HAlsTD-BOOK AND SELF-TEACHER, FOB THE $al l^mnt §mx& of ©iiMda, COMPRISINQ A SKIllES OP QUESTIONS WITH ANSWERS AND EXPLANATIONS. BY OAPT. E. CONNOLLY, Teacber of Navigation and Nautical istronomy, 53 WATER STREET, SAINT JOHN, N. B. m'-'r'K-H AFFAIRS ' DEC 15 1355 I Mori hern !?cs.r ",.';;-) i_;\ v OVTAWA ' "■ SAINT JOHN, N.*^^^ McKlLLOP & JOHNSTON, PRINTERS, CANTERBURY STREET. 1876. 6^7 MtoiVil iiCToriliiig to the Act of Parlii.mont of ranuda, in tin. year Ono Thousan.l KiKht Ilumlml and Sevcuty-six, l.y Cai.t. U. Cox.nom.y, in tlio Otticc of tli.- Minister of Agriculturi'. PREFACE. In preparing this Self-Tkaciiku for the young and iuexperionc-ed Mariner, I have hegun at the beginning, and explained tlie Tables to be used, the method of using them, with the numbers of the pages, and several examples for correcting seconds and tenths. My reason for 80 doing is, that in my experience as teacher, I have known pupils to have been kept days seeking for the Tables and explanations, not know- ing how to use them at sea, having had no one to instruct them. This work will prove a valuable guide for them previous to attending the school to prepare for examination. In conclusion, the young Navigator will find on perusing this little book, that I have left no stone unturned to make all that is necessary for passing an examination as simple as possible, and that l>e will find pleasure and benefit in the perusal ot its pages, whether lie is at sea, and when at anchor, or lying in harbor. K. CONNOLLY. N. B.— I would feel grateful to any of my friends who may find discrepancies in this work, to tell or comnmnicate with me, as some may have crept in; having had no assistant, I have worked every (piestion myself. XoTiCK.— I have in press, and shall shortly publish a book entitled "Seamanship Simplifikd," which I think will prove of great value to young Mariners. ERRATA. Page 9. — + Logs for Answer, re.id 4884. " 14.— Parallel sailing, 5th Question, read 2° 10' W. " 1"). — Mercator's sailing, 1st Example for distance, read 10?A. " 20.— Tides, Tanera, read A. M. 1.3, p. m. 1.44. " 21.— St. John Tide, read a. m. 14', v. M. 38'. " 32.— Day's Work, for Lat. left read 51° 25'. " 34.— Day's Work, read course S. 33° 30' W., Dist. 88 miles ; Lat. in 50° 11' N., Long. 11° 6' W. " 35.— Day's Work, read Long. 75° 00' W. " 43.— Last line Answer, 21° 59' 67" S. " 46.— First Question, read Lat. C8° 9' 19" N. " 47.— First Questien, read April 30th. " 49.— Amp., read Long. 150° 10' E., Dev. 5° 5' 30" E. " 51.— Deviation, read 2° 45' E. " 51.— April 10th, read 5h. 30m. " 54. — Example 3rd, read fast, — for gaining, read losing. " 66. — First Question, read 2m. 9s. " 83.— Ex Meridian, Lat. read 52° 32' S. " 86.— Star, read Lat. 26° 50' 47" S. " 90.— Deviation, Ship's head at N. E., read 15° 37' E. " 92.— Chr., read Long, by Acct. 75° 12' W. ; Chr. Sli. 20m. 20s. " 94.— Ex Meridan O^S. " 131.— Chr. Long., read Long 166° 51' 45" W. " 132.— Day's Work, read Course S. 15° W. ; Long. 176° 56' W. " 134.— Day's Work, read Lat. in 52° 59' N. " 135.— Stars Dec, read 12° 34' 18'^ N. LOGAKITHMS. The Natural number is found in Table XXIV, Norie, pages 88 to 103; also, the Mantissa corresponding thereto, and is found by looking at the left of page under No. at top ; it extends to 999, Required, the Log. corresponding to 999. Look in page 103 and under No. left side of page, and under from tup the Log. is 99956. Next, require the Log. corresponding to 9999. Look for the first three figures as above, and the fourth at the last column under 9,— the answer will be 99957. But it often happens that the Log. of more than four figures is required, then proceed thus : Find the first four figures as above, then the remaining figures, multiply by the value found in column marked Biff, at right of page, and cut off as many as are over four in the Natural No., and if only one, cut off one; but if two, cut off two, and all in excess accordingly. See the following examples : — . Required, the Log. of 22222. The value of the first four figures is 346744 ; now you require the value of the fifth or remain- ing figure 2,— the diff. in column is 195 multiplied by 2: 2 X 195=390; then by cutting off one figure from 39 0, leaves 39 to be added : 39 + 346744= (equal) 346783. Next, find the Log. of 333333. The value of the first four is 522835, and the diff. is 130x33=42.90, or 43 : 43 -{-522835 = (equal) 522878. Again, find the value of 4444444, Find the first four as above, and in diff. column stands 98 multiplied by the last three figures, — the answer is 647818. Again, find the value of 66666666. Find the value of the first four figures as stated above,— which is 823865, and the diff. is 65 multiplied ( x ) by the four remaining figures giTes 823908. i^° See following page for questions worked. N. B. — If the figures cut off are under 5, 50, 500, reject them; but if over, add one more to the Mantissa. 6 HAND BOOK AND SELF-TEACHER. NATURAL NUMBER GIVEN TO FIND LO(JAKITIIM\. Nat. No. 22222. ,346744 195 Diff. + 39. X 2 excess of four (see page a. ) Ans. = 346783 Nat. No. 333333. 522835 + 43. Aus. = 522878 Nat. No. 4444444. 647774 + 44 Ans, = 647818 39'0 1 30 Diff. X 333 excess of four. 390 390 390 • 43-290 444 excess of four. X 98 Diff. 3552 3996 Nat. No. 66666666. 823865 + 43 Ans. = 823908 43-512 or 44. 6666 excess of four. X 65 Diff. 33330 39996 43-3290 EXAMPLES FOR EXERCISES. 1. Nat. No. 22. 2. ' 333. 3. ' 4444. 4. ' 55555. 5. ' 666666. 6. ' 7777777. 7. ' 123401. 8. ' 1234002. 9. « 12340003. Ans. 1 -.342423. « 2-522444. " 3-647383. " 4-744723. " 5-82390a. " 6-890856. " 5-091319. " 6-091326. " 7-091315. Every Natural number requires an Index, and is one less than the number itself— (see examples above) ; and the Index to a LOGARITHMS. 7 mixed number i^ one less than the whole numbers contained in the (juestion :— the index to 1-23 is ; to 12-3 is 1 ; to 123-4 i^ 2 ; 1234'.') is 3. The first contains only one whole number, and is less than one ; the secimd, two whole numbers, and one is less than two. Tlierefore, all indices are found accordingly, and will be easily found in the tollowing examples. INDICES FOR MIXED NUMBERS. The index for a mixed number is one less than contained in the whole number and stands thus : — The figures to the left are the whole nimibers, and those to the right are called mixed. 2'34.5— 0. 12-345—1. 123-345—2. 1234-345—3. 12345-345—4. In taking whole and mixed numbers from the Tables, take them out as if they were all whole, the index only is changed. Ex.— Find the Log. of 2-345 = 0-370133. It is quite clear that you cannot have but in the index, as there is only ont s'rhole number in the question, the rest being mixed numbers. LOG. OR MANTISSA GIVEN TO FIND NATURAL NUMBER. In the above examples tlie Natural number calls for one figur« less, and if the Log. be given to find the Nat. number, tkat number must contain one more whole number than the index of Log. given. Suppose the Nat. No. of Log. 3-46871)0 b« rt- (juired. Find the Log. in Table XXIV, and in No. at left side will be foimd 294, and at the top of the page will be found 3, which is to be placed after — 2943 — and gives the answer, a? the index is 3 it calls for four whole numbers. Again, if the Nat. No. 5-361335 be required, this cannot be foimd to agree with any number, so take the next less, 361161, and the differ- ence between them is 174 by annexing two cyphers, and divide by the number 189 found in diff. col. gives 96 to be placed after the figures found in No. col. and under the top figure gives answer, 229796. It is plain that the index calls for six figures, and they must be found by the above rule. But if the Log. could be found to agree, then sufficient cyphers may be added to make up for what the index calls for. It nuist l)e remem- bered that only one cypher must be added at a time. See the following examples. 8 HAND BOOK AND SELF^EACHER. EXAMPLES. 1st. — Natural No. corresponding to Lojj. 0-1 15278 = 1'304. The decimal point placed between first and second, as index 0- requires one whole number. 2nd.— Lojj:. 1 -115278. Ans.— 13-04, Index between second aiifll third. 3rd.— Log. 4-432789 next less, 432049 An». 2708S-8 100)1400(88 1280 1200 1280 In the above example the in- dex called for five whole num- ber. By a cypher added to the difference between the given IiO§. and the next less, and di- vided by diff. of col. at right side gives 88 nearly, annexed to the four figures found, and decimal point placed after fifth answer. And 5-432789 next less, 432649 Ans. 270887-5=160)1400(875 1280 , gives 1200 '1120 800 890 The index five requires six whole numbers. Two cyphers are added to find the required number, then, as there is a diff. of 80 over, another cypher in added, which gives one more, and it is a decimal. TIW NATURAL NUMBER REQUIRED FOR THE FOLLOWING LOGS. Logs. 0-245678 1-345678 2-456789 3-987654 4-876543 5-654321 6-666666 7-777777 8-111111 9-999999 Ans. 1. 1-7607 2. 22-1657 3. 286-278 4. 9719-7 5. 95255-7 6. 451144-68 7. 4641571-3 8. 59948216-7 9. 129155223-3 0. 9999571627-9 MULTIPLICATION OF LOGARITHMS. 9 MULTIPLICATION OF LOGARITHMS. Add the Lofj^s; of the multiplier and the multiplicand, the Nat. number corresponding thereto will be the answer. Multiply 22=1 -.342423 by 222=2-365488 Ans. 5104=,3-707911 In this example the sum of Logs, was found to agree abreast of 510 in Nat. No. col., and un- der the 4 from top, gives the answer, 4 whole numbers, as index is 3. Mul. 22-2= 1-346352 222-2=2-346744 Multiply 333 = 2-522444 4444=3-647774 Ans. 1479850=6-170218 169968 n. less- ALns. 4932-84=3-693097 693023 n. less. Diff. 88)740(84 704 360 352 8 The general rule is, there ought to be as many decimals in the answer as are in both numbers. Diff. 294)2500(850 2352 1480 1470 100 In the above example, thn index being 6 called for 7 whole numbers, therefore, cyphers had to be added to find enough in the quotient to annex the first four figures found. QUESTIONS PGR EXERCISE. Multiply 234 by 456, 6456 by 42. 25-4 by 29-7. 289-4 by 2-46. ii Ans. (4 U (( 106704. 145152. 754-38, nearly. 711-92, nearly. 10 HAND BOOK AND SELF-TEACHER. DIVISION OF LOGAEITHMS. There is no necessity for many examples in Division, as it is performed similar to Multiplication, only that one Log. is sub- tracted from the other, also the index, and the ahswer is found us in Multiplicatioji. Divide 4789 = 3-680245 by 842 = 2-925312 Divide 47-94=1-680698 bv 1-29=0-110590 Ans. 5.687 = 0-754933 Ans. 37-16 = l-570108 TABLE XXV. LOGARTHMIC SINES, SECANTS, TANGENTS, &c. These tables are very essential, as they are employed in solv- ing five of the questions that are proposed at the Examination Board, and are found thus : — If the angle is given, and under 45°, it will be found at the top, but from 45*^ to 90*^ it will be at the bottom ; and when the degrees exceed 90 take its supplement, that is, what the angle wants of 180, and if a Sine, Tangent or Secant, take the Sine, Tangent and Secant. Suppose you want the Sine of 20" 20 ^— look at the top of Table XXV, and abreast of 20 ^ in the col. marked M the Log. Sine is — 9-540931. Suppose the Sine of 120^ 20 ^ subtract from 180.00=59.40 and Sine from the bottom of the page, and miles at the right side stand Sine =9-936062. Another method is, — take 90'' from the angle, and take Co-Sine for Sine, Co-Secant for Secant, and Co-Tangent for Tangent. As in the above case, take 90 from 120.20 it leaves 30.20, and Co-Sine is 9-936062. But if the angle to seconds be required, take the diff. abreast of the Log. given to miles, multiply by the seconds and cut otf two figures to the right and add to the given Log. If the angle 30^ 20^ 20^' to find Log.,~tlie Log. given for 30^20' is 9-936062, the diff. is 123 multiplied ( X ) by the 20, equal ( = ) to 24^ 60, by cutting off the two figures to the right it leaves 24 or 25 to be added f + ) to 936062, gives the Log. 9-936087. But if a Co-Sine, Co-Secant or Co-Tangent b( given, subtract the diff. Co-Sine SINES, SECANTS, TANGENTS, ETC. 1 1 Tequired of 40° 4()'40'^ Corresponding Log. to 40° 40' is 9-879963, diff. 181 x 40=72,40, sub. gives 9-S79891. It will l)e remembered when the figures cut off are less than 50 they are to be rejected, but greater ones are to be added. A few examples will show when they are to be added or rejected. EXAMPLES. Find Log. Bine 35° 45 1 ^b ' '-9766598 292 diff. + 161. x55 Ans. 9-766759 • 160,60 The two figures cut off exceed 50, one more is added. Find Log.Co-Siue 25°35^45//=:9-955186 101 diff. — 45. x45 Ans. 9-955141 - 505 • 404 -45/45 The two figures cut oft', less than 50, are rejected. THE LOG. GIVEN TO FIND THE ARC. Tf a Sine, Secant or Tangent be given, seek in the Tables, and if it be found to agree, there will be no seconds, but if not, take the next less Log., also the diff. betweeu it and the given Log., to that diff. annex two cyphers, and divide by the diff. found in col. marked Diff., and the quotient will give the seconds required. But if a Co-Sine, Co-Secant or Co- Tangent be given, take tlie next greater Log. and annex the seconds found to the degrees and minutes. Find the Arc corresponding to Log. Sine 9-452078 next less, 452060 Diff. 713)1800(02 1436 Diff. 364 The next less log gives 16" 27' and by annexing what \f found in the quotient 02, or 3 nearly, we have the answer, 16^' 27'04'^ Find Arc of Co-Sine 9-975233. This is found to agree exactly in the col., and the Arc corresponding is 19° 10''. .i;2 HAND BOOK AND SEXF-TEACHER. Ans. 50'^ 49^ 59". Find Arc of Co-Secant 0-1 10525 next greater, 0-110626 171)1010(59 seconds. 855 1530 1539 11 All Degrees less than 45'' will be found at top of page, and miles found in left hand col. ; but all over 45^ at the bottom, and miles in right hand page. Log. Sine, (( (( " Co-Sine, (( (( " Secant, n a " Co-Secant, (( a a (C a n Tangent, (( EXAMPLES FOB PRACTICE. 5° 11/00// 5 11 44 76 20 00 76 20 35 17 25 00 17 25 25 72 29 00 72 29 29 9 25 00 9 25 45 Co-Tangent, 68 49 00 68 49 09 (( Ans. 8-955894. 8-956913. 9-373414. 9-373111. 0-020382. 0-020398. 0-020620. 0-020611. 9-219710. 9-220296. 9-588316. 9-588260, a t( (( ' a a ■ <; a (( a Sine, Co-Sine, Secant, Co-Secant, Tangent, LOG. GIVEN TO FIND ARC. 9-763067 Ans. 35°25/00/' 9-765726 0-764940 0-402222 9-817850 Co-Tangent, 8-411639 n (C (( (( (( 54 19 58. 80 06 33, nearly, 23 19 59. 33 19 20, nearly, 88 31 19. PARALLEL SAILING. If a ship sails on a parallel of Lat. she will of course be making all diflf. of Long., and if you sail on a parallel of Lat. within five degrees of the Equator, the distance run, or the de- parture will be the diff. of Long. But the more you sail toward PARALLEL SAILING. 13 file N. or S. tlie miles of Long, become less, for in Lat. 60^ the degree of Long, is only 30 miles, and will decrease in propor- tion as you approach the Poles, at which points it becomes nothing. Tlie rule is very simple and will be found thus : — Take the Secant of the Lat. Table XXIV (rejecting 10 of in- dex) and common Log. Table XXIV of departure (or distance run), add both and their sum found in Table XXIV will give the dist. in Nat. number col. EXAMPLES. In Lat. 60^, Secant, (XXV) 0-301030 Departure 120, Log. (XXIV) 2-079181 Diff. Long. 240. 2-380211 In Lat. lO'' 30^ Secant, 0-007334 Departure 140, Log. 2-146128 Diff. Long. 142-4 2-153462 In Lat. 78° 35', Secant, 0'703461 Departure 999, Log. 2-999565 Diff. Long. 5046-9 3-703026 702947 next less Loj^, 86)790(J'«- 774 In Lat. 30^* 30' N., and Long. 177<=* 20 ' W., sailed 420 dae West, — What is the Long, in ? Secant of Lat. 30* 30' = 0-064680 Log. of Dept. 420 = 2-623249 Diff. Long. =6)487-4 = 2-687929 8-7 W. Long. Diff. 177-20 W. 185-27 Exceeds opposite 360-00 Meridian, take from 360, and changes from W. to E. Longitude. 174-33 E„ 2 14 HAND BOOK AND SELF-TEACHER. QUESTIONS FOR PRACTICE, In Lat. 47'' 47 ' and depart. .333. Ans. 495-G In Lilt. 22 22 and depart. 22-2. " 240.1 In Lat. 11 11 and depart. Ml. " M31 In Lat. 77 27 and depart. 777. « 2576 In Lat. 5? 00 and Lon^. 2* 10' E., departure made to the East 80*1 :- -Re([iiired the Long. in. Ans. 00 00 00, or Mer. Green wicli. In Lat. 60^ and Long. 175 W., a ship sails due West 150 in-iles — What Long, is she then in ? Neither in E. or W., but 180 from Greenwich, MERCATOR'S SAILING. It is generally preferred to find the course from one Port or headland to another, and particularly when the dist. is large. The course and distance is found by tlie following rule : — Place one Lat. under the other and subtract the less from the greater, if both '.je N. or both be S. ; but if one is N. and the other S., add tliem, which will give you the true diff. of Lat. in degrees and miles ; then multiply the degrees by 60 and take in the miles, — it will then be all miles. Next take each Lat. at the top of Table 3 (meridonal parts), and the miles in the side col., and in tlie angle will be found the meridional diff. (which are all miles) and add or sulttract, as was done with both Latitudes. Next find tlie diff. of Longitude, and if they are of same name, take their difference, but if of contrary names, their sum. If the degrees exceed 1 80 take that sum from 360°, and convert it into miles, as you did the Latitude. Wlien you get your diff. of Lat., be sure and name it either North or South, as the case may be, and do the same with the Long., for a great many mistakes arise through such neglect. A few examples will suffice to show how they are named. A ship in N. Lat,, and decreasing her Lat., the course will be South ; but increasing, will be North, — the same in South Lat. Likewise with Long., — if you are in West Long, and decreasing, the course is E. ; if increasing, tlie course is West. It often occurs that you change from one Long, into another, — that is mercator's sailing. lo crossing the opposite Meridian (180), — you still will be steering the same course. Then put down the diff. Long, and add 10 to the index, and under it put the Mer. diff. of Lat. and sul>tract. That will give the Tangent course in Table XXV, and aljreast will be found Secant, and that added to]JLog. of diff. Lat., Table XXIV, will give the distance. Ex.— A ship in Long. 178^20/E., sails to 17(1'' 20 / W., although she changes her Long., she does n<:»t chnigeher course, she will be still steering E., and would until she returned to the same place that she left. EXAMPLES. Ship from Lat. 40'' 40^ N., and Long. 44*^ 44' W., sails unH) she arrives at Lat. 55*^ 55 ' N., and Long. iyQ*^ 5^ ' W — Wliat is her course and dist. ? Meridoiiiil parts. Lat. A. 40'^ 40/ N. 2675 Long. A. 44^" 44/ W. Lat. B. 55 55 N. 4065 56 5^ W. 15 15 1390 12 12 60 60 915 N. 732 W. Diff. Long. 732 2 + 10 12 864511 Secant course =0 053129 M. parts, 1390 3 143015 L.of diff. Lat. 915, 2 961442 Tang. course N. 27 46 W. = 9 721497 Dist. 1027=3 014571 In the above example the ship sails from a low to a high N., and from a low to a high W., therefore the course is N. and W., she increases both. Lat. A. 26° 26 / N. 1 645 Long. A. 35^ 35 / W. Lat. B. 15 15 N. 926 Long. B. 25 25 W. 11 11 716 10 10 60 60 671 S. 610 E. Diff. Long. 610 2 + 10 12 785330 Sec. course, 118523 Mer. parts. 716 2 854913 L. of diff. Lat.67I, 2 826723 Tang, course S. 40 26 E.=:9 930427 Dist. 88 1*5 = 2 945246 16 HAND BOOK AND SELF-TEACHER. Lat. A. 30* 3f)/ S. 2363 Lon^. A. 137° 37 ' E. Lat. B. 38 38 N. 2517 l.onir. K 15H 56 W. 75 14 4880 60 294 360 33 00 65 60 27 3927 E. T). Long. 3927 2 + 13 13 594061 Secant course, 108376 M. parts. 4880 3 688420 Lono-. Dif. Lat. 4514, 3 654562 Tang. course N. 38 49 E. =. 9 905641 Dist. 5793 = 3 762938 In tliis example the ship sailed from S. to N. Lat. and crossed the Equator, and as she had to run the 36" 36 ^ miles of South- ing to reach tlie Equator, and 38° 38 ' of Northing, hoth Lats. must he added. She also sailed from one Long, into another and crossed the opposite Meridian, therefore, botli Longs, must be added ; and each Long, being greater than 180°, it must be subtracted from 360° before it is reduced to mile^. N. B. — It must be remembered that 10 must be added to the index of the difference of Long, in all cases. EXAMPLES FOR PRACTICE. In the following examples the course and dist. is required. Lat. A. 3*^ 33 / N. Long. A. 4° 44 ' E. Lat. B. 4 44 S. Long. B. 5 55 W. Ans.— S. 45° 00' W. Dist., 100-4. Lat. A. 5° 55 ' S. Long. A. 9° 29 W. Lat. B. 6 26 N. Long. B. 19 19 E. Ans. N. 86° 59 ' 30/ ' E. Dist., 590-7. Eequired, the course and dist. from Cape Sable in Lat. 43° 23/ N., and Long. 65° 37^ W.,to Cape Clear, Ireland, Lat. 51° 26 'N., Long. 9° 29 ' W. Ans.— N. 77° 56 ^ E. Dist., 2310 miles. Required, course and dist. from Cape Sable, Lat. 43° 23 ^ N., Long. 65° 37' W., to Cape of Good Hope, in Lat. 33° 54' S., and Long. 18° 24'E. Ans.— Course S. 44° 49 ^ E. Dist., 6357. Required, course and dist. from Halifax, Lat. 44° 26 / N., TIDES. 1 7 l.ong. 63° 34 1 W., to Monte Video, in Lat. 34'=' 53 ' iS., and Long. 56"=' 15 / W. Ans.— Course, S. 4» 43/ E. Dist., 4772. TIDES.