Any ordinance or resolution passed by the Council shall be signed by the President of Council or other presiding officer and presented to the Mayor by the Clerk of Council.  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 by delivery to the Clerk of Council, which objections shall be entered in full on the journal of the Council.  The Mayor may approve or disapprove the whole or any item of an ordinance appropriating money, but otherwise his approval or disapproval shall be addressed to the entire ordinance or resolution.  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.  When the Mayor has disapproved an ordinance or resolution or item of it, as herein provided, the Council may, but in no event later than the next regular meeting, reconsider it and pass or adopt it by vote of two-thirds (2/3) of the Members elected to Council; in such event it shall take effect as if it had on that day received the signature of the Mayor.  In all such cases the votes shall be taken by yeas and nays and entered upon the journal.