Errors still more serious had nearly resulted, a few years since, in a war with Mexico. By the treaty of Guadalupe Hidalgo, in 1848, the boundary line between the United States and that country was in part described by reference to the town of El Paso, as laid down on a specified map of the United States, of which a copy was appended to the treaty. This boundary was to be surveyed and run by a joint commission of men of science. It soon appeared that errors of two or three degrees existed in the projection of the map. Its lines of latitude and longitude did not conform to the topography of the region; so that it became impossible to execute the text of the treaty. The famous Mesilla Valley was a part of the debatable ground; and the sum of $10,000,000, paid to the Mexican Government for that and for an additional strip of territory on the southwest, was the smart-money which expiated the inaccuracy of the map--the necessary result, perhaps, of the want of good materials for its construction. It became my official duty in London, a few years ago, to apply to the British Government for an authentic statement of their claim to jurisdiction over New Zealand. The official _Gazette_ for the 2d of October, 1840, was sent me from the Foreign Office, as affording the desired information. This number of the _Gazette_ contained the proclamations issued by the Lieutenant Governor of New Zealand, "in pursuance of the instructions he received from the Marquis of Normanby, one of Her Majesty's principal Secretaries of State," asserting the jurisdiction of his government over the islands of New Zealand, and declaring them to extend "from 34° 30' North to 47° 10' South latitude." It is scarcely necessary to say that south latitude was intended in both instances. This error of 69° of latitude, which would have extended the claim of British jurisdiction over the whole breadth of the Pacific, had, apparently, escaped the notice of that government. COMMERCE AND NAVIGATION. It would be easy to multiply illustrations in proof of the great practical importance of accurate scientific designations, drawn from astronomical observations, in various relations connected with boundaries, surveys, and other geographical purposes; but I must hasten to 3. A third important department, in which the services rendered by astronomy are equally conspicuous. I refer to commerce and navigation. It is mainly owing to the results of astronomical observation, that modern commerce has attained such a vast expansion, compared with that of the ancient world. I have already reminded you that accurate ideas in this respect contributed materially to the conception in the mind of Columbus of his immortal enterprise, and to the practical success with which it was conducted. It was mainly his skill in the use of astronomical instruments--imperfect as they were--which enabled him, in spite of the bewildering variation of the compass, to find his way across the ocean.