from
Bouvier's Law Dictionary, Revised 6th Ed (1856)
TERM ATTENDANT ON THE INHERITANCE. This phrase is used in the English courts
of equity, to signify that when a term has been created for a particular
purpose, which is satisfied, and the instrument by which it is created does
not provide for a cesser of the term, on the happening of the event, the
benefit in it becomes subject to the rules of equity, and must be moulded
and disposed of according to the equitable interests of all persons having
claims upon the inheritance; and, when the purposes of the trust fire
satisfied, the ownership of the term belongs in equity, to the owner of the
inheritance, whether declared by the original conveyance to attend it or
not.
2. Terms attendant on the inheritance are but little known in the
United States. 1 Hill. Ab. 243.