The superior court for the judicial district of New Haven, on the application of the selectmen of the town of West Haven, and the superior court for any judicial district, on the application of the oyster-ground committee of any town in such judicial district, shall appoint a committee of three disinterested persons, not residents of the town within the boundaries of which any natural oyster, clam or mussel beds exist, to ascertain, locate and describe, by suitable boundaries, all the natural oyster, clam or mussel beds within the boundaries of such town. The committee so appointed shall first give three weeks’ notice, by advertising in a newspaper published in or nearest to such town, of the time and place of their first meeting for such purpose. Such committee shall hear parties who appear before it and may take evidence from such other sources as it deems advisable and shall make written designations by ranges, bounds and areas of all the natural oyster, clam and mussel beds within the boundaries of such town, and shall make a report of its doings to the superior court, which report, when accepted by said court, shall be recorded and shall be a final and conclusive determination of the extent, boundaries and location of such natural beds at the date of such report. The clerk of the court shall transmit to the town clerk of each of said towns a certified copy of such report, which shall be recorded by such town clerk in the book kept by him for the record of applications, designations and conveyances of designated grounds. Such public notice of such application to the superior court, and of the time and place of the return of the same, shall be given by such selectmen or oyster-ground committee as any judge of the superior court may order. The selectmen of the town of West Haven and the oyster committees of other towns, upon a written request, signed by twenty electors of their respective towns, shall make such application to the superior court within thirty days after receiving a copy of such written request, and such application shall be privileged and shall be heard and disposed of at the term of said court to which such application is returned. All expenses incurred by such selectmen and oyster-ground committees in such applications, and the doings thereunder, and the fees of such committees so appointed by the court, shall be taxed by the clerk of said court and paid upon his order by the state. The fees of such committees shall not exceed five dollars per day for each member thereof and shall be in full for all services, expenses and disbursements under such appointment, and the comptroller shall keep an account of such expense separate from that of the shellfish commission. Any designation of ground for the planting or cultivation of shellfish, made more than five years prior to the time of the making of such application for the appointment of such committee and within the areas so established by such report of such committee, shall be valid.