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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 heavily illustrated with mathematical diagrams. It also contains a 1785 copy of a ship log for a 1772 voyage from England to Madeira, (21 pages).

"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.

The Practical Mathematics manuscript contains definitions and problems related to algebra, geometry, trigonometry, navigation, and surveying. Many of the problems are accompanied by illustrated figures and/or practical examples.

The Practical Mathematics manuscript contains definitions and problems related to algebra, geometry, trigonometry, navigation, and surveying. These categories are divided into specific applications; the section on algebra deals with topics such as basic algebraic statements, algebraic fractions, simple and quadratic equations, and arithmetical and geometrical progressions. Most of the problems are accompanied by illustrated figures and/or examples of concepts' practical applications. A section concerning globes pertains to both terrestrial and celestial globes, and includes a list of the signs of the zodiac, as well as descriptions of navigational methods, accompanied by a compass rose and charts, including "Mercator's Charts."

The manuscript also explains methods for determining location and time by observing celestial objects, and contains instructions for keeping ships' logs and surveying notes. A section on navigation includes a copied log from the voyage of the Pegasus from England to Barbados (January 31, 1737-March 22, 1737), as well as a map showing the coasts of France and Spain and the islands around Barbados. Some of the surveying problems are illustrated with a sailing ship, a tree, and a turret.

• Algebra
  • Simple Equations
  • Quadratic Equations
  • Arithmetic Progressions
  • Geometric Progressions
• The Use of Globes
  • Terrestrial Globe
  • Celestial Globe
• Spherical Geometry
• Spherical Trigonometry
  • [Acute] Angled
  • Right Angled
  • Oblique Angled
• "To Find the Prime or Golden Number"
• Geometry
• Trigonometry
  • Plain Trigonometry
  • Spherical Trigonometry
• Navigation
  • Latitude
  • Longitude
  • Sailing
    • Plain Sailing
    • Traverse Sailing
    • Mercator's Sailing
    • Parallel Sailing
    • Oblique Sailing
    • Plain Sailing by Arithmetic
• Observation by the Meridian Altitude or Zenith Distance of the Sun or Stars
• Rules for Keeping a Journal [Ship's Log]
• Astronomy
• Dialing
• Surveying
• Mensuration
  • Mensuration of Superficies
  • Mensuration of Solids
  • Measuring of Timber

The Zaccheus Brown notebook contains information compiled between 1782 and 1783 on arithmetic, sailing and navigation, and surveying, as well as a log of the Phoenix's voyage from New Jersey to the Virgin Islands in 1789. Mathematical and navigational problems are often illustrated with diagrams, and the volume also contains an example of a Mercator chart of the Caribbean.

The Zaccheus Brown notebook (175 pages) contains information on arithmetic, sailing and navigation, and surveying, as well as a log of the Phoenix's voyage from New Jersey to the Virgin Islands in 1789.

The first 112 pages, compiled from 1782-1783, are comprised of information about mathematics and sailing and contain a brief ship's log. Mathematical subjects include square and cube roots, geometry, and plane trigonometry; Brown copied and solved mathematical problems, which are often illustrated with diagrams. Instructions for aiming cannons appear in the section about trigonometry. Brown also described sailing methods such as plane, traverse, oblique, Mercator, parallel, middle latitude, and current sailing, as well writing instructions for turning a ship windward and for determining location. The parts of the volume concerning sailing also contain problems, diagrams, and an example of a "Plane Chart" and "Mercator's Chart." The Mercator's chart shows the locations of islands in the northern Caribbean Sea. The notebook's other subjects include the compass, calculating the phases of the Moon, and the Gregorian calendar. A final section pertains to surveying.

Zaccheus Brown's notebook also contains logs concerning the voyage of the Endeavour (9 pages) and the schooner Phoenix (58 pages). The Endeavour log, attributed to "L. H," notes the ship's journey "from the Cape" in late June and early July 1783. The Phoenix log details Brown's voyage from June 17, 1789-September 1, 1789 from Salem, New Jersey, to the Virgin Islands and back to Virginia. Some of Brown's daily entries about his voyage on the Phoenix include charts recording the ship's course and position, along with additional remarks on wind speed and direction. Brown occasionally discussed other aspects of his voyage, such as the pidgin language spoken by the ship's Dutch crew and his premonitions after bad weather and delays. He also described the port and the island of Saint Thomas, a Dutch colony (currently part of the United States Virgin Islands).

The volume contains illustrations of a man in the sun, a compass rose, and a fish and man; the latter drawings are flourishes on the heading for the section of the book on cube roots. The back endpaper includes a table of angles related to navigation.