# NavList:

## A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding

**Re: Sumner's Line (Navigation question)**

**From:**Frank Reed CT

**Date:**2006 Feb 7, 01:45 EST

Bill wrote: "An ID 10-T question." First, thank you for making me look this up. To save anyone else the effort, if you write out ID-10-T, and drop the dashes... and make the "1" look more like an "I", you get IDIOT. Myself, I don't believe in "idiot" questions. They're usually GOOD questions. And so Bill asks his idiotic question: "I continually see references to the classic "time site," but none of my texts actually spell out how it was done or the equation(s) used. The best I can surmise is that with a know/given latitude and time, longitude may be determined. Any help on how it was practiced and and the math behind it (list or on-line references) would be appreciated." A very good query, Bill. A time sight is the 20th century name for the classic sight used in navigation from the late 18th century through the 1940s to determine local time at sea. It is, in many ways, a remarkably simple thing. Taking a time sight turns your sextant into a sundial. When we use a sundial, aligned to the correct latitude, we read off the Sun's local hour angle in hours and call it the time. A sundial also has to be aligned exactly north-south, but we can live without that alignment if we have an almanac available. From the almanac, we can get the Sun's declination (we still need the correct latitude for a time sight, just as with a sundial), then the Sun's altitude, which can be measured accurately with a sextant, automatically yields the Sun's local hour angle. This hour angle is exactly the same thing as the observer's local apparent time. In other words, if I measure the Sun's altitude, and do a little math on it (see below) and get, for example, 45 degrees, then the local apparent time is just 3pm exactly (or 9am if the Sun is east of the meridian). To reiterate, a time sight with a sextant performs exactly the same task as a sundial yielding the same information, the local apparent time, much more accurately and without the need for an exact north-south alignment. So what's the math that converts a measured altitude into an LHA? This is an easy spherical triangle problem. The Sun's local hour angle is the angle measured at the elevated celestial pole between the observer's meridian and the arc from the pole to the Sun (draw it!). To calculate that angle, we can use the three sides of the spherical triangle made by the Sun, Zenith, and the Elevated Celestial Pole. I won't spoil the fun. You try it out for yourself. Draw that triangle and solve for LHA using the cosine formula. That's it! On a calculator, it's easy. Note that it was popular in the logarithms-paper-and-pencil era to solve this triangle using the haversine formula instead of the cosine formula. It's a little longer, but you don't have toworry about as many "cases". That's what you'll find in old editions of Bowditch. It's conceptually the same thing as the cosine formula --just a different way to skin a cat. After we've done our time sight with our sextant (or read our sundial), and we have learned that the local apparent time is, say, 3pm exactly, what next? As we know, the difference between local time and absolute time, typically GMT, is exactly the same thing as the difference in longitude between the observer's location and the absolute time location, typically Greenwich. But there's a catch. Local apparent time runs a little fast or slow during the year compared with accurate clocks. That difference is the so-called "equation of time". So if you use a sundial and you want to know if it's accurate, you need to have a table of the equation of time handy. Many sundials in public settings have tables or graphs affixed to them or posted nearby (unfortunately, for most people, these tables usually create the impression that the sundial is "broken"). For out time sight, if we're going to determine longitude by getting GMT from a clock, then we need to correct the time sight by adding in an equation of time correction taken from the almanac. Before chronometers came along, there was an alternative approach. With lunar distances, it was easy enough to tabulate predicted geocentric lunar distances directly in "Greenwich apparent time", in effect making the celestial "lunar chronometer" read apparent time instead of mean time. That way, if it's 3pm by a local time sight and 9pm by a lunar distance sight, the longitude difference is simply 6 hours (or 90 degrees) exactly. No correction required. Until 1834, the tabulated lunar distances in the Nautical Almanac were listed for every three hours of Greenwich Apparent Time. After that year, they're published for every three hours of Greenwich Mean Time, for better comparison with chronometers. There were also "novelty" chronometers designed to read apparent time instead of mean time. This was really pointless, so they didn't last. Notice that a time sight, like a well-adjusted sundial, requires accurate knowledge of latitude. This dependence on latitude is minimized if the Sun bears nearly due east or nearly due west. Alternatively, you can take a sight to determine latitude simultaneously with the time sight, but this was rarely done in practice until the 20th century. Time sights started to become obsolete with the rise of the "New Navigation" (line of position navigation) in the late 19th century, but they were still widely practiced as the standard sights for determining local time, and hence longitude, as late as the 1940s. One more time: Sun's measured altitude (corrected) ---> cosine formula ---> Local Apparent Time Local Apparent Time + Equation of Time ---> Local Mean Time GMT (from chronometer or lunar) - Local Mean Time ---> Longitude -FER 42.0N 87.7W, or 41.4N 72.1W. www.HistoricalAtlas.com/lunars