Filling the page

[Reilly]

I have consulted section "5.5.1 Vertical spacing inside a system" in 
the manual for Lilypond 2.11.

I am preparing to print orchestral part. A typical part fills 
approximately 1.6 to 1.75 pages. I want to increase the vertical 
spacing to fill out two pages evenly.

I attempted to use the code provided in the manual:

\new Score \with
{
  \override VerticalAlignment #'max-stretch = 
#ly:align-interface::calc-max-stretch
}

I could not get this code to work or change the vertical spacing of the 
staves in any way.

(1) I don't understand \new Score. I always use \score. Are they 
different? How so?
(2) I don't understand \with { some Lilypond code }. I typically insert 
overrides in the music or in contexts (see below).
(3) I don't understand #ly:align-interface::calc-max-stretch.

I do read the manual (but can miss things). I have read 6.1.4 without 
comprehension.
I do search the archives (but can miss things).
I am stymied.

Much obliged for any help.

Jeremiah

Here's my code for the part.      \tuba has 173 measures of music.

\score {
        \new Staff << \keepWithTag #'part \tuba >>
                \layout {
                                \context {
                                \Score
                                        \override BarNumber #'padding = #'2.3
                                        \override BarNumber #'direction = #DOWN
                                        \override BarNumber #'font-size = #2
                                        \override BarNumber #'break-visibility 
= #end-of-line-invisible
                                } % closes context

                                \context {
                                \Staff
                                        \override TimeSignature #'style = 
#'numbered
                                } % closes context
                        } % closes layout
        } % closes score