The long expected trial trip of the Adriatic has been successfully made, and the ship is now on her first voyage to Liverpool. It is the wish of all America, and it is, perhaps, just to say, of the world, that she may prove superior to any steamship previously constructed. She is, certainly, the largest yet afloat; and during the latter hour of her trial trip made the greatest speed on record, for vessels of her class. In coming up the harbor on Monday morning, the 16th inst., she ran from an accurately-ascertained point off Sandy Hook, to an equally definite point near Governor's Island, a distance of 2l statute miles, in one hour and four minutes. This is a trifle over twenty miles per hour. Long and sharp river steamers have frequently moved from twenty to twenty-five miles per hour, but heavy sea-going vessels rarely exceed sixteen. The great speed of the ship in this instance should not, however, lead to too extraordinary expectations in regard to her performance, on account of a circumstance not alluded to in the daily papers—the disuse of her " cut-off" during the whole trial. On starting from the dock it was found that the valves slammed too violently when dropped in the manner intended, and the engines were, consequently, adjusted to work with the steam following the piston at full pressure during the entire stroke. This method of working consumes steam very rapidly, and develops somewhat more power than when worked properly ; and the rapid run was probably due to the fact that a high pressure of steam existed in the boilers at the commencement, and was expended to develop extraordinary power in running down ae she reared hi dock. The "dash pots," as the parts are. technically termed which check the lescent of the valves, are to be replaced by larger or more efficient ones. The trial trip, so far as it was a trial, Was successful, but it demonstrated nothing definite with regard to the working of the valves, nor with regard to the normal speed of the ship under proper conditions. The model appears to be, as was generally expected, exceedingly well adapted to high speed, and the heavy work of the engines has been proved admirably perfect. It is yet possible that the valve gear will be subjected to several alterations, though nothing has been definitely proved that points to such a necessity.