Regularity (-lrt), n.
Etymology: [Cf. F. régularité.]
The condition or quality of being regular; as, regularity of outline; the regularity of motion.
Shades of meaning
Fernald has no entry of its own for regularity; he lists it under system.
Where he writes about it:
Regularity applies to the even disposition of objects or uniform recurrence of acts in a series. — from system
There may be regularity without order, as in the recurrence of paroxysms of disease or insanity; there may be order without regularity, as in the arrangement of furniture in a room, where the objects are placed at varying distances. — from system
Order commonly implies the design of an intelligent agent or the appearance or suggestion of such design; regularity applies to an actual uniform disposition or recurrence with no suggestion of purpose, and as applied to human affairs is less intelligent and more mechanical than order. — from system
The most perfect order is often secured with least regularity, as in a fine essay or oration. — from system
There is a regularity of dividing a treatise into topics, paragraphs, and sentences, that is destructive of true rhetorical system. — from system