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    Re: Vertical Angle Measurement Errors
    From: Bill Morris
    Date: 2013 Apr 1, 15:55 -0700

    G'day, Bruce

    In general, a scale-reading instrument, as opposed to a micrometer one, should not suffer from backlash. All may have centring errors but in the Wild T2 and many other theodolites, readings are taken simultaneously from each side of the scale, so centring errors should not apply.

    The coincidence-reading vertical bubble on the T2 is effectively of 15 seconds sensitivity per 2.5 mm of bubble movement. A gap of 0.16 mm between the ends of the bubble is detectable, but only just, so the instrument is at its absolute limit of precision when reading to single seconds. It doesn't matter how extended the optical micrometer scale might be. The sensitivity of the bubble is a limiting factor.

    I have just taken a series of 16 sights of the top of a barn 6 km (3.2 nm) away to see what their dispersion about the mean might be. The distance correspnds to a height of eye of about 3 metres. The standard deviation was 4.3 seconds, with a range of 16 seconds. At this distance, on a patchy overcast day, air temperature 22 deg C, the atmosphere bubbles and pops, so that the roofline was seldom a straight line for more than a few seconds at a time and it shimmered, sometimes above and sometimes below the initial setting, rather as I have described for my sea horizon observations, without the wave and swell. Three fence posts near the structure sometimes appeared sharp but more often were blurred or even invisible.

    Given the atmospheric variation and the effects of wave and swell I think it would be optimistic to expect vertical readings to have accuracies better than 10 to 20 seconds. Nothing much is going to alter that apart from taking myriads of readings that give results bearing no relationship to practical observations at sea. The Soviet Navy presumably came to the same conclusion and provided dip meters.

    Bill Morris
    New Zealand

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