Between of futher and futhermore

Further (If seen as an adjective) - in addition, moreover
Eg: "computer chess games are getting cheaper all the time; furthermore, their quality is improving"

Now if Further seen as a Adverb : Meaning.. More distant in degree, time, or space..
Brief Explanation : It is again a comparative form of the very FAR, and here the meaning of further becomes just equal to Further more.