On the day named in the notice, or to which the hearing is adjourned, the board shall hear proof of the publication and service of notice. If the proof is satisfactory, the board shall hear the allegations of the petition and any objections to the granting of the application, and proofs in support of each. If from the proofs it appears that the public good or convenience will be promoted thereby, the board may grant to the applicant the right to erect or construct a wharf or chute as prayed for, and to take tolls for its use for the term of twenty years.