The way it was done, Markus was that if Smith thought his ship would make the same 546 miles distance between Noon April 14./15 as she made between Noon April 13/14, he would first have subtract from 546, the number of miles he had to run from Noon to The Corner...47-00'West. By calculation, that amount was 124 miles. the resultant would be 546 -124= 422 miles to run from 5-50 pm until Noon the next day on a course of 265 True. Over that distance, Titanic would change her longitude by 9 degrees 26 minutes giving her a DR Longitude of 56-26' west at Noon April 15. That longitude is 3 hours 46 minutes SLOW of GMT.Jim, I think one can not conclude from 47 minutes that a slow down was exspected. The clocks are changed by integer number of minutes and the 47 minutes are the result of round up or down. I think Smith calculated that way:
22 knots, 24,8 hours, 545,6 miles to exspect.
Starting Point: 43-02 N 44-31 W
Monday noon: 41-23 N 56-20 W
Difference of longitude: 11°49' * 4 = 47 minutes 16 seconds, round down 47 minutes.
21,5 knots, 24,7 hours, 532,1 miles to exspect
Starting Point: 43-02 N 44-31 W
Monday noon: 41-24 N 56-02 W
Difference of longitude: 11°31' * 4 = 46 minutes 4 seconds, round down 46 minutes.
1 Minute of time represents 11 miles more or less.
The Input value for result 47 minutes will be 543 miles plus/minus 5.
They intended to alter the clock by 47 minutes, so most likely they exspected 22 knots for the next day.
Boxhall obviously thought the ship had over-shot. Otherwise how could Titanic have been 'right on the track' at 7-30pm sights and make good a course up to then of 266 True? If anything, she should have been gradually making a course to the southward of the intended track as the local Magnetic Variation reduced.
What is the tolerance zone for "right on the track"? You are native speakers, I am not. But based on my stomach feelings I should say if the star position is found one or three miles south of the track after a run of 170 miles after the last fix this is a fairly good result, the term "right on the track" still may be used.
Boxhall's CQD has been calculated either with course 265 or 266. It is located one mile south of the track. That means, the 7-30-or-40 position must have been 1 mile south of the track if calculated with 265°, or 2.5 miles south of the track if calculated with 266°.
This is just the first uncertainty. The second uncertainty arises by the error of Boxhall's CQD. If only he made a speed or time error, the correct CQD would be one mile south of the track, but if he switched the 42/48 columns in the traverse tables the latitude would be the same, the longitude would be 50-00, the correct CQD would be 2 miles south of the track. Smith's wrong CQD is 2 miles south of the track! At least these two would coroborate then!
Thus we have four possibilities to relocate the 7-30-or-40 Position:
1 / 2.5 / 2 / 3.5 miles south of the track.
The 265/266 uncertainty:
Pitman said in USA "South 84 or 86 west would be the true course we were making after 5.50; south 84 or 86, I am not quite certain which, was the true Course...
May be we can take this as evidence for 266. He knew they were 1 degree deviating from the prescribed course, he just could not remember which side. What bothers me however is Boxhall:
15671. The effect would be she would have run a little bit further on the old course and then on the new course she is gradually making back to the line?
- That is my impression of the idea which Captain Smith had in altering that course and setting it to that time."
He explained immediately before that 265 was the prescribed course, and 266 instead was steered to compensate the late turn.
This was his "Impression".
But was this "Impression" based on a calculation "afterwards" to find a turning Point at 5.50 which would match his wrong CQD Position?
Such turning point could have been:
41-55:30 N 47-10:30 West
Distance to 41-46 N 50-14 W: 137 miles; Course 86°
Speed with/without clock retarded: 21,3 / 23,5 knots
Since the longitude at Noon April 14 was 2 hours 58 minutes SLOW of GMT then. if Titanic did cover a total of 546 miles, the clocks would have required to have been altered 48 minutes, not 47 minutes. However, since Captain Smith ordered the clocks to be adjusted by 47 minutes, he must have expected to increase his westerly longitude by 9 degrees 11 minutes, not 9 degrees 26 minutes. 15 minutes of longitude in latitude 42 north on a course of 265 True equates to a distance of 11 miles, so in fact, Captain Smith did not expect to cover more than 534 miles between Noon April 14 and Noon APRIL 15.
As for the expression "Right on the Track". That is exactly what was meant. There was no tolerance. It was all done by calculation and not plotted on a chart.
Here's how: Since the Track was 264.75 True from The Corner at 42-00'North, 47-00' West, if the calculated bearing of the corner form a fixed position was North 084.75 East True, then that position was "Right on the line" (yes, Sam, I did notice in that last post... told you I can't count.)
I agree with you that Boxhall's course of 266 True could only have been from a DR position which was southward of The Corner, thus confirming his belief that Titanic had over-shot it before she turned. He made the mistake of thinking the ship passed exactly through the planned turning point...I do not believe that it did.