Well,Pete,either u or Dirac[1] have it all mixed up.I'd go for you,as Dirac got a Nobel prize and i've been taught GR from his book[1].
Your formula #2 is valid for contravariant vectors ([1],eq.3.3,page 6) (a.k.a.vector,which is defined on the tangent bundle to a flat/curved [itex] \mathbb{M}_{4} [/itex])...So how about getting it all done correctly or,don't give that link anymore and exlude it from your post.
Daniel.

[1]P.A.M.Dirac,"General Relativity",1975.
