The Knoxville (Tenn.) Whig, of June 25, brings us an official report of the proceedings of the Eastern Tennessee Union Convention which assembled at Greenville on June 17. Hon. THOS. A.R. NELSON acted as President. On the fourth day of the session the Declaration of Grievances and Resolutions were finally adopted as follows, without division:

We, the people of East Tennessee, again assembled in a Convention of our Delegates, make the following declaration in addition to that heretofore promulgated by us at Knoxville, on the 20th and 31st days of May last.

So far as we can learn, the election held in this State on the 8th day of the present month, was free, with but few exceptions, in no part of the State other than East Tennessee. In the larger parts of Middle and West Tennessee, no speeches or discussions in favor of the Union were permitted. Union papers were not allowed to circulate. Measures were taken in some parts of West Tennessee, in defiance of the Constitution and laws, which allow folded tickets, to have the ballot numbered in such manner as to mark and expose the Union votes. A disunion paper, the Nashville Gazette, in urging the people to vote an open ticket, declared that "a thief takes a pocket-book or effects an entrance into forbidden places by stealthy means -- a tory, in voting, usually adopts pretty much the same course of procedure." Disunionists, in many places, had charge of the polls, and Union men, when voting, were denounced as Lincolnites and Abolitionists. The unanimity of the votes in many large counties where, but a few weeks ago, the Union sentiment was so strong, proves beyond doubt that Union men were overawed by the tyranny of the military power and the still greater tyranny of a corrupt and subsidized Press. In the City of Memphis, where 5,613 votes were cast, but five freemen had the courage to vote for the Union, and these were stigmatized in the public Press as "ignorant traitors, who opposed the popular edict." Our earnest appeal to our brethren in the other divisions of the State was published then only to a small extent, and the members and names of those who composed our Convention, as well as the counties they represented, were suppressed, and the effort made to impress the minds of the people that East Tennessee was favorable to secession. The Memphis Appeal, a prominent disunion paper, published a false account of our proceedings, under the head, "THE TRAITORS IN COUNCIL," and styled us, who represented every county but two in East Tennessee --" the little batch of disaffected traitors who hover round the noxious atmosphere of ANDREW JOHNSON's home." Our meeting was telegraphed to the New-Orleans Delta, and it was falsely said that we had passed a resolution recommending submission if 70,000 votes were not cast against secession. The dispatch added that "THE SOUTHERN RIGHTS MEN ARE DETERMINED TO HOLD POSSESSION OF THE STATE THOUGH THEY SHOULD BE IN A MINORITY. Volunteers were allowed to vote in and out of the State in flagrant violation of the Constitution. From the moment the election was over, and before any detailed statement of the vote in the different counties had been published, and before it was possible to ascertain the result, it was exultingly proclaimed that separation had been carried by from 50,000 to 70,000 votes. This was to prepare the public mind to enable "the Secessionists to hold possession of the State though they should be in a minority." The final result is to be announced by a Disunion Governor, whose existence depends upon the success of secession, and no provision is made by law for an examination of the vote by disinterested persons, or even for contesting the election. For these and other causes, we do not regard the result of the election as expressive of the will of a majority of the freemen of Tennessee. Had the election everywhere been conducted as it was in East Tennessee, we would entertain a different opinion. Here no effort was made to suppress secession papers, or prevent secession speeches of votes, although an overwhelming majority of the people were against secession. Here no effort has been made to prevent the formation of military companies, or obstruct the transportation of armies, or to prosecute those who violated the laws of the United States and of Tennessee against treason. The Union men of East Tennessee, anxious to be neutral in the contest, were content to enjoy their own opinions, and to allow the utmost latitude of opinion and action to those who differed from them. Had the same toleration prevailed in other parts of the State, we have no doubt that a majority of our people would have voted to remain in the Union. But, if this view is erroneous, we have the same (and, as we think, a much better) right to remain in the Government of the United States than the other divisions of Tennessee have to secede from it.

We prefer to remain attached to the Government of our fathers. The Constitution of the United States has done us no wrong. The Congress of the United States has passed no law to oppress us. The President of the United States has made no threat against the law-abiding people of Tennessee. Under the Government of the United States, we have enjoyed, as a nation, more of civil and religious freedom than any other people under the whole heaven. We believe there is no cause for rebellion or secession on the part of the people of Tennessee. None was assigned by the Legislature in their miscalled Declaration of Independence. No adequate cause can be assigned. The Select Committee of that Body asserted a gross and inexcusable falsehood in their address to the people of Tennessee when they declared that the Government of the United States has made war upon them. The secession cause has thus far been sustained by deception and falsehood; by falsehoods as to the action of Congress; by false dispatches as to battles that were never fought and victories that were never won; by false accounts as to the purposes of the President; by false representations as to the views of Union men; and by false pretences as to the facility with which the secession troops would take possession of the Capital and capture the highest officers of the Government.

The cause of secession or rebellion has no charms for us, and its progress has been marked by the most alarming and dangerous attacks upon the public liberty. In other States, as well as our own, its whole course threatens to annihilate the last vestige of freedom. While peace and prosperity have blessed us in the Government of the United States, the following may be enumerated as some of the fruits of secession:

It was urged forward by members of Congress who were sworn to support the Constitution of the United States, and were themselves supported by the Government.