Of essence divided?

[distaiyi]

No: HPFGUIDX 154300

In HP and the OotP, page 470 of the hardback US edition...

Harry is telling Dumbledore about his dream about Mr. Weasley...

'"Naturally, naturally," murmured Dumbledore apparently to himself,
still observing the stream of smoke without the slightest sign of
surprise. "But in essence divided?"'

This to me appears to bolster the argument that perhaps Nagini is a
horcrux for LV. If LV was not part of the snake how could harry see
through the snakes eyes...

This has probably all been covered before and I simply missed it.