Authorising justices of the peace to appoint, on the nomination of the authority, persons to act as constables within any limits within which the authority have jurisdiction in relation to the harbour and within one mile outside any such limits, and to dismiss persons appointed by virtue of this paragraph, and conferring on persons so appointed, while acting within any such limits as aforesaid or within one mile outside any such limits, the powers which a constable has within his constablewick.