NavList:

40+ years ago I purchased a copy of "On Finding the Latitude and Longitude in Cloudy Weather, Etc" by AC (Cloudy Weather) Johnson R.N. The book gathered dust in my bookshelf until two days ago. It has always been my ambition to not only understand the document but make use of it. I have finally succeeded!

Johnson's method involves two time sights with the position determined by calculation rather than by plotting as in the Sumner method. I calculated longitudes by the hav formula and Norie.  For the Sumner I calculated the azimuth by ABC tables.  For Johnson I used his tables to find the azimuth.

Here are the results:

GPS position  S41 06.5

                       E 175 05.2

Sumner Tangent method   S 41 07

                                          E175 05

Cloudy Weather  S 41 06.9

                           E175 05.5

Now the caveats. 

  - At this time of year I can only take sights during the middle of the day. As a result  the LOP cut was only 40°.

 - I am not very tidy when doing a Sumner plot.

  -  Johnson's  tables require double interpolation. I read the tables very quickly (carelessly?).

In view of the above it may be pure luck that I was so close.

There was a small amount of cheating involved. Johnson's method involves the multiplication and division of several numbers. I used a calculator. Johnson describes how his tables can be used to multipy and divide numbers. My next step will be to use his tables and eliminate electronics completely.

I am also looking at Brent's ex-meridian tables. He gives a method of solving a Sumner in which a long is assumed and a lat calculated, the oppopsite of the usual Sumner. I am still working on this.

Finally, the New Navigation may be useful for checking the accuracy of sights but I find the Old Navigation much more interesting.