15 Professor Robert Cribbs’ opinion of the 1418 map

Opinion of Professor Robert Cribbs


Liu Gang’s map of the world dated from 1418 has good estimates of the latitude and longitude of much of the world. How could Chinese explorers determine the longitude of the lands that they discovered in order to make the map? There is evidence that the Chinese could make rough measurements of longitude from onboard a ship using the moon and from shore using either the moon or sun. The Chinese had the mathematical tools, knowledge of the orbit of the moon and sun, and appropriate tools for the task. These along with astronomers and mathematicians were carried onboard ships in Zheng He’s fleet.


For the past 300 years (prior to radio and satellite navigation) the determination of longitude during a voyage required a clock that maintained accuracy for long time periods – a chronometer. What technology could the Chinese use to determine longitude prior to the availability of chronometers? Astronomical events could be used to determine longitude but few would be visible without a telescope.
Gavin Menzies suggested using an eclipse of the moon to determine longitude. This method, which is described in ancient texts, supplies the time synchronization in the absence of a chronometer. However it is not very practical – the time of the eclipse must be predicted, the sky must be clear at both the prime meridian and each observer position, the longitude can be calculated only after the voyager returns home to compare his readings with those made at the prime meridian, the eclipse must be visible at both the prime meridian and the voyagers location, if it is cloudy one must wait for the next eclipse, etc.

The explorer can use observations of the location of the sun or moon among the stars to determine his position if he has an ephemeris for the sun or moon at the prime meridian.

The Principle

Both the sun and moon appear to move among the fixed stars. The sun completes its trek in one year (about 1 degree/day) and the moon about 12 times per year (about 12 degrees/day). Both appear to be about ½ degree across when viewed from earth so the sun moves twice its diameter each day and the moon 24 times its diameter. If the explorer knew the position of either among the stars each day at the prime meridian then a measurement at his location would determine longitude. His position would be at an intermediate position from that in his ephemeris between two days. A simple proportion would supply a rough estimate of longitude.

Putting the principle into practice is not so easy. The sun moves at an irregular speed. This irregularity repeats every year – it is called the equation of time. Furthermore one cannot see both the sun and stars at the same time. The practical consequence of this is that longitude measurements using the sun can only be made over a period of one day – and only on a stable platform – the shore, not a ship. The orbit of the moon is much more irregular than the sun and the pattern does not repeat each year. The ancient Babylonians discovered the Saros cycle. The pattern of the moon repeats every 223 lunations (about 18 years) but 120 degrees to the west. In 669 lunations the pattern repeats at the same location. With this knowledge an ephemeris could be prepared that allows the determination of longitude by determining the position of the moon among the stars. The advantage of the moon over the sun is that it provides 12 times the accuracy. Furthermore there is a time each day where the moon and the stars can be simultaneously seen so measurements can be made on board a ship.

Did the Chinese possess the knowledge of the orbit of the moon? Did they have the mathematical tools to convert their measurements to longitude? Did they have the instruments and people on board the ship to make the measurements? The answer is yes to all questions.

The Chinese use a lunar calendar. Most months are 29 days but leap days are added at irregular intervals to guarantee a new moon at the beginning of each month. Leap months are added to keep the seasons from changing from year to year (as happens with the Arabic lunar calendar). Each new emperor published a calendar incorporating this information along with the time of eclipses and other astronomical information so Chinese astronomers particularly studied the moon. It was reported that if errors occurred the astronomer committed suicide.

The famous Chinese astronomer Guo Shoujing (1231-1314) had water clocks with temperature compensation and escapements to provide high resolution time accuracy for astronomical observations, a “pinhole camera” to sharpen shadows cast by the sun and moon, mathematical tools for polynomial generation and interpolation, and other inventions for measurements. Many of these tools along with a torqueta were carried onboard Zheng He’s fleet. The torqueta allowed the measurement of angles between the moon and stars to be made onboard ship. The torqueta also contained an analog computer that permitted reference stars not near the plane of the ecliptic or meridian to be used for the longitude determination.

The Chinese had the knowledge, history of observation, and practical tools for determining longitude. The astronomers were highly motivated to be accurate. There is evidence that these tools were used by Zheng He and perhaps others based on lists of items loaded onboard their ships.

Robert Cribbs Qualifications

Mr. Cribbs has his B.S. in physics and M.S. in mathematics. He was adjunct professor of engineering at California State University, Sacramento, visiting professor of scientific archeology at Cairo University, Egypt, and lecturer in ancient music at the art institute in Cairo. He was an accreditor for ABET (Accreditation Board for Engineering and Technology – to accredit university programs in engineering). He was founder of several companies involved with medical ultrasound and high speed imaging. He published a few hundred articles in archeology, music, medicine, nondestructive testing and ultrasound. He is an open water diver and pilot with a multiengine instrument rating.

He is currently President of Sonipulse in El Dorado Hills California.

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