THE INDIAN WAR. A dispatch from Bismarck, D. T., [1] dated July 22d says:

The steamer Josephine, with Colonel Hughes, [2] of General Terry's staff, has arrived.

General Terry [3] has moved his supply depot from Powder river to Big Horn, where he still waits for reinforcements and supplies. The Far West [4] reached that point Monday.

General Terry's Crow scouts who left after the Big Horn battle, have returned. They report Indians in the Big Horn mountains ready for business, and could not be induced to pass that vicinity. An effort was made by General Terry to communicate with General Crook, [5] and the scouts reported that they were driven back. On the 9th, couriers were escorted up Tullock's Forks some distance, and struck across through the Rosebud region. These are the messengers Colonel Hughes thinks, that General Crook speaks of in his recent official report.

Colonel Hughes does not credit the report of Sitting Bull's death, and thinks the Indians' loss was much lighter than is reported and he doubts if the troops, as re-inforced, will be able to engage them. General Terry has asked for artillery which Colonel Hughes hopes to take back with him.

On the Eleanor Carroll, which left this afternoon for the mouth of the Big Horn, were General Forsyth [6] and Colonel Otis and command. Horses, recruits and supplies will follow on the Western, Saturday.

A Fort Thompson, Dakota letter of the 15th, says that advices there from the Black Hills are that a proposition is gaining ground among the miners to raise a force to march to Missouri and kill every Indian, man, woman, and child in the camps from Standing Rock to Yankton agency and burn and destroy the agencies. Nearly two hundred men have been killed and 1000 head of stock run off since February.

Since the disaster on the Little Big Horn, great fears are entertained that Sitting Bull will turn on the north side of the Black Hills and with his strong force, burn the towns and sweep the miners from the gulches. Active measures are now being taken for defence in such an emergency.

Indian runners have arrived at the agencies from hostile camps, to give information of the battle of Little Big Horn and its results, and to induce others to join the war bands on the Yellowstone. The Indians are greatly elated over their success, and make no secret of it. Disaffection is spreading at the agencies and will almost certainly take a sanguinary form.

A Fort Laramie special of the 22d inst. says: Gen Merritt having been advised that 800 Cheyennes were about leaving the agency to join Sitting Bull made a forced march on the nights of the 15th and 16th insts., and encamped on Hot Creek under the bluffs in front of the line that the Indians were obliged to travel. On the 17th the war parties came in sight and Merritt with his seven companies kept out of sight. The Indians saw the wagon train in the distance in which were two companies of infantry. The Indians kept out of sight of the train in expectation of capturing it, while Merritt was watching the Indians unknown to the latter. Two couriers drove ahead to go to the creek when half a dozen Indians went for their scalps. Buffalo Bill and the scouts who were under Merritt quickly intercepted the small Indian party and just as they sprang for the men Buffalo Bill and his scouts fired into and killed two of them. The Indians turned on the scouts and the latter sprang from their horses and met the daring charge with a volley. "Yellow Hand" a young Cheyenne chief, came foremost, singling "Bill" as a foeman worthy of his steel. Cody coolly knelt and taking deliberate aim sent a bullet through the chief's leg and into his horse's head, down went the two and before his friends could reach him a second shot from Bill's rifle laid the redskin low.

The reserve Indians came on with a rush from the ridge in the rear, bent on annihilating the party. To their astonishment, however, a long blue line popped up in their very front and company K., with Col. Mason at the head, dashed at them. Leaving their dead the Cheyennes scattered back helter skelter to the ridge, but their fire was wide and their stand a short one. Company after company debauched from behind the bluff and utterly disheartened the Indians rushed for the reservation, leaving behind all their provisions.

Gen. Merritt pursued them till night when the whole command went into camp at the agency. The Indians left their dead and admit having more wounded. They also lost six ponies. Their friends at Red Cloud say they never conceived how the 5th cavalry could get there in time to head them off. The regiment sustained no loss. It arrived at Laramie yesterday and leaves for Crook's camp to-morrow, the 23d inst.

A Washington special says Gen. Sherman has been able by a judicious distribution of the troops on the seaboard to draw enough men to reinforce the army operating against the Indians, and no volunteers will be wanted. Gen. Sheridan reports that everything will be ready for an active campaign in a few weeks, and it is believed he will take the field himself. Sheridan will make his headquarters at Goose Creek, near the Rosebud. The three columns operating against the Indians will aggregate about 4000 men. Gen. Sherman estimates the fighting strength of the Sioux at 2,500 men, and it is his purpose to make their punishment such as they never shall forget. Dispatches received by Gen. Sherman last evening state that Gen. Merritt will not reach Gen. Crook till August 1st. when Gen. Terry will form a junction with them. Low water in the Yellowstone river may delay movements.