The procedure for the adoption of ordinances shall be as follows:
   When an ordinance is first introduced it shall be known as a bill. If such bill receives the three (3) affirmative votes required for its introduction, it shall be put upon its final passage no sooner than three (3) days after its introduction; provided, that no bill for the grant of any franchise shall be put upon its final passage within thirty (30) days after its introduction; and provided further that an urgency ordinance may be passed by a four-fifths vote of the City Council. Every bill after it has finally passed the Council shall be signed by the Mayor Pro Tem and then presented forthwith to the Mayor. The Mayor shall return the bill to the Council within ten (10) days (Sundays excepted) after receiving it. If the Mayor approves it, the Mayor must sign it, and the same shall then become an ordinance; but if the Mayor shall disapprove it, it shall be returned, with the Mayor's objections in writing, to the Council. If the bill is not returned with such approval or disapproval within the time specified herein, it shall take effect as an ordinance as if the Mayor had approved the same.