A petition for the formation of a district, verified by the affidavit of one of the petitioners, may be presented to the board of supervisors at a regular meeting thereof by:
(a) The owners of one-half or more of any body of swamp and overflowed, salt-marsh, or tidelands, or other lands subject to flood or overflow, susceptible of one mode of reclamation who desire to reclaim the land.
(b) The owners of one-half or more of any body of swamp and overflowed, salt-marsh, or tidelands susceptible of one mode of reclamation, and already reclaimed, or in progress of reclamation, and not included in any district, who desire to form a district for the maintenance, protection, or repair of the reclamation works, in, upon, or appertaining to such body of lands, or for the completion of the reclamation thereof.