1. When this so called mystery vessel seen from the Californian was stopped, is was on a line of bearing SE true. The evidence comes from two officers, 3/O Groves and 2/O Stone, at the time that Stone took over the watch about 12:15 AM Californian time. Both officers said that Californian's head was point ENE by standard compass, and the mystery vessel was right off their starboard beam. The Apprentice Gibson confirmed that relative position when he came on deck shortly afterward. The compass bearing to the vessel was SSE magnetic. Magnetic variation was reported as 24 degrees west, about 2 points. This puts the observed steamer SE true from Californian.
2. Both Californian and Titanic were stopped by that point. Although both ships were slowly swinging around somewhat (Californian much more so than Titanic from the evidence given), this only affects the relative bearings that lights and rockets were seen, not the distance between.
3. The 8 white rockets observed from the vessel whose lights "looked queer" later on, were seen to come from over the vessel or beyond. Gibson was able to see a flash which he assumed came from the deck of that vessel when he saw the 6-th rocket go up through glasses. These days, everyone agrees that these rockets were the socket distress signals being sent up from Titanic. That puts Titanic on a line of bearing of SE true (135°) from Californian when both ships were stopped. Californian was therefore on a line-of-bearing 315° true from Titanic.
4. The Carpathia was coming up on a course of 308° true (N 52° W). This comes from Capt. Rostron and confirmed by his 2/O James Bisset. At 3:20 AM Carpathia was firing rockets. This is confirmed by a wireless message received on Mount Temple. Both Stone and Gibson reported seeing rockets very low on the horizon at that time. (Actually Gibson said they were rockets, while Stone called them lights.) Bear in mind that Gibson was only reporting relative bearings of what he saw. Any headings he gave for his ship came from what Stone had told him. Gibson did not take any compass bearings but Stone allegedly did.
Carpathia was making only about 15-16 knots at the time she was firing those rockets. Rostron said he stopped his engines about 4 AM. At 3:20 AM the Carpathia would be 10 miles away from lifeboat No. 2, the one that 4/O Boxhall was in. Since Rostron later said that he was 4-5 miles from the ice field when he first saw it after the sun came up, and that the wreckage from Titanic (including overturned collapsible B) was seen 2-3 miles from that icefield, I put Carpathia about 2 miles from the wreckage when he picked up Boxhall's boat, or about 12 miles to the SE of the wreckage at 3:20 AM.
5. The wreckage, the ice field, and everything else afloat at that time in that area, was drifting with the local current. The best estimate for the drift comes from the Californian which placed the wreckage at 11:20 AM at 41° 33' N, 50° 01' W. This was based off of her noontime sun sight location taken soon after leaving the scene of the wreckage, and can be confirmed from the location reported by the Frankfurt when she spotted Californian coming out out the pack ice at local apparent noon. We also know the precise location Titanic foundered and the time interval in between. The average current set and drift calculates to 197° true at 1.1 knots. (see my article Collision Point for details).
Shown below is a chart of the area I derived for 3:20 AM Californian time.
1. the location of the Titanic wreck site,
2. the location of the wreckage at 11:20 AM Apr 15,
3. the Boxhall CQD position,
4.the Californian position reported to the Antillian for 6.30 PM Apr 14,
5.the Dead Reconning (DR) track line of Californian from her noontime location of Apr 14 to make 42° N, 51° W that Capt. Lord mentioned in his 1959 affidavit,
6. the DR location for Californian on that track line for 10:21 PM Apr 14 when she stopped,
7. the two sun lines taken at 5:00 PM and 5:30 PM on that track line that Capt. Lord wrote about in his 1959 affidavit,
8. the reported stopping point for Californian given by Capt. Lord at the 1912 inquiries,
9. the approximate location of Carpathia at 3:20 AM Apr 15 and her approach course line of N 52° W true,
10. an Estimated Position (EP) for Californian at 3:20 AM, at the time Titanic's lights went out (2:05 AM Californian time seen by Gibson on her wheelhouse clock), and an EP for Californian for when she stopped at 10:21 PM Apr 14, and
11. the approximate location and lay of the nearby ice field at 3:20 AM Apr 15.
The general lay of the ice field was draw from decriptions given by Capt.s Lord, Moore, and Rostron. It was described as running from NW to SE on the eastern side by Rostron, and from NNW to SSE true on the western side by Lord and Moore. Up where Californian was stopped it was described as being about 2-3 miles in width, while down near where Carpathia was it was estimated at 5-6 miles in width. Californian stopped close to the eastern edge of the field; while Titanic wreckage was seen 2-3 miles off the eastern edge of the field from the Carpathia.
The Californian came under the influence of the Labrador current some time between noon and 4 PM on the 14th based on logbook data supplied to the Senate investigation by Capt. Lord. This would have set Californian south of the DR track line she was on that is shown on the chart. I show that by time she stopped at 10:21 PM, she would have dridted about 5 south of the line.. A westward component of current drift was noticed by Capt. Lord and was accounted for when the Antillian ice report was sent out. As I said elsewhere, I don't believe a Pole star sight was ever taken at 7:30 PM as later claimed, and if it were, I doubt it showed the ship remained on the same exact latitude as she was at noon. Her course according to evidence given by Capt, Lord was S 89° W (269°) true (BI 6710).
Given the observation that the two ships, Californian and Titanic, had to be on a line NW-SE true when both were stopped, and given the now known location of the Titanic wreck site, restricts the possible location of Californian at the time Titanic's lights went out (2:05 Californian time, 2:17 Titanic time) to a 315° line-of-bearing taken from the wreck site location, give or take a few degrees.