(a) The bonds shall be dated, numbered consecutively, and be signed by the president of the district board and the district treasurer. The district treasurer shall sign any coupons. Any signatures or countersignatures may be mechanically reproduced by any means, except that one of the signatures shall be signed by hand.
(b) If the president of the district board or the district treasurer whose signature appears on a bond or coupon ceases to hold that office before the delivery of the bonds or the coupons to the purchaser, the signature is nevertheless valid and sufficient for any purpose as if the president or treasurer had remained in office until the delivery of the bonds or coupons.