If the owner of any stray or strays, taken up under authority of the act to which this is a supplement,¹ shall not appear upon notice given or having appeared, shall neglect or refuse to make or tender reasonable satisfaction to the party injured, for the damages sustained by reason of the trespass of such stray and for the costs of keeping; or if such injured party shall not accept the satisfaction which may be offered, it shall be the duty of such injured party to make immediate application to any justice of the peace² of the proper county, who shall proceed upon such application in the manner directed by the act to which this is a supplement.