University Military School. – The school lately established at the University of Virginia, for military instruction, has been started under most happy auspices, so far as the prospects of the school itself are concerned. – It is now in a very flourishing condition, about one hundred young gentlemen having already entered, and the applications daily received for admission being numerous. The school bids fair to equal that of any military academy in the South. The chief instructor of the corps is Major George Ross, a graduate of the Virginia Military Institute, a thorough military man, who is aided by Capt. Thos. U. Dudley, Jr., of this city, as assistant instructor. Four lectures per week are to be delivered to the students by Prof. M. Schele de Vere and Dr. D. K. Tuttle, on military science, &c. The Cadets have already gone into camp, and the strictest discipline prevails. The University seems to be most excellently adapted for the above purpose. The following Cadet officers have been appointed, viz: Robt. E. Lee, Jr., (son of Gen. Lee,) Captain of Company A; John W. Maury, (son of Lieut. M. F. Maury,) 1st Lieut.; C. W. Trueheart, of Texas, Captain of Company B; Summerfield Smith, of Va., 1st Lieut. From the Richmond Dispatch, 10 July 1861, p. 2.