In counties and cities providing specialized court service programs prior to July 1, 1973, as provided in §§ 16.1-234 and 16.1-235, and under the rules of the Department the traveling expenses incurred by a probation officer, court service officer or other officer of the court when traveling under the order of the judge, shall be paid out of the county or city treasury. One-half of such expenses shall be reimbursed to the city or county by the Department out of funds appropriated for such purposes.