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Webster 1913 Edition

Noun.

The state or quality of being orderly.

Noun.

[from orderly.]

Regularity; a state of being methodical.

The state of being orderly.

orderliness ‎(usually uncountable, plural orderlinesses)

The fact of having a regular, proper and systematic arrangement.
- 2002, Colin Jones, The Great Nation, Penguin 2003, p. 205:
  Voltaire had drawn on Newton to demonstrate an allegedly divine orderliness in the natural world which left no space for God's intervention in human affairs [...].
Orderly behaviour.

regularity; proper arrangement