-HOME PORTS. In all the Ports of Great Britain and tlie West of Europe, as far as Gibraltar, and to the Cattagat in the North 8ea, tlie Tides can be easily found, as there are several Ports of Reference, or Standard, and in these Ports they are known every day in the year by means of a Tidal Gauge. But as Wxk^xe are about two hundred intermediate Ports, or liarbors, tliat ha\o no Tidal Gauge, ;. d as it is often necessary to ascertain the Tides in all these Ports, tliere are Constants given in the A(huir;dity Tide Tables, from page U)3 to 108, wliich are to be added or subtracted as marked abreast of tlie Port sought. Constant is tlie num})er of hours and minutes that elapse between the time of high water at the Standard Port and the Port you are looking for. When Constant is added ( + ) the Tide will be later in the day ; but if subtracted ( — ) the Tide will be earlier. For instance, — You wish to know what time it will be high water at Dorchester, (Bay of Fundy) ; St. John would be the Port of Keference, as the Tide is known there every day, and it is high wnter full and change days at llh. 21m. Now, as the flood tide, runs nearly E., mid Dorchester lifting to the eastward, the Constant is +, and the Tide must necessarily be later in the day ..' Dorcliester than at St. John. Again, you wish to ascertain ,',hat time it will 1)6 high water at Quoddy Head on a certain day. The flood Tide runs by Quoddy in an easterly direction towards St. John, and the time which elapses is about 45 minutes, tlierefore that 45 minutes is the Constant to be — from high water at St. John, and consequently the hlgli Water at Quoddy Head will answer 45 minutes before the St. Jolm high water. I think t]\e young Mari- ner will easily discern how the Constants are to Ite applied, and by referring to the above explanations will have very little trouble in finding the time of high water on any day at any of the Home Ports. The Constants, and how to Apply them to the Morxinc; (A. M.) AND Evening (P. M.) Tides found in the Tide Taules. If Constant is add. ( + ) — found in pages 103 to 108 — add to 18 HANI) BOOK AND SELF-TEACHEU. tlie tiine foiinrl in tlie calendar of tlie month and day, smd it will ^i\e tlie A. M. and i'. M. Tides respectively ; but when Constant is added to A. M. Tide and it exceeds 12 hours, it will j^ive the P. M. Tide hy takinjj^ 12 hours from it ; then you must take the evening's Tide before, and if it exceeds twelve hours you will have a morning Tide, but if not, you will only have a i*. M. Tide tliat day. When Constant is subtracted ( — ) and is less than the Tidefc: ji^iven, it will give the two Tides that day ; but if — and a blank marked thus — occurs in the A. M. column, take the P. M. Tide and subtract, and if the subtraction can }»e made without borrowiujii; 12 hours, there will be one P. M. Tide that day ; but if you have to borrow twelve hours it will g\\e the A. n. Tide, and then take the next morning tide and borrow 12 hours and that will give the P. M., but if you can make a subtraction with- out borrowing 12 hours, there will be only an A. M. and no v. M. Tide that day. Whenever the Constant is — nnd exceeds the A. M. Tide in the calendar, that Tide must be rejected, and use the P. M. Tide instead, and if necessary, 1 2 hours must be bor- rowed, the same as if a blank ( — ) occurred. .The following examples will l)etter illustrate to the pupil how to employ the Constants. (Tide Table for 1873 used.) Ex. — Suppose you wish to know what time high water will occur at Dartmouth on April 1st, 1873. Look in Tide Table, page 107, and you will see Dartmouth, and abreast stands Con- stant — Oh. 33m., and .in right col. under kStandard Ports will stand Davenport, — that will be the Port of Reference for Dart- mouth ; next look in calendar for April, and find Davenport, and in the morning col. stands 8h. 4m.. and in afternoon col. stands 8h. 21m. Now by add. (+) (Constant Oh. 33m. to both Tides, it will give 8h. 37m. for morning, and 8h. 54m. for after- noon Tide. Find the time of high water at Ballycotton, April 8, 1873, Waterford is Port of Reference, and Constant is sub. ( — ), Oh. 26m., and in col. for April and under Waterford is 2h. 11m. forenoon, and 2h. 42m. afternoon, and Constant — Oh. 26m. gives lb. 45m. A. M., and 2h. 16m., P. M, EXAMPLES. Find time of high water A. M. and P. M. at Cherbourg on May 4th. TIDES. — HOME PORTS. 19 h. m. h. m. Brest, Port of Reference, 8 52 A. M. 9 32 P. M. Const. + 4 02 4 02 h. in. P. M. of 3rd, 8 19 12 54 P. M. 1 34 P. M., 5th 4 2 12 no use. 00 11 A.M. 4th day. 00 54 It will he seen hy the above Tides that by -f Constiint to A. M. Tide it exceeds 12 hours, and makes it u P. M. Tide, — and \>y -f- to P. M. Tide, it makes it A. M. Tide of oth day, — so the Tide of tlie evening of the 3rd had to be used, imd Constant add. ( + ) to it exceeded 12 hours, and made an A. M. Tide of 4th day. Find A. M. and P. M. Tides at Exmouth, May 20th, Davenport, Port of Reference. A. M. 11 41 ]'. m. of 19th. + 38 h- m- 11 00 00 19 P. M. ?? 11 38 no use. Only a P. M. Tide on the 20th, as Constant 4 to P. M. Tide of previous P. M. Tide does not exceed 12 hours. Find time of high water A. M and P. M., at R'dtimore, Ire- land, on May 6th. Queenstown Port of Reference. h. m. h. ni. A. M. — P. M. 30. A. M. 7th 1 04. Const. — 38. 38. A. M. 11 52. 26. 7th day. no use. When Constant is — as above, and the subtraction can be made without borrowing 12 hours from the following Tides, there will only be one Tide that day. It will also be seen that the A. M. Tide is within 8 minutes of noon, and as a general thing there must elapse about 12 hours and 25 minutes between each consecutive Tide. Find time of high water at Cromarty on June 24th. h. m. h. in. Leith, Port of Reference. A. M. 1 40 P. M. > 01 Const.— 2 21 A. M. 1 i 40 no p. M. so FIAND BOOK AND SELF-TEACHER. In the above Tide the Constant is greater than the A. M. Tide, therefore it miirtt be rejected, and the afternoon Tide used in- stead, and as ;i Hii])traction couhl not be made, 12 liours had to he borrowed, which made it a forenoon Tide ; and as the Con- stant couhl 1)0 subtracted from the following morning Tide with- out ])orrowing 12 liours, there is only an A. M. Tide thnt day. Find the A. M. and p. m. Tides at the following Ports : — A. M. 1'. M. Jan. 8th. Ballycotton (Ireland), Ans. No. 22 Fel). otli. Bristol (England), " 00 02 00 30 Mar. 3()th. Tort Patrick (Scotland), " No. 00 18 April .3th. Llanelly (Wales), " 11 34 No. May 4th. Ballycastle Bay (Ireland), " Noon. June nth. Ordforness (England), " 11 15 11 35 July 27th. Douglass (Isle of Man), " 00 19 00 49 Aug. 3rd. Tanera (Summer Isles), "11 39 No. Sept. 1st. Alderney (Cinq Isles) " No. 00 37 It may not be amiss to state here that when a blank ( — ) occurs in the A. M. col. and Conet. is sub. ( — ) if a subtraction can be made from the P. M. col., there will be only a P. M. Tid« that day. Also, if Const. + and — in P. M. col., if the sura of Const, and A. M. Tide does not exceed 12 hours, there will Ije only an A. M. Tide that day. TIDES.— FOREIGN PORTS. In finding the time of high water for any Foreign Port the Constant is to be applied in the same manner as in tlie Home Ports. But you must first find a Const, by taking Brest as a Standard, and the time of high water on full and change days is 3h. 47m., and the difference between that and the full and change days of any other port that exceeds five degrees to the W. or E. is the Const. And to know when the Const, is + or — place full and change of Brest and the Port required ; take their difference, and if Brest is the least, the Const, is + , but if greatest — . It is quite plain that if the full and change happen at St. John llh. 21m., that of Brest 3h. 47m., the dif- ference is 7h. 34m. That is, St. John Tide is later 7h. 34m. in the day than at Brest ; therefore, by -f 7h. 34m. to the time of high water found at Brest in the Admiralty Tide Tables, on any day, will give the time of high water at St. John. But as TIDES. — FOIIEIUN PORTS. 31 the Moon liiis some influence over the water it requires anotlier small correction, found thus: Take tliediff. of Transit between the two days ( found in left cor., marked Moon's Transit, Tide Tables), and the Lonjjf. of the recjuireil Port in side col., in the angle of meeting will he a correction to be -\- in W. Lung, and — in E. It may be remarked here, that as the Transit of the Moon is computed for the meridian of Greenwich, and as Brest is 4^ degrees to the W. of Greenwich, it will cause a small error, which, however, can be avoided by -f- 4^ degrees to all places in W. Long., and — in E. The following examples will show more plainly to the learner how the corrections are to be applied. Require the time of High Water at St. John, Long. 66^ W., on Jan. 30th, 1873. h. m. Standard, Brest 3 47. High Water at Brest 30th . h. rii. h. m. St. John 1131. A. M. 4 50. P. M. 5 10. No use. Const. + 7 34. 4 30 Evening 29th. Const. + 7 34. 7 34 00 24. Cor. + 00 10. 00 04 00 10 P. M. 00 34. Transit 30th, " 31st, h. 1 2 m. 50. 42. A.M.0O 14 Long. 66'^ Cor. 52. Table XVI, Norie. 70^ Constant + to A. m. exceeds 12 hours, makes a P. M. Tide. The preceding Tide of 29th must be taken, and as it exceeds 12 hours it gives a morning Tide. June 1st, 1873. — Require the A. m. and P. M. Tides at Trin- comalie (Ceylon). h. in. h. m. Brest, 3 47 High water at Brest, June 1st, 7 30 a.m. Trincomalie, 8 18 Const. + 4 31 Const. + 4 31 12 01 Cor. — 10 Transit, June 1st, 5 13 " May 31st, 4 27 11 51 A. M. Cor. — 46 Table XVI, Norie. 3 22 HAND BOOK AND SELF-TKACIIKIl. Til tlie precediii*:^ Tide the Const, added to the Brest Tide ex- cet^is 12 hours, hut lis the cor. reduced it to llh. 5lm. it makes iin A. M. of it, iind it l)eiug only 9' troin noon, there can be no other Tide tluit day. August 1st, 1H73. — Rerjuire the A. M. and P. M. Tides at Hal- ifax, N. S., Lon^r. 6.3 W. Ii. III. h. in. Brest, 3 47 Higli water at Brest, Aug. 1st, 8 24 Halifax, 7 49 Const. + 4 02 li. m. Const. + 4 02 Tide of July Slst, 8 03 00 26 Const. + 4 02 Cor. + 9 00 05 35 P. M. Cor. -f- 9 00 14 A. M. In working the last Tide, the Const. + to A. M. makes a P. M. Tide, and taking the previous evening and adding the Const., it exceeds 121i., or crosses over midnight, therefore it gives an A. M. Tide. October 1st, 1873. — Require the A. M. and P. M. Tides, Kyau- ch»u Bay (Yellow Sea), Long. 120^ E. h, tn. High water at Brest, Oct 1st, 10 57 + 1 13 h in. Brest, 3 47 . 12 10 Kyau-chau, 5 00 — 19 Const. + 1 13 A. M. 11 51 no p. M. In the last question, the Const, being + to the A. M. Tide at Brest, it exceeds 12h. and makes it a P. M. Tide; but cor. for Long. P^. 19^ when subtracted bought it back to A. M. Tide, and being so near there can be no P. M. Tide that day. QUESTIONS FOR PRACTICE. Required the A. M., and P. M. Tides at the following Ports : — 1873. A. M. r. 11. Feb. 28. St. John, N. B., Long. 66« W. Ans. No. 19 May 22. Pei-ho, Long. 122^ E. " No. 13 Dec. 19. Parsboro, N. S., Long., 65'' W. " No. 5 Sept. 2. Hakodadi, Japan, Long. 135° E. " No. 3 Nov. 23. Yarmouth, N. S., Long. 66° W. "11 50 No. Oct. 12. N. York, U. S. Long. 74° W. " No. 10 day's work. 23 DAY'S WORK. Wliat is called a day's work is the course or courses, tlie diff'. of Lat. and departure, and finally to ascertain the true course and dist., the Lat. and Lonjj;. in, and her true position at noon. Each course a vessel sails on is subject to two corrections, aud sometimes to three. The tirst two are variation and deviation ; the former is caused by the maji^etisra of the earth, the latter by the iron used in the construction of the ship, and these two are to be used when a ship is sailing before the wind, or the wind right after her ; but when she is hauled by the wind, or the wind on either side, she is then making lee-way, and that m»*8t be allowed on each course with the variation and deviation. I think it would be out of place to state here the amoimt of lee- way caused by the different sails, the speed the ship has through the water, and the nature of the sea at the time, — for of these a careful Master or Mate will soon judge by several means wben at sea ; and as lee-way will be in its proper place in all th« ««- amples in this work, there is no need of further remarks. HOW TO CORRECT COURSES. All courses must be reckoned from the N. towards the E. and W., and from the S. towards the E. and W. : that is, — the points, or degrees, increase from nothing up to 8 points, or 90 degrees. Easterly variation and deviation are always allowed to the right. Westerly to the left, and lee-way if allowed opposite to the wind. Suppose a ship's course N. N. E., wind N. W., variation 1|E., deviation ^ E.,— What would be her true course ? N. N. E., or N. 2 E. Var. + 1^ E. allowed to the right hand. 3| Dev. + :|^ E. to right, also. 4 Lee-way, going free. True course, N. 4 E., or N. E. The course is N. 2 points E., and sa it increases towards Mae 24 HAND BOOK AND SELF-TEACHER. E. bv var. and dev. added, both being Easterly, makes the course N. E. or N. 4 E. Compass course N. N. E., wind E. by N., lee-way ^, dev. | E., var. 2^ E. N. N. E., or N. 2 E. In this example the lee-way is sub- Lee-way — ^ tracted, as she is on the starboard — tack and drifting towards the N., 1^ and lessens the points, but the Dev. + f dev. and var. are added, as both — being E., therefore, true course 2i N. ^ E. Var. + 2} N. E. ^ E. ^ Compass course N. W. by W. ^ W., wind N., lee-way 1|, dev. 1| W., var. 2^ W. Co. N. 5| W. In this ex. the ship is steering Lee-way + H between N. and W., and the wind from the N., the lee-way 7 is towards tlie W. ; also dev. Dev. 4- If and var. being W. is allowed to the left, and all three 8 1 added puts her out of N. into Var. + 2^ the angle of S. and W., and when the course exceeds 8 11 pts., sub. from 16. (Sse form 16 of work.) S.W.byW.,orS.5W. 5 Compass course S. ^ E., wind E. by S., lee-way 1^, var. ^W., dev. l^W. Co. S. ^ E. In this ex. the course is S. ^ E., or 1^ ^ left of S., lee-way to right, — the lesser is subtracted from the S. 1 W., — 1 greater, and changes the angle Var. — 1;^ from S. E. to S. W., var. being — W., allowed to left, changes the S. ^ E., ^ anglfe .3 S. E., and dev. +, be- + l| ingW. gives the course as below. — N. B. — The learner should S. 2 E., or S. S. E., 2 never forget, that all courses day's work. 25 which cross over N, or »S., the lesser must be — from the greater ; but over E. or W. must be -|- , and then — from 1 80 if in de- grees, — if in points, from 16. Compass course W, S. W., wind S., lee-way 2^, dev. 2-| W., var. 3 E. This angle is to the N. and W., but the dev. aing W., it is — and changes back to S. and W. without being sub- tracted from 1 6 ; and as vari- ation is 4- it changes agam to N. and W., and being over 8— 16. W. ^ N., or N 7^ W. 7^ The next page will show the Traverse Table as kept at sea-, all courses by compass corrected, the difF. of Lat. and departure for each course, and Tables 1 and 2 explained. Co.W.S.W.orS, Lee-way + . 6 W. Dev. 2f Var. + 5i 3 16 26 HAND BOOK AND SELF-TEACHEE. DAY'S WORK. H. 1 2 3 K. g Courses. Wind. Lee- way. 2i Dev. Remarks. 4 4 N. 4 4 4 4 E. N. E. HW. Departure taken at noon from a point of land in Lat. 42^ 4 5 6 7 4 4 5 2 N. E. 5 2 5 2 E. S. E. 2| i^w. 30/ N., and Long. 74°20'W. Bear- ing by compass S. S. W., dist. 10 8 5 2 miles. 9 3 6 E. o. fe. E. 2 IfW. 10 3 6 • 11 3 6 12 1 3 6 6 6 S. E. E. N. E. UE. Dev. as per Log. 2 6 6 4 3 6 6 4 6 6 5 3 3 S.S.E. S. W. U IE. Var. 3| E. 6 3 3 7 3 3 8 3 3 9 10 11 4 4 S. W. 4 4 4 4 S. by E. H 1|E. Current setting S. S. E.(cor. Mag.) l^ miles per hour 12 4 4 for the whole day. 1st course, N. Lee-way + 2^ left or N. 2^ W. Dev. + li left. Var. 3| True course N. :^ E. ^ right of N. In this course her head is N., the wind E. N. E., or on her right side, so she is on the starboard tack, and 2^ pts. lee-way day's work. 27 drives her to the W. Dev. being W. is also added, a;nd increases more to the W. ; but the var. being E., and allowed to right, must be subtracted. Now, as the var. is more than the lee-way, and dev. S^ pts. places her to the left of N., the lesser must be subtracted from the greater, which places her to the right of N., hence N. ^ E. is true course. 2nd course. N. 4 E. or 4 R. of N. Lee- way, — 2| left. - u Dev. 1|- left. i 4 8| right. True course, N. 3^ E. 3|- right of N. This course crosses over N. twice, and each time the lesser has to be su))tracted from the greater. Her head being 4 points R. of N., dev. and lee-way combined make 4^, that is, ^ point to L. of N., or N. ^ W., and var. being R. 3f , the \ pt. must be subtracted, and changes from the N. W. angle to N. E. 3rd course. E. or 8 Lee-way — 2 Dev. 6 If H Var. + 3| True course E. 8 4th course, S. 4 E. Lee- way — 1^ Dev. — 2| Var. — 3f True courses. 1 W. 1 S. E. angle to the S. W. The ship's head is E., the wind S. S. E., so she is on the star- board tack, and lee-way is sub- tracted from 8 pts., leaving 6 pts. to R. of N. Dev. is sub- tracted also, it being to the L., or W., gives 4^ pts. ; but var. being E. is allowed to R. and added to 4^ makes the true course N. 8 pts. E., or E. In this course her head is S. 4 pts. E., wind E. N. E., she is making no lee-way ; the dev. being l^ E. is subtracted, as also is the var., but as the var. is greater than the course, the lesser must be subtracted from greater, and crosses from the 28 HAND BOOK AND SELF-TEACHER. 5th course S. 2 E. Lee-way + 1^ Dev. 1 Var. — •2i 3f True course S. 1|- "VN T • H 6th course s. 4 W. Lee-way + 2i Dev. + 8 Var. — 3f -111 16 Her head is S. 2 E., wind S. W., she is on the starboard tack, and lee-way 1^ is added, but dev. being E. and allowed to K. is subtracted, also the var., and as in the last course, the lesser must be subtracted from the greater, in crossing North or South. In this course she is heading S. W., the wind is S. by E., — slie is on the port tack, and the lee-way is added, being opposite to the wind, also the dev. and var. ; all combined put the course across W., and as it exceeds 8 pts., must be subtracted from 16, which changes it from S. W. angle to N. W. True course N. ^ W. H Depart, course S. S. W., opposite pt. N. N. E. N. 2 E. The opposite pt., is always taken Dev. — 1^ for a dep. course, and dev. is gener- — ally given as for the first course, | and variation allowed, as on all Var. + 3f other courses. — True course, N. 4|- E. 4^ Current course S. 2 E. 3| True course S. 1| W. If Nothing but var. is allowed on the current courses, as the dev. is allowed on each course during the whole 24 hours. TAKING COURSES AND DISTANCES FROM TABLE I. Enter the Table with the course at the top (if under 4 pts.) and .list, from left hand col. abreast will be the ditf. of Lat. and dep. in the tirst two cols. ; but if the course exceeds 4 pts. it must be taken from the bottom of page, when Lat. becomes dep. and dep. Lat. ; if there are miles and tenths in the dist., day's work. 29 tliey must he taken out as if tliey were whole num})er8, and make the last fi^^uie of the whole niunhcr a decimal; if there are tenths in the coL, and they are alxne .'>, one (Ij must l)e added to the tenth that is pointed off. For instance: find Lat. iind dep. correspond iuj,' to 2()'"(), tiie course 2^ pts. Look in 'ttihle 1, pa;jfe 10, in one of the cols, marked " dist.,*' until you liud 20(1, and in the next cols, of diff. of Lat. and dep., — iu Lat. coh stands 1H1"7, and in dep. col. 1)7*1 ; now, hy pointin;^: off the last figure of each they will stand thus, — IH-l, i)'7 ; and as the figiue pointed off from difl'. Lat. is 1, one more is added for the 7 tenths, it heing over 5, and would be placed in tlw Traverse Table IH'2 Lat., 9*7 dep., nothing being added to dep., as the tenth in the col. is under 5. Again, if you wish to find the diff. of Lat. and dep. for 33^*8. This cannot be taken out as above, as the Tables give only as higii as 300''. It is found thus, — under 2^ pts., at top and find in dist. col. 38 /, and in two next cols, of Lat. and dep. is 29*1 Lat., lo'tl dep., next Uike the 8 tenths in a dist. col. also, and in Lat. is 07* 1, and in (hsp. 03*8. Now the miles found must be made tenths and added to the tenths of the 33 ', and if the figure that stands for tenths is over 0, 1 tenth more is to be added to the tenths already found. Lilt. Dep. First found, 29-1 15-6 Second found, 7 4 Proper diff. 29-8 16-0 The 8 tenths in dep. is over 5, and 1 more is added to the 3, which makes it four. Whenever the course is taken from the top, the greatest is to be placed in the N. or S. cols. ; but when found at tlie bottom, the greatest must be placed in the W. or E. cols. Wiien all the courses and dists. are taken out and placed in their proper cols., as will be seen in the annexed form, all are to be added up, and the lesser Lat. taken from the greater, also, the lesser dep. taken from the greater, and named after the Lat. and dep. which are the greatest. If the most is in the N. and E. cols., the course will be N. and E. ; but if in S. and W., the course will be S. and W. TO FIND THE COURSE AND DISTANCE. Seek in Table 1 until Lat. and dep. are found to agree (or nearly), and the course will be found at the top if Lat. is most, 4 30 HAND BOOK AND SELF-TEACHER. but at bottom if dep. is most, and the dist. will be found in the dist. col. at left hand. TO FIND THE LAT. AND LONG. With the diff. of Lat. found placed under the Lat. left, add if t)f same name, but sub. if of contrary names, and that will give the Lat. in ; then add both Lats. and divide by 2, which will give mid Lat. ; then find the mid Lat. at top of Table 1, if it is under 4 pts. or 45^, })ut at the bottom if over 4 pts. or 45*^ ; then find the dep. in Lat. col., and in the dist. col. will stand diff. of Long., — if it exceeds 60 miles divide by 6 and it will be in degrees, place it under the Long, left, and if of same name add, but if of different names sub., and it will give the Long in. The above k finding the diff. of Long, by mid Lat., and as it is sufficiently correct in short distances such as Day's Work, no notice will be taken of any other method here. The learner must remember, that if a ship be near the Equa- tor in N. Lat., and the diff. of Lat. made S. will exceed the Lat. left ; the Lat. left must be sub. from the diff. of La,t., and the remainder will Ije named S. Tlie same precaution is necessary in passing the meridian of G-reenwicli or Long. ;/ ; })ut in passing from one Long, into anotlier at the opposite meridian, or 180*^, both must be added, and the sum taken from .360*^, and named after the latter. Ex. 1st.