"Elements of Navigation," a manuscript adaptation of John Robertson’s work of the same name, provides instruction and practical exercises in arithmetic, geometry, trigonometry, geography, astronomy, and navigational principles (781 pages). The volume is illustrated with mathematical diagrams. It also contains a 1785 copy of a ship's log for a 1772 voyage from England to Madeira (21 pages). The book is divided into 14 primary chapters, 11 of them preceded by an ink or watercolor illustration of buildings, ships, and places, such as the watercolor drawings "The Desire in a Storm" and "A west View of Islington, old Church." (See below for complete list.) Several chapters are further divided into sections, and most chapters or sections are followed by problems, questions, case studies, answers, and explanations. Please see the box and folder listing below for a table of contents.
The volume begins with explanations of basic mathematical principles, including arithmetic operations, decimals and fractions, roots and powers, notation, and "Tables of English Money, Weights, and Measures" (pp. 9 verso-10 verso). This chapter is followed by theorems and problems of geometry and trigonometry. The subsequent section on geography contains prose explanations of the discipline's foundations, such as the shape of the Earth, the concept of latitude and longitude, and the currently known world. Remarks on the continents are accompanied by tables showing major countries, principal cities, rivers, and mountains. The tables for North and South America are split, and individual states within the United States are identified as "countries," as are California, New Mexico, Old Mexico, Louisiana, Canada, New Britain, New Wales, and others. Introductory geographic material also includes content on winds, tides, and bodies of water. A segment on "chronology" introduces several scales for measuring time, and explains the reasoning behind concepts such as the leap year and the "Golden Number" (pp. 147-147 verso).
The remainder of the work focuses on the art of maritime navigation. Several topics include: the calculation of compound courses, oblique and windward sailing, sailing in currents, and globular sailing. The sections devoted to each topic are comprised primarily of rules or theorems, exercises, and illustrations of practical applicability. A chapter on "spherics" introduces spherical geometry and trigonometry. Two chapters on astronomy explain concepts in "star astronomy," "terrestrial astronomy," and "spherical astronomy," such as the composition of the Solar System, planetary movements, and mathematical applications. The final 80 pages contain information on the art of sailing and expand on principles previously discussed. These pages include instructions on how to calculate the location of a ship at sea, make necessary observations, and correct a ship's course, among other similar topics.
The final 21 pages consist of a log from an unknown ship traveling from England to Madeira in 1772, transcribed by James West in 1785. Between July 2 and July 11, the log contains notes on the weather, wind direction, and general remarks of occurrences on board as the ship prepared for its journey at Deptford, London. On one occasion, the author mentioned a sailor being disciplined for drunkenness (July 3). Between July 12 and July 28, the log documents the weather, wind direction, ship's location, use of various sails, and other information compiled throughout the course of each day. The ship arrived at Madeira on July 28. The log is followed by a brief note by James West concerning the location of Funchal, Madeira.
The non-mathematical illustrations separating the book's chapters are done in ink or watercolor, and depict rural scenes and sailing ships.
- [View of a village, with a man fishing in a river], p. 2
- [View of a river, with a cylindrical building in the foreground and a church in the background], p. 76
- [View of an arched gateway, with attached buildings and bridge], p. 114
- [View of a stone building with a high-peaked roof, alongside a body of water], p. 138
- "The Victor in a calm sea," p. 187
- [Oval-framed view of two persons sitting beside a river, with a ship and fortifications in the background], p. 202
- "The Desire in a Storm," p. 223
- [Oval-framed view of a small sailing vessel on shore beside a stone building], p. 241
- "A west View of Islington, Old Church," p. 267
- "Teneirs House," p. 319
- "At Abingdon 1782," p. 349
The royal coat of arms of the British monarch is imprinted on the volume's front and back covers.