The Washington correspondent of the Cincinnati Enquirer in a late letter touches slightly a point which has received considerable attention at the South. The writer says:

Private letters received in this city from distinguished Southern politicians hold out one hope for the reuniting of the Union after secession has taken place, and making it stronger and firmer than ever; that is, the reconstruction of the Government upon such principles as will make all the States co-equal, at the bottom of which lies the right of the master to his property, wherever he may take it, and an equality in the tariff laws, or more plainly speaking, free trade.

This idea is by no means unplausible. It is absolutely certain that in less than ninety days nearly all, if not all, the cotton States will have withdrawn from the Union. Whether their policy will be regarded as wise and judicious or as hasty and reprehensible, is not germane to the question. We are alluding to a state of fact which, as far as human foresight can discern, will positively exist within a few weeks. Moreover, although we cannot predict with so much of an apparent certainty that the frontier slave States, such as Maryland, Virginia, Kentucky, Missouri and Tennessee, will unite with the South in the secession movement, the daily development of public opinion in those commonwealths justifies the belief that they will ultimately imitate the conduct and share the fortunes of the cotton growing States. The result will be eventually that probably in six months every slaveholding State, with the possible exception of Missouri, will combine under a single government, republican in form, and with a Constitution assimilating in all its best features the instrument which has hitherto united the several States of the Confederacy. He must be but a superficial observer of human motives and actions who can take any other view of the future than this. South Carolina has seceded, and her single example will prove more irresistibly contagious than ten thousand appeals from the public men of the South. Already has the intelligence thrilled to the heart of the community, and stirred the secession fever to a fiercer paroxysm than ever.

When once the South shall have displayed its independence, and the determined assertion of its rights, we hazard little in saying that the effect upon the North will be tremendous. That section thus far has been rendered just sufficiently uneasy to indulge in wearisome platitudes about the Union, and to address warm appeals to the South to pause and await the future. When, however, the act which the North hardly seems yet to anticipate shall have been consummated; when the South shall be completely cut off from the North; when New England, the Middle States and the Northwest are left to mourn a Union dissevered by their folly and wickedness, and are compelled to confront the frightful commercial calamities which must ensue, and the progressive decadence to which they will be exposed, we may feel well assured that the insane fanaticism which has proved the prolific fountain of the evils present and prospective under which the country labors, will be utterly discarded. This will be no temporary and transient victory of sound principles over the reckless and destructive tenets of abolition, but it will be a crushing, overwhelming and enduring triumph. The South now rejects all proffers of compromise because she knows they are the mere offspring of alarm and financial distress, and because she has abundant cause to fear that her consent would be construed into timidity and a base surrender of right, and that Black Republicanism would soon revive from its seeming humiliation. But when experience will have demonstrated the manifest dependence of Northern industry upon Southern agricultural labor, and the impossibility of high Northern prosperity without Southern co-operation, we may not unreasonably expect such propositions for a new compact emanating from the North as the South may regard with deliberation, and may possibly accept.

It is to our knowledge that a large proportion of the citizens of New Orleans, who, though heretofore proud of their nationality, are now ardent advocates of secession, are greatly influenced in the decision they have reached by this very idea of forming at some future period another and a better Union, upon a basis of complete equality, and with inviolable constitutional guarantees. The reconstruction of the Government hereafter is by no means a chimerical notion—especially if the Federal powers throw no insuperable obstacles in the way, by an insane effort at coercion. If the Southern States are left to the peaceable exercise of their sovereignty, there will be no insurmountable objection to another Union. Such a consummation will materially depend upon the changes which events may bring about in the feelings and convictions of the people of the non-slaveholding States. If they resolve once and forever to put down Abolition, and to respect the South, it may be that the Providence which is now separating us will bring us together once more in a more durable compact, and under happier auspices.