 55 27 4 13 23 34 0.15 •15 •17 .18 .18 54 18 47 19 40 20 33 21 26 1. 13 '•13 1. 13 1. 13 M3 26 35 45 5S 28 6 CIS •17 .17 .18 .18 17 49 18 42 19 35 20 28 21 21 '•13 1. 13 1. 13 M3 1. 15 28^^ 16 26 37 0.15 ■•7 .20 69 68 67 66 80.9 80.4 80.0 79-5 79.0 25 20 27 28 29 22 25 23 18 24 II 25 4 57 '•'3 '•'3 1-13 1. 13 1. 13 45 57 28 10 23 37 0.20 .22 .22 •23 •23 22 19 23 12 24 5 57 25 50 1. 13 1. 13 1. 15 1. 13 1.15 17 29 42 55 29 9 0.20 .22 .22 .23 • 23 22 13 23 6 58 24 SI 25 43 M3 I.IS 1. 13 1.15 MS 49 29 I 14 27 41 0.20 .22 .22 .23 .25 62 61 78.4 77^9 77-4 76.9 763 30 31 32 33 34 26 50 27 42 28 35 29 27 30 19 1.15 '•13 1.15 1.15 1. 15 SI 29 6 22 38 55 C.25 •27 .27 .28 .30 26 42 27 34 28 26 29 18 30 10 1. 15 I. IS 1. 15 1. 15 I. IS 23 38 54 30 II 28 0.2s .27 .28 .28 • 30 26 35 27 27 28 19 29 10 30 2 1. 15 I.IS 1. 18 1. 15 1. 18 56 30 II 27 44 31 I 0.25 .27 .28 .28 •32 60 59 58 56 75-8 75-2 74.7 741 73-5 3| 36 38 39 31 II 32 3 54 33 45 34 36 1. 15 1. 18 1. 18 1. 18 1.18 30 13 31 SI 31 II 32 0.30 •33 •33 •35 .38 31 2 53 32 45 33 36 34 27 1. 18 i.iS 1. 18 1. 18 1. 18 46 31 5 25 45 32 7 0.32 .33 •33 .37 .37 53 31 44 32 35 33 26 34 17 1. 18 1. 18 1. 18 1. 18 1.20 20 39 59 32 19 41 0.32 •33 • 33 .37 .38 55 54 53 52 51 72.9 723 71.7 71.1 70.5 40 41 42 43 44 35 27 36 18 37 9 38 50 1.18 1. 18 1. 18 1.20 1.20 55 32 18 42 33 7 33 0.38 .40 • 42 •43 •45 35 18 36 8 37 48 38 38 1.20 1.20 1.20 1.20 1.20 29 52 33 17 42 34 8 0.38 .42 •42 •43 •47 35 7 36 47 37 37 38 26 1.20 1.20 1.20 1.22 1.22 33 4 27 51 34 17 44 0.38 .40 •43 •45 .45 50 69.8 69.1 68.5 67.1 45 39 40 34 39 28 36 39 IS 35 II 45 66.3 t a 6o_' A b A 60' a 60' A b A 60' a 60^ A 6 A 60' a ^ = 25*30' d = 2&'0' d = 2&*2(y 2.097 a = 25° 30' A 45 4t> 47 48 49 50 SI 5^ 53 54 55 50 57 58 59 6o 6i 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 8i 82 83 84 85 86 87 88 89 90 / / 39 40 1.22 34 0.^ 40 29 1.22 28 41 18 1.22 58 42 7 1.22 35 29 56 1.22 36 I 43 45 1.25 35 0. 44 33 1.28 37 10 , 45 20 :.2« 46 . 46 7 1.28 38 24 , 54 1.28 39 4 . 47 41 1.30 45 0.' 48 27 1.33 40 28 49 12 1-33 41 13 57 1.36 59 50 41 1.36 42 48 51 25 1.40 43 39 0. 52 8 1.43 44 32 , 50 1-43 45 27 . 53 32 1.46 46 25 i.< 54 13 1.50 47 25 I. 53 i.i;o 48 28 I, 55 33 1.58 49 33 56 II i.SS 50 41 49 1.67 51 51 57 25 1.67 53 5 58 I 1.76 54 21 35 1.82 55 41 59 8 1.88 57 4 40 1.94 58 30 60 II 2.07 59 59 40 2.14 61 31 61 8 2.22 63 6 35 2.50 64 45 59 2.61 66 27 62 22 2-73 68 12 44 3.00 70 63 4 3-53 71 51 21 3-75 73 44 37 4.29 75 40 51 5.00 77 38 2. 64 3 6.00 79 39 2. 13 «.57 81 41 2. 20 lO.O 83 44 2. 26 20. c 85 49 2. 29 60.0 87 54 2. 30 90 _A_ 60' ^M b I A I 85 6c/ 2.050 a = 26^ 0' A / / 39 28 1.22 34 36 O.i 40 17 1.22 35 4 41 6 1.22 34 55 1.25 36 5 42 43 1.25 37 43 31 1.28 37 II 0. 44 18 1.28 46 . 45 5 1.28 38 23 . 52 1.28 39 I . 46 39 1.30 41 47 25 '•33 40 23 o.- 48 10 1-33 41 6 55 1.33 51 49 40 1.36 42 38 .! 50 24 1.40 43 26 .1 51 7 1.43 44 17 O.J 49 1.43 45 10 52 31 1.43 46 6 . 53 13 1.50 47 3 i.< 53 1.50 48 3 i.< 54 33 1-54 49 5 i.< 55 12 i.S8 50 10 50 1.62 51 18 56 27 1.67 52 28 57 3 1. 71 53 42 38 1.76 54 58 58 12 1.88 56 17 44 1.88 57 39 59 16 2.00 59 4 46 2.07 60 32 60 15 2.22 62 3 42 2.31 63 37 61 8 2. "JO 65 14 32 2.61 66 55 55 2.86 68 38 62 16 3.16 70 24 35 3-33 72 13 53 4.00 74 4 63 8 4.29 75 58 22 5-45 77 54 33 6.00 79 52 2. 43 «.57 81 52 2. 50 1 0.0 83 53 2. 56 20.0 85 55 2. 59 60.0 87 57 2. 04 90 - 6 I ^ I 60' 03 _A 60/ 2.006 a = 26° 30' 60' A [Page 237 / / 39 15 1.22 35 II 40 4 1.22 40 53 1.25 36 10 41 41 1.25 41 42 29 1.25 37 14 43 17 1.28 48 44 4 1.28 38 23 51 1.30 39 45 37 1.30 ^S 46 23 1.30 40 18 47 9 1.33 41 54 1.36 43 48 38 1.3& 42 28 49 22 1.36 43 15 50 6 1.40 44 4 49 1-43 55 51 31 1.46 45 48 52 12 1.46 46 43 53 1.50 47 41 53 33 1-54 48 41 54 12 I.S8 49 43 50 1.58 50 48 55 28 1.67 51 55 56 4 1.67 53 5 40 1. 71 54 18 57 15 1.82 55 33 48 1.88 56 51 58 20 1.94 58 13 51 2.00 59 37 59 21 2.14 61 4 49 2.22 62 34 60 16 2.40 64 7 41 2. so 65 43 61 5 2.61 67 22 28 3.00 69 4 48 3.16 70 48 62 7 3-53 72 35 24 4.00 74 24 39 4.29 76 16 53 5.45 78 10 63 4 6.67 80 5 13 «.';7 82 2 20 10. 84 26 20.0 86 29 60.0 88 30 90 ^ b A d = 26°30' _A 60' 0.48 .50 •52 •55 •57 0.58 .62 .63 .67 .70 0.72 •75 .78 .82 .85 0.88 •92 •97 .00 •03 .o3 .12 •'7 .22 .25 •30 •37 .40 •45 .50 •55 .60 •65 .70 •73 .78 .82 .87 .90 •92 •95 •97 2.00 2.00 2.00 6c/ 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 2^ 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 I 66.3 65.6 64.8 64.0 63.2 62.4 61.6 60.7 59-8 58.9 58.0 57^0 56.0 54^9 53-9 52.8 51^7 505 49^3 3.1 46.8 45-4 44.1 42.7 41.2 39-7 38.1 36.5 349 33^2 31-4 29.6 27.8 25-9 239 21.9 19.9 17.8 iS6 135 "•3 9.1 6.8 4.6 2.3 0.0 Page 238] 1.963 1.921 1.881 \ a = 27° 0' a = 27° 30' a = 28° 0' \\ \ * \d 6c/ \ t A \ d 60' \ t A \ d 60' \^ t A \ A A \ A z 60' *\ A z\ 60/ A \ A z \ 60' ^\ i8\ / / / / / / ^ '•'3 27 0.00 ••13 27 30 0.00 1. 13 28 0.00 90 90.0 I 53 I. II .02 53 M3 30 .02 53 1.13 .02 89 89-5 2 I 47 1.13 I .02 I 46 I. II 31 .02 I 46 '•'3 I .02 88 89.1 3 2 40 I. II 2 .02 2 40 M3 32 .02 2 39 1. 13 2 .02 87 88.6 4 3 34 1. 13 3 .03 3 33 '•'3 33 • 03 3 32 1. 13 3 •03 86 88.2 5 4 27 I.I I 5 0.05 4 26 '•13 35 0.05 4 25 '•i3 5 0.05 85 87.7 6 5 21 '••3 8 .05 5 19 1-13 38 .05 5 18 '•13 8 •05 84 87.2 7 6 14 1-13 II .05 6 12 1.13 41 .05 6 II '•i3 II .OS 83 86.8 8 2 7 I.I I 14 .05 7 5 I. II 44 .07 7 4 1.15 14 .07 82 86.3 9 8 I I-I3 17 .07 59 '•13 48 .07 56 1-13 18 .07 81 85.8 10 54 1. 1 3 21 0.08 8 52 1.13 H 0.07 8 49 1. 13 22 o.oS 80 853 1 1 9 47 I.I ! 26 .08 9 45 1. 13 56 ,oS 9 42 1. 13 27 .oS 79 84.9 12 10 41 1. 1 3 ^i .08 10 38 1-13 28 I .10 to 35 1. 15 32 .08 78 84.4 13 II 34 I-I3 36 .10 II 31 I. IS 7 .10 II 27 1. 13 37 .10 77 839 14 12 27 1-13 42 .12 12 23 1. 13 13 .10 12 20 '•13 43 .12 76 834 IS 13 20 1. 13 49 0.12 13 16 '•13 19 0.12 13 13 1. 15 SO 0.12 75 82.9 i6 14 13 1-13 56 .12 14 9 i^i3 26 ••3 14 5 1. 13 57 .12 74 82.5 17 15 6 I-I3 28 3 .13 15 2 i^i3 34 •13 58 1.15 29 4 ••3 73 82.0 iS ^ 59 1.13 II •13 ^ 55 1. 15 42 •13 15 so 1. 15 12 ••5 72 81.5 19 16 52 i-'3 19 •'S 16 47 I-I3 SO •15 16 42 i^'3 21 • •5 71 81.0 20 17 45 1. 15 28 0.15 17 40 1.15 59 0.17 17 35 1. 15 30 0.17 70 80.5 21 18 37 1.13 27 .17 18 32 1. 15 29 9 •17 18 27 LIS 40 • 17 6q 79-9 22 19 30 1. 1 5 47 .18 19 24 1. 13 19 .18 19 19 LI5 SO .18 68 79-4 23 20 22 1. 13 58 ,iS JO 17 I. IS 30 .18 20 II 1.15 30 I .iS 67 78.9 24 21 15 1.15 29 9 .20 21 9 LIS 41 .20 21 3 LIS 12 .20 66 78.4 ^1 22 7 1. 13 21 0.20 22 I 1. 15 53 0.20 55 1. 18 24 0.22 65 77.8 26 23 i.iS 33 .22 53 1. 15 30 5 .22 22 46 1. 15 37 .22 64 77^3 27 52 1.15 46 .22 23 45 1. 15 18 .23 23 3^ I.I8 SO .22 63 76.8 28 24 44 LM 59 •23 24 37 1. 18 32 .23 24 29 1. 15 31 3 .25 62 76.2 29 25 36 1. 18 30 13 .25 25 28 1. 15 46 .25 25 21 1.18 18 .25 61 75-6 30 26 27 1. 15 28 0.27 26 20 1. 18 31 I 0.25 26 12 I.I8 33 0.27 60 7SI 31 27 19 1. 15 44 .27 27 II 1. 18 16 .28 27 3 1.18 49 • 27 59 74-5 32 28 II I. 18 31 .28 28 2 1. 18 33 .28 54 LI8 32 5 .23 58 73^9 33 29 2 1. 18 17 .30 S3 1. 18 SO •30 28 45 1.20 22 .30 57 73-3 34 53 1,18 35 .30 29 44 1. 18 32 8 •30 29 35 L18 40 .32 56 72.7 35 30 44 1. 18 53 0.32 30 35 1. 18 26 0.33 30 26 1.20 59 0-33 55 72.1 36 31 35 1. 18 32 12 .33 31 26 1.20 46 •33 31 16 1.20 33 19 •33 54 7I-S 37 32 26 1.20 32 •35 32 16 1.20 33 6 •35 32 6 1.20 39 •37 53 70.8 38 33 16 1.20 53 .37 33 6 1.20 27 .37 56 1.20 34 I •37 52 70.2 39 34 6 1.20 33 15 .38 56 1.20 49 .38 33 46 1.22 23 .38 51 69-5 40 5? 1.20 38 0.38 34 46 1.22 34 12 0.4c 34 35 1.22 46 0.40 50 68.8 41 35 46 1,20 34 I .42 35 35 1.22 36 •42 35 24 1.22 35 10 •42 49 68.1 42 36 36 1.22 26 •43 36 24 1.22 35 I •43 36 13 1.22 35 •43 48 67.4 43 37 25 1.22 52 •45 37 13 1.22 27 •45 37 2 1.25 36 I • 4^ 47 66.7 44 38 14 1.22 35 19 •47 38 2 1.22 54 •47 50 L2S 28 .48 46 66.0 45 39 3 47 51 36 22 38 38 57 4S 65.2 a 6(y b A a 6°Qf 1963 1921 i88i [Page 239 45 4 b 47 48 49 SO 31 52 53 54 55 b^ 57 58 59 60 61 62 63 64 ^1 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 ol 82 83 8.' 85 86 87 8S 89 90 / / 39 3 1.22 3 5 47 O.i 52 1.2=; 36 16 40 40 1.25 46 41 28 1.28 37 17 42 15 1. 28 50 43 2 1.28 38 24 0. 49 1. 28 39 , 44 36 1.30 37 . 45 22 1-33 40 15 . 46 7 1-33 55 52 1.33 41 37 0. 47 37 1.36 42 20 48 21 1.36 43 5 49 5 1.40 '^2 48 1.43 44 41 50 30 1.43 45 32 0. 51 12 1.46 46 25 53 i.-;o 47 21 . 52 33 1.50 48 18 I. 53 13 1.58 49 18 I. 51 1.58 50 20 I. 54 29 1.62 51 24 55 t 1.67 52 31 42 1. 71 53 41 56 17 1.76 54 53 51 1.82 56 8 57 24 1.88 57 25 Sb 2.00 58 46 58 26 2.07 60 9 55 2.14 61 35 59 23 2.22 63 4 50 2.40 64 36 60 15 2.61 66 II I, 38 2.73 67 48 I, 61 3.00 69 28 20 3.16 71 II 39 3-53 72 56 5 b 4.29 74 43 62 10 4.62 76 33 23 5.00 78 24 35 6.67 80 18 44 8.<;7 82 12 51 12.0 84 8 56 20.0 86 5 59 60.0 88 2 63 90 ^' b A d = 2T0' _A_ 60' / / 38 51 1.25 36 22 39 39 1.25 5^ 40 27 1.28 37 21 41 14 1.28 53 42 1 1.28 38 26 48 1.28 39 43 35 1.30 36 44 21 1-33 40 13 45 6 1-33 52 SI 1.33 41 32 46 36 1.36 42 14 47 20 1.36 57 48 4 1.40 43 42 47 1-43 44 29 49 29 1-43 45 18 50 II 1.46 46 9 52 1.46 47 2 51 33 1.50 57 52 13 1.54 48 54 52 1.58 49 54 53 30 1.58 50 56 54 8 1.67 52 44 1.67 53 7 55 20 1.76 54 16 54 1.7b 55 27 56 28 1.88 56 42 57 1.94 57 59 31 2.00 59 18 58 1 2.07 60 41 30 2.22 62 6 57 2.31 63 34 59 23 2.40 65 5 48 2.61 66 38 60 II 2.86 68 14 32 3.00 69 52 . 52 3-33 71 33 61 10 3-53 73 16 27 4.29 75 2 41 4.62 76 50 54 5-45 78 39 62 5 6.67 80 30 14 «.S7 82 22 21 12.0 84 16 26 20.0 86 10 29 60.0 88 5 30 90 0.48 .50 •53 •55 •57 0.60 .62 .65 .67 .70 0.72 •75 .78 .82 .85 0.88 .92 •95 .00 •03 .07 .12 • 15 .18 .25 .28 •32 .38 .42 •47 •52 •55 ,60 .63 A cZ = 27°30' 60' / / 38 38 ^•25 36 57 39 26 1.28 37 26 40 13 1.28 56 41 1.28 38 28 47 1.28 39 I 42 34 1.30 36 43 20 1-33 40 12 44 5 ^33 49 SO '•33 41 28 45 35 1.36 42 8 46 19 1.36 50 47 3 1.40 43 34 46 1.40 44 19 48 29 1-43 45 6 49 II 1.46 55 S2 1.46 46 46 50 33 1.50 47 38 51 13 1.50 48 33 S3 ..58 49 30 52 :.i 1.58 50 30 53 9 1.62 51 31 46 ...67 52 35 54 22 1. 71 53 41 57 1.76 54 5C 55 31 1.82 56 I 56 4 1.88 57 15 3^ 1.94 58 31 57 7 2.07 59 50 36 2.14 61 12 58 4 2.22 62 36 31 2.31 64 3 57 2. CO 65 32 59 21 2.61 67 4 44 2.86 68 39 60 5 3.. 6 70 16 24 3-33 71 55 42 3-75 73 36 58 4.29 75 20 61 12 4.62 77 6 25 5-45 78 53 36 7.50 80 42 44 8. .-7 82 32 51 12.0 84 23 56 20.0 86 iq 59 60.0 88 7 62 90 0.48 .50 •53 •55 •58 0.60 .62 .6c; .67 .70 ©•73 •75 .78 .82 .85 0.87 .92 •95 ,07 6b 42 3 45 19 i.3(> 44 46 3 1.40 43 26 46 1.40 44 9 47 29 1-43 55 48 II 1-43 45 42 53 1.46 46 31 49 34 i.';o 47 22 50 14 1-54 48 14 53 1-54 49 9 51 32 1.5S 50 6 52 10 1.58 51 5 48 1.67 52 6 53 24 1. 71 53 10 59 1. 71 54 16 54 34 1.76 55 24 55 8 1.88 56 35 40 1.88 57 48 56 12 2.00 59 3 42 2.07 60 21 57 II 2.14 61 42 39 2.31 63 5 S8 5 2.40 64 31 30 2.50 65 59 54 2-73 67 29 59 16 2.86 69 2 Z7 3-16 70 38 56 3-33 72 16 60 14 4.00 71> 56 29 4.29 75 37 43 4.62 77 21 56 6.00 79 6 61 6 6.67 80 53 15 lO.O 82 41 21 12.0 84 30 26 20.0 86 19 29 60.0 88 9 30 90 ^ 6 A ' rf = 28°30' 60' 0.50 .50 •53 •57 •57 0.60 .62 .65 .68 .70 0.72 •77 .78 .82 0.87 .92 •95 .9S 1.02 1.07 1. 10 1. 13 i.iS 1.22 1.25 1.30 1-35 1.38 1-43 1-47 1.50 '•55 1.60 1.63 1.67 1.68 1-73 1-75 1.78 1.80 1.82 1.82 1.83 1.85 _A_ 60/ a = 29°0' 6c/ A a = 29° 30' 38 12 59 39 46 40 32 41 18 42 4 49 43 34 44 18 45 2 46 46 29 47 II 53 48 34 49 14 54 50 II 51 12 49 52 26 53 2 37 54 II 44 55 16 47 56 17 46 57 13 39 58 4 27 49 59 9 28 45 60 o 14 26 36 45 51 56 59 61 o 1.94 2.00 2.07 2.22 2.31 2.40 2.61 2-73 3.00 3.16 3-53 4.00 4.29 5.00 6.00 6.67 lo.o 12.0 20.0 60.0 60' A 38 5 35 39 6 l^ 40 II 46 41 22 42 o 39 43 19 44 I 45 45 30 46 17 47 6 57 48 50 49 44 50 41 51 40 =;2 41 53 44 54 49 55 57 57 7 58 19 59 34 60 52 62 12 63 34 64 58 66 25 67 54 69 26 71 o 72 36 74 14 75 54 77 36 79 19 81 4 82 50 84 36 86 24 88 12 90 o _A_ ec/ 0.50 •52 •53 •55 .58 0.60 .63 .65 .67 .70 0-73 •75 .78 .82 .90 •95 .98 1.02 1.05 1.08 '•13 1. 17 1.20 1.25 1.30 '•33 i^37 1.40 1-45 1.48 '•53 '•57 1.60 1.63 1.67 1.70 1.72 '•75 ^•71 '•77 1.80 1,80 1.80 ec/ 1>7 59 38 46 39 32 40 18 41 4 49 42 34 43 18 44 2 46 45 29 46 1 1 53 47 34 48 15 55 49 34 50 13 51 51 28 52 4 40 53 14 48 54 21 52 55 23 52 56 20 47 57 13 37 58 o 21 41 59 o 17 32 45 57 60 7 15 22 26 29 30 / 1.28 38 40 1.30 39 10 1.30 41 1.30 40 13 1.33 46 '•33 41 21 1.36 57 ..36 42 35 1.36 43 14 1.40 54 1-43 44 36 '•43 45 20 1.46 46 5 ..4^-^ 52 1.50 47 41 '•54 48 32 '•54 49 25 '.5S 50 19 1.62 51 15 1.67 52 14 1.67 53 14 1.76 54 17 ..76 55 22 T.82 56 29 1.94 57 39 1.94 58 SI 2.07 60 5 2.14 61 21 2.22 62 40 2.31 64 2 2. so 65 25 2.61 66 51 2.85 68 19 3.CX3 69 49 3.16 71 22 3-53 72 56 4.00 74 33 4.62 ■j6 II 5.00 77 51 5.00 79 32 /•5o 81 14 8^57 82 58 '5-° 84 43 20.0 86 28 60.0 88 14 90 d = 29°0' - & A 11 (Z = 29°30' 60' 0.5c 52 53 55 5« 0.60 M .65 .67 .70 0.73 •75 .78 .82 .85 .90 •93 .98 1. 00 1.05 1.08 1. 12 1. 17 1.20 1.27 '•32 '•37 1.38 1.43 '•47 1.50 '•55 '•57 1.62 ••63 1.67 1.68 1.70 '•73 1.75 '•75 ^•71 1.77 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 19 18 17 16 15 14 13 12 II 10 9 8 7 6 5 4 3 2 I 64.1 633 62.5 61.7 60.9 60.0 59^1 58.2 57-2 56.3 55-3 54^3 53-3 52^2 5I-I 50.0 48.8 47.6 46.4 45-2 43-9 42.6 41.2 39-8 38^4 36.9 35-4 33-8 32.2 30.6 28.9 27.2 25-5 23^7 21.8 20.0 18. 1 16.2 14.2 12.2 10.2 8.2 6.2 4.1 2.1 0.0 55901°— 18- -16 Page 242] 1.732 1.698 Z664 A a = 30° 0' a = 30° 30' a = 31° 0' c\ \ "■ 6& A \ t A 60' \ d 60' A \ t Z\ A 60' \ h d \ 60' A \ Z < A 60' A / / / / / c / p I. IS 30 0.00 1.15 30 30 0.00 1. 18 31 0.00 90 90.0 I 52 1. 15 .02 52 1. 18 30 .02 SI 1.15 .02 89 89-5 2 I 44 1. 15 I .02 I 43 1. 15 31 .02 I 43 1.18 I .02 88 89.0 3 2 36 1. 15 2 •03 2 35 1. 15 32 •03 2 34 1. 15 2 •03 ^7 88.5 4 3 28 1. 15 4 .03 3 27 1. 18 34 .03 3 26 1. 18 4 •03 86 88.0 5 4 20 1. 15 6 0.03 4 18 1. 15 3^ 0.03 4 17 1. 18 6 0.03 ^5 ii-^ 6 5 12 1. 15 8 •OS 5 10 1. 15 38 •05 5 8 I. IS 8 .05 84 86.9 7 6 4 1. 18 II .07 6 2 1. 18 41 .07 6 1. 18 II .07 83 86.4 8 55 1.15 15 .07 Si 1. 15 45 .07 51 LIS 15 .07 82 85-9 9 7 47 1. 15 19 .07 7 45 1. 18 49 .07 7 43 1. 18 19 .07 81 85-4 10 8 39 1. 15 23 0.08 8 36 1.15 53 0.08 8 34 1. 18 23 0.08 80 84.9 11 9 31 1. 18 28 .08 9 28 1. 18 58 .08 9 25 I.I8 28 . 10 79 84.4 12 10 22 1. 15 ZZ .10 10 19 1. 15 31 3 .10 10 16 1. 18 34 . lO 78 83.8 13 II 14 1. 15 39 .10 II II 1. 18 9 .12 II 7 1. 18 40 . 10 77 833 14 12 6 1. 18 45 .12 12 2 1. 18 16 .12 58 1. 18 46 .12 76 82.8 15 57 1. 15 52 0.12 53 1. 18 23 0.12 12 49 I.I8 53 0.13 75 82.3 16 13 49 1. 18 59 .13 13 44 1. 18 ^? •13 13 40 1. 18 32 I .13 74 81.7 17 14 40 1. 18 31 7 •15 14 35 1. 18 3! •13 14 31 1,18 9 .13 73 81.2 18 15 31 1. 15 16 .15 15 26 1. 18 46 •15 15 22 1.20 17 •»5 72 80.6 19 16 23 1. 18 25 .15 16 17 1. 18 55 •17 16 12 i.rS 26 •17 71 80.1 20 17 14 1. 18 34 0.17 17 8 1.18 32 5 0.17 17 3 1.20 36 0.17 70 795 21 18 5 1. 18 44 .18 59 1. 18 15 .18 53 1.18 46 .18 69 79.0 22 56 1. 18 55 .18 18 so 1. 18 26 .18 18 44 1. 20 57 .18 68 78.4 23 19 47 1.20 32 6 .20 19 41 1.20 37 .20 T9 34 1.20 33 8 .20 tl 77.8 24 20 37 1. 18 18 .20 20 31 1.20 49 .20 20 24 1.20 20 .22 66 77^3 25 21 28 1. 18 30 0.22 21 21 1.20 33 I 0.22 21 14 1.20 33 0.22 ^5 76,7 26 22 19 1.20 43 .23 22 II 1.20 14 .23 22 4 1.20 46 •23 ^4 76.1 27 23 9 1.20 57 .23 23 I 1.20 28 •23 54 1.20 34 •23 63 75-5 28 59 1.20 33 II .25 SI 1.20 42 •25 23 44 1.22 14 .25 62 74-9 29 24 49 1,20 26 .25 24 41 1.20 57 .27 24 33 1.20 29 .27 61 74-3 30 25 39 1.20 41 0.28 25 31 1.20 34 13 0.28 25 23 1.22 45 0.28 60 73-7 31 26 29 1.20 58 .28 26 21 1.22 30 .28 26 12 1.22 35 2 .28 ^t 730 32 27 19 1.20 34 15 •30 27 10 1.22 47 •30 27 I 1.22 19 • 30 58 72.4 33 28 Q 1.22 33 .30 59 1.22 35 5 •32 50 1.22 37 •32 57 71.8 34 58 1.22 51 .33 28 48 1,22 24 • 32 28 39 1.25 56 •33 56 71. 1 35 29 47 1.22 35 II 0.33 29 37 1.22 . 43 0.35 29 27 1.25 36 16 0-33 55 70.4 69.8 3b 30 36 1.22 31 .35 30 26 1.25 36 4 • 35 30 15 1.25 36 .35 54 37 31 25 1.25 52 .37 31 14 1.25 25 • 37 31 3 1.25 57 .38 53 69.1 38 32 13 1.25 36 14 .38 32 2 1.25 47 .38 51 I.2S 37 20 •38 52 68.4 39 33 I 1.25 17 .38 50 1.25 37 10 .40 32 39 1.28 43 .40 51 67.7 40 49 1.25 n 0.42 33 38 1.28 ^i 0.40 33 26 1.28 38 7 0.40 50 66.9 41 34 2>7 1.25 25 .43 34 25 1.28 „ 58 .43 34 13 1.28 31 •43 ^t 66.2 42 35 25 1.28 51 .43 35 12 1.28 38 24 •45 35 1.30 57 .45 48 65-4 43 36 12 1.28 38 17 •47 59 1.28 51 •47 46 1.28 39 24 •47 ^Z 64.7 44 59 1.28 45 .48 36 46 1.30 39 19 .48 S6 33 1.30 52 .48 46 639 45 37 46 39 14 37 32 48 ^7 19 40 21 45 63.x 60' 6 A 6c/ A 60' A t a T 60' a A h 6c/ a T b 60' a rf = 30° 0' rf = 30°30' (? = 31° 0' I 732 1.698 1.664 [Page 243 \ a = SO°0' a - 30° 30' a = 31°0' \\ \ * \ d 60' \ ^ A \ \ A Z\ 60' aX^ A Z\ 60' r \ A Z\ 6(/ \ o / / / / / / 45 37 5 1-33 40 55 0.50 36 51 1-33 41 28 0.50 36 37 1.36 42 1 0.50 45 62.1 41. 50 1-33 41 25 •52 37 36 1.36 58 •53 37 21 1.36 31 •53 44 61.2 47 38 35 1.