NavList:

About a year ago I posted a preprint describing how the Secant, Tangent and Semi-tangent scales on a device called a Plane Scale could be used to solve problems in spherical trigonometry and hence navigation by graphical constructions on the plane. This was done by exploiting some remarkable properties  of stereographic projection. In researching the history of the Plane scale I had come across John Aspley's 17th century work, Speculum Nauticum, which describes an early version. It lacks the scales mentioned above and is therefore limited to solving problems in plane trigonometry. Aspley shows a diagram of the front side of his Plane Scale but only provides a description of the two "Lines of Longitude" scales on the back. There are descriptions by later authors of these scales but I was left with lingering doubts about exactly what they what they looked like. Drawing on Aspley's description and worked examples in his text I believe I now have a precise understanding of the nature of these scales and can replicate Aspley's calculations. My conclusions are written up in the attached document. I also attach a set of blank scales in case anyone is interested in whipping out their dividers and following along with Aspley. (Note: I have used the 1647 edition of Speculum Nauticum rather than the 1624 edition as the former is available as a better quality version online)

Robin Stuart

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