The board shall, from time to time, establish such rules and regulations for meetings of the board and for the administration of the city employes' retirement fund created by this act, and the various accounts thereof, as may be deemed necessary. It shall keep such data as shall be necessary for actuarial valuation purposes. The actuary of the board shall periodically make an actuarial investigation into the mortality and service experience of the contributors to, and beneficiaries of, the fund, and shall adopt for the retirement system one or more mortality tables, and certify to the board annually the amount of appropriation to be made by the city to the fund to build up and maintain adequate reserves for the payment of the city's share of the retirement allowances provided by this act.