^6 56 •55 38 20 ,.36 42 30 •S3 38 5 1.36 43 3 •55 43 60.4 48 39 19 1.36 42 29 •57 39 4 1.36 43 2 •57 49 1.40 36 •57 42 59-5 49 40 3 ..36 43 3 •58 48 1.40 36 •58 39 32 1.40 44 10 .58 41 58.6 50 47 1.40 38 0.60 40 31 1.40 44 II 0.62 40 15 1.43 45 0.60 40 ^11 51 41 30 1.40 44 14 .63 41 14 «-43 48 .63 57 ••43 45 21 •63 32 56.8 52 42 13 1-43 52 .6^ 56 1.43 45 26 .65 41 39 1.43 59 .65 38 55-9 53 55 1.43 45 31 .68 42 38 1.46 46 5 • 67 42 21 1.46 46 38 .67 ^l 54-9 54 43 37 1.46 46 12 .70 43 19 1.46 45 .70 43 2 1.50 47 18 .70 36 53-9 55 44 18 1.46 54 0.72 44 1.50 47 27 0.72 42 1.50 48 0.72 35 52-9 ';6 59 1.50 47 17 •75 40 1.50 48 10 •75 44 22 '•54 43 •75 34 518 57 45 39 1.50 48 22 .78 45 20 ••54 55 .78 45 I '•54 49 28 •78 33 508 58 46 19 1-54 49 9 .80 59 '•54 49 42 .80 40 '•58 50 15 .80 32 49-7 59 58 1.58 57 .83 46 38 1.58 50 30 •83 46 18 1.62 51 3 •83 31 48.6 60 47 36 1.62 50 47 0.87 47 16 1.62 51 20 0.87 55 1.62 53 0.8 <; 30 47^5 61 48 13 1.62 51 39 .9c 53 ..67 52 12 .88 47 32 ..67 52 44 .88 29 28 46.3 62 50 1.67 52 iz .92 48 29 1.67 53 5 .92 48 8 1.71 53 37 .92 45-1 63 49 26 1.71 53 28 •95 49 5 1. 71 54 •95 43 1.76 54 32 •93 11 43-9 64 50 I 1. 71 54 25 .98 40 1.76 57 .98 49 17 ..76 55 28 •97 26 42.6 65 36 1.76 5 5 24 1.03 50 M 1.82 55 56 1. 00 51 1.82 56 26 1. 02 25 4i^3 60 51 10 1.88 56 26 1.05 47 1.88 56 56 1.05 50 24 1.88 57 27 1.03 24 40.0 67 42 1.88 57 29 1.08 51 19 1.94 57 59 1.08 56 1.94 58 29 1.07 23 38.7 68 52 14 1.94 58 34 1. 12 50 1.94 59 4 1. 10 51 27 2.07 59 33 1. 10 22 37.3 69 45 2.00 59 41 1. 15 52 21 2.07 60 10 '•«3 56 2.07 60 39 1. 12 21 359 70 53 15 2.07 60 50 1. 18 50 2.14 61 18 1. 18 52 25 2.14 61 46 1. 17 20 34^S 71 44 2.22 62 I 1.22 53 18 2.22 62 29 1.20 53 2.22 62 56 1.20 19 18 33^0 72 54 II 2.22 63 14 1.27 45 2.31 63 41 1.25 53 20 2.3' 64 8 1.22 315 73 38 2.40 64 30 1.28 54 1 1 2.40 64 56 1.27 46 2.50 65 21 1.25 17 16 30.0 74 55 3 2.50 65 47 '•32 36 2.50 66 12 1.30 54 10 2.61 66 36 1.28 28.4 75 27 2.61 67 6 1-35 55 2-73 67 30 1-33 33 2.73 67 S3 1.32 15 26.8 76 50 2.86 68 27 1.38 22 2.86 68 50 '•37 SS 2.86 69 12 '•35 14 25.2 77 56 II 3.00 69 50 1.42 43 3.00 70 12 1.40 55 16 3.. 6 70 33 1.38 13 23^5 78 31 3.33 71 15 1.45 56 3 3^33 71 36 1.42 35 3^33 71 56 1.40 12 21.9 79 49 3-53 72 42 1.48 21 3^53 73 I '•45 S3 3^53 73 20 1.42 1 1 20.1 80 57 6 3-75 74 II 1.50 38 4-00 74 28 1.48 56 10 4.00 74 45 '•45 10 18.4 16.6 81 22 4.29 75 41 1.52 53 4.29 75 57 1.50 25 4.62 76 12 1.48 9 8 82 36 4.62 77 12 1.55 57 7 5.00 77 27 1.52 38 5.00 77 41 1.48 14.9 83 49 5-45 78 45 '•57 19 5-45 78 58 1.53 50 5-45 79 10 1.52 7 6 13- 84 58 6.67 80 19 1.58 30 6.67 80 30 1-57 57 I 6.67 80 41 '•S3 11.2 85 9 8.57 81 54 1.60 39 7.50 82 4 ••57 10 8^57 82 13 '•53 5 9.4 80 16 1 0.0 83 30 1.62 47 10.0 83 38 1.58 17 lO.O 83 45 '•55 4 7-5 87 22 12.0 85 7 1.62 53 15.0 85 13 1.58 23 15.0 85 18 '•57 3 H 88 27 30.0 86 44 1.63 57 30.0 86 48 1.60 27 30.0 86 52 '•57 2 3.8 89 29 60.0 88 22 1.63 59 60.0 88 24 1.60 29 60.0 88 26 '•57 I 19 90 30 90 58 90 30 90 0.0 a ecy b _A_ a 6c/ & A a Co' b A a t A fo' A 60' ^ 6ry ^ = 31° 30' d=^22°0' r/ = 32°30' Page 246] i 54° 1.483 K o = 33°0' a = 33° 30' a = 34° 0' \- \ * \ .25 22 6 1.25 37 8 .25 63 74-3 28 23 II 1.25 20 •27 23 3 1.25 51 .27 54 1.25 23 .25 62 73-6 29 59 1.25 36 .27 51 1.25 37 7 .27 23 42 1.28 38 .28 61 73-0 30 24 47 1. 25 52 0.28 24 39 1,28 23 0.28 24 29 1.28 55 0.28 60 723 31 25 35 1.25 37 9 •30 25 26 1.28 40 •30 25 16 1.28 38 12 .30 59 71.7 32 26 23 1.25 27 .30 26 13 1. 28 58 •32 26 3 1.28 30 •32 58 71.0 33 27 II 1.28 45 .32 27 1.28 38 17 •32 50 1.28 49 .32 57 703 34 58 1.28 38 4 •33 47 1.28 36 .33 27 37 1.28 39 8 •33 56 69.6 35 28 45 1.28 24 0-35 28 34 1.28 56 o^35 28 24 1.30 28 0-35 55 66.9 30 29 32 J. 28 45 •37 29 21 1.30 39 17 .37 29 10 1.30 49 •37 34 68.1 17 30 19 1.30 39 7 .38 30 7 1.30 39 .38 56 1.30 40 II •38 53 ^l-^ 38 31 5 1.30 30 .38 53 1.30 40 2 •38 30 42 '•33 34 .38 52 66.7 39 51 1.30 53 .40 31 39 1.30 25 •42 31 27 '•33 57 .42 51 6S9 40 32 Z7 1.30 40 17 0-43 32 25 1-33 50 0.42 32 12 1^33 41 22 0.42 50 65.2 41 33 23 1-33 43 •43 33 10 '•33 41 15 •43 57 ^•33 47 •45 49 ^^.1 42 34 8 1-33 41 9 •45 55 1.33 41 •47 33 42 1.36 42 14 •45 48 43 53 1-33 36 .48 34 40 1.36 42 9 •47 34 26 1.36 41 .48 47 62.8 44 35 38 1.36 42 5 .48 35 24 1.36 37 .48 35 10 1.40 43 10 .48 46 61.9 45 36 22 34 36 8 43 6 53 39 45 61. 1 a 60' 6 A a 60' h _A^ a 6c/ h A a t A 6c/ A 6c/ A 60/ d = 33° 0' d = 33° 30' ^ = 34° 0' 1.540 1.5" 1.483 [Page 247 4.S 46 47 48 49 50 51 52 53 54 55 ^7 q8 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 78 79 80 81 82 ^3 S4 85 80 87 88 89 90 a = 33° 0' A / / ^^6 22 ,.36 42 34 ^7 6 1.36 43 4 50 1.40 36 38 33 r.40 44 9 39 16 1.40 43 59 I 43 45 18 40 41 1.46 54 41 22 1.46 46 32 42 3 1.46 47 II 44 1.50 SI 43 24 1.54 48 33 44 3 1.54 49 16 42 1.58 50 I 45 20 ..s« 47 58 1.62 SI 35 46 35 ..67 52 24 47 II 1.71 53 15 46 1. 71 54 8 48 21 1.76 55 3 55 i.8z 59 19 28 1.82 56 57 50 I '•94 57 57 32 2.00 58 58 51 2 2.00 60 I 32 2.0T 61 6 •^2 I 2.22 62 13 28 231 63 22 54 2.40 64 33 53 19 2.50 65 40 43 2.61 67 54 6 1-73 08 16 28 3. CO (^9 34 48 3.16 70 54 55 7 3-33 72 I K 25 3-7S 73 38 41 4.0c 75 2 56 4.62 76 27 56 9 5.00 77 54 21 6.00 79 22 31 6.67 80 51 40 8.57 82 21 47 lO.O 83 52 53 15.0 85 23 57 30.0 86 55 59 60.0 88 27 57 QO _A 60' 0.50 ■53 ■55 •57 58 o, 60 ^6j ,65 .67 .70 0.72 •75 •77 ,8c .82 0,85 ,88 .92 .93 •97 ■23 = 33° 30' A 6o_' A Co' 9 1 / 36 8 ..36 43 6 52 1.40 37 37 35 1.40 44 8 38 18 I 43 41 39 1-43 45 15 42 1.43 50 40 24 1.46 46 27 41 5 1.50 47 4 45 1.50 43 42 25 I 50 48 23 43 5 1-54 49 5 44 I 58 48 44 22 1.58 50 33 45 1.62 51 19 n 1,62 52 7 46 14 ..67 56 so 1. 71 53 47 47 25 ..76 54 39 59 1.76 55 33 48 33 1.88 56 20 49 5 1.88 57 26 37 1-94 58 26 50 8 2.00 59 -^7 38 2,07 60 30 51 7 2.14 61 34 35 2.22 62 40 ^z 2 2.31 63 48 28 2.40 64 58 53 2.i;o 66 10 S3 17 2^73 67 24 39 ^•73 68 39 54 I 3.00 69 55 21 3-33 71 14 39 3-53 72 34 56 3-75 73 55 55 12 4.00 75 18 27 4.62 ■j6 42 40 5.00 78 7 52 6.00 79 34 56 2 7.50 81 2 10 8.57 82 30 17 lO.O 83 59 23 15.0 85 29 27 30.0 86 59 29 60.0 88 29 30 90 _A 60' 0.52 .52 •55 •57 .58 0.62 .62 .65 .67 .70 0.72 •75 •77 .80 .82 0.85 ■87 .90 ■93 •95 60^ A i^ = 33°30' 60' A 35 53 36 36 37 19 38 2 44 39 26 40 7 48 41 28 42 7 46 43 25 44 3 40 45 17 S3 46 28 47 3 37 48 10 42 49 14 44 50 14 43 51 10 37 52 3 27 50 53 12 33 53 54 II 28 44 58 55 II 22 32 41 48 53 57 59 56 o 2.00 2,00 2.07 2.22 2.22 2.31 2.50 2.G1 2-73 2.86 3.00 3^33 3^53 3-75 4.29 4.62 5-45 6.00 6.67 8-57 12.0 15.0 30.0 60.0 60^ A 43 39 44 9 41 45 14 48 46 23 59 47 37 48 16 56 49 37 50 20 51 5 SI 52 38 53 27 54 18 55 10 56 4 59 57 56 58 55 59 55 60 57 62 I 63 7 64 14 65 23 66 34 67 46 69 o 70 16 71 33 72 52 74 12 75 34 76 57 78 21 79 46 82 38 84 6 85 34 87 2 88 31 90 o A 60' •53 •55 •57 .58 0.60 .63 .65 .67 .68 0.72 •75 •77 .78 .82 0.85 .87 .9c •92 •95 d = 34°0' C 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 20 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 II 10 9 8 7 6 5 4 3 2 I 61. 1 60.3 59-4 58.S 57-6 56^7 557 54-8 53-8 52^8 51.8 50.7 49.6 48^5 47-4 46.3 4SI 43-9 42.7 41-5 40.2 58.9 37-6 36.2 348 334 32.0 30^5 29.0 27s 259 24-3 22.7 21. 1 19.4 17.7 16.0 14-3 12.5 10.8 9.0 7.2 1% 1.8 ao Page 248] i-455 1 428 1.402 B 10 1 1 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 a = 34° 30' a = 35°0' 60' / / 1.22 34 30 0. 49 1.20 30 I 39 1.22 31 2 28 1.20 Z^ 3 i« 1.22 34 4 7 1.20 36 0. 57 1.22 39 5 46 1.22 42 35 1.22 46 7 24 1.20 50 8 14 1.22 55 0. 9 3 1.22 35 52 1.22 6 10 41 1.22 12 II 30 1.22 19 12 19 1.22 26 0. 13 « 1.22 34 57 1.25 42 14 45 1.22 ^ 51 15 34 1. 25 3b I 16 22 1.22 II 0. 17 II 1.25 22 u 59 1.25 23 18 47 1.25 45 19 35 1.25 57 20 23 1.25 37 10 0. 21 II 1.28 24 5« I.2S 39 22 46 1.28 54 23 Z2, 1.28 i^ 10 24 20 1.28 26 0. 25 7 1.28 43 54 1.30 39 I 26 40 1.30 20 27 26 1.30 40 28 12 1.30 40 0. 5« 1.30 21 29 44 1-33 43 30 29 1.33 41 6 31 14 1.33 30 59 1-33 54 0. 32 44 1.36 42 19 33 28 1.36 46 34 12 1.36 43 13 50 1.40 42 35 39 44 II <=3 ^ b c? = 34*'30' 60' 60' A o 49 38 27 17 6 55 44 33 22 5 6 7 8 II 9 o 48 10 37 11 26 12 14 13 3 51 14 40 15 28 16 16 17 4 52 18 40 19 28 20 15 21 3 50 22 37 23 24 24 II 57 25 44 26 30 27 16 28 2 47 29 32 30 17 31 2 46 32 30 33 14 58 34 41 35 24 25 25 60; A 35 o o I 2 4 6 9 12 16 20 25 30 36 42 49 36 4 13 22 31 41 52 37 4 16 28 41 o 55 38 10 25 41 57 39 15 33 52 40 II 31 52 41 14 37 42 I 26 51 43 18 45 44 14 43 0.00 .02 .02 .03 •03 0.05 .05 •07 .07 .08 o.oS 0.13 •15 •15 •15 •»7 0.18 0.23 •25 •25 .27 •27 0.30 .30 .32 • 32 • 33 0-35 •37 •38 .40 •42 0.42 •45 •4'; .48 .4S _A 60' ii = 35° 0' a = 35° 30' d, 60' A_ 60' / / 1.22 35 30 49 1.22 30 I 38 1.22 31 2 27 1.25 32 3 15 1.22 34 4 4 1.22 36 53 1.22 39 5 42 1.25 42 6 30 1.22 46 7 19 1.22 50 8 8 1.2^ 55 56 1.22 36 9 45 1.25 6 10 33 1.22 12 II 22 1.25 19 12 10 1-25 27 58 1.25 35 13 46 1.25 43 14 34 1,25 52 15 22 1. 25 37 2 16 10 1.25 12 58 1.28 23 17 45 1.2^ 34 18 33 1.28 46 19 20 1.28 59 20 7 1.28 38 12 54 1.28 26 21 41 1.28 41 22 28 1.28 56 23 15 1.30 39 12 24 I 1.30 29 47 1.30 46 25 33 1.30 40 4 26 19 1.30 23 27 5 '•33 43 50 1.33 41 3 28 35 1-33 24 29 20 1-33 46 30 5 1.36 42 9 49 1.36 33 31 33 1.36 58 32 17 1.40 43 23 33 1.40 50 43 1.40 44 17 34 26 1.40 45 35 9 45 15 6^' b A <; = 35°30' 0.00 .02 .02 .03 .03 0.05 .05 ,07 .07 .08 0.08 •13 0.13 • 13 .'5 • 17 • 17 0.18 .18 .22 0.23 •25 •25 •27 .28 0.28 •30 •32 •33 .33 0-35 • 37 .38 .40 •42 0.42 .47 •5^ _A 60' 90 89 88 l7 86 82 81 80 7? 78 76 75 74 73 72 71 70 69 68 67 66 65 64 63 62 61 60 59 58 57 56 55 54 53 52 51 50 48 47 46 45 90.0 89.4 88.9 88.3 87.7 87.1 86.6 86.0 854 84.8 84.2 83.6 83.0 82.5 81.9 81.3 80.7 80.1 79-4 78.8 78.2 77.6 77.0 76.3 75-7 750 74-4 73-7 73-0 72.4 71.7 71.0 70.3 69.6 68.9 68.1 67.A 66.6 659 65.1 64.3 635 62.7 61.9 61.0 60.2 M5S 1.428 1.402 [Page 249 a -34° 30' a=35°0' a = 35" 3(y V k d 60' A z\ A 60' > d \ bo/ A z\ A 60' > d \ 6 36 22 '•43 42 •52 36 6 '•43 45 14 •52 51 ••43 45 .53 44 59^3 47 37 4 1.43 45 13 •55 48 1.43 45 •55 36 33 1.46 46 17 •55 43 58^4 48 46 ■•43 46 •57 37 30 1.46 46 18 •57 37 14 1.46 50 •57 42 57-S JO 38 28 ..46 46 20 .58 38 II 1.46 52 .58 55 1.50 47 24 •58 41 56.6 50 39 9 1.46 55 0.60 52 1.50 47 27 0.60 38 35 1.50 59 0.60 40 55.6 51 50 1.50 47 31 .63 39 32 1.50 48 3 .63 39 15 1.54 48 35 .62 39 54-7 52 40 30 1.50 48 9 .65 40 12 1.50 41 .63 54 '•54 49 12 •65 38 53-7 53 41 10 1. 54 48 .67 52 1.54 49 19 .67 40 33 '•54 51 .67 37 52^7 54 49 1.54 49 28 .68 41 31 1.58 59 .70 41 12 ..58 50 31 .68 36 51-7 55 42 28 1.58 50 9 0.72 42 9 1.58 50 41 0.70 50 1.62 51 12 0.70 35 50^7 56 43 6 1.62 52 •73 47 1.62 51 23 .73 42 27 1.62 54 •73 34 49.6 57 43 1.62 51 3^ •77 43 24 1.67 52 7 •71 43 4 1.67 52 38 •75 33 43.5 58 44 20 1.67 52 22 .78 44 1.67 53 .78 40 1.71 53 23 .78 32 47^4 59 56 1.67 53 9 .82 36 1. 71 53 40 .80 44 15 1. 71 54 10 .80 31 46^3 60 45 32 1.71 58 0.83 45 II 1. 71 54 28 0.83 50 1.76 5? 0.83 30 45-2 61 46 7 1.76 54 48 .87 46 ..76 55 18 .87 45 24 1.82 55 48 .85 29 44.0 62 41 1.76 5 5 40 .88 46 20 1.82 56 10 .88 57 1.82 56 39 ,88 28 42.8 63 47 15 1.82 56 33 .92 53 1.88 57 3 .90 46 30 1.88 H ^l .90 ^Z 41.6 64 48 1.88 57 28 •95 47 25 1.94 57 .93 47 2 1.94 58 26 .92 26 40.4 65 48 20 1.94 58 25 0.97 56 1.94 58 53 0.97 33 2.00 59 21 0.95 25 39.x 60 51 2.00 59 23 1. 00 48 27 2.07 59 51 .98 48 3 2.07 60 18 .98 24 37-8 (>7 49 21 2.07 60 23 1.03 56 2.07 60 50 1,02 32 2.07 61 17 1.02 23 36^5 68 50 2.14 61 25 1.05 49 25 2.14 61 51 1.05 49 I 2.22 62 18 1.03 22 35-2 69 50 18 2.22 62 28 1.08 53 2.22 62 54 1.07 28 2.22 63 20 1.05 21 33.8 70 45 2.31 63 33 1. 10 50 20 2^3> 63 58 1. 10 55 2.40 64 23 1.08 20 32^4 71 51 II 2.40 64 39 1.13 46 2.50 65 4 1. 12 50 20 2.50 65 28 1. 12 19 3i^o 72 36 2.50 65 47 1. 17 51 10 2.50 66 II 1.15 44 2.50 66 35 1. 13 18 29-5 73 52 2.61 66 57 1.20 34 2.61 67 20 1. 18 51 8 2^73 ^l 43 1. 15 'Z 28.1 74 23 2-73 68 9 1.22 57 2.86 68 31 1.20 30 2.86 68 52 1. 18 16 26.6 75 45 2.86 69 22 1.25 52 18 3.00 69 43 1.22 51 3.00 70 3 1.22 IS 25.0 76 53 6 3.16 70 37 1.27 38 3.16 70 56 i.2<; 52 II 3.16 71 16 1.23 14 235 77 25 3-33 71 53 1.28 57 3^33 72 II 1.28 30 3-53 72 30 1.25 13 21.9 78 43 3.53 13 10 1.32 53 15 3-75 73 28 1.28 47 3^75 73 45 1.27 12 20.3 79 54 4.00 74 29 1-33 31 4.00 74 45 1.32 53 3 4.00 75 I 1.30 II 18.7 80 15 4 29 75 49 1-37 46 4.29 76 4 '•33 18 4.62 76 19 I^32 10 17. 1 81 29 4.62 77 II '•37 54 4.62 77 24 1-37 31 5.00 77 38 1-33 9 154 82 42 5-45 78 33 1.40 13 5-45 78 46 '•37 43 5^45 78 58 1.33 8 138 83 53 6.00 79 57 1.40 24 6.67 80 8 1.38 54 6.00 80 18 '•37 7 12. 1 84 55 3 7.50 81 21 1.42 33 7.50 81 31 K38 54 4 7.50 81 40 '•37 6 10.4 85 II 8.57 82 46 '•43 41 8.57 82 54 1.42 12 ro.o 83 2 1.38 5 8.7 SO 18 12.0 84 12 1.45 48 12.0 84 19 1.42 18 12.0 84 25 1.38 4 7.0 87 23 15.0 85 39 1.45 53 15.0 85 44 1.42 23 15.0 85 48 1.40 3 5-2 88 27 30.0 87 6 1.45 57 30.0 87 9 1.42 27 •50.0 87 12 1.40 2 3-5 89 29 60.0 88 33 '•45 59 60. c 88 34 '•43 29 60.0 SB 36 1.40 I 1-7 90 30 90 55 90 30 90 0.0 S 60' 6 A d 60' 5 A a 60' 6 A a t A 1 60' A 60' A 60' d = S4>°2(y d = 35°0' ^/ = 35°30' Page 250] 1.376 I-35I 1.327 ir \b a = 36° 0' a = 36° 30' a = 37°0' \ 'v \d 60' \ t A \ d 60' X t A \ d 60' \ t A A b\ ^\ A z\ 60' h\ A Z\ 60' h\ A z\ 6c/ A A / / I / / / 1.22 36 0.00 1.25 36 30 0.00 1.25 37 0.00 90 90.0 I 49 1. 25 .02 48 1.25 30 .02 48 1.25 .02 89 89.4 88. {; 2 I 37 1.22 I .02 I 36 1.22 31 .02 I 36 1.25 I .02 88 3 2 26 1.25 2 .03 2 25 1.25 32 •03 2 24 1.25 2 •03 87 88.2 4 3 14 1.22 4 •03 3 13 1.25 34 •03 3 12 1.28 4 .03 86 87.6 5 4 3 1.25 6 0.05 4 I 1.25 36 0.05 59 1.25 6 0.05 85 87.0 51 1.25 9 .05 49 1.25 39 .05 4 47 1. 25 9 .05 84 86.4 7 5 39 1.22 12 .07 5 37 1.25 42 .07 5 35 1.25 12 .07 83 85.8 8 6 28 1.25 16 .07 6 25 1.25 46 .07 6 23 1.25 16 .07 82 85.2 9 7 16 1.22 20 .08 7 13 1.25 50 .oS 7 II 1.28 20 .08 81 84.6 10 8 5 1.25 25 0.08 8 I 1.25 55 0. 10 58 1.25 25 0. 10 80 84.0 1 1 53 1.25 35 .10 49 1.25 37 I .10 8 46 1.25 31 .10 79 834 12 9 41 1.25 36 .12 9 37 1.25 7 .10 9 34 1.28 37 .10 78 82.8 13 10 29 1.25 43 .12 10 25 1.25 13 .12 10 21 1.28 43 .12 77 82.2 14 II 17 1.25 50 .12 II 13 1.28 20 .12 II 8 1.25 50 . 12 76 81.6 15 12 5 1.25 57 0.13 12 1.25 27 0.13 56 1.28 57 0.13 75 80.9 16 53 1.25 37 5 .13 48 1.25 35 •15 12 43 1.28 38 5 •'5 74 80.3 17 13 41 1.25 13 •'S 13 36 1.28 44 •15 13 30 1.28 14 •15 73 79^7 18 14 29 1.28 22 •17 14 23 1.28 53 •17 14 17 1.28 23 •'7 72 79^1 19 15 16 1.25 32 .18 15 10 1.28 38 3 •'7 15 4 1.28 33 .i8 71 78.4 20 16 4 1.28 43 0.18 . 57 1.28 13 0.18 51 1.28 44 0.18 70 77^8 21 51 1.28 54 .18 16 44 1.28 24 .20 16 38 1.28 55 .18 69 77.1 22 17 38 1.2S 38 5 .20 17 31 1.28 36 .20 17 25 1.30 39 6 ,20 68 76^5 23 18 25 1.28 17 .22 18 18 1.28 48 .22 18 II 1.30 18 .22 67 75-8 24 19 12 1,28 30 .22 19 5 1.28 39 I .22 57 1.30 31 •23 66 75-2 25 59 1.28 43 0.23 H 1.30 14 0.23 19 43 1.30 45 0.23 65 74-S 20 20 46 1. 28 57 •25 20 38 1.30 28 .25 20 29 1.30 59 •23 64 73-8 27 21 33 1.30 39 12 .25 21 24 1.30 43 •25 21 15 1.30 40 13 .27 63 73^1 28 22 19 1.30 27 •27 22 10 1.30 58 .27 22 I 1.30 29 •27 62 72.S 29 23 5 1.30 43 .28 56 K30 40 14 .28 47 '•33 45 .28 61 7i^8 30 51 1.30 40 0.28 23 42 '•33 31 0.28 23 32 1-33 41 2 0.28 60 71.0 31 24 37 1.30 17 •3° 24 27 1.30 48 •30 24 17 '•33 19 •30 5§ 70^3 32 25 23 1.30 35 •32 25 13 ^•3i 41 6 •32 25 2 '•33 37 •32 58 69.6 33 26 9 »-33 54 •33 . 58 '•33 25 •33 . 47 '•33 56 •33 57 68.9 34 54 ••33 41 14 •33 26 43 '•33 45 •35 26 32 1.36 42 16 •35 56 68.1 35 27 39 J-33 H 0-37 27 28 1.36 42 6 0.35 27 16 1.36 37 0-35 55 ^i 36 28 24 1.36 56 •37 28 12 1.36 27 •37 28 1.36 58 •37 54 37 29 8 1.36 42 18 '3^ 56 1.36 49 •38 44 1.40 43 20 •38 53 65^9 38 5| 1.36 41 .38 29 40 1.36 43 12 .40 29 27 1.40 43 .40 52 6SI 39 30 36 1.36 43 4 .42 30 24 1.40 36 •42 30 10 1.40 44 7 • 42 51 64-3 40 31 20 1.40 29 0.43 31 7 1.40 44 I 0.42 53 1.40 32 0.43 50 63s 41 32 3 1.40 55 •43 50 1.40 26 •45 31 36 1-43 58 .43 4§ 62.7 42 46 1.40 44 21 •47 32 33 1.43 53 •45 32 18 '•43 45 24 •47 48 61.3 43 33 29 1.40 49 •47 33 15 1.43 45 20 .48 33 "•43 52 •47 47 61.0 44 34 12 1.43 45 17 .48 57 1.43 49 .48 42 1.46 46 20 .48 46 60. 1 45 54 46 34 39 46 18 34 23 49 45 59-3 a 6& h _A_ a 6 25 38.1 66 39 2.07 60 46 •97 47 I 5 2.14 61 12 •97 51 2.14 61 39 •95 24 36^8 67 48 8 2.14 61 44 1. 00 43 2.14 62 10 .98 47 19 2.22 62 36 •97 23 3S5 68 36 2.22 62 44 1.02 48 1 1 2.22 63 9 1.02 46 2.22 63 34 1. 00 22 34-2 69 49 3 2.31 63 45 1.05 38 2.40 64 10 1.03 48 13 2.4c 64 34 1.02 21 32.8 70 29 2.40 64 48 1.07 49 3 2.40 6s 12 i.o<; 38 2.50 65 35 1.05 20 31S 71 54 2,50 65 52 1. 10 28 2.50 66 15 1.08 49 2 2.50 66 38 1.07 19 30.1 72 50 18 2.61 66 58 1. 12 52 2.73 67 20 1. 10 26 2.73 67 42 1. 10 18 28.6 73 41 2-73 68 5 1. 15 50 14 ^•73 68 26 i^ij 48 2.86 68 48 1. 12 17 27.2 74 51 3 2.86 69 14 1. 17 36 3.00 ■'')9 34 1. 15 50 9 3.00 69 55 i^i3 16 257 75 24 3.16 70 24 1. 18 56 3.16 70 43 1. 18 29 3.16 71 3 1. 15 15 24-3 76 43 3-33 71 35 1.22 51 15 3-33 71 54 i.iS 48 3^33 72 12 1. 18 14 22.7 77 52 I 3-53 72 48 1.23 33 3-53 73 5 1.22 51 6 3-75 73 23 1.20 13 21.2 78 18 3-75 74 2 1.25 50 3^75 74 18 1.2"; 22 4.00 74 35 1.20 12 19.7 79 34 4.00 75 17 1.27 52 6 4.29 75 33 1.25 37 4.29 75 47 '•23 II 18. 