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“Now, in the first place, the method proposed is more natural than the latter, because, when the two sides are taken together, their trigonometrical relation to each other is immediately perceived, which, when they are separate is not so apparent. Again, since the term sine or cosine is determined altogether by that side which we make radius, the term radius should, according to the natural progress of ideas, immediately precede the term sine, cosine, &c."page 28.

After this introductory chapter, we come to what may be considered more peculiarly the object of this treatise. In general the cases into which the different sailings may be divided, are used merely as a vehicle for exercising the learner in plane trigonometry. That error has been avoided here, as every example which is given in the chapter which explains these matters, is a useful problem in navigation. We must not, however, thus hastily dismiss that part which treats of what is usually called great circle sailing. Most mariners are aware that this method alone gives the proper courses to be steered, in order to make most directly to any distant port to which the vessel may be bound ; but it also shews something more. By this sailing, it may be ascertained how far a ship may deviate from her apparent direct course, in search of a wind, or from any other cause, without increasing the number of miles that she has to run, in order to reach her destination. Highly useful as this method of navigation appears, it has hardly ever been practiced, owing to the complicated form in which the rules have been laid down! Kerigan in his laborious work on navigation, published in 1826, has attempted to simplify the rules, but the directions which he gives are of too complicated a nature to be followed by the generality of seamen. In the work before us, all these difficulties are completely mastered, and great circle sailing is now rendered almost as easy as Mercator's. The plan which Lieutenant Raper adopts for solving the different cases by inspection is very short, and will be the method commonly used at sea. This is effected by a new and original table devised by himself, and will be hereafter of the utmost importance in the science of navigation. Without entering into any long account of this table, we shall only generally state, that by its aid spherical triangles can be solved much in the same manner, that plane right-angled triangles may be solved by the aid of what is commonly called the traverse table.

After the sailings, we have an excellent and original chapter on taking departures, in which the most accurate and useful methods of ascertaining distances from the land are clearly explained.

In that portion of the work which treats of nautical astronomy, no rule is omitted for any possible case that may occur, and the work concludes with a chapter explanatory of the proceedings that are necessary for the safe navigating of a ship; in short, pointing out the best manner of making a practical application of all the matters which have been previously treated.

Many of the tables are quite original. Table 3, which is entitled spherical traverse table, we have already alluded to as performing for spherical triangles all that the present common traverse table does for right angled triangles. This table will no doubt be very soon extensively used, more particularly if the author performs his promise of publishing it separately in a more extended form. After the logarithmic sines, &c., is given a table for interpolation, by which the seconds if required may be taken out at once. Table 61 is the log. sine square calculated to fifteen seconds of space, and six places of logarithms, and is used in all the rules given in nautical astronomy, the answer being always to be found in this table. All the tables used in clearing the lunar distance are so arranged, that allowance may either be made or omitted for the height of the barometer and thermometer. But it would be only trying the patience of the reader to proceed further, therefore, the last table to which we shall refer, is that containing maritime positions, although not placed last in this work, as it comes in its natural and legitimate order, immediately after the table of meridional parts. It has been too much the practice for authors to compile this table, principally from such books of navigation as have preceeded their own,

ENLARGED SERIER.NO. 2.-VOL. FOR 1841.

not paying sufficient attention to the longitudes more accurately ascertained, and to be found inserted in Foreign and English sailing directions ;-in the proceedings of the geographical society, in the pages of this journal, or occasionally only in manuscript, either at the hydrographical office, or in the possession of individuals. But we are happy to find this is far from being the case here. We have carefully exanıined Lieutenant Raper's table, and it appears to us, to have been mainly compiled from those very sources of information to which we have already alluded, sources which have hitherto been too much neglected; in short, we may consider, that we have a compendium of what is actually known on this subject, so that we have now a starting point to go from in the future attempts that may be made, to determine with greater accuracy the longitudes of maritime places.

But we have other matters pressing on us for attention, and we must again defer the remainder of our notice of this valuable work for another number.

NEW CHARTS.

(Published by the Admiralty.) Tue NATUNA ISLANDS Surveyed by M. E. Paris, in the Corvette La Favorite,

commanded by M. La Place.-1831. With this chart, a ship may approach the islands in any direction with confi. dence to within a few miles; indeed, we consider it an indispensible accompaniment to Horsburgh's account of the islands, as there are several minor points in which the two authorities differ in some degree, and one or two dangers appear that are not alluded to by Horsburgh. T'he STRAIT OF MALACCA–WESTERN Part.

