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Capt. the Hon. C. L. Irby, H.M.S. Ariadne.
Lieut. R. Ingram, H.M.S. Gloucester.

Admiral Jones, 10, Curzon Street, May Fair.
Capt. Theobald Jones, R.N., Barnsbury Row, Islington.
Mr. Jeringham, H.M.S. Galatea.

1

The Rev. J. Kirkby, Sheerness Dockyard.

Capt. Abraham Lowe, R.N.
Lieut. Gower Lowe, H.M.S. Valorous.
Alexander Lumsdale, esq., Master Attendant, Plymouth Dock-yard.
Mr. H. Lawrence, R.N., Kingston, near Portsea.
Mr. Thomas Lock, Weymouth, 2 copies.

Capt. The Hon. J. A. Maude, H.M.S. Glasgow.
Capt. Jas. Mangles, R.N.
Capt. Joseph Maynard, R.N.
Capt. W.J. Mingaye, H.M.S. Hyperion.
Capt. Andrew Mitchell, R.N.
Capt. John Molesworth, R.N. Clapham.
Capt. C.R. Moorsom, R.N.
Capt. William Mudge, R.N.
Lieut. S. Meredith, H.M. Cutter Vigilant.
Capt. C. Morton, R.N., Lower Eaton Street, Grosvenor Place.
J. M'Crea, esq., Surgeon, R.N., Barnsbury Row, Cloudesley Square.
John M'Arthur, esq., Hinton Lodge, Horndean, Hants.
Mr. George Miller, R.N., Portsmouth.
Lieut. Thomas M'Gowan, R.N.

Admiral the Right Hon. Earl Northesk, Commander in Chief, Plymouth.
Capt. the Right Hon. Lord Napier, R.N.
Lieut. H. Nurse, R.N., Pinner, Middlesex.
Mr. Joseph Nalder, Guildhall, London.

Rear Admiral Sir E. W.C. R. Owen, K.C.B. and M.P.
Rear Admiral R. D. Oliver, Dublin.
Rear Admiral the Right Hon. Lord James O'Bryen.
Capt. Hayes O'Grady, R.N.
Capt. W. F. W. Owen, H.M.S. Eden.
B. E. O'Meara, esq., Montague Square.
Mr. Joseph Oakey, R.N.

Vice Admiral C. W. Paterson, Cosham, Hants.
Capt. Lord William Paget, William and Mary Yacht.
Capt. William E. Parry, F.R.S., R.N., Hydrographer to the Admiralty.
Capt. Charles G. R. Phillott, R.N.
Capt. W. H. Pierson, R.N., Havant.
Capt. H. Prescott, C.B., R.N., Farnham, Surrey.
Lieut. J, T. Paulson, R.N.
Mr. J. B. Paddon, H.M.S. Galatea.
George Peel, esq., George Yard, Lombard Street.
Mr. Joseph Pym, Bartholomew Close.

Capt. J. C. Ross, R.N.
Capt. Edwin Richards, R.N.
Lieut. Harry B. Richards, R.N.
Lieut, Curtis Reid, R.N., Southampton.
Lieut. Benj. Roberts, H.M.S. Wolf.
Mr. Percival Roberts, H.M.S. Wolf.
Lieut, Edward Rogier, R.N.
Mr. Rolland, H.M.S. Galatea.

The Right Hon. Earl Spencer, K.G., &c. &c.
Admiral the Hon. Sir R. Stopford, K.C.B., Commander in Chief, Portsmouth.
Thomas Asherton Smith, esq., M.P., Penton Lodge, Andover.
Capt. W. Sanders, R.N., Kingston, Portsea.
Capt. Thomas Sanders, H.M.S. Maidstone.
Capt. G. R. Sartorius, H.M.S. Pyramus.
Capt. G. F. Seymour, C.B., R.N., Hampton Court.
Capt. Charles Shaw, R.N.
Capt

. Henry Shiffner, R.N., Sompting Abbotts, Shoreham.
Capt. Houston Stewart, R.N.
Capt. Charles Strangways, R.N.
Capt. C. B. Strong, R.N., King's Terrace, Portsmouth.
Capt. H. E. P. Sturt, R.N.
Lieut. Archibald Sinclair, R.N.
Lieut. M. A. Slater, R.N.
Lieut. Thomas Spark, H.M. Revenue Cutter Fancy.
Lieut. John Steane, R.N., Ryde.
Lient. W. B. Stocker, R.N., Poole.
Lieut

. George F. Stow, H.M.S. Espoir.
The Rev. T. Surridge, H.M.S. Ocean.
The Rev. J. E. Surridge, M.A., R.N.
Mr. George Starr, R.N.
Mr. George Saulez, Alton, Hants.
Mr. W. D. Snooke, Professor of Mathematics, Ryde, Isle of Wight.
Mr. W. Selby, Portsmouth.

