knuckle under vs kowtow

knuckle under

verb
  • To yield or cooperate when pressured or forced to do so. 

kowtow

verb
  • To bow to or show obeisance to. 

  • To bow very deeply. 

  • To grovel, act in a very submissive manner. 

  • To kneel and bow low enough to touch one’s forehead to the ground. 

noun
  • The act of kowtowing. 

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