Some comments on 1421: the year China discovered the world by Gavin Menzies.
I haven't read 1421, just looked up the discussion of longitude after reading some ambivalent comments on Amazon. First thing that struck me were some errors of fact.
Page 367: "Even more startling, the longitudes on the Cantino are correct to within thirty nautical miles - a mere thirty seconds of time."
But thirty nautical miles is actually two minutes of time. Very basic; as a British naval commander, Menzies ought to know this. The statement on page 606 is correct: "Since one degree is the equivalent of four minutes of time..." It is easy to work out from the fact that there are 360 degrees in 24 hours and 60 miles in a degree.
Menzies claims (page 370, 601) that the Chinese had estimated the "length of lunation - the interval between new moons" at 29.530591 days. But the apparent moon's movement is uneven; from our point of view it speeds up and slows down and the interval between new moons varies. To try to get a handle on the moon's movement was a major reason for the establishment of the Greenwich Observatory. I think it used to publish "mean lunations." To find the moon's position to navigational accuracy for any given instant requires computing a large number (20 or 30) of trigonometric expressions using complex combinations of periods varying between 27 to 29 days (as I recall) and adding them together. I don't see how the Chinese could have done this. That said, I am not sure it matters for the purposes of finding longitude.
Page 375: "The brilliance of the method is that, unlike calculations for latitude neither sextant nor a clock is required."
Well, a clock is not required for latitude. This is a most elementary misunderstanding for a naval officer. For latitude, all you need to know is the date and to have a table of the sun's declination (in effect the sun's latitude) every day - which indeed they could well have had. The observer finds latitude with almost no calculation by measuring the sun's elevation at noon. Measuring the sun's elevation at sea is difficult and requires a sextant to achieve decent accuracy, but on land it is relatively easy. Columbus had a list of declinations; he did not have a sextant (not invented till over a century later) but had an astrolabe (illustrated on page 393) for measuring the sun's elevation that probably gave him latitude accurate to about 60 miles if his ship was in calm water. He had no way to get longitude.
Page 376: "The Portugese did not have enough ships to determine longitude by trigonometry."
This sentence makes no sense. The number of ships is utterly irrelevant to both longitude and trigonometry.
The author has the explorers finding longitude by eclipses. Lunar eclipses do not occur very often - only about twice a year and often only partial (which are not very useful) and each only visible by half the planet. All eclipses during the two years of the 1421 expedition (and anytime whatsoever) are known. The astronomyprofessor, John Oliver, whom Menzies talks about on page 374-5 and who writes part of Appendix 2 would know that. Why aren't we given the exact dates and times of the eclipses? Any eclipse also has to be observable, meaning that (a) one has to be on the side of the planet facing the moon at the time (this is also accurately calculable) and (b) the sky must be cloud-free. Why aren't we told when the eclipses occur and from where they are observable?
Oliver, of the University of Florida, http://www.astro.ufl.edu/~oliver/lelo/ explains the idea of longitude by eclipse to some extent and the results of his experiment are briefly reported at http://www.astro.ufl.edu/~oliver/lelo/results.html which shows the accuracy as half a degree to one and half degrees (30 miles to 90 miles) which is not as good as the book claims. Oliver does not really explain the details of the observing process.
The explanation on page 371-4 is confused. A lunar eclipse can provide the time and if you know the time you can then find your longitude. The moment of eclipse is the entry and exit of the moon into the earth's shadow and that occurs when it occurs, ie it is an identical instant for any observer who is in a position to see it. If everyone who sees it starts a clock, all those clocks will be showing the same time.
Zheng He did not have precise predictions of when eclipses will occur. If Zheng He had had a list giving the dates and accurate times of eclipses over the next couple of years he would have been able to set a clock by a lunar eclipse he observed in, say, Madagascar and by this means he would have transferred Peking standard time (or whatever he called it) to Madagascar and from that he could observe a star to work out his longitude there and then. Without such a list of predictions he would have to compare, at the end of the voyage, his observations with similar observations made at Peking and figure out the Madagascar longitude retrospectively. This requires both him and the astronomers back in Peking to know that an eclipse is coming up and to have clear weather.
He needs a clock to keep the time he has found. The clock would have to run long enough to time the period between the moment(s) of eclipse and the moment a known star crossed the meridian. The idea, page 604-5, that you would see a star cross the meridian at the same moment the eclipse occurs is not practical; if it were, no clock would be needed. A sophisticated clepsydra (which the Chinese had, according to page 602) could well time a short period - half an hour or so - which, if they had 1200 stars catalogued, might be all that is necessary.