1 80 49 4.62 76 33 1.30 20 4.62 76 48 1.27 51 4.62 77 I 1. 25 10 16.5 81 'S3 2 5.0c 77 51 1.30 33 5.00 78 4 1. 28 52 4 5.00 78 16 1.27 9 8 14.9 82 14 5-45 79 9 1.33 45 5-45 79 21 1.30 16 6.00 79 32 1.28 13-3 83 25 6.67 80 29 1-33 56 6.67 80 39 '•32 26 6.67 80 49 1.28 I 11.7 84 34 7.50 81 49 1-35 53 5 7.50 81 58 1.32 35 7.50 82 6 1.30 6 10. 85 42 8.57 83 10 1-35 13 lo.o 83 17 '•33 43 lO.O 83 24 1-32 S 8.4 86 49 12.0 84 31 1-37 19 12.0 84 37 1-33 49 12.0 84 43 1.32 4 6.7 87 54 20.0 85 53 '•37 24 20.0 85 57 1-35 54 20.0 86 2 1.32 3 5-0 88 57 30.0 ^7 15 1-37 27 30.0 87 18 1-35 57 30.0 87 21 1.32 2 3^4 89 59 60.0 88 37 1.38 29 60.0 88 39 '•35 59 60.0 88 40 1^33 I 1-7 90 54 90 30 90 53 90 0.0 6c/ b A 60' A ecy h A 1 a a , h a a t T 60^ A 6& ' ~A 6o> i = 36°0' d = 36°30' d = 3T(y Page 252] 1.303 X.280 X.2S7 10 1 1 12 13 14 15 16 17 18 19 20 21 22 ^3 24 25 26 27 28 29 30 31 32 33 34 35 3(^ 17 38 39 40 4' 42 43 44 45 a =37° 30' 60' A 60' y / 1.25 17 30 0. 48 1.2S 30 I 35 1.25 31 2 23 1.2S 32 3 10 1.25 34 S8 1.21; 36 0. 4 46 1.28 39 5 33 1.2S 42 . 6 20 1.25 46 . 7 8 1.28 51 , 55 1.28 56 0. 8 42 1.25 38 I 9 30 1.28 7 10 17 1.28 13 II 4 1.28 20 51 1.28 28 0. 12 38 1.28 36 • 13 25 1.28 45 ^ 14 12 I.'^O 54 58 1.28 39 4 15 45 1.30 14 0. 16 31 1.30 25 17 17 1.30 37 18 3 1.30 49 49 1.30 40 2 19 35 r.30 15 0. 20 21 1.30 29 21 7 ■•33 44 52 1-33 41 22 37 1.33 16 23 22 1.33 ZZ 0. 24 7 1.33 52 52 1.36 42 8 25 36 1.36 27 26 20 ..36 47 27 4 1.36 43 8 0. 48 1.40 29 28 31 1.40 51 29 M 1.40 44 14 57 1.40 38 30 40 ••43 45 3 0. 31 22 '•43 28 12. 4 r.46 55 45 ..46 46 23 33 26 1.46 51 34 7 47 20 08 A 6c/ d = 37°30' a = 38°0' 60' A 6 2.40 2.50 2.61 2.73 2.86 3.00 3.00 3-33 3^53 3-75 4.00 4.29 5.00 5.00 6.00 5.67 7.50 8.57 lO.O 15.0 20.0 30.0 60.0 60' A 49 53 50 23 54 51 26 59 52 33 53 8 44 54 21 59 55 39 56 19 57 I 44 58 28 59 13 59 60 47 61 35 62 25 63 16 64 8 65 2 57 66 53 67 50 68 48 69 47 70 47 71 49 72 51 73 55 75 o 76 5 77 II 78 18 79 26 80 35 81 44 82 54 84 4 85 15 86 26 87 37 90 o _A 60' 0.5c •52 •53 •55 •57 0.58 ,60 .62 .63 .67 0.67 .70 •72 •73 •75 0.77 .80 .80 •83 •85 0.87 .90 •92 •93 •95 0.97 .98 1. 00 •03 •03 .07 .08 .08 1. 10 1. 12 .13 ■15 ••5 ••7 •17 1. 18 .18 1.20 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 II 10 9 8 7 6 5 4 3 2 I 57-5 56.6 5S7 54-8 53-8 52.8 51-9 50-9 49.8 48.8 47-7 46.7 45-6 44-5 43-4 42.2 41.1 39-9 38.7 37-5 36^2 35-0 33-7 32^4 3i^i 29.8 2S.4 27.1 25-7 243 22.8 21.4 19.9 18.5 17.0 155 14.0 12.5 10.9 9.4 7.8 6.3 4-7 3^1 1.6 0.0 rf = 40°0' Page 256] I .171 I. 150 1.130 I a = 40° 30' a = 41°0' = 41° 30' \ \ * 60' A \ < A Z\ 60' K 60' A Z\ A 60' 60' A A 60' A o / / / / / / O 1.30 40 30 0.00 '•33 41 0.00 '•33 41 30 0.00 90 90.0 I 46 1-33 30 .02 45 '.30 .02 45 '•33 30 .02 ^2 89-3 2 I 31 1.30 31 .02 I 31 '•33 I .02 I 30 '•33 31 .02 88 88.7 3 2 17 '•33 32 •03 2 16 '•33 2 •03 2 IS '•33 32 .03 §7 88.0 4 3 2 1.30 34 .03 3 I '•33 4 ■03 3 '■33 34 •0? 86 87.4 5 48 1.30 36 0.05 46 '•33 6 0,05 45 ..36 36 ©.or ^5 86.7 6 4 34 '•33 39 .07 4 31 1.30 9 .07 4 29 '•33 39 .07 ^ 86.1 7 5 19 1.30 43 .07 5 17 '•33 13 .07 5 14 '•33 43 .07 83 85.4 8 6 5 '•33 47 .07 6 2 '•33 17 .07 59 '•33 47 .07 82 84.7 9 50 1.33 51 .08 47 '•33 21 .oS 6 44 '.36 51 .oS 81 84.1 10 7 35 1.30 56 0. 10 7 32 '•33 26 0. 10 7 28 1.33 56 0. 10 80 83^4 II 8 21 '•33 41 2 .10 8 17 '•33 32 .10 8 13 '■33 42 2 .10 79 82.7 12 9 6 1.33 8 .10 9 2 '•33 38 . 10 58 ..36 8 .10 78 82,1 13 51 '•33 14 .12 47 1.36 44 .12 9 42 ..36 14 .12 77 81.4 14 10 36 '•33 21 • 13 10 31 '•33 51 .13 10 26 '•33 21 •'3 76 80.7 I', II 21 '•33 29 0.13 1 1 16 1.36 59 0,13 II II ..36 29 0.13 75 80.0 i6 12 6 '•33 37 •■'5 12 '•33 42 7 ■'5 55 1.36 37 •'5 74 79^3 17 51 1.36 46 •'5 45 1.36 16 •17 12 39 1.36 46 .17 73 78.7 i8 13 35 ••33 55 .'7 13 29 1.36 26 •17 13 23 1.36 56 •17 72 78.0 19 14 20 1.36 42 5 .18 14 13 1.36 36 •17 14 7 ..36 43 6 .18 71 77-3 20 15 4 '•33 16 0.18 57 1.36 46 o.iS 51 1.40 17 0.18 70 76.6 21 49 ..36 27 .20 15 41 1.36 57 .20 15 34 1.36 28 .20 69 75.9 22 16 33 1.36 39 .20 16 25 1.36 43 9 .22 16 18 1.40 40 .20 68 7S2 23 17 17 1.36 51 .22 17 9 1.36 22 .22 17 I 1.40 52 .22 f7 74-4 24 18 I 1.36 43 4 •23 53 1.40 35 .22 44 1.40 44 5 •23 66 73-7 25 45 '•36 18 0.23 18 36 1.40 48 0.25 18 27 1.40 19 0.23 65 73-0 26 19 29 1.40 32 •25 19 19 1.40 44 3 •25 19 10 1.40 33 •25 64 72.3 27 20 12 1.40 47 .27 20 2 1.40 18 .25 53 '■43 48 .27 f3 7i^S 28 55 1.40 44 3 .27 45 1.40 33 .27 20 35 '■43 45 4 ■27 62 70.8 29 21 38 1.40 19 .28 21 28 '•43 49 .28 21 17 '.43 20 ,28 61 70.0 30 22 21 1.40 36 0.30 22 10 '•43 45 6 0.30 59 '•43 37 0.30 60 &3 31 23 4 '•43 54 .30 52 '•43 24 •32 22 41 '•43 55 •30 59 68.5 32 46 '•43 45 12 •32 ^3 34 '•43 43 •32 23 23 1.46 46 13 •32 58 ^^•7 33 24 28 '•43 31 .33 24 16 '•43 46 2 •33 24 4 1.46 32 .33 57 66.9 34 25 10 1.43 SI •35 58 1.46 22 •33 45 1.46 52 .33 56 66.1 35 52 1.46 46 12 ^•35 25 39 1.46 42 ^•35 25 26 1.46 47 12 o^37 55 6S3 36 26 33 ..46 33 •37 26 20 1.46 47 3 •37 26 7 1.50 34 .37 54 64^5 37 27 14 1.46 55 .38 27 I 1.50 25 •38 47 1.50 56 .38 53 63-7 38 55 1.46 47 18 .40 41 1.50 48 .40 27 27 1.50 48 19 .38 52 62.9 39 28 36 1.50 42 •42 28 21 1.50 48 12 .42 28 7 1.50 42 • 42 51 62.0 40 29 16 1.50 48 7 V^ 29 I 1.50 37 0.42 47 '•54 49 7 0.42 50 61.2 41 56 '•54 32 ■43 41 '■54 49 2 • 43 29 26 '•54 32 .43 ^2 60.3 42 30 35 1.54 58 •45 30 20 '•54 28 •45 30 5 ..58 58 •45 48 59^4 43 31 14 '•54 49 25 .48 59 1.58 55 •47 43 ..58 50 25 .47 47 58.5 44 53 1.54 54 .48 31 37 ..58 50 23 .48 31 21 ..58 53 .48 46 57-6 45 T,2 32 50 23 32 15 52 59 51 22 45 56.7 60' A 60' A 60^ b A ■L' a ■ h 7- a h a, a t A " 60' A Oo' A 60' a = 40° SO' rf=4ro' d = 4>i°30' 1. 171 1.150 1. 130 [Page 257 a = 40° 30' d\ 60' A 6(y a = 41°0' A A^ 6 45 31 42 1.62 51 51 0.50 31 25 1.62 52 21 0.48 31 9 1.67 52 50 0.4S 45 56.0 46 32 19 1.67 52 21 .52 32 2 1.67 50 •50 45 1. 71 53 19 .50 44 550 47 55 1.67 52 •52 38 1. 71 53 20 • 53 32 20 1. 71 49 •52 43 54-1 48 33 31 1.67 53 23 •53 33 13 1. 71 52 •53 55 1. 71 54 20 •53 42 53-1 49 34 7 1. 71 55 .57 48 1. 71 54 24 •55 33 30 1.76 52 •55 41 52.1 50 42 1.71 54 29 O.S7 34 23 ..76 57 0.57 34 4 1.76 55 25 0.57 40 51-2 51 35 17 ..76 55 3 .58 57 1.76 55 31 .58 38 1.82 59 •58 39 50.2 52 51 1.82 38 .62 35 31 1.82 56 6 .60 35 II 1.82 56 34 .60 38 49.2 53 36 24 1.82 56 15 .62 36 4 1.82 42 .62 44 1.82 57 10 .62 ^l 48.1 54 57 1.82 52 .63 37 1.88 57 19 .63 36 17 1.94 47 .62 36 47.1 55 37 30 1. 88 57 30 0.65 37 9 1.88 57 0.65 48 1.94 58 24 0.65 35 46.0 56 38 2 1.94 58 9 .68 41 1.94 58 36 .68 37 19 1.94 59 3 .67 34 45-0 57 33 1.94 50 .68 38 12 2.00 59 17 .68 50 2.00 43 .68 33 43-9 58 39 4 2.00 59 31 •72 42 2.00 58 .70 38 20 2.07 60 24 .68 32 42.8 59 34 2.0c 60 14 •72 39 12 2.07 60 40 •72 49 2.07 61 5 •72 31 41.7 60 40 4 2.07 57 0.75 41 2.14 61 23 0.73 39 18 2.14 48 0.73 30 40^5 61 33 2.14 61 42 •77 40 9 2.14 62 7 •75 46 2.22 62 32 .75 29 39-4 62 41 I 2.22 62 28 .78 37 2.22 52 .78 40 13 2.22 63 17 •75 28 38.2 63 28 2-3' 63 15 .78 41 4 2.31 63 39 .78 40 2.31 64 2 .78 ""l 37-0 64 54 2.31 64 2 .82 30 2.31 64 26 .82 41 6 2.40 49 .80 26 3S8 65 42 20 2.40 51 0.83 56 2.40 65 15 0.82 31 2.50 65 37 0.82 25 34-6 60 45 2.40 65 41 .85 42 21 2.50 66 4 •83 55 2.50 66 26 • 83 24 33^4 67 43 10 2.61 66 32 .88 45 2.61 54 .87 42 19 2.61 67 16 .85 23 32.1 68 33 2.61 67 25 .88 43 8 2.73 67 46 .88 42 2.73 68 7 .87 22 30.9 69 56 2-73 68 18 .90 30 2.86 68 39 .88 43 4 2.86 59 .88 21 29.6 70 44 18 2.86 69 12 0.92 51 2.86 69 32 0.90 25 3.00 69 52 0.88 20 28.3 71 39 3.00 70 7 •93 44 12 3.16 70 26 •93 45 3.16 70 45 •92 19 18 27.0 72 59 3.. 6 71 3 •97 31 3.16 71 22 •93 44 4 3^33 71 40 •93 257 73 45 18 3-33 72 I •97 50 3-33 72 18 •95 22 3-33 72 36 •93 'I 16 24-3 74 36 3-53 59 •98 45 8 3-53 73 15 .98 40 3^53 73 32 •95 23.0 75 53 3-75 73 58 1. 00 25 4.00 74 14 0.98 57 4.00 74 29 0.97 15 21.6 76 46 9 4.00 74 58 1. 00 40 4.00 75 13 1. 00 45 12 4.00 71 ^l .98 14 20.3 77 24 4.29 75 58 1.03 55 4.29 76 13 1. 00 27 4.29 76 26 1. 00 13 18.9 78 38 4.62 77 1.03 46 9 4.62 77 13 1.02 41 5.00 77 26 1. 00 12 '1-5 79 51 5.00 78 2 1.05 22 5.00 78 14 1.03 53 5.00 78 26 1.02 II 16. 1 80 47 3 6.00 79 5 1.07 34 6.00 79 16 1.05 46 5 6.00 79 27 1.03 10 14.6 81 13 6.00 80 9 1.07 44 6.00 80 19 1.05 15 6.67 80 29 1.03 9 8 13-2 82 23 6.67 81 13 1.08 54 7.50 81 22 1.07 24 7.50 81 31 1.03 II.8 83 32 8.57 82 18 1.08 47 2 7.50 82 26 1.07 32 7.50 ^^ 33 1.05 7 6 10.3 84 39 8.57 83 23 1.08 10 lO.O 83 30 1.07 40 1 0.0 83 36 1.05 8.8 85 46 12.0 84 28 1. 10 16 12.0 84 34 1.08 46 12.0 84 39 1.07 5 7.4 86 51 15.0 85 34 1. 10 21 15.0 85 39 1.08 51 15.0 85 43 1.07 4 5-9 87 55 20.0 86 40 1. 12 25 20.0 86 44 1.08 55 20.0 86 47 1.07 3 4.4 88 58 60.0 S7 47 1. 10 28 60.0 87 49 1.08 58 60.0 87 51 1.08 2 30 89 59 60.0 88 53 1. 12 29 60.0 88 54 1. 10 59 60.0 88 56 1.07 I i-S 90 48 90 30 90 47 90 0.0 a 60' h _A a 60' 6 A 60' a — 6 _A_ a t A 60' A 6c/ A 6 65-7 64.9 64.1 63.2 62.ZI 61.5 60.6 59^8 58^9 58.0 56.1 SS-2 60' I 054 1 036 1.018 [Page $261 \ a = 43° 30' a=44°0' a =44° 30' \ \ ** \ d 60' ^ t A d 60' \ ^ A \ d 60' ~^x < A \ A r \ A z\ 60' r \j A Z\ 60' h \ A 2\ 60' ^\ P\ o / / / / / / 45 ?,o 51 ..67 53 19 0.4S 30 34 1.67 53 47 0.48 30 17 1. 71 54 16 0.4S 45 55-2 40 31 27 1. 71 48 •50 31 10 1. 71 54 16 •50 52 1.76 45 .48 44 54-3 47 32 2 1. 71 54 18 •52 45 ..76 46 •52 31 26 1.76 55 14 •52 43 53-3 48 37 ..76 49 •53 32 19 1.76 55 17 •53 32 1.76 . 45 •52 42 52-4 49 00 1 1 ..76 55 21 •53 53 1.82 49 •53 34 1.82 56 16 •55 41 51-4 50 45 1.76 . 53 0.57 33 26 1.82 56 21 0.57 33 7 1.82 49 0.55 40 50-4 51 34 19 1.82 56 27 .58 59 1.82 55 •57 40 1.88 57 22 •57 39 49.4 ^2 52 1.88 57 2 .58 34 32 1.88 57 29 •58 34 12 1.88 56 .58 38 43.4 5 3 35 24 1.88 37 ,60 35 4 1.94 58 4 .60 44 1.94 58 31 .60 37 47-3 54 56 1.94 58 13 •63 35 1.94 40 .62 35 15 2.00 59 7 .62 36 46-3 55 36 27 1.94 51 0.65 36 6 2.00 59 17 0.65 45 2.00 44 0.62 35 45-2 56 58 2.00 59 30 .65 36 2.00 56 .65 36 15 2.07 60 21 .65 34 44.2 57 37 28 2.00 60 9 •67 37 6 2.07 60 35 .67 44 2,07 61 .67 33 43-1 58 58 2.07 49 .70 35 2.07 61 15 .68 37 13 2.14 40 .68 32 42.0 59 38 27 2.14 61 31 .70 38 4 2.14 56 .70 41 2.14 62 21 .68 31 40.9 60 55 2.14 62 13 0.72 32 2.22 62 38 0.72 38 9 2.22 63 2 0.70 30 39-7 61 39 23 2.22 56 •75 59 2.22 63 21 •72 36 2.31 44 .73 29 38^6 62 50 2.31 63 41 •75 39 26 2.31 64 4 •75 39 2 2.40 64 28 •73 28 37.4 63 40 16 2.40 64 26 •77 52 2.40 49 •77 27 2.40 65 12 •75 27 36.3 64 41 2.40 65 12 .80 40 17 2.50 65 35 .78 52 2.50 57 .78 26 35^ I 65 41 6 2.50 66 0.80 41 2.50 66 22 0.80 40 16 2.50 66 44 0.78 25 33^9 66 30 2.61 48 .82 41 t; 2.61 67 10 .80 40 2-73 67 31 .80 24 327 67 53 2.61 &7 37 .85 28 2-73 58 .83 41 2 2-73 68 19 .82 23 31-4 68 42 16 2.86 68 28 .85 50 2.86 68 48 .83 24 2.86 69 8 •83 22 30.2 69 37 2.86 69 19 .87 42 II 3.00 69 38 •87 45 3.00 58 •85 21 28.9 70 58 3.00 70 II 0.88 31 3.00 70 30 0.87 42 5 3.16 70 49 0.85 20 27.7 71 43 18 3.16 7^ 4 .90 51 3.16 71 22 .88 24 3.16 71 40 .88 19 26.4 72 37 3-33 58 .92 43 10 3.33 72 15 .90 43 3^53 72 33 .88 18 25.1 73 55 3-33 72 53 .92 28 3^53 73 9 .92 43 3-53 73 26 .90 17 23.8 74 44 13 3-75 73 48 •95 45 3-75 74 4 •93 17 3-75 74 20 .92 16 22.4 75 29 4.00 74 45 0.95 44 I 4.00 75 0.93 33 4.00 75 15 0.92 15 21. 1 76 44 4.29 75 42 •97 16 4.29 . 56 •95 48 4.62 76 10 •93 14 19.7 77 58 4.29 ■j6 40 .98 30 4.62 76 53 •97 44 I 4.62 77 6 .95 13 18.4 78 45 12 5.00 77 39 .98 43 5.00 77 51 •97 14 5.00 78 3 .97 12 17.0 79 24 S-45 78 38 1. 00 55 5^45 78 49 .98 26 5-45 79 I •97 II 15-6 80 35 5-45 79 38 1. 00 45 6 6.00 79 48 1. 00 37 6,00 59 0.97 TO 14.2 81 46 6.67 80 38 1.02 16 6.00 80 48 1. 00 47 6.67 80 57 .98 9 12.8 82 55 7.50 81 39 1.03 26 7.50 81 48 1. 00 56 7.50 81 56 1. 00 8 11.4 l^ 46 3 8.57 82 41 1.03 34 8.57 82 48 1.02 45 4 8.57 82 56 1. 00 7 lO.O 84 10 10.0 83 43 1.03 41 1 0.0 83 49 1.02 II lO.O 83 56 1. 00 6 8.6 fs 16 12.0 84 45 1.05 47 15.0 84 50 1.03 17 15.0 84 56 1. 00 5 7.2 86 21 15.0 85 48 1.05 51 15.0 85 52 1.03 21 15.0 85 56 1.02 4 5-7 87 25 20.0 86 51 1.05 55 20.0 86 54 1.03 25 20.0 86 57 1.02 3 4-3 88 28 60.0 87 54 1.05 58 60.0 87 56 1.03 28 60.0 87 58 1. 02 2 2.9 89 29 60.0 88 57 i.os 59 60.0 88 58 1.03 29 60.0 88 59 1.02 I 1.4 90 30 90 46 90 30 90 0.0 a 60' h A z 60' b A 2 60' h A a t A 60' A 60' A bo' ^ = 43° 30' (Z = 44°0' 7 72 19 57 1.50 48 6 .18 50 '•54 36 •17 43 '•54 49 6 .'7 71 7S9 20 13 n 1.50 17 0.18 13 29 1.50 46 0.18 13 22 '•54 16 0.18 70 75-1 21 14 17 1.50 28 .20 14 9 1.54 57 .20 14 I '•54 27 .20 69 74-3 22 5^ 1.54 40 .20 48 '•54 49 9 .20 40 '•54 39 .20 68 73-5 23 15 36 1.50 52 .22 IS 27 1-54 21 .22 15 19 1.58 51 .22 67 72.8 24 16 16 1.54 49 5 22 16 6 '•54 34 .23 57 1.5S 50 4 •23 66 72.0 25 55 1.54 18 0.23 45 '•54 48 0.23 16 35 1.58 18 0.23 65 71.2 26 17 34 1.54 32 .25 17 24 1.58 50 2 •25 17 13 1.58 32 •23 64 70.4 69.6 27 18 13 1.58 47 .25 18 2 ..58 17 •25 51 1.58 46 •25 63 28 51 1.54 50 2 .27 40 ..58 32 .27 18 29 1.58 51 I •27 62 68.8 29 19 30 1.58 18 .28 19 18 ..58 48 ,28 19 7 1.58 17 .28 61 67.9 30 20 8 1.58 35 0.28 56 1.58 51 5 0.28 45 1.62 34 0.28 60 67.1 31 46 \.^% 52 .30 20 34 1.62 22 .30 20 22 1.62 51 .30 5^ 66.3 32 21 24 1.62 51 10 •32 21 1 1 1.62 40 .30 59 1.62 52 9 .32 58 n-i 33 22 I 1.62 29 •32 48 1.62 58 .32 21 36 1.67 28 .32 57 34 38 1.62 48 •33 22 25 1.62 52 17 •33 22 12 1.67 47 •33 56 637 35 23 15 1.62 52 8 0-35 23 2 ..67 37 0-35 48 1.67 53 7 ^•33 55 62.9 36 52 1.67 29 •37 38 ..67 58 •35 23 24 ..67 27 • 35 54 62.0 1>7 24 28 1.67 51 •37 24 14 1.67 53 19 •37 24 1. 71 48 •37 53 61.1 38 25 4 1.67 53 13 •38 50 1. 71 41 •38 35 1.71 54 10 .38 52 60.3 39 40 1.67 36 .38 25 25 1. 71 54 4 .40 25 10 1.76 33 .38 51 594 40 26 16 1. 71 59 0.40 26 1. 71 28 0.40 44 ..76 56 0.40 50 57^5 41 51 1.7! 54 23 .42 35 1.76 52 •42 26 18 ..76 5 5 20 .42 40 4^ 27 26 ..76 48 •43 27 9 1.76 55 17 .42 52 ..76 45 .42 48 56^6 43 28 1.76 55 14 •45 43 1.76 42 •45 27 26 1.82 56 10 • 43 47 55-7 44 34 ..76 41 •45 28 17 1.82 56 9 •45 59 1.82 36 •45 46 54^8 45 29 8 56 8 50 36 28 32 57 3 45 53.8 60' a — & A a 60' b A a 60' 6 A a t A 60' A 6(y A 60' r/ = 46°30' d=^ro' d = M°ZO' 0. ?49 0933 0.916 [Page 265 \ fl-46°30' a = 47^0' a = 47° 30' \ V \ d 60' X t A ^ d 60' X t A \ d 60' \ t A »\ A A \ A z\ 60' r \ A Z\ 60' r N A z\ Cc/ ^\ o / / / / / / 45 29 8 1.82 s6 8 0.47 28 50 1.82 56 36 0.47 28 32 1.82 57 3 0.47 45 53^8 46 41 1.S2 36 .48 29 23 1. 88 57 4 .48 29 5 1.88 . 31 .48 44 i 529 47 30 14 i.SS 57 5 .50 55 1.88 33 .48 37 '•94 58 .48 43 51^9 48 46 I.8S 35 .52 30 27 1.88 58 2 •52 JO 8 1.94 29 .50 42 509 49 31 18 1.94 58 6 '52 59 1.94 33 •52 39 '•94 59 •52 41 49.9 50 49 '•94 17 0-53 31 30 2.00 59 4 0.53 31 10 2.00 59 30 '^•53 40 48.9 51 32 20 1.94 59 9 •55 32 2.00 . 36 .53 40 2.00 60 2 •53 3§ 47-9 52 51 2.0Q 42 •57 30 2.00 60 8 •57 i^ 10 2.07 . 34 .55 38 46.9 53 IZ 21 2.07 60 16 .58 i2> 2.07 42 •57 39 2.07 61 7 •57 H 45-9 54 50 2.07 SI .58 29 2.07 61 16 .60 12, 8 2.14 41 .58 36 44.8 55 34 19 2.07 61 26 0.62 58 2.14 52 0.60 36 2.14 62 16 0.60 35 43-8 56 48 2.14 62 3 .62 34 26 2.22 62 28 .60 34 4 2.22 . 52 .62 34 42.7 'r.7 35 16 2.22 40 .63 53 2.22 63 4 •63 31 2.31 63 29 .62 33 41.6 ^8 43 2.22 63 18 .65 35 20 2.31 42 .65 57 2.3' 64 6 •63 32 40^5 59 36 10 2-3' 57 .67 46 2.31 64 21 .65 35 23 2.40 44 .65 31 39-4 60 36 2.40 64 37 0.68 1>^ 12 2.40 65 0.67 48 2.40 65 23 0.67 30 38^3 DI 17 1 2.40 65 18 .68 }>7 2.50 40 .68 ze 13 2.50 66 3 .67 29 37-2 62 26 2.<;o 59 .70 17 I 2.50 66 21 .70 Z7 2.61 . 43 .70 28 36.0 ^l 50 2.61 66 41 •73 25 2.61 67 3 •72 1,7 2.61 67 25 .70 27 34-9 64 38 13 2.61 67 25 •73 48 2-73 46 •73 23 2.73 68 7 •72 26 33-7 65 36 2-7? 68 9 0.75 38 10 2-73 68 30 0.73 4 5 2.86 . 50 0.73 25 32^5 60 58 2.86 54 •75 32 2.86 69 14 •75 38 6 2.86 69 34 •73 24 313 67 39 io 3.00 69 39 .78 53 3.00 59 ■71 27 3.00 70 18 •75 23 30.1 68 39 3.00 70 26 .78 39 13 3.00 70 45 •11 47 3.. 6 71 3 •11 22 28.9 69 59 3-16 71 13 .80 11 3^33 71 31 .80 39 6 3-33 49 .78 21 27.7 70 40 18 3.33 72 I 0.82 SI 3-33 72 19 0.80 24 3-33 72 36 0.78 20 26.5 71 36 3-53 50 .82 40 9 3^53 71 7 .82 42 3-53 73 23 .80 19 25.2 72 53 3-53 7'>> 39 .83 26 3-75 56 .82 59 3-75 74 II .82 18 24.0 73 41 10 3-75 74 29 .85 42 3-75 74 45 •83 40 !■; 4.00 75 .82 ^l 22.7 74 26 4.29 75 20 .87 58 4.29 75 35 .85 30 4.29 49 .83 16 21.4 75 40 4.29 76 12 0.87 41 12 4.29 76 26 0.85 44 4.29 7^ 39 0.85 15 20.1 76 54 4.62 77 4 .88 26 4.62 77 17 .87 58 ^.00 77 30 •85 14 18.8 77 42 7 5.00 57 .88 39 5.00 78 9 .88 41 10 5.00 78 21 .87 13 'I'^ 78 19 5.00 78 50 .90 51 5^45 79 2 .88 22 5-45 79 13 .87 12 16.2 79 31 6.00 79 44 .90 42 2 6. CO SS .88 33 6.00 80 5 .88 II 14.9 80 41 6.67 80 38 0.92 12 6.67 80 48 0.90 43 6.67 58 0.88 :o 13^6 81 50 7.50 81 33 •93 21 7.50 81 42 .90 52 7.50 81 51 .88 I 12.2 82 58 7.50 82 29 .92 29 8^S7 82 36 .92 42 8.75 82 44 .90 10.9 83 43 6 lO.O 83 24 •93 36 lO.O 83 31 •92 7 lO.O ^i 38 .90 I i1 84 12 1 0.0 84 20 .93 42 lO.O 84 26 .92 13 12.0 84 32 .90 8.2 85 18 15.0 85 16 0.95 48 15.0 85 21 0.93 18 15.0 85 26 0.90 5 6.8 86 22 15.0 86 13 •93 52 15.0 86 17 .92 22 15.0 86 20 •92 4 5-5 87 26 30.0 87 9 •95 56 30.0 87 12 •93 26 30.0 87 15 .92 3 4.1 88 28 30.0 88 6 .95 58 30.0 88 8 •93 28 30.0 88 10 .92 2 2.7 89 30 — 89 3 .95 43 — 89 4 •93 30 — 89 5 .92 I 1.4 90 30 90 90 30 90 0.0 1 60' & A % 60' I A a 60' h A a t A !