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XXVIII. Logarithms of numbers..
Table.
Page.
XXV. Correction of the logarithmic difference for the sun's, or star's appa-
rent altitude
51
XXVI. Correction of the logarithmic difference for a planet's apparent
52
XXVII. Natural versed sines, and natural sines
53
62
75
84
XXXI. Logarithmic middle time
XXXII. Logarithmic rising...
86
87
XXIX. Proportional logarithms..
XXX. Logarithmic half elapsed time
XXXIII. To reduce points of the compass to degrees, and conversely....
XXXIV. Logarithmic sines, tangents, and secants to every point and quar-
97
XXXV. Logarithmic secants to every second in the semi-circle
XXXVI. Logarithmic sines to every second in the semicircle...
XXXVII. Logarithmic tangents to every second in the semicircle
XXXVIII. To reduce the time of the moon's passage over the meridian of
Greenwich to the time of her passage over any other meridian 100
XXXIX. Correction to be applied to the time of the moon's reduced transit
in finding the time of high water at any given place.......... 102
Reduction of the moon's horizontal parallax on account of the
spheroidal figure of the earth..
XL.
XLI.
... 104
Reduction of terrestrial latitude on account of the spheroidal
figure of the earth .....
105
XLII. A general traverse table, or difference of latitude and departure 106
XLIII. Meridional parts .... .... 113
XLIV. The mean right ascensions, and declinations of the principal fixed
stars
.... 114
XLV.
117
Acceleration of the fixed stars, or to reduce sidereal time into
mean solar time ...
XLVI. To reduce mean solar time into sidereal time....
XLVII. Time from noon when the sun's centre is in the prime vertical;
being the instant at which the altitude of that object should be
observed, in order to ascertain the apparent time with the great-
est accuracy...
XLVIII. 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
XLIX. Amplitudes of a celestial object reckoned from the true east or
west point of the horizon
122
L.
LI.
LII.
LIII.
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
latitude and the declination being of contrary names ..... 138
The miles and parts of a mile in a degree of longitude at every
degree of latitude .....
144
LIV.
LV.
LVI.
LVII.
Proportional miles for constructing Mercator's charts....
To find the distance of terrestrial objects at sea ...
To reduce the French centesimal division of the circle into the
English sexagesimal division; or, to reduce French degrees
into English degrees, and conversely
145
147
... 150
A general table for gauging, or finding the content of all circular
headed casks......
LVIII. Latitudes and longitudes of the principal sea-ports, islands, capes,
shoals, &c. in the known world; with the time of high water,
at the full and change of the moon, at all places where it is
known.....
Alphabetical reference to the preceding table
Form of a transit table .....
152
154
155
Miscellaneous numbers with their corresponding logarithms
A table showing the true time and degree at which the hour and
minute hands of a well-regulated watch, or clock, should
exactly meet, or be in conjunction, &c. in every revolution.... 155
A concise system of decimal arithmetic
156
SOLUTION OF PROBLEMS IN PLANE, AND SPHERICAL TRIGONO-
METRY
......
168
Plane trigonometry, solution of right angled triangles ........ 171
solution of oblique angled triangles........ 177
Spherical trigonometry, solution of right angled triangles.. 181 182
solution of quadrantal triangles
solution of oblique angled triangles.... 197
Solution of problems relative to the difference of latitude and dif-
ference of longitude
Solution of problems relative to the errors of the log line and the
Solution of a very useful problem in great circle sailing..
To find the time of high water at any known place To make out a day's work at sea by inspection.....
272
SOLUTION OF PROBLEMS IN NAUTICAL ASTRONOMY
To convert longitude, or parts of the equator into time
To convert time into longitude or parts of the equator
Given the time under any known meridian, to find the corres-
296
ponding time at Greenwich
297
Problem.
IV.
Given the time at Greenwich, to find the corresponding time
under a known meridian....
V.
VI.
VII.
To reduce the sun's longitude, right ascension, declination, and,
also, the equation of time as given in the Nautical Almanac,
to any other meridian, "and to any given time under that
meridian
To reduce the moon's longitude, latitude, right ascension, declin-
ation, semi-diameter, and horizontal parallax, as given in the
Nautical Almanac, to any other meridian, and to any given
time under that meridian
To reduce the right ascension and declination of a planet, as
given in the Nautical Almanac, to any given time under a
known meridian
298
302
307
...
VIII.
To compute the apparent time of the moon's transit over the me-
ridian of Greenwich .....
... 309
IX.
Given the apparent time of the moon's transit over the meridian
of Greenwich, to find the apparent time of her transit over any
other meridian......
312
X.
To compute the apparent time of a planet's transit over the meri-
dian of Greenwich ...
313
XI.
Given the apparent time of a planet's transit over the meridian of
Greenwich, to find the apparent time of its transit over any
other meridian.....
