How much space is occupied by footline?

Question

This is said in TeXbook about page dimensions:

Plain TEX sets \vsize=8.9in (not 9in, since \vsize doesn't include the space for page numbers at the bottom of each page)...

According to definition of \makefootline, the space occupied by it is 24pt. According to definition of TeX's pt we get 24/72.27 = 0.3in

According to TeXbook space occupied by footline is 0.1in, but it is 0.3in. This implies that bottom margin must be 0.8in, not 1in (how to trace that?).

Besides, it is strange that \nopagenumbers leaves 24pt at the bottom of page, because if we don't want page numbers, why do we want extra space? (e.g., headline does not contain anything by default - and it does not hold any extra space) Wouldn't the definition of \nopagenumbers be more reasonable if it was \gdef\makefootline{}? (in this case also \vsize must also probably be increased by 24pt)

These are definitions of \makefootline and \nopagenumbers from plain.tex, to make the question self-consistent:

\def\makefootline{\baselineskip24\p@\lineskiplimit\z@\line{\the\footline}}
\def\nopagenumbers{\footline{\hfil}} % blank out the footline

The following topics provide additional info:

How to draw borders around page contents
How is a page produced in the output routine?

Answer 1

Exercise 23.2 in The TeXbook and top of page 253 suggest that \nopagenumbers is used mainly in conjunction with setting \headline, with \voffset set to 2\baselineskip (i.e., 24pt, exactly the height of \makefootline). In this case those extra 24pt, which are introduced by \makefootline, are below page contents and are simply invisible - this is why it is sufficient to redefine only \footline. Also, maybe \nopagenumbers does not suppress those 24pt to make it possible to switch page numbers on/off temporarily, and preserve the same layout across all the pages.

As for 8.9in: The margins include the footline and the headline. Thus in plain TeX the bottom margin is actually about 0.8-inch.

Here are the calculations:

<11-inch paper height> - <1-inch top offset> - 
<\vsize=8.9-inch from plain.tex> - 
<\baselineskip=24pt from the definition of \makefootline>
[ - <the depth of the last line of text> ? ]
= 11 - 1 - 8.9 - 24/72.27 ~ 0.8-inch

EDIT

The clue is (probably) that \vsize is an integral multiple of the \baselineskip, meaning that you will not get warnings if you have a page without any explicit vertical white space. Most probably \vsize was calculated from the number of lines that the author wanted to fit on the page.