The jackhammer being used underground is moving far too slowly to effectively be breaking stone. Additionally, the entire piece of machinery should not be moving - only the internal hammer and chisel.
Sydney says that the authenticity of the journal of the French explorers dated 1605 is being determined by radiocarbon dating. For an item supposedly about 400 years old, in 2001, when the episode takes place, a typical uncertainty for dating for samples younger than 10,000 years would have been about +/- 50 years, meaning that the book would have been dated anywhere from 1555 to 1655, rendering the dating non-conclusive.