A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: Frank Reed
Date: 2016 Aug 26, 13:20 -0700
Sounds like a relatively long-winded way of saying "Latitude by Double Altitudes". This was also known as the Douwes problem in the 18th century. Because there are mathematical tricks to it, this particular technique for finding latitude became exceptionally popular among land-bound mathematicians --almost as popular as finding techniques for clearing lunars. I have seen little evidence that it was ever used with any significant frequency by practical navigators. For them, latitude by Noon Sun was good enough in the era when ships were slow. By the later 19th century, when vessels were fast enough that the latitude might change a great deal from one noon to another, the double altitude method was superseded by lines of position. And indeed, it's easiest to understand as a case of crossing two lines of position. Since the watch may be "incorrect", you get no longitude from the process --only a latitude. If you want to do this today, you assume a reasonable watch error, work the sight up as a normal pair of LOPs, cross them for a fix, and then throw away the longitude. Not so magical!
To read more about these methods, search for Joel Silverberg's article on latitude by double altitudes. He used to be a frequent contributor to NavList some years ago.
And yes, a position "by account" is a position by "dead reckoning". There's no difference, only linguistic fashion.