— A ship is in Long. ITO'^ 10^ W., and sails due W. 140 miles=2^20'+179'^ U^=181° 30^— 360* = 178» SQ/E. Ex. 2nd. — A ship is in Long. 0*40' W. and sails 49' E., — What Long, will she be in? 0-40— 0-49 = 9' E. The ship crosses over the first meridian, and as the dist. made E. ex- ceeded tlie Long, left, the lesser is taken from the greater, and named E. after the latter. It would benefit the learner to fill in the blank spaces in the following Table with a dash or cross, previous to entering the Traverse Table. For instance, — in the first course she is making N. and E., and notliing in S. and W. cols., &c. DAY S WORK. 31 Dist. Diff. Lat. Departure, True Courses, N. 1 E. N. 3i E. E. S. 1 W. S. 1^ w. S. 4^: W. N. 4^ E. S. 1| W. 17-6 20-8 14-4 26-4 13-2 9-6 10- 36- N. 17-6 16-1 s. 25-9 12-6 6-5 33-9 E. 9- 13-2 14- 7-7 43-9 28-2 15-7 5-2 3-8 7-1 12-1 6-3 50-0 78-9 50-0 28-2 Dep. Diff. Lat. and 28.9 Grives course S. 2^ E., dist. 32/. Lat. left, 42° 30' Diff. of Lat. 28-9 =29 S., and is — from tl names. Lat. in, 42 1 N. from the Lat. left, being of different 2)84 31 Mid Lat., 42 15 Found in Table 2 gives diff. Long. For dep., 15-7 = 21 ' E. The diff. Long, is also of a Long left, 74° 20 W. different name to Long. left, therefore subtracted. Long in, 73 59 W. This is the only Day's Work that will be in pts., and the learner will easily comprehend by the explanations given how to use it practically at sea. I have made it my study to treat all questions practically, without superfluities, for the ben- efit of the young mariner, so that they may be readily under- stood and more easily mastered. Moreover, as it is intended only for those that are preparing to pass an examination in Canada, and as they are to work all in degrees, it would only be lost time for the pupil to go through different Day's Work in pts., the changes of courses, etc., etc. 32 HAND BOOK AND SELF-TEACHER. H. Courses. K. 2 O 2 Winds. Lee- way. 12 Dev. Kemarks. 1 N. 24 W. 4 w. M5 E. A point of land 2 4 2 in Lat. 31^25' 3 4 3 N., Long. 9^ 29^ 4 4 3 W. Bearing by 5 N. 45 W. 5 2 N. 24 E. 5 4-20 W. compass N. 22" 6 5 3 30' E., dist. 12 7 5 3 miles. 8 5 2 9 N. 67 W. 3 4 N. 4 15-30 W. 10 3 4 11 3 4 Dev. as per Log. 12 3 8 1 S. 22 W. 8 3 N. 67 W. 2E 2 8 3 3 8 3 4 5 S. 45 W. 8 7 3 5 N. 70 W. 5 5E. Var. 25° 30 ^W. 6 7 5 7 7 2 8 7 2 9 S. 67 W. 3 4 S. 5 W. 15 3E. Current (cor. 10 3 4 mag.)S. 15"E., 11 3 4 25 miles in the 12 3 4 24 hours. S. 22 30 W. dep. course. N. 22 00 W. 1st course. -f 1 15 E. dev. R. — 12 00 Lee-way R. -23 45 • 10 00 25 00 var. L. — 1 15 dev. L. S. 1 15 E. true course. 8 45 + 25 30 var. L. N. 34 15 W. true course. day's work. 33 N. 45 00 W. 2nd course. + 5 00 Lee-way L. 50 00 + 4 20 dev. L. 54 20 4- 25 30 var. L. N. 79 50 W. true course. S. 22 00 W. 4th course. + 2 00 Lee-way E. 24 00 25 30 var. L. S. 1 30 E. true course. N. 67 00 W. 3rd course, -f 4 00 Lee- way L. 71 00 + 15 30 dev. L. 86 30 + 25 30 var. L. 112 00 exceeds 90^, 180 00 S. 68 00 W. true course. S. 45 00 W. 5th course. — 5 00 Lee-way L. 40 00 + 5 00 dev. L. 45 00 25 30 var. L. S. 19 30 W. true course. S. 67 00 W. 6th course. 15 00 Lee- way R. 82 00 + 3 00 dev. R. 85 00 25 30 var. L. S. 59 30 W. true course. S. 15 00 E. current course. + 25 30 var. L. S. 40 30 E. true course. a^— ^rrri FT ii n ■ wi ^i —imiiiMmBi r-^rw NO;:T'-i:^M AFFAIRS . >. ■ V . I , ; V 1 I ■ 1 : . I ) '„ , J ( \ J i..o U Mort: 34 HAND BOOK AND SELF-TEACHER. Courses. Dist. N. s. E, W. S. 2*^ E. N. 34 W. N. 80 W. S. 68 W. S. 2 E. S. 20 W. S. 60 W. S. 41 E. 12 17 21 26 33-2 29-4 13-6 25 14 1 3 6 12 9 7 33 2 27 4 6 8 18 9 4 1 2 16 4 9 5 20 7 24 1 10 11 8 17 7 108 00 18 76 1 18 — . 17 7 ( ))9,0 3 Dep. 58 1 Diff. Lat. — 1 30 S. Lat. left, 51 25 N. Lat. in, 49 55 N. 2)101 20 Diff. Lat. 90'', and dep. 58* 1, gives true c'rse S. 33^^ 00 W., and dist. 108 miles. Mid. Lat. 50 40 Diff. Long. 93 = 1 33 W. Long, left, 9 29 W. Long, in, 11 02 W. It has already been remarked that previous to entering the Traverse Table to take out the diff. of Lat. and dep. for each course, it would be well to fill up the vacant spaces with a dash as above. In the first course she is making Southing and Easting, and the diff. of Lat. goes in the S. and E. cols, and nothing in the N. and W. There are numerous mistakes made by putting the Lat. and dep. in the wrong cols., especially when in a hurry, and the at- tention is drawn to the cols., in the Epitome ; but by a strict observance of the above method a mistake cannot be made. The diff. of Lat. 90 '3 and dep. 58-1 is found to agree in Ta- ble 2, at top of page at 33°, and as diff. of Lat. is S., and dep. day's work. 35 W., the course will be S. 33^ W. ; in the adjoining dist. col. is found 108 miles, which is the distance made good. By adding the Lat. in and Lat. left, and dividing ))y 2 the middle Lat. in found, and that taken as a course ; and dep. in a Lat. col. will give ditf. of Long, in a distance col. H. Courses. K. o Winds. Lee- way. Dev. Keniarks. 1 S. 2-49 E. 9 3 S. 60 E. 2-50 3 W. A point of land 2 9 6 m Lat. 40" 20 ' 3 8 3 N., Long. 74" 4 5 5 40 'W. Bearing 5 S. 70 E. 5 7 N. 40 E. 4 14 W. by compass N. 6 5 7 22"30'W. dist. 7 5 6 15 miles. 8 5 7 9 N. 25 W. 6 4 N. 45 E. 20 4E. 10 6 4 11 7 6 12 7 5 Dev. as per Log. 1 N. 61 W. 7 4 N. 15 19 E. 2 8 3 3 6 6 4 5 5 Var. 16 W. 5 S. 70 W. 4 4 N. 42 W. 25 14 E. 6 4 7 7 4 7 8 3 9 Current (cor. 9 N. 30 E. 3 9 N. 40 W. low. mag.) S. 23 W, 10 3 8 Dist. 12 miles 11 3 G during the 24 12 3 5 hours. - ,1 Corrected Courses. S. 42'' E. S. 19 E. N. 84 E. N. 57 W. N. 73 W. S. 43 W. N. 4 E. S. 7 W. Diff Lat. 26/5. Dep. 20/4. True Course, S. 36° 30. Dist. 33 /. Lat. in, 39^ 53 N. Lonff. in, 75'^ 06 ' W. 3^' HAND BOOK AND SELF-TEACHER. u. 1 Ccurses. K. 9 'Si 1 8 Winds. Lee- way. Dev. Remarks. s. S. 67 E. 1-45 W. A point of land 2 9 8 in Lat. 43^ 30 ' 3 9 8 N. Long. 66^ 4 9 6 20 /\V. Bearing 5 S5615\V 8 7 N. 57 W. 20 10-15 W. by compass N. 6 8 7 45^ 30^ E. dist. 7 8 3 12 miles. 8 8 3 9 S. 45 W. 7 6 N. 67 \V. 14 7-30 W. 10 7 ti 11 12 6 5 4 4 Dev. as per Log. 1 N67 30\V 4 8 S. 46 W. 12 7-15W. 2 4 ^ / 3 4 3 4 4 2 Var. 14° W. 5 S 67 30\V 3 6 S. 12E. 3 8-45 W. 6 o O 6 7 3 4 8 3 4 9 N78 45W 2 8 S. 67 E, 12 W. Current (cor. 10 2 8 mag.) S. 45 W. 11 2 8 10 miles during 12 2 6 the 24 hours. Corrected Couvsos. Dep. S. 30« W. Dist. 12 miles 3. Diff.Lat. 124^^6, Dep. 50 /•8 1st. S. 16 E. " 39 " True course, S, 22^^ W. 2d. S. 12 W. " 34 " Dist. 135 miles. 3d. 8. 10 W. " 27 " Lat. in, 41^ 25 N. 4th. N. 77 W. " 18 " Long, in, 67^ 29 W. 5th. S. 48 W. « 14 " 6th. S. 75 W. " 11 " Cur H. 31 V r. (6 10 " TO CONVERT TIME INTO LONGITUDE. The circ\imferenee of tlie earth is 360", and the sun makes that circuit in 24 hours, and by dividing 360° by 24 it give& TO CONVERT LONGITUDE INTO TIME. 37 15°, SO the Sim travels at the rate of 15° per hour. If we wish to know what Loni,ntude corresponds with any num])er ot hours, minutes and second-o, we multiply the hours by GO and divide the sum by 4. ist Ex.— T time. 2d Ex.— 2 time. 3d Ex.~4 24 8 time. X 60 X 60 X 60 -4)60 -v-4)120 -4)264-8 15° Long, 30 Long. 66-2 Long. In the last example the hours are multiplied by 60, the minutes brought in or added, the seconds brought down and the whole divided by 4 gives the Longitude, 66*^ 2^, which is the Longitude of St. John; so when it is noon m t^t. John, it will be twenty-four minutes and eight seconds past 4 o clock ar London, or the meridian of Grreenwich. Another method is, to multiply the hours by 3 and by 5. 1st Ex.- 1 2d Ex.- 2 3d. Ex.— 4 24 8 X 3 X 3 ^ ^_ ~Z 6 13 12 24 X 5 5 . 5 15 Long. 30 Long. 66 2 Long. ai)oxe.} . TO COXVERT LONGITUDE INTO TIME. Multiply the seconds, minutes and hours by 4, and divide tlie product by 60. 1st EX.-15 2d EX.-30 3d Ex.-66-2 X 4 X 4 X 4 -6,0)6/0 -6,0)12/0 -6/0)^6^ 1-0 time. 2 time. 4 24-8 time. In dividing- by 60 one hgure is cut off, which makes it Short Division (no quotient), and the figure cut off is minutes ; it there is a remainder after dividing by 6/0 it is placed before the figm-e cut off, and the seconds will remain the same. 6 38 HAND BOOK AND SELF-TEACHER. BY SKOONI) MKTHOT). 1st Ex. -^3)lo^ 2dEx. -^3)30^ 3d Ex. -^ 3)66 2 9 -^5)5 ^5)10 -^5)22 00 40 1 time, 2 time. 4 24*8 time.. GREENWICH DATE. As (xreenvvich date is required to work all problems in Nauti- cal Astronomy, and as all the elements of the heavenly bodies are ^iven for Apparent and Mean noon at the meridian of Greenwich, they are given in the Nautical Almanac for every day in the year. But the navigator has a different meridian every day, and must necessarily compute the change between the meridian of (rreenwich and his meridian ; therefore, he must ascertain what time it is noon at Greenwich, or, what is termed the " Green- wich date." It is found thus : — Convert the Longitude into time, and if West, add to the time at ship ; but if East Long- itude, subtract, and it will give the Greenwich date. But if Civil Time be kept, and it is morning, or A. M., at ship, 12 hours must be added before applying the Longitude, for the Civil day begins at midnight, and the Greenwich, or Astronomical day at noon ; therefore, 8 hours in the morning. Civil day, will be 20 liours Greenwich, or Astronomical day. It should be remembered that when 12 hours are added to the A. M. Civil time it changes the day one less, as Greenwich, day begins 12 hours before tlie Civil day is ended. All the elements used in this work are for the year 1876, with the exception of the Tides, as a copy of them cannot be had yet. EXAMPLES. January 1st, at 3h. 30m., P. M., in the Long, of Cape Clear, gt) 29^ W., recpiired the Greenwich date. Time, 3h. 20m. Long 9^ 29/ W. + 37 56 4 Greenwich Time = 3 57 56 37 56 in time. February 2nd, at 8h. 20m., A.M., in the Long, of 8t. John, N. B., 66*^ 2' \d" W., required the corresponding Greenwich time. GREENWICH DATE. 39 Civil time, Feb. 2nd., 8 20 A. M. Long. 60" 2 ' 12 4 Astronomical day, 1st, = 20 20 0^0)20/4 8 4 24 8 4 24 8 in tinit. 24 44 8 24 Greenwich date, Feb. 2d, = 44 8 By adding 12 liours to the Civil time it changes the day one less, but Long. W. added exceeds 24 hours, and clianges it ba^k again to the 2nd day, so it will be 44 ' 88. past noon at Green- wich. March 4th. — When the sun is on the meridian in Long, in (16* 2 ' W., what is the time at Greenwich ? h. m. a. Noon, = 00 00 00 Long. 66 2 + 4 24 8 X 4 G. Date, 4th, = 4 24 8 -=-6,0)26,4 8 4 24 8 in time. April 8th. — In Long. 120° 20' E., when the sun was on the meridian what was the time at Greenwich ? Noon, 8th, 00 00 00 Long. 120 20 E. — 8 1 20 X 4 G. Date, 7th, = 15 58 40 -=-6/0)48,1 20 8 1 20 in time. May 10th.— At 8h. 20m. A. M., in Long. ISO*' 40' E., what is the time at Greenwich ? Time, ,8 20 00 Long. ISO"^ 40 ' E. + 12 X 4 Astronomical date, 9th, = 20 20 00 -=-6,0)52,2 40 — 8 42 40 8 42 40intim«. G. date, 9th, = 11 37 20 In the two last examples you are in East Longitude, and as the sun will be seen there 8h. 42m. 40s. before it will at Green- wich, the Long, must be subtracted to give Greenwich time. 40 HAND BOOK AND SKLF-TKACHKH. June 20th.— At 3.4/5 v. m., in Long. 50^' 20 ^ E., what is lli« corresponding Greenwicli time ? Time, 2()tli, 3 'i'') ()0 Long. oU" 20' -f- 24 4 lyth, 27 45 00 (vO)2:J,7 20 — 3 57 20 3 57 20 G. date, HHli, = 23 47 40 In this example tlie Long. tinTKul into time evecf'ds \]h; hoiirtr of P. M. time at the sliip, 24 lioiirs must l»e added to the ship's time, and change tlie day from the 20tli to the lUth. All (juestions similar to this puzzles tlie })egiiiner, and I am often asked, — Why, that hy adding 24 hours to the given time at ship it don't make it a day more, instead ot a day less ? Tlie beginner, hy carefully exaining the al)ove question, can see that if he losses a day, he will gain in the hours ; for there can- not he 271). 45m. in a day, and as his J^ong. is K., and exceeds the time at ship, 24 hours have to l)e added to enable him to make a subtraction. TO CORRKCT THK SUN'S DECl.INATIOX. The sun's Declination is what is N. or S. of the E(|nator, and is given in the Nautical AImana(^ for every day in the year, for (Ap.) apparent and (M. T.) mean noon at the meridian ol (ireenwich. But as the mariner changes his meridian every day, and seldom, if ever, ow the meridian of Greenwich, he ought to be able to calculate the change of Declination between that given in the Nautical Almanac and his time, whether in W. or E, Long. There will be only one rule given here, and that is by " hourly difference" and middle time. Middle time is the difference ot the hourly change of decl. at noon of one day, and at noon of the next day, and will be found to agree, nearly, with any of the other methods, and more accurate than some. RULE. Take out of the Nautical Almanac the decl. from page 1st for App. time, and from page 2nd for M. T. ; also, the hourly diff. Multiply the hourly diff. by the hoiu's and parts of an hour that TO (JOllUKCT THE SUN'S DKC'LINATION. 41 yon are to tli and reject the seconds altogether. KXAMTLKS. 187G, Jan. 1st. — ^In Lonjij. 9'^ 29^ W., when the sun is on the meridian what is the correct decl. A. T. ? Decl., page I., 23 2 :M\ H, D., 12-05 Lcmg. 9^ 29 ^ W. — 8 -(kS 4 Cor. Decl. S., 23 2 28 3615 37 56 in time. 7230 6)379 7/5915 •63 pts. of an hr. 43 HAND BOOK AND HELF-TKACIIKIl. In tliip; ex. there is no necessity for takinfj middle time, as it is only '^3 of an hour from (ireenwich noon, and the clianjj^e of Decl. only 12s, so hy miiltiplyin^j; the II. D. hy the decimal found, and cutting; olf 4 figures, as there is a decimal of 2 Hj^ures in the H. l).,and 2 decimals in the time, which leaves 7^5915 — 8s. nearly, to be subtracted, because the decl. is decreasinjj;. 187(5, Feb. 1st. — When th^^ sun is on tlie meridian in a place the Louji^. of which is 88" 58^ E., required cor. decl. Decl. page 1st., 17 11 42 — 412 H. D. 42-48 5-93 12744 38232 21240 Long. 88" 58 4 Cor. Decl. 17 7 30 6)35/5/ 52 5 55 52 ■ 6)25/1,9064 6)559 4-12 (nearly). -93 pts. In tliis (|uestion the Long, turned into time is 5h. 55m. 52s.. 30 tlie H. I). 42-48s. is multiplied by tlie hours and decimal of an hour, that is, of 55m. 52s., =-93, aud after cutting off the 4 decimal tigiu'es there will yet remain three, which are seconds, then by cutting off I figure, and the remaining 25 divided by 6, will be minutes, — which must be subtracted as the decl. is de- creasing, and we have the cor. decl. for the ship's place. 1876, March 19th.— At 7h. 20m. P. M. In Long. 174" 48" W., what will be the Decl. h. m. Time at ship, 7 20 Long. 174" 48' Lonjr. M. time + 11 39 12 W. 4 G. Date, - 18 59 12 6)69,9 12 11 39 12 Decl. page 1st, 19th, 0" 17M9" 18 46 H. D., 59-27 19 57 53343 5927 6)112/6/13 18 46 TO CORRECT THE HUN'H DECLINATION. 48 Tlif middle time is neglected in this question, as it i8 '3 only between both noons, and as the cor. is greater than the decl. the decl. is suhtructed from the cor. and changes decl. from S. to N. 187(). — April nth, at 8h. 2.5m., A. M., App. time, in Long. 115^ 50' E., what will he the sun's decl. ? Decl. I()tb,8^ir2/' H. D. 5.5-19 lOth noon. Long. 115^ 50 'K. 54-84 nth " 4 2)11-03 t))4(),3 20 55-01 mid. diff. 7 40 20 !" h. III. H. Time at ship, 11th, 8 25 00 Being A. M., at ship, 12 hours 4-12 is added to reduce it to As- tronomical time, and the loth, 1^0 25 00 Long, in time subtracted, it — 7 43 20 being E., gives (rreenwich time, 12h. 21m. 40s., on the G. date 10th, = 12 21 40 10th. Then the seconds and minutes divided by 6, 6)217 we have 12h. 3()m., which is multiplied by mid. dif)'., 12-36 55'Ols., gives 11m. 19s., or X 55-01 20 cor. to be added to decl,, 1236 6180 • 6180 6)67,9/236 Increasing + 11 19 or 20 DecL 11th, 8 11 2 Cor. decl. = 8 22 21 QUESTIONS FOR EXERCISES. 1876.— Jan. 10th, in Long. 40'' 40m. W., when the sun is on the meridian, what is the cor. decl. ? Ans. 11° 59m. 57s. S. 44 HAND BOOK AND SELF-TEACHER. 187f;.— FeL. 20t}i, in Long. 120'' 30m. E., when the sun is on the meridian, wluit is the cor. decl. ? Ans. 11*^ 9m. 25s. S. 187(i.— March 21st, at 8h. 20m., P. M., Long. 140" W., re- quired the sun's cor. decl. Ans. 00^ 47m. Is. N. 1876.— Dec. 20t]i, at 8h. 40m., A. M., Long. 178^ oOm. E., required the sun's cor. decl. ? Ans. 23*^ 26m. 49s. S. TO FIND THE LATITUDE BY THE SUN'S MERIDIAN ALTITUDE. First note the Altitude as read oiT the Sextant or Quadrant, and it it has an error apply it by the sign + or — . Next tind the altitude in Table IV, and abreast in the next col. to tlie right will stand the refraction, always subtraction. Next, on same page, under Table V, will stand the dip., and is found by looking down the col. under height ; and abreast, under dip. is the cor., always subtraction. The next cor. is parallel Table VI, always addition, (a.) Then take out of Nautical Almanac the Semi-diameter, page 2, and if lower limb (marked) L. L. or ^ it is added, but upper limb (marked U. L. or "o^ it is subtraction, and that will give the true altitude of the Sun's centre. Subn-act the true altitude from 90*^ and you will have the zenitli dist., to be named opposite to the bearing of the sun. That is, if the sun is to the N. when the observation was taken, tlie zenith dist. is called S. But if it bears S. from you it is named N. Next place the Sun's cor. decl. under the zenith dist., and if of same name add, but if contrary names subtract, and you have the latitude called after the name of the greater. State the « question as below: 1876, Jan. 20th.— In Long. 120*^ 30 ^ E, the obs'd alt. _0_ ])earing S. was 30^ ,30/ 30'/, index cor.— 1 ' '2,0", height of eye 21 feet. lve([uired the Latitude. (a.) The Refraction and Parallex together may be taken out from Table XVIII., Norie. TO FIND LATITUDE BY THE SUN S ALTITUDE. 45 Obs'd alt. 30^ 30' 30/' Sun's decl. 19th, 20 24 39. Cor. — 1 20 Cor. for 16th, — 8 28. 30 29 10 Sun'scor. decl. = 20 16 11. Ref.IV, - 1 37 H. diff. 19th, 31-27. 30 27 33 " " 20=.32-23. Dip. V, _ 4 23 " ^ ' 2)63-50. 30 23 10 „., ,.^ — 7- Pari. VI, + 8 Mid. diif. 31 wo, 30 23 18 Long. 120^ 30/ E. Semidr. + 16 17 "^ True alt., 30 39 35 ^^48/2 00 90 00 00 - 8 2 00 Zen.dist. 59 20 25 N. 24 00 00 Sun's decl. 20 i 6 1 1 S. ^ , ^ , (t. date 19th, 15 58 00 Lat. 39 4 14 N. Mid. diff. 31-75 G. date, x 16 hours, nearlv. 19050 3175 6/0)50/8,00 8-28 N. B.— G-reenwich date will be employed in all the questions in this work. May 15th.— In Long. 66'^ 40' W., obs'd alt. _0_ bearing S. was 40'' 40' 40//, cor. + 2/ 20/ /, height of eye 14 feet, re- quired the Lat. 46 HAND BOOR AND SELF-TEACHER. Alt 40 40 40 Decl. 16th, 19« V 2 ^ ' H. diff. 3494 Cor. + 2 20 Incr. -f 2_33 341 4 40^3' 00 T9~03 35 2)690J^ I^^^' ~_ ^ ^ Mid.diti\ 34-54 40 41 52 Long. 66^ 20 ^ 4-4 2 I>ip- — ^^^ 1 6908 40 38 16 6)26,, 5 '20 13816 Par + 7 13816 ^^'- ^ O. date, 40 25 20 ^ 40 58 23 ■ 6)15/2/6668 Semidr. + ___15^ 6)2_5_3 — -— True alt. 40 13 14 '42 90 00 00 Zen. 49 46 46 N. Dec. + 19 3 35 N. Lat. 68 50 21 N. Same name +. 1876, Juae 30th.— In Long. 74^ 50^ W., obs'd alt. © bearing N. was 33^ 33/ 33 '^ index cor. — 1 ' 20'^ height ot eye 22 feet, required the Lat. Alt. Cor. 33 33 33 Su — 1 20 n's deci. 30th, -^6 V ioi>. Dec. cor. — 51 Cor. decl. 23 8 25 Long. 74« 50 'W. , n. uin. vuo 10-66 Ref. Dip 33 32 12 1 26 33 30 46 4 30 2)20-31 10-15 nearly 5 .50*75 Par. 33 26 16 + 8 33 26 24 Semidr.— 15 46 6)29, 9 20 4 59 20 Different names. True Zen. Decl. alt. 33 10 38 90 00 00 dist. 56 49 22 S. 23 8 25 N. Lftt. 33 40 57 S. Named after the greater. AMPLITUDE. ,47 1876, April 3rd.— In Long. 44*^ W., obs'd alt. _0^ bearing N. was 74" 50' 40", height of eye 20 feet, cor. — 2' 19", jte- (juired the Lat. d. m. s. d. m. a. s. (1. Obs. alt. 74 50 40 Decl. 14 58 03 H. D. 4561 Long. 44 Cor. — 2 19 Cor. + 2 11 4498 4 74 48 21 Cor.decl.l5 00 14 2)9059 6)17/6 Ref. — 15 -^ Mid. diff. 45-29 2, 56 74 48 6 2-9 Dep. — 4 17 2-9 40761 74 43 49 9058 Par. -f 2 74 43 51 6)13/1/341 Semidr. + 15 54 Cor, 2-11 74 59 45 90 00 00 Zen. dist. 15 00 15 S. Cor. decl. 15 00 14 N. Lat. 00 00 1 S. AMPLITUDE. Amplitude is the bearing of any of the heavenly bodies when rising or setting, and is named E. in the morning, and \V. in the evening. It is of great benefit to the navigator to correct any errors that may arise in his compass from the different cargoes taken on board, and also in sailing along coasts of a mineral nature. Every Master of a vessel, no matter wliether off the coast or on it, should be able to detect an error in his com- pass by an Amplitude. There is no necessity of an Azimuth compass to get the sub's mag. amplitude. It can be found correct enough by taking the compass on deck and placing any small bar, or even the parallel rule edge on the compass card and towards the centre of the «un, read off the bearing, and you have the sun's magnetic amplitude. 