From The South

Washington, May 18. The following was received to day at head quarters of the army : " Memphis, May 17. lo II. Halleck, General-in-Chief : " Papers of the 14th, from Vickstrarg and Jacksou report that Grant defeated Gregg's Brigade at Raymond on Tuesday, the 12th. The rebel loss is admitted in the papers to be 700. " The next day Gregg was reinforced by General W. II. I. Walker, of Georgia when he was attacked at Mississippi Springs, and driven towards Jaokson on Thursday. A telegram from Cantón says the Federáis had taken Jackson from the enat, probably by a cavalry movement. General Joseph Johnston ar.rived at Jackson on the 13th and went out towards Vicksburg with three brigades. - He must have been west of Jaekson when the capture was made by onr forees. - The foroo whieh fought Gregg's brigade was frona Port Hudson, and Walker's was from Jordán. Uvery hcrse fit for service in Mississippi is olaimed by the rebel government to inouut their troops. Grant has struck the railroad near Edward's Station. (Signed) S. A. HULBURT. Major-General. Murfreesboro, May 17-10 P. M. The Chattanooga Rebel of tho 16th, says Grant bas taken Jackson, Mississippi. He took it after a hard day's fight. Rebel papers contain the following : " Mobile, May 14. Jackson, Miss., is occupied by the Federáis. We fought all day but could not hold the city." Philadelphia, May 18. The followiug is a special to the Bulletin : Cincinnati, 18th. A letter from Russellville, Ky , states that on Wednesday a party of sixty mounted guerrillas fired on a train near South Union. The guard on tho train returued the fiïe and routed the rebels, with the loss of ono killed and one wounded. The rebels are oollecting a larga oavalry forco south of the Cumberland, and a largo infantry forcé in East Tennessee. Washington, May 19. The official dispatch below was received at headquarters of tho army to-day. "Raymond, Miss., May 14, l via Memphis, 12 P. JU. 18. ' ) 'To Major General H. W. Halleck : " McPherson took this place on the I2th iust. after a brief fight of more than two hours. üur loss is 51 killed and 180 wounded. The enemy's is 75 killed, buriod by us, and 186 prisonerscaptured! bosides the wounded. McPberson is now at Clinton. "Gen. Sherman is on the direct road to Jacksoc. "Gen. McClernand is bringiDg up the rear. (Signed) U. S. GRANT. Major-General Commanding." The President is in reoeipt of a j patch this afternoon from General Hulburt, who telegraphs from Memphis, that information has been receivod there from a citizsn of Jaokson, that the enomy evaeuated Vicksburg on Saturday last, and waa andeavoring to esoape Grant by moving up in a northwesterly direction, betwean Big Black and Yazuo Rivers, towards Lexiagton aod the Mississippi River. Mobile papers of the 14 tb. admit the defeat of Gregg and Walker, but try to break its force by-alleging that reinforoement8 from South Carolina and Tennessee are moviug on Gen. Grant, with the expectation of crushing his army. The following is a telegram from Gen. Hulburt, dated Memphis, receired here to day : " Gtm Grant has taken Jackson, the Capital. Eight thousand to ten thousand mountad men are concentrated near Okolona, threatoning an advance in the direction of the Memphis Railroad." A citizen just. up from Jackson snys the enemy abandoned Vicksburg on Sundiiy, which is twenty miles northwest of Jackson. Cairo, May 20. The steacner Continental, from below, brings news that tbo rebels evacuated Warrenton, after destroying their bat teries. The gunboat Cricket, frora Young's Poiut, vvith goverumout dispatches from Admiral Portar has arrived. Several iron-clads are stationed at various points on Eed Eiver. The rebels have a raft above Alexandria, for the purpose of proteeting their cotton boats, suveral of which aro reported above. Warrenton, Blay 14. To Hon. Gideon Welles, Secretary of the Navy: I have the houor to inforni you that I arrived off the uiouth of the Red Itiver on the morniüg of the 4th inst., and on the 5th took possession of Fort De Russy, about eight miles from the mouth. On tho evening of the 6th I took possession of Alexandria without resistauee. Gen. Bauks arrived in Alexandria on the evening of the 7th, and I tu; ned the city over to him. (Sigued) DAVID Q. POHTEB, Acting Bear Admiral,