If any person feels aggrieved by the findings of the physician giving the examination provided for in the preceding section, he may by written notice served upon the head of the fire department within thirty (30) days after he has been rejected for reinstatement, name one licensed physician to act with said examining physician, and the two said physicians shall, within eight (8) days thereafter, select a third physician, and the three said physicians shall, within ten (10) days thereafter, jointly examine said person, and within five (5) days thereafter certify to the State Board their findings. The findings of any two of said physicians shall be binding on all parties as to the physical and mental conditions of such person. If the two examining physicians first selected are unable to agree upon a third, then the presiding judge of the Oklahoma County district court shall name the third physician.