Section 8. If land is held by lease of a person having an estate therein determinable on a life or on a contingency, and such estate determines before the end of a period for which rent is payable, or if an estate created by a written lease or an estate at will is determined before the end of such period by surrender, either express or by operation of law, by notice to quit for non-payment of rent, or by the death of any party, the landlord or his executor or administrator may recover in contract, a proportional part of such rent according to the portion of the last period for which such rent was accruing which had expired at such determination.