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The opposite face of the Oughtred Circles of Proportion is the 'Horizontal Instrument', essentially a portable sundial. Along with a working model of the horizontal instrument that was rendered by Rob Davenport for 56 N, I've produced a PDF containing versions of the Horizontal instrument for latitudes between latitudes 30 and 59 N.
One of the reasons I undertook this project was to learn to read 17th-century technical English, which I still find very difficult. It proved so difficult that I resorted to using modern sources to provide the trigonometry needed to program it. More on that here.
As a side comment, Oughtred's 'Circles of Proportion and the Horizontal Instrument' reads as if it were two different works tacked together. I suppose that's plausible given he reportedly did not invent the two devices at the same time.
Part 2 is devoted to the Horizontal Instrument and dialing (the art of making sundials). Along with instructions for various useful computations that one might perform with the instrument, he includes instructions for how to make the instrument, and other dials or other orientations of this dial.
This instrument is based on a stereographic projection of the daytime sky onto a flat plane. Oughtred created it when he was quite young, still in university. He believed that he was the first to invent this kind of projection (not the Stereographic projection, itself, which is quite ancient, but projecting to a horizontal plane for a dial). However, it's known now several individuals on the continent actually had created such projections earlier.
I found while generating for multiple locations, the Horizontal Instrument is not suited for very low latitudes, because Oughtred uses a movable index and puts an hour scale on the inside of the projection. As the latitude decreases, the stereographic projections become narrower and lower, effectively closing in on the center of the device. At latitudes nearing 30 N, parts of the face of the computer will be covered by that index.
The compression at low altitudes also means the spacing between lines is compressed, so it becomes more difficult to use the instrument.
horiz.pdfThis is a PDF file for The Horizontal Instrument.
This version of it is almost complete, and certainly workable now. I have verified that the azimuth scale on the indicator should work for all latitudes, and have used the disc to execute a few computations from Oughtred's book.
There should be two other Poles on the face (apparently related to the ecliptics). I've so far not been able to determine how they are to be placed.
There is a description of a 'Pinne', which is to be used for some measurements. It had me worried because there was no description as to how it would be made. As it turns out, the length of the pin is not important, other than it is long enough to provide a shadow across the disc - This is so that you can see what angle the sun is at by the intersection of the pin's shadow on the circumference.
This version is using the period-appropriate Julian calendar rather than our modern Gregorian calendar. You will need to add 11 days to correct it to modern calendars when attempting date specific computations.
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