Gen. Sheridan and party reached Chicago in return from a very successful buffalo hunt on the Western plains, on Wednesday morning, in fine health and spirits. Some incidents of the trip are thus given by the Chicago Evening Journal:

"The party left Chicago on the 20th ultimo, by the Chicago and North-western Road, John C. Gault, Esq., Superintendent, tendering the Director's car to the General for his party. At Omaha a like courtesy was shown by Mr. Sickles, Superintendent of the Pullman Car Company on that road. The trip was most delightful. On arriving at North Platte, Major-Gen. Emory and Major J.H. Brown, the commander of the expedition, met the party, which was escorted by them to Fort McPherson, a pleasant ride of seventeen miles over the plains. About two miles from the post several companies of cavalry, with a regimental band, were drawn up, and received Gen. Sheridan, and were reviewed by him, after which the party were presented to the officers of the post and their ladies, who also had come out in carriages and on horseback. The party were escorted to Camp Rucker, where quarters were assigned, and the day spent in choosing horses, target practice, &c., concluding with a grand hop at the post.

At 8 o'clock next morning tents were struck, and the grand march begun, Lieut. E.M. Hayes, Quartermaster, and "Buffalo Bill," the observed of all observers," -- splendid in form, the beau ideal of the rough rider that he is - as scout and guide. The advance was lead by Gen. Sheridan and Major Brown; eighty-five mounted men, fourteen wagons, three ambulances, and led horses for the party, constituted the outfit. Twelve miles out leave was taken of the ladies and officers who thus far accompanied the party, and the first camp was reached on Plum Creek, eighteen miles, which in honor of the commander, was named "Camp Brown, my Boy."

The march was commenced for the grand hunt at an early hour next morning. A cup was voted to the slayer of the first buffalo, and one also for the first elk. About ten miles out, seven buffalo were seen on a distant hill; the command was halted, and seven "solitary horsemen might have been seen," led by Buffalo Bill, and all eager for the chase. Gen. Fitzhugh secured the first tongue and brush, and became winner of the cup. Crosby made a good second, and Livingston third, while Jerome, the younger, brought in the trophies from the fourth. Camp was reached at about 2 o'clock, which, in honor of one of the most gallant soldiers in the service, was named "Camp Jack Hayes." Before the camp-fires were lighted, Wilson brought in an elk of about 600 pounds avoirdupois, and became the winner of the cup.

The next was a regular field-day. The party camped on the Beaver, and "Camp Cody," named in honor of Buffalo Bill, was filled with trophies taken from forty buffalo. Gen. Stager brought in six, Lawrence Jerome four, and every one of the party two or three. All having now killed buffaloes, but little interest was taken in the numerous herds seen on the adjacent hillsides, except to secure enough for use in the camp.

Elk, antelope, black-tailed deer, coyotes, jack rabbits, skunks, pocupines, prairie dogs, rattlesnakes, wild turkeys, mallard, teal and woodduck, and three or four kinds of fish, embraced the game found and secured - Fitzhugh shooting the first buffalo, Wilson the first elk, Crosby the first antelope, Rucker the first Coyote, Sheridan the first rabbit, and Leonard Jerome the first wild turkey. The finest elk were killed by Lieut. Hayes, Fitzhugh and Johnson, weighing nearly 1,000 pounds.

The first day's march was to Camp Brown, on Plum Creek, 18 miles; the second to Camp Jack Hayes, on the Medicine, 30 miles; the third to Camp Asch, on the Republican, 13 miles; the fourth to Camp Cody, on the Beaver, 15 miles; the fifth to Camp Stager, on the Short Nose, 24 miles; the sixth to Camp Jerome, on the North Solomon, 24 miles; the seventh to Camp Sam Johnston on the South Solomon, 25 miles; the eighth to Camp Davis, on the Saline, 30 miles; and on the ninth to Camp Hecksher, 15 miles.

On their arrival at Fort Hayes, on the Kansas and Pacific Railroad, a palace car was in waiting, having been placed at the disposal of Gen. Sheridan by the Superintendent of that road, in which the party, by the courtesy of the Superintendents of the Hannibal and St. Joseph and the Chicago, Burlington and Quincy roads, were brought safely home, and the grand hunt was successfully completed without an accident, and with thousands of pleasant memories clustering around it."