circumstantially vs on accident

circumstantially

adv
  • In respect to circumstances; not essentially; accidentally. 

  • in a circumstantial manner 

  • In every circumstance or particular; minutely. 

on accident

adv
  • Accidentally; not intentionally; because of error, misfortune, or lack of caution. 

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