For sorae weeks, and espeoially for some days pust, the news from the several military expeditions, and tbeir fields of operation, has hcon perplexingly obscure The whoreabouti of Sherman's twenty thonsand, and their deftinatioi) - the fortune pr misfoftunes oí Smitn's ton tbousand cavalry - the purposet and prospecta óf Kilpatricka's gallopade - huve been problema of the most ptofound and absorb ing interest, and only inforicr in imme diato i ir por la nee to these "ere the queutions of Longstreet's looation, of the signnificance of Grant'a dernongtrations from GbattSDODg, and of the prospect r.f' a eo-operative movement íainst Mobile from New Oileuns. - Besidesüll these, we were held in suspense for a duy or two as to the char acter and extent of our disaster in Florida. Some of these mattere) are notv partially, and others, whoüy, cleared tip. - Shennan, if we mny judco by our latest rebel advices, which are Up to about the close of last moiith, is nrw back at Vioksburg, aa thoy reported him a fow days ago to be pushing bis way there. Whatever rnay have been in view in the movement of bis column over the vast spaces it traveled - from Chattanooga to Memphis, from Mcmphis to Vicksburg, from Vioksburg to Meridian and proba bly to Sel ma - it would seem that tiiat oliject had been baillked. It tha purpose was to attacK Mobile, then wejudgo it was a doublé failure - for, in the first plico, Smitfa'a cavalry foree, (without the aid of whioh the moveinent of such an infaniry force a that oí Sherman through snch a , gion as he had to traverse was i , tibie) f ai led to effect a junction ; and, in the Becond place, Sherman eould have do inteation of attaoking Mobile : with the body of troops and the 1 tary iinpleinenta he had in hand, unles-s ■ he were supported by a c" "perating i flrrny and nuvy in front of the city, and ; no show of Bueh oo-operatioo was ever made by Genera] liunks, though a show of it was made by Admira] Par ragú t. If, agaiu, Sherman intended by a stupendous flauk movetnent to compe! a retreat of Joo Johnston's army, that also was uneuccessful ; and, iu faut, il aeema to have faileci so fur as eflecting any great object was conceroed unlesa wo credit tlie not very cr ditubly theory that Gun. Grant meant in iome way or other t. effect the just effected retreut of Longstreet by iotroducing general confusión and panic tbroughout the Southwest. At all evento, and whatever luwe been the objeot ol ihe oxpedition wo infer frmn the rebel dis patches and froin the cii cumstances of the caso that Sherman58 no lotiger on the offensive; and though the tc!ü grarns sent ua concerning hitn this morning are both s!ale and stupid, we should not be astonishod to learn byaud-by that the opening ol tliis month had f'ound bina in Vicksburg. Sinilh's oavalry column, a!so, about which there has been so ruucli anxiety, and on the suocesaful unión with which the fortunes of Sherman's expedition so largely depended has now returned to Memphis, having been driven back to the point from which it started by the rebel cavalry who gathered from all points against t. The public have been told of Smith's great huccchs, in that he dest.royed ao miiny bunhels of rebel grain and tore up so rnany rebtd rails; bat to assign tliis as the object is an insult to common sense. Smith failed. We have given during the last duy or two 8Uüh details as have come to hand of the very latest rush on to Kichmond. We have notyetfull statements of movements, purposes and results, but wejudge tbut Kilpatrick and nis men had a gloriaos ride from the Rápidas into the very suburbs of Richmond, and we are only sorry that having got so very close to the person of Jeff, he did not get jnst a little closer, eeize thu traitor by the hiir. tiing him on behind, and give hirn a ride to Washington on the horse's rninp. Whun we know exactly and really wbat Kilpatrick in:ended 'o do, we shull be ble íojudge more accurately whether he iccomplistied it. Beulde the light we have got on these three great expeditions, we think it ínay be taken for grantod r.ow that Longstreet is out uf Kast Tennessee, where he haö boon hoverfog foi tha lasi fonr months, threatening Koos vil Ie snd roaking hirnself obnoxious ge:!e;-nily.--T If ïio be not punnitted to eouie back, th't.s may So acconnted one ot the moet important süorcsses of late days, for he c:innot plant Lis foroe in any other poition where it will aonntfor as mucti UB it did in East Tennesee. Grint's late denionstrations froni Cha'tanoogu tppear now to havo been but demonstrations, and the ielteM of our correspondent this morning f'urnish tho ürst intthgibie details of thein. - Had Smith and 8 herman sueceeoled, we think it iltogother ükely that Grant would have oarried his demonstrations much farther than he did.