Whenever any person shall be desirous to make use of a private road laid out on the petition and at the expense of others, such person may apply by petition to the court of quarter sessions of the respective county, to be admitted to participate in the privilege of the said road, and thereupon such court shall have power to determine what sum he shall contribute to the persons at whose expense the said road was laid out, and also what further sum he shall pay to the owners of the soil over which the said road was made, and upon the payment thereof, such person shall be entitled to equal rights and privileges, and be subject to like duties and liabilities with the original applicants for said road.