SEWARD THE REPUBLICAN NOMINEE. – It is well known that Horace Greeley has been opposed to the nomination of William H. Seward by the Chicago Convention, preferring that of Mr. Bates of Missouri, upon grounds of expediency. We have on previous occasions stated our own well-settled conviction that Mr. Seward would certainly be the candidate. A private letter of the 20th ult., from Mr. Greeley, which we perused last evening, gives it up, and concedes the strong probability, if not certainty, of that gentleman’s selection as the standard-bearer of the Republican party in the coming campaign.