Artificially produced chemical elements heavier than uranium have been known for more than seventy years and the number of superheavy elements continues to grow. Presently 26 transuranic elements are known. This paper examines the earliest scientific interest in the very heavy elements and the related question of an upper limit of the periodic system. In the period from the 1880s to the early 1930s, three kinds of questions appealed to a minority of physicists, chemists and astronomers: (1) Why is uranium the heaviest known element? (2) Do there exist transuranic or superheavy elements elsewhere in the universe, such as in stellar interiors? (3) Is there a maximum number of elements, corresponding to a theoretical limit for the periodic system? The early attempts to answer or clarify these questions lacked a foundation in nuclear physics, not to mention the total lack of experimental evidence, which explains why most of them were of a speculative nature. Although the speculations led no nothing, they are interesting in their own right and deserve a place in the history of the physical sciences.
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