For the purpose of carrying out the provisions of sections 2-1601 to 2-1608, there may be created in each county or combination of counties within the State of Nebraska an organization to be created in the following manner: Whenever a number of farm operators of a county or counties effect an organization for doing extension work in agriculture and home economics, adopt a constitution and bylaws as are not inconsistent with the Cooperative Extension Service of the University of Nebraska, and are recognized by the extension service as the official body within the county or counties for carrying on extension work in agriculture and home economics within the county or counties, such organization may make such regulations and bylaws for its government and the carrying on of its work as are not inconsistent with the provisions of such sections, except that for the purposes of such sections only one such organization shall be recognized in any one county or counties so affiliated. Any farm operator or spouse of a farm operator who is a legal voter in the county may at any time petition the county board to appropriate a sum of money from the general fund of the county, as provided by section 2-1604, for the purpose of employing and maintaining a county agricultural agent and for carrying out generally the purposes as expressed in sections 2-1601 and 2-1602. It shall be understood that for each family operating a farm, there shall be only one person whose name shall be counted in judging the sufficiency of such petition. When any farm operator or spouse of a farm operator has so petitioned the county board, both spouses shall be deemed members of the county extension organization provided for in sections 2-1601 to 2-1603 and shall be entitled to all voting and participating rights thereto.