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    Henry's equal altitudes
    From: Frank Reed
    Date: 2009 Apr 25, 21:54 -0700

    Henry Halboth, you wrote:
    "I am somewhat surprised at the time and space being devoted to the subject 
    matter. Determination of Lar/Long at or by Noon Sight, also by the way 
    Chronometer Error, has been around long enough to have grown a full beard. I 
    alone have used it for over 60-years with generally good results and have 
    previously posted current examples on this List."
    Yes, you did, and thank you for posting your results. There's nothing better 
    than evidence from the field! I can't seem to find one of those posts right 
    now. Maybe someone else could search the archive find the relevant message?? 
    (thanks in advance)
    "The subject has been rather fully described and discussed by Raper, Bowditch, 
    Lecky, and a host of others"
    What you are referring to is longitude by equal altitudes, generally using 
    single altitudes on either side of noon, with no correction for motion of the 
    observer (or changes in object declination) and no attempt to imrpove the fix 
    by statistical means. Though "longitude by equal altitudes" is clearly the 
    ancestor of the sorts of fixes we've been discussing, it is not the same 
    And you wrote:
    "- all of whom specify rather significant restrictions, or perhaps 
    limitations, to its use, both as respects altitude and azimuth, which are 
    apparently ignored by the present proponents of it as a universal panacea."
    Do you suppose it's just possible that I do in fact know about the limitations 
    discussed by those authors?? :-) They refer to a very limited form of this 
    observation. The limitations can generally be overcome using simple 
    procedures that make it much more flexible, and in some ways, even easier. 
    I've outlined my method for doing this, and others have their ideas. By the 
    way, no one that I know of is calling this a "universal panacea" though one 
    of GH's posts claimed that this was the case. Don't fall for his "straw man" 
    You added:
    "One striking difference in the method as now proposed and that traditionally 
    employed is the graphing technique advocated to obtain the altitude at LAN."
    The graphing technique, as commonly presented, is quite primitive. For 
    example, a recent edition of Bowditch suggests that the navigator should 
    'fair a curve' through the points (or some similar language). What use is 
    that? If you place some points on a graph in front of typical potential 
    navigators, their curves rarely resemble parabolas and they would rarely lead 
    to a useful solution of the problem. People have a tendency to draw smooth 
    curves passing as close as possible to each data point, which is not correct. 
    That's why one needs some more effective means of finding the axis of 
    symmetry of the curve.
    But just to reiterate, you are completely correct that the equal altitudes 
    method is the real basis for all of these things, at least from a certain 
    point of view. And in some circumstances, it's just what the doctor ordered. 
    I've got a USN Mark II sextant from 1945 that includes a complete table of 
    instructions and basic almanac data that would have enabled a navigator with 
    very basic skills to get a fix using this method. I'll attach some pictures. 
    But to repeat, we can do much better than this today, and with very little 
    extra effort.
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