When expenses for any such improvement shall be assessed in a special assessment district, and there shall be lands belonging to the City or school district fronting upon such improvement, such part of the expense of such improvement as in the opinion of the assessor making the special assessment would be justly apportionable to such City or school district property, and to any interior squares or spaces formed by the intersection of streets, were they assessable, shall be paid from the general city funds, and the balance of such expense shall be assessed upon the remaining lots and premises included in the special assessment district.