The trade with the British colonies in the West Indies has not as yet been arranged, by treaty or otherwise, to our satisfaction. An approach to that result has been made by legislative acts, whereby many serious impediments which had been raised by the parties in defense of their respective claims were removed. An earnest desire exists, and has been manifested on the part of this Government, to place the commerce with the colonies, likewise, on a footing of reciprocal advantage, and it is hoped that the British Government, seeing the justice of the proposal and its importance to the colonies, will ere long accede to it. The commissioners who were appointed for the adjustment of the boundary between the territories of the United States and those of Great Britain, specified in the 5th article of the treaty of Ghent, having disagreed in their decision, and both Governments having agreed to establish that boundary by amicable negotiation between them, it is hoped that it may be satisfactorily adjusted in that mode. The boundary specified by the 6th article has been established by the decision of the commissioners. From the progress made in that provided for by the 7th, according to a report recently received, there is good cause to presume that it will be settled in the course of the ensuing year. It is a cause of serious regret that no arrangement has yet been finally concluded between the two Governments to secure by joint cooperation the suppression of the slave trade. It was the object of the British Government in the early stages of the negotiation to adopt a plan for the suppression which should include the concession of the mutual right of search by the ships of war of each party of the vessels of the other for suspected offenders. This was objected to by this Government on the principle that as the right of search was a right of war of a belligerent toward a neutral power it might have an ill effect to extend it by treaty, to an offense which had been made comparatively mild, to a time of peace. Anxious, however, for the suppression of this trade, it was thought advisable, in compliance with a resolution of the House of Representatives, founded on an act of Congress, to propose to the British Government an expedient which should be free from that objection and more effectual for the object, by making it piratical. In that mode the enormity of the crime would place the offenders out of the protection of their Government, and involve no question of search or other question between the parties touching their respective rights. It was believed, also, that it would completely suppress the trade in the vessels of both parties, and by their respective citizens and subjects in those of other powers, with whom it was hoped that the odium which would thereby be attached to it would produce a corresponding arrangement, and by means thereof its entire extirpation forever.