There's a version of the Tree of Life I've run across a few times in Waite's writings but it never clicked until just now. It's from an article by Waite (Kabalistic Alchemy), first published (according to R. A. Gilbert,
Hermetic Papers of A. E. Waite) in
The Journal of the Alchemical Society, Vol. 2, Part 9, January 1914, pp. 43-58. According to Waite, in the
Aesh Mezareph, or,
Book of Purifying Fire there are two versions of the Tree which show correspondences for the sephiroth and metals. The Tree in the image below is from the "second system."
Kether, Chokmah and Binah correspond to Philosphical Mercury, Philosophical Salt and Philosophical Sulphur respectively. Mercury represents the central pillar, Salt the right pillar and Sulphur the left pillar. In the FRC, Waite moves Philosphical Mercury, Philosophical Salt and Philosophical Sulphur down to Tiphareth, Chesed and Geburah respectively, but they keep their pillar assignments. Seems to me a very like source of influence on Waite for his later arrangement in the FRC. Writing in
The Secret Tradition in Alchemy on the subject of the two arrangements in
Aesh Mezareph Waite says:
"As such, I consider that the first tabulation is almost manifestly incorrect; but if the second should be preferred to the first, it is not therefore unimpeachable. I have met with other attributions in more secret Kabalistic systems and these are still better, though not perhaps perfect;"
Could be a reference to the attributions he ultimately opted for in the FRC, or maybe not, hard to say.