Theodor Benfey's arrangement is an example of a continuous (spiral) table. First published in 1964, it explicitly showed the location of lanthanides and actinides. The elements form a two-dimensional spiral, starting from hydrogen, and folding their way around two peninsulas, the transition metals, and lanthanides and actinides. A superactinide peninsula is already slotted in.[1]
Earlier, in 1869, Mendeleev had mentioned different layouts including short, medium, and even cubic forms. It appeared to him that the latter (three-dimensional) form would be the most natural approach but that "attempts at such a construction have not led to any real results".[2][n 1] On spiral periodic tables, "Mendeleev...steadfastly refused to depict the system as [such]...His objection was that he could not express this function mathematically."[4]
^Mendeleev, DI (1869). "On the correlation between the properties of the elements and their atomic weight". Zhurnal Russkoe Fiziko-Khimicheskoe Obshchestvo. 1: 60–77 (note 2).
^Stewart, PJ (2018). "Chapter 3: Amateurs and professionals in chemistry: The case of the periodic system". In Scerri, E; Restrepo, G (eds.). Mendeleev to Oganesson: A Multidisciplinary Perspective on the Periodic Table. Proceedings of the 3rd International Conference on the Periodic Table, Cuzco, Peru 14–16 August 2012. Oxford: Oxford University Press. pp. 66–79 (68). ISBN978-0-86380-292-8.
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