| 6^ A 60' ^ 60' £Z = 46°30' rf = 47''0' q' = 47°30' Page 266] apoo 0. 885 aj J69 K a = 48°0' a = 48° 30' a = 49° 0' V \" X^' 60' \ t A \ d 60' \ * A \ d ^' \ < 1 A A A A \ A Z \ 6(y h\ A Z\ 60' aX^ a ZX^ 6(y ^\ A o / .20 67 72.0 24 15 19 1.62 52 2 .22 15 9 1.62 32 .22 5? 1.67 53 I .22 66 71.2 25 . 56 1.62 15 0.23 46 1.67 45 0.23 15 35 1.67 14 0.23 65 7o^3 26 16 33 1.67 29 •25 16 22 1.67 59 .25 16 II ..67 28 64 69-5 27 17 9 1.67 44 •25 58 1.67 53 13 .25 47 1.67 42 •25 63 68.7 28 45 1.67 59 .27 17 34 1.67 28 .27 17 2-\ 1. 71 57 •27 62 67.8 29 18 21 1.67 53 15 .27 18 10 1.71 44 • 27 58 1. 71 54 13 •27 61 67.0 30 57 1.67 ^l 0.28 45 1.71 54 0.28 18 z?> 1. 71 29 0.28 60 66.1 31 19 33 1.71 48 ,28 19 20 1. 71 17 .28 19 8 ..76 46 .2$ 59 653 32 20 8 1. 71 54 5 .30 55 1. 71 34 .30 42 1.76 55 3 .30 58 tn 33 43 1. 71 23 .32 20 30 1.76 5- •32 20 16 1.76 21 .30 .57 34 21 18 1.76 42 .32 21 4 1.76 55 II •V- 50 1.76 39 •32 56 62.7 35 53 1.76 55 I ©•33 38 ..76 30 o^33 21 24 1.82 58 0-33 55 61.8 3(> 22 26 1.76 21 •35 22 12 1.76 50 .33 57 1.82 56 18 •35 54 60.9 37 23 1.76 42 .35 46 1.82 56 10 •37 22 30 1.82 39 .35 53 60.0 38 34 1.82 56 3 •37 23 19 1.82 32 •37 23 3 1.82 57 •37 5- 59-1 39 24 7 1.82 25 .38 52 1.88 54 .37 36 1.88 22 .37 51 58^2 40 40 1.82 48 0.40 24 24 1.88 57 16 0.38 24 8 1.88 44 0.38 50 57^3 41 25 13 1.88 57 12 .40 56 1.88 39 .40 40 1.94 58 7 .40 49 : 56-3 42 . 45 1.88 „ 36 •42 25 28 1.88 58 3 .42 25 II 1.94 31 .40 48 i 55^4 43 26 17 1.88 5^ I .42 26 1.94 28 .42 42 1.94 55 .42 47 54.5 44 49 1.94 26 .43 31 1.94 53 •43 26 13 1.94 59 20 •43 46 53-5 45 2J 20 52 27 2 59 19 44 46 45 52^5 a 6(y b A a 60' h A_ a 60' & A a / A 60' ^ 60' A 60' c ? = 49° SO' d = 50^ 0' cf = 50°3a I 0. 854 0.839 0.824 1 Pag( b269 \ a = 49° 30' a=50°0' a = 50° 30' k V \ d ^'"' \ * A \ d 60' \ i A \ d 60' \. t A A A r V"-" Z\ 60' A \ A z \ 60' A \ A z\ 6cy A ^\ o J S ' / / 1 / 45 27 20 ■•94 58 52 0.45 27 2 2.00 59 19 0.45 26 44 2.00 59 46 0.43 45 525 40 51 2.00 59 19 ■47 32 2.00 46 •45 27 14 2.07 60 12 •45 44 51.6 47 28 21 1. 00 47 .47 28 2 2.00 60 13 •47 43 2.07 39 •47 43 50.6 48 51 2.00 60 15 .48 32 2.07 41 .48 28 12 2.07 61 7 .4S 42 49.6 49 29 21 2.07 44 .50 29 I 2.07 61 10 .50 41 2,07 36 .48 41 48.6 50 50 2.07 61 14 0.52 3? 2.14 40 0.50 29 10 2.14 62 5 0.50 40 47.6 51 30 IQ 2.14 . 45 .52 58 2.14 62 10 •52 38 2.22 35 •52 39 46.6 52 47 2.14 62 16 •53 30 26 2.22 41 •53 30 5 2.22 61 6 .52 38 45-6 53 31 15 2.22 48 •55 53 2.22 63 13 •53 32 2.31 . ^7 •S3 37 44-5 54 42 2.22 63 21 •55 31 20 2.31 45 •55 58 2.31 64 9 •55 36 43-5 55 32 9 2.3' . 54 0.57 46 2.31 64 18 0.57 31 24 2.40 42 0.55 35 42.4 56 35 2.^0 64 28 •58 32 12 2.40 52 •57 49 2.40 65 15 •57 34 41.4 57 33 2.40 65 3 .60 37 2.40 65 26 .60 32 14 2.40 49 •58 33 40.3 58 25 2.40 39 .60 !>}> 2 2.50 66 2 .60 39 2. ^0 66 24 .60 32 39-2 59 50 2.50 66 15 .62 26 2.50 38 .60 33 3 2.61 67 .60 31 38.1 60 34 14 2.61 52 0.63 50 2.61 67 14 0.63 26 2.73 36 0.62 30 37^0 61 1>7 2.61 67 30 •65 34 13 2.71 52 •63 48 2.73 68 13 .63 29 35-9 62 35 2-73 68 9 .65 35 2.86 68 30 .65 34 10 2.86 51 .63 28 34-8 63 22 2.86 48 .67 56 2.86 69 9 .65 31 2.S6 69 29 •65 27 33^6 64 43 2.86 69 28 .68 35 17 2.86 48 .67 52 3.00 70 8 .67 26 32^S 65 36 4 3.00 70 9 0.70 ^l 3.00 70 28 0.6S 35 12 3.16 48 0.67 25 3i^3 60 24 3.16 51 .70 58 3.16 71 9 .70 31 3.16 71 28 .68 24 30.2 67 43 3.16 71 11, .72 36 17 3.33 51 .70 50 3.33 72 9 .68 23 29.0 68 37 2 3-33 ■J1 16 •72 35 3.33 72 32, •72 36 8 3-33 50 .7c 22 27.8 69 20 3-53 59 •73 53 3-53 71 16 •72 26 3.7s 73 32 •72 21 26.6 70 37 3-75 73 43 0.75 ?>7 10 3.75 59 0.73 42 3^75 74 15 0.73 20 25^4 71 53 3-75 74 28 •75 26 4.00 74 43 •75 58 4.00 59 •73 19 24.2 72 38 9 4.00 75 13 •n 41 4.00 75 28 •75 37 13 4.0c 75 43 •73 18 23.0 73 24 4.29 59 •77 56 4.29 7(^ 13 •77 28 4.29 76 27 •75 17 21.8 74 38 4.62 76 45 .78 38 10 4.62 59 •77 42 4.62 77 12 •75 16 20.5 75 51 4.62 77 32 0.80 23 5.00 77 45 0.78 55 5.00 57 0.77 15 193 70 39 4 5.00 78 20 .80 35 l^.OO 78 32 -'S 38 7 5.45 78 43 .78 14 18.0 77 16 5-45 79 8 .80 47 6.00 79 19 ^78 18 6.00 79 30 •78 13 16.8 78 27 6.00 56 .82 57 6.00 80 6 .80 28 6.00 80 17 .78 12 155 70 37 6.67 80 45 .82 39 7 6.67 54 .80 3^ 6.67 81 4 •78 II 14.2 80 46 7.50 81 34 0.82 16 7.50 81 42 0.82 47 7.50 51 0.80 10 130 81 54 7.50 82 23 .83 24 7.50 82 31 .82 55 7.50 82 39 .80 9 11.7 82 40 2 lO.O 83 13 .83 32 lO.O 83 20 •83 39 3 lO.O 83 27 .82 8 10.4 83 8 10,0 84 3 .85 38 lO.C 84 10 .82 9 lO.O 84 16 .82 7 9.1 84 14 12.0 54 .85 44 I2.0 59 •83 15 15.0 85 5 .82 6 7.8 85 19 15.0 85 45 0.85 49 15.0 85 49 0.83 19 15.0 54 0.82 5 6^5 86 23 20.0 86 36 .85 53 20.0 86 39 .83 23 20.0 86 43 .82 4 5-2 87 26 30.0 Zj 27 •85 56 30.0 87 29 •83 26 30.0 87 32 .82 3 3-9 88 28 30.0 88 18 •85 58 30.0 88 19 •85 28 30.0 88 21 .82 2 2.6 8q 30 — 89 9 .85 40 — 89 10 .83 30 — 89 10 .83 I 1^3 90 30 90 90 30 90 r 0.0 a 60' 6 A a 60' b A a ^' 6 _A_ a / A ec/ A 60' A 60' rf = 49°30' fZ = 50°0' tf = 50°30' Page 270] 0.810 0-795 0.7S1 \b a = 51°0' a = 51° 30' a = 52°(y I \' \ d 60' \< A \ d 60' \ t A \ d 6& |\ i A A b\ ^ \ A z\ 60' A \ A z\ 60' * \ A z\ 60' A A / / / / / / g i.;& 51 0.00 1.62 51 30 0.00 1.62 52 0.00 ?° 90.0 I 38 1.58 .02 37 1.58 30 .02 37 1.62 .02 8q 89. a 2 I 16 1.62 I .02 I 15 1.62 31 .02 I 14 1.62 I .02 88 88.4 3 53 ..58 2 •03 52 1.62 32 .03 51 1.62 2 •C3 P 87.7 4 2 31 1.58 4 .03 2 29 ..58 34 •03 2 28 1.62 4 •03 86 86.9 5 3 9 ..58 6 0.05 3 7 1.62 36 0.05 3 5 1.67 6 0.05 !5 86.x b 47 1.62 9 •.07 44 1.62 39 .05 41 1.62 9 .05 ^ 8S3 7 4 24 ..58 13 .07 4 21 1.62 42 .07 4 18 1.62 12 •07 ^3 84.5 S 5 2 1.62 17 .07 58 1.62 46 .c8 55 1.62 16 .08 82 83.7 9 39 1.62 21 .08 5 35 1.62 51 .08 5 32 1.67 21 .08 81 82.9 10 6 16 1.58 26 o.oS 6 12 1.62 56 0.08 6 8 1.62 26 0.08 80 82.x I I 54 1.62 31 .10 49 1.62 52 I . 10 45 ..67 31 . 10 79 8i.d S0.6 12 7 31 1.62 37 .12 7 26 1.62 7 .10 7 21 1.62 37 .10 78 13 8 8 1,62 44 .12 8 3 1.62 13 .12 58 1.67 43 .12 77 79-8 14 45 1.62 51 .12 40 ..67 20 •13 8 34 1.67 50 •>3 76 79-0 IS 9 22 1.62 58 0.13 9 16 1.62 28 0.13 9 10 1.67 58 0-I3 75 78.2 16 59 1.62 52 6 ••5 53 ..67 36 •15 46 ..67 53 6 •»3 74 77-4 17 10 s6 1.62 15 •15 TO 29 1.67 45 •15 10 22 ..67 14 •15 73 76.S 18 II 13 ..67 24 .17 II 5 1.67 54 •'5 58 ..67 23 •«7 72 75-7 19 49 1.62 34 .17 41 1.67 53 3 •'7 II 34 1. 71 33 •>7 7^. 74-9 20 12 26 ..67 44 0.18 12 17 1.67 13 0.18 12 9 ..67 43 0.18 70 74.1 21 13 2 1.67 55 .18 53 ..67 24 .18 45 1. 71 54 .18 6q 73-3 22 38 ..67 53 6 .20 13 29 ..67 35 .20 13 20 1. 71 54 5 .20 68 72.5 23 14 14 1.67 18 .20 14 5 1. 71 47 .22 55 1.71 17 .20 67 71.6 24 50 ..67 30 .22 40 1.71 54 .22 14 30 1. 71 29 .22 66 70.8 25 15 26 1. 71 43 0.23 15 15 1.71 13 0.22 15 5 1.71 42 0.22 65 70.0 7;6 16 I 1. 71 57 •23 . 50 1.71 26 •23 40 1.76 55 •23 ^4 69.1 27 36 1. 71 54 II •25 16 25 1. 71 40 •25 16 14 ..76 55 9 •25 63 68.3 28 17 II 1.7! 26 •27 17 ..76 55 •25 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 18 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 14 .28 42 1.76 43 .28 18 29 1.82 56 II .28 5§ 64.8 32 19 29 1.7^^ 31 .30 19 16 1.82 56 •30 19 2 1.82 28 .30 58 63.9 33 20 3 1.76 49 •30 49 1.82 18 .30 35 1.82 46 •30 ^l 63.1 34 37 1.82 56 7 .32 20 22 1.82 36 •32 20 8 1.82 57 4 •32 56 62.2 35 21 10 1.82 26 0-33 55 1.82 55 0.32 41 1.88 23 0.32 55 61.3 3(^ 43 1.82 46 •35 21 28 1,88 57 14 •33 21 13 1.88 42 • 33 54 60.4 37 22 16 1.88 57 7 •35 22 1.88 34 •35 45 1.88 58 2 • 35 53 59- § 38 48 1. 88 28 •35 32 1.S8 „ 55 •37 22 17 1.94 23 •35 52 5S.6 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 0.3S ^1 1.94 39 0,38 23 19 1.94 59 6 0.38 50 56.7 41 24 23 1.94 34 .40 24 6 1.94 59 2 .38 50 2.00 29 .38 49 48 55-8 42 54 1.94 58 .40 37 2.00 25 .4c 24 20 2.00 52 • 38 54-8 43 25 25 2.00 59 22 .42 25 7 2. 00 49 .40 50 2.07 60 15 •42 46 53-9 44 55 2.00 47 •42 37 2.00 60 13 •43 25 19 2.07 40 .42 52-9 45 26 25 60 12 26 7 39 48 61 5 45 52.0 a 60' b A a 60' h A a 60' 6 _A a / A 60' A do' A 60' d = 5i°0' J = 51° 30' c? = 52°0' o.Sio 0-795 0.781 [Page 271 \ a = 51°0' a = 51° 30' a = 52° 0' \ ^ c\ V \ d h\ 60' A z\ A 60' 60' A z\ A 60' 60' A z\ A 60' \ ' ^0 ' / ^ ° ' ,< ^0 / p 45 26 25 2.00 60 12 0-43 j(j 7 2.07 60 39 o^43 25 48 2.07 61 5 ^•43 45 52.0 46 55 2.07 38 •45 36 2.07 61 5 •43 26 17 2.07 31 •43 44 51.0 47 27 24 2.07 61 5 •47 27 5 2.14 31 •45 46 2.14 . 57 •45 43 50.0 48 53 2.14 33 •47 33 2.14 58 •47 27 14 2.22 62 24 •47 42 49.0 49 28 21 2.14 62 I .48 28 I 2.14 62 26 .48 41 2.22 52 •47 41 48.0 50 49 2.14 . 30 0.50 29 2.22 ^ 55 0.48 28 8 2.22 63 20 0.48 40 47.0 51 29 17 2.22 63 .50 56 2.22 62, 24 .50 35 2.31 49 .50 39 46.0 52 44 2-31 . 3° •52 29 23 2.31 r 54 •52 29 I 2.31 64 19 .50 38 45-0 53 30 10 2.31 64 I •S3 49 2.31 64 25 •52 27 2.40 49 .52 37 43^9 54 36 2.31 ZZ .53 30 15 2.40 . 56 •53 52 2.40 65 20 •53 36 42.9 55 31 2 2.40 65 5 0.5s 40 2.50 65 28 0.55 30 17 2.50 .. 52 ^•53 35 41.8 56 27 2.50 38 •57 31 4 2.50 66 I •57 41 2.50 66 24 •55 34 40.8 57 51 2.50 66 12 .58 28 2.50 35 •57 31 5 2.61 57 •57 33 39-7 58 32 15 2.50 47 •58 52 2.61 67 9 •57 28 2.61 67 31 •57 32 38.6 59 39 2.61 67 22 .60 32 15 2^73 43 .60 51 2.73 68 5 .58 31 37-5 60 33 2 2.73 58 0.60 37 2^73 68 19 0.60 32 13 2.73 40 o.t;8 30 36^4 61 24 2.86 68 34 .62 59 2.86 55 ,60 35 2.86 69 IS .60 ^§ 35^3 62 45 2.86 69 1 1 •63 ZZ 20 2.86 69 31 .63 56 3.00 51 .62 28 34-2 ^i 34 6 2,86 49 •63 41 3.00 70 9 .63 ZZ 16 3.CX) 70 28 •63 ^l 33-1 64 27 3.00 70 27 .65 34 I 3.00 47 .63 36 3^i6 71 6 .63 26 31^9 65 47 3.16 71 6 0.67 21 3^i6 71 25 0.65 55 3^33 44 0.63 25 30.8 66 35 6 3-33 46 .67 40 3^33 72 4 •67 34 13 3^33 72 22 .65 24 29.6 f7 24 3-33 72 26 .68 58 3^53 44 .67 31 3-53 73 I .67 23 28.5 68 42 3-53 73 7 .70 35 15 3^53 7Z 24 .68 48 3^53 41 •67 22 273 69 59 3-75 49 .70 32 3-75 74 5 .70 35 5 3^75 74 21 .68 21 26.1 70 i^ 15 3-75 74 31 0.72 48 4.00 47 0.70 21 4.00 75 2 0.7c 20 24.9 71 3J 4.00 75 14 •72 36 3 4.00 75 29 .70 36 4.29 44 .70 19 237 72 46 4.29 57 .73 18 4.29 76 II .72 50 4.29 76 26 .70 18 22.5 73 37 4.62 76 41 •73 32 4.62 H •73 36 4 4.62 77 8 .72 'I 21-3 74 13 4.62 77 25 •75 45 4.62 77 38 •73 17 5.00 51 •72 16 20.1 75 26 5.00 78 10 0.75 58 5.00 78 22 ©•73 29 5.00 78 34 o^73 15 18.9 76 38 5-45 55 '77 Z7 10 5-45 79 6 •75 41 5-45 79 18 •73 14 17.7 77 49 6.00 79 41 ■77 21 6.00 51 •75 52 6.00 80 2 •73 13 16.5 78 n 59 6.00 80 27 •77 31 6.67 80 36 •77 Z7 2 6.67 46 •75 12 15.2 79 38 9 6,67 81 13 .78 40 6.67 81 22 •77 II 7.50 81 31 •75 II 139 80 18 7.50 82 0.78 49 7.50 82 8 0.77 19 7.50 82 16 0.77 10 12.7 81 26 8.57 47 .78 57 8.57 54 .78 • 27 8.57 S3 2 •77 9 11.4 82 33 lO.O 83 34 .80 38 4 lO.O 83 41 .78 34 lO.O 48 •77 8 10.2 l^ 39 lO.O 84 22 ,80 10 12.0 84 28 •78 40 12.0 84 34 ■77 7 8.9 84 45 15.0 85 10 .80 15 i5^o 85 15 .78 45 12.0 85 20 •77 6 7.6 85 49 15.0 r 58 0.80 19 15.0 86 2 0.78 50 20.0 86 6 0.78 5 6.4 80 53 20,0 86 46 .80 23 20.0 49 .80 53 20.0 53 •77 4 5^1 87 56 30.0 ^7 34 .82 26 30.0 87 Z7 .78 56 30.0 87 39 •78 3 3^8 88 58 30.0 88 23 .80 28 30.0 88 24 .80 58 30.0 88 26 .78 2 2.6 89 39 — 89 II .82 30 — 89 12 .80 38 — 89 13 .78 I 1-3 90 90 30 90 90 0.0 a 60' h _A_ a 60^ h -A a 6^ & A a t A 60' A 60' A 60' d = bi°(y d = b\°2Q' d = 52°0' Page 272] 0.767 0.7S4 0. 740 V = 52° 30' a=53°0' a = 53" 30' V \ " \ d 60' \ < A \ d 60' \^ A \ d 60' \ i A \ \ b\ h\ A z\ 60' ^ \ A z\ 60' A \ A z\ 60' ^\ ^\ o 1 / / y / 1 i.f).--. 52 30 0.00 r.67 53 0.00 ..67 53 3^ 0.00 90 90.0 1 il ..6- 30 .02 36 ..67 .02 36 1. 71 30 .02 89 89.2 2 I 13 1.62 31 .02 I 12 ..67 I .02 I II ..67 31 .02 88 88.4 3 50 ..67 32 •03 48 ..67 2 •03 47 ..67 32 •03 87 87.6 4 2 26 1.62 34 .03 2 24 ..67 4 •03 2 23 1.71 34 •03 86 86.8 5 3 3 ..67 36 0.05 3 1.67 6 0.05 58 1.67 36 0.05 85 86.0 39 ..67 39 .05 36 ..67 9 •'^5 3 34 1.71 39 .05 84 85.2 7 4 15 1.62 42 .07 4 12 ..67 12 .07 4 9 1.67 42 •07 83 84.4 83.6 8 52 -.67 46 .07 48 1.67 16 .07 45 1.71 46 .07 82 9 5 28 1.67 50 .08 5 24 1.67 .20 .oS 5 20 1.67 50 .08 81 82.8 10 6 4 ..67 55 0. 10 6 r.67 25 o.oS 56 r.71 55 O.oS 80 82.0 1 1 40 1.67 53 I .10 36 1. 71 30 . 10 6 31 1.71 54 .ro 79 81.2 12 7 16 ..67 7 .10 7 II ..67 36 .12 7 6 r.71 6 .ro 78 80.4 13 5^ ..67 13 .12 47 1. 71 43 .12 41 r.71 12 .12 77 79.6 14 8 28 ..67 20 .12 8 22 1.67 50 .12 8 16 r.71 19 •13 76 78.7 15 9 4 ..67 27 0.13 58 1.71 57 0.13 51 r.7i 27 0,13 75 77-9 lO 40 1. 71 35 .'S 9 Vc 1. 71 54 5 •13 9 26 r.7r 35 •13 74 77.1 17 10 15 ..67 44 •15 10 8 r.71 13 •IS lO I 1. 71 43 ••5 73 76.3 18 51 1. 71 53 .'5 43 1. 71 22 •17 36 r.76 52 •«5 72 75-5 19 II 26 1. 71 54 2 •«7 II x8 1. 71 32 .17 II 10 1.76 55 I ••7 71 74.6 20 12 I 1. 71 12 0.18 53 1.76 42 0.17 44 1.76 II 0.18 70 73-8 21 36 1. 71 23 .18 12 27 1. 71 52 .18 12 18 1.76 22 .18 69 73-0 22 13 II 1. 71 34 .20 13 2 1.76 55 3 .20 52 1.76 11 .rS 68 72.1 23 46 ..76 46 .20 36 1.76 15 .20 13 26 1.76 44 .20 67 71-3 24 14 20 ..76 58 .22 14 10 ..76 27 .22 14 1.76 56 .22 66 70.4 25 54 ..76 55 II 0.22 44 1.76 40 0.22 34 1.82 56 9 0.22 65 69.6 26 15 28 ..76 24 •23 15 t8 1.82 53 •23 15 7 1.82 22 •23 64 68.7 27 16 2 ..76 38 •25 ^ 51 ..76 56 7 •25 40 1.82 36 .23 63 67.9 28 36 1.76 53 •25 16 25 1.82 22 •25 16 13 r.82 50 •25 62 67.0 29 17 10 1.82 56 8 •27 58 1.82 37 ■25 46 1,88 57 5 •27 61 66.1 30 43 1.82 24 0.27 17 31 1.88 52 0.27 17 18 r.88 21 0.27 60 65.2 31 18 16 1.82 40 .28 18 3 t.82 57 8 .2? 50 r.88 17 .28 59 64.4 32 49 1.82 57 .28 36 1.88 25 .28 18 22 1.88 54 .28 58 635 33 19 22 1.88 57 14 .30 19 8 1.88 42 •30 54 1.88 58 II •30 57 62.6 34 54 1.88 l^ •32 40 1.88 58 •3- 19 26 r.94 29 •3° 56 61.7 35 20 26 1.88 51 0.32 20 12 1.94 19 0.32 57 r.94 47 0.32 55 60.8 3 t \ A 60' A o / ^° ' / / 23 5^ ^ / 45 •24 34 2.22 62 49 0.40 24 15 2.22 63 14 0.40 2.31 ^3 40 0.40 4°5 50.9 40 25 I 2.22 63 13 .42 4^ 2.31 . 38 .42 24 22 2-3J 64 4 .42 44 49-9 47 28 2.31 38 •43 25 8 2.31 64 3 •43 48 2.31 29 .42 43 48.9 48 . 54 2.31 64 4 •45 ^ 34 2^3i 29 •43 25 14 2.40 54 •43 42 47-9 49 26 20 2.31 31 •45 26 2.40 55 •45 39 2.40 65 20 .43 41 46.9 50 46 2.40 . 58 0.47 25 2,40 65 22 0.45 26 4 2.50 46 0.45 40 45-9 51 27 II 2.40 65 26 •47 50 2.50 49 •47 28 2.50 66 13 •47 39 44,8 52 36 2.50 .. 54 .48 27 14 2.50 66 17 •48 52 2.50 41 •47 38 43-8 53 28 2.50 66 23 .48 3S 2.61 . 46 .48 27 16 2.61 67 9 .48 37 42.8 54 24 2.61 52 .50 28 I 2.61 67 15 •50 39 2.61 38 • 48 36 41.7 55 47 2.61 67 22 0.52 24 2.61 .0 "^5 0.50 28 2 2.73 68 7 0.50 35 40.7 56 29 10 2-73 .0 53 •53 47 2^73 68 15 •52 24 2.86 37 •52 34 39^6 57 32 2-73 68 25 .53 29 9 2.86 46 •53 45 2.86 69 8 •52 33 38^6 58 54 2.86 57 .53 30 2.86 69 18 •53 29 6 2.86 39 •52 32 37^5 59 30 15 2.86 69 29 •55 51 3.00 50 •53 27 3.00 70 10 •53 31 36^4 60 ^^ 3.00 70 2 0.57 30 II 3.00 70 22 ^•55 47 3.00 42 0.55 30 35-3 61 56 3.00 36 •57 31 3.00 55 •57 30 7 3.16 71 15 .55 29 34^3 62 31 16 3.16 71 10 .58 51 3.16 71 29 •57 26 3^33 48 •57 28 33-1 63 35 3-33 45 .58 31 10 3^33 72 3 .58 44 3-33 72 22 •57 27 32.0 64 53 3-33 72 20 .60 28 3-53 38 •58 31 2 3-53 56 .58 26 30^9 65 32 II 3-53 56 0.60 45 3-53 73 13 0.60 19 3^53 73 31 0.58 25 29.8 66 28 3-53 73 32 .62 32 2 3.53 49 .60 36 3^75 74 6 .60 24 28.7 67 45 3-75 74 9 .62 19 3^75 74 25 .62 52 3^75 42 .60 23 27-5 68 53 1 3.75 46 •63 35 4.00 75 2 .62 32 8 4.00 75 18 .62 22 26.4 69 17 4.00 75 24 .65 50 4.29 39 .63 23 4.29 55 .62 21 25.2 70 32 4.29 76 3 0.65 33 4 4.29 76 17 0.63 37 4.29 76 32 0.62 20 24.1 71 46 4.62 42 .65 18 4.62 55 .65 51 4.62 77 9 • 63 19 22.9 72 59 4.62 77 21 .67 31 4.62 77 34 .65 33 4 5.00 47 .65 18 21.8 73 34 12 S.oo 78 I .67 44 5.00 78 13 .67 16 5.00 78 26 .65 17 20.6 74 24 5-45 41 .67 56 5^45 53 .67 28 5-45 79 5 .65 16 19.4 75 35 5.45 79 21 0.68 34 7 5^45 79 33 0,67 39 6.00 44 0.65 15 18.2 76 46 6.00 80 2 .68 18 6.00 80 13 .67 49 6.00 80 23 .67 14 17.0 77 5f 6.00 43 .70 28 6.67 53 .68 59 8.57 81 3 .67 13 15.8 78 35 6 7.50 81 25 .70 37 7.50 81 34 .68 34 8 7.50 43 .67 12 14.6 79 14 7.50 82 7 .70 45 7.50 82 15 .68 16 7.50 82 23 .68 II 13^4 80 22 8.57 49 0.70 53 8.57 56 0.70 24 8.57 83 4 0.68 10 12.2 81 29 8.57 83 31 .70 35 1 0.0 83 38 .70 31 1 0.0 45 .68 9 II.O 82 36 12.0 84 13 •72 6 lO.O 84 20 .70 37 12.0 84 26 .68 8 9^8 83 41 12.0 56 .72 12 12.0 85 2 .70 42 12.0 85 7 .70 7 8.6 84 46 15.0 85 39 •73 17 15.0 44 .70 47 15.0 49 .68 6 7-4 85 50 iS.c 86 23 0.72 21 20.0 86 26 0.72 51 20.0 86 30 0.70 5 6.1 86 54 20.0 87 6 •72 24 20.0 87 9 •72 54 20.0 87 12 .70 4 4.9 S7 57 30.0 49 •73 27 30.0 52 .70 57 30.0 54 .70 3 3-7 88 . 59 60.0 88 33 •72 29 60.0 88 34 •72 59 60. c 88 36 .70 2 2.5 89 36 — 89 16 •73 30 — 89 17 •72 35 — 89 18 .70 I 1.2 90 90 30 a 90 90 ° 0.0 60' b A 60' b A 60' A a a a I a ^ A 60' A 60' A M ^ = 54° 0' ^ = 54° 30' d = 55°0' ] Page 276] .687 0.