Hello Hans!

The quintessence symbol is a very important one in alchemy. Here are some quotes of posts I once wrote on the Lexicon forums alchemy threads that  may help you (or at least I hope so).

Long before the HBP release, I wrote this:

"The quintessence is one of the most important symbols in alchemy. It means that, for alchemists, at the 4 elements (air, earth, water and fire) a fifth should be added : this fifth essence was the spiritual nature of the spirit of the universe. It was in each of the 4 elements and at the same time above them. This "spirit" was represented in the water by a dolphin, in the air by an eagle, on earth by men and in the fire by THE PHOENIX !

So, if we see the four houses of Hogwarts as the representations of the four elements, then his headmaster is, symbolically, the quintessence of the four: at the same time in each of them and above them, as their leader, I mean a kind of role model in the Wizarding World, the most skilled, experienced and wise wizard."

We also said then that "4 Privet Drive" was a very interesting address for Harry in that regard since:

"we can find the fifth element here too : there, Harry is under the constant watch of Dumbledore, through Mrs Figg. Dumbledore was the one who chose 4 Privet drive to be the place where Harry will live and put his own protection there. More, if we remember the Howler Petunia received, his influence on her is very powerful and she never forgot it. From what we can deduce that in Privet drive too, Dumbledore is the quintessence : at the same time part of the 4 (the 3 Dursleys and Harry as the 4 elements) and also above them."

Now, when the HBP was released I made quite a jump on my chiar when I read that Harry was reading a charm book called: "Quintessence, a quest"!

Which led me to write that then:

"I do believe that the title of this book, is a hint to Dumbledore, the more after the "White tomb" chapter and the white smoke/phoenix symbolism! And, funnily enough, Dumbledore goes through all the elements with Harry during their last trip together: water (they swim), fire (that he conjures to make the Inferi leave them), air (they ride broomsticks) and he is with Harry, a man, for the earth element. So, after his death, DD really becomes "this fifth essence, the spiritual nature of the spirit of the universe." We said "It was in each of the 4 elements and at the same time above them" and I believe that it means that, from where he is, DD is, more than ever, protecting Harry. Maybe was it the only way for him to continue guiding him and he knew it, hence his inevitable death...

But there is certainly more! Harry is with Dumbledore during his last journey, through the 4 elements, as Dumbledore was above the 4 houses at Hogwarts, so will become Harry when he will succeed in uniting the houses in book 7, so to restore the balance again. The quintessence is a path to harmony, and Dumbledore, the 5th element, has not finished helping him in that quest." And Fawkes can perfectly be seen as DD's spirit watching over Harry.

"Quintessence is, at the same time, inside and above all the other elements. For the alchemists, it represented the spiritual nature of the essence of the universe. And it reminds me of Dumbledore's words in OotP, about the locked door in the Department of Mysteries: "It contains a force that is at once more wonderful and more terrible than death, than human intelligence, than the forces of nature." Love, "more terrible than the forces of nature", the quintessence... it fits perfectly! "

It is quite late here so I hope what I wrote makes sense (sort of...) and you may find it useful. :-)

Warm regards to all (and a special waving to Iris: glad to see another French HP lover here! :-D)