NavList:

The technique for generating a latitude from a so-called ex-meridian sight is quite accurate within some reasonable limitations (which you can find by numerical simulation and experimentation, or by deriving the equation from the usual spherical triangle solution for altitude). But you'll note that the calculation is dependent on the accuracy of a couple of parameters. The most important of these is the time from noon. How would you know this time in a real navigation situation? Of course it is derived from your longitude. 

Frank Reed