My real point is that some of the pieces just don't fit. When pieces of a hypothesis don't fit it is time to figure out "why" and revise the hypothesis. Could be some sort of very minor variation or could be something more significant. I don't pretend to know which but I do know we are unlikely to find out unless we are willing to question everything.
I'm grateful that you don't mind me questioning your line of reasoning.
It's part of "everything."
Sorry, Marty, but a line of longitude is, most definately, an LOP. Take a look at your globe. See those long lines running north and south and passing through both poles? Those are lines of longitude (which, by the way, constitute great circles of the earth). Note that they run true north and south (180/360).
Yes, I understand what a line of longitude is.
And I understand the idea that a chronometer synchronized with GMT is used to determined longitude. I've read the book twice.
The sunline based LOP we have been discussing is the collection of points which constitute a line at a right angle to the observed azimuth of the sun, in this case 157/337. Since these lines are, by definition, not parallel they must cross at some point.
Yes, I understand how a LOP is derived from a celestial observation.
That point is called a fix.
Mathematically, it is a point. Topographically, it is a region. There is a whole branch of science
devoted to measurement. The iron law of measurement is that all measurements are accompanied by an error bar; there is a
limit to the precision of the instrument. At a given time on a chronometer, your "line of longitude" is not a line but a band as broad as the plus-minus precision of your instrument. If you only have a second hand, the limit of the instrument is plus-minus one second, assuming that the chronometer is in perfect synch with GMT. The limits of precision of the sextant depend on how fine the lines are that are engraved on it. Then there is the question of eye height when making the observation, which brings in the limits of precision in the altimeter (not shown in this drawing).
In this case, it isn't a particularly desirable fix because the intercept angle of the two LOPs is too shallow (only 23 degrees), but it is still a valid fix.
I agree that you have to draw your sun-LOP through the longitude you've determined from your chronometer--it's the only way to put the sun-LOP on your chart.
One line does not make a fix.
Absolutely true, but we have two lines! And, as I mentioned later, a point based on DR.
Yes--accompanied by another large error bar.
The accumulation of uncertainties would be reduced by more sitings, but you never get down to the purity of mathematical lines and points.
I have also learned that the moon was still above the horizion at the time in question so that adds a 4th bit of information. Do you begin to see why I'm having a bit of trouble with the idea that FN was, basically, wandering around lost?
The thought that he was "wandering around lost" derives from two pieces of evidence:
- It sounds that way in
AE's last transmission.
- They never arrived at Howland.
Maybe Fred did aim for an offset.
Maybe he didn't.
Until we find his charts, we won't know for sure.
Whatever method he used, Howland didn't turn up where he expected it to. "We must be on you but cannot see you."
What simply won't float is that FN didn't know which way to turn.
OK. We can give up that idea. AE still said they were searching "the line" ... "north and south." They made the turn as Fred calculated, got to where Howland should have been, and didn't see it. Gary says at this point that they coulda, shoulda, woulda done a box search, and got lost about four hours later, with Fred doing constant updates of sun and moon LOPs all the way. TIGHAR's theory, as yet unproven to the degree that will stand up in the court of Idiots United, is that they found their way to Niku, by one means or another.
The only way I can make that work is if the 157/337 line were based on something OTHER THAN his sunline LOP. If it were an advanced LOP, FN sould have known which way to turn.
What the
professional navigators who started this whole question in the 1980s noticed was that the line in the last transmission is the LOP that would be expected from a sun sight near dawn. If you've got an alternative explanation for how AE picked those numbers, have at it.
As for what AE did or didn't know or understand, I'm less conflicted. She really doesn't seem to have been all that great a pilot and certainly wasn't what I would refer to as a "professional". Too many questionable decisions for me to rank her as much more than a "driver".
And an extremely photogenic driver at that.