4.7 The initial consonant is usually lenited when the noun or verbal noun is governed by the preposition ar: ar bhád; ar bhealach; ar bhord (= ar thábla); ar chaoi; ar chor ar bith; ar chuntar; ar dheis; ar dhóigh (= ar shlí); ar dhul amach; ar fhaitíos; ar fheabhas; ar mhodh; ar shiúl (= imithe); ar theacht abhaile dom.

4.8 The noun is not lenited in the cases below:

• in certain phrases which denote a state, such as the following: ar bith; ar bogadh; ar buile; ar cois (= ar siúl); ar crochadh; ar díol; ar dóigh (= ar fheabhas); ar doimhne; ar fad; ar fáil; ar fán; ar fiuchadh; ar forbhás (= corrach); ar fónamh; ar fuaidreamh; ar gor; ar maos; ar meisce; ar seachrán; ar siúl (= á dhéanamh; tosaithe); ar tarraingt; ar tiús; ar triomú

• in the following phrases if the noun isn’t qualified (usually involving a general situation):

  No qualification	But with qualification
  ar barr	ar bharr an tí
  ar cairde (= gan airgead síos)	ar chairde fada
  ar colbha	ar cholbha na leapa
  ar corr	ar chorr an bhoird
  ar deireadh	ar dheireadh an bháid
  ar muir	ar Mhuir Meann
  ar tír	ar thír na hÉireann
  ar tosach	ar thosach an tslua

• in the following phrases, despite the fact that the noun is qualified: ar ball [beag]; ar béal maidine; ar bord [loinge]

The second particle of these compound prepositions is not lenited: ar feadh; ar fud; ar son; ar tí.

From Graiméar Gaeilge na mBráithre Críostaí (An Gúm, 1999)