The middle latitude is the mean latitude 49Â° 6.5' minus the mid-lat correction 8'= 48Â°58.5'
Dlong 783 cosine mid- latitude 48Â° 58.5' = true departure 513.95 nautical miles, divided by
Dlat 151=tan course 73Â° 37.6'.
Dlat 151 secant course 73Â° 37.6' =535.675 miles. This mid-latitude calculation method for a spherical earth would be consistent with 1912 practice.
The difference from what I did and what Capt. Collins did in the mid lat calculations is that he used a "mid-lat correction" factor to get an adjusted number for the departure distance. He claims that this would be consistent with 1912 practice, and that is where I have to differ.
Let's look at the data.
For the run posted for June 17:
Log showed 534, I got 534.36 (534), Capt. Collins gets 536.675 (537)
For the run posted for June 18:
Log showed 542, I got 541.54 (542), Capt. Collins gets 542.719 (543).
Another example, take the rhumb line from noon June 19 (41-33N, 54-47W) to noon June 20 (40-41N, 66-50W):
Log showed 548, I get 547.2 (547), by meridian parts you would get 549.260 (549).
Take Voyage #2 westbound on rhumb line from noon Jul 17 (41-15N, 57-26W) to noon Jul 18 (40-35N, 68-49W):
Log showed 518, I get 517.7 (518), by meridian parts you would get 519.671 (520).
So is is clear, at least to me, that the method used by those officers working out the distances on the Olympic were not worried about such things as mid-lat correction factors in computing the middle lat. This is not even mentioned in Bowditch. Is is likely that they used transverse tables to get their results which require some interpolation of the data to be performed. I doubt they would have bothered to use a mid-lat correction factor even if they had those available.
In any event, the values that I obtained using the mid latitude method as I described in detail
in the above post of Thursday, July 5, 2007 - 5:26 pm, produce results which agree quite nicely with the distances recorded in the log. To me, that is what counts.