A State Election was held in Connecticut during the month, which resulted in the election of Seymour, Democrat, Governor, by a majority of 459. He received 31,574 votes: Kendrick, Whig, 28,312; Scattering, 2803. In the Senate are 15 Democrats and 5 Whigs: in the House the Democratic majority is 41. ---- In Rhode Island, the election resulted in the success of Philip Allen, Democratic candidate, for Governor, by about 400 majority: S. G. Arnold, Whig, has been chosen Lieutenant-Governor. In the House there have been 41 Whigs and 28 Democrats elected; three vacancies to fill. In the Senate, 16 Whigs and 13 Democrats have been chosen, and there are two seats vacant. Mr. WEBSTER has written a letter to G. A. Travenner, Esq., of Virginia, in reply to inquiries as to the proceedings in Congress on the resolution of Mr. Jackson, noticed under our Congressional summary. Mr. Webster reiterates his own entire approbation of the Compromise measures, as necessary and expedient, and of the Fugitive Slave Law, as "entirely constitutional, highly proper, and absolutely essential to the peace of the country." He thinks that the public mind, both North and South, will eventually come right upon this subject, and does not believe that further agitation can make any considerable progress in the North. He had noticed with regret the proceedings in Congress referred to, and in regard to them, he had only to say, "that gentlemen may not think it necessary or proper that they should be called upon to affirm by resolution that which is already the existing law of the land." He did not believe that any positive movement, to repeal or alter any or all the Compromise measures, would meet with any general encouragement or support. At all events, he adds, "my own sentiments remain, and are likely to remain, quite unchanged. I am in favor of upholding the Constitution in the general, and all its particulars. I am in favor of respecting its authority and obeying its injunctions; and to the end of life shall do all in my power to fulfill, honestly and faithfully, all its provisions. I look upon the Compromise measures as a proper, fair, and final adjustment of the questions to which they relate, and no re-agitation of those questions, no new opening of them, will ever receive from me the least countenance or support, concurrence or approval, at any time, or under any circumstances."