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This article was constructed from a posting by William D. Ricker from Sep 1992.
In general terms, point size is a relative measure of the size of a font. It used to have a more concrete meaning in the ``old days'' of typeography.
In the world of Photo-typesetters and digital fonts, the distance from the top of the tallest ascender to the bottom of the longest descender is only an approximate lower bound on the point size of a font; in the Old days, it was almost always a firm lower bound, and there was warning on the exception.
Point-size is the measure of default or minimum inter-baseline distance; inter line distance in absense of leading, a/k/a ``set solid''. If you don't know if the text was set solid or leaded, you can't tell the point-size with a measuring glass unless you know if the type design includes built-in space betweed adjacent, set-solid lines.
Exceptions to the points size equals ascender to descender size rule:
([William D. Ricker's] metal font of Ray Shaded, cast on a Monotype Display caster, has ``vertical kerns'' if you will: the hanging shaded tail of the Q and some punctuation below the 24pt body, because it has no lower-case. It might be better described as being 36/24, thirty-six point type cast on a twenty-four point body, since the cap A is about the height and density of a Ultrabold 36pt A in many other fonts. It would be called 36/24 Caps if a lowercase had been cast on a 36 point body, but since only UC was ever cut, as UC-only titling, it was standardly issued and refered to as a 24 point titling---much to the confusion of non-cognoscenti.)
Net result: unless you know it's Adobe Times Roman or whatever and just want to know what point size & leading options were, you can't measure the size with a definition and an optical micrometer. The defnition is embodied/manifested in the typesetting ``hardware'', even if it is software, not the product.
What about Knuth's assertion that point size is ``a more-or-less arbitrary number that reflects the size of type [a font] is intended to blend with''?
That statement is true only in the context of MetaFonts. MetaFonts (and this definition) are perfectly adequate for Knuth's purposes but not fully descriptive of all of typography. And definitely not conformant to established usage.
This is not meant to condemn heterodoxy, but just to warn that while the ASCII markup notations in Knuth's ``Second Great Work'' [TeX and MetaFont] are even more widely disseminated than his wonderful coinage of mathematical notations in ``The First Great Work'' [The Art of Computer Programming, volumes I, II, and III], MetaFont has not been accepted as an encoding for all useful fonts for the future, and the defintions of font characteristics in MetaFont context must be taken with a large grain of salt when used with fonts outside the MetaFont font-generation paradigm.
Knuth's quotation, when applied to a (non-MetaFont) font designer, overstates the arbitrariness of the design choice; the designer was stating in the old days that you'd need a saw, a file, or a caster with his matrices if you wanted to use negative leading to set his type closer than he wanted to see it set; and today, in Photo/digital composition, the designer is either indicating the opinion of the original metal-head or his own design advice as to what the minimum distance between adjacent baselines should be.
Also, point size is very poor predictor of blending, except in a mechanical sense in terms of not-overflowing the same rectangles. Some faces to blend in the same line with 12 point type will need to be 10/12 or 14/12, due to differences in the way they fill the space. (The overall leading should fit the body type.) Harmony and contrast of overall color, shape, style, etc. are much more important considerations for blending than body-size. (For two types to work together, there must be sufficient harmonies between them to work together and sufficent contrasts to be easily distinguished. See Carl Dair's books.)
If one wants to understand usage of typographical terms in the general milieu, the Chicago Manual of Style's appendix on Typesetting for Authors is a good capsule presentation of history and terminology; if one wants the nitty-gritty on how digital type does, or at least should, differ and be treated differently from just copies of metal, see Richard Rubinstein, Digital Typography, MIT Press. On type in general, consult D.B. Updike in a library (out of print), or A(lexander) S. Lawson (who covers electronic type in his latest revision!).