Philadelpbia, June 6. Wc havo luid a desperate struggle at Port Hudsoii, the result of whioh is, at preseut, unkuown. The troops are eoniident of ultímate sucoess, and havo lost none of thcir onthusiasm - eveu the wounded, display great anxiety and earnestness to return to the secue of conflict. The eneloscd mèngre list of thoso killed and disablcd will refiei t a decp gloom in the North, as it has don heretofórc. Sinco Friday, May 22f, a continuous boinbardir.cnt has been maintaincd by Admiral Farragut's fleot, and the First Vermont Butïcry, Captain Hibbard, has annoyed the battery. During the day, at oue o'olocli in the nfternoon, on Wcdnesday, the battlo commenoed, the lincs exteuding for a distance of ncarly four miles m front of the enomy's works. - The extremo rigbt was givcu to Gen. Weitzel, Gen. Grover oeeupying the next position, Gen. Augur the third, and Gen. Shertoan the left. Cn the left the Hundred and Fifth fifth New York, Lieut. .Col. Abel Smith, was orderud to discharge their muskets and charge upon the cnemies works. For the foHowing details of the movement I am iudebted to Sergeant Major Cassel and A. Palmer : Gon. Sberman i.ntended to eai'ry a section of the fortificatious at the point of tho bayonet. The Second Duyrea Zouaves and the Hundred and Seventy-seventh New York made a desperate onset, and wcre met by a rain storm of bullcts. Lieutenant-Colonel Smith, of the former regiment, was sevorely woundod. Finding it impossiblo to sucoessfully accomplish tho daring purpose, a retreat was effected. Colonel Clark, of the Sixth Michigan, carried the colors of his regiment inside the first rebel flagstaif. The One Ilundrcd and Twcnty-cighth New York, Col. Cowles, immediately foliowed, and wero within the walls of the earth when both regiments were forced to retire on account of a lack of support by the Fifteentli New Hampshiro. Col. Cowles was killed. - ■ Colonel Clark was so terribly stunned by shell while retreating, that he remained senseless for an hour. General Neal Dow was slightly wounded, and Gen. Öhcrman rallied, took chargo of Dow's Brigade when he reccived a compound fracture of tho right leg from a grape shot. Captain ladean of Gen Sherman's staff was senously wounded, Sergeant Major Palmer of tho Second Duyrea Zouaves obtained four assistants and carricd him on a litter for a distanceoftwo miles to tho hospital. After the death of Col. Cowles tho command of the One Hundred and Twenty-eighth New York, devolved upon Captain Gifford who was almost iin.r.odiately wounded. Captain Keyes,. a mere youth, then assumed tho duties of Colonel. The struggle lasted unlil five P. M., when a general order was dispatched along the lines to retreat and take the original position occupied at the commencement of the acción ; unable to give even a conjeoture as to the result. General Wcitzell is reportcd to have taken two batterics. The propellor lila arrived here last oveuing from Balon Rougo. Generáis Sherman and Dow were brought down upon stretchers; the body of Col. D. S. Cowles was on board. Heavy canuonading could bo heard at Port Hudson. Our loss heavy. Reported to be at least 4,000. The rebels could not have had over 10,000 men. New York, June 10. Advices by the Cahawba states that reinforcements from Brashcar City and otherpoints, to the number of six thousand, reached Gen. Banks on tho 20th and olst, and our troops outnumbered the rebels four to one. The rebels aro entirely hemmed in, and no suceor can reaeh them. Their foree was variously stated at from 6,000 to 10,000. They are vrell supplied with corn meal, but have few other provisions, and a small supply of ammunition. It was believd to bc impossible for them to hold out long. Cincinnati, Juno 10. Tho Gazctte has the following from Soutliern papers : " Dispatches from Jackson fo tho 3d inst. to tho Mobile Register say that Port Hudson is closely bcsieged. The news from that quarter is conflioting. It is belioved that the accounts herctofore reported of fighting thero are greatly exaggorated. The Yankees have abandoned the New Orlcang and Jackson Railroad. They burncd tho Marehes Bridge and destroyed the fortifications thero."