Any ordinance or resolution passed by the Council shall be signed by the President or other presiding officer and presented forthwith to the Mayor by the Clerk. If the Mayor approves such ordinance or resolution he shall sign it within ten (10) days after its passage or adoption by the Council; but if he does not approve it, he shall return it to the Council with his objections within said ten (10) days, or if the Council be not then in session, at the next regular meeting thereof, which objections the Council shall cause to be entered in full on its journal. If the Mayor does not sign or veto an ordinance or resolution after its passage or adoption, within the time specified, it shall take effect in the same manner as if he had signed it. The Mayor may approve or disapprove the whole or any item or part of any ordinance or resolution appropriating money. When the Mayor refuses to sign an ordinance or resolution or part thereof and returns it to the Council with his objections, the Council shall, after the expiration of not less than one week, proceed to reconsider it and, if upon reconsideration, the resolution or ordinance or part or item thereof disapproved by the Mayor be approved by the vote of two-thirds of all the members elected to the Council it shall take effect without the signature of the Mayor. In all such cases the votes shall be taken by "yeas" and "nays" and entered on the journal.