Unless such petition is to be presented to the annual meeting of said board of supervisors, or at an earlier meeting already appointed by the board to be held at least 30 days prior to such annual meeting, it may contain a request for a special meeting of said board, and may be delivered to the clerk of said board, who shall have authority, and whose duty it shall be, to call a special meeting of said board not more than 20 nor less than 10 days from the time he shall receive the petition. It shall be the said clerk’s duty to inform all the members of said board to be found in the county of such meeting and the purpose thereof at least 5 days before such meeting is to be held, and at whatever meeting such petition is to be heard. It shall be the duty of such petitioner to give notice in writing to the township board at each township named and to the common council of any city and to the village council of any village named of the intention of the petitioner to ask for the hearing upon the same at such meeting, and of the purpose thereof. Such notice shall be delivered to the clerk of every township, city and village named, and if such clerk is not readily found, then to any member of the township board, and the mayor or some member of the common council of the city or cities named, and to a member of the council of the village or villages named, as the case may be, at least 7 days before said board is to be asked to hear said petition. For the purpose of facilitating by said board their determination of the kind and cost of the bridge proposed to be constructed or reconstructed, each township, city and village named in the said petition may present a plan or plans and specifications of such proposed bridge with or without drawings, and an estimate of each as to the cost thereof.