Editing F-number (section)

=== Aperture numbering systems ===
[[File:No1-A Autographic Kodak Jr.jpg|thumb|right | A 1922 Kodak with aperture marked in U.S. stops. An f-number conversion chart has been added by the user.]]

At the same time, there were a number of aperture numbering systems designed with the goal of making exposure times vary in direct or inverse proportion with the aperture, rather than with the square of the f-number or inverse square of the apertal ratio or intensity ratio. But these systems all involved some arbitrary constant, as opposed to the simple ratio of focal length and diameter.

For example, the ''Uniform System'' (U.S.) of apertures was adopted as a standard by the [[Royal Photographic Society|Photographic Society of Great Britain]] in the 1880s. Bothamley in 1891 said "The stops of all the best makers are now arranged according to this system."<ref>C. H. Bothamley, ''Ilford Manual of Photography'', London: Britannia Works Co. Ltd., 1891.</ref> U.S. 16 is the same aperture as {{f/|16}}, but apertures that are larger or smaller by a full stop use doubling or halving of the U.S. number, for example {{f/|11}} is U.S. 8 and {{f/|8}} is U.S. 4. The exposure time required is directly proportional to the U.S. number. [[Eastman Kodak]] used U.S. stops on many of their cameras at least in the 1920s.

By 1895, Hodges contradicts Bothamley, saying that the f-number system has taken over: "This is called the {{f/|''x''}} system, and the diaphragms of all modern lenses of good construction are so marked."<ref>John A. Hodges, ''Photographic Lenses: How to Choose, and How to Use'', Bradford: Percy Lund & Co., 1895.</ref>

Here is the situation as seen in 1899:
[[File:Diaphragm Numbers.gif|center|823 px]]

Piper in 1901<ref>C. Welborne Piper, ''A First Book of the Lens: An Elementary Treatise on the Action and Use of the Photographic Lens'', London: Hazell, Watson, and Viney, Ltd., 1901.</ref> discusses five different systems of aperture marking: the old and new [[Carl Zeiss|Zeiss]] systems based on actual intensity (proportional to reciprocal square of the f-number); and the U.S., C.I., and Dallmeyer systems based on exposure (proportional to square of the f-number). He calls the f-number the "ratio number", "aperture ratio number", and "ratio aperture". He calls expressions like {{f/|8}} the "fractional diameter" of the aperture, even though it is literally equal to the "absolute diameter" which he distinguishes as a different term. He also sometimes uses expressions like "an aperture of f 8" without the division indicated by the slash.

Beck and Andrews in 1902 talk about the Royal Photographic Society standard of {{f/|4}}, {{f/|5.6}}, {{f/|8}}, {{f/|11.3}}, etc.<ref>Conrad Beck and Herbert Andrews, ''Photographic Lenses: A Simple Treatise'', second edition, London: R. & J. Beck Ltd., c. 1902.</ref> The R.P.S. had changed their name and moved off of the U.S. system some time between 1895 and 1902.