What is the origin of the term “f-stop” in photography?

This is a matter of some debate, and the truth is that you can pick up any number of photography books (or visit any number of photography websites) and read a variety of answers to this question, the most common of which tend to be:

• Focal Stop
• Focal Ratio
• Factorial System
• Fractional Stop
• Fractional Diameter
• Finestra Stop (Finestra is Italian for 'window')

As with many historical 'facts,' the truth is quite a bit messier than many of these sources would seem to indicate, and the real reason that we use 'f-stops' today to some extent defies a quick explanation.

The Wikipedia F-Number article actually has a rather complete (and well cited) history of how we got here, but some of the 'high points' are:

• In the late 1800's there were a variety of aperture systems which all operated more-or-less the way we are all familiar with, which is to say that the concept of letting more or less light through a lens via an aperture system was being used extensively, even if the different systems used different naming conventions. (Well-known systems at the time included Sutton and Dawson's 'apertal ratio,' and Dallmeyer's 'intensity ratio')
• In 1858 John Waterhouse invents a system of metal discs with different sized holes to act as the aperture which literally get dropped into a slot in a lens. He called them 'Waterhouse Stops' because the discs were literally stopping light from entering the camera. This is likely the first instance of the use of the word 'stop' as it relates to aperture.
• In 1895 John A. Hodges first champions the 'fractional number' system (which he abbreviated to 'F-number') in defiance of the Photographic Society of Great Britan's use of the 'Uniform System (U.S.)' This is the first recorded instance of the 'fractional number' and is likely the original meaning of the 'f' in F-stop.
• In 1901 C. Welborne Piper first proposes a unified system of describing aperture marking called the 'f-diamater' (or fractional diameter) after observing similarities between a half-dozen of the more popular methods of the day.
• From the early 1900's through about 1920, the most common way to refer to Piper's unifying system was as the 'f-number.'
• In 1961 the American national Standards Institute (ASA) officially adopted the 'f-number' as the specification for photoelectric photographic meters. Essentially codifying the term and making 'f-number' the common phrase used to describe aperture for camera manufacturers of the day.
• While the phrase 'f-number' has morphed somewhat since 1961 to the now more commonly used 'f-stop' we use today, there is currently no standardized and generally accepted definition for the 'f' in f-stop. In fact, it has variously been referred to as focal, factorial, fractional, and many other designations by a wide variety of sources over the last 120ish years to the point where even though the system itself has been standardized, there simply is no singular recognized designation for the 'f' in f-stop.