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For anyone who does not have software that can read WordPerfect files, here is 
the text from Jim's announcement of his book (note: I edited the text very 
slightly, replacing italicized book titles by quoted titles).

-FER

Jim's text begins here:

Authorhouse has just published my book, "The Noon Fix", and it is available 
from them or Barnes and Noble. I hope no one is offended by this 
announcement. My apologies if this comes across as advertising (and I checked 
with Frank who said it's ok). But you don't have to buy the book to know what 
it's about. The following is the gist of it:

INTRODUCTION
When I first tried the double altitude method to determine longitude, I 
quickly found that north-south boat movement affected the time of maximum 
altitude. I immediately started looking for a simple, direct method of 
compensating for it. When none was forthcoming, I wrestled with the 
mathematics to derive the equation for the time between maximum altitude and 
meridian transit (Reference 1). That was a bit messy, but it worked. But 
recently, the simple, direct method hit me. Like many others, I slapped my 
head, muttering, "Why didn't I think of this before?"

THE METHOD

The double altitude approach averages the times for equal altitudes before and 
after meridian passage. But north-south observer movement and declination 
change need to be considered, since they affect the measured altitudes. From 
reference 1, (Sn - d) is the rate of movement between the observer and the 
body, where Sn is the northerly component of speed, and d is the rate of 
change of declination, here positive if the change is northerly. Multiplying 
this by the time between observations gives the resultant change in altitude.
At meridian transit the navigational triangle has become a line. At this time, 
the change in sextant altitude (Δhs) is (Sn - d)ΔWT, where ΔWT is the 
difference in watch times between observations. It can be simply added to or 
subtracted from the initially measured altitude hs. Averaging the times of 
the initial hs and the adjusted second hs gives the time of meridian transit. 
That's it!

Relying on single observations is not recommended, but it does illustrate the 
basic approach. Reference 1 describes a graphical method for determining the 
time of maximum altitude. There the rising and setting altitudes are plotted 
versus watch time. Adjusting the setting line determines the time of LAN at 
their intersection.

DISCUSSION

The intent of this method was to simplify the approach. But three unexpected 
bonuses resulted. The first is that the method is insensitive to the body 
selected. The same approach can be used to get the time of meridian transit 
for all bodies, including the moon. The second is that the asymmetry of the 
altitude-time curve due to north-south motion is automatically considered. 
The third is that changes in longitude are also automatically considered. 
These benefits accrue because the method utilizes the data contained in the 
slope of the altitude lines. Consider an observer with a westward component 
of movement. His measured altitudes will rise and fall at a lesser rate than 
an observer traveling along a meridian. Thus the hs versus WT lines will have 
a flatter slope. This means that there will be a greater WT difference 
between equal altitudes. Thus the resultant change in hs will be greater, and 
the time difference between maximum altitude and meridian transit will also 
be greater.

CONCLUSION

While the method was aimed at getting the simplest backup to GPS, other uses 
may materialize. That it's more accurate than the equation in reference 1 
(and its predecessor in the "Admiralty Navigation Manual" some fifty plus 
years earlier) could be of benefit.




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