48 HAND BOOK AND SELF-TEACHER. TO FIND THE TRUE AMPLITUDE. The Secant of the Lat., rejecting 10 from index, and the Sine of the sun's cor. decl. added. The Sine corresponding to the sum will be the true amplitude, named E. if ol)served in the morning, and W. if observed in the evening, also after the sun's decl. That is, if the observation is made in the morning, and the decl. S., the amp. is E. and S., and in the evening W. and S. TO FIND THE ERROR. If the true and mag. amplitudes are of the same name, take their diff., but if of opposite names take their sums (that is. if one is N. and the other S.), and it will give the error. TO NAME THE ERROR. If the true amp. falls to the right of mag. amp., it is named E., but if to the left, it is named W. Suppose tlie sun's true amplitude was E. 20*^ 30' S., and the mag. amp., or bearing by ship's compass, was E. 10" 30' S., the true amp. is to the right, and the error would be called E. Or, fancy you are looking at both suns, point a hand at each (no matter whether morning or evening), and if the true sun is abreast of your right hand i1 will be E., but if to the left it will })e W. The error found is caused by local attraction, — that is, the iron that is used in building the sliip ; also, by iron cargoes taken on board, — both draw the needle of the compass either to the W. or to the E. from the N. point, and is named tlie Error. Rut there is another error, called Variation, that affects the compass needle, which is caused by the magnetism of the earth, and acts different on the needle in dift'erent Latitudes, and sometimes it will be of the same name as the error (caused by local attraction) and different at other times, so both combined is called tlie Correct Deviation of the Compass. TO FIND THE DEVIATION. Having found the error, place under it the variation as given on the chart. Change name — If itbeE. call it AV., and if \V., call it E. ; tlien if they be of different nami^s, take their ditf. and name the Deviation after the greater ; but if of the same name, add, and it will be the same name as both. Or, let the variation keep the same name, and if of different names, add. AMPLITUDE. 49 but same name, subtract, and the diiference, or sum (as the case may be) will be the Deviation. Then, to name the Deviation, you must suppose yourself look- ing towards the N., and if the variation falls to the ri^lit of the error, the Deviation is to be named E., but if to theleit of error, W. N. B. — I would advise the learner to practice tlie first method (change names of var.), as he will have little or no trouble in naming the Deviation. _P- S. — When tlie sun's decl. is nothing, tlie true amplitude will be E. in tlie morning and W. in the evening. Also, if your Latitude is nothing, that is, you are on the l^cpiator, tlie sun's correct decl. will be the true amplitude named after tlie decl., and wlien the error is nothing (00 00), that is, the t^"^ and niagnetic amplitude are equal, the variation will be ,]ie deviation of an opposite name. EXAMPLES. 1876, Jan. 1st.— At 4h. 20m. A. M., apparent time at ship, in Lat. 50^ 20 ^ N. and Long. 150^ 10 ' W., tlie sun's magnetic amp. was E. 12° 30^8. and var. 20° 15 / E., reciuired the^dev. h. m. s. d. in. s. s App. time, 1st. 4 20 00 Decl. 23 2 36 Diff. 1205 12 00 00 — 29 1320 Dec. 31st., 16 20 00 Cor decl. 23 2 7 10 00 40 2)2525 LonjT. 150° 10' -^iid dilf. 1262 26 20 40 "* 4 2-3 24 6^0)60/0 40 3786 G. Date, 1st., 2 20 40 — '■ 2524 10 00 40 Lat. 50° 20' Secant, 0-194961 ^ Decl. 23 2 Sine, 9-592373 20. 026 True amp. E. 37° 48^ 30/^ S. 9-787433 Mag. amp, E. 12 30 S. Error, 25 18 30 E. True, being to the right of mag. Var. 20 15 \V. Change name of var. Dev. 3 30 E. Named after the greater. 50 HAND BOOK AND SELF-TEACHER. 187€,'Feb. 2nd.— At 6h. 30ra. P. M., apparent time at ship, in Lat. 10^20'S., and Long. 17H^ 50 ^ E., sun's mag. amp. was W. 30^^ 20' S., and var. 7" 10' W., required the dev. h. m. s. App. time 2d. 6 30 24 d. m. s. Decl. 17 11 42 13 21 Diff. 4248 4322 30 30 11 47 20 Cor. decl. 16 58 21 Long. 176^ 50' 4 2)8,570 4285 late, Jan. 1st., 18 42 40 18-7 29995 '34280 4285 6)70/7 20 Time, 11 47 20 6,0)80,1/295 13 21 Lat. 10» 20' Sect. 0-007102 Decl. 16 58 Sine, 9-465108 True amp. VV., 17 15 30 S. 9-472210 Mag. amp. W., 30 20 00 S. Error, Var., Dev., 13 4 30 E. True, being to right of mag. 7 10 00 E. Change name of var. 20 14 30 E. 1876, March 20th.— At 6.40 P.M., in Lat. 50^' 00m. and Long. 30^ 30m. E., the sun set by compass VV. 2^ 45m. N., and var. on chart 2" 45m. W., required the dev. (1. m. s. Decl. 20th. 5 52 4 33 Cor. decl. 1 19 Civil time, 20th. 6 40 Long, in time, — 2 2 G. date, 4 38 H. diff. 5924 4-6 (i. Hi. Long. 30 30 E. 4 35544 23696 6)12,2 00 — In time, 2 2 6,0)27,2/504 4 32 3 nearly. AMPLITUDE. 51 rt. m. ». d. ni. H. Decl. 119 Sine, 6-68866o True amp. W. 2 45 N. Lat. 50 00 Sect, 0-191933 Mag. amp. W. 2 45. N. 9-780598 Error, 0~(r~0 next less, — 764756 Var. 4- 2 49 E. (ci>^"«« liainc.) Diff. -^ 34762)158420(45// Dev. 2 49 W. 139048 193720 173810 In the above example the decl. shows no degrees, but minutes and seconds, therefore it is necessary to iind its value from the select pages at tlie beginning of Table XXV., as it gives the value of the nearest second ; and as the diff. of the logs diffeied materially when the minutes were found, the next less lias to be taken, and the difterence divided by the diff. found in col. t<> find the seconds. It is not necessary to go into such close cal- culations in an amplitude, but the pupil should })e acquainted with the Table. 1876, April 10th.— At 4h 30m. A. M., in Lat. 42^^ 40m. N., and Long. 74'^ 50m. W., the sun's mag. amp. was E. 4^ 25m. S., var. by chart 15" 00m. E., required the dev, d. in. «. s d. m. Dec. 9th. 7 48 54 Diff. 5552 Long. 74 50 Inc. -I- 20 56 5519 4 Corded. 8 9 50 2)11071 6,0)29^^) 1,. Mid. diff. 5535 M. time, 4 59 20 Civil time, 10th 5 30 22-5 12 27675 9th, 17 30 11170 4 59 20 11170 O. date, 9th. 22 29 20 6,0)125,6/375 20 56 Decl. 8 10 Sine, 9-152451 Lat. 42 40 Sect. 0-133530 True amp. E. 11" 8 20 N. 9-285981 Mag. amp. S. 4 25 S. 285766 Error, 15 33 20 W. 1069)2150(20 15 W. (change name) 2138 Dev. 30 33 20 W. ~~T20 — 52 HAND BOOK AND SELF-TEACHER. QUESTIONS FOR PRACTICE. 187(), May 2()th.— At Th. 30m. P. M., in Lat. 45^ 15ra. N., and Long. ()()*^ 20m. W., the sun's mag. amp. was W. 1*^ 50m. N., var. by chart 10^ 20m. W., re([uired the dev. of compass. Ans. dev. '67'^ 54m. E. 1876, Jmie 30th.— 4h. 40m. A. M., in La(. 48«' 40m. N., and Long. 50'^ 30m. E., the sun's mag. amp. was E. 30"^ 20m. N., var. by chart 19" 40m. E., required the dev. of compass. Ans. dev. 25'^ 55m. W. 1870, July 5th.— At 8h. 15m. P. M., in Lat. 69° 00m. N., and Long. 79*^ 50m. E., the sun's mag. amp. was W. 40'^ 30m, S., var. by chart was 33*^ 20m. E., required the dev. of compass. Ans. dev. 13^ 21m. 30s. E. 1870, Aug. 15th.— At 4h. 40m. A. M., in Lat. 00° OOra. OOs., and Long. 28*^ 10m. W., the sun's mag. amp. was, P]. 3" 40m. N., and var. by chart was 4" 20m. W., required the dev. of com- pass. Ans. 5*^ 57m. W. 1870, August 29th.— At 7h. lOm.P.M., in Lat. 45^ 15m. N., and Long. 06*^ 20m. W., mag. amp. was W. 4* 15m. N., var. l)y cliart 17'^ W., required the dev. of compass. Ans. 25^^ 33m. 30s. E. 1876, Sept. 23rd.— At 4h. 40m. A. M., in Lat. 50'^ 30m. N., Long., 38"^ 10m. W., mag. amp., was S. 90" E., var. lO'' 20m., W., re(][uired dev. of compass, Ans. 10^ 34m. 41s. E. 1870, Oct. 1st., at 5h. 30m., P. M., in Lat., 45° 40m. N., Long. 174° E., mag. amp. was W. 25° 20m. S., var. 22^^ 20m. W., re- quired the dev. by compass. Ans. 53" 11m. 45s. E. 1876, Nov. 20th.— At 5h. 30m. A. M., in Lat. 15° 50m. S., Long. 27° 00m. E., sun's mag. amp. was S. 76° 45m. E., var. by chart 4° 20m. W., required the dev. of compass. Ans. 11° 40m. E. 1876, Dec. 30tli.— At 6h. 20m. P. M., Lat. 40° 40m. N., Long. 70° 00m. W., sun's mag. amp. W. 10° 20m., var. by chart 9° 11 m. W., required the dev. of compass. Ans. 11° 38m. W. TO FIND THE DAILY RATE OP A CHRONOMETER. 53 TO FNID THE DAILY RATE OF A CHRONOMETER. Every Master who trades to tlie West Indies, no matter liow small his vessel, should be able to ascertain the daily rate of his Chronometer, both by the sea and an artificial horizon. There is no necessity for having an artificial horizon on board, as one can be made very simply, — by covering the head of a cask with molasses, or even with water, a true altitude can be found inde- pendent of the sea horizon. There are very few Ports in which a sea horizon is visible when lying at anchor. Very few Chro- nometers keep a uniform rate, and when Masters of vessels find that their Chronometers have lo^t or gained, and do not agree with the land they have made or the Port they are in, become uneasy, and perhaps may rate them by Chronome- ters of other vessels, for few, if any, like to send them ashore in the West Indies. The rate is found thus : — If a Chrono. is fasti . . If fast 1 , . and more fast, | 8^^"^°^' and less fast, J ^'''''^' If slow \ , . If slow 1 . . and more slow, | ^'^^^°g' and less slow, | ^^^^^^S- EXAMPLES. If a Chrono. was fast of Greenwich Mean Time 4m. 3s. 4t. on Jan. 1st, and on Jan. 21st fast 5m. 58s. St., what would be tlie daily rate ? m. 8. t. Fast, — 4 3 4 In this example the Chrono. More fast, 5 58 3 is fast and more fast, — the diff. is taken, and divided 1 54 9 by the interval, 20 days, 60 which gives rate 5s. 7t., nearly. Whenever the re- 20)114-9(5s. 7t. mainder is less than half 100 gaining. the divisor it is rejected, ^ut if greater, one tenth is 149 added to the quotient. If 140 there be minutes in the diff. they must be brought into 9 seconds before dividing by the days. 54 HAND ROOK AND SELF-TEACHER. A Chrono. was slow 2m. 4s. 8t. on Feb. lOtli, and Fel). 20th slow 2m. 88. St., what is her daily rate ? III. H. t Slow, 2 4 8 More slow, '2 8 8 10)40(-4t., losing. 40 C)n March 3rd, a Chrono. was fast lli. 20m. 10s. 4t., and on March 23rd was fast Ih. 18m., refjuired the daily rate. h. in. a. t. Fast, 1 20 10 4 Less fast, 118 Same name, subtract. 2 10 4 60 20)1304(63. 5t., losing 120 104 100 4 On April 30th, a Chrono. was fast 2h. 45m. 57s. 8t., and on May I7th v^as fast 2h. 45m. 12s. 9t., required the daily rate; li. m. s. t. Slow, 2 45 57 8 Less slow, 2 45 12 9 17)44 9(2-6. Gaining. 34 1 09 1 02 7 On May 29th, a Chrono. was slow 22s. 4t., and on June 7th was slow 4s. 4t., required the daily rate. Slow, 22 4 Less slow, 4 4 9)18 0(2s. Graining. TO FIND THE ACCUMULATED RATE. 55 June 2()tli, a Chrono. was fast 4tn. 24s. 7t., and on June .30th svas 4m. 27s. 7t. Reciuired the (hiily rate. in. n. t. Fast, 4 24 7 More fast, 4 27 7 10)30(-3t. Gaining. QUESTIONS FOR PRACTICE. On July 10th, a Chrono. was slow 15m. 10s. 9t., and on JiJy 22nd was slow 17m. 50s. 4t., recjuired the daily rate. Ans. 13'3. Losing. ■ August 29th, a Chrono. was fast Ira. 10s. 4t., and on Sept. 10th was fast Ira. 17s. 8t., required the daily rate. Ans. r)*2. Gaining. Sept. 21st, a Chrono. was slow 31i. 57ra. 49s. 9t., and on Oct. 15th was slow 3h. 59m. 59s. 7t., required the daily rate. Ans. -5*4. Losing. Cm Nov. 29th, a Chrono. was fast Ih. 14ra. 20s., and on Dec. 14th was last Ih. 13m. 16s. St., required the daily rate. Ans. 4'2. Losing. TO FIND THE ACCUMULATED RATE. The Accumulated Rate is what a Chronometer gains or loses in any number of days. The day that it is sent on board, the daily rate is given, and by multiplying the days and decimals of a day by the daily rate, it will give what is lost or gained in the interval. Suppose you had a Chrono. on board from Jan. 27th to Feb. 21st., and at 8h. 20m. A. M., you wished to find the accumulated rate, the daily rate being 8s. 6t., gaining. Civil Time, 21st., 8h. 20m. + 12 Interval from Jan. 27tli Astro. Time, 20th, 20 20 to Feb. 20th = 24d. 8h. (1. Inter. 24 8 In this example the Chrono. gained Daily rate, x 8-6 8s. 6t. per day, and the interval was 24 days and 20 hours ; then you have to find what part of a day 20 hours is. By adding a 6 0)21 3 28 cypher (0) to the 20 it makes it 200, and dividing that by 24 you 1488 1984 Accum. date, 3 33 fi^d the decimal of a day. 56 HAND BOOK AND SELF-TKAClThTR. Another metliod is to multiply by tin* days only, and take parts for the hours, divide into tlie daily rate. Thus : — Days, 24 Or thus, 24 12h. is ^ -j- daily rate, 8'G 12h. is ^ 4- 8-6 8h. is ^ 14-4 14-4 192 192 4-3 6 is ^ -f- 4'3 2-8 2 is I -^ 2-1 (V0)21,3,5 I 6/0)21/3,5 Same as above, 3 33 5 3 33 5 N. B. — The first method is tlie most simple, and as the be- ginner often becomes confused in takinjjf and dividing the part* of a day, as in the last, it is desirable that the first be used. From noon, March 10th, until April 15th, at 4h. p. M., a Chrono. loses 2s. 9t. per day, what is the accunuilated rate ? Interval, 36-2 2nd method, 36 2-9 4 is I -f- 2-9 6/0)10/4/98 3258 324 724 72 5 Ace. rate, 1 45 nearly. 6/0)10,4/9 1 45 QUESTIONS FOR PRACTICE. From May 30th until June 29th, at 4]i. A. M., a Chrono- meter loses daily 4s. 2t. What is the accumulated rate. Ans. 2m. 3s. P'rom August 29th until Sept. 4th, at 8h. P. M., a Chrono. gains 98. 8t. What is the accumulated rate ? Ans. Im. 2s. From Sept. 5th until Dec. 29th, at 5h. A. M., a Chrono. loses daily Is. 2t. What is the accumulated rate ? Ans. 2m. 16s. From Jan. 10, 1876, until Nov. 21st, at 9h. p. m., a Chrono. gains daily 8s. 4t. What is the accumulated rate ? Ans. 44m. 18s. OREENWICn DATK BY CITnONOMKTKR. 57 TO FIND TIIK (HlKKWVICll DATK HY CIIRON'OMKTKR When a (-liiouoiueter is tiiken on hoard, it is sohloin, if ever, on Greenwich Mean Time, — that is : to show the same hours, minutes and se(!onds as sliown at the Royal Ohservatctry at Mean noon. And wliat she is fast or sh)W is called the Oriuiual Error, which is to Ik; achled if 8h)W, and suhtracted if fast. Tlien the accumulated rate (as alre;i,dy shown) is to he ajiplied and you have Mean Time at Greenwich. At the Dominion Board Examination the approximate Longitude is jifiven, with the A. M. or P. M. hours at siiip, t(» find the ;i[)proximate (rreeii- wich day. As no day \» jj^iven hy the (Chronometer, — only hours, minutes, and seconds,— therefore to know whether it is A. M. or P. M. hy Chronometer proceed thus : Set (hnvn the Ikmus, minutes and seconds as jj^iveu at ship, and if A. M., add 12 hours, and put the day one hack ; next, turn tlie Lonjjfitude into time, and if W. add to shiji's time, hut if K. siihtract, ;ind you have the Cfreenwich date nearly; if the Chronometer dif- fers ahout 12 hours from the time found, 12 hours must he added to make hotli a^ree nearly. (Previous to 1872 tlie daily rate was given, hut now the candidate has to find the daily rate in all examph's given.) 1876, Jan. 2yth.— At Hh. 20m., A. M.,in Long. 03" 30m. W., a Chrono. indicated OOh. 24m. 40s., wliich was slow 8m. 00s. 3t.: on Jan. 1st, and on Jan. 10th was slow 8m. 14s. tit. Required the •Greenwich date hy Chronometer ? h ni ' m. s, t. 29th, 8 20 Slow, 8 00 3 Long. 63 30 12 8 14 6 X 4 28th, 20 20 9)14 3( I -(i, '^ISiS"' (i, 0)25, 4 00 4 14 9 4 14 00 24 34 53 24 00 54 (1. 29th, 00 34 Interval from Jan. 10 to 29th, 19 h. m. 8. X 1*6 daily rate. Chr. 00 24 40 + 8 14 6 last rate, 114 19 32 54 6 — + 30 ace. rate. 30^4 LosinV Gr. date, 29th, 33 24 6 58 HAND BOOK AND SELF-TEAGHER. The Civil time was 8h. 20m., A. M., 12 hours had to be added to reckon from noon of the previous day, wlien the Astronomi- cal day commenced, and had to be reduced a day less, from the 2f)th to the 28tli ; l)ut Long, beinj^ W., and turned into time had to be added, and the sum exceeded 24 hours, 24 had to be sub- tracted whicli brou<^ht the day to the 29th again, and gave the (Tret'nwich date nearly. The Chrono. indicated only a few minutes past noon, and the last rate (original) slow added, also ace. rate losing (slow and more slow) added, gave correct (freenwich date, agreeing nearly with approximate date. 1876, April 30th.— At 3h. 49m. P. M., in Long. 179" 38 / K, a Chronometer indicated 3h. 43m. 4s., wliich was slow 8m. 6s. Nov. 13tli, 1875, and on Jan. 10th, 1876, was slow 6m. 33s. 8t. for Mean noon at Grreenwich. Required the Greenwich date by (Chronometer. It. m. t;. m. 8. 30th, 3 49 00 First rate slow 8 6 Long. 179 38 24 00 00 2d rate less " 6 33 8 - 4 29th, 17 49 00 Interval, 132 2 6/0)71,8 32 — 1 1 58 32 E. 60 1158 32 App. Go date 29th 15 50 28 58)922(1-6 gaining 58 Chr. 3^4 31 342 + 6 33 8 last rate. 10 348 21 Jan. 29 Feb. 31 March. 29 April. 3 49 37 8 2 57 3 52 34 8 12 00 00 1 1 n.rr Interval frmn 10th Jan. tc llyf I lyth April. G. date, 29th, 15 52 35 8 x 1*6 daily rate. 664-2 1107 6^0)17,7/12 2 57 ace. rate. • In thie (juestion it was r. M. at ship, but A. M. at GraenwicJj. GREENWICH DATE BY CHRONOMETER. 5D" because the ship's time was in advance of Chrono, 12 linnrs, nearly,— 12 hours liad to be added to Chrono. time to make if correspond with ship's date. 1876, Jmie 14th. — At 8h. 30m., A. M., Longitude by acct. 38" 50/ E., a Chrono. indicated 6h. 00m, 58s., which was slow 6m. 00s. It. on April 19th, and on May 11th was slow 2m. 24s. 6t. for Grreenwich Mean noon. Required the Crreenwich date by Chrono. in. E. t. 14th, 8 30 &low, 6 00 1 April 19th. Long. 38 50 12 00 less slow, 2 24 6 May 11th. 4 20 30 3 35 5 22 Inter. 6,0)15^5 20 2 35 20 E. 60 2 35 20 I3th, 17 54 40 22)2159(9-8 gaining. 198 31 179 11 176 — h. m. s. 20 May. Chr. 6 00 58 3 13 June. + 2 24 6 original. ' 33-9 6 03 22 6 9-8 5 32 ace. rate. 2712 Gr. date, 5 57 50 3051 12 6/0)33,2/22 G-. date, 13th, 17 57 50 5 32 In the above question it was A. M. at ship and A. M. at Green- wich, therefore 12 hours had to be added to both dates to reduce them to Astronomical time. The Original rate, slow, wan added, Init being slower than the first rate, the Ace. rate was gaining and had to be subtracted. 1 876, Feb. 10th.— At 91i. 00m. A. M., Long. l)y acct. 8^ 50 ' W., a Clirono. indicated lOh. 21m. 59s., wliich was fast 34m. 40s. 9t. on Oct. 30t]i, 1875, and on Dec. 2nd, 1875, was fast 39m. 01s. 4t. for Mean noon at Greenwich. Required the Greenwicli dato by Chronometer. 60 HAND BOOK AND SELF-TEACHEK. in. s. t. lOth 9 00 Fast, 34 40 9 Oct. 30 Long. 8^ 50 M .. 12 More last, 39 1 4 Dec. 2 4 21 00 4 20 5 32 35 20 35 20 6 31 9th,2l 35 20 33)250-5(7-9 2 231 — Chr. 10 21 59 29 Dec, _ 39 1 4 295 31 Jan. 297 9 Feb. 9 42 57 6 9 11 'i 69-8 7-9 9 33 46 6 12 6282 4886 6)55/ 1/42 ~9~rr a.date,2133 47 TO FIND THE HOUR ANGLE. The Hour Angle is the Apparent time from noon when an' observation is taken, and is named A. M. if taken in the morn- in- '»• «■ d. ni. (1. Alt., 17 46 50 Decl. 21 2 -f- 90 — HI 2' P. D. Lat., 28 45 Secant, 0-057136 Cosine, 9-289600 P. D., 11 1 2 Co-Sec, 0-029945 — 584 Co-Sine, 9-289016 Sine, 9-941878, 2)157 33 50 9-289()l(i Half-sum, 78 46 55 Alt., — 17 46 50 Diff. 1061 X 55 Rem. 61 00 05 5305 li. ni. s. Hour Angle, 3 37 3 = 9-31797/5 5305 — 80 583/55 9-941819 18 = 3s. Diff. 117 + 59 5 9-941878 58,5 .f Dc'5;iSoTi;>'le;i"^' "^' '''''■ •'""'^ '' '^'''^^"^"^ "'^'"-^ '^'^l exceeding 90, UK.S.,.H,n True alt. 27° 45^ 20^^, Lat. 45" 30/ N., decl. lO'^ 20/ S. Required the Hour Angle, or App. time. Decl. 10« 20/ S. - 90 = 100° 20/ P. Dist. Alt., 27 45 20 Lat., 45 30 Secant., 0-154338 P. D., 100 20 Co-Secant, 0-007102 «^~^"T~ 8-749055 375H 2)173 3.3-20 Co-Sine, 8-747553 — 1502 x 40 Half-sum, 86 47 40 Sine, 9-933242 8-747553 1 502'^40 27 45 20 ' 8-842235 9-9.33217 126 Rem. 59 2 20 _ 175 + 25 20 Hour Angle, 2h. 2m. 19s. 4s. = 59 9-933242 2.5. 20 8 (32 HAND BOOK AND SELF-TEACHER. True alt, 40^ 37' 50/^ Lat 36'' 40/S.,decL 12« 25' 18'' S. Required the App. time from noon, or Hour Angle. Decl. 12'^ 25' 18^/— 90=77^34^42/' Alt. 40 37 50 Lat. 36 40 Secant, 0-095759 P. D., 77 34 42 Co-Secant, 0-010287 2)154 52 32 Half-sum, 77 26 16 Co-Sine, 9-337459 40 37 50 Sine, 9-777517 Rem. 36 48 26 9-221022 Hour Angle, 3h. 12m. 34s. 75 27=:4s. -010307 20 47 42 -010287 94 188 19,74 337610 151 945 16 337459 5670 945 777444 + 73 151/20 281 77-7517 26 1686 562 73,06 Note.— The Hour Angle can be found independent of Table XXXI, thus :— Divide the sum of the four logs by 2, take the result in Sine col., Table XXV, and the degrees at the top, and minutes in left col., which multiply by 2 and turned into time will give the Hour Angle. Ex. — The sum of Logs in last question was 19-221012 -^ 2 Sine, 24 4 7 "TeToSlT X 2 next less, 477 48 8 14 Diff. 471)3400(^07 X 4 3297 6/0)19,2 32 56 Hour Angle, 3 12 33 nearly as above. LONGITUDE BY CHRONOMETER. 63 LONGITUDE BY CHRONOMETER, Tn fiiidinor the Lorioitude by Chronometer, it is necessary to rind the ]Mean Time at ship first, and the difference l)etween that and the Mean Time shown by a Chronometer will be the Longitude in time ; but both must agree in dates, that is,— it must not be one day at ship and another at Greenwich. Suppose the Mean Time found at sliip was 2()li. 5()m. 30s., Jan 20th, and Mean Time shown by Chronometer was 8h. 30m"' on Jan. 21st. The diff. is 12h. 20m. 30s.; now, if this differ- ence be multiplied by 60 and divided by 4, it will exceed any -Longitude, that is,— it will exceed ISO''. 