A neat useful sailing chart,—the authorities for which appear to be for the Coast of Sumatra, Lieutenants W. Rose, and R. Moresby, the Strait of Calam, Capt. W, F. W. Owen, Rn., Penang Island and Strait, Lieut. T. Woore, RN., the Arroa Islands and North Sands, Capt. D. Ross, of the Bombay Marine, and the whole adapted to the valuable Directory of Capt. Horsburgh. THE STRAIT OF Malacca.-EASTERN Part.

A similar neat chart; the authorities as before stated : the Siac river and the Straits adjacent to it forming a prominent feature. Tue ARROA ISLANDS WITH THE NORTH SANDS AND CALAM STRAIT.

Shewing on an enlarged scale the navigable approaches to these dangers, and a useful chart to vessels availing themselves of the advantage of entering the Malacca Strait by the secure passage afforded by the Calam Strait. The BASHEE AND BINTANG CHANNELS.

We congratulate our seamen, on having thus in a convenient and useful form even the meagre results of navigators as long as they are carefully digested.

This chart we find which is most important, as shewing the high road between Formosa and the Phillipine Islands, has been constructed from loose and conflicting authorities, as is shewn by its unfinished appearance, but great pains have been taken to render it as useful as possible, and it is decidedly more correct than any former publication of this part.

PROMOTIONS AND APPOINTMENTS.
PROMOTIONS.

LIEUTENANTS–J. E. F. Risk, com

mission dated November 6th, 1840, to CAPTAIN—R. Shepheard Triscott. stand next in seniority to Ř. White. COMMANDER-T. H. Holman.

J. H. Woolward, the Hon. G. D. Keane, LIEUTENANT-J. Allen, (a).

C. R. Carter, commission dated Novem(The above are the annual coast guard ber 5th, 1840, and to stand on the list promotions.)

for seniority immediately after F. H. COMMANDERS-A. Murray, (b) and Stanfell. L. G. Heath, for passing best R. Duncan , commissions dated Novem examination at the Royal Naval Colber 4th, 1840,

lego.

PURSERSC. Dealy, W. G. Tomlin- lent to Monarch-L. C. H. Tonge to son, R. T. Crispin, J. Brickwood, W. Vernon-0. Borland, and J. Borlase to Stanway, J. Harkshaw, W. H. Dutton, Excellent-B. Young to Phoenix-M. R. L. Sutherland, E. A. Smyth, and H. Lloyd to Hecate-H.D. Chads from ExH. Chimmo.

cellent to Endymion-H. de Lisle do. to DEPUTY INSPECTOR OF HOSPITALS Phoenix-D. Ń’Leod Mackenzie do. to S. J. Swayne.

Iris A. Key from Cleopatra to Excellent-G. S. Boys from Buzzard to

Vernon-W. Willie to Albert, (st. v.) APPOINTMENTS.

-F. Martin to Ferret --W. Baugh

to Impregnable-E. Hill to Indus. CAPTAIN-C. Wyvill to Cleopatra, SECOND Masters-W. Diaper to Athol

COMMANDERS-J. Richardson (b) to -W. Pettigrew to Pluto-G. Hicks Phænix-The Hon. H. A. Murray to to Nightingale-J. Scarlett (acting) to Wasp-G.G. Loch to Vesuvius-A. Mur- Queen. ny to Hydra-C. Birkett to Bellero- Vol. Ist CLASS—W. Babbington to phon-WH.Hall to Benbow W. Clark Indus. to Edinburgh-D. Curry to Hastings, Master's ASSISTANT-C. E. Maitland W. Toby to Powerful – H. Bingham to Phoenix. to Princess Charlotte-G. Lowe to Re- Assistant SURGEONS-C. Daniell to tenge.

