by chance vs circumstantially

by chance

prep
  • Unexpectedly, accidentally; without foreplanning. 

  • Possibly; perhaps. 

circumstantially

adv
  • in a circumstantial manner 

  • In respect to circumstances; not essentially; accidentally. 

  • In every circumstance or particular; minutely. 

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