For the benefit of those readers not very familiar with navigation let me explain that the calculations that I and Capt. Collins have have been posting here regarding the distance from Daunt's Rock to the corner for Olympic's maiden voyage are in a sense both correct. Capt. Collins calculated a total distance of 1680.4 nautical miles, and I came up with 1677.6 nm. How can that be?
The difference is in the methods and assumptions being used.
What Capt. Collins did, using meridian parts calculations throughout, was to start from Daunt's Rock LV and go to a point south of the Old Head of Kinsale and then to a point 3 miles south of Fastnet Light. That gave him a distance of 56.1 nm. From there he took a rhumb line course (constant course angle) to the reported noon position for June 16, which by meridian parts calculation, is 372.3 nm. The total distance for the first day was given by adding these two distances together which gave 428.4 nm, which is close to the 428 nm written in the log card. The distance for the second day was given by taking a rhumb line from the noon position for June 16 to the noon position for June 17. That gave 535.7 nm by meridian parts calculation, compared to 534 nm that was written in the log. The next distance was given by taking a rhumb line from the noon position for June 17 to the noon position for June 18. This gave 542.7 nm by meridian parts calculation, compared to 542 nm written in the log. Finally, the rhumb line distance from the noon position for June 18 to the corner is 173.6 nm. Total distance adds up to 1680.4 nm.
What I did is add up the distances reported in the log for the first three days to the noon position for June 18, which was 428+534+542=1504. I then added to that the 173.6 nm from noon to the corner to get 1504 + 173.6 = 1677.6 nm. The difference between the two methods is 2.8 nm.
We can do the same using the data from Olympics 2nd and 3rd voyages. The results are 1680.4 Vs. 1674.6, a difference of 5.8 nm for voyage No. 2; and 1680.1 Vs. 1676.2, a difference of 3.9 nm for voyage No. 3. Using the distances written in the log cards for voyages 1, 2, and 3 westbound, we see distances to the corner that are about 3 to 6 miles shorter than if we take the sum of the rhumb line distances between the points listed.
So why doesn't these two methods come out the same? Why is the method I used give shorter distances than the method used by Capt. Collins? Part of the answer is that the daily runs were rounded to the nearest whole mile so few tenths may be lost. Part of the answer is in the way distances were calculated using a spherical earth model and mid latitude method, not meridian parts. And part of the answer may be in the way the ship was navigated while following the great circle route.
The Olympic did not follow a single rhumb line course from one noon position to the next while on the great circle track to the corner. From detailed data that I looked at from several 1931 Olympic crossings, the logbook shows that they changed true course headings mostly about every 6 hours. (Sometimes as little as 5 hours or as much as 7 hours, but most changes appeared to be about every 6 hours or thereabouts.) This means they were changing course about every 3 degrees in longitude more or less. The distances between two noon positions along the GC track would therefore be less than the single rhumb line distance between the two noon positions because they tried to follow the great circle track fairly closely, more so than what I expected they would do. I believe this is why the distances recorded on those three log cards consistently resulted in a somewhat shorter distance to the corner than what those straight rhumb line distances would give.
