We suppose that there was not a man, in or out of the Charleston Convention, who did not anticipate the proposal of a new compromise on the rights of the States in the Territories, as a necessary consequence of the withdrawal of the Cotton States from the Convention. The Southern people have been so often cheated by words in the shape of compromises, that, of course, it would be presumed that they could be cheated again. Accordingly, after the close of the twelfth ballot for President had taken place, and the Convention was about to adjourn, Mr. HOWARD, of Tennessee, announced that the Tennessee, Kentucky, and Virginia delegates, had agreed on a resolution, which was presented to them by the delegation from New York, as follows:

Resolved, That the citizens of the United States have an equal right to settle with their property in the Territories of the United States; and that, under the decision of the Supreme Court of the United States, which we recognize as the correct exposition of the Constitution of the United States, neither the right of persons nor property can be destroyed by Congressional or Territorial legislation.

He proposed to offer the resolution, whenever the proper opportunity occurred, as the ultimatum of the South.

Our readers will understand the true purpose of this “ultimatum of the South,” when they remember, that no party at the North has contended that “the right of persons or property can be destroyed by Congressional or Territorial legislation.” The Abolitionists at the North contend that there can be no property in slaves, and that, therefore, there is none to destroy. The resolution does not use the word slave or slavery. It does not recognize the right of property in slaves. Thus, therefore, the most rabid Abolitionist might vote for the resolution. But, again, it does not touch the question of Squatter Sovereignty. Mr. DOUGLAS never contended that a Territorial Legislature could “destroy slave property.” He admits that there is property in slaves; but he asserts that a Territorial Legislature, by “unfriendly legislation” (by taxation, for instance) can prevent slaves from entering a Territory, whilst by failing to legislate for the protection of slave property, it might be exposed to such hazards as will effectually exclude it from a Territory. Slave property, like property in obscene prints or opium, or ardent spirits, may be subjected to a heavy license law or discriminating taxation, by which it can be prevented from entering a Territory. This is the position of Squatter Sovereignty. When, therefore, the resolution offered by Mr. HOWARD affirms that “neither the right of persons nor property can be destroyed by Congressional or Territorial legislation”—every Squatter Sovereignty adherent in the Convention can vote for it. It does not touch their heresy, nor is it intended to touch it. The resolution is the old device of deceiving those who are willing to be deceived. The reference to the Dred Scott case is equally evasive—“That under the decision of the Supreme Court of the United States, which we recognize as the correct exposition o f the Constitution o f the United States.” But what is the exposition of the Constitution of the United States this decision has made? The Squatter Sovereignty Democrats contend that it has made no exposition condemning their heresy. If this is so, the recognition of its expositions commits them to no denial of Squatter Sovereignty; and they manifest what they suppose the decision determines when they say in the words following in the resolution, that “neither the rights of persons nor property can be destroyed by Congressional or Territorial legislation.” Even WILLIAM H. SEWARD, and the whole Black Republican party, could vote for this resolution. They contend that Congress can, by its legislation, prevent slavery from entering a Territory; but they do not claim the power in Congress to “destroy” it. The Southern Delegates in the Convention present, as their patriotic and triumphant ultimatum, what every Black Republican and Squatter Sovereignty Democrat in the whole Union may support. That is, certainly, a most “remarkable way of vindicating the rights of the South! And when do they propose to present this august “ultimatum?” Why, after the nomination of President and Vice President of the United States is completed. By a resolution, which they voted for, the Convention determined that no nomination for President or Vice President should be made until the Convention had first settled the platform of principles upon which the nomination should rest. The Convention, after six days’ agitation and debate, has adopted the platform upon which it proposes to put its nominees. That platform is Squatter Sovereignty. The resolutions, affirming the rights of the South, have been rejected; and now, after both platform and nomination shall be completed—and not before—these heroic vindicators of the rights of the South propose to introduce into the Convention the miserable cheat invented by New York “as the ultimatum o f the South.” Suppose that this ultimatum was rejected (of which, however, there is not the slightest probability), what would they do? Go out of the Convention? The Convention will go out itself; for, having accomplished by their aid all it came to do (made a platform and nominated candidates on it for the Presidency), of course it will adjourn. The only danger is that the Convention, having finished its business, may adjourn without considering the grand “ultimatum of the South,” and thus get out before the delegates from Virginia, Tennessee and Kentucky. There may yet be a pretty race.