W. J. Beal’s paper ["Phyllotaxis of cones", Am. Nat. 7 (1873): 449–53] shows incompleteness of HA’s theory, but does not invalidate his basic principles on origin of leaf arrangement or the broad applicability of the theory.

Has rewritten paper on leaf arrangement after criticism by Royal Society referees. Has found new factor influencing leaf arrangement, i.e., spontaneous variability in the number of vertical leaf-ranks.