PREFACE.

THOUGH the following Treatise on Navigation has been composed primarily as a text-book for schools, it contains matter which will be found deserving the attention of the experienced mariner.

In it will be found all the problems required by the practical navigator, with the rules for solving them; also the demonstrations of these rules, together with examples illustrative of each, and a number of exercises to be solved by the pupil -these exercises being more numerous than those contained in any other treatise now in use.

The rules have been given in the most concise form of which they are susceptible, so as not to destroy their perspicuity; and it is hoped that no pupil who has ordinary talent and application will find difficulty in understanding them.

The processes of performing many of the calculations have been considerably shortened, and several problems have been solved in a manner altogether new. Among these may be specially mentioned the rules for Great-circle Sailing, and likewise those for Ex-meridian Altitudes, both of which will be found worthy of the best attention of every mariner, as the solutions are more simple than any hitherto given. The rule

here given for ex-meridian altitudes of the sun, from which to obtain the latitude of the place, is more extensively useful than that commonly given (especially when a good chronometer is on board), being independent of any approximate latitude; but the further the time of observation is from noon, the more accurately should that time be known to obtain correct results.

In order to render this Treatise demonstrative without reference to any other work, sections on Plane and Spherical Trigonometry have been introduced; first, the rules of Right-angled Plane Trigonometry are deduced and illustrated by examples wrought out at length, and followed by numerous exercises for practice by the pupil. The rules for the various cases of Oblique-angled Plane Trigonometry are then deduced, and followed by illustrative examples and appropriate exercises for practice. After these follow the problems in Navigation which depend on these rules, with examples wrought at length, and exercises so numerous as cannot fail to render the pupil expert at their solution.

In like manner, after having given the definitions of Nautical Astronomy, with rules, examples, and exercises in Preparatory Problems, the rules of Right-angled Spherical Trigonometry are demonstrated, and illustrated by examples wrought at length, followed by numerous problems in Nautical Astronomy which can be solved by them. Then follows the investigation of rules for the cases of Oblique-angled Spherical Triangles, which are then applied to the solution of the more advanced problems in Nautical Astronomy, such as finding the time and azimuth from an observed altitude of the sun; and here a new rule is given for finding both the time and azimuth with very little more labour than that used in finding one of them by the rules commonly given.

Rules (followed by examples wrought at length, and arranged in the most convenient form) are also laid down for finding both the latitude and longitude of a place by double altitudes of the sun. A new and very simple process is here explained by which both the latitude and longitude of a place may be found, from two altitudes of the sun, by construction on a Terrestrial Globe; and from it is deduced Sumner's new method of finding a ship's place at sea, followed by two examples of its application wrought out at length.

The demonstrations of four different methods of Clearing the Lunar Distance and of finding the longitude by Lunar Observations are also given, followed by examples shewing the best arrangement of the calculations. These methods

are all perfectly accurate, and require only the use of the ordinary tables of natural and logarithmic trigonometrical functions. Those, however, who wish shorter methods, and will be satisfied with near approximations, should consult Thomson's Lunar and Horary Tables.

Though the demonstrations of nearly all the rules are given, yet the rules are so enunciated that all the exercises may be solved by them, without mastering their demonstration as is generally done in other treatises; but every navigator will derive a special pleasure from knowing the reason of the operations he performs, and will be thereby much better qualified for advancement in his profession, since the knowledge thus acquired will enable him to pass his examinations before the Nautical Board with more ease and credit.

The exercises that require the use of the Nautical Almanac have all been given for the year 1866, so that the use of that almanac is desirable; but as some may use this work on Navigation who may not find it convenient to obtain that

almanac, the data necessary to be extracted therefrom to obtain
the solution, are generally given at the end of each question,
so that it may be wrought intelligibly without its use; but
those who have access to the almanac, should use the data
there given, as additional exercises in familiarising them with
the many important uses of that volume.

The answers to the exercises, which are inserted before
the Appendix, have all been carefully checked, and upwards
of a hundred have been recalculated, after being printed,
without a single error having been discovered.

The Chapter in the Appendix on the use of the Barometer,
Weather Forecasts, and the Law of Storms, has been compiled
from the best authorities on these subjects; and it is hoped
it will be found of no small importance to the intelligent
mariner, who should constantly watch how far the rules and
laws there stated agree with his own experience, that he may
be the better able to adapt himself to the various and fre-
quently trying positions in which his ship may be placed.

The other subjects contained in the Appendix are all of
interest to seamen, who, it is hoped, will derive much improve-
ment from their careful perusal. The Commercial Chapter
was furnished by Mr James Bolam of the Board of Trade
Nautical School, Leith.

For further information as to the subjects treated of in
the Work, the reader is referred to the Table of Contents.

JAMES PRYDE.

EDINBURGH, 1867.