Section 13. Whenever any fire-warden, or person employed by him, shall have rendered service in the extinguishment of fire which may have burned within two or more counties, the district fire-warden shall render to the Commissioner of Forestry his report, as hereinbefore required, relating to each of the said counties, in order that the expense of extinguishing fire may be rightly and properly distributed between or among the counties in which fire may have burned.