grammar - "At one end of the street" vs. "At the one end of the street"

"At one end of the street" vs. "At the one end of the street"

Which phrase is more correct?
or
Are they both correct only the meaning is slightly different?
or
Are both fine meaning the same?

assuming that it's part of the following context: "You'll find the street easily. There's a school at (the) one end of it. There's a hospital at the other end."

Answer

Probably by reason of symmetry, you'll sometime find "the one" in expressions

the one end ... the other end

In fact, we have the illustrious example of Benjamin Franklin from his Memoirs (1840) describing experiments in the electrical conductivity of bodies of water:

[L]et the one end [of the wire] communicate with the water, and let one person stand in the other brook....

But the Ngram viewer shows an least 20:1 preference for leaving off the article.