Whenever the Department of Finance and Administration under the direction of the Governor's office makes an airplane or airplanes available to some department, institution or agency of the State of Mississippi, the actual cost for the operation thereof during the time the aforesaid airplane is so assigned shall be charged to and paid for by the aforesaid department, institution or agency into the special fund set up in Section 61-13-17 for the operation of such airplanes, except planes used by the Governor and Lieutenant Governor.