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    Re: Intercept Method or Marcq St. Hilaire
    From: Antoine Couëtte
    Date: 2020 May 14, 09:52 -0700


    As a complement to Greg's post - and although you already know it - I would summarize Marcq St. Hilaire's (probably him, but some historians think that it might rather have been Villarceau I think) fundamental concept as follows :

    (1) - I observe heights in a sextant which I can transform into "Centers of Bodies Geocentric Heights". I have to accept that they all are the direct signature of only my true position (albeit unknown, or at least : currently not known with sufficient accuracy).

    (2) - If am now assuming for such actual unknown position that I am exactly at my "Best continuously updated DR position", at which Geocentric Height and in which Azimuth should I observe from the Earth Center each Body Center at the time of its own observation ?

    (3) - By comparison of (1) and (2) for each Body we get (3.1) an Intercept (3.2) and an Azimuth which altogether enable retrieving the actual position from the DR position as long as at least 2 different Bodies have been observed.

    In earlier French Terminology the exact equivalent for "Best DR Position" was "Vertical Estimé" (Estimated Vertical ?) frequently encountered in former literature.

    Whatever the computation process used for deriving the Geocentric Heights and Azimuths, and as long as you compare Actual Geocentric Heights to Computed Geocentric Heights from your Estimated Vertical (i.e. from your Best DR Lat / Lon), i.e. as long as you are using the concept depicted in (1), (2) and (3) here-above, then you are using the Marcq St. Hilaire's method.

    Another complete/unequivocal name for this method could be - or better: should be - "Intercept(s) and Azimuth(s) Method" , nonetheless by contraction it is most usually known as the "Intercept Method".

    You can immediately see the logical conclusion :

    Yes, since the United States Power Squadrons Intercept Method makes use the concept (1), (2) and (3) depicted here - with some add-on fine tuning about the optimum way to choose a convenient DR position to expedite computations - this method in its essence is exactly the same as the Marcq St. Hilaire's method.

    Best Regards,

    ⚓  Antoine M. Couëtte 

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