There is a novel idea within this short book, that painting cannot be described with any extant descriptive language but can perhaps be expressed through the nomenclature of alchemy. It is certainly interesting and the result can be cute, but Elkins might have better put it to a short polemical essay rather than this book-length project.
The first thing to get straight is that Elkins is not discussing paintings here. Rather, he is writing about the actual act of painting itself, what it is like to live among oils and paints and brushes and the mess of an artist's studio. Elkins, who trained as a painter before shifting into academia, argues that art critics and historians cannot grasp what painting actually is because all they care about is the painting itself, not the work that goes into it. This is, by his own occasional admission, not even strictly true, but it doesn't let it get in the way of his sweeping claims.
The main point for him is that because the critics and historians have so neglected the act of painting itself, there is no way to describe what painting actually is. However, he claims, if we turn to the language of alchemy we can discover a cognate language that describes the act almost perfectly. So far so good, but the detachment of painting as verb and noun makes this a curiously anti-aesthetic argument that never really comes to much of a point.
There are too many romantic depictions of painters laboring in their studios, about how they are different from other people, and how they are the equivalent of alchemists experimenting in labs with noxious materials and trying to create the perfect combination. It's all a little confused, because while the aesthetic is ignored in the argument on the formal level, it is actually deployed constantly to describe painters and what they do, as well as a huge reliance on the search for the sublime that both painters and alchemists seek. The sublime is, of course, very much an aesthetic category, so the argument more or less falls apart here.
While the book is very nicely written at the sentence level and Elkins has a decidedly poetic touch at points, the argument is very thin and never really develops into anything substantial. It's a shame because there is no doubt something in this, but it would have worked better if the claims Elkins makes were more modest and the analogy of painting to alchemy was given a more lighthearted touch.