As others have pointed out, you don’t need the logarithms. Tables of logarithms, trig-functions, & logs of trig-functions aren’t needed now that we have scientific-calculators, computers, spreadsheets, etc. Just use the trig-functions directly, as the others have said.
. You made a good choice when you chose the Horizontal-Dial. There are good reasons why it’s the most popular stationary dial. . For one thing, it’s the easiest one to build, & also the easiest to set up. . For another thing, the marking of its hour-lines is easily explained . Additionally, it can be read from any direction (though you have to stand fairly near to it), & it tells time whenever the Sun is up (unless it’s shaded by something). . About the explanation of the marking of the Horizontal-Dial’s hour-lines: . Start with a Disk-Equatorial. It’s a circular disk with equally-spaced hour lines radially marked around the gnomon that passes through the disk’s center, perpendicularly to the disk. It’s mounted so that the disk is parallel to the equator. It has a stick-gnomon going through it, through its center, perpendicular to the disk, & therefore parallel to the Earth’s axis. . The relation between the gnomon-stick’s length down from the lower face of the disk, & the disk’s diameter can be chosen so that when the device is laid on the ground, resting on the disk-edge & on the bottom-end of the long gnomon-stick, the gnomon will be parallel to the Earth’s axis . Disk-Equatorials have been mounted directly on the ground in that form. I once read that dials of that type were the earliest known sundials. . So, to make a Horizontal-Dial from an Equatorial-Disk Dial of that type: . Extend, project, the hour-lines to the ground. . The projected lines will intersect the ground along an east-west line. . To each of those intersections, draw a line from the point where the bottom-end of the gnomon-stick touches the ground. . Those are the hour-lines of the Horizontal-Dial. . The 6:00 line wouldn’t intersect the ground, because the line would be horizontal, but it’s evident that, the closer the time is to 6:00, the more closely the direction of the Horizontal-Dial’s hour-line approaches perpendicular to the noon hour-line. So just make the 6:00 hour-line perpendicular to the hour-line. (That’s neatly automatically achieved by the formula.) . Of course, on the summer side of the equinoxes, the day will start before 6:00 a.m., & end after 6:00 p.m. For those times’ hour-lines, just (for example) extend the 7:00 a.m. hour-line across the dial-plate, to make the 7:00 p.m. line. …doing the same for the other p.m. times that have sunshine. . When you read the definitions of the sine & the tangent, it will be obvious that the formula is just a mathematical expression of the above-described method for constructing the hour-lines of the Horizontal Dial. On Tue, Aug 9, 2022 at 1:50 AM Bryan Mumford <br...@bmumford.com> wrote: > I’m working from Albert Waugh’s book “Sun dials, Their Theory and > Construction”. On page 45 he presents a method for computing hour lines. I > lack significant math skills, but I know how to work Excel. I don’t > understand how he is calculating these values. > > He says, for example, that “log tan t” of 7°30’ is 9.11943. > > In my simple-minded way I asked Excel to show me log(tan(7)) and got a > very different value. > I tried converting 7°30’ to radians and that didn’t get any closer. > > How can I calculate "log tan t" or "log sin latitude” with Excel to get > the values he shows? > > I anticipate further problems with the last two columns, but you have to > start somewhere…. > > - Bryan > > > > --------------------------------------------------- > https://lists.uni-koeln.de/mailman/listinfo/sundial > >
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