[For the puposes of clarity, when I refer to Cape Belsham, I am referring to the middle of the three peninsulas on the north shore of Elephant Island. The expedition, via the Reginald James chart, in the Wordie paper, identify that as Cape Belsham.]
[There are other landmasses which have been alternatively identified as Cape Belsham. The eastern most point of Elephant Island is one candidate. Another is the northern most point, as given in the Ethiopics. These do not agree with the expedition's identification. These are not given any further notice in this response.]
I have no evidence that Worsley obtained the position of Cape Belsham from any specific reference, be it epitome or not.
I'll merely reiterate the same claim as I made before. Cape Belsham figures prominently in the log. It is used to determine his chronometer error, using the coordinates of a known landmass, to wit Cape Belsham, in a time tested manner.
I will restate that I find it incredulous that Worsley would have attempted to memorize the coordinates of a multitude Antarctic landmasses. He must have retrieved the coordinates of Cape Belsham from some sort of reference.
If he did attempt it from memory, he made a real botch of it, as none of the references I have found supply the coordinates Worsley did. Yet his position as given in the log agrees remarkably with modern charting. This is the nub of the conundrum.
I have never been successful determining precisely which references Worsley had with him. As Frank indicates, it may be found via a specific typographical error or the like. My suggestion is that the coordinates given for Point Wild, and the close proximity of Cape Belsham, would be a tell tale in a reference. In other words, the reference would give close to the same coordinates that Worsley did. Again, no reference I have found, that includes Cape Belsham, has ever provided such a set of coordinates.
Until recently, all of the published books show Worsley with just one chronometer on the Caird, yet the log clearly indicates the presence of two chronometers on board. Perhaps the log does indicate further references, but I did not obtain all of the pages of the log, just the pages of the journey and a scant few others.
We can assume that Endurance had a veritable library of Antarctic references on board. Again, I am unaware of any comprehensive list. That doesn't mean it doesn't exist, just that I am unaware of it. Should such a list exist, it would be a fairly simple matter to search them exhaustively for Cape Belsham.
Another reference that may be the source of the Cape Belsham coordinates is a map. Several maps showing the Antarctic Peninsula and of course Elephant Island did exist prior to the journey. The thumbnail of the German map (1912) showed a rather fanciful Elephant Island, albeit with three peninsulas on the north shore. None were identified as Cape Belsham. There are obviously many others. I am firm in my belief that Endurance had as many charts as were available.
I have a hard copy of Moore's Epitome of Navigation, London, 1828. Whilst it does not provide Cape Belsham or even Elephant Island, it specifically mentions Clarence Island 61°2'S 54°10'W. Close enough to 29104 yet not accurate. The coordinates given by Worsley are only 40 arc minutes away, or roughly 20 nautical miles. I would think perhaps you could see the mountains above the sea!
My hard copy of 1848 Norie's Epitome has Elephant Island, specifically Cape Valentine as 61°5'S 54°55'W. No indication as to which point is referred to, yet Cape Valentine on 29104 is the eastern most point of Elephant Island.
Interestingly, my 1849 Bowditch states that Cape Valentine is 61°3'S 54°40'W, again with no indication as to which landmass, but agrees quite closely with 29104, there given as 61°8'S 54°40'W