To find the apparent time of a star's transit over the meridian of
any known place...
317
XIII.
To find what stars will be on, or nearest to the meridian at any
given time ...
319
XV.
XVI.
XIV. Given the observed altitude of the lower or upper limb of the
sun, to find the true altitude of its centre
Given the observed altitude of the lower or upper limb of the
moon, to find the true altitude of her centre....
Given the observed central altitude of a planet, to find its true
altitude
XVII.
Given the observed altitude of a fixed star, to find its true
327
SOLUTION OF PROBLEMS RELATIVE TO THE LATITUDE..
328
I.
Given the sun's meridian altitude, to find the latitude of the
place of observation.....
... 328
II.
Given the moon's meridian altitude, to find the latitude of the
place of observation...
330
III.
Given the meridian altitude of a planet, to find the latitude of
the place of observation
333
.....
Given the meridian altitude of a fixed star, to find the latitude of
the place of observation ..
Given the meridian altitude of a celestial object observed below
the pole, to find the latitude of the place of observation...... 336
VI. Given the altitude of the north polar star, taken at any hour of
the night; to find the latitude of the place of observation.... 337
VII. Given the latitude by account, the sun's declination, and two
observed altitudes of its lower or upper limb; the elapsed time,
and the course and distance run between the observations; to
find the latitude of the ship at the time of observation of the
greatest altitude ...
XII.
341
354
Given the altitudes of two known fixed stars observed at the same
instant, at any time of the night; to find the latitude of the
place of observation, independent of the latitude by account,
the longitude, or the apparent time of observation 347
Given the latitude by account, the altitude of the sun's lower or
upper limb, observed within certain limits of noon, the
apparent time of observation, and the longitude; to find the
true latitude of the place of observation.....
Given the latitude by account, the altitude of the moon's lower or
upper limb, observed within certain limits of the meridian, the
latitude of the place of observation...
Given the latitude by account, the altitude of a planet's centre
observed within certain limits of the meridian, the apparent
time of observation, and the longitude; to find the true latitude
of the place of observation
Given the latitude by account, the altitude of a fixed star observed
within certain limits of the meridian, the apparent time of
observation, and the longitude; to find the true latitude of the
place of observation......
358
... 362
365
.... 368 369
To find the latitude by an altitude taken near the meridian below
the pole .....
Captain William Fitzwilliam Owen's general Problem for finding
the latitude....
371
Given the interval of time between the rising or setting of the
sun's upper and lower limbs; to find the latitude....
373
SOLUTION OF PROBLEMS RELATIVE TO THE APPARENT TIME...... 375
To find the error of a watch by equal altitudes of the sun...... 377
To find the error of a watch by equal altitudes of a fixed star .. 380
Given the latitude of a place, and the altitude and declination of
the sun; to find the apparent time of observation, and, thence,
the error of the watch. Method I.......
383
Method II. Of computing the horary distance of a celestial
object from the meridian.....
388
Method III. Of computing the horary distance of a celestial
object from the meridian....
.... 390
Method IV. Of computing the horary distance of a celestial
392
Given the latitude and longitude of a place, the altitude, right
ascension, and declination of a known fixed star, and the sun's
right ascension; to find the apparent time
Given the latitude and longitude of a place, and the altitude of a
planet; to find the apparent time of observation......
Given the latitude and longitude of a place, the estimated time
at that place, and the altitude of the moon's limb; to find the
apparent time of observation
394
....
397
400
SOLUTION OF PROBLEMS RELATIVE TO FINDING THE ALTITUDES OF
THE HEAVENLY BODIES......
403
Given the latitude and longitude of a place, and the apparent
time at that place; to find the true and the apparent altitude
of the sun's centre
404
of a fixed star...
of a planet
Given the latitude and longitude of a place, and the apparent time
at that place; to find the true and the apparent altitude of the
moon's centre
SOLUTION OF PROBLEMS RELATIVE TO THE LONGITUDE
To convert apparent time into mean time ...
406
.... 408
.. 410
413
415
To convert mean time at Greenwich into apparent time........ 416
Given the latitude of a place, and the observed altitude of the
sun's limb; to find the longitude of that place by a chrono-
meter or time-keeper
Given the latitude of a place, and the observed altitude of a
known fixed star; to find the longitude of that place by a
chronometer or time-keeper...
417
420
planet; to find the longitude of the place of observation by a
chronometer or time-keeper......
423
moon's limb; to find the longitude of the place of observation
by a chronometer or time-keeper.
426
To find the longitude of a ship or place by celestial observation,
commonly called a LUNAR OBSERVATION
431
Method I. Of reducing the apparent to the true central
distance ....
433
Method II. Of reducing the apparent to the true central
distance
436
Method III. Of reducing the apparent to the true central
438