A special correspondent of the Chicago Times, who accompanied Maj. Thornburgh in liis cliase after the niurderous Cheyenne Indians, furnishes tlie following account of that expeilition and its remarkable experiences : Tho march has been through a country which is a geographical blank, and a desert untenanted by scarcely a living thing. The wagon trains were abandoned at the Platte rivor, two of them being stuck in tho qnicksand. The men took two days' rations on their saddles and started northward toward White Tail creek, where tho scouts reported the savagcs encamped. A fog so dense that it obscured object twenty yards away bewildered the scouts, and before they struek the trail, eight miles away, twenty miles had been traversec: in objectlcss detours, and the savage.s had cscaped. Their camp fires were smoldering and their trail was still fresh The column pushed on with scouts supposed to know all about the country but they proved their uttor ignorance by leading the column through an inaccessible country and losing the trail. The track of the savages was finally diacovered by members of Thornbtirgh's staff, and the cavalry moved on at the highest possiblo speed. We made a dry camp underneath the hills, where a semi-circle of rifle pits had been dug in the sand. We pressed the savages so closely that twenty ponies had been abandoned, and near the rifle pits there were some with packs on their backs all wet with perspiration. During the night the Indians were heard arounc the camp, but the scouts were not able to strike them. The command was in the saddle before daybreak, following the trail, which led toward the south Seventy-five miles had been traversec without a drop of water. The day was hot and dusty, and the men and animáis suffered frightfully. A private of Company H of the Fourth Infantry, dismounted by the falling o: his horse, was left on the road to waii for Mauck's command, which was following twenty miles in our rear. Two hours after the column passed out o: sight ho was attacked by several Indians He took refnge in the rifle-pits, anc stood them off several hours. The Indians, circulating around him, poured a hot fire upon him, and, althongh some of their bullets ciit his clothing, he escaped unhurt, Mauck's command appearing in sight just after the Indians succeeded in shooting the trigger of his gun. We reached a smal creek near the North Platte river on Sunday noon. The men were almos' unable to articúlate from the effects o: their torturing thirst. The wagontrain, left in the rear, was attacked bj fiftéen Indians. The guard repelled the assault until relieved by the arrival o) Mauck. All tho scouts who had been engaged deserted the expedition, and Col. Thornburg could only push on in a northern direction in hopes of striking the trail. Finally we struck thegrea' sand hills of Nebraska. The sand was knee-deop to the horses and was carriec by the wind in blinding clou ds. Ceaseless currents of wind piled it up in monstrous castles or whirled il up into drifts like snow. The column marched forty-five miles withoni water and with no food save a little liard-tack and raw bacon. Just as the sun was going down our glasses rovealed a lake in the distance. We reached it a 8 o'clock, Irat found it to be bitterly alkaline. The next day we struck Carlton's trail and followed it, abandoning all hopes of intercepting the Indians Tho best horses in the command 'were sent forward bearing couriers, to ask Carlton's assistance. We marched forty miles, and passed en routo a camp made by Carlton's men. Horses and men, dropping out of Carlton's column from exhaustion, came straggling into our oamp, near an alkali lake, at all hours during the night. Wednesday morning the probability that thewhole command would perish in tho sand was gcnerally disenssed. New couriers were sent forward, and every eflbrt made by the commanding officer to relieve the increasing distress of the troops. He succeeded at 3 o'clock in eommunicating with Carlton, and an liour later we eamped on the headwaters of the Snake river, where Carlton's relief met ns. The horses were so thin that the men almost pulled them over in attempting to mount. The expedition is a complete failure so far as the capturo of tho renegade Cheyennes is concerned. It failed beeanse illy fltted out, something for which Thornburgh cannot be held responsible. Another cause of the failure was the unreliable character of the scouts fnrnishcd the expedition. The department of the Platte was outgeneraled. The savages baffled the troops at every point, and led them into the sand-hiÜs, from which they might never havo emerged.