Representatives of life tenant may recover proportion of rent from under-tenant.

Where any tenants for life shall happen to die before or on the day, on which any rent was reserved or made payable upon any demise or lease of any lands, tenements, or hereditaments, which determined on the death of such tenant for life, the executors or administrators of such tenant for life shall and may in an action on the case recover of and from such under-tenant or under-tenants of such lands, tenements, or hereditaments, if such tenant for life dies on the day on which the same was made payable the whole, or if before such day then a proportion, of such rent according to the time such tenant for life lived, of the last year, or quarter of a year or other time in which the said rent was growing due as aforesaid, making all just allowances or a proportionable part thereof respectively.