( 575 0.662 \b a = 55° 30' a = 56°0' a = 56° 30' V V \ d 60' \ t _A \ d 60' \ t A \ d 60' \ * A A b\ h\ A z\ 60' h\ A z\ 60' }i\ A z\ 6c/ ^\ ^\ o / / / 9 ' / / 1.76 55 30 0.00 1.76 56 0.00 1.82 56 30 0.00 §° 90.0 I 34 1.76 30 .02 34 1.82 .02 33 1.82 30 .02 89 89.2 o I 8 1.76 31 .02 I 7 1.76 I .02 I 6 1.82 31 .02 88 88.3 3 42 1.76 32 .03 41 1.82 2 •03 39 1.82 32 .03 ll ^^s 4 2 16 1.76 34 .03 2 14 1.76 4 •03 2 12 1.82 34 .03 86 86.7 5 50 1.76 36 0.05 48 1.82 6 0.05 45 1.82 36 0.05 !5 85-9 6 3 24 1.82 39 .05 3 21 1.82 9 •°5 3 18 1.82 39 .05 ^ 85^0 7 57 1.76 42 .07 54 1.76 12 .07 51 1.82 42 .07 ^3 84.2 8 4 31 ..76 46 .07 4 28 1.82 16 .07 4 24 1.82 46 .07 82 83^4 9 5 5 1.76 SO .08 5 I 1.82 20 .07 57 1.82 50 .07 81 82.5 10 39 1.82 55 0.08 34 1.82 24 0.08 5 30 1.82 54 0.08 80 81.7 1 1 6 12 1.76 56 .08 6 7 1.82 29 .10 6 3 1.88 59 . lO 79 80.8 12 46 1.82 5 .10 40 1.82 35 .10 35 1.82 57 5 .10 78 80.0 13 7 19 1.76 II .12 7 13 1.82 41 .12 7 8 1.88 II .12 77 79.2 14 S3 1.82 18 .12 46 1.82 48 .12 40 1.82 18 .12 76 78.3 15 8 26 1.82 25 0-13 8 19 i.8a 55 0.13 8 13 1.88 25 0.12 75 77-§ 16 59 1.82 33 .13 52 1.82 57 3 •13 45 1.88 32 •13 74 76.6 17 9 32 1.82 41 •IS 9 25 1.88 II •13 9 17 1.88 40 •15 73 75^8 18 10 5 1.82 50 .15 57 1.88 19 •15 49 1.88 49 •15 72 74-9 19 38 1.88 59 •17 10 29 1.88 28 •17 10 21 1.88 58 •«5 71 74.1 20 II 10 1.82 57 9 0.17 II I 1.88 38 0.17 53 1.88 58 7 0.17 70 73^2 21 43 1,88 19 .18 33 1.88 48 .18 II 25 1.94 17 .18 69 72^3 22 12 15 1.88 30 .18 12 s 1,88 59 .18 56 1.94 28 .18 68 71-5 23 47 1.88 41 .20 37 1.88 58 10 .20 12 27 1.94 39 .18 67 70.6 24 13 19 1.88 S3 .20 13 9 1.94 22 .20 58 1.94 50 .20 66 69.7 25 51 1.88 5^ I 0.22 40 1.94 34 0.22 13 29 1.94 59 2 0.22 65 68.9 26 14 23 1.94 18 .22 14 II 1.94 47 .22 ^4 1.94 15 .22 ^4 68.0 27 54 1.94 31 •23 42 1.94 59 •23 31 2.00 28 .23 63 ^I-' 28 15 25 1.94 45 •23 15 13 1.94 14 •23 15 I 2.00 42 •23 62 66.2 29 56 1.94 59 .25 44 2.00 28 .25 31 2.00 56 •25 61 65-3 30 16 27 1.94 59 14 0.27 16 14 2.00 43 0.25 16 I 2.00 60 II 0.25 60 64.4 31 58 2.00 30 .27 44 2.00 58 .27 31 2.00 26 .27 59 63-5 32 17 28 2.00 46 .28 17 14 2.00 60 14 .27 17 I 2.07 42 •27 58 62.6 33 58 2.00 60 3 .28 44 2.07 30 .28 30 2.07 . 58 .28 5Z 61.7 34 18 28 2.00 20 .28 18 13 2.07 47 .30 59 2.07 61 15 .28 56 60.8 35 58 2.07 37 0.30 42 2.07 61 s 0.30 18 28 2.14 32 0.30 55 59^9 36 19 27 2.07 55 •32 19 II 2.07 23 • 30 56 2.14 . 50 •30 54 58^9 37 56 2.07 61 14 .33 40 2.14 41 .32 19 24 2.14 62 8 •32 53 58.0 38 20 25 2.14 34 •33 20 8 2.14 62 •33 52 2.14 27 •33 52 ^Y 39 S3 2.14 54 •33 36 2.14 20 •33 20 20 2.22 47 •33 51 56.1 40 21 21 2.14 62 14 ^•35 21 4 2.22 40 ^•35 47 2.22 63 7 0.33 50 55-2 41 49 2.22 35 • 37 31 2.22 ^3 I •37 21 14 2.22 27 • 35 49 48 54.2 42 22 16 2.22 57 •37 58 2.22 23 •37 41 2.31 48 • 37 53-3 43 43 2.22 63 19 .38 22 25 2.31 45 •37 22 7 2.31 64 10 •37 47 46 52-3 44 23 10 2.22 42 .38 51 2.31 64 7 .38 33 2.40 32 .38 51^3 45 37 64 5 23 17 30 58 55 45 50^3 a 60' b A a 60' 6 ^ a 60' 6 _A a t A 1 6c/ A 6c/ A 60' £Z = 55°30' (i = 56°0' (^ = 56° 30' 0.687 0.675 0.662 [Page 277 ? a = 55° 30' a = 56°0' .... a = 56° 30' ^ \ * A 60' A \ i A 60' 60' A z\ A 60' 60^ A z\ A 60' A o / / / 1 / l ^° ' 45 23 n 2.31 64 5 0.40 23 17 2.31 64 30 0.40 22 58 2.40 64 55 0.38 45 50.3 40 24 3 2.40 ' 29 .40 43 2.40 54 .40 23 23 2.40 65 18 .40 44 49.4 47 28 2.40 53 .42 24 8 2.40 65 18 •42 48 2.40 42 .42 43 48.4 48 53 2.40 65 18 .43 33 2.40 43 •42 24 13 2.50 66 7 •42 42 47^4 49 25 18 2.40 44 .43 58 2.50 66 8 .43 37 2.50 32 •42 41 46.4 SO 43 2.50 66 10 0.45 25 22 2.50 34 0-43 25 I 2.61 r 57 0.43 40 45^3 51 26 7 2.50 37 •45 46 2.61 67 .45 24 2.61 67 23 •45 ^2 44-3 52 31 2.61 67 4 •47 26 9 2.6l 27 •45 . 47 2-73 .0 5° •45 38 43^3 53 54 2.73 32 •47 32 2-73 54 •47 26 9 2.73 68 17 •47 37 423 54 27 16 2-73 68 .48 54 2.73 68 22 .48 31 2^73 45 •47 36 41.2 55 38 2.73 29 0.50 27 16 2.86 51 0.48 53 2.86 69 13 0.47 35 40.2 56 28 2.73 59 .50 37 2.86 69 20 •50 27 14 3.00 41 .48 34 39^ I 57 22 2.86 69 29 •SO 58 3.00 50 •5° 34 3.00 70 10 •5° 33 38.1 58 43 3.00 59 •52 28 18 3.00 70 20 •52 „ 54 3.00 40 •5=- 32 37-0 '59 29 3 3.00 70 30 •S3 38 3.00 51 .52 28 14 3.16 71 10 •52 31 35-9 60 23 3.16 71 2 ^•53 58 3.16 71 22 o^53 33 3^16 41 0.52 30 34-9 61 42 3-33 34 •55 29 17 3^33 54 •53 52 3^33 72 12 •53 29 28 33^8 62 30 3-33 72 7 .55 35 3^33 72 26 •55 29 10 3^S3 44 •53 32^7 63 18 3-33 40 •57 53 3^53 59 •55 27 3^53 73 16 •55 11 31.6 64 36 3-53 71 M •57 30 10 3-53 7Z 32 •55 44 3^53 49 •55 26 30-5 65 53 3-53 48 0.58 27 3-75 74 5 0.57 30 I 3^75 74 22 0.57 25 29.4 66 31 10 3.75 74 23 .58 43 3^75 39 .58 17 4.00 56 •57 24 28.2 67 26 4.00 58 .60 59 4.00 75 14 .58 32 4.00 75 30 •57 23 27.1 68 41 4.29 75 34 .60 31 14 4.29 49 .60 47 4.29 7^ 4 •58 22 26.0 69 55 4.29 76 10 .60 28 4.29 76 25 .60 31 I 4.62 39 .60 21 24.8 70 32 9 4.29 46 0.62 ♦ 42 4.62 77 I 0.60 14 4.62 77 15 0,58 20 23^7 71 23 4.62 77 23 .62 55 4.62 37 .62 27 4.62 5° .60 19 22.6 72 36 5.00 78 .63 32 8 5.00 78 14 .62 40 5.00 78 26 .62 18 21.4 73 48 5-45 3! .63 20 5^45 51 .62 52 5-45 79 3 .62 17 20.2 74 59 5-4r 79 16 .65 31 5-45 79 28 .63 32 3 6.00 40 .62 16 19.1 75 33 10 6.00 55 0.65 42 6.00 80 6 0.63 13 6.00 80 17 0.62 15 17.9 70 20 6.00 80 34 .65 52 6.67 44 • 63 23 6.67 54 .63 14 16.7 77 30 6.67 81 13 .65 33 1 6.67 81 22 .65 32 7.50 81 32 .63 13 15^6 78 39 7.50 52 •67 10 7.50 82 I .65 40 7.50 82 10 .63 12 14.4 79 47 8.57 82 32 .67 18 8.57 40 •65 48 8.57 48 .63 II 13-2 80 54 8.57 83 12 0.67 25 8.57 83 19 0.67 55 8.57 83 26 0.65 10 12.0 81 34 I lO.O 52 .67 32 1 0.0 59 •65 33 2 lO.O 84 5 .65 I 10.8 82 7 12.0 84 32 .68 38 12.0 84 38 .67 8 12.0 44 .65 9.6 83 12 12.0 85 13 • 67 43 15.0 85 18 .67 13 15.0 85 23 .67 I 8.4 84 17 15.0 53 .68 47 15.0 58 .67 17 15.0 86 3 .65 7.2 85 21 20.0 86 34 0,68 51 20.0 86 38 0.67 21 20.0 42 0.65 5 6.0 80 24 20.0 87 15 .68 54 20.0 87 18 .68 24 20.0 87 21 .67 4 4.8 87 27 30.C 5^ .70 57 30.0 59 .67 27 30.0 88 I .67 3 3-6 88 29 60.0 88 38 .68 59 60.0 88 39 .67 29 60.0 41 .65 2 2.4 89 30 — 89 19 .68 34 — 89 19 .68 30 — 89 20 .67 I 1.2 90 30 90 90 1 30 90 0.0 a 60' 6 A a 60' ft A a 60' 6 A a t A 60' A 60' A 60' ^ = 55° 30' (i = 56°0' ^ = 56° 30' Page 278] 0.649 0.637 0.025 I a = 57°0' a = 57° 30' a = 58°0' \\' 'V \ d (>i6 41 .48 32 36^5 59 50 3.16 31 .50 25 3.16 50 .50 27 I 3-33 72 10 .48 31 35^5 60 28 9 3-33 72 I 0.52 44 3-33 72 20 0.50 19 3^33 39 0.50 30 34-4 61 27 3.33 32 .52 28 2 3-53 50 •52 37 3-53 73 9 •50 29 33^3 62 45 3-53 73 3 •S3 19 3-53 71 21 •52 54 3^53 39 •52 28 32^2 €>Z 29 2 3-53 35 •S3 36 3-53 52 .53 28 II 3^75 74 10 •52 ^1 3i^i 64 19 3-75 74 7 •S3 53 3-75 74 24 •53 27 4.00 41 .52 26 30.0 65 35 4.00 39 0.55 29 9 4.00 56 o^53 42 4.00 75 12 ^•53 25 28.9 66 50 4.00 75 12 •S7 24 4.00 75 28 •55 57 4.00 44 •55 24 ^i 67 30 5 4.00 46 •57 39 4.29 76 I •57 29 12 4.29 76 17 •55 23 26.7 68 20 4.29 76 20 •57 53 4.62 35 •55 26 4.62 50 •55 22 25-6 69 34 4.62 54 .58 30 6 4.62 77 8 •57 39 4.62 77 23 •55 21 24-5 70 47 4.62 77 29 0.5S 19 4.62 42 0.58 52 5.00 « 5^ 0.57 20 233 71 31 5.00 78 4 .58 32 5.00 78 17 •58 30 4 5.00 7& 30 •57 19 22.2 72 12 5-45 39 .60 44 5-45 52 •58 16 5-45 79 4 .58 18 21. 1 73 23 5-45 79 15 .60 55 5-45 79 27 .58 27 6.00 ^9 •58 17 19.9 74 34 6.00 51 .60 31 6 6.00 80 2 .60 37 6.00 80 14 •58 16 18.8 75 44 6.00 80 27 0.62 16 6.67 38 0.60 . 47 6.67 49 0.58 15 I7^6 76 54 6.67 81 4 .62 25 6.67 81 14 .62 56 6.67 81 24 .60 14 16.5 77 32 3 7.50 41 • 63 34 7.50 51 .60 31 5 7.50 82 .60 13 15-3 78 II 7.50 82 19 .62 42 7.50 82 27 .62 13 7.50 ^^ .60 12 14.1 79 19 8.57 56 .63 50 8.57 83 4 .62 21 8.57 83 12 .60 II 13-0 80 26 10.0 83 34 0.63 57 1 0.0 41 0.62 28 lO.O 48 0.62 10 11.8 81 32 lO.O 84 12 •63 32 3 10. 84 18 .63 34 12.0 84 25 .62 9 10.6 82 38 12.0 SO •63 9 12.0 56 .63 39 12.0 8s 2 .62 8 i'5 83 43 12.0 85 28 .65 14 15.0 85 34 .62 44 15.0 39 .62 7 8.3 84 48 15.0 86 7 •65 18 15.0 86 II .63 48 15.0 86 16 .62 6 7-1 85 52 ■20.0 46 0.63 22 20.0 49 0.63 52 20.0 53 0.62 5 5-9 86 55 30.0 87 24 .65 25 30.0 87 27 .63 55 30.0 87 30 • 63 4 H 87 57 30.0 88 3 .65 27 30.0 88 5 .65 57 30.0 88 8 .62 3 3-6 88 59 60.0 42 .65 29 60.0 44 •63 59 60.0 45 .63 2 2.4 89 33 — 89 21 .65 30 — 89 22 .63 52 — 89 23 .62 I 1.2 90 90 30 90 90 0.0 u 6(y b A a 60' b A a 60' b _A a t A 6cy A 60' A 60' d = 5T0' d^STSO' fZ = 58°0' Page 280] 0.613 0.60X 0.589 \ a = 58° 30' a = 59° 0' a = 59° 30' ^' \ ** \ d 60' \ * A \ l 4 .28 44 2.22 31 .28 29 2.31 58 •27 56 60.0 35 17 26 2.22 21 0.28 17 II 2.31 48 0,28 55 2.31 64 14 0.28 55 59^0 36 53 2.22 38 .28 37 2.31 64 5 .28 17 21 2.31 31 .28 54 58.1 37 18 20 2-3' . 55 .3° 18 3 2.31 22 •30 47 2.40 48 • 30 53 57-1 38 46 2.31 64 13 •32 29 2-3' 40 •3c 18 12 2.40 65 6 .30 52 56.2 39 19 12 2.31 32 •32 55 2.40 58 •32 37 2.40 24 •32 51 55-2 40 38 2.40 , 51 0.33 19 20 2.40 65 17 0.32 19 2 2.40 43 0.32 SO 54-3 41 20 3 2.40 65 II •33 45 2.40 3f •33 27 2.50 66 2 •33 49 53-3 42 28 2.40 31 •35 20 10 2.50 56 •35 51 2.50 22 .33 48 523 43 53 2.50 .. 52 •35 34 2.50 66 17 •35 20 15 2.50 42 •33 47 51-4 44 21 17 2.50 66 13 •35 58 2.50 38 •35 39 2.61 67 2 •35 46 50^4 45 41 34 21 22 59 21 2 23 45 49.4 60' & A 60' b A 60' b A a a a a t A 60' A 60' A 60' d = 58°30' d = 59°0' ^ = 59° 30^ 0. 613 o.6oi 0.589 [Page 281 \ a = 58° 30' a = 59°0' a = 59° 30' V V \ d fxy \ t A \ d 60' \ t A \^ t \ A 60' h \ 60' A \ z t \ A > d 60' A \ z t \ A 60' \ o / ^0 4 / ^0 / / ^0 / g 2.00 60 0.00 2.00 60 30 0.00 2.07 61 0.00 90 90.0 I 30 2.00 .02 30 2.07 30 .02 29 2.07 .02 8q 89.1 2 I 2.00 I .02 59 2.00 31 .02 58 2.07 I .02 88 88.3 3 30 2.00 2 •03 I 29 2.07 32 .03 I 27 2.07 2 .03 87 ll-^ 4 2 2.00 4 •03 58 2.00 34 •03 56 2.07 4 .03 86 86.5 5 30 2.00 6 0.03 2 28 2.07 3^ 0.03 2 25 2.07 6 0.03 85 85.6 6 3 2.00 8 •05 57 2.07 38 •05 54 2.07 8 .05 84 84.3 7 30 2.07 II .05 3 26 2.00 41 ■05 3 23 2.07 II •05 83 839 8 59 2.00 14 .07 56 2.07 44 .07 52 2.07 14 .07 82 83.0 9 4 29 2.00 18 .08 4 25 2.07 48 •07 4 21 2.07 18 .07 81 82.2 10 59 2.00 23 0.08 54 2.07 52 0.08 SO 2.07 22 0.08 80 81.3 II 5 29 2.07 28 ,08 5 23 2.07 57 .08 5 19 2.14 27 .08 79 80.4 12 58 2.00 33 .08 52 2.07 61 2 .10 47 2.07 32 .10 78 79-5 13 6 28 2.07 38 .10 6 21 2.07 8 .10 6 16 2,14 38 .10 77 78.6 14 57 2,07 44 .12 50 2.07 14 .12 44 2.07 44 .10 76 77.8 15 7 26 2.07 SI 0.12 7 19 2.07 21 0.12 7 13 2.14 50 0.12 75 76.9 i6 55 2.07 58 •13 48 2.07 28 . 12 41 2.14 57 .12 74 76.0 17 8 24 2.07 61 6 •13 8 17 2.14 35 ••3 8 9 2.14 62 4 •'3 73 75-1 i8 53 2.07 14 •13 45 2.07 43 •13 37 2.14 12 •13 72 74-2 19 9 22 2.07 22 •15 9 14 2.14 51 •15 9 5 2.14 20 •IS 71 73-3 20 51 2.14 31 0.15 42 2.14 62 0.15 33 2.22 29 0.15 70 72.4 21 10 19 2.07 40 .17 10 10 2.14 9 •17 10 2,14 38 •17 69 71-5 22 48 2.14 50 .18 38 2.14 19 .17 28 2.22 48 •17 68 70.6 23 II 16 2.14 62 I .18 1 1 6 2.22 29 .18 55 2.22 58 .18 P 69.7 24 44 2.14 12 .18 33 2.14 40 .18 II 22 2.22 63 9 .i8 66 68.8 25 12 12 2.14 23 0.20 12 I 2.22 SI 0.20 49 2.22 20 0.18 65 67.9 2D 40 2.22 35 .20 28 2.22 63 3 .20 12 16 2.22 31 .20 ^4 67.0 27 13 7 2.22 47 .20 55 2.22 15 .20 43 2.31 43 .20 63 66.1 28 34 2.22 59 .22 13 22 2.22 27 .22 13 9 2.31 55 .22 62 65.2 29 14 I 2.22 63 12 .23 49 2.31 40 •23 36 2.31 64 8 .22 61 64.2 30 28 2.22 26 0.23 14 15 2.31 54 0.23 14 2 2.31 21 0.23 60 633 31 55 2.22 40 •25 41 2.31 64 8 •23 28 2.40 35 •23 5§ 62.4 32 I 5 22 2.31 55 .25 15 7 2-31 22 .25 S3 2.31 49 •25 58 61.S 33 48 2-31 64 10 .25 33 2.31 37 •25 IS 19 2.40 65 4 •25 5? 60.5 34 16 14 2.31 25 •27 59 2.40 52 •27 44 2.40 19 .27 56 59-6 35 40 2-31 41 0.28 16 24 2.40 65 8 0.27 16 9 2,40 35 0.27 55 58.6 36 17 6 2.40 58 .28 49 2.40 24 .28 34 2.50 51 •27 54 57-7 37 H 2.40 65 15 .28 17 14 2.40 41 .28 58 2.50 66 7 .28 53 567 38 56 2.40 32 •30 39 2.50 58 •30 17 22 2^50 24 •30 52 55-8 39 18 21 2.50 50 .30 18 3 2.50 66 16 .30 46 2.50 42 .30 51 54-8 40 45 2.50 66 8 0.32 27 2.50 34 0.32 18 10 2.61 67 0.30 50 53-9 41 19 9 2.50 27 •33 51 2.61 53 •32 33 2.61 18 •32 42 52.9 42 H 2.61 47 .33 19 14 2.61 67 12 .32 56 2.61 37 .32 48 519 43 56 2.61 67 7 • 33 37 2.61 31 ■33 19 19 2.73 56 .33 47 50.9 44 20 19 2.61 27 •35 20 2.61 51 •35 41 2.73 68 16 •33 46 50.0 45 42 48 23 68 12 20 3 3fi 45 49.0 60' b A 60' 6 A 60' b A a a a a t A 60' A 60' A 60' d = 60°0' d = 60°30' t? = 61°0' 0.577 0.566 0.554 [Page 283 \b a = 60° 0' a =60° 30' a = 61°0' \ \" \ d 6c/ i\ i A \ d 60' \ t A \ d 6-55 10 "•5 81 36 12.0 50 .57 6 12.0 56 .57 27 12.0 85 3 •53 9 10.3 82 41 15.0 85 24 .57 II 15.0 85 30 .55 42 15.0 35 •55 8 9.2 83 45 15.0 0. 58 .s? 15 15.0 86 3 •57 46 15.0 S6 8 •55 7 8.0 84 49 20.0 86 32 • -57 19 20.0 27 •57 50 20.0 41 •55 6 6.9 85 52 20.0 87 7 0.58 22 20.0 87 II O.S5 53 30.0 87 14 ^•55 5 5-7 86 55 30.0 42 .57 25 30.0 44 •57 55 30.0 47 •55 4 4.6 87 57 30.0 88 16 .58 27 30.0 88 18 •57 57 30.0 88 20 •55 3 3-4 88 59 60.0 51 .57 29 60.0 52 •57 59 60.0 53 • 57 2 2-3 89 30 — 89 25 .58 30 — 89 26 .57 29 — 89 27 •55 I I.I 90 90 30 90 90 0.0 a 60' b A a 60' b A a 'y~\ h A a t "a" 6c/ A 60' ^ 1 60' d = 60°0' ^ = 60° 30' d = 6i°0' Page 284] .543 0.532 0.521 \ a = 61° 30' a = 62° 0' a = 62° 30' V \ * \ rf 60' \ ^ 6_ \cf 60' \ , t A \ d 60' \ t A \ A A \ A Z\ 60' A \ A z \ 6c/ h\ A z \ 60' ^\ ^\ o / ^° ' / / / / ^ O 2.07 61 30 0.00 2.14 62 0.00 2.14 62 30 0.00 90 90.0 1 29 2.14 30 .02 28 2.14 .02 28 2.22 30 .02 89 89.1 2 57 2.07 31 .02 56 2.07 I .02 55 2.14 31 .02 88 88.2 3 I 26 2.14 32 .02 I 25 2.14 2 •02 I 23 2.14 32 .02 87 ll"^ 4 54 2.07 33 •03 53 2.14 3 •03 51 2.22 33 •03 86 86.5 5 2 23 2.07 35 0.05 2 21 2.14 5 0.05 2 18 2.14 35 0.05 85 85.6 6 52 2.14 38 •05 49 2.14 8 .05 46 2.14 38 .05 84 84.7 7 3 20 2.07 41 .05 3 17 2.14 11 •OS 3 14 2.22 41 •05 ^3 83.8 8 49 2.14 44 .07 45 2.14 14 .07 41 2.14 44 .05 82 82.9 9 4 17 2.14 48 .07 4 13 2.14 18 .07 4 9 2.22 47 .07 81 82.0 10 45 2.14 52 0.08 41 2.22 22 0.07 36 2.22 51 0.08 80 81.2 II 5 13 2.14 57 .08 5 8 2.14 26 .08 5 2 2.14 56 .08 79 80.3 12 41 2.14 62 2 .08 36 2.14 31 .10 31 2.22 63 I .08 78 79-4 13 6 9 2.14 7 .10 6 4 2.22 Z7 .10 58 2.22 6 .10 77 78.5 14 37 2.14 13 .10 31 2.14 43 .10 6 25 2.22 12 .10 76 77.6 15 7 5 2.14 19 0.12 59 2.22 49 0.12 52 3.22 18 0.12 75 76.7 i6 33 2.14 26 .12 7 26 2.22 56 .12 7 19 2.22 25 .12 74 75-8 17 8 I 2.14 33 .13 n 53 2.22 ez 3 •13 46 2.31 32 • 13 73 74-9 i8 29 2.22 41 .13 8 20 2.22 II .13 8 12 2.21 40 .13 72 74.0 19 56 2.14 49 •'5 47 2.22 19 •13 39 2.31 48 •13 71 73^i 20 9 24 2.22 58 0.15 9 M 2.22 27 0.15 9 5 J.3I 56 o.is 70 72.2 21 51 2.22 63 7 .«7 41 2.22 36 •15 31 2.31 64 5 •'5 69 71-3 22 10 18 2.22 17 .17 10 8 2.31 45 .17 57 2.31 14 .17 68 70.4 23 45 2.22 27 •17 34 2.31 55 .17 10 23 2.31 24 .17 ^I ^2-5 24 II 12 2-31 37 .18 II 2.31 64 5 .18 49 2.31 34 .18 66 68.5 25 38 2.31 48 0.18 26 2.31 16 0.18 II 15 2.31 45 0.18 ^5 67.6 26 12 4 2.31 59 .20 52 2-3' 27 .20 41 2.40 56 .18 64 66.7 27 30 2-31 64 II .20 12 18 2.31 39 .20 12 6 2.40 65 7 .20 63 65.8 28 56 2.31 23 .22 44 2.40 51 .22 31 2.40 19 .20 62 64.9 29 13 22 2.31 36 .22 13 9 2.40 65 4 .22 56 2.40 31 .22 61 639 30 48 2.31 49 0.23 34 2.40 17 0.22 13 21 2.40 44 0.22 60 63.0 31 14 14 2.40 65 3 .23 59 2.40 30 •23 46 2.50 57 •23 5§ 62.1 32 39 2.40 17 .23 14 24 2.40 44 .23 14 10 2.50 66 1 1 •23 58 61.1 33 IS 4 2.40 31 .25 49 2.50 58 •25 34 2.50 25 •23 5? 60.2 34 29 2.50 46 .25 15 13 2.50 66 13 •25 58 2.50 39 •25 56 59-2 35 . 53 2.50 66 I 0.27 . 37 2.50 28 0.27 15 22 2.61 54 0.27 55 58^3 36 16 17 2.50 17 .27 16 I 2.50 44 •27 45 2.61 67 10 •27 54 57-3 37 41 2.50 33 .28 25 2.61 67 • 27 16 8 2.61 26 .27 53 56-4 38 17 5 2.50 50 .28 48 2.61 16 .28 31 2.61 42 .28 5^ 55-4 39 29 2.61 67 7 .30 17 II 2.61 32 .28 54 2.73 59 .28 51 54-4 40 52 2.61 25 0.30 34 2.73 50 0.30 17 16 2.73 68 16 0.28 50 535 41 18 15 2.73 . 43 .32 56 2-73 68 8 •30 38 2-73 33 .3c 49 525 42 37 2-73 68 2 •32 18 18 2.73 26 •32 18 2.86 51 •30 48 51S 43 59 2.73 21 •32 40 2-73 45 •32 21 2.86 69 9 • 32 "^l 50.5 44 19 21 2.73 40 .33 19 2 2.86 69 4 •33 42 2.86 28 .32 46 49-5 45 43 69 23 24 19 3 47 45 48.6 a 60' h A a 60' I A a 60' b A a f A 6& A 60' A 60' £^ = 61° 30' (i = 62°( y d = 62"30' 0.543 0.532 0.521 [Page 285 \ 6 a =61° 30' a=62°0' a = 62° 30' \1 \ * \<^ 6c/ \ t A \ d 60' \ t A \ d 60' \ t ' \ \ b\ A \ A Z\ 60' h N^ A Z\ 6c/ ^ \ A Z^ \^ / A P\ o / 1 / / / / 45 19 43 2.86 69 0.33 19 23 2.86 69 24 0.33 19 3 2.86 69 47 33 45 48.6 46 20 4 2.86 20 .35 44 2.86 44 .33 24 3.00 70 7 . 33 44 47.6 47 25 2.86 41 •35 20 5 3.00 70 4 •35 44 3.00 27 35 43 46.6 48 46 3.00 70 2 •37 25 3.00 25 .35 20 4 3.00 48 . 35 42 45.6 49 21 6 3.00 24 •37 45 3.00 46 .37 24 3.16 71 9 35 41 44.6 SO 26 3.00 46 0.37 21 5 3.. 