Ralph, if you are referring to "
The Brightness Scale of Exterior Scenes and the Computation of Correct Photographic Exposure," I don't remember anything about 18% reflectance in that paper (although it's been more than a few years since I've thoroughly read the paper). In fact, I remember finding it interesting that it's not mentioned in any of Jones' seminal papers. I believe the perceived importance of 18% gray is primarily promoted from popular photographic writings.
The 18% gray card is more of a visual reference than an exposure device; however, it should be noted that the instructions that comes with the Kodak Neutral Gray Card says that if the card is used for metering an exterior scene, the exposure should be increased by 1/2 stop. This would indicate an effective 12% reflectance (to be clear, exposure meters are NOT calibrated to reflectance).
Rob, I've written rather extensively about K. There's a 20 plus page document available at
http://64.165.113.140/content/benskin/. It's titled "Defining K." One of the problems of deriving information from the standards is that the purpose of the standard isn't about theory. All the research and supporting arguments for what's in a particular standard comes from scientific papers. The one exception to this is in the appendixes in the standard for general purpose photographic exposure meters (ANSI PH3.49 - 1971). The standard makes it clear that the appendixes are not part of the standard. The various sections that explain K are almost verbatim from the previously published paper
Re-evaluation of Factors Affecting Manual or Automatic Control of Camera Exposure by James F. Scudder, C.N. Nelson, and Allen Stimson (also available at the above link). Here is an excerpt from the paper's abstract:
"The film exposure level maintained by an automatic control in a camera depends primarily on the film speed but several other variables can manifest substantial influence. The effects of field-luminance distribution and spectral sensitivity, as well as sensitometric, optical and photometric relations are expressed analytically and the equations for camera exposure are derived. The resulting constant relates the ASA standard film speed to the preferred exposure for an area in an average scene having the average luminance indicated by the meter. This constant, when combined with nine variables which are a function of camera design, meter design, and scene structure, provides an equation that is simplified by substituting empirical values for all but three parameters. The exposure constant is expressed as a function of the lens transmission, spectral characteristics of the detector and the discrimination of the field luminance measurement."
I've attempted to explain this to you a number of times in the past. By evaluating the variables in the equation for K, it's purpose can be better understood. I did a breakdown of the variables in Defining K that might be useful. Rob, I hope to adequately explain that while you got the math correct, your interpretation and application of K is in error. There is a lot to unpack and I'm still trying to determine an approach and how much effort I want to put into it. But something to think about for starters, you determined correctly that the ratio of C and K produces the effective average reflectance of the reflective meter (12%), but then mistakenly conclude meter's are calibrated to 8%. And yes, the 8% correlation is just a coincidence.