After the organization of any such company as aforesaid, they may prepare a map or plan of the section or sections of the stream or streams, the navigation of which they propose to improve, and a plan for the improvement of the same, which shall show and set forth the several points in such stream where improvements are proposed to be made and the nature and character of such improvements, and may submit the same to the board of control, and make application to said board for their approval thereof and their assent to the proposed improvements, whereupon the said board shall designate some regular meeting of their body at which said application shall be had. The company shall cause notice of said application and the meeting of the board fixed for the hearing thereof to be published once in each week for [the] 6 successive weeks next preceding the first day of said regular meeting in some newspaper published in Detroit, in some newspaper published in Grand Rapids and East Saginaw, and also in some newspaper published in the town where said corporation has its office, if there be one, and if not then in some newspaper of the same or an adjoining county, and also in some newspaper published nearest the place where said improvements are to be made, and shall cause proper proofs of said publication to be filed with the board of control. At the meeting designated therefor, or at such subsequent meeting as the hearing shall be adjourned to, the board of control shall proceed to hear and determine the matter of said application, on which hearing all parties interested therein may appear and be heard. If upon such hearing, the board shall be of opinion that the construction of the proposed improvement will be a public benefit, and that the company is a proper one to make the same, they shall endorse upon such map or plan their approval thereof, and their assent to the construction of the improvement proposed, and shall also fix the time within which the same shall be completed by the company. Said board of control may, in their discretion, alter or amend such plan or plans before approving the same, or may, at any time after such approval consent to the alteration of such plans, upon the petition of the company which shall have presented the same after the publication of a notice of the hearing of said petition in the same manner required in this section upon the hearing of the original application.