Upon the written petition of a majority of the qualified electors of any county bordering upon a navigable stream and having territory in cultivation subject to overflow, or any subdivision of a county consisting of not less than thirty-six (36) square miles, where the subdivision borders upon a navigable stream and contains territory in cultivation subject to overflow, being filed in the county court of the county, requesting an order to prevent the running at large of hogs, sheep, and goats within the county or subdivision, as the case may be, it shall be the duty of the court to make such an order when the petitioners have complied with this subchapter and subchapter 1 of this chapter.