a. [ Cf. Mean intermediate. ] (Law) Middle; intervening; as, a mesne lord, that is, a lord who holds land of a superior, but grants a part of it to another person, in which case he is a tenant to the superior, but lord or superior to the second grantee, and hence is called the mesne lord. [ 1913 Webster ]

Mesne process, intermediate process; process intervening between the beginning and end of a suit, sometimes understood to be the whole process preceding the execution. Blackstone. Burrill. --
Mesne profits, profits of premises during the time the owner has been wrongfully kept out of the possession of his estate. Burrill. [ 1913 Webster ]