Apollo-D. Thompson, and D. Whip. LIEUTENANTS-F. P. B. J. Sulivan, ple to Haslar hospital-A. Stewart to and T. Heard to Powerful--E. W. San- Portsmouth dockyard-D. A. Newman ders to Bellerophon-C. D. O'Brien, and to Plymouth dockyard-J. Peters to F.H. Stanfell to Benbow-G E Patey Pluto --T. K. Beatty to Queen-J. Anto Carysfort-H. Stewart to Castor-G. drews to Ranger - Ř, Hayward to EdinJ. R. Snow, and S. F. Short to Cyclopsburgh-T. K. Beattie to Stromboli–D. -J. Blackmore to Edinburgh-Å. D. Gamble to Revenge-T. Miller to Stupart to Gorgon-J. A. Shears to Queen-D. O'Callaghan to Phoenix-G. Hastings-R. M. Floud to Hazard-H. Řae, MD., to Caledonia.-W, R, Dalton Warren to Pique-A. Farquhar, R. Jen- to Lizard—0. Ferguson to Nightingale ner, A. Cumming, R. Hoops, J. Allen, - J. Harvey to Raven. J. M. Smyth, R. White, G. Johnson, Clerks-W. Bateman (in charge) T. Whipple, L. P, Burrell, and G. H. to Lizard v, Millingham, appointment Sunderland to Princess Charlotte-G. cancelled-J. W. Cole (in charge) to Wyke to Revenge-W. Chamberlain Nightingale-T. Mundy (in charge) to to Stromboli-M. H. Rodney, and W. Ferret Gennys to Talbot-R. Williams to Thun- Mr. Doyle, clerk of the Apollo, and derer-J. M. Boxer to P

to Vesuvius-W. K. Mr. Parminter, clerk of the Phænix, have O. Priee, Wasp-W. F. M. Tollemache passed their examination for pursers. Pelican-E.N. Troubridge to Southamp- NAVAL INSTRUCTORS -J, Addison, W. ton—The Hon. C. Keane, and J. San. Witmarsh to Excellent to qualify. derson to Excellent.

Coast GUARD—Lieutenant- Richard MASTER-R. B. Graham to Hazard. Bayley Bowden to be chief officer, MATEs-L. P. Pigott, W. H. Bridge, Mates-William Henry Walters, and from Excellent, and G. M. Greathead Charles Frederick Collett (1835) to be to Indus—C. J. F. Ewart, from Excel chief officer,

MOVEMENTS AND STATIONS OF HER MAJESTY's Navy.
AT HOME.

ATHOL, 28, (tr. sh.).Jan. 3d, left Ports

mouth for Cork. ÆTNA, 6, Lieut. com. J. Wilson, Avon, (st. v.) Lieut.com. R. Prit. Liverpool.

chard, Plymouth station. ALBAN, (st. v.) Mr.J King, 24th Dec.

BELLEISLE, 72, Capt. J. T. Nicholas, put into Cork, 28th sailed.

Plymouth. ALBERT, (st. v.) Capt. D. Trotter, on CALEDONIA, 120, Capt. H. Eden, Ply, way to Deptford.

mouth. ÁPOLLO, (tr. sh.), Mr, A. Karley, left CAMPErdown, 104, Capt. Sir H. L. Portsmouth.

Baker, Sheerness. ASTRBA, 6, Capt. J. Plumridge, Fal

Comet, (st. v.) Lieut. F. Syer, Ply, mouth.

mouth.

ENDYWION, 38, Capt. Hon. F. Grey, TWEED, 20, Com. H. Douglas, Portsin Plymouth Sound.

mouth. EXCELLENT, Capt. Sir T. Hastings, VERNON, 50, Captain W. Walpole, Portsmouth.

Sheerness. FERRET, 10, Lieut. W. Thomas, home Victory, 104, Capt. F. E. Loch, Portsstation.

mouth. HARLEQUIN, Chatham.

WILBERFORCE, (st. y.) Com. Allen on IMPREGNABLE, 110, Capt. T. Forrest, way to Deptford. Plymouth. INCONSTANT, 36, Capt. Pring, 28th

ABROAD. December left Plymouth, with supplies for homeward bound.

ACHERON, (st. v.) Lieut.-com. A. KenIndus, 84, Capt. Sir James Stirling, nedy. Portsmouth.

ACORN, 16, Com. J. Adams, Cape of Iris, 28, Capt. H. Nurse, 18th Jan. Good Hope. in the Downs on way to Portsmouth. ACTA EON, 26, Capt. R. Russell, South

LIGHTNING, (st. v.) Lieut.-com. R. America. N. Williams, home service.

ALECTO, (st. v.) Lieut. com. W. Hos. LIZARD, (st. v.) Lieut. W. G. Estcourt, wason, Mediterranean. Portsmouth.

ALGERINE, 10, Lieut.-com. T. H. LUCIFER, Capt. W. F. Beechey, sur. Mason, East Indies. veying St. Georges Channel.

ALLIGATOR, 26, Capt. Sir J. J. G. MASTIFF, (s.v.) Mr. G. Thomas, WoolBremer, East Indies. wich.

