[Krom Mío Chicago Time.] Crooktb Kxpedition, Eosxbud Cbkkk CamiO -M ni M ;lh;i, Juno 17, via Fort Fettennau, Wyominj!, J uur XI. ) Pursuantto order, this ontire command, excopting 100 mon, left with Maj. Furoy to defend oiir wngou train, broke camp ou Goose Creck, at dawn ou June 1C, nd, accompanied by tbc Snake and Crow ndians, marched over forty miles that lay, and halted for the night in Montana Ferritory. Our whole force, mcluding tlio Indians, was in the neighborhood of 1,200 nen. "We had been halted about one ïour, our horaes unsaddled and grazing, when at 8:30 this morning tho report of irearms was distinctly heard from beliud the northorn bluffs in tho diroction of the canon. Soon af terward the Snakü ind Crow scouts camo running over th jill to inforui Orook that Sittiug Buil, with his whole ayailable force of Bionx, was advancing in quick timo to attuck is in camp. Two companies of tüe Second Cavalry and the samo numbor of infantry were ordered to deploy as skirmishers and snpport the Indian piekets. Hardly had they reached tho 3rost when volley after volley from the Sioux announced that the tight had commenced iu earnest. From our camp wc could seo the encmy s warming incrowds upon the higher range of bluffs in overy direction on a line ol at least two miles. They wcro all mounted, and fired with wonderful rapidity. Maj. Randall, our Chief of Scouts, aidod by Lieut. Bourko, rallied our friendly Indiajis and led them to attack the center of the Sioux. The latter recoived them with successive volleys, and, after a gallant flght, Kandall's redskins wero compelled to keep within shelter of the lowor range of hills, the number of Sioux opposed to them being overwhelruing. Observing this state of affairs, Col. Royall ordered the first battalion of the Third Cavalry, consisting of A, E, I aud M companiesunderCol. Mills, to advance, mounted, and charge the central bluffs, so as to drive back the enemy in that rection. Xhis order was executed with a brilliancy and celcrity seldom equalcd, under a sweeping hostile fire, which mado a volcano of tho plateau between the lower bluffs above our camp and the highor ones occupied by Sitting BulJ. The battalion eharged at full gallop with fierce ringing cheers, halted for a moment to pour in a witheriug volley, and then gajloped up the ascent to the creBt of tho ridge. Despite their great munbers and splendid position, the Sioux center broke and ran iiko a pack of wolves, taking shelter on other bluffs, 1,200 yards behind, for this battleground is a succession of ridges for miles on miles. The battalion then dismounted and deployed as skixmisbers along tho position they had carried. While this was boing done on tho center and right, tho second battalion of the Third Cavalry, consisting of companies B, D, P and L, under Col. Henry was ordered to attack Sitting Buli's right, which they did, driving i back even with tho Sioux center and left. The third battalion o the same regiment, companies C and M, under Col Van Vleit, was ordered to o e cupy tho northern bluffj in our rear, so as to checkmate any attack from tha point. The fighí now became general and eontinued until past noou almos without interruption, the Sious proving themselves the best fightinr Indians tha ever fired a shot. Beaten'on one ridge they retired behind auother, so that we were compelled to keep followiug them pp, exposing our line all the tiinc. Firing from their ponies, their shots wcro generally a littlo too h'gh until lato in the action - a fortnate thing for us. At a quarter past 12 o'clock Mills' battalion, excepting one company, detached after the flrst charge to support the left, was orJored to vacate its position on the right center, and mako easfc ward ürst, and then north down Eosebud creek, through the canon, at the end of which, seven miles distant, was situated the Sioux villago. To enter the canon, the left of the hostile line had to bo forced, and Mills ordered Company E, of the Third, under Capt. Alcx. Sutorius, to charge up the bluff and carry the position, which was speedily accomplished. The Indians, however excellent as skirmishers, have uot yct learned the