Following is a link that discusses an interpretation of the Elijah/Elisha double portion anointing that differs from the LW interpretation. If this stuff interests you, then I recommend reading the link; otherwise, don't read it. If the link gets lost in translation, you can find the article at letusreason.org/Pent2.htm (the topic is anointing).
[www.letusreason.org]
[www.letusreason.org]