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THE RIGHT HONOURABLE GILBERT, EARL OF MINTO, G.C.B., &c., &c.,
VICE-ADMIRAL SIR CHARLES ADAM, K.C.B., M.P.,

REAR-ADMIRAL SIR WILLIAM PARKER, K.C.B.,

REAR-ADMIRAL THE HONOURABLE GEORGE ELLIOT, C.B.,

CAPTAIN SIR EDWARD THOMAS TROUbridge, barT., M.P.,-and

THE RIGHT HONOURABLE LORD DALMENY, M.P.,

HER MAJESTY'S LORDS COMMISSIONERS FOR EXECUTING THE OFFICE OF LORD HIGH ADMIRAL OF THE UNITED KINGDOM OF GREAT BRITAIN AND IRELAND,

THIS TREATISE,

DESIGNED TO AFFORD TO THE NAVIGATOR A COMPREHENSIVE

AND PRACTICAL GUIDE

TO THE SCIENCES OF NAVIGATION AND NAUTICAL ASTRONOMY, AND NOW ADAPTED TO THE IMPROVED ELEMENTS CONTAINED IN

THE NAUTICAL ALMANAC;

IS,

BY THEIR PERMISSION, MOST RESPECTFULLY AND GRATEFULLY

DEDICATED,

BY THEIR LORDSHIPS' MOST HUMBLE

AND MOST OBEDIENT SERVANT,

THE AUTHOR.

PREFACE.

ALTHOUGH the importance and general utility of the subjects treated of in this work are sufficient to recommend it to public attention, without the aid of prefatory matter, yet, since there is an extensive variety of nautical publications now extant, I think it right to say something relative to what I have done, were it for no other purpose than that of satisfying the reader that the present work is widely different from any former treatise on nautical and mathematical subjects. The following observations will develope my motives for commencing so laborious an undertaking.

In perusing the various nautical publications which have appeared for many years past, I observed that they all fell considerably short of the objects at which they professed to aim ;-some, by being too much contracted, and others by not including all the necessary tables, or by being generally defective: and that, therefore, a great deal remained to be done, particularly in the tabular parts, beyond what had yet been brought before the public.

Of the nautical works that came under my notice, some have proved, on examination, to be so inaccurately executed, as to be entirely unfit for the consultation of any person not sufficiently skilled in the mathematics to detect their numerous errors. Many of the works in question are extremely incomplete, through their want of particular tables, and their logarithms not being extended to a sufficient number of decimal places such as those by Mendoza Rios, where the decimals are only continued to five places of figures, and where the logarithmic

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tangents are entirely wanting; for, although the addition of a logarithmic sine and a logarithmic secant will always produce a logarithmic tangent, yet there are few mariners so far acquainted with the peculiar properties of the trigonometrical canon, as to be able to find by Rios's tables the arch corresponding to a given logarithmic tangent.* Hence, when the course and the distance between two places are to be deduced from their respective latitudes and longitudes, by logarithmical computation, the mariner is invariably obliged to have recourse to some other work for the necessary table of logarithmic tangents. Besides, since none of the nautical works now in use exhibit the principles upon which the tables contained therein have been constructed, the mariner is left without the means of examining such tables, or of satisfying himself as to their accuracy; though it is to them that he is obliged to make continual reference, and on their correctness that the safety of the ship and stores, with the lives of all on board, so materially depend.

Notwithstanding that Mr. Taylor's Logarithmical Tables are the most extensive, the best arranged, and by far the most useful for astronomical purposes, of any that have ever appeared in print,-yet, since they do not contain the necessary navigation tables, they are but of little use, if of any, to the practical navigator: and, since the same objection is applicable to the very excellent system of tables published by the learned Dr. Hutton, these are, also, ill adapted to nautical purposes, and but rarely consulted by mariners.

Being thus convinced that there was something either deficient or very defective in all the works that had hitherto been published on this subject, I was ultimately led to the conclusion that a general and complete set of Nautical Tables was still a desideratum to mariners: with this conviction on my mind, I was at length induced to undertake the laborious task of drawing up the following work; in the prosecution of which I found it necessary to exercise the most determined perseverance and industry, in order to surmount the fatigue and anxiety attendant on such a long series of difficult calculations.

These points premised, it remains to present to the reader a familiar and comparative view of the nature of this work, and of the improvements that have been made in the tables immediately connected with the elements of navigation and nautical astronomy: confining the attention to those that possess the greatest claims to originality, or in which the most useful improvements have been made.

Table VI. contains the parallaxes of the planets in altitude; and

* See Remark, page 98; with diagram and calculations, page 99.

will be found particularly useful in deducing the apparent time from the altitudes of the planets, and, also, in problems relating to the longitude. The hint respecting this was originally taken from the Copenhagen edition of "The Distances of the Planets from the Moon's Centre, for the Year 1823;" but this design has been considerably enlarged and improved upon.

Table VIII. is so arranged that the mean astronomical refraction may be taken out at first sight, without subjecting the mariner to the necessity of making proportion for the odd minutes of altitude, This improvement will have a tendency to facilitate nautical calculations.

Table X.—The arrangement of this table is an improvement of that originally given by the author, in his treatise called "The Young Navigator's Guide to the Sidereal and Planetary Parts of Nautical Astronomy." By this improved table, the correction of the polar star's altitude may be readily taken out, at sight, to the nearest second of a degree, by means of five columns of proportional parts; and, to render the table permanent for at least half a century, the annual variation of that star's correction has been carefully determined to the hundredth part of a second. By means of this table, and that which immediately follows (Table XI.), the latitude may be very correctly inferred at any hour of the night, in the northern hemisphere, to every degree of accuracy desirable for nautical purposes.

Tables XIII. and XIV. contain the equations to equal altitudes of the sun these have been computed on a new principle, so as to adapt them to proportional logarithms, by means of which they are rendered infinitely more simple than those given under the same denomination in other treatises on nautical subjects; they will be found strictly correct, and, from their simplicity, a hope may be entertained that the truly correct and excellent method of finding the error of a watch or chronometer by equal altitudes of the sun, will be brought into more general use.

Tables XV. and XVI., which are entirely new, contain correct equations for readily reducing the longitudes, right ascensions, declinations, &c. &c., of the sun and moon, as given in the Nautical Almanae, to any given meridian, and to any given time under that meridian.

Table XVII. contains the equation corresponding to the mean second difference of the moon's place in longitude, latitude, right ascension, or declination: this table, besides being newly-arranged, will be found more extensive than those under a similar denomination, usually met with in books on navigation.

Table XVIII. is so arranged as to exhibit the true correction of the moon's apparent altitude corresponding to every second of horizontal parallax, and to every minute of altitude from the horizon to the zenith: