A clear perception of these advantages determined Gen. Grant to adopt the position at Petersburg. He was aware that Richmond could not be directly invested except with a very large army. He desired to accomplish the results which such an investment would give. He sought to cut off the city from its principal channels of communication--to deprive it of its main resources. Have these purposes been effected? At the time we write it is announced that the army occupies the railroad leading to Weldon, thus breaking the communication with North Carolina; that our cavalry has destroyed a portion of the road leading to Lynchburg; that the forces operating under Gen. Hunter have also destroyed portions of the Virginia Central and the road between Gordonsville and Lynchburg; they have also damaged the James River Canal. The only railroad communication now existing between Richmond and the South is that by way of Danville. Before this reaches our readers we trust that the effects of these efforts to isolate the capital of the confederacy will become evident; that the rebel army will be forced to leave its intrenchments and meet our brave soldiers in the field, and that the conflict may have resulted in victory for the cause of the country and of freedom. The various steps of the process by which the army gained the position at Petersburg are already well known. From the time the camps at Culpepper Court House were broken up, until the lines were established south of the James river, the series of movements consisted in masterly marches by the left, compelling the enemy constantly to fall back from his intrenched positions to points farther in his rear. Such movements were not, however made until after trials of the enemy in the front, some of which resulted in splendid partial successes. They were, however, not conclusive. The flank movements of our army belong to that class which are considered among the most difficult in warfare, requiring great skill in commanders to arrange their details, and endurance and discipline in the troops to effect them. It is no easy matter to change position in the face of a wary and vigorous enemy, ready to fall upon any exposed point in the long array of a marching column. Yet, several times, the manoeuvre has been skilfully and successfully performed, and each time the rebels have learned it too late to profit by the chances offered for a surprise.