The proceedings referred to appear, by the letter of the lieutenant-governor of New Brunswick and the report of the officer acting on the part of Great Britain as warden of the disputed territory (copies of which accompanied Sir Charles R. Vaughan's note), to be the construction of a road to the Restook River, passing, as is alleged, through 15 miles of the disputed territory, and supposed by the warden to be intended to intersect the St. John River in the Madawaska settlement. The undersigned is happy to have it in his power to afford at once such explanations upon this subject as he trusts may be satisfactory. By a communication received from the governor of Maine, in answer to a representation recently made by Sir Charles R. Vaughan concerning other alleged encroachments on the disputed territory, it will be seen that no part of the road now constructing by that State is believed to be within the territory of which the British Government has ever been in the actual possession since the treaty of 1783, and that it is not designed to extend the road beyond the Aroostook. The apprehensions entertained of its being extended to the St. John River in the Madawaska settlement appear, therefore, to be groundless, and, if the views of the governor of Maine as to the locality of the road be correct, it would seem that its construction can afford no just cause of complaint, as it is not supposed that such improvements made by either party within that part of the territory which has been in its possession, or so considered, since the treaty of 1783 are contrary to the spirit of the existing understanding between the two Governments. It will be seen, moreover, as well by the communication from the governor of Maine as by one received from the governor of Massachusetts on the same occasion, that a conciliatory and forbearing disposition prevails on their part, and that no measures will be taken or any acts authorized by them which may justly be considered as a violation of the understanding in regard to the disputed territory. The undersigned has nevertheless been directed by the President to transmit copies of Sir Charles R. Vaughan's note and its inclosures to the governors of Maine and Massachusetts, and to repeat to their excellencies his earnest desire that as far as depends on them no departure from the understanding between the two Governments may be permitted.