certain works have completed during the week, and others are in the course of construction, by the officers and men of the Fiftieth New York Volunteer Engineers, attached to this army, under the immediate direction and supervision of Lieutenant-Colonel Spaulding, commanding the detachment. The following extracts from his weekly report of this date, set forth the nature and progress of the various duties intrusted to them:

Major Brainerd reports that from Sunday until Friday, both inclusive, parts of Companies D, F, G, and M, under the immediate supervision of Captain McGrath, were engaged in building corduroy roads in the covered ways in rear of the line of works from the left of Fort Sedgwick to the Norfolk railway. During the week there have been laid 3,000 feet of corduroy, properly secured with side rails, and covered with earth. Four hundred and ninety wagon-loads of corduroy material were used in this work. The worst parts of the roads in these covered ways are corduroyed, and the whole is now passable, yet a slight rain has demonstrated the necessity of continuing the work until the whole of these ways are floored with corduroy. Captain McGrath commenced this morning with his company cutting and hauling material for a fraise around Fort Sedgwick, in addition to the abatis and wire entanglement now in front of the fort. Captain Schenck has been engaged with his company during the week upon Fort Alexander Hays. Two traverses and the timber work of a magazine have been built and a bomb-proof partially framed. Sand-bags have also been put in position to protect the barbette guns. The remaining work on this fort will be completed early in the coming week. I directed Captain Schenck to proceed this morning to Fort Sedgwick and take charge of the detail of men for inclosing the work with an infantry parapet in the rear. Also to render Lieutenant Benyaurd any assistance he might require in repairing the fort. Captain Folwell, upon Fort Wadsworth, and Captain McDonald upon Fort Dushane, each with their respective companies, have been employed in completing these works. They report these forts complete, both in interior works and outer defenses, and they were this morning turned over to their respective garrisons. I directed Captain Folwell to proceed to Battery Numbers 26 this morning with his company and inclose the work with an infantry parapet in the rear, calling upon the corps garrisoning the fort for such assistance as he might require. Captain Hine has had charge of Forts McMahon and Blaidell, working his own company and details of infantry. Captain Hine reports the exterior of Fort McMahon complete, the platform ready for the guns, and the magazine nearly ready for use. A traverse of about 100 feet in length is being built, which will also be made a bomb-proof. The parapets of Fort Blaidell are nearly complete, but nothing has as yet been done in the interior. Captain Van Brocklin has been engaged in superintending the construction of Fort Stevenson, working his own company and an average detail of 1,400 infantry during each day and 500 each night; also ten teems hauling material for revetments. The embankment for the parapets is about half done, that of the front side being nearly completed, and the revetment has kept pace with the parapets. The subterranean drains are completed and covered and the three magazines and galleries finished. Three hundred gabions have also been delivered for reverting embrasures. This is a very heavy work and will be the last to be completed of the several works mentioned in this report. Captain Dexter had continued the work on Fort Patrick Kelly, working, besides his own company, a daily detail of about 600 men. The revetment is nearly completed and the parapets about two-thirds done. The platforms for the four guns in embrasure and for one of the guns en barbette are completed, as also the banquette on four of the faces. Captain Palmer has during the past week been engaged with his company upon Battery Numbers 40. The work is now prepared for one barbette gun and will be ready for the other barbette gun this evening. It is expected that the platforms and embrasures will be prepared for the other four guns by to-morrow evening.

In the topographical department I have the honor to report that during the week my principal assistant, Major Weyss, assisted by Mr. Theilkuhl, was directed to survey the line of the military railroad from its junction with the City Point and Petersburg road to that of the Weldon road; of the corduroy road between the Jerusalem plank road near Jones' and the Globe Tavern, and of several shorter corduroy roads in the same neighborhood. These surveys, together with that of the new line between Forts Sedgwick and Haskell, have been plotted and added to the detailed map (scale eight inches to the mile), which has been for some time in course of preparation, showing the different lines occupied by the U. S. forces in front of Petersburg, together