The Great Republic.

It is a source of satisfaction to know that the damage by the burning of this noble vessel is considerably less than was at first supposed. She was got afloat on Tuesday morning. This was accomplished by building a temporary stern, (that part of the vessel having been burnt away,) and inclosing the whole after part of the hull, which was the deepest in the water, in canvas, to stop the leakes. Five steam pumps were then put aboard, and the twelve feet of water in her were exhausted at the rate of one foot per hour. Only about one third of the cargo was touched by the fire, leaving at least three thousand tons, damaged by water, in the lower holds. These decks occupy about twenty-four feet from the keel upward, and that part of the vessel, which includes all below copper, is in a sound condition; so that her late commander, Capt. L. McKay, yesterday remarked that she might yet be made into as fine a steamer as floats. The two upper decks, (the promenade and spar,) are wholly gone, with the timbers; but a large quantity of cargo stowed in that part of the vessel, cotton, grain, rosin, &c., are in course of removal. Half a dozen schooner loads have already been taken away, -- all, of course, greatly damaged. Among other articles, is a great quantity of corn, in bulk and in bags. That part most badly burnt will be good for nothing. the clean portions, injured only by water, will be chiefly valuable to make starch of. It is to be sold today, together with the remains of rigging, old junk, &c. Laborers are employed in cutting up the masts and clearing away all incumbrances from the uppper decks, before commencing below.

Capt. Sturgis, agent of the underwriters, has charge of the wreck. The large quantity of flour below decks is expected to be got out in a tolerable good condition. Barrels of flour submerged in water are not ordinarily penetrated by it more than two inches in about three weeks; and good Southern barrels, such as were on the Great Republic, are preserved much better. The weat is also below decks.

What disposition will be made of the hull, is altogether uncertain.

N.Y. Journal of Commerce, 5th.