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    Re: CN and Mason-Dixon line
    From: Frank Reed
    Date: 2013 Nov 27, 11:11 -0800

    Bruce, you wrote:
    "I've always been curious about the historical background of dip measurement data, and assumed the basic work was done by British astronomers. I guess you know if you are a close student of "dip", as Danson states, James Bradley published in 1720 a table of refraction "for the correction of astronomical measurements for the light bending effects of the atmosphere". That is really early! Amazing to me."

    Yes, it's amazing how early they got this worked out. But this is NOT connected with dip. There is frequent confusion between the problem of anomalous dip (which involves variations in refraction which are not predictable) and the problem of astronomical refraction of the positions of celestial objects ABOVE the horizon (which includes sensitivity to temperature and pressure which are highly predictable and dependable down to altitudes as low as one degree above the horizon).

    Anomalous dip depends on the details of the layering of air of different temperatures in the lowest layers of the atmosphere. Without detailed knowledge of the variability of density on the whole line of sight from the observer out to the horizon, the dip can only be estimated based on mean conditions. But amazingly the details of the layering in the atmosphere completely "cancel out" in the problem of astronomical refraction. So if there's a layer of hot air a mile high, it has no impact at all on astronomical refraction for celestial objects higher than a degree above the horizon. All of the complexity of the atmosphere through the troposphere and the stratosphere and beyond is completely irrelevant to astronomical refraction. The theoretical principle that makes this amazing result possible was first described by Cassini back in the 1650s. The layering of the atmosphere is irrelevant. Only the temperature and pressure right at the observer's location determine the airmass above. So strangely enough, astronomical refraction, involving the whole atmosphere from sea level right out to the "edge of space" is a much simpler problem than horizontal refraction and anomalous dip. The only technical problem not resolved by Cassini's analysis was the curvature of the atmosphere (due to the curvature of the Earth).

    You added:
    "I checked the 1802 Bowditch & Kirby Table VII Depression Dip of the Horizon (and also Bowditch 1837), and the dip table is basically the same as present. I conclude the original astronomical work and calculations for dip were done in early to mid 1700s. Really astounding the excellence of the early astronomers and mathematicians."

    The dip tables are based on a simple assumption: the atmosphere gets cooler with altitude at a constant rate. As we've discussed many times (possibly 'ad nasueam'), rays of light travelling nearly horizontally bend downward at a rate of some number of minutes of arc rotation per nautical mile depending on the detailed atmospheric layering. And since minutes of arc and nautical miles are really the same thing, this "rate" is actually a dimensionless number, call it "k". Depending on the actual "lapse rate" (the rate at which the atmosphere gets cooler with altitude) that constant k can be anywhere in the range from 0 to somewhat greater than 1, but on average it's around 0.12. But it varies, and as low as 0.05 and as high as 0.25 are relatively common, so what should we publish? Bowditch faced this decision back in 1802. He was at this time a highly skilled mathematician (self-taught!) but he was not much of an experimenter or observational scientist. Rather than checking the possible table values against observations (a tricky task even today since, as you know, anomalous dip close to shore may be very different from anomalous dip on the open sea), Bowditch instead made his decision based on an "appeal to authority". It was form of debate, not science, that convinced him.

    Meanwhile, in the eighteenth century, astronomers completed the project begun by Cassini by determining the modifications of the refraction tables due to the curvature of the atmosphere and also the specific dependence on temperature (barometric pressure is easy, but for temperature, you need to figure out where absolute zero is). In practice it was easier back then to agree that the curvature problem could be solved with a great deal of mathematical work involving "numerical integration" but it was equivalent to making measurements. In other words, you let the atmosphere do the numerical integration for you. There's no point developing generalized mathematical tools when there's only one atmosphere to simulate! Observations were used to complete the earliest accurate tables for atmospheric refraction.


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