12 20 30 60 4>740 30 Long, in 185 7 30 E. — 360 00 = 174 52 30 W„ Therefore, 24 hours must be added to the date in advance, and put one day back to make both dates agree. By adding 24 hours to the 21st day, shown by the Chronom- eter, it will reduce it to the 20th, then the difference is the Lon- gitude. h. in. Time by Chrono., 21st day, 8 30 00 24 M. T. Greenwich, 20th day, 32 30 00 M. T. at Ship, 20th day, 20 50 30 11 39 30 60 4)699 30 Long. 1 74 52 30 W. tn the first case, the Longitude is East, as the ship's time !«» greatest, but of different dates ; but in tlie latter it is W as Greenwich is best, on same dates. ' It has been explained already, that bv adding 24 hours to the day m advance it will make it one day less, but it gains in the hours, as in the last example. 64 HAND HOOK AND SKLF-TKACHKIt. TIh^ Lonoitiule nijiy l.c foimd, in the first case, })y leavin^^ both tiiiif'S (litrmnit dales and tnkiiij,^ tlie result from 'M\i)'\ iiml „;iniiii<.- 11,(. Longitude opposite. It is more plain and simple lo follow the last rul(s wliieli wdl not lead the learner into so many mistakes. KXA.MTLKS. lS7(i. Jan. .Slst.- At ^h. r)()m., P. M., in Lat. 42" 00^ N and Lon-r. l,v acct. oir ;>()' W., tin; observed alt. _0_ was 14^ 15 20" index cor. + 2m. lOs., hei<,dit of eye 17 feet, when a Chrono. indicated (ill. 4!)m. lOs., which was slow 12m. OOs. lt.,on(ireen- svich Mean Time Jan. 2nd, and on Jan. 23rd slow 11m. 20s. 4t. Kecpiired the Lon^. in. Inter., 21 davs, from 2nd to 23rd Jan. Lonj;. 50 50 7 ,/ A Ship's time, 3 5() 00 l.ono-. f- 3 23 20 App. G. date, 7 13 20 Timehyriir., 49 10 Oriu-. error, + 1 1 20 4 Slow, 12 00 1 Slow, 1 : 20 4 6)20, 3 20 Int. 21)31) 7(l-9KainmK. 3 23 20 21 187 1 89 d. 7 00 30 4 2nd Int. from 23rd to 31st. 8-3 Accl. rate, 15 o•aiIlin<,^ + 1-9 d.r. M.T. G.,31st. 7 00 14 4 Ol.s. alt., 14 i'5 20 Cor,, 4 2 10 747 83 (i. in, H. Decl., 31st, 17 28 42 — 4 55 15,77 14 17 30 Dip., — 3 57 Cor Decl., 17 23 47 31st, 41-72 4- 90 00 00 H.D. 32nd, 42-48 14 13 33 r. IMst., 107 23 47 2)84-20 Hef. par., — 3 33 14 10 00 fllmi-Di., + Hi H> Cor. alt., 14 2(1 Hi Mid. ditf. 42.10 7 6)29/4,70 Cor., 4.55 LONGITIJDK MY f •iri{nN()M KTHH. 65 fl m. H. Cor. Jilt., 14 2(1 K; L:it., 42 00 00 Sec. 0-l2S!)27 P. IM.sl., 107 23 47 Co-Seo. 0-020272 (Jo-Sin.' !M4S02(i 2)l(i,'i r>{) .S Sine, J)-9(ior,-)() H. Slim, 81 ')5 1 J)-2<)277') Alt., 14 2(1 K) (;r, Rem., fi7 2S 4'> 13 (2s.) 0-020.']03 ()5 :n 47 •020272 I.5.J 2(10 {)(;.-;-> 11 ,".0, ;'>.") 31) H7 9{;')jrj() 4') h. in. H. allele, 3 22 42 43,-, Kciuiition, + 13 43 34H M. T. S., 31st., 3 ;^(; 25 Qo 1/^ ALT.G.,31si., 7 00 1', ' K(|u:ition, 31st, 13 40 Diff. -378 Long, in time, 3 23 50 1^ 3 7 X GO L -^ 4)203 oO Cor. Equation, 13-43 2. (i4(; iiong. in, r>0 57 30 W. In this example it was P. m. at ship and W. I>on^ntn(le, and conseciuentJy of same date, so tliat tlie e.piation was Jidded in il. A., without sul)tractini>- or addinir 24 hours, and tlie differ- ence between tlie Mean Time at «hip and mean time at (ireen- wich gave tlie Longitude in time. 1870, Jan. 28tli.— At 4h. 01m. i>. m., in Lat. 28^ 45 ' N Long, by acct. 170^ 55 ' E., alt. O 17^ 4()' 30'^ index cor. — 3m. 2oa., height of eye 16 feo^t, time by (Hirono. 4h. 31m. 30s which was fast Im. Ids. 2t. Chrono., 4 31" 30 U 23 40 + 1 3 Int. 16cl.)139-2(8-7 losing. 1 OK Oii'T l"t. fi'i'in Jiin. Ist 1^0 ^" ' U.Jau.a7tl.. 4 32 33 + 3 52 4 36 25 12 00 00 112 609 38-50 112 522 39-33 174 2)77-83 6)23/2/29 M.T. G. 27th,16 36 25 38-91 Ace. rate, + 3-52 irsing. G.D. 16-6 Alt., 1 7 46 30 Cor. 3 25 Decl. 18 32 53 23346 10 47 23346 17 43 05 3891 Dip. — 3 50 Cor. Dec, , 18 22 06 6/0)64/6906 17 39 15 Cor. Dec, , 18 22 06 Cor. ref. 2 49 4- P. D. 90 00 00 H. 10-47 17 36 26 108 22 06 Diff. -516 Semi-Di., -f- 16 17 .m 16.6 Eqna., 12-57 — T. Alt., 17 52 43 +9 3096 Lat., 28 45 00 Sec 0-057136 3096 P. D., 108 22 06 Co. Sec 0-022707 Cor. Eq. 13-06 516 Co-sine, 9-335384 2)154 59 50 Sine, 9-935855 H. sura, 77 29 55 9-351082 Alt.,- 17 52 43 090 59 37 12. 18(3) 949 55 4745 4745 8, 56 56 123 12 14/76 521/95 LONGITUDE BY CHRON(\MCTEE. H7 Hour An<,rle, 28th, 3 4(5 13 Kqn. 4- 13 7 3 o9 20 24 00 00 M. T., 8hip, 27th, 27 59 20 M. T., Greenwich, 27th, 16 36 2.5 11 22 55 60 4)682 55 Long, in, 170 43 45 E. In the above example the Hour Angle was 2SMi day, v m but the ship being in a high E. Longitude, and that subtraote'd troni time at ship brought the day back to the 27th, Greenwich date, and the H. A. was on the 28th, conse.iuontlv thev were of different dates, therefore 24 hours had to be added to ship-.- date, a _ it was in advance, to reduce it to the 27th (hiv and Greenwich date. •^' 1876, Nov. 25th.--At 7h. 50m. a. M„ Lat. 40^ 10' S Lontr 72 59^ W., Alt. _0 was 33- 50' 50'/, index cor. + loi I'" height of eye 18 feet. Time by Chron. 71i. 40m. 59s., which was tast 32m. 02s. Oct. 18th, and on Nov. 7th fast 29m. 50s. f o • Mean Time at Greenwich. Required the Longitude at time of observation. ' Int. from Nov. 7th h. m. to 25th is Time at Ship 7 5 18-3 fast 32 02 Oct. 18th ^^ ^ 6-6 « 29 50 Nov. 7th 19 50 1098 "2X2 Long. + 11 31 56 1098 60 31 21 56 6)12,0.78 1st Inter. 20)132(6-6 losin... 24 j.^O „ 2 1 ace. rate losinjj: App.T.25th, 7 21 56 120 120 fift HAND nyOK AND SKLF-TKAf'HKR. Tiiiir l)v (^ii-., 7 40 yj Loii^^ 172^ 59/ 7 11 09 (;,0)()9,1 5H Aoc. riitf, I '2 1 11 31 5(i M.T. (i.^othw in 10 ,1. m. ... 21 00 00 Dec'l. 25tli, 20 53 3') 2S7r. liicr., f 3 23 H. Dit. 2777 31 13 11 (I. 111. s. Cur. Decl., = 20 oH 58 2)5().)3 ()l,s. Alt., 33 50 50 90 00 00 Cur. -f 1 15 '^^'^^^ P. Dist. =:= (19 03 02 (J. 1). X 7-2 33 52 05 Dip — 4 4 K(in. 12 4014 5(152 Dee.,— 4 87 19782 33 48 01 ('or. 18, — 118 Cur. K(]u. =r 12 45 00)20,3.472 33 4(143 0-ll(;809 3-23 Semi-l)i., + K5 15 ()-029704 _. 9-498444 H. 1>. •78(; (\n: Alt. = 34 02 58 9-785274 G. D. x ()-2 Lat., 40 10 00 (U) 03 02 9-430231 1570 . ._ 47l() Sum 2)143 K) 00 Half-sum, 71 38 00 Hour An-;le, 25tli, 4 10 05 Alt., — 34 02 58 24 Rem'd, 37 35 02 App. T. G., 24t,h, 19 49 55 E' lf;7-40 J2 '' 35 2 4 ^ 4 nth, 20 3(T00 2 58 6,0);i7o-40 U 10 40 GO '___' , H H)40 App. date, nth, 9 19 20 1st Int. 21 )178(8-o losing. IfiH X 30-4 2nd int. fwuri Chrono. 9 58 50 1 2th Jan. to Orig. rate, — 35 2 4 108 340 lllli Feb. 105 2550 9 2347 6 Ace. rate, + 418 4 3 (;)25^8/40 G. M. T., = 9 28 0(i TYh]^. r. losmg. Alt., 10 02 50 Decl. 11th, 14 07 52 4914 ^^'or., — 2^ 7 48 41,72 10 00 00 Cor. Decl., ^ 14 00 04 2)988^ Dip, — 4 11 ^ 4943 9 55 49 0-201128 (i, D. x 9-47 Cor.,— 5 9 0'013098 '~i77<71n 9-112342 •'^"^f^^^l SemiDi i- ^a1^ «-i^79283 '^2 t^erai-Di., f lb 14 44487 /^/^,. Au TTrTwTTT 9"305851 , Coi. Alt. =r 10 Ob 54 . fi 0)4fK 8, 1021 Lat., 51 00 00 ___ -i-' P. D., 104 00 04 17 (3j ^^^'- '^"^^ Sum, 2)165 06 58 Half sum, 82 33 29 Ait., — 10 06 54 72 26 35 Equa. 14m. 30s'. No. Cov. 9 70 HANI) BOOK AND SELF-TEACHER. H(Mjr Angle ;'2th, 3 33 48 24 nth, E(iuatian, = 20 26 12 4- 14 30 M. T. Ship nth, M. T. G. nth, = 20 40 42 = 9 28 G 11 12 3(1 60 4)672 36 Long. = 168 9 E, TO FIND THE DEVIATION OF THE COMPASS BY AN AZIMUTH. Azimuth is the angle at the Zenith between the meridian ot the observer and the circle of altitude passing through the " The true Azimuth is found by adding together the Secant of the true Altitude, the Secant of the Latitude, the Co-Sme ot tlie lialf-fium and the Co-Sine of the remainder. The remam- der is found by subtracting the half-sum from the Polar distance, or if the half-sum is greater than the Polar distance, subtract tlie Polar distance from the half-sum. In either case it will be the remainder. ^ wir -n Half the sum of these four Logs., found in Table XXV., will give the Sine of half the true Azimuth, which, multiplied by 2, will be the true Azimuth. TO NAME THE TRUE AZIMUTH. If the Latitude is S., name the Azimuth N., and if the Lat- itude is N., name it S., (always opposite to the ship's Latitude; towards the E. in the morning, and towards the W. in the even- ing. That is, if the observation was taken in the morning, and DEVIATION OF COMPASS Di' AN AZIMUTH. 71 the Latitude of tlie ship S., the Azimuth would be N. and ?'., but iu the evening it wouhi be N. and W. The ditference between the True Azimuth and the IVTtignetic u tlie Error, — to be named E. if the True Azimuth is to the right of the Magnetic, but if to the left it is named W. Hotli Azimuths muat be named from the same point ; one cannot be N, and the otlier S., — if so, subtract either one from 180^ and it will cliange the name to the same as tlie other. Tlie Magnetic Azimuth is the bearing of the 8un from tli<' •ship by an Azimuth compass, fitted with sight vane and reflector, but as few of our merchant ships have them on board, a descrip- tion of them here would be useless. A substitute may be simply found. Thus : — place a small piece of putty or dough on the centre of the ship's compass, stick into it any small rod, a piece of cane, or a straight stem from a broom, so as it will stand perpendicular, and the reHection on the compass will l)e the op- posite bearings of the Sun, or Magnetic Azimuth, which will be accurate enough for any practical purpose. I have often prac- ticed the latter method, and found the error, ami had very little difficulty even when the motion of the ship was considerable, 'ffie Deviation is found the same as in an Amplitude, by placing imder the Error the Variation (by changing the name), and it same name their sum will be the Deviation, but if of contrary names their difference will be the Deviation, named after the greater. The Polar Distance is found as given already, — that is^ if Lat. and Decl. are same name take the Difif., but if contrary names, the sum. If the ship's latitude is 0', name the true Azi- muth opposite to the declination. If one Azimuth be named N. and E., and the other N. and W., their sum will be the error. It must be remembered that the Deviation found is not tlu Deviation to be allowed on all courses steered, — it is only the Dev. for the point she is on at the time. EXAMPLES. Being P. M. at ship, the true Alt. was SO'' 20 ^ Decl. 10« 20 / N., and Lat. 20«' 30' S. Required the true Azimuth. •y 2 HAND BOOK AND SET-F-TEACHEH. .1. 111. ''• "1- P. Dist., 100 20 Decl. 10 20 N. Alt., 50 20 Secant, 0-194961 90 00 L'dt., 20 30 Secant, 0-028412 P. Dist., 100 20 2)171 10 Half Sum, — 85 35 Co-aine, 8-886542 100 20 Rem., 14 45 Co-sine, 9-985447 2)19-095362 20 40 Sine, =- 9-547681 2 T. A/. N., 41 20 W. fn tliis question it being P. M. at sliip, and the Lat. S., the true Azimuth is named N. opposite to the liat. and W. as it was r. M. N. B. There is no necessity to correct the Logs for ( '^) se- conds, as tlie nearest minute is sufficient. When the second* arp imder 30 reject them, bwt 30 or over take one minute. Peing P. M. at ship, the true Alt. was 20" 40', Decl. 23" 10/, S., Lat" was oO*-" 50 ^ S. Kequired the true Azimuth. rl. ni. rt. 111. p. List., 66 50 Decl. 23 10 S. Alt., 20 40 Secant, 0-028887 90 00 Lut., 50 50 Secnnt, 0-199573 P. Dis. (]i) 50 2)138 ?0 Half sum, 69 10 Co-sine, 9-551024 ei^ 50 Keni., 2 20 Co-sine, 9-999640 2)19-777124 77 5 Sine,' = 9-888562 2 T. Az. N. 154 10 E. DEVIATION i)F COMPASS BY AN AZIMVTH. 7.V In this Example the Lat. and Decl. are same name, the Dit'l". is Polar Dist., and the Half Sum exceeds it, so the Polar Dist. had to be sulitracted from tlie Half Sum t'> get a remainder. THE TRUE AND MACJNETKJ AZIMUTH GIVEN TO FINJ^TIIK ERROR, Suppose True Azimuth was N. 41 " 20' W., and the Maj;- netic Azim .V. 30^ 20' W. Reciuired the Error. True Azimutli N., 4\ 20 W. Mag. " N., 30 20 W. Error, = U 00 In (lie ahove example the True and Mag. Azimutlis ;.ie In-'I; reckoned from th.e same point, N., and tlieir Dift'. is tlie Eiiur, and is named W., because, by looking from tlie centre of th* comr^ass in the direction of both Azimuths, it vvill be stcu th;.t the True Azimuth is more to the W. than the Magnetic Azi- muth, and also to the left of it, and is named W. Suppose the True Azimuth was N. 154'^ 10' E., and the Magnetic S. 40^ 30' E. Required the Error. (1. in True, N., 154 10 E. 180 00 S., 24 50 E. Mag. Az. S., 40 30 E. p:rror, 15 40 E. In this case the True and Magnetic Azimuths are of con- trary names ; the True had to be sul)tracted from 180'-, a\ hid changed its name from N. to S., the same as Magnetic, and tlie difference is the error. Suppose the true Azimutli was S. 5*^ 40' W., and ^Magnetic was S. 10*^ 50' E. Required the Error. True Azimuth, S., 5 40 W. Mag, " S., 10 50 E. Error, 16 30 E. In this case one Azimuth was S- and W., and the other S. and E. Both added gives the Error. TO FIND THE DEVIATION BY AN AlilMUTH. 1876, May 30th, at 3° 30' 40", P. M., in Lat. 4r' 5i!<, ^^, 74 HAND BOOK AND SELF-TEACHER. l.oiij,^ 95*^ 40/ W., Sun's Mag. Azimuth N., 120« 30' W., Alt _o. 45^ 40' 50^', Index Cor. 4- 2' lb'', height of eye 12 feet, Hiui the variation by Cliart was 12*^ 20' E. Required the Dfe- viation. h. m. s. d. m. h. Ship's Time, 3 30 40 Decl. 20th, - 20 06 53 Long. + 6 22 40 -f 5 5 App G. Date 20tb,=: 9 53 20 Cor. Decl., - 20 11 57 d. m. 8. ()b,'d Alt., 45 40 50 90 00 00 ind. Cor., +2 15 P. Dist., 69 48 03 Alt., 45 54 48 Dip., — 45 43 05 3 19 45 39 46 48 45 38 58 15 50 Lat. 41 58 2)157 40 51 Cor. table 18, — 48 H. Sum, 78 50 25 — 69 48 3 Semi-Dia. + 15 50 Rem'r, 9 2 22 True Alt., 45 54 48 37 27 H. Diff. 3080 2 G. Date, x 99 True Az. S., 74 54 W. 27720 180 00 27720 " " N., 105 6 W. 6 0)30.4,9 20 Mag. '' N., 120 30 W. 5,5 Error, 1 5 24 E. Variation, 12 20 W. c. name. co-secant,. 0-1 57706 co-secant, 0-12869i) Deviation, 3 4 E, after greatest. co-sine, 9-287048 co-sine, 9*994580 sum, 2)1 9-568033 sine, = 9-784016 The Declination- and Lat. being of same name, their Diff. is the polar dist. The True Azimuth id named S. and W., and DEVIATION OF a)MPASS BY AN AZIMUTH. 7o Magnetic N. and W. The True is taken from 180', whch -changes the name N,, and same as Magnetic, tlieir Ditf. is then the Error, named E. As True is to the right of Magnetic, then change name of Variation from E. to W., and as the Error anci Variation are of contrary names, their Dilf. is the Deviation T)aro.ed after the greatest. AZIMUTH. 1876, Dec. 26th, at 8h. 10m. 20s. A. M., Lat. 16^ 02 ^N., Long. 129^ 30/ W., Mag. Azimuth S. 70" 19 ' E., ObsVl Alt. 0_ 20° 15/, Index cor. + 2^5'', height of eve 16 feet, :\m\ ^'ariation by Chart was H'^ 59 ' E. Required the Deviation. I'- 'u- s d. m. s. 12 00 00 Obs'dAlt., 20 15 00 Ship's Time, 8 10 30 Index Cor. + 2 05 20 1 7 05 Long. 8 38 Dip. — 3 50 20 13T5 Cor. Alt. 18,-2 26 20 10 20 8 38 *ZH 48 20 24 Ap. Gr. Date 26th, — 4 48 20 20 10 49 Semi Dia. 4- 16 18 P. Dist, 113 20 58 Alt. 20 27 7 T. Alt. 20 27 07 Lat. 16 2 Secant, 0-028271 Sum, 2)149 50 05 Secant, 0-017231 Co-sine, 9-415347 H. Sum, — 74 55 02 Co-sine, 9-89:3946 P. Dist., 113 20 58 Sum, 2)9-354795 Sine, = 9-677397 Kem., ~ 38 25 5(y Half Az., 28 24 2 Lon,?'. 1 29 30 4 True Az. S., 56 48 E. _ Mag. Az. S., 70 19 E. 6,0)51,8 00 Error, 13 31 E. 838 00 Var., 6 59 W. change name. Devi., 6 32 E, after the greatest. 7i) HAND nOOK AND SELF-TEACHER. Decl. 2fitli, 23 2127 II. Diff., 395 • — 29 G. D., X 4-8 Cor. Dec, 23 20 58 4760 90 00 00 2380 P. Dist., 113 20 58 28^560 In iliis (jimstion the declination heing S., and Lat. N., their .Sum is tlie P. Dist. The Sum of Logs gave the Sine of lialf rhe Tiiie Azimuth, which, multiplied by 2, gives True Azimuth reckoned from opposite I^nt. S. towards tlie E., it heing A. M. Now, as the Magnetic Azimntli is reckcmed from S., they are (tf tlio same name, and the Diff. is the Error, named E., as tiie 'i'lue Azinuith is to tlie right of the Magnetic, tlien the Varia- tion given on tlie Cliart is 6^ 59 ^ E. -is changed to W., and as they nn; of contrary names their Diff«n'ence is the Deviation named after the greatest. AZIMUTH. 1870. March 1 9th, at 9h. 3m. A. M., in Lat. 42^ 59/ N., Long. 91" W., Sun's Magnetic Azimuth S. 45^01' E., Alt. _0_ 32" 40', height of eye 18, and Var. I)y Chart 25« 29' W. H("|uired Deviation. Ii. 111. (i. in. s. Time at Ship, 9 5 Decl. 19tli, 17 57 Long. 91 12 — 3 8 4 18th, 21 5 Cor. Decl. -0 14 49 6)36,4 Long. +64 t 900000 6-4 27 9 P. Dist. 90 14 49 24 Ap. (J. Date 19th, rr 3 9 DEVIATION OF COMPASS BY AN AZIMUTH. 77 H. Difr. 59 27 3 Obs. Alt.. 32 40 00 Dip., — 4 4 9' =r 'fl, 177 81 9 88 32 35 56 Cor. Alt. 18th, - 1 21 aO)18/7/r)9 32 34 35 3-8 Seini-Diam., + 16 5 0-075672 True Alt., 32 50 40 =r 0-135755 3-iit., 42 49 = 9-083332 P. Dist. 90 14 49 9-996546 2)165 54 29 2)19-291305 H. Sum, 82 57 14 9-645652 Hem., 7 17 35 Sine, S,, 26 16 E. 2 True Az. S., 52 32 E. Ma^r. Az. S., 45 1 E. Error, 7 31 W. Var., 25 59 E. change name. Deviation, 18 28 E. 1876. Feb. 26th, at 2h. 30ra. P. M., in Lat. 4" 50 ' N., Lou-. 166^ 50^ E., Magnetic Azimuth N. 116'^ 34/ W., Obs. Alt. _o^ 60^ 36^ 50'/, height of eye 19 feet. Required the Devialioi), Variation to be 7^' 15 / E. Mnp a Tmie, 2 50 Obs. Alt., (>() 36 50 24 Dip., 4 11 25th, 26 50 60 32 39 11 7 20 Cor. 1 8, 28 App. G. Date 25th, 15 42 40 60 32 11 Semi-Dia., + 16 11 True Alt., := 60 48 22 10 HAND ROOK AND SELF-TEACHER. }». Dist., 98 58 26 Alt., 60 48 22 Lat., 4 50 =z 0-311705 - 0-001547 = 9-127060 Sum, 2)164 36 48 = 9-981361 Long., 166 50 4 6,0)667 20 H. Sum, — 82 18 24 P.Dist., 98 58 26 -2)19-421673 11 7 20 Kern., 16 40 2 Sine,= 9-710836 d. s. (1. s. m. HalfAz., 30 55 Deel. 25th, 9 13 00 2 — 14 34 True Az. S., 61 50 W. Cor. DecL, 8 58 26 180 90 00 00 N,, 118 low. P.Dist Mag. Az. N., 116 34 W. Error, 1 36 W. Var., 7 15 W. change name. Dev., 8 51 W. t., H. G. 98 58 26 Diff., Date, X 55 67 15 7 ne. 38969 27835 5567 6^0)8/7,4,019 14 34 FINDING THE LATITUDE BY REDUCTION TO THE MERIDIAN. When the Sun's Altitude cannot be ol)taiued at noon to get the Latitude, an Altitude may be taken about 30 minutes either before or after noon, (and by two corrections, one for the cor- rected declination, and another for the corrected altitude, found in Towson's Taljles,) the Latitude thus found will not differ materially from that at noon, and will answer for all practical purposes. Rule. — The first thing to be done is, find the time from noon or (hour angle,) put down the time shown by watch (if a. m.,) add 12 hours, add or subtract what she is fiist or slow, as the case may be. Then if tlie ship changed her longitude since the watch was regulated, (which is generally done about FLNDINCJ LAT. 15Y REDUCTION TO MERIDIAN. 79 Hli. A. M.,) turn the lunnritude into time, and if it is E. add, but W. subtract, and the result is tlie hour an;,^le. But if it is A. M, it must he subtracted from 24 hours, for tlie lutur anole found will be from the preceding noon, and the hour angle"re(|uired must 1)6 from the nearest noon. If p. m. when the observation was taken, the time past noon will be the hour angle. The next thing is, the Greenwich date has to be found. To correct the declination to the apparent time shown by watch, add W. longitude, and subtract E. ; if A. M., subtract from the hours, minutes and seconds tliat are taken from 24 to find the hour angle, hut if 1'. M., to the hour angle itself ; and it will gi\e the Greenwich date. Note. -The difference of long, that the ^hip makes is to br applied the opposite to find the hour angle to the Longitude ot the ship to find a Greenwich date. TO FIND THE HOUR AXirLE. EXAMPLES. Jan. 2(), P. w., at Oh. 30m. 40s. by watch, which was found t«. be fast 10m. 22s. on app. time, the diff. of Long, made to the E. ,31 ''•4. Required the Hour Angle at the time of observation Time by watch, 6 .30 40 DifF. Long. 31-4 Fast, ' — 10 22 '^ 4 20 is 6)12, 5, () Diff. Long. E., 4- 2 6 — __ 2-H nearlv. Hour Angle, — 22 24 In this Example the watch showed Oh, 30m. 40s., and wae fast 10m. 22s., which had to be subtracted, and since the watch was regulated she changed her time 2m. 6s., which had to be added also, as the watch was losing on time goinc to the E.. and the result was the Hour Angle. Feb. 27th, P. M., at 2h. 20m. 30s. by watch, which was found to be fast 2h. 21m. 10s. on app. time, the diff. of Long, made to the E. since the watch was regulated was 38 ''•6. h. m. s. • Time by watch, 2 20 30 L'iff; Long., 38-6 Fast, — 2 21 10 4 Feb. 26th, 23 59 20 6)15 4.-4 -b 2 .34 1-^ 2/. 34 -4 Hour Angle, 00 1 54 80 HAND BOOK AND SELF-TEACHER. Ill this case the vvatcli was faster than the time shown by liei past noon ; then a subtraction could not he made without bor- rowing 24 hours, and that put the time back to the 26tli, bii< as tlie ship was making Easting, that time had to be added, and exceeded 24 houia by Im. o4s., which was the Hour Angle past noon. jMarch 30th, P. M., at Oh, 20m. 40s. by watch, which was sk)\v 10m. 20s., and diff. Long, made to the W. 15 ''4. Required Hour Angle. Time by watch, 20 40 Diff. Long 15 '-4 -f- 10 20 4 3100 6)6/1,6 1 2 1*2 nearly. Hour Angle, 29 58 April 10th, A. M., at llh. 20m. 40s. by watch, whicli was found to })e slow 10m, 20s. on app. time, the diif. Long, made to tlie W. since tlie watch was regulated was 14m, 8s. Required the Hour Angle. li. ni. s. Time by watch, 11 20 40 Diff. Long., 14 8 4- 12 4 April 9th, ISlow, + , 23 20 40 10 20 23 31 00 5& 9th, 23 30 01 24 59/2 Hour Angle, 29 59 It was A. M. when the observation was taken, and when all tlie corrections were applied it was 23h. 30m. Is. from apparent noon on the 9th, but as the Hour Angle is re(]^uired for the nearest noon, that time had to be taken from 24 hours, and tlie result, 29m. 59s., was the Hour Angle. ]May 20th, A. M., watch showed 4h. 50m. 20s., which wae found to be 5h. 10m. 10s. fast on app. time, and diff. Long, made to the W. since the watch was regulated was 19 '*8, Re- quired the Hour Angle from nearest noon. FINDING LAT. BY UEDUCTTON TO MEllIDIAN. Si' h. Ui. s Time by watch, 4 50 20 Diff. Lon^^, 19 ^-H Fust, -^ 5 10 10 4 23 40 10 (I o;7 9 2 — 1 19 _ 1 1!