I am interested in hearing (well, actually reading) your view of alchemy, because it seems to me you have it very linked with the art of transumation. That could be a result from the interpretations of alchemy from some series or another *cough cough* Full Metal Alchemist *cough cough*, which however may not be the same to the original idea of alchemy or my idea of its.
To my knowledge (/opinion), alchemy is just the art/science/magical domain that attempts to turn some metal into another (some people wanted moar gold). Also, I'm not sure if the actual alchemists believed in the Elixir of life, but it certainly can be produced by the Philosopher's Stone in Harry Potter. Transumation/transfiguration, however, is a much more general magical art that enables one to transform objects, plants, animals, people, oneself into other objects, plants, animals, people, give them different appearance. Of course, that certainly must have some limitations, though I shall not give any at the moment.
What do you mean when you say alchemy and transumation.