apportion vs prorate

apportion

verb
  • To divide and distribute portions of a whole. 

  • Specifically, to do so in a fair and equitable manner; to allocate proportionally. 

prorate

verb
  • To divide proportionately, especially by day; to divide pro rata. 

How often have the words apportion and prorate occurred in a corpus of books? (source: Google Ngram Viewer )