6 71 8 0.37 43 3.16 30 37 40 43.5 51 46 3.16 71 8 •38 24 3.16 30 .37 21 2 3-33 52 37 39 42.5 52 22 5 3.16 31 .38 43 3^33 52 .38 20 3-33 72 14 37 3« 41.5 53 24 3.16 54 .40 22 I 3^33 72 15 .40 38 3-33 36 38 37 40.5 54 43 3-33 72 18 .40 19 3-33 39 .38 56 3-53 59 38 36 395 55 23 I 3-53 42 0.42 37 3^53 71 2 0.40 22 13 3-53 71 22 40 35 38.4 56 18 3-53 71 7 • 42 54 3^53 26 .42 30 3-53 46 40 34 37-4 57 58 35 3.53 32 •42 23 II 3^53 51 .42 47 3.75 74 10 42 33 36.3 H 3.75 57 .43 28 3-75 74 16 .42 23 3 3-75 35 42 32 35-3 59 24 8 3-75 74 23 .43 44 4.00 41 .43 19 4.00 75 42 31 34.2 60 24 3-75 49 0.43 59 4.00 75 7 0.43 34 4.00 25 42 30 33-2 61 62 64 40 4.00 75 15 .45 24 14 4.00 2,i •43 49 4,00 50 43 29 32.1 55 4.00 42 •45 29 4.00 59 •45 24 4 4.29 76 16 43 28 31.0 25 10 4.29 76 9 •47 44 4.29 76 26 .45 18 4.62 42 45 27 30.0 24 4.29 n •47 58 4.62 53 .45 31 4.62 77 9 45 26 28.9 65 38 4.62 77 5 0.47 25 II 4.62 77 20 0.47 44 4.62 36 45 25 27.8 66 51 5.00 ^^ •47 24 5.00 48 .47 57 5.00 78 3 45 24 26.8 67 26 3 5.00 78 I •48 3f 5.00 78 16 .47 25 9 5.00 30 47 23 25.7 68 15 5.00 30 .48 48 5.00 44 .48 21 5-45 58 47 22 24.6 69 27 5-45 59 .50 26 5^45 79 13 .48 32 5-45 79 26 47 21 23-S 70 38 5-45 79 29 0.50 II 6.00 42 0.48 43 6.00 54 48 20 22.4 71 49 6.00 59 •50 21 6.00 80 II .48 53 6.00 So 23 48 19 21.3 72 59 6.00 80 29 •50 31 6.00 40 •50 2^ 3 6.67 52 48 18 20.2 73 27 9 6.67 59 .50 41 6.67 Si 10 .50 12 6.67 81 21 48 'I 19. 1 74 18 6.67 81 29 .52 50 7.50 40 .50 21 7.50 50 5° 16 18.0 75 27 7.50 82 0.52 5f /•SO 82 10 0.50 29 7.50 82 20 48 15 16.9 76 35 8.57 31 .52 27 6 8.57 40 .52 17 8.57 49 •50 14 15-8 77 42 8.57 83 2 .52 13 8.57 83 II .50 44 S.57 83 19 ,50 13 14.7 78 49 8.57 33 • 53 20 lO.O 41 .52 51 lO.O 49 .52 12 13-5 79 56 lO.O 84 5 •53 26 lO.O 84 12 .52 57 lO.O 84 20 50 II 12.4 80 28 2 12.0 37 0-53 32 12.0 43 0.53 27 3 12.0 50 52 10 "•3 81 7 12.0 85 9 •S3 Z7 12.0 85 15 .52 12.0 85 21 .50 9 10.2 82 12 15.0 41 •S3 42 15.0 46 •S3 13 15.0 51 52 8 9.0 P 16 15.0 86 13 .53 46 15.0 86 18 •52 17 20,0 86 22 52 7 7-9 84 20 20.0 45 •53 50 20.0 49 •53 20 20.0 53 52 6 6.8 85 23 30.0 87 17 0.55 53 20.0 87 21 0.52 23 20.0 87 24 •52 5 S7 86 25 30.0 50 •53 56 30.0 52 •53 26 30.0 55 •52 4 4^5 87 27 30.0 88 22 •55 58 60.0 88 24 •53 28 60.0 88 26 .53 3 3-4 88 29 60.0 55 •53 59 60.0 56 •53 29 60.0 58 52 2 23 89 30 — 89 27 .55 28 — 89 28 • 53 30 — 89 29 52 I I.I 90 30 90 90 30 90 0.0 a 6(y 6 A a 6(y 6 A a 6c/ / b . A a t A M A 6(y A 6 ry _ d=ei°zo' (i = 62°0' rf = 62°30' Page 286] c .510 0. 499 a/ 188 \b a = 63°0' a = 63° 30' a = 64°0' V V \^ 60' |\ ^ A \ d 60' \ t A \ (/ 60' \' — «\ b\ A \ A z\ 60' A\ A ^ \ 60' h \ A ^ \^ 60' ^\ A o / ^° ' / / / / p 2.22 63 0.00 2.22 63 30 0.00 2.31 64 0.00 90 90.0 I 27 2.22 .02 27 2.22 30 .02 26 2.22 .02 89 89.1 2 54 2.14 I .02 54 2.31 31 .02 53 2.31 I .02 88 88.2 3 I 22 2.22 2 .02 I 20 2.22 32 .02 I 19 2.31 2 .02 87 87.3 4 49 2.22 3 .03 47 2.22 33 •03 45 2.31 3 •03 86 86.4 S 2 16 2.22 5 0.03 2 14 2.31 35 0.03 2 II 2.22 5 0.03 85 85-5 6 43 2.22 7 .05 40 2.22 37 •05 38 2.31 7 .05 ^ 84.6 7 3 10 2.22 10 .05 3 7 2.22 40 .05 3 4 2.31 10 .05 83 83-7 8 37 2.22 13 .07 34 2.31 43 .07 30 2.31 13 .07 82 82.8 9 4 4 2.22 17 .07 4 2.22 47 .07 56 2.31 17 .07 81 81.9 10 31 2.22 21 0.08 27 2.31 51 0.07 4 22 2.31 21 0.07 80 81.0 II 58 2.22 26 .08 53 2.22 55 .08 48 2.31 25 .oS 79 80.1 12 5 25 2.22 ^l .08 S 20 2.31 64 .08 5 14 2.31 30 .08 78 79.2 13 52 2.31 ^6 .10 46 2.31 5 .10 40 2.40 35 .08 77 78.3 14 6 18 2.22 42 .10 6 12 2.31 II .10 6 5 2.31 40 .10 76 77-4 15 45 2-3> 48 0. 10 38 2.31 17 0.12 31 2.40 46 0.12 75 76-5 i6 7 II 2.22 . 54 .12 7 4 2.31 24 .12 56 2.31 53 .12 74 75-6 17 38 2.31 64 I •13 30 2.31 31 .12 7 22 2.40 65 .12 73 74-7 i8 8 4 2-31 9 •13 56 2.40 38 •13 47 2.40 7 .13 72 73-8 19 30 2.31 17 .13 8 21 2.31 46 .13 8 12 2.40 15 •13 71 72.9 20 56 2.31 25 0.15 47 2.40 54 0.13 37 2.40 23 0.13 70 72.0 21 9 22 2.31 34 •IS 9 12 2.40 65 2 •15 9 2 2.40 31 •15 69 71.0 22 48 2.40 43 •>5 37 2.40 II •17 27 2.40 40 •15 68 70.1 23 10 13 2.31 . 52 •17 10 2 2.40 21 •17 52 2.50 49 .17 67 69.2 24 39 2.40 65 2 .18 27 2.40 31 •17 10 16 2.40 59 •17 66 68.3 ''I II 4 2.40 13 0,18 52 2.40 41 0.18 41 2.50 66 9 0.18 65 67-3 26 29 2.40 24 .18 II 17 2.50 52 .18 1 1 5 2.50 20 .18 64 66.4 27 54 2.40 35 .20 41 2.50 66 3 .18 29 2.50 31 .18 63 655 28 12 19 2.50 47 ,20 12 5 2.50 14 .20 53 2.61 42 .20 62 64.6 29 43 2.50 59 .20 29 2.50 26 .22 12 16 2.50 54 .20 61 63.6 30 13 7 2.50 66 II 0.22 53 2.50 39 0.22 40 2.61 67 6 0.22 60 62.7 ^I 31 2.50 24 •23 13 17 2.50 52 .22 13 3 2.61 19 .22 ^2 61.7 h 55 2.50 38 •23 41 2.61 67 5 •23 26 2.61 32 .22 58 60.8 33 14 19 2.50 52 .23 14 4 2.61 19 •23 49 2.61 . 45 •23 37 59-8 34 43 2.61 67 6 .25 27 2.61 33 .23 14 12 2.73 59 .23 56 58-9 35 15 6 2.61 21 0.25 50 2.73 47 0.25 34 2-73 68 13 0.2s 55 57.9 36 29 2.61 36 .25 I 5 12 2-73 68 2 •25 56 2.73 28 .25 54 570 37 . ^^ 2-73 .. 51 .27 34 2.73 17 .27 15 18 2.73 43 •27 53 56.0 38 16 14 2-73 68 7 .28 56 2.73 33 •27 40 2.86 59 .27 52 550 39 36 2.73 24 .28 16 18 2-73 49 .28 16 I 2.86 69 15 •27 51 54-1 40 58 2.73 41 0.28 40 2.86 69 6 0.28 22 2.86 31 0.28 50 53.1 41 17 20 2.86 58 .30 17 I 2.86 23 .28 43 2.86 48 .28 ^2 52.1 42 41 2.86 69 16 •30 22 2.86 40 .30 17 4 3.00 70 5 .28 48 5I-I 43 18 2 2.86 34 .30 43 3.00 58 •30 24 3.00 22 •30 47 50.2 44 23 2.86 52 •32 18 3 3.00 70 16 .32 44 3.00 40 .30 46 49.2 45 44 70 II 23 35 18 4 58 45 48.2 a 60' b _A a 60' b A a 60' b A a / T 60' A 6S 42 2.50 28 •'5 33 2.61 57 ••5 69 70.8 22 9 17 2.50 9 •'S 9 6 2.50 Z7 •IS 56 2.61 67 6 •'5 68 69.9 23 41 2.50 18 •'5 30 2.50 46 •17 9 19 2.61 15 •15 P. 69.0 24 10 5 2.50 27 •17 54 2.61 56 •17 42 2.61 24 •17 66 68.0 25 29 2.50 37 0.18 10 17 2.50 67 6 0.17 10 5 2.61 34 0.17 65 67.1 26 53 2.50 48 .18 41 2.61 16 •17 28 2.61 44 .17 64 66.2 27 II 17 2.61 59 .18 II 4 2.61 26 .18 SI 2.61 54 .18 63 65.2 28 40 2.61 67 10 .18 27 2.61 37 .20 II 14 2.73 68 5 .18 62 64-3 29 12 3 2.61 21 .20 50 2-73 49 .20 36 2-73 16 .20 61 633 30 26 2.61 33 0.22 12 12 2.73 68 I 0.20 58 2.73 28 0.20 60 62.4 31 49 2-73 46 .22 34 2.73 13 .20 12 20 2-73 40 .20 59 61.4 32 13 II 2.6l . 59 .22 56 2.73 25 .22 42 2.86 52 .22 58 60.5 33 34 2.73 68 12 •23 13 18 2.73 38 .23 13 3 2.86 69 5 .22 5? 59-5 34 56 2.73 26 •23 40 2.73 52 • 23 24 2.86 18 •23 56 58.6 35 14 18 2.73 40 0.23 14 2 2.86 69 6 0.23 45 2.86 32 0.23 55 57-6 30 40 2.86 . 54 .25 23 2.86 20 .23 14 6 2.86 46 .23 54 56.6 3^ 15 I 2.86 69 9 •25 44 2.86 34 .25 27 2.86 70 •25 53 55-7 38 22 2.86 24 •27 15 5 2.86 49 .27 48 3.00 15 •25 52 54-7 39 43 2.86 40 •27 26 3.00 70 5 •27 15 8 3.00 30 •25 51 53-7 40 16 4 3.00 56 0.27 . 4^ 3.00 21 0,27 28 3.16 45 0.27 50 52-7 41 24 3.00 70 12 .28 16 6 3.00 37 •27 . 47 3.16 71 I •27 42 51.8 42 44 3.00 29 .28 26 3.16 53 .28 16 6 3.16 17 .28 48 50.8 43 17 4 3.00 46 .30 45 3.16 71 10 .28 25 3.16 34 .28 4Z 49.8 44 24 3.. 6 71 4 .30 17 4 3.16 27 .30 44 3.16 51 .28 46 48.8 45 43 22 23 45 17 3 72 8 45 47.8 a 60' 6 A a 6c/ 1 b A a 6 38 2-73 22 .17 26 2-73 49 .18 10 13 2,86 17 • 17 63 65.0 28 II 2-73 32 .18 48 2.86 69 .18 34 2.86 27 .18 62 64.0 29 22 2.73 43 .20 II 9 2.86 II .18 55 2.86 38 .18 61 63.1 30 ' 44 2-73 55 0.20 30 2.86 22 0.20 II 16 2.86 49 0.18 60 62.1 31 12 6 2.86 69 7 .20 51 2.86 34 .20 37 3.00 70 .20 59 61. 1 32 27 2.86 19 .20 12 12 2.86 46 .20 57 3.00 12 .20 58 60.2 33 48 2.86 31 .22 11 3,00 58 .22 12 17 3.00 24 .22 57 [59-2 34 13 9 2.86 44 .23 IZ 3.00 70 II .22 37 3.00 37 .22 56 58.3 35 30 3.00 58 0.23 13 13 3.00 24 0.22 57 3.00 50 0.22 55 57-3 36 50 3.0c 70 12 •23 11 3.00 17 .23 13 17 3.16 71 3 .22 54 56-3 37 14 10 3.00 26 •23 '^l 3.00 51 •23 36 3.16 16 .23 53 55-4 38 30 3.00 40 •25 14 13 3.16 71 5 •25 55 3.16 30 .23 52 54-4 39 SO 3.16 55 •25 32 3.16 20 .25 14 14 3.16 44 •25 51 53-4 40 IS 9 3.16 71 10 0.27 51 3.16 35 0.25 33 3.33 59 0.25 50 52-4 41 28 3.16 26 •27 15 10 3.16 50 •27 51 3-33 72 14 •25 42 51-4 42 . 47 3.16 42 • 27 29 3-33 72 6 •27 15 9 3-33 29 •27 48 50.5 43 16 6 3.i6 58 •27 . "^7 3-33 22 •27 27 3-33 45 .27 4? 49-5 44 25 3-33 72 14 .28 16 5 3.33 38 .28 45 3-S3 73 I .28 46 48-5 45 43 " 1 23 55 16 2 iS 45 47^5 a 60' 6 A a Co' h A a 60' b ^ a t A 6c/ A 6c/ A 6c/ (^ = 66^0' rf = 66°30' d = 6T0' 0.445 0435 0.424 [Page 291 \ 6 a = 66°0' a = 66° 30' a = 67°0' \ \ * \ d 60' \ ^ A \ d 60' \ t A \ d 60' \. t A \ b\ h\ A z\ 60' A \ A Z\ 60' A \ A Z\ 60' ^\ P\ • 9 ' / / / 9 ' / J, 45 16 43 3-33 72 3^^ 0,30 16 23 3-53 72 55 0.28 16 2 3-53 73 18 0.27 45 47-5 40 17 I 3-53 49 .30 40 3-53 73 12 .28 19 3-53 34 .28 44 46^5 47 18 3-53 73 7 .30 57 3-53 29 .30 36 3^53 51 .28 43 4S5 48 35 3-53 25 .30 17 14 3^53 47 •30 53 3^75 74 8 .30 42 44-5 49 52 3-53 43 .32 31 3^75 74 5 •30 17 9 3-75 26 •3° 41 43-5 50 18 9 3-75 74 2 0.32 47 3^75 23 0.32 25 3^75 44 0.32 40 42.5 51 25 3-75 21 •32 18 3 3-75 42 •32 41 4.00 75 3 •30 39 41.4 52 41 3-75 40 .33 19 4.00 75 I .32 56 4.00 21 •32 38 40.4 53 57 3-75 75 •33 34 4.00 20 •33 18 II 4.00 40 •32 37 39^4 54 19 13 4.00 20 •33 49 4.00 40 .33 26 4.29 59 .33 36 38.4 55 28 4.00 40 0.35 19 4 4.29 76 o^33 40f 4.29 76 19 o^33 35 37^4 56 43 4.29 76 I •35 18 4.29 20 •35 54 4.29 39 •33 34 363 57 57 4.29 22 .35 32 4.29 41 .35 19 8 4.62 59 •33 33 35-3 5« 20 II 4.62 43 • 37 46 4.62 77 2 •35 21 4.62 77 19 •35 32 34^3 59 24 4.62 77 5 • 37 59 4.62 23 •35 34 4.62 40 •35 31 33-2 60 37 4.62 27 0.37 20 12 4.62 44 0.37 47 5.00 78 I 0.35 30 32.2 61 50 4.62 49 •37 25 5.00 78 6 .37 59 5.00 22 •37 29 31.2 62 21 3 5.00 78 II •38 37 5.00 28 • 37 20 II 5.00 44 •37 28 30.1 63 15 5.00 34 •38 49 5-45 50 •37 23 5^45 79 6 •37 27 29.1 64 27 S-45 57 •38 21 5^45 79 12 •38 •34 5^45 28 •37 26 28.0 65 38 5-45 79 20 0.40 II 5.45 35 0.38 45 6.00 50 o^37 25 27.0 66 49 6.00 44 .40 22 6.00 58 • 38 55 6.00 80 12 •38 24 25.9 67 59 5.00 80 8 .40 32 6.00 80 21 .40 21 5 6.00 35 .38 23 24.8 68 22 9 6.00 32 .40 42 6.67 45 .40 15 6.67 58 •38 22 23^8 69 19 6.67 56 .40 51 6,67 81 9 .40 24 6.67 81 21 .38 21 22.7 70 28 6.67 81 20 0.42 22 6.67 33 0.40 33 7.50 44 0.40 20 21.6 71 37 7.50 45 .42 9 7.50 57 .40 41 7.50 82 8 .40 19 20.6 72 45 7.50 82 10 •42 17 7.50 82 21 .40 49 7.50 32 .40 18 19^5 73 53 7.50 35 • 42 25 8.57 45 .42 57 8.57 56 .40 'I 18.4 74 23 I 8.57 83 •43 32 8.57 83 10 .42 22 4 8.57 83 20 .40 16 17^4 75 8 8.57 26 0.42 39 8.57 35 0.42 II lO.O 44 0.40 15 16.3 76 15 1 0.0 51 •43 46 1 0.0 84 •42 17 lO.O 84 8 .42 14 I5^2 77 21 lO.O 84 17 •43 52 lO.O 25 •42 23 112.0 33 .40 13 14. 1 78 27 12.0 43 •43 58 12.0 50 •42 28 12.0 57 .42 12 13^ I 79 32 12.0 85 9 •43 23 3 12.0 85 15 .43 33 12.0 85 22 .42 II 12.0 80 37 15.0 35 0.43 8 15.0 41 0.42 38 15.0 . 47 0.42 10 10.9 81 41 15.0 86 1 •43 12 15.0 86 6 •43 42 15.0 86 12 •42 9 9.8 82 45 15.0 27 •45 16 20.0 32 •43 46 20.0 37 .42 8 H 83 49 20.0 54 •43 19 20.0 58 •43 49 20.0 87 2 •43 7 6 l^ S4 52 30.0 87 20 •45 22 30.0 87 24 • 43 52 30.0 28 •42 6.5 85 54 30.0 47 0.43 24 30.0 50 ^•43 54 30.0 n 53 0.42 5 5-5 86 56 30.0 88 13 •45 26 30.0 88 16 •43 56 30.0 88 18 •43 4 4.4 ^7 58 60.0 40 •45 28 60.0 42 .43 58 60.0 „ 44 .42 3 3-3 88 59 60.0 89 7 •43 29 60.0 89 8 •43 59 60.0 89 9 • 42 2 2.2 89 24 — 33 •45 30 — 34 •43 23 — 34 •43 I I.I 90 90 30 90 90 0.0 a 60' h _A a 6& h A a 60' 6 A tt ^ A 6c/ A 60' A 60' ^ = 66° 0' 7 • 03 2 15 2.73 7 •03 2 12 2-73 37 .03 84 84.4 7 40 2.61 39 .05 2,7 2.73 9 .05 34 2.86 39 .03 83 82.6 8 3 3 2.61 42 .05 59 2.61 12 .05 55 2.73 41 .05 82 9 26 2.61 45 .05 3 22 2.73 15 •°5 3 17 2-73 44 .07 81 81.6 10 49 2.73 48 0.07 44 2.73 18 0.07 39 2.73 48 0.07 80 80.7 II 4 II 2.61 52 .07 4 6 2.73 22 .07 4 I 2.86 52 .07 79 79-8 12 34 2.73 .0 56 .08 28 2.73 26 .08 22 2.73 56 .07 78 78.9 13 56 2.61 68 I .08 50 2.73 31 .08 44 2.86 69 .08 77 77-9 14 5 19 2-73 6 .10 5 12 2.73 36 .08 5 5 2.73 5 .08 76 77.0 15 ^ 41 2-73 12 0. 10 34 2.73 41 0. 10 27 2.86 10 0. 10 75 76.0 16 6 3 2.73 18 ,10 . 56 2.86 47 .10 48 2.86 16 .10 74 75-1 17 25 2-73 24 .10 6 17 2.73 53 .10 6 9 2.86 22 .10 73 74-2 18 47 2-73 30 .12 39 2.86 59 .12 30 2.86 28 . 10 72 73-2 19 7 9 2-73 37 .12 7 2-73 69 6 .12 51 2.86 34 .12 71 72.3 20 31 2.73 44 0.13 22 2.86 13 0.12 7 12 2.86 41 0.12 70 71.4 21 53 2.73 . 52 .13 43 2.86 20 .13 33 2.86 48 •13 69 70.4 22 8 15 2.86 69 .13 8 4 2.86 28 •13 54 3.00 56 •13 68 69.5 23 36 2.86 8 .13 25 2.86 36 •13 8 14 3.00 70 4 •13 67 68.5 24 57 2.86 16 •IS 46 2.86 44 •'5 34 3.00 12 •15 66 67.6 25 9 18 2.86 25 0.17 9 7 3.00 53 o.is 54 3.00 21 0.15 65 66.6 26 39 2.86 35 •'7 27 2.86 70 2 .17 9 14 3.00 30 ••S 64 657 27 10 2.86 45 .17 48 3,00 12 •17 34 3.00 39 •17 63 64.7 28 21 2.86 55 •17 10 8 3.00 22 •17 54 3.00 49 •17 62 63.8 29 42 3.00 70 5 .18 28 3.00 32 .18 10 14 3.00 59 .18 61 63.8 30 XI 2 3.00 16 0.18 48 3.00 43 0.18 34 3.16 71 10 0,18 60 61.8 31 22 3,00 27 .20 II 8 3.16 54 .18 53 3.16 21 .18 59 60.9 32 42 3.00 39 .20 27 3.16 71 5 .20 II 12 3.16 32 .18 58 59-9 33 12 2 3.00 51 .20 46 3.16 17 .20 31 3.T6 43 .20 57 58.9 34 22 3.16 71 3 .20 12 5 3.16 29 .20 50 3-33 55 .20 56 58.0 35 41 3.16 15 0.22 24 3.16 41 0.22 12 8 3-33 72 7 0.20 55 57.0 36 13 3.16 28 .22 43 3.16 54 .22 26 3-33 19 .22 54 56.0 37 19 3.16 41 •23 13 2 3-33 72 7 .22 44 3-33 32 .22 53 551 38 ^l 3.33 55 .23 20 3-33 20 .23 13 2 3-33 45 •23 52 54-1 39 56 3-33 72 9 •25 38 3-33 34 •23 20 3-33 59 .23 51 53-' 40 14 14 3.53 24 0.25 56 3.33 48 0.23 38 3-53 73 13 0.23 50 52.1 41 32 3-33 39 •25 14 14 3-53 71 2 •25 55 3-53 27 .23 49 j 51.1 42 5? 3.33 54 .25 31 3.53 17 .25 14 12 3-S3 41 •25 48! 50.1 43 15 8 3.53 7i 9 •27 48 3-53 32 .27 29 3-75 56 •25 '^J 49.2 44 25 3-53 25 •27 15 5 3-53 48 •25 45 3-75 74 II 46 48.2 45 42 41 22 74 3 15 I 26 1 45 47.2 a ec/ 6 A a 6 13 •27 57 4.29 34 •27 41 42.9 50 56 4.29 76 8 28 33 4.29 29 0.27 15 II 4.29 5$ 0.27 40 41.9 51 16 10 4.29 25 28 47 4.29 45 .28 25 4.62 77 6 •27 3g 40.8 52 24 4.29 42 . 2S 16 I 4.62 77 2 .28 38 4.62 22 .28 38 39-8 =5 3 38 4.62 59 . 30 M 4.62 19 .28 51 4.62 39 •27 37 38^8 54 SI 4.62 77 17 • 30 27 4.62 36 .30 16 4 5.00 55 .28 36 37^8 • 55 17 4 4.62 3^ = 1° 40 4.62 54 0.30 16 5.00 78 12 0.30 35 368 56 17 5.00 „ 53 3 = 53 5.00 78 12 .30 28 5. CO 30 .2S 34 35-8 57 29 5.00 78 11 , 32 17 5 5.00 30 .30 40 5.00 47 .30 33 34-7 58 41 5.00 30 32 17 5.45 48 .30 52 5-45 79 5 •3° 32 33-7 59 53 5.00 49 . 32 28 5-45 79 6 .32 17 3 5.4s 23 .30 31 32.7 60 18 5 5.45 79 8 32 39 5-45 25 0.32 14 6.00 41 0.32 30 31.6 61 16 5-45 27 33 50 5-45 44 .32 24 6.00 80 .30 29 30.6 62 27 6.00 47 33 18 I 6.00 80 3 ■32 34 6.00 18 .32 28 29.6 63 37 6.00 80 7 33 II 6.00 22 .33 44 6.00 37 .32 27 28.S 64 47 6.00 27 33 21 6.67 42 ■ 32 54 6.67 56 ■32 26 27-5 65 57 6.00 47 35 30 6.67 81 I o^33 18 3 6.67 81 15 0-33 25 26.5 66 19 7 6.67 81 8 33 39 6.67 21 .33 12 6.67 35 •32 24 25-4 67 16 6.67 28 35 48 6.67 41 •33 21 7.50 54 .33 23 24.4 68 25 7.50 49 35 57 7.50 82 I •35 29 7.50 82 14 .33 22 233 69 33 7.50 82 10 35 19 5 7.50 22 ■35 37 7.50 34 .33 21 22.3 70 41 7.50 31 37 13 8.57 43 0.35 45 8.57 54 0.35 20 21.2 71 49 8.57 53 35 20 8.57 83 4 •35 52 8.57 83 15 .33 19 18 20.2 72 56 8.57 83 14 37 27 8.57 25 .35 59 8.57 35 •35 19.1 73 20 3 10. 36 37 34 lO.O 46 .35 19 6 lO.O 56 •33 17 18. 1 74 9 lO.O 58 37 40 lO.O 84 7 • 35 12 lO.O 84 x6 .35 16 17.0 75 15 1 0.0 84 20 37 46 10.0 28 0.37 18 12.0 37 0.35 15 16.0 76 21 12.0 42 37 52 12.0 50 • 35 23 12.0 58 •35 14 14.9 77 26 12.0 85 4 37 57 12.0 85 II • 37 28 12.0 85 19 •35 13 13-8 78 31 12.0 26 38 20 2 15.0 33 •37 33 15.0 40 •37 12 12.8 79 36 15.0 49 ■37 6 15.0 55 •37 37 15.0 86 2 •35 II 11.7 80 40 15.0 86 II .38 10 15.0 86 17 0.37 41 15.0 23 o^35 10 10.7 81 44 20.0 34 .38 14 20.0 39 ■37 45 20.0 44 •37 q 8 9.6 82 47 20.0 57 ■37 17 20.0 87 I ■37 48 20.0 87 6 •37 8.5 83 50 20.0 87 19 .38 20 20.0 23 •38 51 30.0 28 •35 I 7-5 84 53 30.0 42 .38 , 23 30.0 46 •37 53 30.0 49 •37 6.4 85 55 30.0 88 5 .38 25 30.0 88 8 0.37 55 30.0 88 II 0.37 5 5-3 86 57 60.0 28 .38 27 60.0 30 •38 57 60.0 33 •37 4 4-3 87 58 60.0 51 .38 28 60.0 53 •37 58 60.0 55 •35 3 3-2 88 59 60.0 89 14 .38 29 60.0 89 15 • 37 59 60.0 89 16 .37 2 2.1 89 21 — o7 ■38 30 — 37 .38 20 — 38 •37 I I.I 90 90 30 90 00 0.0 i- a 60' h - A a be/ 6 A a 6(y b _A a t A t )C/ A ecy A 60' d = 69° 0' (Z = 69°30' d = 70°0' Page 296] •354 0.344 0.335 \ a = 70° 30' a = 71°0' a = 71° 30' \\ \ * \ d oc/ \ t A \ d 60' \ t A \ 5 8 9 3-75 75 2 •«3 61 62.1 30 53 3-75 17 0.15 39 3-75 44 0.15 25 4.00 10 0.15 60 61.2 31 9 9 3-75 26 •17 55 4.00 53 •15 40 4.00 19 •'5 59 60.2 32 25 3-75 36 ■'7 9 10 3-75 75 2 •IS 55 4.00 28 •'5 58 59-2 33 41 3-75 46 •<7 26 4.00 II .17 9 10 4.00 37 •'5 57 58.2 34 57 3-75 56 •17 41 4.00 21 •17 25 4.29 46 •'7 56 57.2 35 10 13 4-. 00 75 6 0.17 56 4.00 31 0.17 39 4.00 56 0.17 55 56.3 30 28 4.00 16 .18 10 1 1 4.00 41 .18 54 4.29 76 6 .18 54 55-3 37 43 4.. 00 27 .18 26 4.29 . 52 .18 10 8 4.29 17 •17 53 54-3 2^ 58 4.00 38 .20 40 4.29 76 3 .18 22 4.29 27 .18 52 53-3 39 II 13 iJ.OO 50 .18 54 4.29 14 .18 36 4.29 38 .18 51 52-3 40 28 4.29 76 I 0.20 II 8 4.29 25 0.20 50 4.29 49 0.18 50 51-3 41 42 4-29 13 .22 22 4.29 37 .20 II 4 4.62 77 .20 49 50-3 42 56 4.29 26 .20 36 4.29 49 .20 17 4.62 12 .20 48 49-3 43 12 10 4.29 38 .22 50 4.62 77 I .20 30 4.62 24 .20 "^l 48.4 44 24 4.29 51 .22 12 3 4.62 13 .22 43 4.62 36 .20 46 47-4 45 38 77 4 16 26 56 48 45 46.4 a »' b A a 60' b _A a r,o' i _A_ a / A 6c/ A 1 60' A 60' d = l 2°(y d = 72 °20' d = l, 3°0' 0325 0-315 0308 [Page 299 \b a = 72° 0' a = 72° 30' a = 73°0' \\ \ ** \^ 60' \ t A \ d 60' \ t A \. d 60' \ t _A \ b\ h\ A z \ ec/ h\ A z\ 60' h N. ^ \Z\ ec fA ^\ o / / i / / / 4 43 .28 I I.O 90 30 90 90 30 90 0.0 6c/ 5 A 6c/ 6 A 60' 6 A a a a a t ^ 1 6c/ A 6c/ A 6c/ d = 13°30' d = 74°0' (i = 74°30' Page 302] 0.268 0.. 