> 33 38 51 24 Hour An.!4le, ~ 21 09 In this example it wa? A. M. at ship, ;iiifl the vvatcli showed 41i. 50m. 208., whicli could not he in tlie forenoon, and if 12 iiours were added would }»e = 161i. 50m. 20s., and llie 5h. 10m. 10s. slie was fast subtracted, \\nuld (,ave 1 Ih. 40m, 10s. tlie pre- vious day, wlien no observation could lie taken. To find the correct Hour Angle 24 hours had to be added to what tlie watcli sliowed, and what slie wns fiiwt subtracted, and ditf. of Long, also, and the result sul)tracted from 21 hours gave Hour Angle. 187n. May 20th, a. m., Long. lon^4n' W., Obs. Alt. _0 N. was 31 '^ 50 ' 40^', Index Cov. + 52^/, lieight of eye 20 feet, time by watch -th. 50m. 20s., whicli was found to be fast 5h. 10m. 10s. on app. time at ship, diff. Long, made W. since the watch was regulated was 19 ''8. Required the Lat. h. in. 8 ,1 ni Time by watch, 4 50 20 DifT. Long, \^)^'H Long. 10(5 40 Fast, — 5 10 10 ' 4 4 23 40 10 - 1 19 23 38 51 24 00 00 21 09 23 38 51 7 6 40 30 45 31 24 6)7/9/2 6/0)42/6 40 Change of time, 1 19 7 6 4(^ App. T. Ship 19,--rr 23 38 51 ^ ,^ Sim"s Peel. 20th, 20 06 50 Cor. -f 3 25 H. Angle, Cor. Decl. = 20 10 15 App. T. Ship, 23 38 51 1st August, -}- 4 42 Long Aug. Dec!., 20 14 57 U, Date 20th, 6 45 3i H'2 HAND IK)OK AND SELF-TEACHER- 01)s. Alt., 31 oO 40 N. 3()>^() ('<»!■., + 52 H. DilT., 2994 31 .31 32 2)(JU74 Dip., ~ 4 17 Mid. Time, = 3037 31 47 15 Ct. Date, -f (wH Kef. 18th, — 1 25 1S222 31 45 50 212.'»9 .Semi-l)i;i., -I 15 50 18222 True Ah., 32 0140 6/0)20/5/2992 Au«r. 2iul, + 8 9 3 2.5 Aug. Alt., 32 09 49 90 00 00 Hour Angle and Decl. gave In- dex (49). Zen. Dist., 57 50 1 1 S. m ^ Decl, 20 14 57 N. Index for 48, = 7 56 " " 52, = 8 36 Dat., - 37 35 14 S. 3)40 + 13 7 56 Cor. Aug., 8 9 Tliis is tlie same example as tlie last, and gives same Hour Angle. But all the corrections are employed here and the Lat. found. It was A. M. at ship, and the app. time found was from noon of the previous day, which had to be subtracted from 24h., and gave tlie Hour Angle from nearest noon. In taking H. Angle, 21h. 09m., (from Towson's Tables,) agreeing with Decl., gives Index No. (49), which could not be found under the Alt., the nearest two, 48 and 52 had to be used, their difference taken, and, divided by 3, gave a correction to be added to the next less augmentation, 7*56, and gave 8'' 9//, correct aug- tnentation for Alt. Note. — Even by taking the nearest Index to (49) = 48, and taking the direct cor., 7' 56'', it would make only a difference of 13''', which would make no material error in the Lat. It should l)e remeniiiered that in an A. M. observation it must Ic 23 liours ;.pp. time, and p. m. no hours. FL\1)LN(J LAT. HY HEDLCTi(JN TU MKIUDIAN. 83 EXAMPLES. 1«76. .J;in. 2(itli, i\ M., Long. 52" 20/ E., ()})s Alt O N was 55^ 50 / 40'/, Index cor. -- 2 '9'/, liei^dit, c.f Kye itteet] time of watdi 30m. 40s., which was t'ound to be fast 10' 22' ' on app. time at ship, ditf. Long, made to the E. since tlie wiit'ch was reguhited was 3r-4. Keipiired the Lat. li. m. s. I Time by watcli, 00 30 40 DitT. Long. 31 /-I LonLr. 52 20 Fast, 10 22 00 20 18 6/0)12/5.6 6,0)20/9 20 (Change of time, + 26 Hour Angle, 00 22 24 Long., — 3 29 20 Cor. 2 6 nearly. 3 29 20 Decl. 25th, 19 2 52 12 58 G. Date 23rd, = 20 53 04 Cor. Decl., = 18 49 54 <1. rn. 8. ''^"^- l«ti -t 6 Obs. Alt., 55 50 40 Index Cor., — 2 9 Aug. Decl., 18 55 00 55 48 31 I>ip-, — 4 11 H. Diff., Kef. 18, 55 48 31 4 11 55 44 20 49 55 43 32 15 49 55 59 20 10 46 56 10 06 90 00 00 33 49 54 18 55 3679 3765 2)7444 Mid. Time, 3722 G. Date, 20-9 hemi-Dia., -f 3349.S True Alt., 55 59 20 74440 Aug. 2nd, -f AuiT. Alt 6/0)77/7/^90 1258 nearly. Zen. Dist., 33 49 54 S. Hour Angle and Decl gave Decl., +18 55 S. Index (55). Corresponding Cor. for Alt. I-at., 52 44 54 S. = 10' 46/ In this example, after the correction being applied to the .v-atch, and the change of time made E., it gave the Hour Angle ; it being P. M. at sliip, and the diff. of ship's Long, sub- tracted because E., gave Greenwich date. With the Hour S4 HAND BOOK AND SELF-TEACHER. Angle 22' 24 '\ and the cor. decl. gave first Augmentation for decl. 5' ^" and corresponding No. (55) under the True Alt. gave second Augmentation for Alt. 10' iG''. 1876. April 9th, A. M., in Long. 30° 10^ W., obs. Alt. _0 S., was 36^ 59' 50", Index cor. — 1' 4", height of eye 12 feet, time of watch Ih. 02m., which was found to be fast Ih. 21m. 208. on app. time, and diff. Long, made to the E. was 21 '-2. Required the Lat. by reduction to the Meridian. h. m. M. d. rn. Time by watch, 1 2 00 Lif. Lon. E., 2r-2 S. Lon. 53 10 W. Fast, 1 21 10 4 4 33 40 50 8/4/8 6)21/230 Chg. of time, + 1 25 1 /25 nearly. 3 32 40 Ap. time 8th, 23 42 15 Decl. 9th, 7 48 54 24 Cor., + 3 Hour Angle, 17 45 Cor. Decl., 7 51 54 Aug., + I 24 App. time, 23 42 15 + 3 32 40 Aug. Decl., 7 53 78 H. Diff., 55 52 G. Date 9th, 3 14 55 55 19 Obs. Alt., 36 ^^ 50 Cor., — 1 4 2)110 71 36 58 46 Mid. Diff., 55 35 Dip., — 3 19 G. Date, 3 23 36 55 27 27675 Ref. 18, — 19 11070 .36 54 18 16605 Semi-Dia., -f- 16 6/0)17/9.8875 True Alt., Aug., + 37 10 18 7 35 Aug. Alt., = 37 17 53 90 00 00 Zen. Dist., 52 42 07 N. 7 53 18 N. Lat., 8s 60 35 25 N. 2/59=3'nearl.y Decl. and Hour Angle gives Aug. 1st 1' 24" and Index (38). Index and T. Alt. gives Aug. 2nd 7' 35". FINDING LAT. BY REDUCTION TO MKRLDIAN. 85 The Index 38 could not be had under tlie Alt., but 3(1 ;md 40, so both were added and divided by us and uiven Aua. '^\uL 1876. June ICth, A. M., Long. 24^ 50 ^ E., obs. Alt. O X- was 33^ 10' 15/', Index Cor. -2' 10^/, height .>f eve 1 7 feet» time by watch Oh. 59m. 58s., which was found to 'l,e f:,>t Ih. 18m. 20s. on app. time, diff. Long, made to tl.e E. sin..e the watch was regulated was 13 '-7 Re({uired the Liititu(!e. h. ni. H. ,1 ,1, ^ Time by watch, 59 58 Obs, Alt.. 33 10 15 Fast, — 1 18 20 Cor. ~ 2 10 23 41 38 33 08 ol DifT. Long. + 55 Dip., — .3 57 App. T. ship, 23 42 33 33 04 08 24 Ref. 1th, — 1 20 Hour Angle, = 17 27 33 02 48 Semi-Dia., 4- 15 47 App. T. ship, 23 42 23 Long, of ship, - 1 39 20 Trxe Alf., ?,:] 18 35 Aug., -+- 5 33 G. Date 15th, 22 03 13 Cor. Dec, 23 32 57 Aug., + 3 33 Aug. Alt., 33 24 08 Cor. Dec, 23 32 57 jjO 00 00 Zen. Dist., 55 35 52 S. Aug. Decl., 23 26 30 Aug. Decl., 23 26 30 N. 5 79 Lat., 33 09 22 S. Half Diff., 4 76 Decl. 15th, 23 20 58. Diff. Lon;;. 13 7 2)105 5 1 59' 4 Mid Time, 5 27 Cor. Decl., 23 22 57 54 8 G. Date, + 22 5 ' 2635 Decl. and H. A. = Aug. 1st, 3^ 33 '/ 1054 Index(32)& Alt = Aug.2nd, 5 ^8 ;6/0)lL8/585 Cor. -}- 1-59 U 86 HAND BOOK AND SELF-TEACHER. TO FIND THE LATITUDE BY A FIXED STAR. Tliere is very little difference between finding the Lat. by a Meiedian Alt. of the Sun and finding it by a fixed Star. In fact it is more easily found by the stars ; the dip and refraction is found the same as for the sun (semi-diiisieter and parallax rejected) and the declination requires no correction. Rule. — Correct the Alt. for dip and refraction, then find the star in the Nautical Almanac, page 297 @ 299, and note the right ascension (this is an index), then find that right ascension from page 236 @ 237, and in the next column to the right will be found the declination with the hours and minutes at the top and seconds down the col. There cannot be a mistake made as no other star will have the same right ascension. EXAMPLES. 1876. Jan. 11th. The obs. Alt. of the Star a Leonis (Reg- ulus) was 50^ 40' 30'/ N., Index cor. — 1 ' 30/', height of eye 22 feet. Required the Latitude. m. 8. Obs. Alt. Index Cor. 50 40 30 N. — 1 30 Dip, - 50 39 00 4 30 Ref., 50 34 30 47 True Alt., 50 33 43 90 00 00 DecL, 39 26 17 S. 12 34 19 N. Lat., 16 51 58 S. (Regulus) was found in page 298, N. A., and abreast stood right as- oension, 10k. Im., which was taken for an Index, and found at page 345 (Fixed Stars), marked R. A., and over it (Regulus). the Star required, then, by looking down the extreme left hand col., marked at top (month and day), and abreast of 11th day, and under col. Decl. will be the Decl. to be added, or subtracted, ac- cording to the name of the Zenith dist. 1876. Fe)). 20th. Obs. Alt. of the Star a Argus (Canopus) S. was 59° 20/ 30//, heig '. of eye 14 feet. Required the Lat. TO FIND DEVIATION. 87 d. m. !>. Obs. Alt. 59 20 30 S. Dip., — 3 36 59 16 54 Ref., — 30 59 16 24 90 00 00 Z. Dist., 30 43 36 N. Dec, 52 37 51 S. Lat, 21 54 15 S. TO FIND THE DEVIATION OR LOCAL ATTRAC- .TION OF THE COMPASS. Deviation or local attraction, so caused bv the iron used in the construction of the ship, also the cargo she takes on board, par- ticularly iron. The Deviation so caused can be found by swing- ing the vessel to at least eight points of the compass, and taking the bearing of any conspicuous distant object, and note each bearing when the ship's head in at each point, and if they are all from the same point of the compass, or have like names, add all together and divide by 8 and the result will be the correct magnetic bearing. But if some of the bearings are from the N. and others from the S., substract the less from 180 and they will have like names. But if some are named N. and E. and others N. and W. subtract the least from the greater, and divide by 8. TO NAME THE DEVIATION. If the correct magnetic bearings thus found falls to the mght of compass bearings, it will be E., but if to the left, W. For instance, — if correct bearing of distant object was N. 32*30^ W., and compass bearing N. 42» 30 / W. — 42° 30/ = 10« the De- viation is E., this time falling to the right. 88 HAND BOOK AND SELF-TEACHER. 'J'lie follo\vin;j; form is given at the Examination Board, and the Candidate has to fill the Deviation column : — Sliip's H<;id. Bearinijf of Dist. ( )l)Ject. N. 41 20 W, N. 57 30 W. N. G3 low. N. 59 40 W. N. 44 30 W. N. 23 20 W. N. 18 00 W. N. 23 00 W. Deviation Required. The Deviation is found as follows : N. E, K., S. E., S., s. w., ^v., N. W., • Sliip's head at N. Cor. Mag. hear'g N. 41 19 W Compass bear'g N. 41 20 W Deviation, 1 E Ship's head at N. E. Cor. Mag. bear'g N. 41 19 W Compass bear'g N. 57 30 W Sliip's Head. Bearing of Dist. 01 .i eel. Deviation Required. Deviation, 16 HE Ship's head at E. Cor. Mag. bear'g N. 41 19 W Compass bear'g N. 63 10 W N. 41 20 W. xr ^', nix VI- 01 E. Iti 11 E. 21 51 E. 18 21 E. 3 11 E. 1 7 59 W. 23 19 W. 17 19 W. i> . 111., J.-\ , U 1 ti\J T» . E., N. fiSlOW. S. E., N. 59 40 W. S., N. 44 30W.1 S. W., N. 23 20 \V.\ \y., N. Is no \v : Deviation, 21 51 E Ship's head at S. E. Cor. Mag. bear'g X. 41 19 W Compass bear'g N. 59 40 W N. \V., NT. 23 00 W.| Deviation, 18 21 E 8)330 30 Cor.M.b-s.41 19 Ship's head at S. W. Cor. Mag. bear g N. 4 1 1 9 W Compass bear'g N. 23 20 W Ship's head at S. Cor. Mag bear'g N. 41 19 W Compa.-'s bear'g N. 44 30 W Deviation, 3 11 E Deviation, 1 7 59 W Ship's head at W. Cor. Mag. bear'g N. 41 19 W Compass bear'g N. 18 00 W Deviation, 23 19 W Ship's head at N. W. ' C ■ DAYS WORK. 91 PAPER FIRST. iMultiply 23-4 Divide 45(17 By 345 By 3456 DAY'S WORK. H. Courses. K. 4 lOtht, 4 Winds. Lee Way 15 Devia- tion. Remarkf. 1 S. 27 30 W. S 4()E 8 low Lat. left 43^ 30 ' 2 4 5 N., Long, left 66^ 3 4 6 20 W., bearing hy 4 4 5 Compass N. 30*^30' 5 N. 44 E. 5 5 S 60 E 20 12 E W., Dist 15 miles. 6 5 5 7 4 6 8 4 4 Deviation as per 9 S. 25 E. 3 3 E 10 4 W Log. 10 3 7 11 4 3 12 5 7 Variation 1 9 «* W. 1 S. 10 E. 3 6 S 85 E 13 2 W 2 3 6 3 • 4 4 4 4 4 Current set fcor. 5 S. 1 w. 5 8 S 65 E 40W Mag.)N. 60'E. 12 6 5 4 miles during the 7 6 6 24 hours. 8 6 2 9 S. 45 W. 6 5 S 65 E 15 W 10 6 5 11- 7 5 12 7 5 1876. Jan. 1st, in Long. 63"" 20' W., obs. Alt. 0_ S., was 33* 20/30'', Index Cor. — 2' 10'^ height of eye 12 feeb. Required the Lat. In Lat. 44" 30 /' N., Departure 40 miles. Required diff'. Jiong. Lat. A. 43" 80' N. Long. A. 66© 40/ W. Lat B. 47" 20' N. Long. B. 67° 50 / W. TIDES. 1873, Jan. 2nd, find the time of high water at Bristol and St. John, N. B., Long. 66" W. 92 HAND HOOK AND SELF-TEACHER. AMPLITUDE. 187n, Jiin. 3rd. at 71i. 2()in. A. M., in Lat. 44*^ 30 ^ N., Loiij^^ m» 20 / W., Sun's Ma'4. Amp. E. 29" 30 / S., var. bj Chart 19^ W. Rei|uirft(l Deviation. CITRONOMETER. 1870, Jan. 4tli, at 31i. 40m. i>. M., Lat. 44* 10^ N., Lonn:. hy acct. 75^ 12', ()1)S. Alt. _0_ Hi" 20^ 30", Index cor. + 2' '2'\ heii^ht of eye 14 feet, time by Chr. 7h. 20' 20", and found to be fast 2m. 41s. 4t. on Dec. 4th, and on Dec. lotli fast 2m. 21s. 8t. Kefiuired the Lon;j;. AZIMUTH. 187f), Jan. oth, 7h. 50m. A. M., mean time, Lat. 48" oiV N., Lonj<. 75^ 50' W., Sun's iMa^r. Azimuth S. 57*-' 10' E., obs. Alt. ^ 8" 40' 10/', Index cor. — 1' 50", lieight of eye 16 feet, var. by chart 16* 20' W. Required Deviation. EX. MERIDIAN. 1876, Jan. 6th, p. m., Lon^r. 66© U)' W., obs. Alt. 0_ S. 23* 20 30/', Index Cor. ~ 2' 4", heij^dit of eye 14 feet, time by watch Oh. 30m. 40s., wliicli was fast on app. time 8m. lOs., diff. Long. "VV. 15''8. Required Lat. STAR. 1876, Jan. 7th, obs. Alt. of Star (Sirius) S. of ol)server was 38* 10, height of eye 20 feet. Required the Lat. DEVIATION. Construct a Napier Curve and correct the folh»wing ('ourses: — True course given to find Compass, S. 25* 30 E., and N. 25* 30 E. Ship's Bearing of Head. Dist. Object. N. N. 44 44 W N. E. N. 67 57 W E. N. 72 15 W S. E. N. 61 40 W S. N. 54 54 W s. w. N. 42 20 W w. N. 20 33 W N.W. N. 27 50 W Compass course given to find True, S. 67* 30 W., and N, 67* 30 W. Suppose you were sailing along shore, and two well known olvjects were seen bearing N. 2* 20' W., S. 2* 20' W., with the ship's head at N. 30* E., required correct Magnetic bearings. PAPER :\Iultiply 8974.7 By 49.9 bay's work. SECOND. 03 Divide U.fi By 13.34 DAY'S WORK. H. Courses. K. 7 lOihs, 6 Winds. Lee Way Devia- tion. Keinarks. 1 N. 10 W. W 4 12 E Lat. left 44^' 44' 7 6 8., Lono-. left 84^ 3 7 4 45 W., beariij^- ot" 4 6 9 land vvlien depar- N. 25 E. 5 6 N45\V 12 3 15W ture was taken S. 6 5 6 59^ W., Dis. 14 7 5 5 miles. 8 4 5 9 N. 40 E. 4 3 N20W 14 12 W Deviation 8^ V.. 10 4 3 11 4 6 12 4 5 1 N. 70 E. 3 4 N15E 20 20 W Variation 9^' K. 2 3 4 3 3 4 4 4 4 5 N. 40 W. 4 3 N18E 18 6E Current set (an-. 6 4 2 Mag.)N.40^W. 12 7 5 3 miles from the time 8 6 3 the departure was 9 N. 12W. 6 4 N45E 6 4E taken to the end of 10 6 4 the day. 11 6 4 12 7 5 MERIDIAN ALTITUDE. 1876. Feb. 8th, in Long. 120*^ 40 ' E., oIjs. Alt. 0_ X., was 49«> 10/ 20''', Index Cor. — 2^ 4'^ height of eye 12 feet. Required the Lat. PARALLEL. In Lat. 69*^ 40 / S., Departure 427 miles. Required diff. Long. MERCATOR. Lat. A. 40° 40' S. Long. A. 173^ 30 / E. Lat. B. 20«' 30 ' N. Long. B. 140" 40 ' W. 12 94 HAND BOOK AND SELF-TEACHER. TIDES. 1873, Feb. 7th, find the time of high water at Penzance and Hi-ide (Japan), Long. ISS** E. AMPLITUDE. 1876, Feb, 9th, at^h. 20m., Lat. 43'' 20 ^ N., Long. 66" 40 ' W., Sun's Mag. Amp. E. 22*^ 80/ S., var. bj Chart 17" 30' W. Required Deviation. CHRONOMETER. 1876, Feb. 2nd, at 9h. 59m. A. M., Lat. 54<=' 58 ^N., Long, by acct. 18^ E, obs. Alt. 0_ 14*^ 20 / 10 '^ Index cor. — 15^^ height of eye 15 feet, time by Chr. 9h. 12' 59", and found to be slow 50^/, on January 10th, and on January 25th fast 2^\s. 4t. Required the Long. AZIMUTH. 1876, Feb. 20th, 4h. 20m. P. M., Lat. 37° 59' N., Long. 96* 50' W., Sun's Mag. Azimuth S. 43° 10' W., obs. Alt. ^ 27° 10' 20 /% height of eye 20 feet, var. by chart 12° 40' W. Re- quired the Deviation. EX. MERIDIAN. 1876, Feb. 21st, A. M., Long. 106° 10' W., obs. Alt. ©. was 21° 50' 59 //, Index Cor. + V 2'', height of eye 21 feet, time by watch Oh. 5m. 50s., and fast 29m. 50s., diff. Long, made E. 30'-2. Required Lat. STAR. 1876, Feb. 30, obs. Alt. of Star (Aldebaran) was 29° 52' 10", Index cor. h- 4° 10 ' 7", height of eye 15 feet. Required the Lat. Construct a Napier Curve and correct the following Courses : — Correct Magnetic to find Compass, N. 30° 30/ W., S. 50° 30/E. Compass to find Correct Magnetic S. 70° 26'E.,N. 87° 50/ W. Sailing along a well known coast with ship's head at W., bearing of dis. object was Ship's Bearing of Head. Dist. Object. N. S. 40 40 W N. E. S. 20 10 W E. S. 7 20 W S. E. S. 15 30 W S. S. 41 30 W s. w. S. 66 10 W w. S. 72 40 W N. W. S. 59 10 W day's work. 95 PAPER THIRD. Multiply 333.3 Divide 6660.6 By 223.3 DAY'S WORK. By 777.77 H. 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 II 12 Courses. N. 30 W. N. 10 W. N. 15 E. N. 20 W. N. 10 W. N. K.' lOlhs. Winds.,^^^ Way 4 4 4 4 4 4 5 5 5 5 4 4 5 5 5 5 9 9 9 10 10 10 11 11 6 4 2 2 3 4 3 8 8 4 4 4 6 8 N85W N67W N48W N35 E N 15E N56E 15 10 12 Devia- tion. 15 E 6E 4 W 10 E 6 E 2 E Remarks. Lat. left 48 «> 30' S., I.ong. left 179«> 10'' E., bearing by Compass S. 37^30' W.,Dis. 12 miles. Dev. as per Log. Variation 14° E. Current set (cor. mag.) S. 30° 30' E., 27 miles during the 24 hours. iMERIDIAN ALTITUDU 1876. March 17th, in Long. 177° W., obs. Alt. o S. was 88° 50 ' 50 / /, Index cor. + 3 ' 50 ' ', height of eye 1 6 fe^t. Re- quired the Lat. PARALLEL. In Lat. 49« 40 ' N., 444 miles. Required the ditf. Long. MERCATOR. Lat. A. 2° 10/ N Long. A. 171° 10/ E. Lat. B. 15° 40 'S. Long. B. Io0°20/W. 90 HAND BOOK AND SELF-TEACHER. TIDES. 1 873. March 28tli, Find the time of high water at Wick and at Grindstone Island (Bay of Funday), Long. 65*^ \V. AMPLITUDE. 187f). Afarcli 19th, At 6h. 20m., A. M., in Lat. 46'^ 30' N., Long. ()7" 30/ \V., Sun's Mag. Amplitude E. 3« 20 / S., and variation 14® W. Required Deviation. CHRONOMETER, 1870. March 26th, at 8h. 20m., A. M., Lat 10° S., Long, hv acct. 84^ 50' \V, obs. Alt. 0_ was 30® 30' 30//, Index cor. — 30//, lieight of eye 20 feet, time by Chr. Ih. 58m. 58s., whicli was fast 2h. 2s. It. for Greenwich mean noon Jan. 6th, and on Feb. 5th fast 3h. 50s. 4t. Required the Long. AZIMUTH. • 1876. March 26th, t , 8h. 10m., A. M., in Lat. 40® 50' S., L'.ng. 150" 30/ E., the Sun's bearing by Compass S. 104® 40' 20^'' E., obs. Alt. "^ was 19® 20' 30'^ height of eye 14 feet, A'ar. 14"^ 30' E. Required Deviation. EX. MERIDIAN. 1876. March 19th, A. M., Long. 135® 30' E., obs. Alt. S. 43® 40' 20", Index Cor. — 1' 4'', height of eye 19 feet, time by watqh oh. 40m. 20s., and fast 4h. 10m. 30s., diff. of Long, made E. 3S' 4t. Required Lat. STAR. 1876. M.I roll 19th, obs. Alt. of Star (Arcturus) 30® 40' 20" b(';ivingN., Index Cor. — 3' 2", eye 21 feet. Required Lat. DEVIATION. Construct a Napier Curve and correct the following courses : — Ship's Bearing of Head. T)is. Oliject. N. S. 43 20 E. N. E. S. C^i] 30 E. E. S. 71 40E. S.E. S. 60 30 E. S. S. 53 50 E. s. w. S. 41 10 E. \\. S. 19 ,30 E. N. W. S. 2() 30 E. True course to find Compass N. 33® W., — S. 86® 40' \V. Compass course to find true N. 80® 30" E.,— N. 40® 30" E. Suppose you were sailing up the Bay of Funday and the ship's head at E,, and Par- tridge Island in one with Fort Howe, bear- ing N. 20® 30' E. Required Deviation. day's work. PAPER FOURTH. Multiply 4444.4 Divide 55555.5 97 By 333.3 By 5555.5 DAY'S WORK. H. Course. K. 4 lOths, Winds. Lee Way 20 Devi- ation. Remarks. 1 N. 70 \V. 3 N15W 2130E Lat. left 42 '^ 40' 2 4 4 N., Long, left 61" 3 4 4 5 20' W., bearing by 4 6 Compass S. 70° 30' 5 N. 30 E. 4 6 N35W 10 1020W W., dis. 12 miles. 6 5 7 7 5 5 8 4 6 . 9 10 11 iV. 40 E. 4 4 4 7 8 6 N16W 10 22 W Deviation as per Log. 12 3 8 1 N. 80 E. 2 8 N30E 29 27 W Var. 30° 30' W. 2 2 8 3 3 4 4 4 6 5 6 7 8 N. 25 E. 5 5 4 6 N30W 18 1230W Current (correct Mag.)S. 70'E., 19 5 5 6 6 miles during the 24 hours. 9 N. 20 W. 6 N75W 25 610E 10 6 11 6 5 12 - ■ 6 8 MERIDIAN ALTITUDE. ..i^'Jv Q ^T\ ^^t' ''' ^^''l^- ^^" 2^' ^^•' ^^'^ «^«- Alt. O was 33^ 22 fe., Index Cor. h- 4' 3", height of eye 12 feet Re- quired Lat. PARALLEL. In Lat. 43^ 50' N., Dep. made good was 134 miles. Required dm. Long. ^ MERCATOR. Lat. A. 20 10 N. Long. A. 160 30 W. Lat. B. 30 40 S. Long. B. 132 50 E. 98 HAND BOOK AND SELF-TEACIIER- TIDES. 1873, April 2f)th, find the time of high water at Anticosti Island, Long. 64d. W., and lianjowangie (China) Long. 14od. E. AMPLITUDE. 1876, April 10th, at 4h. 20m., A. M., in Lat. 70d. 30m. N., Long. 108d. 50ra. W., the Sun's Mag. Amp. E. 4d. 20m. N.,and var. lOd. 20m. W. Required Deviation. CHRONOMETER. 1876, April 20th, at 4h. 10m. P. M., in Lat. 2d. 20m. N., Long, by acct. I78d. E., obs. Alt. (^ 31d. 59m. 59s., Index Cor. -T- 2m. 10s., height of eye 16 feet, time by Chr. 3]i. 48m. 8s., which was fast 6m. 4s. 2t. on Nov. 10th, and on Jan. 6th fast 3m. 5s. 8t. Required the Long. AZIMUTH. 1876, April 10th, at 4h. 10m., P. M., in Lat. 52(1. 10m. N., Long. 171d. 10m. E., Sun's Mag. Azimuth S. 79d. 50m. W., obs. Alt. Q lOd. 20m., height of eye 21 feet, and variation to be lOd. 20m. E. Required Deviation. EX. MERIDIAN. 