authorize vs countersign

authorize

verb
  • To grant (someone) the permission or power necessary to do (something); to permit; to sanction or consent to. 

countersign

verb
  • To add a second signature to a document, affirming the validity of the signature of another person. 

  • To sign on the opposite side of (a document). 

noun
  • A second signature added to a document to affirm the validity of the signature of the first person. 

  • The response to a sign or signal. 

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