The Complete Mathematical and General Navigation Tables: Including Every Table Necessary to be Used with the Nautical Almanac in Finding the Latitude and Longitude : with Their Description and Use, Comprising the Principles of Their Construction, and Their Direct Application to Plane and Spherical Trigonometry, Navigation, Nautical Astronomy, Dialling, Practical Gunnery, Mensuration, Guaging &c. &c, Volume 1

Thomas Kerigan

Baldwin and Cradock, 1828 - Nautical astronomy - 664 pages

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Page 527

Table of Contents

Table Page I To convert longitude or degrees into time and conversely	1

Depression of the horizon	3

the earths surface 613	4

Dip of the horizon at different distances from the observer	6

Augmentation of the moons semidiameter	8

Parallax of the planets in altitude	12

Parallax of the sun in altitude	13

Correction of the mean astronomical refraction	15

The miles and parts of a mile in a degree of longitude at every degree of latitude	144

Table Page	145

A general table for gauging or finding the content of all circular	152

SOLUTION OF PROBLEMS IN PlanE AND SPHERICAL Trigono	168

NAVIGATION	211

Solution of problems relative to the errors of the log line and	272

SOLUTION OF PROBLEMS IN NAUTICAL ASTRONOMY	296

Problem Page	297

To find the latitude by the north polar star	17

Correction of the latitude deduced from the preceding table	20

Mean right ascension of the sun	21

Equations to equal altitudes of the sun part First	22

To reduce the suns longitude right ascension and declination and also the equation of time as given in the Nautical Almanac to any given time under ...	25

To reduce the moons longitude latitude right ascension declin ation semidiameter and horizontal parallax as given in the Nautical Almanac to any giv...	30

Equation of the second difference of the moons place	33

Correction of the moons apparent altitude	38

To reduce the true altitudes of the sun moon stars and planets to their apparent altitudes	40

Auxiliary angles	42

Correction of the auxiliary angle when the moons distance from a planet is observed	45

Error arising from a deviation of one minute in the parallelism of the surfaces of the central mirror of the circular instrument of reflection	46

Error arising from an inclination of the line of collimation to the plane of the sextant or to that of the circular instrument of re flection	47

Logarithmic difference	48

Table Page XXV Correction of the logarithmic difference for the suns or stars appa rent altitude	51

Correction of the logarithmic difference for a planets apparent altitude	52

Natural versed sines and natural sines	53

Logarithms of numbers	62

Proportional logarithms	75

Logarithmic half elapsed time	84

Logarithmic middle time	86

Logarithmic rising	87

To reduce points of the compass to degrees and conversely	89

Logarithmic secants to every second in the semicircle	90

Logarithmic sines to every second in the semicircle	93

Logarithmic tangents to every second in the semicircle	97

To reduce the time of the moons passage over the meridian of Greenwich to the time of her passage over any other meridian	100

Correction to be applied to the time of the moons reduced transit in finding the time of high water at any given place	102

Reduction of the moons horizontal parallax on account of the spheroidal figure of the earth	104

Reduction of terrestrial latitude on account of the spheroidal figure of the earth	105

A general traverse table or difference of latitude and departure	106

Meridional parts	113

The mean right ascensions and declinations of the principal fixed stars	114

Acceleration of the fixed stars or to reduce sidereal time into mean solar time	117

To reduce mean solar time into sidereal time	119

Altitude of a celestial object when its centre is in the prime ver tical most proper for determining the apparent time with the greatest accuracy	120

Amplitudes of a celestial object reckoned from the true east or west point of the horizon	122

To find the times of the rising and setting of a celestial object	123

For computing the meridional altitude of a celestial object the latitude and the declination being of the same name	138

