DUBLIN, MARCH 1.– A circumstance occurred to-day which stamps at once the popularity of the ministerial measure of out-door relief to the poor of Ireland, and promises to facilitate its operation throughout the country, so as to ensure not alone favour but success. A deputation of the poor law guardians of Dublin, with the Lord Mayor, who is also chairman, of the North Dublin Poor-law Union, at their head, waited upon the Lord Lieutenant, to represent to him their anxiety to commence immediately the administration of out-door relief to the destitute and able-bodied poor, and to ask his Excellency, after listening with great attention to the deputation, was pleased to give the required sanction, and the deputation then retired, resolving that the system– in anticipation of the temporary relief measure– shall commence forthwith.

I am assured that inspectors are already appointed to select the objects of relief, and that our door assistance to the poor will be in operation in Dublin on tomorrow, or the next day at farthest. The Lord Mayor, the head of this movement, for many years fought the battle of out-door relief against O’Connell, through the columns of the journal of which he was the head. He has been at length successful. –Daily News Correspondent.