First. To explore and survey the lines respectively claimed by the Governments of the United States and Great Britain. Second. To examine and report upon the arguments contained in the report of Messrs. Featherstonhaugh and Mudge addressed to the secretary of state of Her Britannic Majesty for foreign affairs under date of 16th April, 1840. I. In order to the more exact and successful performance of the duties included under the first of the above heads, the boundary line was divided by their instructions into three separate portions, one of which was assigned to each of the commissioners; and while they were instructed to assemble in a board for the purpose of comparing their respective surveys, in view of the performance of the duties included in the second of the above divisions their explorations have been separately conducted. Each of the commissioners has employed the methods and course of action most appropriate in his opinion to the successful fulfillment of his appointed task, and the nature of the surveys assigned to one of them has been of a character widely different from those of his colleagues. The commissioners, therefore, while uniting in a general report of the progress made up to this time in the duties of their appointment, beg leave to submit, in the form of appendices, the narrative of their several operations, with so much of the records of their observations and calculations as they have severally judged necessary to authenticate the conclusions at which they have arrived. The progress which has been made in the labors of the commissioners enables them at this time to lay before you-- 1. A description of the physical features of the disputed territory. 2. A comparison of the heights of the line claimed by the United States with those of the line styled the "axis of maximum elevation" by Messrs. Featherstonhaugh and Mudge. In laying the latter before you they have, in order to avoid delay, made use in part of the published results obtained by those gentlemen, and although they have already detected errors in their inferences they do not consider that by accepting them for the moment as the basis of comparison they can be accused of exhibiting the line claimed by Great Britain in an unfavorable light. I.--DESCRIPTION OF THE DISPUTED TERRITORY.