States; or the prohibition of the inter-state slave-trade; or the refusal to admit a new State on account of the existence of slavery; or the prohibition of the introduction of slavery into Utah or New Mexico; or any act repealing or materially modifying the Fugitive Slave law; upon the faithful execution of which depends the preservation of the Union. In _California_ the Whig State Convention recommend the extension of the pre-emption laws over all except the mineral lands of the State; the donation to each head of a family actually settled upon it, of 160 acres; liberal grants for educational purposes; appropriations for public improvements; the adoption of measures to construct a railroad to connect that State with the valley of the Mississippi; the establishment of steam communication with the Sandwich Islands and with China. The Compromise measures are also cordially commended. The Fourth of July was celebrated with more than usual enthusiasm in almost every section of the country. In Washington, upon the occasion of laying, by the President, the corner stone of the extension of the Capitol, MR. WEBSTER delivered an oration which will rank with his most eloquent speeches. He gave a rapid sketch of the growth and progress of the Republic, from the time when Berkeley prophesied that the star of empire was about to take its westward way. He then portrayed the distinctive nature of American liberty, as distinguished from that of Greece and Rome, or of modern Europe, and altogether peculiar in its character. Its prominent and distinguishing characteristic he stated to consist in the capacity for self-government, developing itself in the establishment of popular governments by an equal representation; and in giving to the will of the majority, fairly expressed through its representatives, the binding force of law; and in the formation of written constitutions, founded upon the will of the people, regulating and restraining the powers of Government; added to the strong and deep-settled conviction of all intelligent persons among us that in order to support a useful and wise government upon these popular principles, the general education of the people, and the wide diffusion of pure morality and true virtue are indispensable. Mr. Webster then proceeded to deposit under the corner stone a document written by his own hand, which, after reciting the circumstances of the ceremony, thus concludes: "If, therefore, it shall be hereafter the will of God, that this structure shall fall from its base, that its foundations be upturned, and the deposit beneath this stone brought to the eyes of men, be it then known that, on this day, the Union of the United States of America stands firm--that their Constitution still exists unimpaired, and with all its original usefulness and glory, growing every day stronger and stronger in the affections of the great body of the American people, and attracting more and more the admiration of the world.