Whenever any adjoining parallel streets or alleys in the city shall have been graded, guttered, curbed, paved, or macadamized, the governing body may, when they deem it necessary, grade, gutter, curb, pave or macadamize any intervening connecting street or alley, or portion thereof; and in all cases when two or more portions of any street or alley have been graded, guttered, curbed, paved, or macadamized, and intervening portions of said street or alley have not been graded, guttered, curbed, paved, or macadamized, the governing body may by resolution cause the intervening portion to be graded, guttered, curbed, paved or macadamized not to exceed two blocks, and levy special assessments to pay for the same, regardless of any protests of the property owners affected thereby.