From the New York Advertiser.

It is very apparent that the States of Georgia and Alabama intend to avail themselves of the opportunity afforded them by the present administration of the national government, to drive off the Indian tribes within their territories, and possess themselves of their lands, by the mere aid of physical force. To accomplish this object, the most unprincipled and extravagant notions are propagated; and the rights of the Indians are treated as things of not the slightest regard.- Such has for a long time been the language of Georgia politicians. It is now, essentially, the language of the President of the United States, and of his Secretary of War.

In a document dated in March last, addressed to the Creeks, after a suitable display of his love for the Indians, of which he has heretofore given them fatal examples, President Jackson informs them, that they and his white children live too near each other to be in harmony and peace; and advises them to go beyond the Mississippi, where their white brothers will not trouble them, nor disturb them. The argument in favor of their removal, derived from the fact that where they now are General Jackson's white children trouble them, will doubtless be justly appreciated, even by the Indians._ They may say, and we have no doubt they will say to their great and affectionate 'Father,'pray, sir, take better care of your white children- it is your duty to govern your family better, and not to punish the red ones because the white ones misbehave.-- Instead of taking the course which is so obviously proper, and which the plainest principles of duty, as well as law point out, General Jackson advises them to go over the Mississippi, where he can protect them.' If he can protect them at several thousand miles distance, it would seem that he might do so only a few hundred. Instead of which, however, he says to them- 'My white children in Alabama have extended their law over your country. If you remain in it you must be subject to their law.' Now, with submission to the chief magistrate of the nation, we very much doubt his authority for making this declaration. The Indian nation is within the limits of the United States, and among the rest, the very tribes that live within the limits of Georgia and Alabama have always been considered by the national government as distinct tribes, not under the jurisdiction of the State Authorities, not amenable to their tribunals. They have formed innumerable treaties with them as such, and laws without number have been passed, first and last, by Congress, for the purpose of protecting their persons and property, and regulating the intercourse with them. From whence then has President Jackson derived the power to take this matter into his own hands, and instead of giving the Indians the benefit of the treaties and laws which have been formed and passed, and are now in force, to say to them, you must now be subject to the laws of Alabama, if you remain in possession of your own lands and property?

But the President is sanctioned by the high legal opinion of Mr. Secretary Eaton, who has gone much more at length into the argument, and advanced more extravagant notions that even those of the 'King his Master.' In a letter dated April 18th,1829, addressed to the Georgia Cherokees, he says:-

'The course you have pursued of establishing an independent, substantive government, within the territorial limits of the State of Georgia, adverse to her will and contrary to her consent, has been the immediate cause which has induced her to depart from the forbearance she has so long practised (sic); and in virtue of her authority, as a sovereign independent State, to extend over your country her legislative enactments, which she and every State embraced the confederacy, from 1781 to the present time, when their independence was acknowledged and admitted, possessed the power to do, apart from any authority, or opposing interference by the General Government.

But suppose, and it is suggested merely for the purpose of awakening your better judgement, that Georgia cannot, and ought not, to claim the exercise of such power_ what alternative is then presented? In reply, allow me to call your attention for a moment to the grave character of the course which, under a mistaken view of your own rights, you desire this government to adopt. It is no less than an invitation that she shall step forward to arrest the constitutional acts of an independent State, exercised within her own limits. Should this be done, and Georgia persist in the maintenance of her rights and her authority, the consequences might be that the act would prove injurious to us ', in all probability, ruinous to you. The sword might be looked to as the arbiter of the interference. But this can never be done. The President cannot and will not beguile you with such an expectation. The arms of this country can never be employed to stay any State of this Union from the exercise of those legimate (sic) powers which attach and belong to their sovereign character. An interference to the extent of affording you protection, ' the occupancy of your soil, is what is demanded of the justice of this country, and will not be withheld; yet in doing this, the right of permitting to you the employment of a separate Government within the limits of a State, and of denying the exercise of sovereignty to that State within her own limits, cannot be admitted. It is within the range of powers granted by the States to the General Government, and therefore not within its competency to be exercised.'

Here we have, in the first place, the reason why Georgia resolves to take the charge of the Cherokees; and in the second, the Cherokees are informed that the United States' government will not attempt 'to stay any State of this Union from the exercise of those legitimate powers which attach and belong to their sovereign character.' And where did Mr. Secretary Eaton obtain his knowledge of these 'legitimate powers.'_ If attempted to be exercised, either by Georgia or Alabama, it will be a gross and unqualified act of usurpation, nor will its character be altered in the slightest degree by the declaration of the President, or the Secretary of War, that the national government will not interfere for the protection of those who are intended to be the victim of it. Georgia has no more right to the lands of the Indians, than she has to the lands in Canada; nor are the Cherokees any more subject to her authority, than are the Indians of the British North West Territories. And if, by the exercise of illegal power, they drive away, and take possession of their lands, it will not be merely an act of meanness towards a feeble body of men incapable of defending themselves, but one of the most arbitrary and unjust character; which, if permitted, will be a perpetual reproach and disgrace to the United States.