BELFAST, _Tuesday, June 26._--Sir John Preston, the head of one of the great Belfast houses, and a former Mayor of the city, dined with us last night, and in the evening Sir James Haslett, the actual Mayor, came in. I find that in Belfast the office of Mayor is served without a salary, and is consequently filled as a rule by citizens of "weight and instance." In Dublin the Lord Mayor receives £3000 a year, with a contingent fund of £1500, and the office is becoming a distinctly political post. The face of Belfast is so firmly set against the tendency to subordinate municipal interests to general party exigencies, that the Corporation compelled Mr. Cobain, M.P., who sits at Westminster now for this constituency, to resign the post which he held as treasurer and cashier of the Corporation when he became a candidate for a seat in Parliament. I am not surprised, therefore, to learn that the city rates and taxes are much lower in the commercial than they are in the political capital of Ireland. Both Sir John Preston and Sir James Haslett have visited America. Sir John went there to represent the linen industries of Ireland, and to urge upon Congress the propriety of reducing our import duties upon fabrics which the American climate makes it practically imposssible to manufacture on our side of the water. Senator Sherman, who twenty years ago had the candour to admit that the wit of man could not devise a tariff so adjusted as to raise the revenue necessary for the Government which should not afford adequate incidental protection to all legitimate American industries, gave Sir John reason to hope that something might be done in the direction of a more liberal treatment of the linen industries. But nothing practical came of it. Sir John ought to have known that our typical American Protectionist, the late Horace Greeley, really persuaded himself, and tried to persuade other people, that with duties enough clapped on the Asiatic production, excellent tea might be grown on the uplands of South Carolina! In former years Sir John Preston used to visit Gweedore every year for sport and recreation. He knew Lord George Hill very well, "as true and noble a man as ever lived, who stinted himself to improve the state of his tenants." He threw an odd light on the dreamy desire which had so much amused me of the "beauty of Gweedore" to become "a dressmaker at Derry," by telling me that long ago the gossips there used to tell wonderful stories of a Gweedore girl who had made her fortune as a milliner in the "Maiden City."