how did the Bedford Canal prove earth's sphericity ?

Answer 1

In 1870, Alfred Russel Wallace accepted a wager offered by a flat-earth proponent John Hampden to prove that the earth was not flat. He used accurate surveying equipment to demonstrate the curvature of the Earth along the length of the Bedford Canal. He won the challenge with a neatly conceived demonstration (the so-called "Bedford Canal experiment") but, on a technicality, not a penny of the wager.

Answer 2

I googled "Bedford Canal" and found the following at Wikipedia:

"The Bedford Level Experiment was a series of observations carried out along a six-mile length of the Bedford Level (the Old Bedford River), Norfolk, England, during the nineteenth and early twentieth centuries. It was an attempt to demonstrate that the Earth was flat. Early results seemed to prove this contention, but most later attempts to reproduce the observations firmly supported the conventional view that the earth is a sphere.
At the point chosen for all the experiments the Level was a slow-flowing drainage canal running in uninterrupted straight line for a six-mile stretch to the north-east of the village of Welney. The most famous of the observations, and the one that was taught in schools until photographs of the Earth from space became available, involved a set of three poles fixed at equal height above water level along this length. As the surface of the water was assumed to be level, the discovery that the middle pole, when viewed carefully through a theodolite, was almost three feet higher than the poles at each end was finally accepted as a new proof that the surface of the earth was indeed curved.
The first investigation was carried out by Samuel Birley Rowbotham (1816-1884), the president of the Flat Earth Society, in the summer of 1838. He waded into the river and used a telescope held eight inches above the water to watch a boat with a five-foot mast row slowly away from him. He reported that the vessel remained constantly in his view for the full six miles to Welney bridge, whereas, had the water surface been curved with the accepted circumference of a spherical earth, the top of the mast should have been some eleven feet below his line of sight.
Rowbotham repeated his experiments several times over the years but his discoveries received little attention until, in 1870, a supporter by the name of John Hampden offered a wager that he could show, by repeating Rowbotham’s experiment, that the earth was flat. The noted explorer and qualified surveyor Alfred Russel Wallace accepted the wager. Wallace, by virtue of his surveyor’s training, avoided the errors of the preceding experiments and he won the bet.
In 1901 explorer H Youle Oldham, a geography professor at Cambridge University, conducted the definitive experiment described ... above."