in public vs publically

in public and publically both are adverbs.

Word	Noun	Adjective	Verb	Adverb
in public	No	No	No	Yes
publically	No	No	No	Yes

As adverbs, in public and publically are synonyms defined as:

in public and publically: in a manner accessible to or observable by the public; openly

Other synonyms of in public include publicly.

in public (adverb)	publically (adverb)
in a manner accessible to or observable by the public; openly	in a manner accessible to or observable by the public; openly