259 0249 \b a = 75°0' a = 75° 30' a = 76° C \ V \ d 60' \ f A \d r,o' \ t A \ rf 60^ \ * A \ b\ h\ A z\ 60' * \ A z\ 6(y Ax. A z\ 60' ^\ o / / / / / 9 ' 3-75 75 0.00 4.00 75 30 0.00 4.00 76 0,00 90 90.0 I 16 4.00 .02 15 4.00 30 .02 15 4.29 .00 89 89.0 2 31 3.75 I .00 30 4.00 31 .00 29 4.00 .02 88 88.1 3 47 4.00 I .02 45 4.00 31 .02 44 4.29 I .02 ^7 87.1 4 I 2 3-75 2 .02 I 4.00 32 .02 58 4.00 2 .02 86 86.1 5 18 4.00 3 0.03 15 4.00 33 0.02 I 13 4.29 3 0.02 85 85.2 6 33 3-75 5 .02 30 4.00 34 .03 27 4.29 4 .03 ^ 84.2 7 49 4,00 6 •03 45 4.00 36 .03 41 4.00 6 .03 83 83.2 8 2 4 4.00 8 .03 2 4.00 38 .03 56 4.29 8 •03 82 82.3 9 19 3-75 10 .05 15 4.00 40 •05 2 10 4.00 10 •03 81 81.3 10 35 4.00 13 0.05 30 4.29 43 0.03 25 4.29 12 0,05 80 80.3 I I 50 4.00 16 •05 44 4.00 45 •05 39 4.29 15 .05 79 79-3 12 3 5 4.00 19 .05 59 4.00 48 .05 53 4.29 18 .05 78 78.4 13 20 4.00 22 .05 3 14 4.29 51 .07 3 7 4.29 21 .05 77 77-4 14 35 4.00 25 .07 28 4.00 55 •05 21 4.29 24 •05 76 76.4 IS 50 4.00 29 0.07 43 4.29 58 0.07 35 4.29 27 0.07 75 75-5 i6 4 5 4.00 33 .08 57 4.00 76 2 .08 49 4.29 31 .07 74 74-5 ^7 20 4.00 38 .07 4 12 4.29 7 .07 4 3 4.29 35 .08 73 73-5 i8 35 4.00 42 .08 26 4.00 II .08 17 4.29 40 .07 72 725 19 50 4.00 47 .08 41 4.29 16 .07 31 4.29 44 .08 71 71.6 20 5 5 4.29 52 0.08 55 4.29 20 0.08 45 4.29 49 0.08 70 70.6 21 19 4.00 57 .10 5 9 4.29 25 .10 59 4.62 54 .08 69 69.6 22 34 4.29 76 3 .10 23 4.29 31 .10 5 12 4.29 59 .08 68 68.6 ^3 .4^ 4.00 9 .10 37 4.29 37 .10 26 4.62 77 4 .10 fl 67.7 24 6 3 4.29 15 .10 51 4.62 43 .10 39 4.62 10 .10 66 66.7 25 17 4.29 21 0. 10 6 4 4.29 49 0. lO . 52 4.62 16 0. 10 ^5 65.7 26 31 4.29 27 • 12 18 4.29 55 .10 6 5 4.62 22 .10 64 64.7 27 45 4.29 34 .12 32 4.62 77 I .12 18 4.62 28 .12 P 637 28 59 4.29 41 .12 45 4.62 8 .12 31 4.62 35 .12 62 62.8 29 7 13 4.62 48 .13 58 4.62 IS .12 44 4.62 42 .12 61 61.8 30 26 4.29 56 0.13 7 II 4.62 22 0.13 57 4.62 49 0.12 60 60.8 31 40 4,62 77 4 .13 24 4.62 30 .13 7 10 5.00 56 •13 52 59-8 32 53 4.62 12 •13 37 4.62 38 .13 22 5.00 78 4 .12 58 58.8 33 8 6 4.62 20 .13 50 4.62 46 .13 34 5.00 II •■3 57 57-8 34 19 4,62 28 •15 8 3 4.62 54 •13 46 5.00 19 •13 56 56-9 35 32 4.62 37 0.15 16 5.00 78 2 0.15 58 5.00 27 0.15 55 55-9 36 45 4.62 46 •15 28 5.00 11 •IS 8 10 5.00 36 •«3 54 54-9 37 58 5.00 55 •15 40 5.00 20 .15 22 5.00 44 •15 53 53-9 ^8 9 10 5.00 78 4 .17 52 5.00 29 •15 34 5.00 53 ••5 52 529 39 22 5.00 14 •'7 9 4 5.00 38 •15 46 5-45 79 2 .>s 51 51-9 40 34 5.00 24 0,17 16 5-45 47 0.17 57 5-45 II 0.17 50 509 41 46 5.00 34 .17 27 5.00 57 •'7 9 8 S-45 21 •'5 -^^ 40.9 42 58 5.00 44 .18 39 5-45 79 7 •17 19 5-45 30 •17 48 48.9 43 10 10 5.00 55 •17 50 5-45 17 .18 30 5-45 40 •'7 "^l 47-9 44 22 5-45 79 5 .18 10 I 5-45 28 •17 41 6,00 50 ••7 ^6 46.9 45 33 16 12 38 51 80 45 45-9 a 6(y b A a 60' b A a 60' b A a t A 6c/ A 60' A 60' ^ = 7 5°0' fZ = 75° 30' d = l 6° 0' 0.268 0.259 249 [Page 303 \ a = 75° 0' a - 75° 30' a = 76°0' c\ \ * \ d 60' \ t A_ \d 60' \ t A \c? 60' \. t A \ A aX^ t z \ 60' A \ A z\ 60' /t \ A Z\ 60' ^\ o / / / / / „o ' „ 45 10 53 5-45 79 16 0.18 10 12 5-45 79 38 0.18 9 51 6.00 80 0.17 45 45-9 40 44 5-45 27 .20 23 6.00 49 .18 10 I 6.00 10 .18 44 44.9 47 55 5-45 39 .18 33 6.00 80 .18 1 1 6.00 21 .18 43 43-9 48 II 6 6.00 50 .20 43 6.00 II .iS 21 6.00 32 .18 42 42.9 49 16 6.00 80 2 .20 53 6.00 22 .20 31 6.00 43 .18 41 41.9 50 26 6.00 14 0.20 II 3 6.00 34 o.i8 41 6.67 54 0.18 40 40.9 51 36 6.00 26 .20 13 6.00 45 .20 50 6.67 81 5 .18 39 39-9 52 46 6.00 38 .20 23 6.67 57 .20 59 6.67 16 .20 38 38.9 53 56 6.67 50 .22 32 6.67 81 9 .20 II 8 6.67 28 .20 37 37-9 54 12 5 6.67 81 3 .22 41 6.67 21 .22 17 6.67 40 .20 36 36.9 55 14 6.67 16 0.22 50 6.67 H 0.20 26 7.50 52 0.20 35 35-9 ^6 23 6.67 29 .22 59 7.50 46 .22 34 7.50 82 4 .20 34 34-9 57 32 6.67 42 .22 12 7 7.50 59 .22 42 7.50 16 .20 33 33-9 58 41 7.50 55 •23 15 7.50 82 12 .22 50 7.50 28 .22 32 32.8 59 49 7.50 82 9 .22 23 7.50 25 .22 58 7-5° 41 .22 31 31.8 6o 57 7.50 22 0.23 31 7.50 38 0.22 12 6 8.57 54 0.22 30 30.8 6i 13 5 7.50 36 .23 39 8.57 51 •23 13 8.57 83 7 .22 29 29.8 62 13 8.57 50 .23 46 8.57 83 5 .22 20 8.57 20 .22 28 28.8 f3 20 8.57 83 4 .23 53 8.57 18 •23 27 ^•57 33 .22 27 27.8 64 27 8.57 18 •23 13 8.57 32 •23 34 lO.O 46 .22 26 26.7 65 34 8.57 32 0.25 7 lO.O 46 0.23 40 lO.O o 59 0.22 25 257 66 41 lO.O 47 .23 13 lO.O 84 .23 46 1 0.0 84 12 •23 24 24.7 67 47 lO.O 84 I •25 19 lO.O 14 •23 52 1 0.0 26 •23 23 237 68 53 ICO 16 •25 25 lO.O 28 .23 58 12.0 40 •23 22 22.7 69 59 lO.O 31 •25 31 12.0 42 •25 13 3 12.0 54 •23 21 21.6 70 14 5 12.0 46 0.25 36 12.0 57 0.23 8 12.0 85 8 0.23 20 20.6 71 10 12.0 85 I •25 41 12.0 85 II •25 13 12.0 22 •23 19 19.6 72 15 12.0 16 .25 46 12.0 26 .23 18 12.0 36 •23 18 18.6 73 20 12.0 31 •27 51 12.0 40 •25 23 15.0 0. 50 •23 17 17-5 74 25 15.0 47 •25 56 15.0 55 •25 27 15.0 86 4 .23 16 16.5 75 29 15.0 86 2 0.25 14 15.0 86 10 0.25 31 15.0 18 0.25 15 15-5 76 33 15.0 17 • 27 4 20.0 25 •25 ^^ 20.0 33 •23 14 14.4 77 37 20.0 33 •27 7 20.0 40 •25 38 20.0 47 •25 13 13-4 78 40 20.0 49 ■25 10 20.0 55 •25 41 20.0 87 2 •25 12 12.4 79 43 20.0 87 4 •27 13 20.0 87 10 •27 44 20.0 17 .23 II 11.4 80 46 20.0 20 0.27 16 20.0 26 0.25 47 20.0 3i 0.25 10 10.3 81 49 30.0 36 • 27 19 30.0 41 •25 50 30.0 46 •25 i 9-3 82 51 30.0 52 .27 21 30.0 56 •27 52 30.0 88 I •23 8.3 83 53 30.0 88 8 .27 23 30.0 88 12 •25 54 30.C 15 •25 I 7.2 84 55 30.0 24 .27 25 30.0 27 •25 56 60.0 30 •25 6 6.2 85 57 60.0 40 0.27 27 60.0 42 0.27 57 60.0 45 0.25 5 5-2 86 58 60.0 56 • 27 28 60.0 58 •25 58 60.0 89 •25 4 4.1 87 59 60.0 89 12 .27 29 60.0 89 13 •27 59 60.0 15 •25 I 31 88 15 — 28 • 27 30 — 29 •25 14 30 .25 ^ \ 2.1 89 — 44 .27 30 — 44 •27 45 •25 I : I.O 90 90 30 90 90 0.0 a 60' b _A^ a 60' h A a 60' & A 1 a t A 6c/ A 60' A 60' ^ = 75^0' d = 75° SO' d = 76° 0' Page 304] .240 0.231 0.222 iv a = 76° 30' a = 77°0' a = 77° 30' ^ \ * \ d 60' \ * A \d 60' \ i A^ \7 43 43-7 48 10 6.67 52 .18 37 6.67 13 •17 15 6.67 34 •«5 42 42.7 49 9 6.67 81 3 .18 46 6.67 23 ••7 24 6.67 43 •'7 41 41.7 SO 18 6.67 14 0.18 55 6.67 33 0.18 33 7.50 53 0.17 40 40.7 31 27 6.67 25 .iS 10 4 6.67 44 .18 41 7.50 82 3 .18 39 39-7 52 36 6.67 36 .18 13 7.50 55 .18 49 7.50 14 •'7 38 38.7 53 45 7.50 47 .18 21 7-5° 82 6 .18 57 7.50 24 .18 37 37-7 54 S3 7-5° 58 .iS 29 7.50 17 .18 10 5 7-5° 35 •17 36 36.7 55 1 1 I 7.50 82 9 0.20 37 7.50 28 0.18 13 8.57 45 0.18 35 35-7 56 9 7.50 21 .20 45 7.50 39 .18 20 8.57 56 .18 34 34-7 57 17 7-5° 33 .20 53 8.57 50 ,18 27 8.57 ^3 I .18 33 33-7 58 25 7.50 45 .20 II 8.57 83 I .20 34 8.57 18 .18 32 32.7 59 33 8.57 57 .20 7 8.57 13 .20 41 8.57 29 .18 31 317 60 40 8.57 83 9 0.22 14 8.57 25 0.20 48 8.57 40 0.20 30 30.6 61 47 8.57 22 .20 21 8.57 37 .20 55 lO.O 52 .18 29 29.6 63 54 8.57 34 .22 28 lO.O 49 .20 1 1 I lO.O 84 3 .20 28 28.6 63 12 I lO.O 47 .2C 34 lO.O 84 I .20 7 lO.O 15 .20 27 27.6 64 7 lO.O 59 .22 40 lO.O 13 .20 13 lO.O 27 .20 26 26.6 65 13 1 0.0 84 12 0.22 46 lO.O 25 0.22 19 12.0 39 0.20 25 25.6 66 19 1 0.0 25 .22 52 12.0 38 .22 24 12.0 51 .20 24 24.6 67 25 12.0 38 •23 57 12.0 51 .20 29 12.0 85 3 .20 23 23s 68 30 12.0 52 .22 12 2 12.0 85 3 .22 34 12.0 15 .20 22 22.5 69 35 12.0 85 5 .22 7 12.0 16 .22 39 12.0 27 .22 21 21.5 70 40 12.0 18 0.23 12 12.0 29 0.22 44 12.0 40 0.20 20 20.5 71 45 12.0 32 ,22 17 15.0 42 .22 49 15.0 0. 52 .22 19 195 72 50 15.0 45 • 23 21 15.0 55 .22 53 15.0 86 5 .20 18 18.4 73 54 15.0 59 •~3 25 15.0 86 8 •23 57 15.0 17 .22 17 17.4 74 58 15.0 86 13 •23 29 15.0 22 .22 12 I 20.0 30 .22 16 16.4 75 13 2 15.0 27 0.23 33 15.0 35 0.22 4 20.0 4J 0.22 15 15-4 76 6 20.0 41 .23 37 20.0 48 •23 7 20.0 56 .22 14 14.4 77 9 20.0 55 .23 40 20.0 87 2 .22 10 20.0 87 9 .22 13 13.3 78 12 20.0 87 9 •23 43 20.0 15 •23 13 20.0 22 .22 12 12.3 79 15 20.0 23 •23 46 30.0 29 .22 16 30.0 35 .22 II "•3 80 18 30.0 37 0.23 48 30.0 42 0.23 18 30.0 48 0.22 10 10.3 81 20 30.0 51 • 23 50 30.0 56 • 23 20 30.0 88 I .22 9 9.2 82 22 30.0 88 5 •23 52 30.0 88 10 .22 22 30.0 14 .22 8 8.2 83 24 30.0 19 .25 54 30.0 23 .23 24 30.0 27 .22 I 7.2 84 26 60.0 34 •23 56 60.0 37 •23 26 60.0 40 •23 6 6.2 85 27 60.0 48 0.23 57 60.0 51 0.23 27 60.0 54 0.22 5 5-1 86 28 60.0 89 2 .2s 58 60.0 89 5 .22 28 60.0 89 7 .22 4 4.1 87 2Q 60.C 17 .23 59 60.0 18 •23 29 60.0 20 .22 3 3-1 88 30 — 31 ■23 13 — 3^ •23 30 33 .23 2 2.1 89 30 — 45 • 2f — 46 •23 30 47 .22 I I.O 90 30 ';.':) 90 30 90 0.0 a 60' b A a 60^ h A a 60' I A a t A 63 44 44.6 47 45 7.50 45 ••5 23 7.50 82 6 •«5 8 I 7.50 27 •13 43 43-6 48 53 6.67 54 •17 31 7.50 15 •15 9 7.50 35 •'5 42 42.6 49 9 2 7.50 82 4 •'5 39 7.50 24 •15 17 8.57 44 •15 41 41.6 50 10 7.50 13 0.17 47 7.50 33 0.15 24 7-5° 53 0.15 40 40.6 51 18 7.50 23 •17 55 7.50 42 •■5 32 8.57 83 2 •'5 30 39-6 52 26 7.50 33 •17 9 3 8.57 51 ••7 39 8.57 II •'5 38 38.6 53 34 8.57 43 •17 10 8.S7 83 I •17 46 8.57 20 •'5 37 37-6 54 41 8.57 53 •17 17 8.57 II •17 53 8.57 29 •'5 36 36.6 55 48 8.57 83 3 0,17 24 8.57 21 0.17 9 9 1 0.0 3^ 0.17 35 35-5 56 55 8.57 13 .18 31 8.57 31 .'7 6 8.57 48 •15 34 34-5 57 10 2 8.57 24 •17 38 lO.O 41 •'7 13 lO.O 57 • 17 33 33-5 58 9 8.57 34 .18 44 lO.O „ 51 •'7 19 lO.O 84 7 •17 32 32.5 59 16 8.57 45 .18 50 lO.O 84 I •17 25 1 0.0 17 ••7 31 31S 60 23 lO.O 56 0.18 56 10,0 II 0.18 31 lO.O 27 0.17 30 30-5 61 29 1 0.0 84 7 .18 10 2 lO.O 22 .18 37 12.0 37 .«7 29 295 63 35 lO.O 18 .18 8 10,0 33 •17 42 12.0 47 •17 28 28.5 63 41 12.0 29 .20 14 12.0 43 .18 47 12.0 57 .18 27 27.5 64 46 lO.O 41 .18 19 12.0 54 .18 52 12.0 85 8 ••7 26 26.5 65 52 12.0 52 0,20 24 12.0 85 5 0.18 57 12.0 18 0.18 25 254 66 57 12.0 85 4 .18 29 12.0 16 .18 10 2 1 2.0 29 .17 24 24.4 67 II 2 12. C 15 .20 34 12.0 27 .18 7 15.0 39 .18 23 234 68 7 12.0 27 .20 39 12.0 38 .20 II 15.0 50 .18 22 22.4 69 12 15.0 39 .20 44 15.0 50 .18 15 15.0 86 I .18 21 21.4 70 16 15.0 SI 0.20 48 15.0 86 I 0.20 19 15.0 12 o.i8 20 20.4 71 20 15.0 86 3 .20 52 15.0 13 .18 23 15.0 23 .18 10 19.4 72 24 15.0 15 ,20 56 15.0 24 .20 27 15.0 34 .18 1 8 18.3 73 28 15.0 27 .20 1 1 20.0 36 .18 31 20.0 45 .18 'J • 17-3 74 32 20.0 39 .20 3 20.0 47 .20 34 20.0 56 .18 16 16.3 75 35 20.0 51 0.20 6 20.0 59 0.20 37 20.0 87 7 0.18 15 iS-3 76 38 20.0 87 3 .22 9 20.0 87 II .20 40 20.0 18 .20 M 14-3 77 41 20.0 16 .20 12 20.0 23 .20 43 20.0 30 .18 13 133 78 44 20.0 28 .22 15 30.0 35 .20 46 30.0 41 .20 12 12.2 79 47 30.0 41 .20 17 30.0 47 .20 48 30.0 53 .18 II 11.2 80 49 30.0 53 0.22 19 30.0 59 0.20 50 30.0 88 4 0.18 10 10.2 81 51 30.0 88 6 .20 21 30.0 88 II .20 52 30.0 15 .20 9 9.2 82 53 30.0 18 .22 23 30.0 23 .20 54 60.0 27 .20 8 8.2 83 55 60.0 31 .22 25 60.0 35 .20 55 60.0 39 .18 7 7-1 84 56 60.0 44 .20 26 60.0 47 .20 56 60.0 50 .20 6 6.1 85 57 60.0 56 0.22 27 60.0 59 0.20 57 60.0 89 2 0.18 5 5.1 86 58 60.0 89 9 .22 28 60.0 89 II .20 58 60.0 13 .20 4 4.1 87 59 60.0 22 .20 29 60.0 23 .20 59 60.0 25 .20 3 31 88 12 — 34 .22 30 — 35 .22 1 1 — 37 .iS 2 2.0 89 — 47 .22 30 — 48 .20 — 48 .20 J 1.0 90 90 30 90 90 0.0 a 60' b A a 6(/ b A a 6(y b _A_ a t A 6^' A 60/ A 6'/ d = lS°0' d = lS°30' d = 19° 0' Page 308] 0185 0.1 76 01 67 \ a = 79° 30 a = 80°0' a = 80° 30' • K \ * \ d 60' \ t A \ d 60' \ t A \ d 60' \ t A \ A ^ \ A z\ 60' /l\ A z\ 60' A \ A z\ 60' f\ /8\ o / / / «o ' / ^0 ' 5-45 79 30 0.00 6.00 80 0.00 6.00 80 30 0,00 90 90.0 I II 5-45 30 .00 10 5-45 .00 10 6.00 30 .00 89 89.0 2 22 5-45 30 .02 21 6.00 .02 20 6. CO 30 .02 88 S8.0 3 32, 5-45 31 .00 31 5-45 I .00 30 6.00 31 .00 87 87.0 4 44 5-45 31 .02 42 6.00 I .02 40 6.00 31 .02 86 86.1 5 5| 5-45 32 0.02 52 6.00 2 0.02 50 6.67 32 0.02 85 85.1 6 I 6 5-45 ZZ .02 I 2 5-45 3 .02 59 6.00 33 .02 84 84.1 7 17 6.00 H .03 13 6.00 4 .03 I 9 6.00 34 .02 83 83.1 8 27 5-45 36 .03 23 6.00 6 .02 19 6.00 35 .03 82 82.1 9 38 S-45 38 .02 33 5-45 7 •03 29 6. GO 37 .02 81 81.1 10 49 5-45 39 0.03 44 6.00 9 0.03 39 6.67 38 0.03 80 80.1 1 1 2 6.00 41 .03 54 6.00 II .03 48 6.00 40 .03 79 79.2 12 10 5-45 43 .05 2 4 6.00 13 .03 58 6.CC 42 •°3 78 78.2 13 21 5-45 46 .03 14 6.00 15 •03 2 8 6.67 44 .03 77 77.2 14 32 6.00 48 .05 24 6.00 17 .05 17 6.00 46 .05 76 76.2 IS 42 5-45 51 0.05 34 6.00 20 0.05 27 6.67 49 0.05 75 75-2 i6 53 6.00 54 .05 44 6.00 23 .05 36 6.00 52 .03 74 ! 74.2 17 3 3 5-45 57 .05 54 6.00 26 .05 46 6.67 54 .05 73 73-2 i8 14 6.00 80 .05 3 4 6.00 29 .05 55 6.00 57 .05 72 72.3 19 24 6.00 3 .07 14 6.00 32 .05 3 5 6.67 81 .07 71 713 20 34 5.45 7 0.07 24 6.00 35 0.07 14 6.CC 4 0.05 70 70.3 21 45 6.00 II .07 34 6.00 39 .07 24 6.67 7 .07 69 693 22 55 6.00 15 .07 44 6.67 43 .07 33 6.67 II .07 68 68.3 23 4 5 6.00 19 .07 53 6.00 47 .07 42 5.67 15 .07 67 67.3 24 15 6.00 23 .08 4 3 6.00 51 .07 51 6.67 19 .07 66 66.3 ^$ 25 6.00 28 0.08 13 6.67 55 0.08 4 6.67 23 0.07 65 65-3 26 35 6.00 33 .07 22 6.67 8x .07 9 6.67 27 .07 64 64.3 -7 45 6. CO 37 .08 31 6.00 4 .08 18 6.C7 31 .08 63 634 28 55 6.67 42 ,oS 41 6.67 9 .08 27 6.67 36 •07 62 62.4 -9 5 4 6.C0 47 .10 50 6.67 14 .08 36 7.50 40 .08 61 61.4 30 14 6.67 53 o.oS 59 6.67 19 0.08 44 6.67 45 0.08 60 60.4 31 23 6.00 58 .10 5 8 6.67 24 .10 53 7.50 50 .08 59 59-4 3^ iZ 6.67 81 4 .10 17 6.67 30 .cS 5 I 7.50 55 .10 58 58.4 33 42 6.67 10 .10 26 7.50 35 .10 9 6.67 82 I .08 57 57-4 34 51 6.67 16 .10 34 6.67 41 .10 18 7.50 6 .10 56 56.4 ^l 6 6.67 22 0. 10 43 6.67 47 0. 10 26 7.50 12 0.08 55 55-4 36 9 6.67 28 .12 . 52 7.50 53 .10 34 7.50 17 .10 54 54-4 17 18 6.67 35 .10 6 7.50 59 .10. 42 7.50 23 .10 53 53-4 S8 27 7.50 41 .12 8 7-5° 82 5 .12 50 7.50 29 .10 52 524 39 35 6,67 48 .12 16 7.50 12 .10 58 8.57 35 . 12 51 Si-4 40 44 7.50 55 0.12 24 7.50 18 0.12 6 5 7.50 42 0. 10 50 50.4 41 52 7.50 82 2 .12 32 7.50 25 .12 13 8.57 48 .12 4? 49.4 42 7 c 7-5° 9 •13 4? 7.50 32 .12 20 7.50 55 .10 48 48.4 43 8 7-5° 17 .12 48 7.50 39 .12 28 8.57 S3 I .12 47 47-4 44 16 7- 5c 24 • '3 56 8.57 46 •13 35 8.57 8 .12 46 46.4 45 24 32 7 3 54 42 15 45 4S4 a 60' 6 A a 60' 6 A a 60' 6 A a t A 60' A 60' A 60' (^ = 79°30' c? = 8 0°0' ^ = 80° 30' 185 0176 0.167 [Page 309 45 46 47 48 40 50 5- 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 ■<■; 1 82 83 S4 8s So 87 88 80 90 79° 30' 60' / / 7 24 7.50 S2 32 0.1 32 7.';o 40 40 8.<;7 48 47 8.57 5G 54 8.57 83 4 8 I 8.^7 12 0.1 8 8.57 21 15 8.^7 29 22 8.57 38 . I 29 1 0.0 47 35 lO.O 56 0.1 41 1 0.0 84 5 47 lO.O 14 . I 53 lO.O 23 59 lO.O 33 . I 9 5 10.0 42 0.1; II 12.0 52 16 12.0 85 I 21 12.0 II 26 12.0 21 31 15.0 31 0. 1' 35 15.0 41 39 ii;.o 51 43 15.0 86 2 47 15.0 12 51 1^0 22 0.1 55 15.0 33 59 20.0 43 10 2 20.0 54 5 20.0 87 4 8 20.0 15 0.1 II 20.0 26 14 30.0 37 16 30.0 47 18 30.0 58 20 30.0 88 9 0.1 22 30.0 20 24 60.0 31 25 60.0 42 26 60.0 53 27 60.0 89 4 0.1 28 60.0 15 29 60,0 27 30 — 38 30 — 49 30 90 ^ b A _A bey 0=80° 0' 6c/ A 60' A _A 6 n° ' / / / / 6.67 81 0.00 6.67 Si 30 0.00 7.50 82 0.00 90 90.0 I 9 6.00 .00 9 6.67 30 .00 8 6.67 .00 89 89.0 o 19 6.67 .cz 18 6.67 30 .02 17 7.50 .02 88 88.0 3 28 6.00 I .oc 27 7.50 31 .00 25 7.50 I .00 87 87.0 4 38 6.67 I .02 35 6.67 31 .02 33 6.67 I .02 86 86.0 5 47 6.67 2 0.02 44 6.67 32 0.02 42 7.50 2 0.02 85 85.1 6 56 6.CC 3 .02 53 6.67 33 .02 50 7-50 3 .02 84 84.1 7 I 6 6.67 4 .02 I 2 6.67 34 .02 58 6.67 4 .02 83 83.1 8 15 6.67 5 .02 II 6.67 35 .02 1 7 7.50 5 .02 82 82.1 9 24 6.67 6 •03 20 7.50 36 •03 15 7.50 6 .02 81 81.1 10 33 6.00 8 0.03 28 6.67 38 0.02 23 7.50 7 0.03 80 80.1 1 1 43 6.67 10 •03 37 6.67 39 •03 31 6.67 9 .02 79 79.1 12 52 6.67 12 .03 46 7.50 41 .03 40 7.50 10 .03 78 78.1 13 2 I 6.67 14 .03 54 6.67 43 .03 48 7.50 12 .03 77 77.1 14 10 6.67 16 .03 2 3 6.67 \ 45 •03 56 7.50 14 •03 76 76.1 15 19 6.67 18 0.03 12 7.50 47 0.03 2 4 7.50 16 0.03 75 75-2 i6 28 6.67 20 .05 20 6.67 49 .05 12 7.50 18 .05 74 74-2 17 37 6.67 23 .05 29 7.50 52 •05 20 7.50 21 .03 73 73-2 i8 46 6.67 26 .05 37 6.67 55 •03 28 7.50 23 .05 72 72.2 19 55 6.67 29 .05 46 7.50 57 .05 36 7.50 26 .05 71 71.2 20 3 4 6.67 32 0.05 54 7.50 82 0.05 44 7.50 29 0.05 70 70.2 21 13 6.67 35 .07 3 2 7.50 3 .07 52 8.57 3\ .05 69 69.2 22 22 7.50 39 •OS 10 6.67 7 •05 59 7.50 35* .05 68 68.2 23 30 6.67 42 .07 . 19 7.50 10 .05 3 7 7.50 38 •05 67 67.2 24 39 7.50 46 .07 27 7.50 13 .07 15 8.57 41 .05 66 66.2 25 47 6.67 50 0.07 35 7.50 17 0.07 22 7.50 44 0.07 65 65.2 26 56 6.67 54 .07 43 7.50 21 .07 30 8.57 48 .07 64 64.2 27 4 5 7-5° 58 .07 51 7.50 25 .07 37 7.50 52 .07 63 63-3 28 13 7.50 82 2 .08 59 7.50 29 .07 45 8.57 56 .07 62 62.3 29 21 7.50 7 .07 4 7 8.57 33 .07 52 8.57 83 .07 61 61.3 30 29 7.50 11 0.08 14 7.50 37 0.08 59 7.50 4 0.07 60 6a3 31 37 7.50 16 .08 22 7.50 42 .08 4 7 8.57 8 .07 59 59-3 32 45 7.50 21 .08 30 8.57 47 .07 14 8.57 12 .08 5^ 58.3 33 53 7.50 26 .oS 37 7.50 51 .08 21 8.57 17 ,07 57 57-3 34 5 I 7.50 31 .08 45 8.57 56 .08 28 8.57 21 .08 56 56.3 35 9 7.50 36 0,10 52 8.57 ^3 I 0.08 35 8.57 26 0.08 55 5S3 ^6 17 "•57 42 .08 59 8.57 6 .10 42 lO.O 31 .08 54 54-3 37 24 7.50 47 .10 5 6 8.57 12 .08 48 8.57 36 .08 53 53-3 38 32 8-57 53 .10 13 8.57 17 .08 55 8.57 41 .08 52 52.3 39 39 8.57 59 .10 20 8.57 22 .10 5 2 1 0.0 46 .08 51 Si-3 40 46 8.57 83 5 0. 10 27 8.57 28 0. 10 8 1 0.0 51 0. 10 50 So-3 41 . 53 8.57 II .10 34 8.57 34 .10 14 8.57 57 .08 49 1 49-3 42 6 8.57 17 .10 41 1 0.0 40 .10 21 1 0.0 84 2 .10 48 1 48.3 43 7 8.57 23 .12 47 8.57 46 . 