AN ACCOUNT OF THE ARRANGEMENT AND IMPROVEMENTS IN THIS EDITION, t THE favourable reception which this Work has met with, emboldens me to present before the public the present Edition; in which I trust, I have introduced such improvements as will continue to me the favour which I so long have had the happiness to enjoy. In my former Editions I had digested the several Articles into a natural and simple order, and endeavoured to show how every thing might be deduced from the first and most simple principles of the Mathematics; in which, I trust, I had so far succeeded, as to render it easy to the most common capacity. How beneficial a work of this kind must be to learners cannot be doubted, when we reflect, that by being thus acquainted with the true principles of things, they will retain better what they have learned, and be enabled to make much greater progress in the art, than could otherwise possibly take place. Indeed, upon a careful perusal of the work, I found the plan I had pursued, so far as regards the parts of Navigation usually taught and practised at sea, could not be amended in the bulk, though some improvements might be made in particular parts. It particularly occurred to me, that I had invariably found young gentlemen, who attended me for a private examination, previous to their passing a public one, deficient in working an observation in all the variety of situations which may take place. In this work I have accordingly elucidated this important article, by giving a rule for every different situation, in which the observer can possibly find himself in respect of the Sun; illustrating each with a projection on the plane of the Meridian. There is introduced into this Edition a Table for the near calculating the time of High-Water, with the assistance of the Nautical Almanack. I pass over many others of smaller note in the first part of the book, such as partial amendments of the style, &c. in haste to give an account of the Arrangements and Additions in the latter part of this WORK, which is for the most part NEW. Previous to the year 1767, when the first NAUTICAL ALMANACK was published, the practice of funding the Longitude at Sea was universally by account. The mode of ascertaining it by taking the Moon's distance from the Sun, or a fixed Star, commonly called the LUNAR OBSERVATIONS, was attended with difficulties insurmountable to most mariners. By the unremitting assiduity of the Astronomer Royal, to whose labours the Nautical Art is much indebted for its present high state of improvement; and by the rewards held out by Parliament, and the consequent improvements in instruments for measuring the Angur Distance; what before was considered as nearly an impossibility, So come into almost general practice. Proud of contributing my quota towards the facilitating this laudable purpose, so highly conducive to the commercial interests of this powerful Empire, I have endeavoured to render this part of the Nautical Art as simple and plain as the nature of the subject will admit. To the description of HADLEY'S QUADRANT is added the description and use of HADLEY'S SEXTANT, with an account of the new mode of dividing the nonius, so that the distance can be read off to fifteen seconds. The method of adjusting the Sextant and Telescope is fully enlarged upon, together with the use of this instrument, in observing the Angular Distance. PARALLAX and REFRACTION are next defined, and illustrated with a Plate. The method of applying the corrections for Parallax and Refraction to the observed distance, in order to reduce it to the, true, is next given. It being frequently complained to me by seamen, that it is next to impossible to find and know the Stars from which the Moon's distance is computed in the Nautical Almanack, I have, to remedy this defect, subjoined to this work two plans of the Stars, one on the plane of the Equator, the other on the plane of the Meridian; a description of the projection and use of these plans is given at large in the work, together with some PRACTICAL DIRECTIONS for knowing the Stars. Next in order is the method of finding the TRUE TIME, in order to re- gulate the going of the watch. The Lunar Observations follow, arranged in a new, clear, and perspicuous manner. The examination of a YOUNG SEA OFFICER, being an abstract of practical seamanship, has been examined by two professional men, and large additions made. We have also added, what we conceive will be an acceptable article in the present times of hostility,-The method of exercising private Ships' Companies for War. In this article, the forms of two Quarter Bills are given, with the Exercise of the great Guns, according to the present practice, and some approved manoeuvres in attacking and defending a single ship. Two additional Tables will also be found, one exhibiting the Proportion of Powder for Sea-Guns, the other the Number of Shot contained in Grapes of different sizes. A variety of methods of relieving Ships in Distress; the best means of saving people from Wrecks; and the process recommended by the Royal Humane Society for recovering drowned persons; will also be found. To the Tables a solicitous attention has been paid. The Tables of Difference of Latitude and Departure for Points and Degrees, have been re-calculated with the greatest care. The Tables of Logarithms of Numbers, and of Artificial Sines, Tangents, and Secants, have been carefully compared with the third edition of Hodgson's Tables, printed in the year 1738; with Gardner's third edition of Sherwin's, printed in the year 1742; and with Dr. Hutton's last edition, by three persons; so that I trust the errors, if any, are few. The Tables which follow have undergone a similar examination. To the Tables of the Sim's Declination, a most scrupulous attention has been paid. The Table of Latitudes and Longitudes of places is corrected by the latest surveys and observations, and great additions made. .Table XIII. For reducing the Sun's Declination to any given Meridian, and to any time under that Meridian, in the first page of vii which you have the proportional parts of the daily difference of the Sun's declination to every minute and every six seconds, answering to every five minutes of time, and to every degree and fifteen miles of Longitude. The second and third pages contain the same proportional parts to every hour, and to every fifteen degrees of Longitude. To the Table XVI. for turning degrees and minutes into time, and the contrary, two columns are added on the right side, for turning minutes and seconds (of an hour) into Longitude, and the reverse. Table XVII. contains the decimal of every minute in twelve hours, being of ready use for finding the proportion of the small difference (in twelve hours) of the Moon's Parallax and Semi-diameter, by taking out the number from the Table answering to the time when the observation was taken, and multiplying the differences therewith, from the product of each cut off four figures from the right hand, the left hand figures are the answers (if no fraction remains); which must be additive or subtractive, according as they are increasing or decreasing. The proportional part of the daily difference of the Sun's or Star's right ascension is found by taking out the number, answering to half the time required, and multiplying the difference therewith, from the product cut off four figures from the right hand, the remaining figures are the answer. Thus you avoid working by the Rule of Three. In the precepts for finding the Longitude by Lunar observation, page 238, you are told to make use of the Log. Sine of 30 degrees*, half the sum of the apparent altitudes, and half the apparent distance. In this edition, which has been carefully examined, improved, and corrected, by JOSEPH DESSIOU, is added Table XXVII. for reducing minutes into seconds, and the contrary, being of use in calculating the proportion of the difference of the Moon's semi-diameter and parallax in twelve hours, &c. *The Log. Sine of 30 degrees is equal to the Natural Sine of half the Radius; and, according to Euclid, Axiom 6, Book I. what things are each of them half of the same quansity, are equal among themselves.. CONTENTS. The common Way of finding a Ship's Tonnage at London To find the Logarithms of Sines, Tangents, and Secants, belonging to To find the Degrees, Minutes and Seconds, corresponding to any given To find the Logarithm of the Sine or Co-sine, for Degrees, Minutes, |