I have burnt the incense cone on the brazier, and added the spider juice.
Flames up nicely as it should, but I can't seem to get on from there.
As I understand it I'm supposed to use the wand I found earlier on top of
the Library, but I've forgotten what it looked like, and the only wand I
have at the moment is wand of weakening, a brown wooden, sorta lightning
shaped wand with a yellow knob at the end.When I use it on the flaming
brazier nothing happens.Would someone please tell me what I'm doing wrong?

You must use the runed wand, found above the library, when you invoke the serpent figurine in the central pedestal in the library.. only then, shall you seek the dominating visasge of the snake..