The Gunter’s Scale uses logarithmic and other scales to assist in numerical and trigonometric calculations. Instead of using a sliding scale like the later slide rule to assist in the addition or subtraction of logarithms, the user of a Gunter’s Scale uses dividers to mark sums and differences. The Gunter’s Scale is particularly specialized for nautical use, as some of its scales make direct solution of dead reckoning problems relatively easy. Developed by Edmund Gunter in 1623, Gunter's Scales or Rules continued to be made and used into the 19th century.
After returning from an unsuccessful exploration trip to Labrador, in 1602 George Waymouth set down to write and illustrate his book The Jewell of Artes. Two copies were apparently presented to the new king, James I, in 1604, possibly as part of a search for employment. Two manuscripts exist, one at the Beineke Library at Yale University, the other in the British Library. James Baxter, founder of the Maine Historical Society, had a copy of the British Library volume made, which was on display at the Tercentenary of Waymouth’s voyage but since has disappeared.
The cross staff measures the angle of altitude of the sun or moon or a star by sighting from one end of a staff, past ends of a cross piece, towards the horizon and the celestial object. The cross arm is moved up or down a graduated staff so that when sighting along the staff the user sees the sun or star and horizon at the ends of the cross arm. The altitude is then read off the staff. The altitude is measured on a scale along the staff.
This illustration comes from Medina's Arte De Navegar, 1545.
This working reproduction of a cross staff shows a scale along the staff and four different length cross pieces, so that different altitudes may be measured precisely. The height of the celestial body to be observed over the horizon determines which scale and arm is used.
Drawing of an astrolabe from Medina's Arte de Navegar, 1545. The seaman's astrolabe was a graduated ring or disc fitted with a sighting rule pivoted at the center. The instrument was suspended so that it hung vertically. The user then turned the sighting rule so that the sun or star could be sighted along it and the altitude read off the ring. It dates back to ancient Greece and was heavily used in the Islamic world. The first records of a seagoing version date to around 1481.
The seaman's quadrant was first used at sea around 1460, about twenty years before the astrolabe. It is a quadrant of a circle, made of wood, with a sight up one side, a scale along the arc, and a hanging weight on a string from the apex of the quadrant. The quadrant was used to tell relative distance traveled north or south from a port of departure, something done more easily than measuring an accurate sun height to determine latitude.
The traverse board is used to keep track of changes in a vessel's speed or course over the period of a four-hour watch. At the end of each watch, the courses and speeds are added together, with the help of traverse tables, or by estimation, and marked in the logbook or on a chalkboard. A peg is put into a hole every half hour for the course steered, and another is inserted to reflect the approximate speed sailed. The traverse board, though used some in the sixteenth century, was more common in the seventeenth century.
The chip log, a log line reel, and the sand glass used for measuring the speed of a vessel through the water. The chip is tossed, the sand glass turned, the line let out, and the number of knots in the line are counted until the sand glass empties. The number of knots that have passed is the speed of the vessel in knots or nautical miles per hour.
This illustration is from Bowditch's New American Practical Navigator,1868, Plate VI.