FORT SUMTER, July 23, 1864 - 8 p. m.

MAJOR: I have the honor to report progress of bombardment and operations in engineer department from the evening of 20th instant to the present:

Captain T. A. huguenin, First South Carolina Infantry, assumed commanding on arriving at the fort, 8 p. m., 20 th instant. At this request I accompanied him over the work and indicated the plans of defense. Two of the quartermaster's barges were sunk at the wharf by fragments of mortar shells. Night firing: Parrott, 61, of which 18 missed; mortar, 210, of which 59 missed; total, 271, of which 77 missed. Working parties engaged on repairs of south and southwest angles; they also completed the filling within heavy revetment at the south end of second tier west casemates. No casualties.

Thursday, July 21 (fifteenth day).- Parrott fire slackened to-day on southwest angle; 1 negro killed about 8 a. m. Day fire: Parrott, 93, of which 11 missed; mortar, 236, of which 37 missed; total, 329, of which 48 missed. Shelling light during the night, the hands being able to work to some advantage. No casualties. Night fire: Parrott, 18, of which none missed; mortar, 29, of which 9 missed; total, 47, of which 9 missed.

Friday, 22nd (sixteenth day).- Fire opened as usual upon southwest angle. The cold crack from top to bottom of scarp-wall at embrasure next north of position in south angle has been plainly increased by the late battering in reserve; also the pier arch, between the two lower tier casemates in same angle, used now for commissary stores, has begun to crack in consequence of the outward thrust upon the scarp-wall. This pier arch is well centered, but the rapid growth of the cracks, one along the crown and extending upward and transversely into the casemate arch of either side, as well as another at the skew-back of the outer pier, indicate plainly the progress of demolition without and the necessity of speedily filling these chambers. Moreover, should the battering of this angle be long kept up, the filling of these lower casemates will not arrest a probable falling outwardly of the scarp-wall on both sides of the postern, which may lead to a disastrous loss of material from top to bottom of the present towering southwest angle. I do not give this up, by any means, but if the existing deficiencies in supply of sand and lumber by quartermaster's department are suffered to continue I do not think I can be answerable for this any more than the weak points in the sea front. I shall endeavor to built a small section of crib-work, reaching from the stone buttress around and across the postern to the embrasure of the telegraph casemate; thus, of not bracing, at least ready to catch and sustain the cracked scarp. It will be necessary to raise the crib at least 10 feet above the berm to make it effective toward the end in view, and also to close the postern permanently, but this last, since the opening of the sally-port at the wharf, is not at all necessary to either the comfort or safety of the garrison; indeed, it would be one less opening to guard. The mortar shelling has done no injury to the fort, although requiring diligent repairs and filling of holes. The battering and shelling of the southwest and southeast angles has largely reduced the material bulk of the same, but repairs have in the case of the former so far arrested anything like breaching, and of the latter have kept up the command and infantry cover, while the gradual filling of the magazines below will effectually add to the strength of this almost indestructible angle. Day fire: Parrott,