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For over a decade Robert R. Newton has engaged in the laudable project of analyzing ancient and medieval astronomical observations in order to obtain improved determinations of the retardation of the Earth's rotation and of the Moon's secular acceleration. More recently he has become better known for his prosecution of Ptolemy, whom he considers to be the arch-criminal of science. The present work is concerned with both subjects.

The object of this book is to determine whether the rate of the rotation of the Earth is subject to a long-period variation independent of the retardation produced by lunar tidal forces. The method used is to examine ancient and medieval observations of the Sun, Mercury, Venus, and Mars to see whether they show accelerations consistent with such a variation, and then to determine its rate. The results found are not positive, nor are they negative, nor are they even inconclusive; they are simply meaningless. Even accepting the author's statistical analyses of the observations and the accelerations, which are very questionable, the accelerations of Mercury and Venus are, when compared to the solar acceleration, far too low, the acceleration of Mars is too high, and the standard deviations of the estimates are so large as to make ail the numerical estimates, including those for the Sun, without value.

But more must be said for the book also seems to be intended as a contribution to the history of astronomy in that the author evaluates ancient Babylonian and Greek, and medieval Arabic observations, and he spends a good many pages on a curious criticism of Ptolemy, with even more curious recommendations for how the old Alexandrian could have done his work better. In view of the fact that Newton has received much attention in both scientific and popular literature, we are compelled to point out what we consider the principal defect, both in this book and in his other publications of an historical character. Newton's work is careless and unreliable to the point that it can be recommended, if at all, only to the reader who is prepared to examine every source of observations and check every computation, i.e., to do all the work over again, and this is far from easy as Newton's exposition is often far from clear. In order to defend this admittedly harsh judgement, we can do no better than to give examples of Newton's understanding and use of sources in making the crucial decisions about whether a report represents an observation or a computation.

We begin with a Babylonian source. On pp. 127-130 Newton explains his reasons for rejecting as computed the contents of CBS 11901, originally published by Kugler (Sternkunde, und Sterndienst in Babel, II, 233 ff.), a text that gives dates in months IV-IX of an unspecified year for summer solstice, autumnal equinox, heliacal rising of Sirius, twelve appearances and disappearances of planets, a lunar eclipse and a solar eclipse. Kugler already expressed the opinion that the information on the tablet was computed rather than observed, and while Newton agrees in this judgement, his analysis shows little understanding of what Kugler wrote and contains a rather strange result. Kugler dated the text to -424 by using the solstice-Sirius interval to narrow the range to -800 to -400, noting that only -424 provided possible eclipses -- lunar 9 October, solar 23 October -- and then letting the planetary dates fall into place. The procedure seems unequivocal, but Newton says he questions the dating, although why is not made clear.

Only for the lunar eclipse is the time of day given, 10^o, i.e., 40 minutes after sunset, and this time refers to the beginning of the eclipse. It is clear that the solar eclipse was not visible in Babylon, but the lunar eclipse, which was total, certainly was, and that the text gives no time for the solar eclipse but a specific time for the lunar eclipse suggests some difference in their reports. But Newton writes that the text offers no grounds for a distinction. The following table gives the time of the beginning of the lunar eclipse from the text and, using 1;49h as its half-duration, from the standard modern tables, all in mean solar time at Babylon:
 
 

The agreement, particularly with Ginzel and Goldstine, is very good. But Newton writes of Kugler's analysis: "He made two errors in his calculations. First, he thought that the time stated for the lunar eclipse is within four minutes of the time calculated from Oppolzer's Canon. However, he made a mistake in copying from the Canon, and the actual error is twenty-four minutes. Second he did not recognize the errors that are present in Oppolzer's times." In fact, as the above table shows, Kugler used Ginzel, and he says so. And what are the errors in Oppolzer's times (which Kugler did not use anyway)? Consider the following table of the times of the syzygies of the lunar and solar eclipses, which occurred at about the same hour:
 

But Newton, who does not give the times of the individual syzygies, says that according to his calculations the syzygy of the solar eclipse should be fifty-five minutes (!) earlier than the syzygy of the lunar eclipse, dwarfing the differences of the sources we have compared and of our own computation. This is an extraordinary result, and if it is true, Newton knows something about calculating syzygies that no one else knows. And this example is not an isolated aberration. In the course of spot checking we have noted instances of incorrectly computed sunrises, confusion of tropical and sidereal year, and other suspicious syzygies. We need hardly point out that in research of this kind, in which the goal is to isolate very small cumulative errors in modern theory, precision in computation is crucial if the work is to have any meaning at all.

