The Public School system shall include kindergarten schools; common schools, consisting of primary and grammar grades; high schools; an Agricultural College; a University, and such other schools as the Legislature may establish. The common schools shall be free. The other departments of the system shall be supported as provided by law: Provided, That high schools may be maintained free in all cities of the first and second class now constituting school districts, and in such other cities and districts as may be designated by the Legislature. But where the proportion of school monies apportioned or accruing to any city or district shall not be sufficient to maintain all the free schools in such city or district, the high schools shall be supported by local taxation.