All introductory books on setting type by hand discuss the various spaces available: two-to-the-em, three-to-the-em, etc. Most say no more about them, and it is natural to assume that these spaces are mathematically exact. Thus a three-to-the-em space for 10pt should be 10/3 = 3 1/3 points. But as should be immediately apparent, these do not always work out to convenient units. In fact, nearly all spacing material cast in the 20th century (at least) was point set: rounded to integral or simple (not thirds!) fractional point set widths.
(One notable exception to the silence about point-set spacing is Ralph W. Polk's The Practice of Printing, which goes so far as to give a table of "Standard Widths of Point-Set Spaces" (p. 35 of the 1945 edition)).
NOTES: See: Wood, Charles Lawson. "The Point System in Spaces and Quads." The Inland Printer, Vol. 39, No. 1 (April, 1907): 92-93.
{Huss 1973} Huss, Richard E. The Development of Printers' Mechanical Typesetting Methods, 1822-1925. (Charlottesville, VA: By the University Press of Virginia for the Bibliographical Society of the University of Virginia, 1973.)
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