The answer depends on which canal you're asking about. There have been three iterations, or versions of the Erie Canal. The original Erie was begun on July 4, 1817 near Rome, NY. It was completed eight years later on October 26, 1825. The second version was begun almost as soon as the first was finished, and that enlargement was completed in about 1862. The final "Barge Canal" that we see today was begun in 1905 and finished in 1918.
We have a video about that. All of our information is second-hand, but we've been told that mules are careful about not drinking polluted water, which could make them sick. Often the water in the Erie was polluted because of things people threw into it. Mules also had smaller feet than horses, which would give them better traction. One source says that they didn't use mules on the Erie much before the Civil War, but then after the war mules were very common on the canal. My guess is that northern soldiers learned something from seeing mules used in the Army that they didn't know before the war.
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