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SIGNS and Abbreviations used in

to a degree of longitude at every

this work

degree of latitude


Decimal Arithmetic

1 Questions to exercise the learner


4 in parallel sailing


Demonstration of the most useful Middle latitude sailing


propositions of geometry

7 Theorerns in middle latitude sail-

Demonstration of theorems in



plage trigonometry

13Table of solutions of the several

Geometrical problems

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

Mercator's sailing



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

ber and the contrary

29 Table of solutions of the various

Multiplication by logarithms 31 cases of Mercator's sailing

Division by logarithms

31 To work a compound course by

Involution by logarithms

32 middle latitude or Mercator's

Evolution by logarithms

32 sailing

The rule of three by logarithms S2 Construction and use of Merca-

To calculate compound interest tor's chart


by logarithms

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

of degrees and minutes

of reflection


To find the degrees, minutes, and To adjust a quadrant


seconds corresponding to any To take an altitude by å fore ob-

log. sine, tangent, &c.

34 servation


To find the arithmetical comple To take the sun's altitude by a

ment of any logarithm

34 back observation

Plane trigonometry

55 Advice to seamen in the choice of

Table of solutions of the various

a quadrant


cases of trigonometry

36 Description and use of a sextant

Right-angled plane trigonometry 37 of reflection

Questions to exercise the learner in To adjust a sextant

right-angled plane trigonometry 40 To measure the angular distance

Oblique trigonometry

40 of the sun from the moon


A short introduction to astronomy To measure the angular distance

and geography

44 of the moon from a star


Esplanations of the terms ūsed in Verification of the mirrors and co-

astronomy and geography

47 loured glasses


Examples ia geography

50 Description and uses of the circle

Plane Sailing

51 of reflection


A table of the angles which every Adjustments of the circle of reflec-
pojnt of the compass makes tion


with the meridian

52 To observe the ineridian altitude

A table of solutions of the several of an object by a circle


cases of plane sailing

53 To measure the angular distance

Questions to exercise the learner of the sun from the moon by a

in plane sailing

58 circle

Traverse sailing

59 To measure the angular distance of

Parallel sailing

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

of meridian distance correspond of the horizon





To find the distance of the land in Second method of finding the ap-
order to calculate the dip 109 parent time at sca


To find the sun's declination 110 Third method of finding the appa-

Variation of the compass

111 rent time at sea


To observe an amplitude or azi To find the apparent time by an

muth by the compass

112 altitude of a fixed star


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-

in calculating an azimuth


nar observations


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

the meridian

115 Second method of working a lu-

Variation observed

117 nar observation


On the dip of the magnetic needle 119 Witchell's improved method of
To find the latitude by a meridian finding the true distance 175

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

passing the meridian

1231 observer


To find the moon's declination 124 To calculate the sun's altitude at

To find the latitude by the moon's


meridian altitude

125 To calculate the altitude of any

To find the latitude by the meri star

dian altitude of a planet 127 To calculate the altitude of the

To find the latitude by double al moon



128To find the longitude by the eclip-

of the sun

128 ses of Jupiter's satellites


of a star

129 To find the longitude by an eclipse

of a planet

129 of the moon


of the moon

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-

taken at different times


tion chart


First method

133 Problems useful in navigation 186

Second method

138 To find the difference between the

Third method


true and apparent directions of

Questions to exercise the learner the wind


in working double altitudes 148To determine the height of a

To find the latitude by one alti mountain by barometers


tude of the sun, having your Mensuration


watch previously regulated 148 Gauging


To find the latitude by the mean Surveying


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-


150 ure


To find the latitude on shore hy To survey a coast in sailing along

means of an artificial horizon 159 shore


To find the latitude by the polar To survey a harbour by observa-


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


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 an occultation


Of winds

210 Problem VIII. To find the longi-

Directions for sailing from Ameri tude of a place from the begin-

ca to India

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-

a Nautical Almanac

214 ning or end of an occultation 590

To find the time of high water by Problem X. To project an eclipse

the tables C and D

216 of the moon


Tables for calculating the time of Problem XI. To project an eclipse

high water

217 of the sun



218 Problem XII. To project an oc-

Gulf Stream

218 cultation of a fixed star


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

or occultation


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

Evolutions at sea

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



passage over the meridian 604

Tables from I. to XLVIII. Problem XVII. Given the lati-

tude of the moon and longi-


tudes of the moon and sun to

Addition and subtraction, using find their angular distance 605
the signs as in algebra

571 Problem XVIII. Given the longi-

Problem I. To find the longitude, tudes and latitudes of the moon

latitude, &c. of the moon

571 and a star to find their angular

Problem II. To find the horary distance


motion of the moon

574 Problem XIX. Given the right

Problem III. To find the eclip ascension and declination to
• fic conjunction or opposition of find the longitude and latitude 606

the moon and sun, or a star 575 Problem XX. Given the longi-
Problem IV. To find the altitude tude and latitude to find the

and longitude of the nonagesi right ascension and declination 607
577 Spheric Trigonometry


Table to facilitate the calcula Improvement of Napier's rules


578 for the circular parts


Abridged rule for calculating the Theorems in Spheries


altitude and longitude of the On finding the latitudes by two


579 altitudes


Problem V. To calculate the Examples for exercise


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
solar eclipse

583! tions in seconds, additive 618



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


tude for parallax and refracSun's declination IV tion

XXIX Equation of Time


To find the moon's declinaFor reducing the Sun's declina


XXX tion

V To find the sun's right ascen-
Sun's right ascension
VI sion

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-
Proportional parts
XI tral mirror

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


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


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


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)



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+ 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
is to be divided by 12. Division may also be denoted by placing two
points between the numbers, thus, 72 : 12 represents 72 divided by 12

or by placing the numbers thus, - which signifies 72 divided by 12.

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 degrees; thus, 45° represents 45 degrees. .

Signifies minutes; thus, 24' or 24 minutes,
Signifies seconds; thus, 44", or 44 seconds.

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.

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