ANDROMACHE, 26, Capt. R. L. Baynes, MONARCH, 84, Capt. J. Chambers, CB. Cape of Good Hope. Sheerness.

ARROW, 10, Lieut.-com. W. Robinson, NAUTILUS, Lieut.-com. G. Beaufoy, Brazils and Cape of Good Hope. Sheerness.

Asia, 84, Capt. W. Fisher, MediterNIGHTINGALE, Lt.-com. W. Southey, ranean. home service.

Basilisk, 6, Lieut. J. C. Gill, South OCEAN, 80, Capt. Sir J. Hill, Sheer- America.. ness.

Beacon, (s. v.) Lieut.-com. Thomas PELICAN, 16, Com. C.G. Napier, 18th Graves, Mediterranean. Jan. in the Downs, on way to Ports Beagle, (s. v.) Com. J. C. Wickham, mouth.

Australia. PHOENIX, (st. v.) Lieut. J. S. Dennis, BELLEROPHON, 80, Capt. C. J. Austin, Portsmouth.

20th Dec, in bay of Marmorice. Pluto, (st. v.) Lieut. W. S. Blount, Benbow, 72, Capt, H, Stewart, 20th Woolwich.

December at Marmorice bay. POICTIERS, 72, Capt. J. Clavell, Chat BLAZER, (st. v.), Lt. com. J. Steane,

12th Dec. left Madeira for West Indies. Queen, 110, Capt. J. W. Montague, BLENHEIM, 72, Capt. Sir H. F. SenPortsmouth.

house, East Indies. Raven, 4, Lieut.-com. D. R. Maple. BLONDE, 42, Capt. T. Bourcbier, East ton, Sheerness.

Indies. SALAMANDER, (st. v.) Com. H. Henry, BRISK, 3, Lieut.-com. G. Sprigg, 24th 30th Dec. at Sheerness from Norway in Oct. arrived at St. Helena on her way to search of HMS. Fairy, 18th Jan. left Cape. Sheerness for Portsmouth.

BRITANNIA, 120, Capt. J. Drake, MeSAN JOSEF, 10, Capt. J. N. Taylor, diterranean. CB., Plymouth.

BRITOMART, 10, Com. O. Stanley, SAPPHIRE, (tr. sh.) Mas..com. G. Australia. Cole, home service,

BUZZARD, 3, Lieut.-com. R. T. LeSAVAGE, 10, Lieut. J. H. Bowker, vinge, Coast of Africa. Plymouth

CALCUTTA, 84, Capt. Sir J Roberts, SEAFLOWER, 4, Lieut.-com. N. Robil- CB. 20th Dec. in Marmorice bay. liard, Portsmouth.

CALLIOPE, 26, Capt. T. Herbert, S. Snipe, 2, Lieut.-com. T. Baldock, America, or sailed for China. Ireland.

CAMBRIDGE, 78, Capt. E. Barnard, Soudan, (st. v.) Com. B. Allen, Dept. 20th Dec. in Marmorice bay. ford.

CAMELION, 10, Lieut..com. G. M. SPEEDY, 2, Lieut.-com. J. A. Wright, Hunter, Brazils and Cape. Sheerness.

CARYSFORT, 26, Capt. H. B. Martin, SPITFIRE, Lieut.-com. J. Evans, CB. Ilth Dec. arrived at Alexandria from Woolwich.

the Levant.

ham,

CASTOR, 36, Capt. E. Collier, 30th 29th Aug. left Aura, for Princess Island, Dec. Malta for Marmorice bay.

coast of Africa. CHARYBDIS, 3, Lieut.-com. E. B. Tin GANGES, 84, Capt. B. Reynolds, CB., ling, West Indies.

13th Dec, in Marmorice bay. CHILDERS, 16, Com. E. P. Halstead, GLEANER, (st. v.) Lt.-com. J. Jeayes, 13th Nov. left Sangor roads on a cruize. West Indies.

CLEOPATRA, 26, Capt. A. Milne, 18th GORGON, (st. v.) Capt. W. HenderNov. left Barbados for Antigua.

son, CB, 20th Dec. in Marmorice bay, Cro, 16, Com. S. G. Freemantle, Grecian, 16, Com. W. Smyth, 4th Brazils and Cape Good Hope.

Oct. left Rio for River Plate, 17th reCOLUMBIA, (st. v.) Master-com. A. turned. Thompson, West India.

