When the public interest or convenience so requires, and whenever, in the opinion of the legislative body initiating the proceedings, the proposed work is of such a character that it directly and peculiarly affects property in two or more cities, or in one or more cities and counties, and that the purposes sought to be accomplished by the work can best be accomplished by a single, comprehensive scheme of work, there is hereby conferred upon the legislative body full power and authority to extend the work or the boundaries of the district to be assessed therefor beyond the territorial limits of the city.