in vain vs spinning one’s wheels

in vain

adj
  • Unsuccessful, failed. 

adv
  • In a disrespectful manner, without honoring the proper meaning; insincerely or without proper respect. 

  • Without success or a result; ending in failure. 

spinning one’s wheels

How often have the words in vain and spinning one’s wheels occurred in a corpus of books? (source: Google Ngram Viewer )