by and by vs distant

by and by

adv
  • After a short time. 

  • After an indefinite period. 

noun
  • Heaven; the hereafter. Usually preceded with "the sweet." 

distant

adj
  • Far off (physically, logically or mentally). 

  • Emotionally unresponsive or unwilling to express genuine feelings. 

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