A letter written during the last session of Congress, dated January 7, 1850, from the Members of Congress from Louisiana, to the Governor of that State, has recently been published. It calls his attention to the constant agitation of the subject of slavery at the North, and to the fact that the legislature of every Northern State had passed resolutions deemed aggressive by the South, and urging the Governor to recommend the Legislature of Louisiana to join the other Southern States in resisting this action. The opinion is expressed that "decisive action on the part of the Southern States at the present crisis, is not only not dangerous to the Union, but that it is the best, many think, the only way of saving it." Among the political events of the month is the publication of a correspondence between Hon. ISAAC HILL, long a leader of the Democratic party in New Hampshire, and Mr. WEBSTER, in regard to the efforts of the latter to preserve the peace and harmony of the Union by allaying agitation on the subject of slavery. Mr. HILL, under date of April 17, wrote to Mr. WEBSTER expressing his growing alarm at the progress of ill-feeling between the different sections of the country, and his conviction that "all that is of value in the sound discrimination and good sense of the American people will declare in favor of Mr. WEBSTER's great speech in the Senate upon that subject. Its author," he adds, "may stand upon that alone, and he will best stand by disregarding any and every imputation of alleged inconsistency and discrepancy of opinion and practice, in a public career of nearly half a century." Mr. WEBSTER, in acknowledging the letter, speaks of it as "an extraordinary and gratifying incident in his life," coming as it did from one who had long "belonged to an opposite political party, espoused opposite measures, and supported for high office men of very different political opinions." They had not differed, however, in their devotion to the Union; and now, that its harmony is threatened, it was gratifying to see that both concurred in the measures necessary for its preservation. His effort, he says, had been and would be to cause the billows of useless and dangerous controversy to sleep and be still. He was ready to meet all the consequences which are likely to follow the attempt to moderate public feeling in highly excited times, and he cheerfully left the speech to which Mr. HILL had alluded, "with the principles and sentiments which it avows, to the judgment of posterity."