To find what stars will be on or nearest to the meridian at	319

Given the observed central altitude of a planet to find its true	325

Given the meridian altitude of a planet to find the latitude	333

Problem Page	337

Given the latitude by account the altitude of a fixed star observed	365

SOLUTION OF PROBLEMS RELATIVE TO THE APPARENT Time	375

Of computing the horary distance of a celestial	392

Problem Page	394

SOLUTION OF PROBLEMS RELATIVE TO FINDING THE ALTITUDES	403

Solution of PROBLEMS RELATIVE TO THE LONGITUDE	413

chronometer or timekeeper	423

distance	433

Problem Page	439

Of reducing the apparent to the true central	445

Of reducing the apparent to the true central	451

tude by account to find the true longitude of the place	470

To find the longitude of a place by the eclipses of the moon	481

Given the latitude of a place the suns altitude and his magnetic	487

rising and setting	506

SOLUTION OF PROBLEMS in GNOMONICS or DIALLING	522

RELATIVE	528

Problem Page	531

Given the distances between three objects situated in a straight	541

Given a base line measured on any elevated level to find its true	547

Given three bearings of a ship sailing upon a direct course	553

find its weight	560

Problem Page	564

To find the number of balls or shells in an incomplete rectangnlar	570

Given the range at one elevation to find the range at another	576

Given the inclination of the plane the elevation of the piece	582

Given the impetus and the elevation to find the horizontal range	589

SOLUTION OF PROBLEMS IN GAUGING	596

SOLUTION OF MiscellaNEOUS PROBLEMS	607

To find the distance of the sun from the earth	614

of the earth	649

SOLUTION OF USEFUL ASTRONOMICAL PROBLEMS	672

doctrine of compound interest	687

Description and use of the general victualling table	717

Common terms and phrases

according added addition angle answering apparent altitude applied approximate arch centre co-secant co-sine column computed Constant log contained Correction corresponding course declination degrees departure determined Diff difference of latitude difference of longitude dist distance divided east equal equation error Example feet give given Greenwich half height hence horizontal parallax hypothenuse interval January less limb logarithmic lower mean measured meridian method middle miles minutes Moon's moon's apparent natural number natural versed sine Nautical noon object observed altitude opposite place of observation planet's points polar Problem Prop proportional radius reduced refraction remainder right ascension rising RULE sailed secant seconds semi-diameter setting ship side spherical star star's subtracted Sun's Sun's right ascension Table taken tangent third transit triangle true altitude variation watch

Popular passages

Page 19 - Given two sides and the included angle, to find the third side and the remaining angles. The sum of the required angles is found by subtracting the given angle from 180�. The difference of the required angles is then found by Theorem II. Half the difference added to half the sum gives the greater angle, and, subtracted, gives the less angle.

Appears in 29 books from 1816-2004

Page 484 - AZIMUTH, in astronomy, an arch of the horizon, intercepted between the meridian of the place and the azimuth, or vertical circle passing through the centre of the object, which...

Appears in 17 books from 1802-1852

Page 212 - For the purpose of measuring angles, the circumference is divided into 360 equal parts, called degrees ; each degree into 60 equal parts, called minutes ; each minute into 60 equal parts called seconds.

Appears in 147 books from 1732-1966

Page 63 - And, if the logarithm of any number be divided by the index of its root, the quotient will be equal to the logarithm of that root. Thus the index or logarithm of 64 is 6 ; and, if this number be divided by 2, the quotient will be = 3, which is the logarithm of 8, or the square root of 64.

Appears in 20 books from 1801-2006

Page 63 - Also, between the mean, thus found, .and the nearest extreme, find another geometrical mean, in the same manner ; and so on, till you are arrived within the proposed limit of the number whose logarithm is sought.

Appears in 21 books from 1811-1917

Page 487 - ... reckoned from the north in north latitude, but from the south in south latitude. � In observations of the altitude of the sun'< loiter limb (by afore enervation) it is u�u�l to �<M 12' for tic cBecl of dip, parallax, ami sern diameter.

Appears in 11 books from 1765-1858

Page 159 - When there happens to be a remainder after the division ; or when the decimal places in the divisor are more than those in the dividend ; then ciphers may be annexed to the dividend, and the quotient carried on as far as required.

Appears in 20 books from 1812-1883

Page 681 - The Young Navigator's Guide to the Sidereal and Planetary Parts of Nautical Astronomy.

Appears in 27 books from 1820-1917

Page 649 - ... position with respect to a luminous body, can cast a circular shadow ; likewise all calculations of eclipses, and of the places of the planets, are made upon supposition that the earth is a sphere, and they all answer to the true times when accurately calculated. When an eclipse of the moon happens, it is observed sooner by those who live eastward than by those who live westward ; and, by frequent experience, astronomers have determined that, for every fifteen degrees difference of longitude,...

Appears in 9 books from 1811-1876

Page 183 - II. The sine of the middle part is equal to the product of the cosines of the opposite parts.

Appears in 132 books from 1723-2002

Bibliographic information

QR code for The Complete Mathematical and General Navigation Tables

Title	The Complete Mathematical and General Navigation Tables: Including Every Table Necessary to be Used with the Nautical Almanac in Finding the Latitude and Longitude : with Their Description and Use, Comprising the Principles of Their Construction, and Their Direct Application to Plane ..., Volume 1 The Complete Mathematical and General Navigation Tables: Including Every Table Necessary to be Used with the Nautical Almanac in Finding the Latitude and Longitude : with Their Description and Use, Comprising the Principles of Their Construction, and Their Direct Application to Plane and Spherical Trigonometry, Navigation, Nautical Astronomy, Dialling, Practical Gunnery, Mensuration, Guaging &c. &c, Thomas Kerigan
Author	Thomas Kerigan
Publisher	Baldwin and Cradock, 1828
Original from	the University of California
Digitized	29 Oct 2007
Length	664 pages

Export Citation	BiBTeX EndNote RefMan

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