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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