The landlord, or other person entitled to the rent may, however, at his election, incorporate, in the notice provided for in the preceding section, the further notice that he will, after he shall have taken possession of the demised premises, lease the premises to some other person, in which case the tenant will still remain liable upon his lease, for the unexpired portion of his term, for the difference between the amount of rent received by the landlord from the new tenant, and the amount payable under the lease of the original tenant, and upon any other covenants or agreements contained in the original lease.