appeared necessary to notice the elementary parts of the sciences, reference has been made to relative problems in "The Young Navigator's Guide," where, it is hoped, the reader will find his inquiries fully satisfied.

The various sciences touched upon commence with a concise system of decimal arithmetic, and complete courses of plane and spherical trigonometry. In the latter, the solution of the quadrantal triangles will be found much simplified.

The practical parts of Navigation begin with parallel sailing; but, with the view of preventing the work from swelling to an unnecessary size, the cases of plane sailing, usually met with in other nautical books, have been omitted in this; as these are, in effect, no more than a mere repetition of the cases of right angled plane trigonometry under a different denomination. Middle latitude sailing will be found exceedingly simplified by means of a series of familiar analogies or proportions: and in Mercator's sailing a series of rational proportions is given; which, it is hoped, may tend to induce mariners to substitute the rules of reason for the rules of rote; and thus do away with the mistaken system of getting canons by heart; a system which has too long prevailed in the Royal Navy.

The two very useful sailings, oblique and windward, which have been hitherto little noticed by mariners, are also rendered so simple, particularly the latter, that it is to be hoped they will, ere long, be brought into general

use.

In current sailing (Example 3,) the true principles of steering a vessel in a current, or tideway are familiarly illustrated. This problem cannot fail of being interesting to every person who is at all curious in the art of navigation.

The solution of a problem in great circle sailing is given, which will be found essentially useful to ships bound from the Cape of Good Hope to New South Wales: comprising a table which exhibits, at sight, all the scientific particulars attendant on the true spherical track between those two places; by which it will be seen that a saving of 585 miles may be effected by sailing near the arc of a great circle as laid down in that table; which saving ought to be an object of very high consideration to all ships bound from the Cape of Good Hope to Van Diemen's Land, or to his Majesty's colony at New South Wales with either troops or convicts; because the length of the voyage on the old track, or that deduced from the common principles of navigation, generally occasions a great scarcity of fresh water, and this, eventually, adds distress to the many privations under which those on board usually labour. In the same problem, there is a table showing the true spherical route from Port Jackson, in New South Wales, to Valparaiso, on the coast of Chili: in this route there is a saving of 745 miles when compared with that resulting from Mercator's sailing; and this must be of considerable importance to the captain of a ship sailing between

these places, who is desirous of making his port in the shortest space of time; particularly since few ships can carry a liberal allowance of fresh water to serve during a passage which measures very nearly one fourth of the earth's circumference.

The introductory problems to Nautical Astronomy will be found ranged in the most natural order; all of which, except those relating to the altitudes of the objects, are concisely solved by proportional logarithms: the greater part of these will appear entirely new to the navigator. The VIth problem relating to the latitude exhibits the method of finding the latitude by an altitude of the north polar star taken at any hour of the night, which will be found very useful in all parts of the northern hemisphere. The VIIIth problem shows the method of finding the latitude by the altitudes of two stars taken at any time of the night, agreeably to the computed spherical distance between them contained in Table XLIV; this method of ascertaining the latitude is general; it will be found very correct, and far less troublesome than that by double altitudes which immediately precedes it.-Problems IX, X, XI, and XII, contain new and accurate methods of deducing the latitude from the altitudes of the celestial bodies observed at given intervals from the meridian: the operation consists of very little more than the common addition of three proportional logarithms, and yet the latitude resulting from it will always be as correct as that deduced from the object's meridional altitudes, provided the watch shows apparent time at the place of observation, and the altitudes be taken within the limits prescribed. These problems will be found highly advantageous to the practical navigator; because, in the event of the sun's, or other celestial object's meridional altitude being neglected to be taken, or of it's being obscured by clouds at the time of transit, he is, thus, provided with the most safe and ready means of determining his latitude with as much certainty as if the altitude of the object had been observed actually upon the meridian either above or below the pole. See remark, page 368.

A most ingenious problem in this part of the work, for determining the latitude, which for neatness and general utility stands unrivalled, has been communicated to the author by the scientific Captain W. F. W. Owen.

In the methods of computing the altitudes of the heavenly bodies, the solutions to the several problems are rendered exceedingly concise and explicit.

The IIIrd, IVth, Vth, and VIth problems relating to the longitude contain the methods of finding the longitude by a chronometer and the respective altitudes of the sun, stars, planets, and the moon; the three last of which will be found considerably elucidated.

The lunar observations commence with the VIIth problem on the longitude. In this problem thirteen methods are given for reducing the ap

parent central distance between the moon and sun, a fixed star, or planet, to the true central distance; several of which are entirely original, and all of them adapted to solve this interesting and important problem in the most simple and expeditious manner.

