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SIGNS and Abbreviations used in to a degree of longitude at every 1 Questions to exercise the learner Demonstration of the most useful Middle latitude sailing 66 7 Theorerns in middle latitude sail- 13Table of solutions of the several 17 cases of middle latitude sailing 68 Construction of the plane scale 20 Questions to exercise the learner Description of Gunter's scale 21 in middle latitude sailing Description and use of the sliding 24 To find the meridional parts cor- Description and use of the sector 26 responding to any degree and To find the logarithm of any num minute 29 Table of solutions of the various Multiplication by logarithms 31 cases of Mercator's sailing 31 To work a compound course by 32 middle latitude or Mercator's The rule of three by logarithms S2 Construction and use of Merca- To calculate compound interest tor's chart 33 of the log-line and half-minute To find the log. sine, tangent, &c. glass corresponding to any number Description and use of a quadrant To find the degrees, minutes, and To adjust a quadrant seconds corresponding to any To take an altitude by å fore ob- To find the arithmetical comple To take the sun's altitude by a 55 Advice to seamen in the choice of Table of solutions of the various a quadrant 93 36 Description and use of a sextant Right-angled plane trigonometry 37 of reflection 94 95 A short introduction to astronomy To measure the angular distance Esplanations of the terms ūsed in Verification of the mirrors and co- 50 Description and uses of the circle A table of the angles which every Adjustments of the circle of reflec- -100 52 To observe the ineridian altitude A table of solutions of the several of an object by a circle 102 53 To measure the angular distance Questions to exercise the learner of the sun from the moon by a 59 To measure the angular distance of 63 the moon from a star by a circle 104 Theorems for solving the several Verification of the mirrors and cases of parallel sailing 64 coloured glasses A table showing how many miles On parallax, refraction, and dip 103 To find the distance of the land in Second method of finding the ap- 156 To find the sun's declination 110 Third method of finding the appa- To observe an amplitude or azi To find the apparent time by an To calculate the true amplitude 112 To regulate a watch by equal alti- To calculate the true azimuth 113 tudes of the sun Questions to exercise the learner To find the longitude at sea by lu- Having the true and magneticam Method of finding the stars used plitude or azimuth, to find the in lunar observations 114 General observations on the tak- To calculate the variation by azi ing a lunar observation muths observed at equal alti To work a lunar observation 166 tudes before and after passing Examples of lunar observations 168 115 Second method of working a lu- On the dip of the magnetic needle 119 Witchell's improved method of altitude of the sun or fixed star 120 Method of taking a lunar observa- To find the time of the moon's tion when you have only one To find the moon's declination 124 To calculate the sun's altitude at To find the latitude by the moon's 125 To calculate the altitude of any To find the latitude by the meri star 178 To find the latitude by double al moon 128To find the longitude by the eclip- 128 ses of Jupiter's satellites 129 To find the longitude by an eclipse 130 To find the longitude by a time- of two different objects, keeper or chronometer taken within a few minutes of To regulate a chronometer by lu- each other, by one observer 130 nar observations - of two different objects, To find the longitude by a varia- 133 Problems useful in navigation 186 138 To find the difference between the 191 in working double altitudes 148To determine the height of a To find the latitude by one alti mountain by barometers 192 tude of the sun, having your Mensuration 193 watch previously regulated 148 Gauging 197 To find the latitude by the mean Surveying 199 of several altitudes of the sun To find the content of a field ly taken near noon by a sextant or the table of diff. lat. and depart- circle 150 ure 201 To find the latitude on shore hy To survey a coast in sailing along means of an artificial horizon 159 shore 203 To find the latitude by the polar To survey a harbour by observa- star 158 tions on shore • 205 To find the time at sea and regu.. Methods of surveying a small late a watch 154 bank or shoal where great accu- Examples to exercise the learner racy is required 206 in finding the apparent time 156) To reduce soundings taken at any Problem VII. To calculate the time of the tide to low water 209 longitude of a place from the To reduce a draught to a smaller observed beginning and end of 210 Problem VIII. To find the longi- Directions for sailing from Ameri tude of a place from the begin- 212 ning or end of a solar eclipse 589 213 Problem IX. To find the longi- To find the time of high water by tude of a place from the begin- 214 ning or end of an occultation 590 To find the time of high water by Problem X. To project an eclipse Tables for calculating the time of Problem XI. To project an eclipse 218 Problem XII. To project an oc- Method of keeping a reckoning at Problem XIII. To calculate the 219 beginning or end of in eclipse To find the lee way and allow forit 221 To correct the dead reckoning 223 Problem XIV. To find the appa- Rules for working a day's work 225 rent time at Greenwich from Examples for working a day's the moon's longitude 227 Problem XV. To find the longi- Journal from Boston to Madeira 231 tude of a place by measuring Explanations of sea terms 249 the distance of the moon from 264 a fixed star not marked in the Catalogue of the Tables, with ex Nautical Almanac amples of the uses of those not Problem XVI. To find the longi- explained in other parts of the tude of a place by the moon's Tables from I. to XLVIII. Problem