The members of the county board of the petitioning county and the county board of the adjoining county, after the date of the Governor’s proclamation aforesaid, shall sit together at all regular and called meetings, as the county board of the adjoining county as it will be constituted after the proclamation aforesaid. Whenever the term of office of any one of the members of the county board of the petitioning county shall expire, by his death or resignation, or refusal to act, or by lapse of time, the expiration of said term, and the manner thereof shall be entered upon the records of the said county board of the adjoining county, and no successor to him shall be elected, and whenever the term of office of any member of the county board of the adjoining county, elected before the date of the Governor’s proclamation aforesaid, shall expire in any of the modes hereinbefore mentioned after the date of said proclamation, a successor to him shall be elected in the adjoining county at large, as it shall be constituted after the date of the proclamation aforesaid, including the territory that had constituted the petitioning county before said proclamation.