The accuracy of timing the star's crossing of the meridian is quite important: four seconds is a mile of longitude. With a telescope equipped with cross hairs, you can achieve that but with some sort of naked eye gunsight arrangement, a few miles error would be expected. I don't quite follow the table on page 606 and the actual observing equipment Oliver used is not explained. In principle, his method is sound. Evidently he has not published his little experiment.
The clepsydra, or water clock, measured time by the period for a container to empty of water. It is subject to variation with temperature and air pressure. On page 604 it is claimed that they could keep time throughout the day and the night. I would be surprised at that. I do not see explained anywhere what the units of measurement of time (our hours, minutes, seconds) were. Quite fundamentally, the useful measurement of time requires some technique which is not continuous (as water running is) but discrete, ie which counts events - such as the swing of a pendulum or the jerky rotation of an escapement (the tick-tick) or the oscillations of a quartz crystal.
An odd aspect to all of this is that if they could find longitude, it would have been pretty academic, ie effectively pure research. No sailor at sea could measure longitude, so knowing the longitude of a destination was not of practical help to the sailor who is trying to get there.
Overall, I think it's all a Velikovskian beat up. Too many errors, too many unanswered questions, too few footnotes, too much readiness to pounce on everything that seems to fit while ignoring counter argument.
Eclipse info lifted from:
http://sunearth.gsfc.nasa.gov/eclipse/LEcat/LE1401-1500.html
Local circumstances at greatest eclipse for every event during the century are presented in the following catalog. The calendar date and Universal Time of the instant of greatest eclipse are found in the first two columns. The eclipse type is given (T=Total, P=Partial, or N=Penumbral) along with the Saros series. Gamma is the distance of the Moon's center from the shadow axis of Earth at greatest eclipse (in Earth radii). The penumbral and umbral magnitudes of the eclipse are defined as the fractions of the Moon's diameter obscured by each shadow at greatest eclipse. The semi-durations of the partial and total phases of the eclipse are given to the nearest minute. Finally, the Greenwich Sidereal Time at 00:00 U.T., along with the Moon's Geocentric Right Ascension and Declination at greatest eclipse complete each record. For a detailed key and additional information about the catalog, see: Key to Catalog of Lunar Eclipses.
For any eclipse in the catalog, the start and end times of the partial eclipse phases can be calculated by respectively subtracting and adding the semi-duration of the partial phase (S.D. Par) to the instant of greatest eclipse. Similarly, the start and end times of the total eclipse can be calculated by either subtracting or adding the semi-duration of the total phase (S.D. Tot) to the instant of greatest eclipse. For a detailed example, see Contact - Key to Lunar Eclipse Catalogs.
To determine whether an eclipse is visible from a specific geographic location, it is a matter of calculating the Moon's altitude and azimuth during each phase of the eclipse. The calculations can be performed on any pocket calculator having trigonometric functions (SIN, COS, TAN). Armed with the latitude and longitude of the location, the lunar eclipse catalog provides all the additional information needed to make the calculations. For the equations and an example of how to calculate the Moon's altitude for a specific location, see Altitude - Key to LunarEclipse Catalogs.
U.T.
Greatest Saros Pen. Umb. S.D. S.D. GST Moon Moon
Date Eclipse Type # Gamma Mag. Mag. Par Tot (0 UT) RA Dec
h h °
1421 Feb 17 19:44 T+ 104 -0.222 2.513 1.418 113m 46m 10.4 10.64 8.4
1421 Aug 13 06:20 T- 109 0.237 2.423 1.454 103m 44m 22.0 22.04 -11.8
1422 Feb 06 19:53 P 114 0.483 2.048 0.927 103m - 9.7 9.94 13.1
1422 Aug 02 23:16 P 119 -0.490 1.961 0.989 94m - 21.3 21.39 -15.9
1423 Jan 26 20:28 N 124 1.154 0.804 -0.290 - - 8.9 9.21 17.3
1423 Jun 24 02:56 N 91 1.392 0.339 -0.701 - - 18.7 18.73 -21.8
1423 Jul 23 13:26 N 129 -1.275 0.542 -0.473 - - 20.6 20.72 -19.5
1423 Dec 17 15:15 P 96 -0.995 1.053 0.040 22m - 6.3 6.31 22.4
1424 Jun 12 07:08 P 101 0.667 1.693 0.608 88m - 18.0 17.96 -22.9
According to Menzies, the Chinese expedition left on 8 March 1421. In the next two years there was only one total eclipse - at 06.20 GMT on 13 August 1421. Multiply the UT by 15 to get the GHA - ie the west longitude of the moon. The dec is the latitude of the moon so the point where the moon is overhead is known. At 06.20 on 13/8/1421 we have: 15 * 6.33 = 95 deg West. That is maybe over Peru. Not visible in China hence useless.