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Response to Dr. Danny Faulkner's Critique of Dodwell

Question: Do you have time to give me a quick response about the following statement by Danny Faulkner:

“Dodwell tabulated many medieval measurements of the obliquity of the ecliptic. In the medieval period the difference between Dodwell’s curve and Newcomb’s curve are smaller than during ancient times. Dodwell acknowledged that most of the medieval measurements of the obliquity did not include discussions of corrections, if any, which were made. He assumed that many of them made the correction for the sun’s semi-diameter, but that they used the much too high Ptolemaic solar semi-diameter, so Dodwell re-computed the obliquity of the ecliptic by first removing the incorrect semi-diameter and then adding the correct one. What was the reason for this? Dodwell found that many of the medieval measurements of the obliquity of the ecliptic agreed with the Newcomb formula, but not with his curve. He even re-computed some measurements on the assumption that some of the gnomon used may have had a conical top, requiring an additional correction. Why? In his own words at the conclusion of his chapter 6, Dodwell wrote,

If we admit that some of the Arab observations were corrected for Ptolemaic parallax, and some were not, and also that, probably in the earliest part of the period, a gnomon with a conical top may sometimes have been used, then the observed mean value of the Obliquity would agree more closely with the new Curve than with Newcomb’s Formula. (Dodwell 6)

That is, Dodwell altered some of the medieval data to better fit his thesis. Which points did Dodwell not correct for the incorrect Ptolemaic solar semi-diameter? The ones that fit his thesis without this correction.”

Response by Barry Setterfield:

Dr. Faulkner appears to have read the Dodwell manuscript in a very undiscerning manner. In Chapter 6, which concerns Faulkner's comments here, Dodwell discussed the data from the Medieval Arabs and Persians between the years 830 AD to 1020 AD. First, Dodwell made it clear there that the extant records showed that no correction had been made for refraction by these observers. As a result, all their observations required a correction for this. Second, he also made it clear that from the time of Al Khujandi (994 AD) and Ibn Junis (1000 AD) the gnomons used had a terminating plate at the top with a hole in it which cast a circular solar image. Prior to that time, Dodwell explicitly states that a plain gnomon was used.

This plain gnomon required a correction for the semi-diameter of the sun and that correction had to be applied to all observations prior to 994 AD. The correction frequently used was that of Ptolemy, which was too great. But some used a different correction. How did Dodwell tell who had and who had not used the Ptolemaic value? It was easy. These observations allowed the latitude of the observatory to be determined. We know the latitude of these old Arab observatories today and they have not changed with time. The latitude obtained for those observatories not using the Ptolemaic data was significantly closer to the true value than those using the Ptolemaic correction. Therefore, contrary to Faulkner’s suggestion, there was nothing arbitrary in the way Dodwell handled the data.

Faulkner then goes on about the conical topped gnomon that some used. In the closing paragraphs of that chapter, Dodwell quotes the Encyclopedia of Islam about this. He briefly calculates how various cones would need different corrections to give a correct value for the axis tilt. However, contrary to Faulkner’s assertion, Dodwell never re-computed the data using corrections for conical topped gnomons. He only established the size of the correction needed.

But one other fact is important. At the end of both Chapters 2 and 6, Dodwell points out that conical gnomons gave values for the axis tilt that were systematically too small. This flies in the face of the fact that the observations of the axis tilt were all much larger than expected. Thus Faulkner’s contention that Dodwell’s application of corrections for conical topped gnomons gave a better fit to his thesis is absolutely without foundation.

One other point needs to be made. Faulkner states in conclusion that “…Dodwell altered some of the medieval data to better fit his thesis. Which points did Dodwell not correct for the incorrect Ptolemaic solar semi-diameter? The ones that fit his thesis without this correction.” This charge has already been answered above. But there is more. In Figure 19, Dodwell plots the axis tilt given by the Arab and Persian astronomers using both the original data as well as the corrected data. The standard axis tilt curve lies above all but 8 of the 50 odd points plotted. This speaks for itself, as the Dodwell curve passes nearly centrally through the cluster.

To conclude, Faulkner’s analysis is faulty and he assumes motives for Dodwell that this great astronomer did not exhibit. In addition, Faulkner has concentrated on the Arab and Persian observations which are in the first millennium AD. He ignores the mass of data for almost two millennia earlier which testify strongly to a significantly higher axis tilt than current theory predicts. In view of these facts, it is apparent that Dodwell’s analysis stands firm, and Dr. Faulkner’s criticism is baseless.