10 27 lO.O 8 .10 47 i 47-3 44 14 8.57 30 .12 54 lO.O 52 .10 33 lO.O 14 .10 46 ! 46.3 45 21 37 6 58 39 20 45 45-3 a Ou' b _A a 60' b _A a 60' b _A_ a t A 60' ~A 60' A 60' d^S 1°0' d = Si [°30' d = S 2°0' 0.IS8 0.149 0.141 [Page 311 \ a = 81°0' a = 81° 30' a = 82°0' \ \- X 6c/ A A 60' A z\ A 60' 60' A z\ A 60' A 45 6 21 8.57 83 37 0, 10 / 6 lO.O / 83 58 0. 10 / 5 39 lO.O 84 20 O.IO 45 45-3 4b 28 10,0 43 .12 6 lO.O 84 4 .12 45 lO.O 26 .10 44 44-3 47 34 8.57 50 .12 12 1 0.0 II .TO 51 12.0 32 .10 43 43-3 48 41 1 0.0 57 .1 2 18 lO.O 17 .12 . 56 lO.O 38 .10 42 42.3 49 47 lO.O 84 4 .12 24 lO.O 24 .12 6 2 12.0 44 .10 41 41.3 SO 53 lO.O II 0.12 30 lO.O 3£ 0.12 7 lO.O 50 0.12 40 403 51 59 lO.O 18 .13 36 12.0 38 .12 13 12.0 57 .ro 39 39-3 52 7 5 lO.O 26 .12 41 1 0.0 45 .12 18 12.0 85 3 .12 38 38.3 53 II 12.0 33 .13 47 12.0 52 .12 23 12.0 10 .12 37 37-3 54 16 lO.O 41 •13 52 12.0 59 .12 28 12.0 17 .10 36 36.3 55 22 12.0 49 0.12 57 12.0 85 6 0.12 33 12.0 23 0.12 35 35-3 56 27 12.0 56 •13 7 2 12.0 13 .13 38 15.0 30 .12 34 34-3 57 32 12.0 85 4 •13 7 12.0 21 .12 42 12.0 37 .12 33 33-3 58 37 12.0 12 .13 12 12.0 28 .13 47 15.0 44 •'3 32 32.3 59 42 12.0 20 • 13 17 12.0 36 •13 51 15.0 52 .12 31 313 60 47 12.0 28 0.15 22 15.0 44 0.12 55 15.0 59 0.12 30 30.3 61 52 12.0 37 .13 26 15.0 51 ••3 59 15.0 86 6 .12 29 293 62 57 15.0 45 •13 30 15.0 0. 59 .13 7 3 15.0 13 •13 28 28.3 63 8 I 15.0 . 53 •15 34 15.0 86 7 .13 7 15.0 21 .12 27 273 64 5 15.0 86 2 • 13 38 15.0 15 .'3 11 15.0 28 •13 26 26.3 65 9 15.0 10 0.15 41 15.0 23 0.13 15 15.0 36 0.13 25 25.2 66 13 15.0 19 •15 46 20.0 31 .13 19 20.0 44 .12 24 24.2 67 17 15.0 28 •13 49 15.0 ^2 .»s 22 20.0 51 •'3 23 23.2 68 21 20.0 36 •15 53 20.0 48 •13 25 20.0 59 ••3 22 22.2 69 24 20.0 45 ••5 56 20.0 56 .13 28 20.0 87 7 •'3 21 21.2 70 27 20.0 54 0.15 59 20.0 87 4 0.15 31 20.0 15 0.13 20 20.2 71 30 20.0 87 3 •'5 8 2 20.0 13 .13 34 20.0 23 •'3 19 19.2 72 33 20.0 12 .15 5 20.0 21 .15 37 30.0 31 .13 18 18.2 73 36 20,0 21 .15 8 30.0 3° • 13 39 30.0 39 .13 'I 17.2 74 39 20.0 30 •15 10 20.0 38 ••5 41 30.0 47 .13 16 16.2 75 42 30.0 39 0.15 13 30.0 47 0.15 43 30.0 „ 55 0.13 15 152 76 44 30.0 48 .17 15 30.0 56 •'3 45 30.0 88 3 .13 14 1 14.2 77 46 30.0 58 .»s 17 30.0 88 4 •15 47 30.0 II •15 13 131 78 48 30.0 88 7 •15 19 30.0 13 •'5 49 30.0 20 .13 12 12. 1 79 50 30.0 16 •15 21 60.0 22 • •'5 51 30.C 28 •13 II ii.i 80 52 30.0 25 0.17 22 30.0 31 0.15 53 60.0 36 0.13 IC 1 10. 1 .Si 54 60.0 35 •15 24 60.0 40 .'3 54 60.0 44 .15 Q 9.1 82 55 60.0 44 •17 25 60.0 48 .'5 55 60.0 53 .'3 8 8.1 83 56 60.0 54 •15 26 60.0 57 .'5 56 60.0 89 I .15 7 1-^ 84 57 60.0 89 3 • Jy 27 60.0 89 6 •15 57 60.0 10 •«3 6 6.1 85 58 60.0 13 0.15 28 60.0 15 0.15 58 60.0 18 0.13 5 51 so 59 — 22 ••5 29 24 •15 59 — 26 .'5 4 i 4.0 ^^7 59 6c. 31 .'7 29 60. G 33 •'5 59 60.0 35 .13 3 1 3-0 88 9 — 41 •'5 30 42 •15 8 — 43 •'5 2 1 2.0 89 — 50 •17 30 51 •15 — 52 .'3 I 1 I.O 90 90 30 90 90 0.0 a 60' b A a 60' b A a ^ b A a t A 6(y A Gc/ ^ 6^ d = Sl°0' ^ = 81° 30' rf = 82°0' Page 312] 0.132 0.123 0.114 I a = 82° 30' a = 83°0' a = 83° 30' X \ * be/ 60' A z\ A 62 31 51 8.57 34 .07 36 lO.O 84 .05 21 12.0 25 .07 52 59-2 32 58 8.57 38 .07 42 lO.O 3 .07 26 lO.O 29 .05 58 58.2 33 4 5 1 0.0 42 .07 48 lO.O 7 .07 ^o lO.O 32 .07 H 57-2 34 II 8.57 46 .08 54 lO.O II .07 38 12.0 36 .07 56 56.2 35 18 lO.O 51 0.07 4 1 0.0 *i5 0.08 43 lO.O 40 0.07 55 55-2 36 24 lO.O 55 .08 6 lO.O 20 .07 49 12.0 44 .07 54 54-2 37 30 8.57 84 .08 12 lO.O 24 .07 54 1 0.0 48 .07 53 53-2 38 37 lO.O 5 .07 18 1 0.0 28 .08 4 12.0 5f .07 52 52.2 39 43 10.0 9 .08 24 lO.O 33 .08 5 12.0 56 .08 51 51.2 40 49 lO.O 14 0.08 30 12.0 38 0.07 10 lO.O 85 I 0.07 50 50.2 41 55 lO.O 19 .10 35 10,0 42 .08 16 12.0 5 .oS 49 49.2 42 5 I 12.0 25 .08 41 12.0 47 .08 21 12.0 10 .07 48 48.2 43 6 1 0.0 30 .08 46 lO.O 52 .08 26 12.0 14 .oS 47 47.2 44 12 lO.O 35 .10 52 12.0 57 .08 31 12.0 19 .08 46 46.2 45 18 41 57 85 2 36 24 45 45-2 a ec/ h A a 60' b _A_ a 6°0' (f = 85'0' (^=86° 0' Page 316] 0.052 003s 0.020 0.017 0.000 t a = ST" 0' a = 88° 0' a = 88° 50' a = 89°0' a = 90° 0' V \ - u 90 4°5 46 9 55 26 37 50 1 1 43 18 44 47 12 57 28 38 51 12 44 19 43 48 14 59 29 40 52 13 4 5 20 42 49 16 88 2 31 41 53 14 45 21 41 50 18 4 32 43 54 I =; 46 21 40 51 20 7 33 44 54 16 46 22 39 52 22 9 35 46 55 17 47 23 38 ^ '^ 24 12 36 48 56 18 48 24 37 54 26 14 37 49 57 19 49 25 36 55 27 17 38 51 57 20 49 26 35 56 29 19 39 53 58 21 5c 26 34 57 31 22 41 55 59 22 5c 27 33 58 33 2S 42 56 I 23 51 28 32 59 34 27 43 58 24 51 29 31 60 36 30 44 89 I 25 52 30 30 61 37 33 45 2 I 26 52 31 29 62 39 35 46 4 2 27 53 32 28 63 40 38 47 5 2 28 53 33 ""l 64 42 41 48 7 3 29 54 34 26 65 43 44 49 9 3 30 54 35 25 66 44 47 50 II 4 32 55 36 24 67 46 50 50 13 4 33 55 37 23 68 47 53 51 15 ^ 34 56 3^ 22 69 48 55 52 17 5 35 56 38 21 70 49 58 S3 19 6 36 5f 39 20 71 50 89 I 53 21 6 37 56 40 19 72 51 4 54 23 7 38 57 41 18 73 52 7 55 25 7 40 57 42 17 53 10 55 27 8 41 58 43 16 75 54 13 56 20 8 42 58 44 15 76 55 16 S6 31 8 43 58 45 c 14 77 55 19 57 33 8 44 58 46 13 78 56 23 57 3S 9 45 59 47 12 79 57 26 58 37 9 47 59 49 II 80 57 29 58 39 9 48 59 50 10 81 58 32 59 41 9 49 59 SI 9 8 82 58 35 59 43 9 50 59 52 83 59 38 59 45 10 51 I 53 7 84 59 41 59 47 10 53 54 c 6 85 59 44 2 5° 10 54 55 5 86 3 47 52 10 55 c 56 c 4 87 51 54 10 5<^ 57 3 88 54 56 10 58 58 2 89 57 58 lO 59 59 I 90 t 90 90 TO 90 90 a 6 a b 1 a 1' a 6 a h d = STO' rf = 88°0' rf = 88°50 d = 89° 0' d = 9 0^0' 1 {Poparts inigio) When Polaris' / > 90" : Z. = (90° + B)-b. Page 318] TABLE Vn. Change ! of Altitude per Minute of Arc of Hour Angl e. r ^, A/1 AlZ d a.Tifl T / same name . fK90° ^L>b: „=-;„= + Ah At ~ T COS. LsinZ f .f>90° . . .: ,,= + ; ,, = + AiZ At ~ = T sin L d and L contrary nam« ;g : .,= -;,.= + | V 0° ^/ \ 5° 10° 15° 20° 25° 30° 35° 40° 45° 50° 55° 60° 65° 70° /C, z\ sin Z' /Z' / / / / / / / / / / / / / / / 0° o. oo 0.00 0. 00 0. 00 0. 00 0. 00 0. 00 0. 00 0. 00 0. 00 0. 00 0. 00 0. 00 0.00 0. 00 0° 2 • 03 •03 •03 •03 •03 •03 •03 •03 ■03 . 02 02 . 02 .02 . 01 . 01 2 4 .07 .07 .07 .07 .07 .06 .06 .06 •05 •05 .04 .04 •03 •03 .02 4 6 . 10 . 10 . 10 . 10 . 10 .09 .09 .09 .08 .07 .07 .06 •05 .04 .04 6 8 • 14 .14 .14 •13 •13 • 13 . 12 . II . II . 10 .09 .08 .07 .06 •OS 8 10 0.17 0. 17 0. 17 0.17 0. 16 0. 16 0.15 0. 14 0.13 0. 12 0. II 0. 10 0. 09 0. 07 0. 06 10 12 .21 . 21 . 20 . 20 . 20 • 19 .18 •17 .16 •15 •13 . 12 . 10 .09 .07 12 14 .24 .24 .24 •23 •23 . 22 . 21 . 20 .19 •17 . 16 • 14 . 12 . 10 .08 14 16 .28 .27 .27 .27 .26 •25 .24 •23 . 21 .19 .18 .16 .14 . 12 .09 16 18 •31 •31 •30 •30 .29 .28 ■27 •25 .24 . 22 . 20 .18 •15 •13 . II 18 20 0-34 0.34 0.34 0.33 0.32 0.31 0.30 0.28 0. 26 0. 24 0. 22 0. 20 0.17 0. 14 0. 12 20 22 •37 •37 •37 •36 •35 •34 •32 •31 .29 .27 • 24 . 21 19 . 16 •13 22 24 .41 .41 .40 •39 •38 •37 •35 •33 •31 .29 .26 •23 . 20 •17 • 14 24 26 • 44 •44 •43 .42 .41 .40 •38 .36 •34 •31 .28 • 25 . 22 .19 •IS 26 28 •47 •47 .46 •45 •44 •43 .41 •38 •36 •33 •30 .27 •23 . 20 .16 28 30 0.50 0. 50 0.49 0.48 0.47 0.45 0.43 0. 41 0.38 0-35 0.32 0. 29 0.25 0. 21 0. 17 30 32 •53 •53 •52 •51 •50 .48 .46 •43 .41 •37 •34 •30 .27 . 22 .18 32 34 •56 •56 •55 •54 •53 •SI .48 .46 •43 .40 •36 •32 .28 .24 •19 34 36 •59 •59 •58 •57 •55 •53 •51 .48 •45 .42 •38 •34 •29 •25 . 20 36 38 .62 .61 .61 •59 •58 •56 •53 •50 •47 •44 .40 •35 •31 .26 . 21 38 40 0. 64 0. 64 0.63 0. 62 0. 60 0.58 0.56 0-53 0.49 0. 45 0. 41 ©•37 0.32 0. 27 0. 22 40 42 .67 .67 .66 •65 •63 .61 •58 •55 • 51 •47 •43 •38 •33 .28 •23 42 44 .69 .69 .68 .67 •65 •63 .60 •57 •53 •49 •45 • 40 •35 •29 24 44 46 .72 .72 •71 .69 .68 •65 .62 •59 ■55 •51 .46 .41 .36 •30 •25 46 48 •74 •74 •73 •72 .70 .67 .64 .61 •57 •53 .48 •43 •37 •31 •25 48 50 0.77 0. 76 0-75 0. 74 0. 72 0. 69 0.66 0.63 0-59 0.54 0.49 0.44 0.38 0.32 0. 26 50 52 •79 .78 .78 .76 •74 •71 .68 •65 .60 •56 •51 •45 •39 •33 .27 52 54 .81 .81 .80 .78 .76 •73 .70 .66 .62 •57 •52 .46 .40 •34 .28 54 56 •83 •83 .82 .80 •78 •75 .72 .68 .64 •59 •53 .48 •41 •35 .28 56 58 •85 .84 •83 .82 .80 •77 •73 .69 .65 .60 •55 ■49 .42 •36 .29 58 60 0.87 0.86 0.85 0.84 0.81 0. 78 o^75 0.71 0.66 0. 61 0. 56 0. SO 0.43 0-37 0.30 60 62 .88 .88 •87 •85 •83 .80 .76 •72 .68 .62 •57 •SI • 44 •37 •30 62 64 .90 .90 .89 •87 .84 .81 .78 •74 .69 .64 •58 •52 •45 •38 •31 64 66 .91 .91 .90 .88 .86 •83 •79 •75 .70 •65 •59 •52 .46 •39 •31 66 68 •93 .92 .91 .90 •87 .84 .80 .76 •71 .66 .60 •53 .46 •39 •32 68 70 0.94 0.94 ©•93 0. 91 0.88 0. S^? 0.81 0.77 0.72 0.66 0. 60 0.54 0.47 0. 40 0.32 70 72 •95 •95 •94 .92 .89 .86 .82 .78 •73 .67 .61 •55 .48 .40 ■33 72 74 .96 .96 •95 •93 .90 •87 •83 •79 •74 .68 .62 •55 .48 •41 •33 74 76 •97 •97 .96 • 94 .91 .88 .84 •79 •74 .69 .62 •56 •49 • 41 ■33 76 78 .98 •97 .96 •94 .92 .89 •85 .80 •75 .69 •63 •56 •49 .41 •33 78 80 0.98 0.98 0.97 0-9S 0^93 0.89 0.85 0.81 0.75 0. 70 0.63 0. 56 0.49 0. 42 0.34 80 82 •99 •99 .98 .96 •93 .90 .86 .81 .76 .70 .64 •57 •50 .42 •34 82 84 •99 •99 .98 .96 •93 .90 .86 .81 .76 .70 .64 •57 •50 .42 •34 84 86 I. 00 •99 .98 .96 •94 .90 .86 .82 .76 •71 .64 •57 •50 .42 •34 86 88 I. 00 I. CX3 .98 •97 •94 .91 .87 .82 •77 •71 .64 •57 •50 .42 •34 88 90 I. 00 I. 00 0.98 0.97 0.94 0.91 0.87 a 82 0.77 0. 71 0. 64 o^57 0. so 0.42 0.34 90 To find -Z7 or sin L, enter column L=0° with L instead of Z\ At Ad To find -TT or cos M enter column L=0° with 90-M instead of 2'. TABLE VIII. [Page 319 Change of Azimuth per Minute x>f Arc of Altitud e. = - tan/i'cotZ^(- - always-wiih. Z' less than 90°). 0° 5° 10° 15° 20° 25° 30° 35° 40° 45° 50° 60° 70° 80° 90° Z' / / / / / / / / / / / / / / 0° ind. o.oo 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 90° 2 CO .40 .20 •13 .10 .07 .06 •05 .04 •03 -03 .02 .01 .01 .00 88 4 OO .80 .40 .26 .19 -15 .12 .10 .08 .07 .06 .04 •03 .01 .00 86 6 oo 1.20 .60 -39 .29 -23 .18 -15 -13 .11 .09 .06 .04 .02 .00 84 8 OO 1. 61 .80 •52 -39 •30 .24 .20 •17 .14 .12 .08 •05 .02 .00 82 10 oo 2.02 1. 00 0.66 0.48 0.38 0-31 0.25 0.21 0.18 0.15 O.IO 0.06 0.03 0.00 80 12 CO 2-43 1. 21 -79 •58 .46 -37 -30 •25 .21 .18 .12 .08 .04 .00 78 14 oo 2.85 1. 41 •93 .69 •53 -43 •36 •30 •25 .21 .14 .09 .04 .00 76 16 CO 3-28 1.63 1.07 -79 .61 •50 .41 •34 .29 .24 •17 .10 •05 .00 74 18 oo 3-71 1.84 1. 21 .89 .70 •56 .46 •39 •32 .27 .19 .12 .06 .00 72 20 oo 4.16 2.06 1.36 1. 00 0.78 0.63 0.52 0.43 0.36 0.31 C.21 0.13 0.06 0.00 70 22 CO 4.62 2.29 1-51 I. II •87 .70 •58 .48 .40 •34 •23 •IS .07 .00 68 24 oo 5-09 2-53 1.66 1.22 •95 •77 .64 -53 -45 •37 .26 .16 .08 .00 66 26 oo 5-57 2.77 1.82 1-34 1-05 .84 .70 •58 •49 .41 .28 .18 .09 .00 64 28 oo 6.08 3.02 1.98 1.46 1. 14 .92 •76 •63 •53 •45 •31 .19 .09 .00 62 30 00 6.60 3-27 2.15 1-59 1.24 1. 00 0.82 0.69 0.58 0.48 o^33 0.21 O.IO 0.00 60 32 oo 7.14 3-54 2-33 1.72 1-34 1.08 .89 •74 .62 •52 •36 •23 .11 .00 58 34 CO 7.71 3-83 2.52 1.85 1-45 1. 17 .96 .80 .67 •57 •39 •25 .12 .00 56 36 00 8.30 4.12 2.71 2.00 1.56 1.26 1.04 .87 •73 .61 .42 .26 •13 .00 54 38 00 8-93 4-43 2.92 2.15 1.68 ^•35 1. 12 •93 •78 .66 •45 .28 .14 .00 52 40 oo 9-59 4.76 ^■'^3 2.31 1.80 1-45 1.20 1. 00 0.84 0.70 0.48 0.31 0.15 0.00 50 42 00 10.29 5-II 3-36 2.47 1-93 1.56 1.29 1.07 .90 .76 •52 ■2,3 .16 .00 48 44 oo 11.04 5-48 3.60 2.65 2.07 1.67 1.38 I-I5 •97 .81 •56 •35 •17 .00 46 46 CO 11.84 5-87 3.86 2.85 2.22 1.79 1.48 1.23 1.04 .87 .60 .38 .18 .00 44 48 oo 12.69 6.30 4.14 3-05 2.38 1.92 1-59 1.32 I. II •93 .64 .40 .20 .00 42 50 oo 13.62 6.76 4-45 3-27 2.56 2.06 1.70 1.42 1.19 1. 00 0.69 0.43 0.21 0.00 40 52 oo 14.63 7.26 4.78 3-52 2.74 2.22 1-83 ^•53 1.28 1.07 •74 •47 •23 .00 38 54 oo 15-73 7.81 5-14 3-78 2-95 2.38 1-97 1.64 1.38 i^iS .80 •50 .24 .00 36 56 oo 16.95 8.41 5-53 4.07 3.18 2-57 2.12 1-77 1.48 1.24 .86 •54 .26 .00 34 58 oo 18.29 9.08 5-97 4.40 3-43 2-77 2.29 1.91 1.60 1^34 .92 •58 .28 .00 32 60 oo 19. So 9.82 6.46 4.76 3-71 3.00 2-47 2.06 ^•73 1^45 1. 00 0.63 0.31 0.00 30 62 00 21.50 10.67 7.02 5-17 4-03 3-26 2.69 2.24 1.88 1.58 1.09 .68 ■2i .00 28 64 oo 23-44 11.63 7-65 563 4.40 3-55 2-93 2.44 2.05 1.72 1. 19 •75 •36 .00 26 66 oo 25.67 12.74 8.38 6.17 4.82 3-89 3.21 2.68 2.25 1.88 1.30 .82 .40 .00 24 68 00 28.29 14.04 9-24 6.80 5-31 4-29 3-53 2-95 2.48 2.08 1-43 .90 •44 .00 22 70 oo 31.40 15-58 10.25 7-55 5-89 4.76 3-92 3-27 2-75 2.31 1-59 1. 00 0.48 0.00 20 72 oo 35-18 17-45 11.49 8.46 6.60 5-33 4.40 3-67 3.08 2.58 1.78 1. 12 1"^ .00 18 74 CO 39.86 19.78 13.01 9-58 7.48 6.04 4-98 4.16 3-49 2^93 2.01 1.27 .61 .00 16 76 00 45-84 22.75 14.97 11.02 8.60 6-95 5-73 4.78 4.01 3^37 2.32 1.46 •71 .00 14 78 OO 53-77 26.68 17-56 12.93 10.09 8.15 6.72 5-6i 4.70 3^95 2.72 1. 71 •83 .00 12 80 CO 64.82 32.16 21.17 15-58 12.16 9.82 8.10 6.76 5-67 4.76 3-27 2.06 1. 00 0.00 10 82 00 86.68 40.3s 26.56 19-55 15.26 12.32 10.16 8.48 7.12 5^97 4. II 2-59 1.25 .00 8 84 oo — 53-96 35-51 26.14 20.40 16.48 13-59 11-34 9^51 7-98 5-49 3-46 1.68 .00 6 86 oo — 8r.io 53-37 3929 30.67 24-77 20.42 17.04 14.30 12.00 8.26 5-21 2.52 .00 4 88 oo — — 78.68 61.41 49.60 40.90 34-13 28.64 24.03 16.53 10.42 5-oS .00 2 90 oo 00 00 03 CO 00 00 00 00 00 00 00 00 00 ind. // 90° 85° 80° 75° 70° 65° 60° 55° 50° 45° 40° 30° 20° 10° 0° t Page 320] TABLE IX. For converting Arc into Time, and the reverse. " H.M. " H.M. ° H.M. " H.M. " H.M. ° H.M. ' M.S. M.S. ' M.S. M.S. ' M.S. ' M. S. " S.^ " s.«s, " S.A S.<\, S. ^ " S. ' I 4 61 4 4 121 8 4 181 12 4 241 16 4 301 20 4 2 8 62 4 8 122 8 8 182 12 8 242 16 8 302 20 8 3 12 63 4 12 123 8 12 183 12 12 243 16 12 303 20 12 4 16 64 4 16 124 8 16 184 12 16 244 16 16 304 20 16 5 20 65 4 20 125 8 20 1H5 12 20 245 16 20 305 20 20 6 24 66 4 24 126 8 24 186 12 24 246 16 24 306 20 24 7 28 67 4 28 127 8 28 187 12 28 247 16 28 307 20 28 8 32 68 4 32 128 832 1S8 12 32 248 16 32 308 20 32 9 36 69 4 36 129 8 36 189 12 36 249 16 36 309 20 36 lO 40 70 4 40 130 8 40 190 12 40 250 16 40 310 20 40 II 44 71 4 44 131 8 44 191 12 44 251 16 44 3" 20 44 12 48 72 4 48 132 8 48 192 12 48 252 16 48 312 20 48 13 52 73 4 52 133 8 52 193 12 52 253 16 52 3^3 20 52 14 56 74 4 56 134 8 56 194 12 56 254 16 56 314 20 56 15 I 75 5 135 9 195 13 255 17 315 21 i6 I 4 76 5 4 136 9 4 iq6 13 4 256 17 4 316 21 4 ■ 17 I 8 77 5 8 137 9 8 197 13 8 257 17 8 317 21 8 iS I 12 78 5 12 138 9 12 198 13 12 258 17 12 318 21 12 19 I 16 79 5 16 139 9 16 199 13 16 259 17 16 319 21 16 20 I 20 80 5 20 140 9 20 200 13 20 260 17 20 320 21 20 21 I 24 81 5 24 141 9 24 201 13 24 261 17 24 321 21 24 22 I 28 82 528 142 9 28 202 13 28 262 17 28 322 21 28 23 I 32 83 5 32 143 9 32 203 13 32 263 17 32 323 21 32 24 I 36 84 536 144 9 36 204 13 36 264 17 36 324 21 36 25 I 40 85 5 40 145 9 40 205 13 40 265 17 40 325 21 40 26 I 44 86 5 44 146 9 44 206 13 44 266 17 44 326 21 44 27 I 48 87 5 48 147 9 48 207 13 48 267 17 48 327 21 48 28 I 52 88 5 52 148 9 52 208 13 52 268 17 52 328 21 52 29 I 56 89 5 56 149 9 56 209 13 56 269 17 56 329 21 56 30 2 90 6 150 10 210 14 270 18 330 22 31 2 4 91 6 4 151 10 4 211 14 4 271 18 4 331 22 4 32 2 8 92 6 8 152 10 8 212 14 8 272 18 8 332 22 8 33 2 12 93 6 12 153 10 12 213 14 12 273 18 12 333 22 12 34 2 16 94 6 16 154 10 16 214 14 16 274 18 16 334 22 16 35 2 20 95 6 20 155 10 20 215 14 20 275 18 20 335 22 20 36 2 24 96 6 24 156 10 24 216 14 24 276 18 24 336 22 24 37 2 28 97 e 28 157 10 28 217 14 28 277 18 28 337 22 28 38 2 32 98 6 32 158 10 32 218 14 32 278 1832 338 22 32 39 2 36 99 6 36 159 10 36 219 14 36 279 18 36 339 22 36 40 2 40 100 6 40 160 10 40 220 14 40 280 18 40 340 22 40 41 2 44 lOI 6 44 161 10 44 221 14 44 281 18 44 341 22 44 42 2 48 102 6 48 162 10 48 222 14 48 282 18 48 342 22 48 43 2 52 103 6 52 163 10 52 223 14 52 283 18 52 343 22 52 44 2 56 104 6 56 164 10 56 224 14 56 284 18 56 344 22 56 45 3 105 7 165 II 225 15 285 19 345 23 46 3 4 106 7 4 166 II 4 226 15 4 286 19 4 346 23 4 47 3 8 107 7 8 167 II 8 227 IS 8 287 19 8 347 23 8 48 3 12 108 7 12 168 II 12 228 15 12 288 19 12 348 23 12 49 3 16 109 7 16 169 II 16 229 15 16 289 19 16 349 23 16 50 3 20 no 7 20 170 II 20 230 15 20 290 19 20 350 23 20 51 3 24 III 7 24 171 n 24 231 15 24 291 19 24 351 23 24 52 3 28 112 7 28 172 II 28 232 15 28 292 19 28 352 23 28 53 3 32 "3 7 32 173 II 32 233 15 32 293 19 32 353 23 32 54 3 36 114 736 174 II 36 234 1536 294 19 36 354 23 36 55 3 40 115 7 40 175 II 40 235 15 40 295 19 40 355 23 40 56 3 44 116 7 44 176 II 44 236 15 44 296 19 44 356 23 44 57 3 48 H7 7 48 177 II 48 237 15 48 297 19 48 357 23 48 58 3 52 118 7 52 178 II 52 238 15 52 298 19 52 358 23 52 59 3 56 119 7 56 179 II 56 239 15 56 299 19 56 359 23 56 60 4 120 8 1 8c 12 240 16 300 20 360 24 Note.— ■^Tien turning seconds of arc into time, and vice versa, it should be remembered that the fractions are sixtieths; thus, the value in time of 42" is not 2.48 seconds, but 2-JI seconds=2'.8. o A^' . \ UNIVERSITY OF CALIFORNIA LIBRARY \ BERKELEY Return to desk from which borrowed. This book is DUE on the last date stamped below. LD 21-100m-ll,'49(B7146sl6)476 YD 267 \5 380074 ^^u f ' UNIVERSITY OF CAUFORNIA LIBRARY / t ra CXBBK I