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I have been reading Admiral of the Ocean Sea by Samuel Eliot Morison this week about Christopher Columbus and his four voyages to China and Japan. That is where he was headed and that is where he thought he was almost to the end of his life. On the fourth voyage he spent Christmas 1502 very near the Isthmus of Panama where the Canal would be built some three hundred years later. Even if the modern canal were available to him it is doubtful if he could have sailed his re-provisioned ships so great a distance as the width of the Pacific Ocean to China, his intended destination.


Columbus had great difficulty in convincing anyone to give him a ship for his explorations to cross the Atlantic Ocean to get to China. He pestered the Royalty of Spain and Portugal and again Spain for years before finally being given three small ships to give it a try. The reason the authorities were so slow about providing the ships was that it was easy to prove that Columbus’s estimation of the distance to China was wrong and it was beyond the reach of the little ships then available. Since Classical Greek times the circumference of the Earth was known exactly. There was the then well known story of Eratosthenes (276-194 BCE) calculating the size of the Earth by observing a deep well near Aswan, Egypt, where the sun reflected off the water on the bottom only one day per year. All that was necessary was to measure the North-South distance to some place on that same day of the year and calculate the angular change from some other point on that line and multiply it out to a full circumference. The method is as accurate as the tools used for measurement, which were precise to only one percent. The astronomers of Columbus’s day probably knew the the diameter of the Earth well within a few percent of its true value. The problem was the very questionable measurements across the continent of Euro-Asia to the coast of China. The authorities estimated it to be about 180° to the west of Portugal. Columbus was saying it was about 80° and he was the one who was wrong, very wrong. However, it all turned out for the better, at least for the Spanish, because two whole continents, with plenty of gold, got in the way and Columbus ran into them on his way to China and claimed them for Spain.

Once at sea Columbus seems to have been lost much of the time. He may have been very nearsighted because he seemed to have great difficulty shooting star positions and even sun positions. He was using an astrolabe which under really good conditions probably isn’t accurate to better than a degree but Columbus was so inaccurate that even on a bobbing ship his error of ten degrees is difficult to explain. He claimed to be shooting the North star sometimes but with no better accuracy did he shoot the sun? Just using your fist and thumb poised on your other fist and thumb can probably get you better than a two degree accuracy, for low altitudes, with a little practice. Later, Francis Drake sailed to California in 1579 and on around the world using a tool little more accurate than your thumb, called a cross staff. That is basically one long stick placed on the bridge of the nose and pointing at the horizon and another stick held perpendicularly to this first stick moved along it until the bottom of the movable stick was on the horizon and the top was on the star whose height was being measured. Then you read the height of the star on the index markers on the first stick. On dry land or a very steady ship’s deck an accuracy of better than half a degree can be obtained. That is a North-South accuracy of about thirty miles. To get your East-West location you need a clock, which no one had until 274 years after Columbus sailed. Clocks became available in 1766 when John Harrison made one and the British sent out  Captain James Cook to survey the oceans. Columbus measured his East-West movement by using a log tied to a rope with knots evenly spaced along it and then counted the knots that passed through one’s fingers during one cycle of a flowing sand minute timer to estimate velocity and calculate distance. With all of the various potential errors with this method a twenty percent error of actual distance covered on a cross ocean trip would be considered good.

The East-West distance covered was badly in error in Columbus’s estimations and the only effort he made to correct it was some observations of the Moon eclipse which gave him his East-West placement to an accuracy of a few hundred miles or better, but until some report of this same eclipse came from the Orient there would still be no way of knowing for sure if Cuba wasn’t an island off the China coast. There is a way that Columbus could have determined his East-West longitude with good accuracy by using a star being eclipsed by the Moon or by carefully measuring the distance between some star near the Moon and comparing that measurement to what that measurement would be when the Moon was at the same angle from the North star back in Spain. The difference will be accurate to the limit of your tools and calculations. But an accuracy to within a hundred miles would have been possible by these naked eye calculations. Columbus was off in his guess by many thousands of miles by the width of the Pacific Ocean plus the width of the continent. This Moon method would have demonstrated that he had found a new world much sooner than was acknowledged.

I wonder how many illusions we are currently living with that are similarly inaccurate and as easily corrected if we only knew how.