1876, April 30th, A. M., Long. o9d. 59m. W., obs. Alt. Q S. was 47d. 47m. 20s., Index Cor. + 2m. 48., height of eye 19 feet, time by watch Oh. 5()m. 59s., whicli was fast Ih. 10m. 153., dilT. Lonar. made to the E. since tlie watch was rey^ulated 19m. 5s. Required the Lat. Construct a Napier Curve, and correct the followiuij courses : True to find Compass, N. 30d. 30m. E., S. 48d. 30m. W. Compass to find True, S, 60d. 30m. W,, S. lOd. 10m. W. Suppose you were sailing along a well- known coast witli the ship's head at N. 33d, E., tlie bearing of dist. object S. 20d. 30m. E., and N. lOd. 40m, W. Re- quired true bearing. Ship's Bearing of Head. Dis. Olvject. N. S. 2 10 E N. E. S. 1 20 W E. S. 9 30 \V S.E. S. 12 10 W S. S. 1 10 W s.w. S. 12 20 E w. S. 14 00 E N.W. S. 6 30 E day's wouk. H. 1 2 3 4 5 G 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12 PAPER FIFTH. Multiply 484-897 Divide 8888-74 By 337-579 ]]y 7777.33 DAY'S WORK. Courses. N. 80 E. N. 60 E. N. 30 E. N. 1 W. N. 4E. N. 62 E. K. 6 6 6 6 3 3 3 3 3 3 3 3 8 8 9 10 5 5 4 3 3 3 3 3 3 3 3 3 9 9 2 5 9 9 4 3 4 4 6 4 9 9 4 6 2 2 2 3 Winds. Lee ; Devi- Way! ation. N20 E North. E. E. N60W N 3E 12 23 20 25 23 E 20 E 4E 2 30E 3E 19E Eemarks. Departure taken from a point of land in Lat. 40d. 40m. N., and in Long. 40d. 40m. W. Bearinj^^ by com- pass S. 40d!' 40m. W. Dist. 10 miles. Deviation, lOd. 10m. W. Variation 15 W. Current set (cor- rect magnetic), S. 88d. E.. 30 miles during the whole 24 hours. MERIDIAN ALTITUDE. 1876. May 13th, in Long. 51d. 40m. W., obs. Alt. O S. was 8 Id. 10m. 40s., Index error + 4m. 2s., height of eye~~18 feet Required the Latitude. ^ ^ 10 leet. PARALLEL. ^'^.^^l^J'r^' ^^^- ^^°^- ^"> Departure was 189 miles. Re- quired diff. Longitude. MERCATOR. Lat. A, 47 47 N. Long. A, 44 44 W. Lat. B, 57 57 N. Long. B, 64 44 W. 100 HAND BOOK AND SELF-TEAClfBR. TIDES. 1873, May 22nd. Find the time of high water at IT. D'Vew, and Batoo Barra (Sumatra), Long. 95d. E. AMPLITUDE. 1876, May 28tli, at 8h. 10m. A. M., Lat. 56d. o8m. S., Long. 41 d. 30m. E., Sun's hearing by compass E. 2d. 4ym. S., Varia- tion 28d. W. Required Deviation. CHRONOMETER. 187G, May 20th, at 3h. 10m. P. M., Lat. 19d. 50m. N., Long. by acct. 14ld. 59m. E., obs. Alt. "o^ 39d. 10m. 20s., Index cor. — 2m. 10s., height of eye 21 feet, time by Chron. Gli. 1 2m. 593., which was fast 2ii. 10s. Jan. 2nd, and on Feb. 22nd fast 3m. 20s. 4t. Required the Long, at the time of observation. AZIMUTH. 1876, May 21st, at 9h. lOna. 20s. A. M., Lat. 53d. o9m. N., Long. 12d. 30m. E., Sun's Mag. Azimuth was S. 58d. 20m. E., obs. Alt. (T) 53d. 10m. 30s., height of eye 22 feet, variation by chart 13d. 10m. W. Required the Deviation. EX. MERIDIAN. 1876, May 20th, P. M., Long. lOOd 30m. W., obs. Alt. (jf) was 41d. 12m. 10s. S., Index cor. + 2m. 4s., height of eye 17 feet, time by watch 6h. 40m. 20s., which, was fast 6h. 20m. 40s. for app. time, diff. Long, made E. 35 miles. Required Lat. STAR. 1876, May 1 8th, obs. Alt. of Star a Hydrse was 28d. 58m. 48s. S., Index cor. -i- 2m. 30s., height of eye 19 feet. Required the Latitude. DEVIATION. Construct a Napier Curve and correct the following courses : — True course to find compass N. 29d. 30m. E., S. 51d. 10m. W. Compass course to find true S. 79d. 40m. K, N. 87d. 50m. W. Ship^s head at N. 45d. E. Bearing of dist. object J^. 2d. 10m. W,, S. 32d. 20m. W. Ship's Bearing of Head. Dis. Object. N. N. 53 20 W N. E. N. 39 00 W E. N. 23 30 W S.E. N. 17 40 W S. N. 32 20 W s.w. N. 53 10 W w. N. 61 40 W N.W.j N. 58 20 W day's work. 101 PAPER SIXTH. Multiply 4of)7-8 Divide 780n'4 By 5678-9 By 34oir7 DAY'S WORK. H. 1 2 3 4 ,5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12 Courses. N. 25 E. N. 65 30 E. N. 3 30 E. N. 43 30E. N. 78 30 E. N. 36 E. K 9 8 7 9 4 4 5 5 5 5 6 6 7 7 7 8 9 9 10 10 10 11 11 12 lOtlis, 7 9 9 4 4 6 4 9 4 8 4 5 7 9 5 5 3 3 6 4 8 Winch N78E N7E N66E N15W Lee Way 9 N28E S 45E 7 30 9 1030 Devia- tion. 14 E 1650E 5 E 1630E 1650E 5E Kemarks. ' — ■^^ — . Lat. left. 40^ 20 ' N., Long, left 81^ 50 W., bearing })y Compass N. 5 1 ^' W. Din. 14 milos. Deviation 9^W. Variation H^'W. Current set fcor. Mag.)N. 57^30 E. 27 miles for the whole 24 hours. MERIDIAN ALTITUDE. 1876. June 12th, Long. 59^ 45 ' E., obs. Alt. O N., was 44^ 20^ 30'-; Index Cor. —:3M0'^ height of eye 19 feet. Required the Lat. PARALLEL. In Lat. 44° 20/ N., Long. 178° 20' W., Departure made good was 230 miles W. Required the Long. MERCATOR. Lat. A. 39° 39' N. Long. A. 170° 10/ E. Lat. B. 14° 14/ S. Long. B. 165° 35 / W. 13 102 HAND BOOK AND SELF-TEACHER. TIDES. 1873, June 17th, required the A.M. and P. M. tides at Hellevoet- slius and Wangaruru (New Zealand), Long. 174" E. AMPLITUDE. 1876, June 3rd, at 4h. 2m., P. M., Lat. 53° 10 ' S., Long. 25^ 10' W., Sun's Mag. Amp. was N. 54« 50' W., var. G« 1 ' \V. Required the Deviation. CHRONOMETER. 1876, June 20th, at 8h. 45m. A. M., Lat. 15'' 20' N., Long, by acct. 35«» 50' E, obs. Alt. _o was 38^* 50/ 59 ", Index cor. — 15'', height of eye 19 feet, time by Chr. 6h. 2" 4", which was slow 6m. 2s. It. on April 15th, and on Maj 20th slow 3m. 5s. 7t. Required the Long. AZIMUTH. 1876, June 26th, at 3h.35m. P. M., Lat. 61 «> 50' N., Long. 66'=' 10' W., Sun's Mag. Azimuth was N. 17" E.,the obs. Alt. ^ 16" 50' 40/', height of eye 21 feet, var. by chart 57" 30' W. Re- quired the Deviation. EX. MERIDIAN. 1876, June 6th, P. M., Long. 144" 44' E., obs. Alt. O^ S. was 50" 9' 20 / ', Index Cor. - 1' 20 ", height of eye 19 feet, time by watch llh. 47m. 30s., and found to be slow 40m. 50s., diff. Long, made W. 18''4. Required Lat. STAR. 1876, June 20, obs. Alt. of Star a Eridana fAchernar) was 47" 10' 14 ' ', Index cor. — 4m. 7s., height of eye 1 9 feet. Required the Lat. DEVIATION. Construct a Napier Curve and correct the following Courses : — True course to find Compass, N. 49° E., S. 78" W. Compass course to find true S. 30" 40 ' ' W., N. 10" 30/ E. Sailing along shore you took the bearing of two distant objects with the ship's head at E. S. E., find correct Magnetic bearing N. 30" 30'E., S. 50" 50' W. Ship's Bearing of Head. Diet. Object. N. N. 2 10 E N. E. N. 13 5W E. N. 15 W S. E. N. 8 low S. N. 3 low s. w. N. 2 5 E w. N. 10 10 E N.W. N. 13 E day's work. PAPER SEVENTH. Multiply 87.4444 Divide 888.777 103 By 899.9999 DAY'S WORK. By 77.666 H. Courses. 1 2 3 4 5 6 7 8 9 10 11 12 1 2 Z 4 5 6 7 8 9 10 11 12 K. N. 67 W. N. 68 W. N. 70 W. S. 80 W. S. 75 W. N. 89 W. 5 5 5 5 5 4 5 4 4 8 4 6 4 4 4 4 3 6 3 2 3 3 4 3 8 4 4 4 4 4 6 5 5 6 6 2 6 2 6 4 6 6 Winds. N 8 W N 6 W N15W S20W S16W S40W Lee Way Devia- tion. 20 17 19 10 15 18 E 19 E 20 E 15 E Remarks. Lat. left 51^ 2.5' N, Long, left 9" 29 W., bearing by Compass N. 22^,30' E., Dis. 10 miles. Dev. as per Log. Variation 25" W. 10 E 20 E Current set (cor. mag.) S. 24" W., 15 miles during tlie 24 hours. MERIDIAN ALTITUDE. PARALLEL. In Lat. 62S departure made 84 ^-S. Required diff. Lon^ ^S- Lat. A. 61^^ 13/ S. Lat. B. 43" 21' N. MEi .TOR. Long. A. 66" 34/ W. Long. B. 19" 5 W E. 104 HAND nOOK AND SELF-TEACHEn. TIDES. 1S7.3. July 29th, find A. M. and P. M, tides at Quilleboeuf ar.d ]l.)Uian}j;!i (New Zealand), Lon^;. 175^ E. AMTLITLDE. IHTf), July 3l9t, at Hh. 20m., A. M., in Lat. 39° 10' N., Lunjr. \;y2" 30/ K., Suu'h Ma^r. Amplituck' was E. 14^ 30' S., variation 3H^ 10^ W. Kequired Deviation. CHRONOMETER, 1870. July 24th, about 9h. .5()m., A. M., Lat 24" .50' 8., Loncf, ])V acct. 1()5" W., obs. Alt. _0 was 2H^ 59' .59//, Index cor. — 4 ' ol ''/, height of eye 14 feet, time by Chr. 8h. 1 7m. 59s., which was fast 3m. 28. 4t. on May 29th, and slow Im. 25s. 8t. on June :U)tli. Ke([uiied the I^ong. AZIMUTH. 187fi, July 3l8t, at 7h. 50m., A. M., in Lat. 22° 50' S., Lnn},^ 49° 50/ E., the Maj8-98 58-88 58-76 '58-62 |58-47 '58-31 5813 57-93 57-71 m 12 12 12 11 11 11 11 10 10 10 10 9 9 9 8 8 8 8 7 7 ^ 6 6 6 5 5 5 5 4 4 4 3 27-16 14-74 1-82 48-42 34-57 20-28 5-57 50-46 34-98 19-15 3-00 46-56 29-84 12-87 55-67 38-27 20-69 2-94 45-05 27-03 8-91 50-70 32-41 14-08 55-71 37-33 18-95 0-58 42-25 23-97 5-76 47-63 Var. in 1 liour. 0-507 0-528 0-548 0-568 0-586 0-604 0-621 0-637 0-652 0-666 0-679 0-691 0-702 0-712 0-721 0-729 0-736 0-742 0-748 0-753 0-757 0-760 0.763 0-765 0-766 0-766 0-766 0-765 0-763 0-760 0-757 0-753 AT MEAN NOON THE SUN'S Apparent Declination. s. s. N. 7 20 6 57 6 34 6 11 47 24 1 37 14 50 27 3 40 16 52 29 5 41 17 5 29 53 1 16 5 5 5 4 4 3 3 3 2 2 1 1 1 N. 1 2 2 2 3 3 4 4 4 40 3 27 50 14 37 1 24 47 4-5 9-3 8-3 2-1 50-8 35-1 15-2 51-4 24-2 53-9 20-8 45-2 7-5 28-1 47-3 5-4 22-7 39-8 56-9 45-5 27-2 7-7 46-7 23-8 58-6 30-7 59-7 25-3 47-1 4-7 17-7 25-8 Semi- diameter.* 16 10-0 16 9-8 16 9-6 16 9-3 16 9-1 16 8-8 16 8-6 16 8-3 16 8-0 16 7-8 16 7-5 16 7-2 16 7-0 16 6-7 16 6-4 16 6-2 16 5-9 16 5-6 16 5-3 16 5-0 16 4-8 16 4-5 16 4-2 16 3-9 16 3-6 16 3-4 16 3-1 16 2-8 16 2-6 16 2-3 16 2-0 16 1-7 * The Scmidianieter for Apparent Noon may be assumed the same as that for Mean Noon. 112 HAND JJOOK AND SELF-TEACH llll. APRIL, 1876. ^ AT APPARENT NOON THE SUN'S Ki| nation of AT MEAN NOON THE SUN'S 1 Time lo ))(' iulilnd to 0/ 5 siilil. from Ajijiarfiit ^ ^ Apparent De iuation. Viir. ill 1 hour. Tiuio. Var. in 1 Iiour. Ap larcnt Dec ination. Scmi- dianiL'tur.* 1 O / " N 4 47 29-5 57-71 la s 3 47.63 0.753 O ' // N 4 47 25-8 / // 16 1-7 2 5 10 32-0 57-49 3 29-60 0-749 5 10 28-6 16 1-5 3 5 33 28-9 57-25 3 11-69 0-743 5 33 25-8 16 1-2 4 5 56 19-8 56-99 2 53-92 0-737 5 5(] 17-0 16 0-9 5 6 19 4-4 56-72 2 36-30 0-730 6 19 1-9 16 0-6 6 6 41 42-4 56-44 2 18-87 0-722 6 41 40-2 16 0-4 7 7 4 13-5 56-15 2 1-64 0-713 7 4 11-6 16 0-1 8 7 26 37-4 55-84 1 44-63 0-703 7 26 35-8 15 59-8 9 7 48 53-8 55-52 1 27-88 0-692 7 48 52-5 15 59-6 10 8 11 2-4 55-19 1 11-39 0-681 8 11 1-3 15 59^3 11 8 33 2-8 54-84 55-19 0-669 8 33 2-0 15 59-0 12 8 54 54-8 54-48 39-30 0-655 8 54 54-2 15 58-7 13 9 16 38-0 54-11 23-74 0-()41 9 16 37-7 15 58-5 14 9 38 12-1 9 59 36-8 53-73 53-33 8-52 0-627 0-611 9 38 12-0 9 59 36-9 15 58-2 15 6-34 15 57-9 16 10 20 51-8 52-91 20-82 0-595 10 20 52-1 15 57-6 17 10 41 56-6 52-48 34-91 0-579 10 41 57-1 15 57-4 18 11 2 51-0 52-04 48-60 0-561 11 2 51-7 15 57-1 19 11 23 34-6 51-59 1 1-86 0-543 11 23 35-5 15 56-8 20 11 44 7-1 r:i-12 1 14-69 0-525 11 44 8-1 15 56-6 21 12 4 28-1 50-63 1 27-OS 0-507 12 4 29-3 15 56-3 22 12 24 37.3 50-13 1 39-01 0-487 12 24 38-7 15 56-1 23 12 44 34-3 49-61 1 50-47 0-468 12 44 35-8 15 55-8 24 13 4 18-8 49-08 2 1-46 0-448 13 4 20-5 15 5 5- 6 25 13 23 50-4 48-54 2 11-97 0-428 13 23 52-2 15 55-3 26 13 43 8-8 47-98 2 21-98 0-407 13 43 10-7 15 55-0 27 14 2 13-6 47-41 2 31-50 0-386 14 2 15-6 15 54-8 28 14 21 4-5 46-82 2 40-53 0-366 14 21 iy6 15 54-6 29 14 39 41-2 46-22 2 49-06 0-345 14 39 43-3 15 54-3 30 14 58 3-2 45-61 2 57-08 0-323 14 58 5-4 15 54-1 31 N15 16 10-3 44-98 3 4-5 8 0-302 N 15 16 12-6 15 53-9 '* The Semidiauieter {or Apparent Noon may be assumed tlie same as that for Me/in Noun, NAUTICAL ALMANAC. MAY, 1876. 113 "5 c AT APPARKXT NOON THE SiLN'S Kipiation of Tinii> to 1)0 sul)t. to Ajiparont Tiiu(>. Var. in 1 hour. AT MEAN NOON THE SUN'8 1 o >, Apparrnt Duclinalioii. Var. in 1 hour. Apparent Deelination. Semi- diameter.* 1 o / " N.lo 16 10-3 44-98 ni s ' 3 4-58 o'-302 O f 'f N.15 16 12-6 15 53-9 2 15 34 2-2 44-34 3 11-57 0-280 15 34 4-6 15 53-7 3 15 51 3S-6 43.69 3 18-03 0-258 15 51 41-0 15 53-4 4 16 8 59-2 43-02 3 23-95 0-235 16 9 1-6 15 53-2 5 16 26 3-7 42-34 3 29-33 0-212 16 26 6-1 15 53-0 6 16 42 51-7 41-66 3 34-15 0-189 16 42 54-2 15 52-8 7 16 59 23-2 40-9() 3 38-41 0-166 16 59 25-6 15 52-5 8 17 15 37-7 40-25 3 42-11 0-142 17 15 40-1 15 52-3 9 17 31 35-0 39-52 3 45-23 0-118 17 31 37-0 15 52-1 10 17 47 14-8 38-79 3 47-7(; 0-094 17 4.7 17-3 15 51-9 11 18 2 3(5-9 38-05 3 49-72 0-069 18 2 39-3 15 51-7 12 18 17 41-0 37-29 3 51-09 0-045 18 17 43-4 15 51-5 13 18 32 26-7 36-52 3 51-88 021 18 32 29-0 15 51-3 14 18 46 53-8 35-73 3 52-08 004 18 46 56-1 15 51-1 1.) 19 1 1-9 34-94 3 51-69 0-028 19 1 4-2 15 50-9 16 19 14 51-0 34-14 3 50-72 0-052 19 14 53-2 15 50-7 17 19 28 20-6 33-32 3 49-17 0-07() 19 28 22-7 15 50-5 IS 19 41 30-4 32-49 3 47-05 0-100 19 41 32-5 1 5 50-3 19 1 9 54 20-3 31-65 3 44-3(i 0-124 1 9 54 22-3 15 50-1 20 20 6 49-8 30-80 3 41-10 0-1 4S 20 6 51-7 15 49-9 21 20 18 58-8 29-94 3 37-28 0-171 •20 19 0-6 15 49-7 22 20 30 47-0 29-07 3 32-91 0-193 20 30 48-7 15 49-5 23 20 42 14-1 28-19 3 28-01 0.215 20 42 15-8 15 49-4 24 20 53 19-9 27-29 3 22-60 0-236 20 53 21-5 15 49-2 25 21 4 4-1 26-39 3 16-68 0-256 21 4 5-6 15 49-0 26 21 14 26-5 25-48 3 10-29 0-276 21 14 27-9 1 5 48-9 27 21 24 26-9 24-55 3 3-43 : 0-295 21 24 28-2 15 48-7 28 21 34 5 23-62 2 56-12 ' 0-314 21 34 6-2 15 48-6 29 21 43 20-6 22-68 2 48-38 1 0-331 21 43 21-7 15 48-5 30 21 52 13-6 21 73 2 40-23 i 0.348 21 52 14-5 15 48-3 31 22 43-7 20-77 2 31-67 0-365 22 44-6 15 48-2 32 N.22 8 50-8 19-81 2 22-73 0-380 N.22 8 51-6 15 48-1 * The Sfiuidiuiuetur ft 14a ir ApiHir •'ut Noon nia> be asiiuiue 1 the same an thattiur Miun Noou. 114 HAND BOOK AND SELF-TEACHER. JUNE, 1876. I & 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 AT APPARENT NOON TUE SUN'S Apparent Declination. N.22 22 22 22 22 22 22 22 22 23 23 23 23 23 23 23 23 23 23 23 23 23 23 23 23 23 23 23 23 23 N.23 8 50-8 16 34-7 23 54-3 30 52-5 37 26-1 43 35-9 49 21-9 54 44-0 59 42-0 4 15-7 8 25-2 12 10-3 15 30-9 18 27-0 20 58-4 23 5-1 24 47-0 26 4-1 26 56-4 27 23-9 27 26-5 27 4.2 26 17-1 25 5-2 23 28-6 21 27-2 19 1-2 16 10-7 12 55'7 9 16-2 5 12-5 Viir. in 1 liuur. 19-81 18-84 17-87 16-89 15-90 14-91 13-92 12-92 11-91 10-90 9-89 8-87 7-85 6-82 5-79 4-76 3-73 •2-70 1-66 0-63 0-41 1-44 2-48 3-51 4-54 5-57 6-59 7-61 8-64 9-65 10-66 Equation of Time to be subt. from to Apparent Time. ni 8 2 22-73 2 13-41 2 3-73 1 53-71 1 43-35 1 32-681 1 21-71 1 10-45 58-93 47-17 35-17 22-96 10-57 1-99 14-69 27-52 40-46 53-48 1 6-55 1 19-65 1 32-75 1 45-82 58-82 11-72 24-50 37-13 49-59 1-84 13-87 3 25-67 3 37-20 1 2 2 2 2 3 3 Var. in 1 liour. 0-380 0-396 0-411 0-425 0-438 0-451 0-463 0-475 0-485 0-495 0-504 0-512 0-520 0-526 0-532 0-537 0-541 0-543 0-545 0-546 0-545 0-543 0-540 0-535 0-529 0-523 0-515 0-506 0-496 0-486 0-475 AT MEAN NOON THE SUN'S Apparent Declination. N.22 22 22 22 22 22 22 22 22 23 23 23 23 23 23 23 23 23 23 23 23 23 23 23 23 23 23 23 23 23 N.23 8 51-6 16 35-4 23 56-0 30 53-1 37 26-6 43 36-3 49 22-2 54 44-2 59 42-1 4 15-9 8 25-3 12 10-4 15 31-0 18 27-0 20 58-4 23 5-1 24 47-0 26 4-1 26 56-4 27 23-9 27 26-5 27 4-3 26 17-2 25 5-4 23 28-8 21 27-5 19 1-5 16 11-0 12 56-1 9 16-8 5 13-2 Sfini- dianieter.* 15 48- 15 47- 15 47- 15 47- 15 47- 15 47- 15 47- 15 47- 15 47- 15 47^ 15 46- 15 46- 15 46- 15 46- 15 46- 15 46- 15 46-' 15 46- 15 46- 15 46-' 15 46- 15 46- 15 46- 15 46- 15 46- 15 46-1 15 46-( 15 46-( 15 46-( 15 46-( 15 46-( ' The Semidiumeter ior Apparent Noou may be assumed the iiaiue a.s that for AJean Noon. NAUTICAL ALMANAC • 115 JULY, 1876. a' 1 AT APPARENT NOON THE SUN'S Efiuation of Time to he added to Aiipiiient Time. Var. in 1 hour. AT MEAN NOON THE SUN'S o Apparont Decl nation. Var. in 1 lioiir. Apparent Decl nutlou. Semi- diameter.* 1 N.23 5 12-5 10-66 1 m 8 3 37-20 0-475 f tt N.23 5 13-2 15 46-0 2 23 44-7 11-66 3 48-46 0-463 23 45-4 15 46-0 3 22 55 52-8 12.66 3 59-42 0-450 22 55 53-6 15 46-0 4 22 50 37-0 13-65 4 10-06 0-436 22 50 38-0 15 46-0 5 22 44 57-4 14-64 4 20-37 0-422 22 44 58-5 15 46-0 6 22 38 54-2 15-62 4 30-34 0-407 22 38 55-3 15 46-0 7 22 32 27-5 16-60 4 39-93 0-392 22 32 28-7 15 46-0 8 22 25 37-4 17-57 4 49-14 0-376 22 25 38-8 15 46-0 9 22 18 24-1 18-54 4 57-96 0-359 22 18 25-6 15 46-1 10 22 10 47-7 19-49 5 6-37 0-342 22 10 49-4 15 46-1 11 22 2 48-5 20-44 5 14-36 0-324 22 2 50-3 15 46-1 12 21 54 26-5 21-39 5 21-91 0-305 21 54 28-4 15 46-2 13 21 45 41-9 22-32 5 29-01 0-286 21 45 44-0 15 46-2 14 21 36 35-0 23-25 5 35-65 0-267 21 36 37-2 15 46-3 15 21 27 5-9 24-17 5 41-82 0-247 \ 21 27 8-2 15 46-3 16 21 17 14-8 25-OS 5 47-51 0-227 21 17 17-2 15 46-4 17 21 7 1-9 25-99 5 52-71 0-206 21 7 4-5 15 46-4 18 20 56 27-5 26-88 5 57-39 0-184 20 56 30-2 15 46-5 19 20 45 31-8 27-76 6 1-55 0-162 20 45 34-6 15 46-6 20 20 34 15-1 28-63 6 5-16 0-139 20 34 18-0 15 46-6 21 20 22 37-5 29-49 6 8-22 0-116 20 22 40-5 15 46-7 22 20 10 39-4 30-34 6 10-71 0-092 20 10 42-6 15 46-8 23 19 58 21-1 31-18 6 12-61 0.067 19 58 24-4 15 46-9 24 19 45 42-9 32-00 6 13-91 0-042 19 45 46-2 15 47-0 25 19 32 44-9 32-82 6 14-61 0-016 19 32 48-5 15 47-1 26 19 19 27-5 33-63 6 14-70 0-009 19 19 31-0 15 47-2 27 19 5 50-9 34-42 6 14-18 0-035 19 5 54-5 15 47-3 28 18 51 55-5 35-20 6 13-04 0-060 18 51 59-2 15 47-4 29 18 37 41-5 35-96 6 11-28 0-086 18 37 45-3 15 47-5 30 18 23 9-3 3672 6 8-90 0.112 18 23 13-1 15 47-7 31 18 8 19-1 37-46 6 5-91 0-137 18 8 22-9 15 47-8 32 N.17 53 11-1 38-20 6 2-30 0-163 N.17 53 15-0 15 47-9 * The Semidiameter for Appartut Nouu may be assumed the same as that Cor JUtan Koon. 116 HAND BOOK AND SELF-TEACHER. AUGUST, 187G. 1 AT APPARENT NOON THE bUN'S IvHiiitinn of Tillii' Id lie iiiMi'il to Mibt. IVnm A|iii!iiciit AT MEAN NOON THE SUN'S o i i Alipiirciit Dtcliiiaiiun. Var. in 1 liudr. Tiiiio. Var. in 1 liuiir. A]) lari'iit Dec illation. Srnii- diaiiR-UT.* 1 N.17 53 IM ff 38-20 Ill s 6 2-30 ()-163 X.17 53 15-0 15 47-9 2 17 37 45-7 38-91 5 58-07 0-189 17 37 49-6 15 48-1 .3 17 22 3-3 39-62 5 53-23 0-214 17 22 7-2 15 48-2 4 17 6 3-9 40 32 5 47-79' 0-239 17 6 7-8 15 48-3 5 16 49 48-0 41 00 5 41-74 0-2 ti4 16 49 51-9 15 48-5 () 16 33 15-8 41-68 5 35-10 0-289 16 33 19-7 15 48-6 7 16 16 27-6 42-34 5 27-87 0-313 16 16 31-5 15 48-8 8 15 59 23-7 42-99 5 20-06 f\.n It — 15 59 27-5 15 48-9 9 15 42 4-2 43-63 5 11-69 0-361 15 42 8-0 15 49-1 10 15 24 29-6 44-25 5 2-75 0-3S4 15 24 33-3 15 49^3 11 15 6 40-1 44-87 4 53-27 0-40() 15 6 43-8 15 49-4 12 14 48 3()-0 45-47 4 43-24 0-42S 14 48 39-6 15 49-6 13 14 30 17-5 46-06 4 32-69 0-450 14 30 21-0 15 49-7 14 14 11 45-1 46-()4 4 21-(i2 0-472 14 1 1 4S-5 15 49-9 15 13 52 590 47-20 4 10-03 0-493 13 53 2-2 15 50-1 16 13 33 59-4 47-75 3 c7-94: 0-514 13 34 2-6 15 50-3 17 13 14 46-9 48-29 3 45-35 0-535 13 14 49-9 15 50-4 18 12 55 21-7 48-.S1 3 32 -2 (i 0-556 12 ,i5 24-6 15 50-() 19 12 35 44-1 49-32 3 18-(hS ().57(i 12 35 46-8 15 50-S 20 12 15 54-5 49-81 3 4-62 0-596 12 15 57- L 15 51-0 21 11 55 53-3 50-29 2 50-09 0-613 11 55 55-7 15 51-2 22 11 35 40.8 50-75 2 35-09 0-634 11 35 43-0 15 51-4 23 11 15 17-3 51-20 2 19-64 0-653 11 15 19-3 15 5l-() 24 10 54 43-1 51-64 2 3-75 0-671 10 54 44-9 15 51-9 25 10 33 58-'' 52-06 1 47-43 0-(;s8 10 34 0-3 15 52-1 26 10 13 4-4 52-46 1 30-71 0-705 10 13 5-7 15 52-3 27 9 52 0'4 52-86 1 13-5.S 0-722 9 52 1-4 15 52-5 28 9 30 47-0 53-24 5607 0-737 9 30 47-9 15 52-8 29 9 9 24-7 53-61 38-19 0-752 9 9 25-3 15 53-0 30 8 47 53-8 53-96 19-97 0-766 8 47 54-1 15 53-2 31 8 26 14-4 N. 8 4 27-0 54-31 54-64 1-41 0-780 0-793 8 26 14-4 X. 8 4 26-8 15 53-4 32 17-46 15 53-7 ' The Semidlameter for App(trcnt Noon may be assumed the same as that for AJean Noon. NAUTICAL ALMANAC. SEPTEMBER, 187(). 117 .a 1 AT APPARKNT NOON Tllli SUN'S Ei|iiatii)n of Tiiiii' to be Nub. from All|l!lf('llt rime. Var. in 1 hour. AT MEAN NOON TIIK SUN'S ** o >> 5 Apparent DecliDiilion. Vnr. in 1 liour. 54-64 A)) (iiroiit iJeil nation. Senil- diameter.* 1 o / // N. 8 4 27-0 ni H 17-46 0-793 N. 8 4 26-8 15 53-7 2 7 42 31-9 54-95 36-63 0-805 7 42 31-4 15 53-9 3 7 20 29-4 55-25 56-08 0-815 7 20 28-5 15 54-2 4 6 58 19-7 55*55 1 iD'U 0-825 6 58 18-5 15 54-4 5 6 36 3-2 55-83 1 35-70 0-835 6 36 1 -7 15 54-6 6 6 13 40-1 5()-()9 1 55-84 0-843 6 13 38-2 15 54-9 7 5 51 10-7 56-35 2 16-16 0-850 5 51 8-5 15 55-1 8 5 28 35-3 56-59 2 36-65 0-857 5 28 32-9 15 55-4 9 5 5 54-3 56-82 2 57-29 0-8()2 5 5 51-5 15 55-6 10 4 43 7-9 57-04 3 18-04 0-867 4 43 4-8 15 55-9 11 4 20 16-5 57-24 3 38-89 0-871 4 20 13-0 15 56-1 12 3 57 20-3 57-43 3 59-83 0-874 3 57 16-5 15 56-4 13 3 34 19-8 57-60 4 20-84 0-876 3 34 15-7 15 56-6 U 3 11 15-3 57-7() 4 41-89 878 3 11 10-8 15 56-9 15 2 48 7-1 57-91 5 2-98 0-879 2 48 2-2 15 57-1 IG 2 24 55-6 58-04 5 24-09 0-879 2 24 50-4 15 57-4 17 2 1 41-2 58-15 5 45-19 0-879 2 1 35-6 15 57-6 IS 1 38 24-2 •')8-25 () 6-2S' 0-878 1 38 18-3 15 57-9 19 1 15 5-0 58-34 6 27-33 0-876 1 14 58-7 15 58-2 20 51 44-0 58-41 6 4S33 0-874 51 37-3 15 58-4 21 28 21-4 58-46 7 9-26 0-87U 28 14-5 15 58-7 22 N. 4 57-8 5S-5() 7 30-10 0-866 N. 4 50-5 15 59-0 23 S. 18 2()-() 58-53 7 50-84 0.861 S. 18 34-3 15 59-3 24 41 51-4 58-54 8 11-45 0-856 41 59-4 15 59-5 25 1 5 16-3 58-53 8 31-92 0-849 1 5 24-6 15 59-8 26 1 28 40-9 58-51 8 52.22 0-842 1 28 49-5 16 0-1 27 1 52 4-8 58-48 9 12-34 0-834 1 52 13-8 16 0.4 28 2 15 27-8 58-43 9 32-26 0-825 2 15 37-1 16 0-7 29 2 38 49-4 58-37 9 51-95 0-815 2 .38 59-0 16 1-0 30 3 2 9-4 58 29 10 11-40 0.805 3 2 19-3 16 1-2 31 S. 3 25 27-4 58-20 10 30-57 0-793 S. 3 25 37-6 16 1-5 * The Semidiameter for Apparent Noon may be assumed the same a> that for A/can Noon. 15 118 HAND llOOK AND SELF-TEACH KR. OCTOBER, 1876. J AT APPARENT NOON THE SUN'8 Knuiition of TtMie to lit' sul)t. t'roin Appurcnt Time. Var. in 1 hour. AT MEAN NOON THE SUN'S 1 Apparent Duullnutiun. Var.iu 1 hour. Apniiront Dee inalion. Senii- (iiaiiioter.'