Capt. N. Thompson, H.M.S. Revenge.
Capt. John Tancock, R.N.
Capt. John Jervis Tucker, R.N., Trematon Castle, Plymouth.
Lieut. John Thompson (b), R.N., North Potherton.
Mr. Thomas P. Thompson, H.M.S. Pyramus.
The Rev. John Taylor, H.M.S. Ramillies.
Mr. S. Tuck, R.N., Kingston Cross, Portsea.
Mr. Joseph Tizard, jun., Weymouth, 2 copies.

The Hon. G. Vernon, Ryde, Isle of Wight.
Capt. A. E. T. Vidal, R.N.

Commodore J. C. White, R.N.
Capt. James Wemyss, R.N. and M.P., Wemyss.
Thomas P. Williams, esq., M.P., Berkeley Square.
Lieut. H. Walker, R.N., Cosham, Hants.
Lieut. William Wilson, H.M.S. Challenger.
Lieut. Joseph C. Woolnough, Com. H.M. Cutter Surly.
Lieut. J. L. Wynn, R.N.
Edward D. Warrington, esq., Charles Square, Hoxton.
Thomas S. Whitney, esq., Newpass, Rathone, Ireland.
Mr. Thomas Woore, H.M.S. Alligator.

The Right Hon. Lord Viscount Yarborough, 2 copies.
Captain Thomas Young, R.N., Fareham, Hants.

CONTENTS.

Table.

Page.

I. To convert longitude, or degrees into time, and conversely

1

II. Depression of the horizon ...

3

III. Dip of the horizon at different distances from the observer

6

IV. Augmentation of the moon's semi-diameter

8

V. Contraction of the semi-diameters of the sun and moon

il

VI. Parallax of the planets in altitude..

12

VII. Parallax of the sun in altitude

VIII. Meau astronomical refraction...

13

IX. Correction of the mean astronomical refraction

15

To find the latitude by the north polar star

17

XI. Correction of the latitude deduced from the preceding table...... 20

XI. Mean right ascension of the sun...

21

XIII. Equations to equal altitudes of the sun, part First..

22

XIV. Equations to equal altitudes of the sun, part Second

22

XV. To reduce the sun's longitude, right ascension, and declination;

and, also the equation of time, as given in the Nautical Almanac,

to any given time under a known meridian

25

XVI. To reduce the moon's longitude, latitude, right ascension, declin-

ation, semi-diameter, and horizontal parallax, as given in the

Nautical Almanac, to any given time under a known meridian 30

XVII. Equation of the second difference of the moon's place.....

XVIII. Correction of the moon's apparent altitude

38

XIX. To reduce the true altitudes of the sun, moon, stars, and planets,

to their apparent altitudes .....

XX. Auxiliary angles

42

XXI. Correction of the auxiliary angle when the moon's distance from a

planet is observed ....

XXII. Error arising from a deviation of one minute in the parallelism of

the surfaces of the central mirror of the circular instrument of

reflection.....

XXIII. 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

XXIV. Logarithmic difference

48

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

altitude ....

52

XXVII. Natural versed sines, and natural sines

53

XXVIII. Logarithms of numbers .

62

XXIX. Proportional logarithms....

75

XXX. Logarithmic half elapsed time

84

XXXI. Logarithmic middle time

86

XXXII. Logarithmic rising. ....

87

XXXIII. To reduce points of the compass to degrees, and conversely...... 89

XXXIV. Logarithmic sines, tangents, and secants to every point and quar-

ter point of the compass

89

XXXV. Logarithmic secants to every second in the semi-circle

90

XXXVI. Logarithmic sines to every second in the semicircle.....

93

XXXVII. Logarithmic tangents to every second in the semicircle

97

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

XL. Reduction of the moon's horizontal parallax on account of the

spheroidal figure of the earth...

104

XLI. 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. Acceleration of the fixed stars, or to reduce sidereal time into

mean solar time ...,

117

XLVI. To reduce mean solar time into sidereal time....

119

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

119

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

120

XLIX. Amplitudes of a celestial object reckoned from the true east or

west point of the horizon ...

122

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

LI. For computing the meridional altitude of a celestial object, the

latitude and the declination being of the same name

.. 138

LII. For computing the meridional altitude of a celestial object, the

latitude and the declination being of contrary names ........ 138

LIII. The miles and parts of a mile in a degree of longitude at every

degree of latitude

144

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