Every bill which shall have passed both Houses shall be presented to the Governor; if he approves he shall sign it, but if he shall not approve he shall return it with his objections to the House in which it shall have originated, which House shall enter the objections at large upon their journal, and proceed to re-consider it. If after such re-consideration, two-thirds of all the members elected to that House shall agree to pass the bill, it shall be sent with the objections to the other House by which likewise it shall be re-considered, and if approved by two-thirds of all the members elected to that House it shall be a law; but in such cases the votes of both Houses shall be determined by yeas and nays, and the names of the members voting for and against the bill shall be entered on the journals of each House, respectively. If any bill shall not be returned by the Governor within ten days after it shall have been presented to him, the same shall be a law in like manner as if he had signed it, unless the General Assembly, by their adjournment, prevent its return, in which case it shall be a law, unless he shall file the same, with his objections, in the office of the Secretary of the Commonwealth, and give notice thereof by public proclamation within thirty days after such adjournment.