To find the measure of the sun's diameter in English miles.... 614 To find the ratio of the magnitudes of the earth and sun ...... To find the rate at which the inhabitants under the equator are carried in consequence of the earth's diurnal motion round its To find the rate at which the inhabitants under any given parallel of latitude are carried, in consequence of the earth's diurnal XVII. To find the length of the tropical or solar year XVIII. To find the rate at which the earth moves in the ecliptic...... XIX. To find the measure of the moon's diameter in English miles .. 617 To find the ratio of the magnitudes of the earth and moon...... To find how much larger the earth appears to the lunar inha- bitants than the moon appears to the terrestrial inhabitants.. 618 XXII. To find the rate at which the moon revolves round her orbit.... 619 XXIII. To find the true distance of a planet from the sun XXIV. To find the comparative heat and light which the different planets XXV. To find the measure of a planet's diameter in English miles .... 621 XXVI. To find the time that the sun takes to turn round its axis XXVII. To find the length of a pendulum for vibrating seconds.... XXVIII. To find the length of a pendulum for vibrating half seconds.... 623 The true method of finding the index error of a sextant, &c. so as to guard against the error arising from the elasticity or spring ΤΟ HIS ROYAL HIGHNESS WILLIAM HENRY, DUKE OF CLARENCE AND ST. ANDREWS, K.G., &c. &c. &c. LORD HIGH ADMIRAL OF THE UNITED KINGDOMS OF GREAT BRITAIN AND IRELAND. MAY IT PLEASE YOUR ROYAL HIGHNESS; THIS Treatise, which I am graciously permitted to lay before your Royal Highness, is the result of long study and labour; the chief aim of which has been, to contribute, in some measure, to the benefit of the Naval Service of His Majesty. To this end, I have sought to combine simplicity, perspicuity, and conciseness, in trigonometrical calculations, in a greater degree than has hitherto been attempted by the writers of nautical works; and to comprise, in one book, a compendium of all the sciences that may be useful or interesting to the practical navigator. That my humble attempt has met with your Royal Highness's approbation and high sanction, I shall ever esteem to be the most honourable circumstance of my life; that it has been deemed worthy of the honour of your Royal Highness's patronage, I cannot but feel as the greatest mark of the condescension of your Royal Highness. I have the honour to subscribe myself, Your Royal Highness's Most obedient, most devoted, And most grateful Servant, THOMAS KERIGAN. Portsmouth, December, 1827. b 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 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' 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 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. *See Remark, page 98; with diagram and calculations, page 99. |