NavList:

Hi Frank

Perhaps you mis-understood what I was trying to convey.

I would assume that he used incremental reckoning on his several year voyages. George pointed out the cross atlantic voyages as a function of his familiarity with them and his detailed research of them, recently presented in the UK at their equivalent Navigation Symposium. I remain convinced that Cook would not have changed his navigational method for any voyage, short or long, navigational methods being so conservative.

George pointed out that he reckoned his longitude from EACH departure, not necessarily just the Lizard. I interpreted that to mean that when he left (took his departure) from Australia, he reckoned his longitude from there. That would indeed result in an accumulation of error.

You wrote:
Round-off error only becomes an issue when the navigation is MORE accurate than the precision of the calculations

Here we dis-agree. Whatever the navigation calculations show, there is almost always a truncation or roundoff error at the last digit. Your absolute, true position will not be properly represented by the digits you show. For example, suppose that your position is represented as W40d 29m 32s. Is that a 32 seconds with 100 trailing zeros after the decimal point? Or, as I contend, just your current representation of position, to the nearest second.

Then you wrote:
Round-off adds a small "random walk" to the data. But if the step size in that random walk is well below the normal uncertainties in the process of DR navigation itself, then the round-off is irrelevant.

Ah! So we do agree that there is some roundoff! Yes, it will be irrelevant when we consider journeys of only a few days or weeks. Of course, this is also a function of the step size of record. Does Cook record to the nearest second, minute or 1/4 degree? Roundoff can and will pose a greater challenge when the period extends to years.

An analoguous situation occurs in robotic equipment. It can be placed into absolute positioning mode (relative to reference location, like the Greenwich meridian) or into incremental mode (relative to where you are right now). Placing the equipment into incremental mode, we command it to go plus 1.234 inches and then back 1.234 inches. With only a few passes, external calibration equipment does not show any accumulation of error. However, over long term, those round off errors DO accumulate, and the calibration equipment will show a significant error. It is a well known problem with incremental positioning and robotics, requiring that the robot find the reference point periodically or face defects in manufacture.

As Cook journeyed through the Pacific, using his incremental reckoning, there could (note: I don't say absolutely must have been) be an accumulation of error. He journeys from England, around the Pacific and returns to England after a long period of time. IF there was an accumulation of error, then he could have a large undershoot (too far out into the Atlantic when he reaches the appropriate latitude) or large overshoot (crashes into Africa). Even with emergent navigational methods like the one of the first chronometers and Maskelynes Tables, finding his absolute longitude would have been a challenge.

So my inquiry remains, do his long term journeys show this accumulation? With today's knowledge of longitude, do his longitudes of Pacific locations agree, or do they show a relative drift with time.

I do hope this clarified what I was trying to convey!

Best Regards
Brad

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