A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: Frank Reed
Date: 2020 Oct 30, 21:06 -0700
Mistake? First, to dispense with a minor detail, you're not talking about "twelve knots per hour", are you? Modern navigators think of knots as a units of speed and badger neophytes who use the term any other way. But in earlier usage, it was a count of actual knots passing through one's hands as the logline paid out. Thus "knots per hour" made sense.
Moving on... Are you worried about his description of Sumner lines? Maybe I'm missing something. As I read it, there is nothing wrong with the paragraphs that you have posted. It's a different way of describing things, but it's not incorrect as it stands. He's describing the merit of a single celestial line of position that yields neither latitude explicitly nor longitude expllicitly. You're somewhere on a line that runs in some direction not aligned with the cardinal compass points, not delineating a latitude of a longitude. Lecky seems to be pointing out that this can be valuable, even critical for safe navigation, in and of itself. When Lecky was writing this c.1880, this was not as obvious as it is today. In fact, it was nearly unknown.
When Sumner first proposed his "lines" and when others followed his lead, they focused on their merit for rather narrow cases of problematic navigation, rather than normal navigation. It took Lord Kelvin's influence to convince Lecky that they represented a completely general perspective on a celestial position fix and incorporated all other methods when viewed as an underlying geometry. Supposedly Kelvin traded letters with Lecky and helped him see the light, but I have read of this only second-hand, so the details may be wrong.