# Around the world in ... how long?

## Andrew Elliott

In around 200 BCE Eratosthenes, a Greek mathematician, geographer and librarian in Alexandria, calculated the size of the Earth.

He knew that in Syene, about 20 days' travel away, at midday on the summer solstice, the sun would be directly overhead. A shaft of sunlight would shine straight down a well shaft, and vertical columns would cast no shadows.

At the same time, in Alexandria, he measured the angle between the sun and the zenith. The angle he measured came to around 1/50 of a circle. He knew Syene to be, in his terms, 5000 *stadia* away. (A *stadion* was 125 paces, defined variously as between 157 and 185 metres. We now measure the Alexandria-to-Syene distance as 840 km, equivalent to a *stadion* that measures 168 m).

Using a little geometry (which, after all, means "Earth-measuring"), he was able to calculate the circumference of the Earth. Depending on which definition of *stadion* you think he used, his answer (250,000 stadia) comes out to between 38,250 km and 46,250. Taking 50 times the distance from Alexandria to Syene (now modern-day Aswan) gives a result of 42,000 km. The true pole-to-pole circumference of the Earth is very close to 40,000 km. Eratosthenes pretty much nailed it. Remarkable for 2200 years ago.

If the distance from Alexandria was a 20-day journey on foot, then Eratosthenes could have worked out that that to walk all the way around the world (assuming such a route was possible) would have taken 1000 days. Using our modern measurement, that means 40 km a day, quite reasonable for a fit adult over good terrain.

As the title suggests, in Jules Verne's novel *Around the World in 80 Days*, his hero Phileas Fogg manages his circumnavigation in 80 days. In fact, as the map below shows, virtually all of the journey occurs north of the equator. The most southerly point is near Singapore, which is pretty much on the equator. The indirect route lengthens the journey. The fact that the circumnavigation is not at the Earth's widest latitude shortens it. These factors more or less balance out and the journey as mapped comes to approximately 38,000 km, just 5% less than the circumference of a great circle. Managing this in 80 days meant that Fogg made an average speed of 475 km per day.

Now, Phileas Fogg (and don't forget his faithful companion Passepartout) made it in 80 days, but how long would it take to circle the Earth using other means of transport? Here's a table showing how long it would take to travel 40,000 km in different ways:

But to close, let's turn to Shakespeare. In A Midsummer Night's Dream, he has Puck say: *I'll put a girdle round about the earth In forty minutes.* That means Puck would be traveling at 1,000 km each minute: that's a megametre per minute.