=73.= =Distance of the Line of Investment from the Work.=--This will result from conflicting conditions. Reasons already given, which need not be repeated, lead to establishing it as near as practicable. On the other hand, the accurate fire of the heavy guns of the place, and vigorous sorties by the defence, cause much annoyance and great loss to a line drawn too near the work. The more recent sieges indicate about 3000 yards from the most advanced works, as the least distance for the line of investment in open country and with an active defence. It may be necessary in some cases to increase this to 4500 or 5000 yards; but with ground favorable to the attack, and a weak and demoralized defence, it may frequently be drawn nearer. =74.= =Strength and Composition of the Besieging Force.=--In former sieges when the place held out until the inner keep was breached and carried by the regular progress of the siege, the ratio of the necessary strength of the attack to the defence was estimated at 7 or 8 to 1, this large ratio resulting from the excessive labor in the trenches and the losses incurred on the close attack. Modern writers (arguing largely upon theoretical considerations) have reduced this estimate to 4 or 5 to 1. No attack on a thoroughly-equipped and well-defended strong place having been carried through all the steps of a regular siege since the introduction of modern arms, absolute data upon this subject are lacking. The besieging force at Strasburg was about 60,000, garrison about 20,000, total length of siege 49 days. The defence was very weak. Belfort, besieging force about 32,000, garrison about 16,000. After a siege of 100 days the approaches were at about 1200 yards from the works, which capitulated by reason of the general surrender of the French. At Metz the besieging force was 150,000 men; the garrison, demoralized by the previous defeat at Gravelotte, surrendered 173,000 men. At Paris the investing force was about 180,000, and the garrison nominally between 300,000 and 400,000, of which perhaps 30,000 were disciplined and effective soldiers; the remainder being made up of remnants of defeated regiments and bodies of the Garde Mobile and Garde Nationale. The investment of Paris was complete on September 19, 1870; its surrender from exhaustion of provisions took place January 29, 1871. Several sorties were made, but the general defence was paralyzed by the character of the troops and inhabitants. At Plevna the Turks had at the outset about 56,000 men, at the surrender 40,000. The Russian force suffered great losses in its assaults, but by continual reinforcement had at the end of the siege about 120,000 men. The defence by the Turks was desperate, but generally passive. One determined sortie was made immediately before the surrender. The surrender resulted from exhaustion of ammunition and provisions. The works were field works only.