In the series of problems relative to finding the variation of the compass by amplitudes, azimuths, transits of the fixed stars and planets, and by observations of the circumpolar stars, Problem II exhibits a new method for computing the true azimuth of a celestial object: and Problems V and VI, contain the methods of reducing or correcting the true and the magnetic courses, between two places, agreeably to any given variation of the compass. An improved azimuth compass card is described in this part of the work, which may be applied to the determination of the longitude by the lunar observations :-See the last two paragraphs in page 499.

The series of problems for finding the apparent times of the rising or setting of the celestial bodies, and of the beginning or the end of twilight; and that for determining the interval of time between the rising or setting of the sun's upper and lower limbs, it is hoped will prove acceptable to the lovers of the science of Nautical Astronomy;-likewise the art of Dialling, which, although it may appear foreign or irrelevant to the pursuits of the mariner, cannot fail to be interesting as a branch of science. It is here treated of in a familiar manner.

The IVth Problem in the mensuration of heights and distances, exhibits the method whereby the officers on board two ships of war can readily ascertain their absolute distance from any fort or garrison which they may be directed to cannonade ;-after which follow several problems that will be found exceedingly useful on many military occasions.-See remark at page 533, and also at page 543. Problem XI. showing the method of reducing a base line, measured on any elevated horizontal plane, to its true level at the surface of the sea; and Problem XIII. exhibiting a new rule for finding the height of a mountain, or other eminence, by means of two barometers and two thermometers, may be of considerable use to engineers, or to others employed in conducting surveys. A problem is also given for finding the direct course steered by a ship seen at a distance; and being a subject highly interesting to all nautical persons, it is reduced to every desirable degree of simplicity both by geometry and trigonometry.

All the problems in Practical Gunnery are readily solved by logarithms: it contains three very concise tables which considerably facilitate the operation for finding the greatest range of a shot or shell, and the elevation of the piece to produce that range. A small table is also given, which will be found extremely useful in problems relating to shells, when it is required that they should strike an object at a given distance.-The rules and operations for computing the time of flight of a shell in Problems XXVII, XXXIV, and XXXVI, will be found very simple and concise.

Although the art of gunnery may, in some measure, be considered as not being immediately connected with that of navigation; yet it is a subject with which all naval officers ought to have some acquaintance ; since it very frequently happens, in time of war, that they are called upon to go on shore with a party of men for the purpose of working the great guns of the besieging batteries in co-operation with his Majesty's Land Forces :-and since this truly interesting art is here, for the first time, unveiled of its mystic dress, and reduced to a state of simplicity, every officer may make himself thoroughly acquainted with it in a very little time, without any other assistance than that afforded in this treatise.

The problems on the mensuration of planes may be found useful on many occasions; particularly to persons employed in carrying on surveys on shore.

Practical Gauging contains a few interesting problems; the last of which will be found essentially useful to such persons as may have occasion to purchase wine, or spirits on his Majesty's account in foreign countries; because it enables them to ascertain, in a very few minutes, the absolute number of gallons contained in any given quantity of foreign liquor, agreeably to the newly established standard or Imperial gallon measure.

The compendium of Practical Navigation, given in this volume, exhibiting the direct manner of making out a day's work at sea, is intended for the benefit of such persons. as may be unacquainted with the elements of geometry and trigonometry: and includes the true method of finding the index error of a sextant or quadrant so as to guard against the error arising from the elasticity or spring of the index bar, with the method of applying the corrections to altitudes taken on shore by means of an artificial horizon.

A new and correct method of finding the longitude of a place on shore by means of the moon's altitude (observed in an artificial horizon,) and the apparent time of observation, follows the above compendium; and will be found of considerable utility in settling the geographical positions of places inland or along the sea coast. An Appendix, which concludes the first volume, contains every thing relating to the doctrine of compound interest; and developes the extraordinary powers of logarithmical numbers in a more striking point of view than any other department of science to which they have been applied.

I have thus given a brief account of the more original parts of the subjects comprised in this work, the completion of which has cost me several years of incessant labour; during which time I had to contend with as many infirmities, vexations, and disappointments as generally fall to the lot of persons doomed to drudge through the toils of life: but stimulated by the hope of ultimately succeeding in rendering myself useful to the Naval Service of his Majesty, and to the nautical world in general, I have been

so far enabled to bear up against the vicissitudes of health and fortune, as to bring my long and arduous task to a close.

How far I have succeeded in my endeavour to supply the desideratum which has been hitherto felt by navigators, it is not for me, but for a generous British public to determine: to their decision I submit my labours, under the conviction that, whatever may be the defects in its execution, they will do justice to my motives, in this attempt to lessen the existing obstructions in the way of attaining a practical knowledge of the elements of Navigation and Nautical Astronomy.

Portsmouth, December 1st.,

1827.

THOMAS KERIGAN.