art of standing a cavalry charge. Mills then moved down the canon rapidly towarc tho villago, according to orders. Hi. place on the bluffs above Ihe camp was supplied with only a few infantry, as the Second Cavalry were detained to sustain his movement. Crook now determinee to charge along this wholo line, and for that puruose ordered HAiirv's ha.ffn.lim to fall back and got tbeir horses, loffc some distaiice in the rear. Fortunately, yitting Buil mistook this preparatory movoment for a retreat. Honry retired aoross au exposed hollow, and the Sioux fought desperately right into nis comrnand. L company, of the Third, Capt. Vroom, was rear-guard, and somo men did not hear the order. They werc imrnediately surroundcd, and almost in a second fifteen of our bravo fellows lay dead and wounded on the bluff. F, I, B, and D eompanies of the Third instantly cotuiterohargp.d, and the wounded, excopt one man, were reaciied by Capt. Andrews and Lieut. Reynolds' comniand. At that moruont tlio brave Henry, a most accomplishcd ollicer, who was an Acting Brigadier during the civil war, was shot in tho face, the ball entering abovo tho rignt cheek bone and coming out at the loft. He was mounted, as nearly all the orticers were, and was a prominent mark. His wound is dangerous, if not fatal. Sitting Buil now discovered the advance of Mills and Noyes on the village. At least 50 warriors and 100 of thoir ponies lay dead along the ridges. The mimbcr of wounded embarrassed the Indian chiof. He had most pf the killed and all of tho injured strappcd to horses and carried otï. Tho Sioux tlien broke and ran in a northwesterly directioD, but dospite all their ollbrts tho Snaises and Crown took thirteon scalps. Information roached Crook that the Indian village was deserted, and ho immodiately sent Capt. Nickersou, of tho staft", to countermarch. Tliis was dono very reluctantly. Tho command faeHl southward once more. Sitting Buil fo.ught to cover the retreat of hi.s womeu and chilInii, whioh was rapidly accomplislu-d. He also hoped to beat Crook in open fight, bnt tho command slept on the field of battle. Our ammunition was failing, our rations neariy out. The Indiana could not then bo suiprised, so it was decided to rely on our base of mipplies and recupcrute. Oen. Crook is now satisfied that the Sioux can and will fight. They aro Vietter armed than his own soldiers. Of the lattor it must bo said that braver men neverfaeed an enemy. They would charge tho Sióux to the gates óf liell had they been allowed. The aotion occupied five hours. Pollo wing a list of our killed and wounded : D Conipany- Sergt. O'Donnell, sevorely wounded. I Company - Sorgt. Meagher, scriously injured; ono private slifihtly wounded. Third Cavalry, First Battalion, E pany - Privato Honry Harokl, daugorously wouuded. I Conipaiiy- Killed, pri vates Win. Allen and Eugeno Flynn; wounded, Sergt. Grosch, soverely; Corjoral Cardy, ecverely; privates Smitb, jinskoski, O'Briei), Stewart and Iieilly, everely. M Company - Woundod, Buglor Snow, dangerously. Second Battalion - Wouuded, Col. Guy V. Heury, conimundiiig battalion, and Captain of D Company, dangerously. 3 Company - Wouuded, private Jacob ítienor, severely. L Company - Killed, Sergt. Nankerchen; privates Mitcholl, 3onnor, Manueit, aud Potte; wóunded, Sergt. Cook, severely; private Krazmer, severely; private JEdwardH, seriously. P Company- Killed, Sergt. Marshall, srivnto Gilbert Koe; wouuded, private lown, sevorely; privato Fischer, severoy; private llutlon, slightly. Pourth lufiuitry, D Company - Privato James A. Devine, privato John H. Terry, pri vato Kiehard Flynn, all severely wound ed. Shoshone Snalse Indians - Killed, ouo warrior; woundod, foiu1 warriors, severely. Crow Indians - Wounded, throe warriors, ouo mortally. TotaJ, ineluding Indians, ton killed and thirty wouuded. Severnl of the slightly wounded are not mentioued. Wc also lost nineteon horses killed, and lie same ïmniber more or loss injured. Between 15,000 and 20,000 ronnds of immunitiou were fired by this command. Tho Sioux havo expended twice that amount - ono cause, doubtless, of their retreat. Thus we colebrated Bunker llill.