Publish or Perish

What’s the origin of this phrase? Our patrons want to know, but the origin has been lost to the ages! F. A. Hetzel has this to say about "publish or perish":

Although no one seems to recall who coined the phrase Publish or Perish to describe the assertion that a university or even college teacher will not be promoted within the system of American higher education unless he conducts original research and proves his capabilities by publishing, the words have provided scholars and their publishers with an unparalleled opportunity to defend the faith. [pp. 101-102]

Hetzel, F.A. (1973). Publish or perish, and the competent manuscript.
Scholarly publishing, 4(2), 101-109.