Where -
(a) the Appeal Commissioners see cause to disallow an objection to a schedule by the inspector or such other officer as the Revenue Commissioners shall authorise in that behalf, or
(b) on the hearing of an appeal, the Appeal Commissioners are satisfied with the assessment, or if, after the delivery of a schedule, they are satisfied with the schedule and have received no information as to its insufficiency,
they shall confirm or alter the assessment in accordance with the schedule, as the case may require.