Note. The forms without on are good colloquial English, but are avoided in the more formal style. No preposition need be supplied in parsing. The noun is an adverbial objective ([§ 109]).

358. Care is required in the use of pronouns as the objects of prepositions.

359. Several words are used either as adverbs or prepositions.

As AdverbAs Preposition
I fell down.I fell down the steps.
Stand by!He stood by the window.
A big dog ran behind.A dog ran behind the carriage.
Keep off!Keep off the grass.

Other examples are:—

For words used either as prepositions or as conjunctions, see [pp. 152–154].

360. Prepositions show various distinctions in use and meaning which must be learned by practice and by the study of synonyms in a large dictionary.