At other times Newton can take schematic numbers as real observations, and draw far-reaching conclusions from them. The "Geminus Parapegma" is a calendar of stellar phases and meteorological correlations found in manuscripts of Geminus (first century A.D.), although it is an unrelated composition --Geminus himself criticizes such correlations -- probably of the second century B.C. Newton considers the parapegma the work of Geminus, whom he dates to "ca. - 100", and finds some very important information in it (pp. 162-73, 291-97) that no one seems to have found before. It contains the number of days the Sun spends in each zodiacal sign, and also says on which day various authorities -- Euctemon, Eudoxus, Callippus -- place the equinoxes and solstices. Now the durations -- which may be partially based upon observation, but are still mostly schematic -- have no relation to any of the authorities named, although the intervals between solstices and equinoxes are rather close to those attributed to Callippus in the Eudoxus Papyrus. But Newton, by reasoning he does not explain and we cannot fathom, decides that they must be the work of Euctemon and, he presumes, Meton, and that they must be the result of observation.

Never mind that the Eudoxus Papyrus gives altogether different intervals for Euctemon; these are dismissed in a footnote.

Now the story becomes interesting. Since the intervals between solstices and equinoxes from the parapegma are rather accurate -- the greatest error being about a day -- and since the intervals between solstices are right on the nose, Newton concludes that Meton and Ecutemon were very good observers, so good in fact that Greek observations never became any better, and most remarkable of all, that solstices could be observed with more accuracy than equinoxes. However, there is one unpleasant historical fact that contradicts Newton's conclusions, namely that according to Ptolemy and the Miletus Parapegma (-108) the solstice associated with Meton and Euctemon, 13 Skirophorion in the archonship of Apsuedes, corresponds to 21 Phamenoth, Nabonassar 316 or 27 June -431, which is one day earlier than the true solstice. This would mean that Meton and Euctemon could observe no better than, dare we say it, Ptolemy. Well then, concludes Newton, the sources must be wrong, the result of later computation or even deliberate fraud, while Meton and Euctemon really observed the solstice correctly on 28 June, and he computes that the odds against their observing the solstice on 27 June are no less than 52 to 1. He then suggests that if 13 Skirophorion of -431 is identified with 28 June, many problems in Greek chronology will be resolved, and this, he says, is one of the major results of his study.

On the other hand, while Newton believes that Meton and Euctemon were very good observers, he does not think highly of Ptolemy's observations, in fact, he believes they are all fraudulent. His reasoning is based mostly upon demanding rather great precision, say, that of the presumed solstice of Meton and Euctemon, and then saying that Ptolemy's observations, which do not meet such standards, must be fraudulent. Conversely, since, at least for the Sun, Ptolemy's observations confirm Hipparchus's theory, Ptolemy must have computed the dates of equinoxes and solstices with Hipparchus's theory, a story going back at least to the early seventeenth century. Through similar reasoning, but not much evidence, the argument is extended to all of Ptolemy's observations, and Newton "proves" his point by computing probabilities like 10200 to 1 that the observations are fraudulent.

This particular subject has already received so much attention that there is not much point in going over it again. Suffice to say that Ptolemy's observations show a systematic error of about a degree due to the inaccurate equinoxes, and beyond that a scattering of random errors. While Ptolemy was surely selecting observations and arranging derivations for presentation in the Almagest on the basis of more extensive analyses than he presented in the book, the accusation of fraud is absurd≈and could as well be directed at Kepler or Newton for the same reasons≈the arguments used to support it strain credibility, and the misuse of probability insults the intelligence of the most naive reader.

But Newton does not stop with fraud, for he wishes also to show that Ptolemy was incompetent, so he sets out a litany of accusations that amount to saying that Ptolemy was a very bad astronomer who could have done much better if he had known what Newton knows. Like the expectation about accuracy of observations, the arguments make anachronistic demands on what someone in antiquity should have been able to do, e.g., Ptolemy should have found the elements for the planets that Newton had his computer find in making a best-fit model for a series of accurate planetary positions in all orbital configurations. And if this were not enough, Newton even holds Ptolemy to blame for the failure of his own project of finding the accelerations of the planets (pp. 410-11):

In spite of the great Hellenistic contributions to astronomy, the surviving Hellenistic data do not let us infer meaningful values of the planetary accelerations. This is enough to make one weep at the damage that Ptolemy has done to the science of astronomy. The real damage does not come directly from the fraudulent data that he produced; we can detect and eliminate them fairly easily. The real damage comes from an indirect effect: Because Ptolemy based his Syntaxis upon fraudulent data, it could pretend to a universality that was denied to works based upon honest data. As a result of its meretricious universality, it displaced the genuine works of Hellenistic astronomy. In consequence, Ptolemy has probably caused us to lose almost all of the vast body of accurate Hellenistic observations.