a second vs another

a second

another

det
  • Not the same; different. 

  • One more/further, in addition to a former number; a second or additional one, similar in likeness or in effect. 

  • Any or some; any different person, indefinitely; anyone else; someone else. 

pron
  • One of a group of things of the same kind. 

  • An additional one of the same kind. 

  • One that is different from the current one. 

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