Upon the adoption of such order by the board of supervisors, as provided for in Section 59-13-3, the clerk of such board shall publish in two weekly issues of some newspaper having a general circulation in the county, a notice of intention to issue bonds for said purposes; if, within fifteen days after the first publication of a copy of such notice twenty-five per cent of the qualified electors of the county if the bonds to be issued are to be county-wide bonds, or twenty-five per cent of the qualified electors of the supervisor’s district if the bonds to be issued are to be district bonds, petition the board of supervisors for an election to determine whether or not such bonds shall be issued, such election shall be ordered by said board of supervisors in which the qualified electors of the county, if the bonds to be issued are county-wide bonds, or of the supervisor’s district, if the bonds to be issued are district bonds, shall be eligible to participate, and if at such election a majority of those voting vote in favor of the issuance of such bonds the same shall be issued, but if a majority shall vote against the issuance of such bonds the same shall not be issued. Such election shall be held and conducted and the returns thereof made as provided by law for other county or district elections. If no such petition be presented within fifteen days after the first publication of such notice, the bonds shall be issued in the manner provided by law. However, in any case where an election has heretofore been held in any county or supervisors district, pursuant to the provisions of this chapter on the question of issuing bonds of such county or supervisors district for the purpose of providing and constructing public harbor improvements, harbor developments, breakwaters, wharves and docks, recreational centers and all buildings in connection therewith, and providing necessary rights of way, and a majority of those who participated in such election voted in favor of the issuance of such bonds, and such bonds have not for any reason been issued, the board of supervisors of such county in which such supervisors district is situated, as the case may be, may, by resolution of such board, adopted at any time within twelve months from and after the passage of this chapter, authorize and direct the issuance of bonds of such county or district under the provisions of this chapter, in an amount not exceeding the amount set forth in the proposition submitted at such election, and for the purposes authorized by this chapter, without the giving of any notice required in this section and without any further election on the issuance thereof.