The county treasurer of the petitioning county shall perform all the duties required of him by law, in the territory that had constituted the petitioning county, during his term of office. He shall assess the taxable property in the territory aforesaid, and shall return his assessment books to the county clerk of the adjoining county, and make all his reports to the county board of the adjoining county; but he shall be liable upon his bond for any breach or breaches of the conditions thereof, in the same manner and to the same extent as if the petitioning county had not been united and annexed to the adjoining county. The compensation to which he may be entitled by law, shall be paid by the county board of the adjoining county out of taxes collected from property in the territory that had constituted the petitioning county, before the proclamation aforesaid. So much of this Section as refers to assessing by the treasurer, shall only be applicable where the petitioning county was not under township organization at the date of the election aforesaid.