# NavList:

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

**Re: Eqn. of time**

**From:**George Huxtable

**Date:**2007 Jan 9, 18:26 -0000

Bill had asked- | "That caused me to wonder if at some time in the past there was | a conscious effort to link the equation of time to some celestial event." And Frank answered- | er... how could there be? Its numerical value follows directly from its | definition. The values on specific dates do change over the centuries and | millennia. Is that what you were asking about? It's quite possible to define equation of time in different ways, and historically, it has indeed been defined in different ways. The first printed version of an equation of time came from Christian Huyghens, in "Kort Onderwys ...", 1665, which has been reproduced in "The Quest for Longitude". It became necessary, in Huyghens' development of an accurate pendulum clock, to provide a way for that "mean-time" clock to be checked from observations of the Sun, using a sundial or some other noon sightline. Remember, in those days, sundial time, from the apparent Sun, was "the time". Equation of time was different from what we know today, in that instead of being split halfway, as it is at present, about equally one way and the other over the year, Huyghens put his zero-point at one extreme value, then at 10 Feb. In that way, it made arithmetic simpler, the correction being always in the same direction. It provided an amount, ranging from zero to 32 minutes, to add to sundial time to establish what a "mean-time" precise clock should read. I put "mean time" in quotation marks for reasons you will see. In 1676, two Tompion "regulator" clocks, each with an enormous pendulum 13 feet long, were got going at Greenwich, showing sidereal time from the stars, and mean solar time from the Sun. They still exist. They were adjusted according to a special fixed telescope that could see Sirius as it crossed the meridian, even in daytime. They provided the working time-scale for the observatory, which would then observe, and predict, the moment of the Sun's meridian passage on that basis. So the purpose of the equation-of-time table had been reversed; instead of its use for adjusting a "mean-time" clock from the Sun, it became a matter of predicting the position of the Sun from a mean-time clock. That solar clock was set to keep what was called "Greenwich Mean Time", and the "Mean" part of the name gets us to the answer to Bill's question. It was taken to be, on average, exactly as much behind the apparent Sun as it was ahead of it. So now, the Equation of Time was measured from a zero-point that was somewhere in the middle of it's range. Not just roughly, but precisely so, splitting the EoT curve, such that the area above it exactly equals the area below it. That's what Bill should find if he looks at the "Total" curve provided by Frank. It's implied in the definition of "Mean". It's implied, also, in the symmetry about zero of the two individual nearly-sine curves, that combine to make up the total. From that zero, the dates of the four zero-crossings follow. They follow a similar pattern, year to year, but change a bit over centuries, as the date of the Earth's perihelion slowly drifts. So, going back to Huyghens, his pendulum clocks had been set, from his own EoT table, to read a steady time at The Hague: not "Mean Time at the Hague", but getting on for a quarter-hour different. You could think of it as being a mean time, I suppose, but not local mean time there, but somewhere else, nearly 4 degrees away in longitude. Although Greenwich "worked" on Greenwich Mean Time, from the first Nautical Almanac in 1767, nearly all predictions were given in terms of Apparent Time, until 1834, when they finally recognised that significant numbers of mariners possessed chronometers and could use mean time. ============================ So how was the EoT table tabulated, to allow the conversion between mean and apparent times? Which way round do you present the sign of the change, when converting one timescale to the other? That's been a source of confusion, and obscurity, ever since. Consider one extreme EoT value, that in mid February, which Huyghens took as his zero. Maskeyne's table, in the Nautical almanac, gives it as 14m 42s, heading the column "add". He tells us in his explanation, that this, "when applied to the apparent time, ... gives the mean ...time". In the modern almanac it's stated differently. The EoT is shown, for each day, at noon and midnight, and the entry is shown either with a shaded background, or without. For February, it's shown shaded. An explanation is given as follows- "The sign is positive for unshaded vales and negative for shaded values. To obtain apparent time, add the equation of time to mean time when the sign is positive" And vice versa. When you have worked out the convolutions of that, it turns out to be the same as for 1767; as it should, of course. The 1864 almanac headed the relevant column, for February, "Equation of time, to be added to apparent time". For other months, it would say "subtracted". Sometimes, that designation switched mid-month. Simplest to understand was that in the old Reed's, which simply attached a + or a - to each entry, and on each page states "Equation of Time is the excess of Mean Time over Apparent time". I think that's also the way round that it's quoted in some European almanacs. Why all this confusion then? Mostly, it's in the adoption of a silly name, "equation of time", which gives no clue as what's to be applied to what, and which way. Much better would be to adopt a simple name that explained itself, leaving no room for confusion, such as "Sun Lag", which would be positive in February and negative in December. Pity that never happened. George. contact George Huxtable at george---.u-net.com or at +44 1865 820222 (from UK, 01865 820222) or at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK. --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to NavList@fer3.com To unsubscribe, send email to NavList-unsubscribe@fer3.com -~----------~----~----~----~------~----~------~--~---