Section 54. Cities by a vote of the board of aldermen, or city council, and towns by a vote at a town meeting, may appropriate money for the cultivation, propagation and protection of shellfish. The board of aldermen, or city council, or selectmen when so authorized by their town may from time to time declare a close season for any or all kinds of shellfish for not more than three years in such waters, flats or creeks, not then the subject of a private grant, within the limits of their respective cities and towns, as they deem proper, and may plant, grow and protect shellfish in such waters, flats or creeks; provided, that no private rights are impaired; and provided, further, that when any close season, declared as aforesaid, shall have ended, such flats, waters or creeks shall not within two years thereafter be licensed for the private cultivation of shellfish.