XVII. Given the lati- tude of the moon and longi- Addition and subtraction, using find their angular distance 605 571 Problem XVIII. Given the longi- Problem I. To find the longitude, tudes and latitudes of the moon 571 and a star to find their angular Problem II. To find the horary distance 574 Problem XIX. Given the right Problem III. To find the eclip ascension and declination to the moon and sun, or a star 575 Problem XX. Given the longi- and longitude of the nonagesi right ascension and declination 607 607 Table to facilitate the calcula Improvement of Napier's rules Abridged rule for calculating the Theorems in Spheries 609 altitude and longitude of the On finding the latitudes by two Problem V. To calculate the Examples for exercise 614 moon's parallax in latitude and Table shewing the variation of the 580 altitude of an object arising Problem VI. To calculate the lon from a change of 100 seconds gitude of a place from the ob in its declination served beginning and end of a Table XX. (New Form) correc 583! tions in seconds, additive 618 ARRANGEMENT OF THE TABLES. Table. Table. DIFFERENCE of latitude To find the time of the moon's and departure for points I passing the meridian XXVIII Ditto, for degrees II Correction of the moon's altiMeridional parts UNI tude for parallax and refracSun's declination IV tion XXIX Equation of Time IV To find the moon's declinaFor reducing the Sun's declina tion XXX tion V To find the sun's right ascen- XXXI Correction for the daily varia Variation of the sun's altitude tion of the Equation of Time VI in one minute from noon XXXII Amplitudes VII To reduce the numbers of Table Right ascensions and declina XXXII. to other given intertions of the fixed stars VIII vals from noon XXXIII Sun's rising and setting IX Errors arising from a deviation For finding the distance of ter of one minute in the parallelrestrial objects at sea X ism of the surfaces of the cen- XXXIV Refraction of the heavenly bo Error arising from a deviation dies XII of the telescope from a plane Dip of the horizon XIIT parallel to the plane of the inSun's parallax in altitude XIV strument XXXV Augmentation of the moon's Correction of the mean refracsemidiameter XV tion for various heights of the Dip for different heights and thermometer and baromedistances XVI XXXVI To find the correction and loga Longitudes and Latitudes of rithm of a lunar observation the fixed stars XXXVII when a star is used XVII Reduction of latitude and horiTo find the correction and loga zontal parallax XXXVIII rithm of a lunar observation Aberration of the planets in lonwhen the sun is used XVIII gitude XXXIX To find the correction and loga Equation of the equinoxes in rithm of a lunar observation longitude XL depending on the moon's al Aberration of the fixed stars in titude XIX "latitude and longitude XLI For finding the third correction Aberration of the fixed stars in of a lunar observation XX right ascension and declina(New Form) Corrections in se XLII conds additive. See Append Nutation in right ascension and ix, page 618 XX declination XLIII For turning degrees and min Augmentation of the moon's utes into time, and the con semidiameter, found by nonatrary XXI gesimal XLIV Proportional logarithms XXII Equation of second differences XLV For finding the latitude by two Table of latitudes and longialtitudes of the sun XXIII tudes XLVI Natural sines and co-sines XXIV Tide Table XLVIE Log. sines, tangents, &c. to Table, shewing the variation points and quarter points XXV of the altitude of an object. Logarithms of numbers XXVI arising from a change of 100 Logarithmic sides, tangents, seconds in its declination, and secants XXVH (page 616) XLVIII tion + Is the sign of addition, and denotes that whatever number or quantity follows the sign, must be added to those that go before it, thus 9+8 signifies that 8 is to be added to 9. Or A+B implies that the quantities represented by A and B are to be added. The sign + is called the positive sign. The sign of subtraction; and denotes that the number following it must be subtracted from those going before it, thus 7–5, signifies that 5 must be subtracted from 7. The sign – is called the negative sign. x Is the sign of multiplication, and shows that the numbers placed before and after it are to be multiplied, thus, 7 X 9 signifies 7 multiplied by 9, which makes 63; and 7 X 8 X 2 signifies the continued product of 7 by 8 and by 2, which makes 112. Multiplication is also denoted by placing a point between the quantities to be multiplied; thus A.B signifies that A is to be multiplied by B. - Is the sign of division, and signifies that the number that stands before it is to be divided by the number following it, as 72+12 shows that 72 72 12 O or Either of these marks is used for connecting numbers together, thus, 3+4x6, or (3+4) X 6, signifies that the sum of 3 and 4 is to be multiplied by 6. = Is the sign of equality, and shows that the numbers or quantities placed before it are equal to those following it: thus 8 X 12=96. Or 8 mul tiplied by 12 are equal to 96, and 7+2X4=36. :::: Is the sign of proportion, and is marked thus, 7 : 14 :: 10 : 20, that is, as 7 is to 14, so is 10 to 20. Or A:B::C:D, that is, as A is to B, so is C to D. Signifies minutes; thus, 24' or 24 minutes, Signifies thirds or sixtieth parts of seconds ; thus, 44"", or 44 thirds. S. Signifies sine. N. S. Signifies Natural sine. Sec. Signifies Secant. Tan. Signifies Tangent. Co-sine, Co-tangent, or Co-secant of an arch signifies the sine, tangent or secant of the complement of that arch respectively. < Signifies Angle; with an s at top Angles, <s. Ad Angled, A Signifies Triangle. A's Triangles. Signifies a square. O or the Sun. O or ) the Moon. * a Star. L. L. Lower Limb. U.L. Upper Limb. N. L. Nearest Limb. S. D. Semi-diameter. P. L. Proportional Logarithm. N. A. Nautical Almanac. 2. D. Zenith Distance. D. R. Dead Reckoning. |