Mr. O’Connell has addressed a long letter to the Irish Political Union, developing his intentions, and calling on the people of Ireland to second him. His principal object he declares to be to impeach Lord Anglesey, Mr. Stanley, and Mr. Blackburne, the Irish Attorney General; and he solicits the people to petition Parliament to that effect, declaring that he will undertake the impeachment himself in the reformed Parliament. The letter terminates thus: “I conclude with this declaration of my own personal intentions. First, I am determined never again voluntarily to pay tithes. Second, I am determined never again to pay vestry cess. Third, I am determined never to buy one single article sold for tithes or vestry cess. Such are my three individual resolutions; let every other man act as he pleases. I have made up my mind to this course. I will not oppose the law, let it take its course; but I decline paying to, or buying from, tithe proctors.”