Whenever a child shall be or heretofore shall have been committed to any House of Refuge which is not exclusively under State control, and shall become or shall have become an inmate thereof, one-half of the expense of maintaining and instructing such child hereafter shall be borne by the county from which such child shall have been received, and the remaining one-half shall be paid out of the appropriations made to such House of Refuge, from time to time, by the State.
11 P.S. § 661