The Complete Mathematical and General Navigation Tables: Including Every Table Required with the Nautical Almanc in Finding the Latitude and Longitude: with an Explanation of Their Construction, Use, and Application to Navigation and Nautical Astronomy, Trigonometry, Dialling, Gunnery, Etc

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Simpkin, Marshall, & Company, 1838 - Nautical astronomy
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Contents

Logarithmic tangents to every second in the semicircle
97
Reduction of latitude on account of the spheroidal figure of the earth
105
Acceleration of the fixed stars or to reduce sidereal time to mean solar
117
A CoNcise System of Decimal Arithmetic
156
PLANE TR16 oxoMETRY
168
Given two sides and an angle opposite to one of them to find the other
178
Solution of PRobleMs IN RIGHT ANgled Sph ERIcs
184
Given the quadrantal side and the other two sides to find the three angles
195
Given two sides and the contained angle to find the other two angles
202
Given the three angles of a spherical triangle to find the sides
209
tude in
216
W Given both latitudes and the distance sailed to find the course and dif
229
Given both latitudes and the departure to find the course distance
232
IV Given both latitudes and the course to find the distance and the longi
242
Given one latitude course and difference of longitude to find the dis
248
How to find the true length of a knot on the log line 720
276
Island at Bass Strait
285
Spherical route from Port Jackson in New South Wales to Valparaiso
294
General Definitions 1 The phenomenon of day and night
296
The equinoctial
297
The ecliptic
298
The declination of a celestial object
299
The perihelion
300
Explanatory Articles 1 The division of time
301
The number of revolutions that the earth takes to complete the solar and the sidereal years
304
An apparent solar day
305
Anticipation of the fixed stars
306
Fršem Page
342
To compute the mean time of a planets transit over the meridian
353
To reduce the moons semidiameter horizontal parallax longitude
361
Given the observed mean time per watch of the suns transit over
368
Given the observed altitude of the lower or upper limb of the sun to find
374
To find the obliquity of the ecliptic
381
To find the latitude by the altitudes of two known fixed stars observed
405
ProBLEMs ReLATIVE to MEAN TIME c
426
Given the latitude and longitude of a ship and the observed altitude
435
Paoblems RELATIve to FINDING THE Altitudes of the HEAv ENLY Bodies
443
To deduce the longitude from a lunar distance when the altitudes are
519
PRoblems Relative to the WARIAtion of the CoMPAss
565
To reduce the magnetic course to the true course
577
ascension and declination
584
Given the latitudes and longitudes of the moon and sun or a fixed star to find the true central distance between them
588
PR on leMs RELATIve to the RisiNG AND Setti Ng of the CELEstiAL BoD1Es c c I To find the mean times of the suns rising and setting
593
To find the mean times of the moons rising and setting
596
To find the beginning and the ending of twilight
601
To find the time of the shortest twilight
603
To find when real night or darkness ceases c
604
To find the interval between the times of the suns limbs touching the horizon of a given place
605
PRoblems IN GNoMonics or DIALLING
606
To find the angles which the hourlines make with the substyle or me ridian line of a horizontal sundial
607
To find the angles on the plane of an erect dial
610
Paoblems IN MENsun ATION I To find the height of an accessible object
613
To find the allowance for the curvature of the earth
628
To reduce an elevated base line to the level of the sea
630
To find the height and distance of a mountain
633
To find the height of a mountain by means of two barometers c c
634
To find the distance of an object by observing the flash of a gun c c
635
To find the course steered by a ship seen at sea
636
PRobleMs 1N GUNNERY I Given the diameter of an iron ball to find its weight
640
To find the diameter of an iron hall
641
To find the diameter of a leaden ball
642
Given the diameters of an iron shell to find its weight
643
To find the size of a shell to contain a given weight of powder
644
To find the size of a cubical box to contain a given weight of powder
645
To find what length of a cylinder will be filled with a given weight of Powder
646
To find the number of balls in a square pile
647
To find the number of balls in a rectangular pile
648
To find the number of balls in an incomplete square pile
649
To find the number of balls in an incomplete rectangular pile
650
To find the velocity of any shot or shell
651
To find the terminal velocity of a shot or shell
652
To find the height from which a body must fall in vacuo to acquire a given velocity
653
To find the greatest range and the elevation to produce that range
655
Given the range at one elevation to find the range at another elevation
657
Given the charge for ome range to find the charge for another range
658
Given the range for one charge to find the range for another charge
659
Given the range and the elcvation to find the impetus
660
Given the range and the elevation to find the greatest altitude
662
Given the inclination of the plane c to find the impetus
663
To find the velocity of a shell when projected with a given charge of powder
664
To find the inpetus velocity and charge of powder
666
Given the inclination of the plane c to find the charge of powder
667
Given the inclination of the plane c to find the time of flight
668
Given the impetus c to find the horizontal range
669
Given the impetus c to find the time of flight on a horizontal plane
670
Given the inclination of the plane c to find the elevation
671
Given the time of flight c to find the elevation
674
Given the elevation c to find the horizontal range 67 1
675
Gšven the time of flight to find the length of the fuze
676
To find the time that a redhot ball will take to cool
677
PRoblems IN GAUGING
679
To reduce the old wine measure into imperial measure
680
To reduce the old ale measure into imperial measure
681
To find the contents of a cask in ale wine and imperial measure
682
WI Given the depth of the ullage to find the quantity in the cask
683
Given the depth of the ullage in a standing cask to find the quantity of liquor in the cask
686
Paoblems IN PRActic Al Navigation I To reduce the suns declination to the time of mean noon
689
Given the suns meridian altitude to find the latitude
691
Given the difference of longitude between two places to find their distance
693
Given the latitude and longitude sailed from to find those come to
695
Given the latitudes and course to find the distance and the longitude come to
698
To make out a days work at sea
700
Of the logbook
706
Of the measure of a knot on the logline
716

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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.
Page 210 - 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.
Page 262 - If two triangles have two angles of the one equal to two angles...
Page 63 - ... progression, to which those indices belong. Thus, the indices 2 and 3, being added together, make 5 ; and the numbers 4 and 8, or the terms corresponding to those indices, being multiplied together, make 32, which is the number answering to the index 5.
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.
Page 156 - RULE. Divide as in whole numbers, and from the right hand of the quotient point off as many places for decimals as the decimal places in the dividend exceed those in the divisor.
Page 157 - 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.
Page 158 - REDUCTION OF DECIMALS. CASE I. . To reduce a Vulgar Fraction to a Decimal Fraction of equal value.
Page 181 - II. The sine of the middle part is equal to the product of the cosines of the opposite parts.
Page 247 - II. the difference of latitude and departure corresponding to each course and distance, and set them in their respective columns : then the difference between the sums of the northings and southings will be the difference of latitude made good, of the same name with the greater ; and the difference between the sums of the eastings and westings will be the departure made good, of the same name with the greater quantity.

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