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Thanks for pointing this out. Doing a Google Books and a Google Web search, it looks like there are three ways different sources use the terminology:

  1. In some references, the terms "double helical" and "herringbone" are treated as interchangeable. For instance Machine Elements: Life and Design (CRC Press).
  2. Sometimes, "double helical" is defined to have a space between the two helical slants and "herringbone" is defined not to have the space. That is the usage your reference has.
  3. Sometimes "double helical" is treated as the more general term, and "herringbone" is the special case when the spacing between the two slants is zero. Wikipedia does this. In this usage, all herringbone gears are double helical, but not all double helical gears are herringbone.

In any case, "herringbone" is indeed the more precise terminology, so I've renamed the file.