In actions for partition of real estate, in which it may be alleged or may appear that any party or person interested therein, not a party plaintiff, is not a resident of the state, or where it is alleged or may appear that any person interested has left the state and it is not known where that person is or whether alive or dead, and, if dead, whether that person has left children, or whether some person unknown to the plaintiff is interested therein, the court before whom the action is pending may order notice to be given to any such party or person, by ordering a copy of its order to be published in some newspaper published in this state for such length of time as it may deem proper, and may also, in its discretion, order letters, postpaid and directed to the party or person, to be deposited in the post office; and where notice is given as ordered by the court, it may proceed and render judgment in the action in the same manner and with the same effect as if the party or person had received actual or personal notice or had appeared and answered to the action.