The BBC reports that a cleaner in a museum Italy threw away an art work by accident. Except that what it says is
It is not the first time artwork has been accidently thrown away by a cleaner.
A search of the BBC News site shows 36 examples of accidently since January 2013. The Microsoft spell-checker accepts it.
Ngram shows accidently practically disappearing in the ten years up to 2008 (its latest record.
Incidently has not been recorded on BBC News since June 2010. It is not accepted by Microsoft.
Publically appears 63 times since January 2013. It is accepted by Microsoft.