NavList:

Frank I take your point about knots through the hand.

David I have a pdf of the 1884 Lecky open at the pages you have posted (must buy a hard copyy). Lecky refers to William Thomson, the 1st Baron kelvin. Clearly Kelvin had a big influence on Lecky. The reason I have Lecky open is that I am trying to understand Alfred Chalice Johnson's (aka Cloudy weather Johnson) double chronometer method. Johnson clearly understood the concept of and advantages of position lines. He understood that position could be determined by taking two time sights and crossing the Sumner lines. There was a downside to the Sumner methor - the amount of computation and the mess created on charts by plotting. In about 1880 Johnson published "On Finding the Latitude and Longitude in Cloudy Weather" in which he introduced the C tables (A+B=C). He described a method for calculating position from two time sights, the ABC tables (johnson's table I and table II) and plane trigonometry.

We can conclude that by the 1880s navigators such as Lecky and Johnson undertood position line navigation although the morning/noon sight method probably remained in use with most navigators well into the 20th century.

I have successfully calculated my latitude by Johnson's method but have not been successful with longitude. I am hoping to sort that out today and maybe will post details of how Johnson's the method works. The 1905 copy of Johnson was the 28th edition - roughly  a new edition each year, suggesting that his method was very popular.