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Soon after I joined this forum I posted about Cloudy Weather Johnson. At the time I probably did not completely understand his double chronometer method and my knowledge of CN was limited. Times have changed and I decided to re-visit Johnson's method. I can now confidently  explain Johnson's double chronometer method in two sentences:

AC Johnson's Double Chronometer method is almost identical to the Sumner tangent (one longitude and an azimuth) method but with one signficant difference. The accurate plot is replaced with a rough sketch and calculated corrections.

I have attached a set of notes that include a worked example. Note that I do not know Johnson's dates of birth and death. If anyone can provide a link to this detail please let me know. I would like to know if he became an Edwardian near death or in his earlier days was a subject of William IV.