Of essence divided?

[distaiyi]

No: HPFGUIDX 154321

I read the Occulemency chapter ( well reread it ) after my original post.

As JKR has said any number of times, she words things very
carefully... In this case she chose the word essence.

1 a : the permanent as contrasted with the accidental element of being 
  b : the individual, real, or ultimate nature of a thing especially
as opposed to its existence c : the properties or attributes by means
of which something can be placed in its proper class or identified as
being what it is
2 : something that exists : ENTITY
3 a (1) : a volatile substance or constituent (as of perfume) 
    (2) : a constituent or derivative possessing the special qualities
(as of a plant or drug) in concentrated form; also : a preparation of
such an essence or a synthetic substitute b : ODOR, PERFUME
4 : one that possesses or exhibits a quality in abundance as if in
concentrated form <she was the essence of punctuality>

Frankly I don't see how we can interpret this as anything but a
question about the essence of Voldemorte or of Nagini. In either case
I find the implication that he believes Nagini is a Horcrux to be
stronger than the implication that he believes Nagini simply to be
possessed.