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I have to make a  correction, the size of a longitude error caused by an error 
in the assumed latitude varies with the co-tan of the azimuth, not the 
cosecant.
So that an azimuth of 135 degrees the co-tan is 1, the longitude will be in 
error equal to the error in the latitude. For a 150 azimuth co-tan = 1.7 so 
longitude error is 1.7 times the error in latitude, 3.1' for a 1.8' error in 
latitude. Azimuth 100 degrees, co-tan = 0.18 so longitude error is only 0.3' 
.

gl
--------------------------------------------
On Fri, 6/5/15, Gary LaPook  wrote:

 Subject: [NavList] Re: The Nautical Mile and the arc minute
 To: garylapook@pacbell.net
 Date: Friday, June 5, 2015, 4:26 PM

 Except
 when the body is on the "prime vertical" azimuth
 90 or 270 in which case the latitude in not needed as the
 resulting longitude line (LOP running 360-180) is not
 sensitive to errors in latitude. Other wise you use your
 noon sight latitude adjusted by DR to the time of the
 afternoon time sight or carry the noon latitude back to the
 time of a morning time sight. So, if the time sight was
 taken at 9:00 and the vessel is moving at 6 knots covering
 18 NM in that time period. If we assume an uncertainty in DR
 of 10% (which is used in flight navigation but probably way
 too high for marine navigation, Frank have you any data for
 DR uncertainty for surface navigation) then the latitude
 uncertainty would be +/- 1.8 minutes used in doing the time
 sight computation for longitude. If the azimuth of the sun
 were 90 degrees then there would be no error in the
 longitude. If the azimuth was 135 degrees then there would
 be +/- 2.5 NM (cosecant times 1.8). If the azimuth was 150
 degrees then 3.6 NM. This is exactly what Sumner did,
 assumed different latitudes and computed the resulting
 longitudes.
 gl

    From: Francis Upchurch
 
  To: garylapook---.net

  Sent: Friday, June 5,
 2015 2:51 PM
  Subject: [NavList] Re:
 The Nautical Mile and the arc minute


 Thanks
 Frank,Wonderful
 exposition of what we are all about.re the
 issue of old time (e.g.time sights) versus Sumner/St.
 Hilaire ,am I correct in thinking that you need accurate
 latitude to get good longitude by the old methods and that
 is not the case for the new methods, and hence their
 appartent superiority? Correct me if I have this
 wrong.Francis



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