The acceptance by a nonresident motor carrier of the rights and privileges conferred by law permitting the operation of motor vehicles on the public highways of this state, as evidenced by the operation of a motor vehicle by the nonresident either personally or through an agent or employee on the public highways of this state, or by the operation by the nonresident either personally or through an agent or employee of a motor vehicle on the public highways of this state other than as so permitted or regulated, shall be deemed equivalent to the appointment by the nonresident motor carrier of the Secretary of State or his successor in office as his agent for service of process or notice in any action, assessment proceedings, or other proceeding against him or his personal representative arising out of or by reason of any provision of this article relating to the motor vehicle or relating to the liability for road tax with respect to operation of the motor vehicle on the highways of this state. The acceptance or operation shall be an acknowledgment by the nonresident motor carrier of his agreement that any such process against or notice to him or his personal representative shall be of the same legal force and validity as if the process or notice were served on him personally or on his personal representative.