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 degrees 30 minutes North to 47 degrees 10 minutes South latitude.”  It is scarcely necessary to say that south latitude was intended in both instances.  This error of 69 degrees 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.

With the progress of the true system of the universe toward general adoption, the problem of finding the longitude at sea presented itself.  This was the avowed object of the foundation of the observatory at Greenwich;[A] and no one subject has received more of the attention of astronomers, than those investigations of the lunar theory on which the requisite tables of the navigator are founded.  The pathways of the ocean are marked out in the sky above.  The eternal lights of the heavens are the only Pharos