apportion vs measure out

apportion

verb
  • To divide and distribute portions of a whole. 

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

measure out

verb
  • to measure an amount or quantity or size that is needed or wanted, to mark the dimensions of something. 

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