engaged vs immersed

engaged

adj
  • attached to a wall or sunk into it halfway 

  • Having the widest part of its presenting part, usually the head, enter the pelvic brim or inlet. 

  • Greatly interested. 

  • Busy or employed. 

  • (of a telephone) Already involved in a telephone call when a third party calls. 

  • being attacked or attacking 

  • Having agreed to marry a particular person (one's fiancé or fiancée) or each other. 

  • Synonym of engagé (“passionately committed to a cause”) 

  • in contact and in operation 

immersed

adj
  • Under the surface of a liquid; sunk. 

  • Deeply involved. 

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