GRIFFON, 3, Lieutenant-com. J. G. D' COLUMBINE, 16, Com. G. Elliott, 6th Urban, 19th Nov. arrived at Barbados. Aug. left Macao for the Bogue.

Hastings, 72, Capt. J Lawrance, CB., Comus, 18, Com. E. Nepean, West Mediterranean. Indies.

HAZARD, 72, Capt. Hon. C. G. J. CONFIANCE, (st. v.) Lieut.-com. E. Elliott, 29th Dec. in Marmorice bay. Stopford, Mediterranean.

Hecate, (st. v.). Com. H. Ward, MeCONWAY, 26, Capt. C.R. D. Bethune, diterranean. East Indies.

Hecla, (st. v.) Lieut.-com. J. Cragg, CROCODILE, 26, Capt. A. Milne, 17th West Indies. Nov. arrived at Jamaica, in twelve days HERALD, 26, Capt. J. Nias, 24th Aug. from Bermuda.

arrived at Anger from Sydney, 9th Oct, CRUIZER, 16, Com. H. W. Gifford, arrived at Singapore, 19th sailed, East Indies.

HORNET, 6, Lieut.-com R. Miller, 30th CURACOA, 24, Capt, J, Jones, Brazil November left Jamaica for Chagres, and Cape.

Howe, 120, Capt, Sir W.0. Pell, 16th CORLEW, 10, Lieut.-com. T. Ross, 3d December at Malta, 30th sailed for MarNov. arrived at Cape of Good Hope, from morice bay. Quillimaine.

HYACINTH, 18, Com. W. Warren, 4th Cyclops, (st. v.) Capt. H. T. Austen, Aug. arrived at Macao, 6th sailed for the ÇB., Mediterranean.

Broadway. CYGNET, 10, Lieut. E. Wilson, coast Hydra, (st. v.) Com. A. Murray, of Africa.

17th Dec. arrived at Malta from BeyDAPHNE, 18, Com. J. W. Dalling, 20 rout. December in Marmorice bay.

IMPLACABLE, 74, Capt. E. Harvey, 20 DEE, (st. v.) J. Sherer, KH., West Dec, in Marmorice bay. Indies.

JASEUR, 16, Com. F. M. Boultbee, 11 DIDO, 18, Capt. L. Davis, cl., 20th December, arrived at Cadiz from GibDec. in Marmorice bay.

raltar, 7th Jan. at Gibraltar. DOLPHIN, 3, Lieut.-com. E. Little JUPITER, (tr. sh.) Mas-com. R. Fulton, hales, 17th Oct. at St. Helena, Ist Nov, East Indies.' at Ascension.

Kite, (st. v.) Lieutenant com. G. DRUID, 44, Capt. H. Smith, CB., 4th Snell, West Indies. Aug. arrived at Macao, 10th sailed for LARK, (s. v.) Lieut.-com. T. Smith, the Bogae.

West Indies, 23d arrived at Havana. EDINBURGH, 72, Capt. W. W. Hen. LARNB, 18, Com. P. J. Blake, 4th derson, kh. 20th Dec. in Marmorice bay Aug. arrived at Macao.

ELECTRA, 18, Com. E. P. Mainwaring, Lily, 16, Com. J. J. Allen, Cape of South America.

Good Hope, EREBUS, Capt. J. Ross, particular ser Locust, (st. v.) Com. J. Lunn, 27th rice.

Dec. left Gibraltar for Malta. Espoir, 10, Lieut.-com. J.T. Paulson, Lynx, Lieut.-com. H. Broadhead, Ist arrived at Lisbon.—7th Jan. with damage Oct. at Accra.

FANTOME, Com. Butterfield, Cape of MagicIENNE, 24, Capt. F. T. Michell Good Hope.

20th Dec. in Marmorice bay. FAVORITE, 18, 19th Aug. at Syd- MAGNIFICENT, 72, Commodore P. J.

Douglas, Jamaica. Fawr, Lieut..com. J. Foote, 12th Magpie, (s. v.) Lieutenant-com. T. S. Oct. arrived at Rio from Buenos Ayres. Brock, Mediterranean.

FIREPLY, (st. v.) Lieut. Winniett, Medea, (st. v.) Com. F. Warden, 13 West Indies.

December left Malta for Levant, 23d at FLAMER, (st. v.) Lieut.-com. W. Rob- Malta. son, West Indies.

MELVILLE, 72, Capt. Hon. R. S. Dun. FORESTER, 3, Lieut-com. Norcock, das, East Indies.

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