* 1 / « S. 3 25 27-4 58-20 Ill 8 10 30-57 0-793 ' " S. 3 25 37-6 16 1-5 2 3 48 43-1 58-10 10 49-45 0-780 3 48 53-5 16 1-8 3 4 11 56-1 57-98 11 8-02 0-766 4 12 6-8 16 2-1 4 4 35 6-1 57-85 11 26-24 0-751 4 35 17-2 16 2-3 5 4 5S 12-9 57-70 11 44-09 0-736 4 5S 24-2 16 2-6 6 5 21 16-0 57-55 12 1-55 0-719 5 21 27-6 16 2-9 7 5 44 15-2 57-38 12 18-59 0-701 5 44 27-0 16 3-2 8 6 7 lO-l 57-19 12 35-19 0-682 6 7 22-1 16 3-5 9 6 30 0-4 56-99 12 51-34 0-663 6 30 12-6 16 3-7 10 6 52 45't) 56-77 13 7-01 0-643 6 52 58-0 16 4'0 11 7 15 25-4 56-54 13 22-18 0-622 7 15 38-0 16 4-3 12 7 37 59-5 56-29 13 36-84 0-600 7 38 12-3 16 4-5 13 8 27-3 56-02 13 50-97 0-577 8 40-3 16 4-8 14 8 22 48-6 55-74 14 4-54 0-554 8 23 1-6 16 5-1 15 8 45 2-8 55-44 14 17-55 0-530 8 45 16-0 16 5-3 16 9 7 9-6 55-12 14 29-98 0-506 9 7 22-9 16 5-6 17 9 29 8-6 54-78 14 41-82 0-481 9 29 22-0 16 5-9 18 9 50 59-3 54-43 14 c3-()5 0-455 9 51 12-8 16 6-2 19 10 12 41-4 ,54-Oi) 15 3()6 0-429 10 12 55-0 16 6-4 20 10 34 14-4 53-68 15 13-63 0-402 10 34 28-1 16 6-7 21 10 55 380 53-28 15 22-96 0-375 10 55 51-7 16 7-0 22 11 16 51.7 52-86 15 3l-(i3 (-347 11 17 5-4 16 7-2 23 11 37 55-1 52-42 15 39-62 0-319 1 1 ,38 8-8 16 7-5 24 11 58 47-8 51-97 15 46-93 0-290 11 59 1-5 16 7-8 25 12 19 29-4 51-49 15 53-55 0-261 12 19 43-1 16 8-1 26 12 39 59-5 51-01 15 59-46 0-231 12 40 13-1 16 8-3 27 13 17-7 50-50 16 4-65 0-201 13 31-2 16 8-6 28 13 20 23-6 49-98 16 9-10 0-170 13 20 37-1 16 8-8 29 13 40 16-9 49-45 16 12-81 0-139 13 40 30-2 16 9-1 30 13 59 57-1 48-89 16 15-75 0-107 14 10-3 16 9-4 31 14 19 23-8 48-32 16 17-92 0-074 14 19 36-9 16 9-6 32 S. 14 38 36-7 47.74 16 19-29 0-040 S. 14 38 49-7 16 9-9 * The Scmidiameter tot Apparent Noou may be assumed the same as that for Mean Noou. NAUTICAL ALMANAC. 119 NOVEiMIiEK, 187<). a o V .a AT APPARKNT NOON THK SUN'S Apnarent Declination. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 H) 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 S. 14 38 14 57 15 16 15 34 15 53 16 11 16 28 16 46 17 3 17 20 17 36 17 52 18 8 18 24 18 39 18 54 19 9 19 23 19 37 19 51 20 4 20 17 20 29 20 41 20 53 21 4 21 15 21 26 21 36 2146 21 55 36-7 35-4 19-5 48-7 2-6 0-7 42-7 8-1 16-6 7-7 41-0 56-0 52-4 29-7 47-5 45*5 23-2 40-2 36-2 10-8 23-5 14-1 42-2 47-4 29-4 47-8 42-4 12-9 18-9 0-2 16-2 Vnr. in 1 hour. Kquntioi uf Time to Ik> nu1>. friiin Appiiri'iit ' Timo. Var. in I liiiiir. 1. ni 16 16 16 16 16 16 16 16 16 15 15 15 15 47-74 47-14 46-53 45-90 45-25 44-59 43-90 43-21 42-49 41-76 41-01 40-24 39-45 38-65|15 37-8315 36-99 14 36-14 35-27 34-39 33-49 32-57 131-64 30-69 !29-73 ;28-76 ,27-77 126-77 25-76 24-74 2370 22-66 14 14 14 14 13 13 13 12 12 12 12 11 11 10 10 n. 1 19-29 19-86 19-61 18-54 l()-63 13-87 10-25 o- / / 0-43 54-22 47-14 39-20 30-39 20-71 10-19 58-82 46-61 33-57 19-71; 49-()()i 33-37 16-37 58-62 1 40-141 20.93 l-Ol 40-40 19-11 57-16 34-56 0-040 0-007 0-027 0-062 0-097 0-133 0-169 0-205 0-241 0-277 0-313 0-349 0S85 0-42 i 0-456 0-491 0-526 0-560 0-594 0-627 0-66() 0-692 0.724 0-755 0-785 0-815 0-844 0-873 0-901 0.928 0-955 AT MEAN NOON TIIK HUN'S Apnaront l)ecllnatIon. , Scrai- (ilnmoler.* S. 14 ,38 49-7 16 9-9 14 57 48-2 16 10-1 15 16 32-2 16 10-4 1 5 35 1 -2 16 10-6 15 53 14-8 16 10-8 16 11 12-8 16 ll-l 16 28 .54-5 16 11-3 16 46 19-7 16 11-5 17 3 28-0 16 11-7 17 20 18-8. 16 12-0 17 36 51-7 16 12-2 17 53 6-5 16 12-4 18 9 2-6 16 12-6 18 24 39-6 16 12-8 18 39 57-1 16 13-0 18 54 54-7 16 13-2 19 9 32-1 16 13-4 1 9 23 48-8 16 13-6 19 37 44-4 16 13-8 19 51 18-6 16 14-0 20 4 31-0 16 14-2 20 17 21-2 16 14-4 20 29 49-0 16 14-6 20 41 53-8 16 14-8 20 53 35-4 16 15-0 21 4 53-5 16 15-2 21 15 47-8 16 15.3 21 26 17-9 16 15-5 21 36 23-6 16 15-7 21 46 4-6 16 15-8 S. 21 55 20-6 16 16-0 * The Semidiaiueter fur Apparent Nuou may be asiiunicd the same as that for Mean Koon. 120 HAND BOOK AND SELF-TFACHER. DECEMBER, 1876. 5 a o AT APPARENT NOON TUE SUN'S Equation of Time to be subt. from AT MEAN NOON T HE SUN'S added to Api)arout 0) ■s <3 Apparent Declination. Var.in 1 hour. XllUC. Var. in 1 liour. Apparent Declination. Semi- diameter.* 1 Of" S.21 55 16-6 22-66 ni s 10 34-56 0-955 S.21 55 20-6 16 16-0 2 22 7-8 21-60 10 11-32 0-981 22 4 11-4 16 16-1 3 22 12 33-4 20-53 9 47-47 1-006 22 12 36-7 16 16-3 4 22 20 33-3 19*45 9 23-03 1-030 22 20 36-3 16 16-4 5 22 28 7-2 18-37 8 58-02 1-054 22 28 10-0 16 16-5 6 22 35 14-9 17-27 8 32-46 1-076 22 35 17-4 16 16-6 7 22 41 56-1 16-16 8 6-38 1-097 22 41 58-3 16 16-7 8 22 48 10-5 15-04 7 39-79 1-118 22 48 12-4 16 16-8 9 22 53 57-9 13-91 7 12-73 1-137 22 53 59-6 16 17-0 10 22 59 1 8-2 12-78 6 45-23 1-154 1-171 22 59 19-7 16 17^1 11 23 4 11-2 11-64 6 17-32 23 4 12-4 16 17-2 12 23 8 3t)-7 10-4« 5 49-03 l-]8(i 23 8 37-7 16 17-3 13 23 12 34-4 9-33 5 20-40 1-200 23 12 35-3 16 17-4 14 23 16 4-4 8-17 4 51-45 1-21-2 23 16 5-1 16 17-4 15 23 19 iro 7-00 4 22-24 1-222 23 19 7-0 16 17-5 16 23 21 40-5 5-83 3 52-79 1-231 23 21 40-9 16 17-6 17 23 23 4(J-4 4-66 3 23-14 1 -239 23 23 46-7 16 17-7 18 23 25 24-1 3-48 2 c3-34 1-244 23 25 24-3 16 17-7 19 23 26 33-6 2-31 2 23-42 1-248 23 26 33-7 16 17-8 20 23 27 14-8 1-13 1 53-42 1-^!51 23 27 14-S 16 17-9 21 23 27 27-6 006 1 23-37 1-2 32 23 27 27-6 16 18-0 22 23 27 12.0 1-24 53-31 1-252 23 27 12-0 16 18-0 23 23 26 28-1 23 25 15-9 2-42 3-60 23 2S 1-250 1-246 23 26 28-1 23 25 15-9 16 18-1 24 (i-()S 16 18-1 25 23 23 35-5 4-77 36-55 1-242 23 23 35-5 16 18-2 26 i/3 21 26-8 5-95 1 6-29 1-236 23 21 26-9 16 18-2 27 23 18 50-0 7--12 1 35-87 1-229 23 18 50-2 16 18-2 28 23 15 45-1 8-29 2 5-26 1-220 23 15 45-4 16 18-2 29 23 12 12-3 9-45 2 34-43 1-210 23 12 12-7 16 18-3 30 23 8 11-6 10-60 3 3-35 1-199 23 8 12-2 16 18-3 31 23 3 43-3 11-75 3 31-99 1-187 23 3 44-0 16 18-3 32 S.22 58 47-4 12.90 4 0-32 1-174 S. 22 58 48-2 16 18-3 • The Semidiameter tor Apparent Noon may be assumed the same as that for Mean Noon. STARS DECLINATION. January 7tb, Sirius, February 30th, Aldebaran, March 19th, Arcturus, May 18th, a. Hydrae, June 20th, Achernar, July 10th, Aldebaran, August 31st, Rigel, September 20tli, Regulus, 16" 34 M6'^ S. 16« 15'37/'N. 19'^49^25/'N. 8« 7' 27// S. 57^ 51 '33'' S. 16^ 15/40//N. 8«^ 20^26'/ S. 12'=' 34/ 18/'N. ADMIRALTY TIDE TABLES. 121 EXTRACTS FROM ADMIRALTY TIDE TABLES, 1873. FOREIGN PORTS. Date. Name of Port. A.M. Tides. P. M. Tides. Moon's Transit High Water at Full & Change. h. in. b. m. h. m. b, in. Long. Jan. 29th, 4 5 4 30 1 7 " 30th, St. John, N. B., 4 54 5 17 2 4 11 21 66° W. May 3L^t, 6 44 7 7 4 27 June 1st, Trencomalie (Ceylon), 7 30 7 54 5 13 8 18 80° E. July 31st, 7 44 8 3 5 11 August 1st, Halifax, N. S., 8 24 8 48 5 54 7 49 63° W. Sept. 30th, 9 15 10 4 7 3 Oct. 1st, Kyau-Chau (Yellov Sea), 10 57 11 47 7 14 5 00 120° E. Feb. 27th, 3 51 4 14 8 2 " 28th, St. John, N. P., 4 36 4 58 42 11 21 66° W. May 2-'nd, Pei-ho (Yellow Sea), 7 35 1 34 3 4C 122° E. " 23rd, 1 3 1 30 8 41 Dec. 19th, Parrsboro', N. S., 3 5 3 26 9 29 17 65° W. " 20th, 3 48 4 10 11 41 Sept. 1st, 9 38 10 23 fi.O 40 " 2nd, Hakodadi (Japan), 11 11 11 57 7 14 5 135° E. Nov. 22nd, 4 40 4 59 8 15 " 23rd, Yarmouth, N. S., 5 18 5 39 1 52 10 9 66° W. Oct. 11th, 6 45 7 09 a.O 50 " 12th, New York, U. S., 7 34 8 00 4 11 5 7 8 13 74° W. 16 122 HAND BOOK AND SELF-TEACHER. EXTRACT FROM ADMIRALTY TIDE TABLES, 1873. HOME POKTS. Date. May Name of Port. A.M. Tides !.( ,1 line a Jan'y a Feb'y 2, 3,1 4, 20, 6, 24, 25, 7, H, 9, 4, 5 March 30, h. 111. Cherbourg, Exmouth, Baltimore, Cromarty, Do., Ballycotton 7 8 11 1 2 11 1 11 P. M. Tides Conhtant Port of Peference. 52 53 41 40 23 29 3 9 20 li. in. 8 19 9 52 30 2 1 2 44 ii. 111. + 42 Brest. + 38 — 38 — 2 21 Do., a March 4, April 5, May 4, 11, June ii. July ii August 3, " 31, Sept. 1 , Bristol, Do., Pt. Patrick, Do., Do., Llaiielly, Ballycastle, Do., Ordfordness Do., 26, Do., 27, Douglass, Tanera, Alderney, 1 10 11 3 4 11 11 8 9 43 54 37 33 30 41 27 15 48 11 30 38 37 1 14 1143 11 1 21 1 K) 1 55 10 58 4 18 5 34 6 4S 11 31 - 26 + 19 58 + 4 — 4 18 — 51 Do., Davenport. Queen stown. J^eith. a Waterford. Weston-Supermare Greenock. Belfast. Harwich. 33 9 00 10 23 + 1 1 — 1 51 4- 2 59 a Holly Head. Thurso. Brest. ANSWERS. 123 ANSWERS TO PAPERS. ANSWERS TO PAPER FIRST. Multiplication 80730 Division 1-321 DAYS WORK. Dep. course S. 58° E. 1st. S. 15" W. 2nd. N. I?'' E. 3d. S. 38^ E. 4th. S. 18- E. otli. S. 19" E. 6th. S. 11« W., current course N. 41" E., true course S. 28° E., dis. 43 miles, Ut. in 43° 8' N., Loner. 65° 31 ' W. MERIDIAN ALTITUDE. True Alt. 33° 30'. Dec. 23" 1/45''. Lat. 33° 28^ 15// N. PARALLEL. Difference Long. 56*08 miles. MERCATOR. Course N. 17° W. Dis. 240-6. TIDES. Bristol 9h. 20m., A. M., 9h. 43m., P. M. St. John Ih. 13m., A. M., Ih. 37m., p. M. AMPLITUDE. Dec. 22° 52/ 21 n. True Amp. E. 33° 01 ' 15//. Deviation 22° 31/ 15// E. CHRONOMETER. Daily rate, Is, 8t. Ace. rate, 57'/. G. date Jan. 4th. 7}i. 18m. 35s. Dec. 22° 44/ 14// S. True Alt. 16° 32' 10//. Equation 5m. lis. Hour Ande 2h. 12m. 35s. L(m2'. 75° 11 ' 15" W. ^ AZIMUTH. True Alt. 8° 44/ 51//. Dec. 22" 39' 27". Sum of Lo^^^s 9-064314. True Azimuths. 13° 20/ E. Error 17° 20/ 54 '/. Deviation 27° 30/E. ' EX MERIDIAN. G. Date Jan. 6th, 4h. 46m. 7s. H. Angle 21 ra. 27s. True 124 HAND BOOK AND SELF-TEACHER. Alt 23'^ 29' 1". Dec. 22° 31/24'/ S. Ist Aug. 5in. 258. 2nd Aug. 5m. 30s. Lat. 43« 48 ' 34// N. STAR. Dec. 22° 52 / 40 ' '. True Alt. 60° 23 ' 3 ". Lat. 52° 29 ' 37 /'. DEVIATION. Cor. Mag. Bearing N. 49° 13/ W. If-,^" 29' W. 2nd. 18° 44' E 3rd. 2i^ 2' E. 4th. 12° 2?/ E. oth. 5° 41 / E. Gth. 6° 53'/ W. 7th. 23° 33/ W. ^8th. 27° 58' W. Correct courses S. 38° E. N. 19° E. Compass courses S. 55° W. W. Ship^ head N. 10° 40/ E. S. 15° 20/ W. ANSWERS TO PAPER SECOND. Multiplication 447837 Division 1-094 DAY'S WORK. Dep. Course N. 67° E. 1st, Course N. 3" E. 2nd Course N 43° E. 3rd, Course N. 57° E. 4th, Course N. 79 K .5th, Course N. 43" W. 6th, Course N. 5° W. 7th, Current N 21° W. True Course N. 32° E. Dis. 6/ miles. Lat. m 43 48' S. Long, in 83° 56^ W. MERIDIAN ALTITUDE. True Alt. 49° 19' 2". Dec. 15° 12' 2". Lat. 55° 52^ 20". PARALLEL. Diff. Long. 1229 miles. MERCATOR. True Course N. 31° 17' 33" E. Dist. 4294-4. TIDES. Penzance Oh. 10m. P. M. Hi-ide 6h. 48m. — 7h. 31m., P. M. AMPLITUDE. Dec. 14° 17' 59". True Amp. E. 20° 33' 36" S. Dev. 15° 33' 30'' E. ANSWERS. 1 25 CHRONOMETER. Daily rate 4s. 9t. Acct. rate 38s. G. date Feb. 1st, 2lh. 11m. .5()s. Dec. 16" 56M4'^ True Alt. 14^ 28/ 26'/. Eciua- tion 13m. o6s. H. Angle Ih. 48m. 30s. Long. 18^ 22' 30'' E. AZIMUTH. True Alt. 17^ 20' 31'/. Dec. 10^.52/47". Sum of Logs 19-213089. True Azimuth 47" 40/ 24'/. Error 4" 30' 24'^ Dev. 17^ 10' 24" E. EX MERIDIAN. G. Date Feb. 21st, 6h. 42m. 40s. True Alt. 22° 7' 53". Dec. lO'' 04' 59". 1st Aug. 2m. 58s. ; 2nd Aug. 6ra. 16s. Lat. in 57^ 14' 30" N. STAR. Dec. le'^ 15' 37//. Lat 43° 53' 24/' S. DEVIATION. Correct Mag. Bearing S. 40" 24' W. 1st, 0° 16' W.; 2nd, 20" 14' E.; 3rd, 33" 4' E.; 4tb, 24" 54/ ; 5th, l** 6' \V. : 6th, 25" 46' W. ; 7th, 32" 16' W. ; 8th, 18" 36' W. ANSWERS TO PAPER THIRD. Multiplication 107755-7 Division 8-571 DAY'S WORK. Dep. Course N. 67d. E. 1st, course N. 14d. E. 2nd, N. 20d. E. 3rd, N. 37d. E. 4th, course N. 5th, course N. 6d. E. 6th, course N. 16d. E. 7th, or dep. course, S. 17d. E. True course N. 24d. E. Dist. 141 miles. Lat. in 46d. 21m. S. Long. 179d. 25m. W. MERIDIAN ALTITUDE. Dec. Od. 53m. 55s. True Alt. 89d. 6m. 54s. l^at. in Id. 46m. 41s. S. PARALLEL. Diff. Long. 686 miles. 120 HAND HOOK AND SELF-TKACHKK. MERCATOR. Course S. 64d. 54m. W. Dis. 2522 miles. TIDES. It Wick 1 Ih. 59m. A. M., no P. M. Cxrindstone Island Uh. 39ra. A. M., 111). 59m. P. M. r \MPLITUDE. G. Date March 18tli, Oh. 22m. 50h. Dec. Od. 18m. 49s. Dev. lid. 17m. 20s. E. CHRONOMETER. Daily rate 3s. 6t. Acct. rate 2m. 56s. 4t. (t. date March 25th, "ill. 52m. lis. Dec. 2d. 4m. 58s. True Alt. 30d. 40m. 17s. E(]uation 5m. 54s. .Hour Angle 3h. 53m. 24s. Long. 84d. 55m. 15s, W. AZIMUTH. True Alt. 18m. 58m. 8s. Dec. 2d. 13m. 52s. Sum of Logs 19-510903. True Azimuth N. ()9d. 25m. E. Error 5d. 54m. 40s. W. Deviation 20d. 24m. 40s. W. EX MERIDIAN. G-. Date March 18th, 14h. 30m. 24s. Dec. Od. 27m. 25s. S. True Alt. 43d. 18m. 5s. 1st Aug., + Om. 13s.; 2nd Aug., ■\- 23m. 30s. Lat. 45d. 51m. 00s. N. STAR. Dec. 19d. 49m. 25s. Lat. 39d. 39m. 16s. S. DEVIATION. Correct Mag. Bearing S. 47d. 53m. E. 1st, 4d. 33m. W.: 2nd, 18d. 37m. E. ; 3rd, 23d. 47m. E.; 4th. 12d. 37m. E.; 5th. 5d. 57m. W.; 6th, 6d. 43m. W.; 7tli, 28d. 23m. W. ; 8th, 2 Id. 23m. W. " Correct courses N. 22d. 30m. W. N. 67d. 30m. W. Compass courses S. 68d. E. N. 57d. 30m. E. ANSWKRS. 127 ANSWERS TO ]>APER FOURTH. ' Multiplication U8131-8 Division 10-00 DAY'S WORK. Dep course N. 62d. E ; 1st course S. 81d. W. ; 2ncl, course l'l-^;-5 .^yd course N. 3d. W.; 4th, course N. o3d. E. ; .5tb, course N. ; 6th co,„se N. 19d. W. ; 7th, or dop. course N. HOd! K; true course N. 8d. E. Distance 99 miles. Eat. in 44d 19m M. Long, m Cld. 2m. W. MERIDIAN ALTITUDE. Dec 8d lom. o5s.. True Alt. 23d. 4m. 41s. Lat. in 65d. lUm. 40s. N. PARALLEL. Diff. Long. 185-7 miles. iMI;:RCATOR. Course N. 51d. 36m. W. Dis. 4910 miles. TIDES. Anticosti Oh. 24m. A. M., Oh. 46m. i'. m. Banjoevvangie No A. M., Oh. 18m. P. M. ^ AMPLITUDE. G-. Date 10th April, 231i. 32m. 10s. Dec. 8d. lOm. 40s. T Amplitude E. 25d. 14m. N. Error 20d. 54m. 30s. W. Devi- ation lOd. 34m. W. CHRONOMETER. Daily rate 3s. It Acct. rate .-m. 25s. Cf. date 19tli, 15h. oOm 2.S Dec lid. 37m. ,34s. T. Alt. 32d. 12m. 53s. Equa- t^ionlm. lOs. Hour Angle 3h.oOm. 16s. Long. 179d. 39m. AZIMUTH. lo'^n^fict!^' n?- ^^?- ^t ^^''- ^^' 4^- 27s. Sum of Logs 19-.02196. Irue Az. S. 90d. 25m. W. Error lOd. 35m. E. Deviation Od. 16m. 15s. E. EX MERIDIAN. G. Date April 30th, 3h.^lm. 58s. Dec. 15d. OOm. 52s. True 128 HANI) BOOK AND HKI-F-TKACHKR. Alt. 47(1. 28m. 34s. 1st Aucr. , + 2m. 37s.; 2iul Au^^, 10m. 41s. Hour Aiij,4e 17m. o8s. l.iit. 57d. 24m. 14s. N. DEVIATION. Correct Ma|,r. Beariiijr S. Id. 21m. 30s. 1st. Od. 49m. K. ; 2nd, 2d. 41m. E. ; 3rd, lOd. olm. E. ; 4th, I3d. 31m. E. ; oth, 2d. 31m. E. ; 6th, lOd. 59m. W. ; 7th, 12d. 39m. W. ; 8th, 5d. 9m. W. Correct course N. 26d. 00m. E. S. 70d. 2()m. W . Compass course S. 49d. OOm. W. S. 8d. OOm. W. Ship's head S. IGd. 30m. E. N. Od. 40m. W. ANSWERS TO PAPER FIVE. Multiplication 13690-97 Division 1-142 DAY'S WORK. Dep. course N. 16d. E. 1st, S. 80d. E. ; 2nd, course N. 88d. E.; 3rd, N. Id. W. ; 4th, N. 14d. W.; 5th, N. 3d. W. ; 6th, S. 89d. E. ; 7th or dep. course, N. 77d. E. True course N. 42d. E. Dist. 110 miles. Lat. in 42d. 02ra. N. Long. 39d. 02m. W. MERIDIAN ALTITUDE. G. Date May 13th, 3h. 26m. 40s. Dec. 18d. 34m. 31s. Alt. 8 Id. 26m. 21s. Lat. 27d. 8m. 10s. N. PARALLEL. Diff. Long. 436-3. MERCATOR. Course N. 49d. 43m. W. Dist. 943-5. TIDES. Isle D'Yew, llh. 54m. A.M., no P. M. Batoo Barra, llh. 26m. A. M., llh. 54m. P. M. AMPLITUDE. G. Date 27th, I7h. 24m. Dec. 21d. 31m. 32s. True Amp. E. 35d.*39m. N. Error 38d. 28m. W. Deviation lOd. 28m. W. ANSVVKHS. 129 CHRONOMETER. G. Date 19th, 18h. 7m. 37s. Daily rate Im. 48. Acct. rate 2m. 2s. True Alt. 3«d. 4f)m. 548. Dec. 20d. ()3m. 3l>8. K(,ua- tioii 3m. 42s. Hour Angle 2h. o3m. lis. Lono-. 141(1. .)(im 308. E. AZIMUTH. G. Date 2()tli, 20h. 2()m. 2()s. True Alt. o2d. 49m. 27s. Dec 20d. 17m. 308. Sum of Lo^s 18-909105. True Az. 8. 33(1. (mu K. Krror 25d. 14m. E. Deviation 3«d. 24m. E. EX MERIDIAN. G. Date 20th, 7h. 4m. True Alt. 40d. 53m. 4.Ss. Dec. 20d. 10m. 24s. N. 1st Aug. 5m. (is.; 2nd Aug. I2m. 9s. Lat ()9d. 9m. 33s. N. STAR. True Alt. 28d. 47m. 17s. Dec. 8d. 7m. 27s. S. Lat. 53d. 5m. 16s. N. DEVIATION. Correct Mag. Bearings N. 42d. 24m. W. 1st, lOd. 5Gm. E • 2nd, 3d. 24m. W. ; 3rd, 18d. 54m. W. ; 4th, 24d. 44m W • 5th, 10d.4m. W.; 6th, lOd. 6m. E. ; 7th, 1 9d. 16m. E. : 8th' 15d. 56m. E. ' True courses 1st, N. 27d. 30m. E. ; 2d, S. 47d. 30m. W. C(^mpass courses 1st, N. 80d. 00m. E. ; 2d, N. 68d. 30m W Ship's head 1st, N. 5d. 30m. W.; 2nd, S. 29d. 20m. W. ANSWER TO PAPER SIXTH. Multiplicat on 25940000 Division 22-84 DAY'S WORK. Dep. course S. 77d. E. 1st, course N. 13d. E. ; 2nd, course N. 74d. E; 3rd, course N. 16d. W. ; 4th, course N. 52d. E. • oth, course N. 89d. E. ; 6th, course N. 24d. E. ; current course N. 41 d. E.; true course N. 44d. E. Dis. 196 miles. Lat. in 42d. 44m. N. Long. 78d. 49m. W. 17 130 HANI) HOOK AND SELF-TKACHKll. MERIDIAN ALTITUDE. G. Date 1 1th, 2()li. Im. True Alt. 44d. 2Hm. 4s Dec. 23d. llm. 30s. Lat. 22d. 20m. Is. PARALLEL. Diff. Long. 322-4. Long, in 17(i(l. IHni. K, MERCATOR. Course S. 22d. 49m. E. Dis. 3507 miles. TIDES. Hellvoetestiiis, 71i. 15m. A. M., 7h. 43m. P. M. Wanganirii, llh. 48m, A. M., No P. M. AMPLITUDE. G. Date 3rd, 51i. 42m. 40s. Dec. 22d. 25m. 3()s. True Amp. W. 39d. 28m. N. Error 4d. lOm. E. Dev. lOd. 22m. E. CHRONOMETER. G. Date lOtli, 18h. 2m. 308; rate 5s. gaining; ace. rate 2m. 34s. Dec. 23d. 27m. 2s. True Alt. 39d. Ira. 15s. H. Angle 3h. 34m. 36s. Equation Im. IGs. Long. 3(5d. Olm. E. azi:\ii;til G. Date 7h. 59m. 40s. Alt. 16d. 59m. 5s. Dec. 23d. 20m. 43s. N. Sum of Logs 19-815487. True Azimuth S. 107d. 55m. W. Error 89d. 06m. Dev. 3 Id. 35m. W. EX MERIDIAN. G. Date 14th, 48m. 10s. Hour Angle 27m. 6s. True Alt. 50d. 18m. 55s. Dec. 22d. 41m. 20s. 1st Aug. 8m. 30s. 2nd Aug. 24m. 56s. Lat. 62d. 6m. 15s. N. STAR. True Alt. 47d. Im. 7s. Dec. 57d. 51m. 33s. Lat. 14d. 52m. 30s. S. DEVIATION. Correct Mag. Bearing N. Id. 30m. W. 1st, 3d. 40m. W. 2nd, lid. 55m. E. 3rd, 13d. 30m. E. 4th, 6d. 40m. E. 5th, ANSWRnS. 181 True Courses, N. 38tl. P:., N. 88d. 30m. W. Compass (V)urse8, S. 28d. W., X. Ud. W Ship's head, N. 36d. 40m. E. S. Gld. 30m. M\ ANSWERS TO PAPER SEVENTH. Multiplication, 78699-8. Division, 1 1 -4436. DAY'S WORK. Dep. course S 16d. W. 1st, course S. 86d. W. ; 2nd, course S 89d. W . ; 3rd course S. 8b-d. W. ; 4th, course S. 80d. W. ; oth, course S. 75d. W. ; 6th, course S. 89d. W. Current course ^J iq ^'"\^°"^«« ^- 73d. W. Dist. 122 miles. Lat. in oOd. 49m. N. Long, in 12d. 34m. W. MERIDIAN ALTITUDE. 06m."m N^^"^' ^^'^' ^^'' ^''- ^^'^' ^^"'" ^^'' ^' ^'^^' '*^^- PARALLEL. Diff. Long. 180-6. MERCATOR. Course N. 34d. 25m. E. Dist. 7606-4. TIDES. 00?'^itllToh.'4Sn/p .1' """• '""• "• »•• "''■'■^"=-' AMPLITUDE. G. Date .30th, 1 Oh. 10m Dec. 18d. 16m. 52s. True Amp. ii-. 23d. 52m. N. Dev. OOd. 12m. W. ' CHRONOMETER. 3m\l%^^'\ "'•ffm 48s Daily rate 8s. 4t. ; ace. rate 6m. 18s. It. True Alt. 29c ' ■'m. gUs. Dec. 19d. 41m 14s 132 HAND BOOK AND SELF-TEACHER. AZIMUTH. Gr. Date 30th, 16h. 30tn. 40s. True Alt. 46d. 42m. 46s. Dec. I8d. 13rn. 00s. N. True Azimuth N. 19d. 40m. E. Error 28d. 00m. W. Deviation 20d. 30m. W. EX MERIDIAN. G. Date 29th, 2h. 40m. True Alt. 4 Id. 28m. 18s. Dec. 18d. 36m. 12s. 1st Aug. 9m. 42s.; 2nd Aug. 25m. 40s. Lat. 66d. olm. 54s. N. STAR. True Alt. 48d. 17m. 24s. Dec. 16d. 15m. 40s. N. Lat. 57d, 58m. 51s. N. DEVIATION. Correct Mag. Bearing, N, lid. 7m. E. Ist, Id. 35m. W. 2nd, 6d. Om. E. 3rd, 17d. E. 4th, 6d. E. 5th, 2d. W. 6th. 9d. W. 7th, lOd. W. 8th, 7d. W. True Courses, N. 63d. 30m. E. S. 87d. W. Compass Courses, S. 2ld. E. N. 27d. 30m. W. Ship's head, N. 18d. E. S. 69d. 30m. W. ANSWERS TO PAPER EIGHTH. Multiplication, 6909634-7. Division, 1-199. DAY'S WORK. Dep. course S. 63d. E. 1st, course S. 19d. E. ; 2nd, course S. 72d. W. ; 3rd, course S. 13d. W. ; 4th, course S. 61d. W. ; 5th, course N. 75d. W. ; 6th, course S. 9d. W. Current course S. 43d. E. True ccKse S. l8d. W. Dist. 87 miles. Lat. in 13d. 5m. N. Long. 176d. 51m. E. MERIDIAN ALTITUDE. True Alt. 51d. 48m. 9s. Dec. I2d. 22m. 54s. N. Lat. 50d. .^4m. 46s. N. PARALLEL. Diif. Long. 391-5. ANSWERS. 133 MERCATOR. Course N. 86d. 7m. E. Dist. 6644. TIDES. Cardigan, 4h. 28m. a. m., 4h. 58m. P. M. Tracadie,4h. 26m. A. M., 4h. 58m. P. M. AMPLITUDE. G. Date 24th, 19h. 19m. Dec. lOh. 38m. N. True Amp E. 15d. 51m. N. Deviation 7d. a9m. E. CHRONOxMETER. G. Date 14th, 201i. 58m. 40s. Daily rate Is. 2t. losing ; ace. rate Om. 59s. True Alt. lOd. 42m. 30s. Dec. 13d. 55m. 24s. Equation + 4d. 12m. H. A. 4h. 11m. 3s. Long. I6d. 22m. 30s. vV , AZIMUTH. G. Date 18th, 17h. 40m. True Alt. 46d. 41m. 27s. Dec 12d. 40m. 58s. N. True Az. N. 43d. 42m. E. Error 8d. 28m. W. Deviation 8d. 52m. E. EX MERIDIAN. G. Date 2nd, 3h. 28m. 2s. Dec. 17d. 35m. 30s. True Alt. 42d. 14ra. 5s. 1st Aug. 14m. 16s.; 2nd Aug. 40m. 2s. Lat. 65d. 35m. 40s. N. STAR. True Alt. 43d. 45m. 46s. Dec. 8d. 20m. 26s. Lat. 54d. a4m. 40s. S. DEVIATION. Correct Mag. Bearing N. 7 Id. 07m. W. 1st, 12m. 13s. E. 2nd, 43m. E. 3rd, 17d. 59m. W. 4th, 22d. 52m. W. 5th, 7d. 27m. \V. 6th, 12d. 3m. E. 7th, lOd. 33m. E. 8th, 12d. 43m. E. True Courses, N. 32d. W. S. 55d. E. Compass Courses, S. 35d. E. N. 59d. W. Ship's head, N. lid. 45m. W. S. 15d. 20m. W. 134 HAND BOOK AND SELF-TEACHER. ANSWERS TO PAPER NINTH. Multiplication, 185809-82. Division, 15-218. DAY'S WORK. Dep. course N. 22d. E. 1st, course N. lid. W. ; 2nd, course N. 4d. E.; 3rd, course N. 46d. E. ; 4th, course N. 69d. E. ; 5th, course N. 88d. E. ; 6th, course N. 66d. W. Current course N. 20d. E. True course N. 27d. 30m. E. Dist. 144 miles. Lat. in 53d. i7m. N. Long. 138d. 43m. W. MERIDIAN ALTITUDE. True Alt. 41d. 57m. 8s. Dec. Od. 7m. 59s. S. Lat. 47d. 22m. 55s. N. PARALLEL. Diff. Long. 278-2. MERCATOR. Course S. 31 d. 45m. E. Dist. 2364 miles. TIDES. Wells Bar, llh. 39m. A. M., no. p m. Tutukaka, llh. 57m. A. M., no P. M. AMPLITUb^: G. Date Sept. 8th, 21h. 40m. Dec. 5d. 8m. 7s. True Amp. E. 5d. 40m. N. Dev. lOm. E. CHRONOMETER. G. Date Sept. 1st, 16h. 9m. 54s. Daily rate 2s. 4t. Ac. rate 30s. True Alt. 62d. 9m. 36s. Dec. 7d. 48m. 49s. Equa- tion 30s. H. Angle Ih. 52m. 22s. Long. 130d. 29m. 30s. E. AZIMUTH. G. Date 1st, 18h. 26m. 50. True Alt. 34d. 20m. 25s. Dec. 7d. 47m. 42s. True Az. N. 72d. 8m. 48s. Error 8d. 21m. 12s. E. Deviation 13d. Im. 12s. E. ANSWERS. 23, EX MERIDIAN. Alf fisf^f P';f"" Yf-P""- '*"• 'O^'^- 4d. 54m. I6s. True STAK. SlI^k'^N. ""■ '""• ''" '''''■ ''"• ^«'»- 32- Ut. 41d. DEVIATION. Correct Mag. Bearing, N. Id. 38m. W. 1st dev 5d Sm W 2nd, 14d. 48m. E. 3rd, 16d. 32m. E. 4th 8d 52m V .)^ ' 3d.50n..E. Gth, 5d. 48m. W. Tth,' 13d!'58m: w"* 8^ f^^^^^^ True Courses, N. 45d. W. S. 50d. E. Compass Courses, S. 23d. W. S. 83d. E. Ship's head, S. 28d. 30m. E. N. 75d. 40m. E.