In the 1760's Charles Mason and Jeremiah Dixon surveyed a line of the same name. They found larger than normal systematic errors, which Henry Cavendish attributed to the gravitational pull of the Allegheny Mountains. Several years later Cavendish did a series of sensitive experiments to determine the gravitational constant, which is in every physics textbook. The journey from a line in the sand to the event horizon of a black hole started more the 2,000 years ago.

We need a reference time and place; for this document it will be:

Toronto, Canada, latitude: 48 degrees, 42 minutes.

Summer Solstice, 2017, Wednesday June 21

Warning; Solar noontime (1:19 PM) is required when shadows fall exactly north.

Only two measurements are required, a stick and the length of its shadow.

## Eratosthenes's MethodAssume that the yellow rays of sunlight are parallel. One line strikes the equator and there is no shadow. Farther north, the black line casts a shadow. The black line crosses two parallel lines so that the shaded angles are congruent to each other.Example: The Tropic of Cancer is about 23.4 degrees north. The distance to the equator is 1617 miles. Circumference of the Earth is 1617 x 360 / 23.4 = 24,877 miles |

Stick: 115.1 cm

Shadow: 42.7 cm

Tangent is 42.7 / 115.1 = 0.371

Angle is arctangent (0.3695652) = 20.354 degrees

Circumference is distance x 360 / 20.354

= 1400 x 17.687

= 24,762 miles which is about 100 miles less than the meridional circumference.

This value is given by Wikipedia,

If we use 1 km = 0.621 the value is 24,886.59 which is off by about 14 miles.