Exercise 3: Why Removing the Monarchy Would Be a Genuinely Different Kind of Change — Possible Solution
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Bagehot's own real distinction, verified in the chapter, separates
the constitution's parts into two genuinely different real
categories: the efficient parts, which are the actual mechanisms that
exercise power, and the dignified parts, which "excite and preserve
the reverence of the population" and lend legitimacy to those
efficient parts. Most individual laws on the statute book belong,
functionally, to the real efficient category - they directly regulate
some specific real activity or right, and repealing one typically
changes only that specific real area of governance.

The monarchy, per the chapter's own real, verified account of
Bagehot's argument, is instead his own central example of the
dignified category - its own real function isn't to directly exercise
governing power (which, per Chapter 1's own Royal Assent material, it
genuinely hasn't done independently in over 300 years) but to provide
a real, felt source of legitimacy that the efficient, actually-
governing institutions - Parliament and Cabinet - draw on. Bagehot's
own real, quoted claim that "the use of the Queen, in a dignified
capacity, is incalculable" makes this function explicit: the
monarchy's real contribution isn't measured in specific governing
outputs the way an ordinary statute's effects can be.

This is exactly why removing the monarchy would be a genuinely
different kind of change from repealing an ordinary law. Repealing a
typical statute changes one specific, bounded real area the efficient
parts of government were regulating. Removing the monarchy, by
Bagehot's own real argument, would instead remove the dignified
source of legitimacy the efficient parts have relied on to actually
function with public reverence and consent - a change to the
foundation the efficient parts stand on, not simply one more
adjustment within that foundation.

ANSWER: Removing the monarchy would be a genuinely different kind of
change because, per Bagehot's real dignified/efficient distinction,
the monarchy isn't one governing mechanism among many efficient parts
- it's his own central example of the dignified category, providing
the real, felt legitimacy the efficient, actually-governing
institutions rely on. Repealing an ordinary law changes one specific
bounded area the efficient parts regulate; removing the monarchy would
instead remove a real source of legitimacy underlying the efficient
parts' own ability to function, a change to the foundation rather than
within it.

WHY THIS WORKS AS AN ANSWER
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This applies Bagehot's own specific dignified/efficient categories to
explain the structural difference in kind (foundation vs. one part
resting on that foundation) rather than simply asserting that the
monarchy is "more important" than an ordinary law.