' »v« , ^ yr’• •I ir' *E3NEW-YORK. THURSDAY, JUNE 2, 1864our pontoon brdge. Cosrra and Dana's brigades drove them off to Hanover Court-house, killing mi nr and! capturing a largo number of prisoner*.The Sixth Corps wu toon at oar heels. Then camethe Second, Eighth and Ninth. In was doomed to disappointment Hie elaborate fortifications wo aid not serve him. Gas.nr irsi on his right Caok, and hamost away to Richmond.8atm day morning Guoa’s division of cavalry was fired Into near Hawis* Shop, Baths* brf fid a was In the advance. The woods seemed aflro with label*, and they soon began to resound with the sharo ▼olleys el our carbines. In a short time DArms' entire brigade was fighting In earnest. Qol. Quaq was ordered to Batiks' support, and the remainder of the division was hotly engaged. Fits Hcan Lai oornmnndfd In person, Ills cavalry corps was all fighting, assisted by a b. lead* of mounted I fre-eater* from South Carolina, comnqajnted by Col. Botlxr. These men had just arrived from toe seaboard, apd admit the warmth of the reception which our troops gave them. Con. splcuoas In the battle were the Fourth ant! Sixteenth Pennsylvania. First New-Jersey, Sixth Ohio andFirst Massachusetts, For a long time these men held Fmauao Lxx back. AH tbo cavalry engaged behaved with valor.We found the rebels strongly entrenched In this wood*, with heavy guns in position ; bat with everr advantage upon their side they were badly bcatee, flying from the field In great confusion, leaving their dead and wounded in our hand*, end orer one hundred prisoners.Ctsoo maintained the contest frora noon till 2 F. M., when Cubtib came lip, formed his squadrons Into Hoe, and charged their works. Griqo's command advanced at the ^atne time with a olwcr. Many a bra re follow fell In this daring nmault. The works were ours. Not an armed rebel could be found for three mites.• The Thirteenth and Sixteenth Pennsylvania, and the Filth add Bercnth Michigan suffered a hoary loss. Cipts. Rod dins and Swam, of the Sixteenth, were wounded. Of the Tenth Pennsylvania, Cnpt. Joins Kum was killed, and Capt. P. Kank, Ltaut*. Srim and McDonald were wounded, al*o Lieut. Bo wax, of tho Fourth Pennsylvania.make a wgy for tho host* of the chosen people of theLord.Wo did not expect, on setting out from the James River, tbat we should get up the Pamunky to White House unmolested by the rebel* or thaix Infernal works. At Fortress Monroe, bow ever. Gen. 8ktb got news authoritatively that Gbaht’s army had crossed the river on Safurday at Hanover Ferry, several miles further up and this lea sons our chances of being attacked. But there !s still•efficient spice of dange/■ to giro zest to theadvance. We learned of lateventlons of ttiha to heard of torpedoes and have that such things are not “ weak In-enemy.” At Fortress Monroe there are harrowing'stories afloat of these tnfernal inventions being scattered about the Pamunky by our Southern brethren without lhot slightest regard to economy, and wo are fast approaching places whero we shsji test the truth o! these suspicions. Ours Is thesecond boat In the line; but if there Is any nervous-nyss It finds on board no expression In words. Gen. Suitr and Several members of his Staff are on the forward deck! within a few feet of mo, conductingthemselves very nonchalantly in view of what might happen. By the by, 1 thlaa Gen. Bumi errs in one thing. He is always at the post or danger. The vicinity of the plLot-hduie, exper anee teaches me, la not the safest place in passing suspected localities. The river at this point Is very narrow. It Is like a stream running through a mountain gorge. The bank «fn the left hand Is perpendicular and nearly a hundred feet Mflh. Oft the crest are two embrasures for rebel guns thoveled out of the stiff red ojay.itThe gnnboaour escort upiiortt (• a length ahead of at. She Isthe river, and by right leads the flset. is he Is commanded by Lieut.-Commander Hindoos. Her bell rings now to slacken speed. Here is a splendid place for mischief, if anv 1* intended, either from guer rillas or torpedoes, If we are not bothered here, I hope to finish this tetter In peace. The brave boys of the jforse, who have been steading all tho trip at their grape-charged guns, ready to blaze away at the first moment, relinquish! their station* and seize muskets. The rest of the transports close in Upon us. A. few moments of susoense. In which f suppose everybody at-ures, all the fleet again movesare evidences of 8nsxnA3i*a visit here tea days since, in plenty of empty hardtack ” boxes, and aeouple of dead horiss, whose speedy burial would b* very desirable. [After finishing the last sentence I gathered myself up from the grata to crush off the little green bags, which were proving a pest, and discovering a stout stake loosely thrust tnto the earth, a few feet off, I attempted to pull It up for a seat* My eye glanced down, and I was saved a piece of sacrilege. The post marked a grave. Its badly written inscription In Ink fold that u BngtJo an Jbrstoh, Company I, Eighth Bliools Regiment,” died Is May, 1662, and was baited there.If ever tho loose earth had been shtped into a mound oyer the body, there is no sign of it sow, and the sergeant's lest resting-place will soon be unknown, like thousands and thousands of others, which make Virginia soil In dee a sacred n—a very Golgotha of honored dust.]Gan. Surra has jusl been riding about to establish his lines. He tells me of a oavaliy man from Gust, who has just come In. Thla man says tbat Giart's cavalry crossed at Ifanovar Ferry on Saturday and the Infantry yesterday. Tbere bad, been fighting, and hard fighting, ever since. Even now 1 hear the boom of heavy guns, and suppose, from tbs rapidity of the reports, that a hard battle is raging. Grant's headquarters are not more than fifteen miles from us, anil to-morrow, at daybreak, If the unloading of •applies and munitions It finished, we shall start on the maroti to meet film.This point will be made secure as a base el supplies, and the Indications at present are that tbs entire Army of the Potomac will be dependent on It, for a bme at leas',Capt. Faxqcqar. or the Engineer Corps, boa given orders for the repair of the railroad bridge at this point, and Lieut. Talvis, with a sufficient force, has got tt nearly into a condition for service* The crewof the gunboat ilortt have enthusiastic ally aided In this work.I have just heard of a tad accident. The reportcomes by one of the transports, that Lieut. Host, com man ding Battery L, Fourth United States Artillery, wlt;i» uroAJifcd by falling overboard on the pAssage un the ilv»r. Hunt was considered one of the best artillery officers In the service. It is hoped that the report of Ins death will prove un'rue.II. J. Weksnloirflle yesterday manting and had not encountered the enemy la force up to that time.Gen. Bnxxroin’i oavalry had had lateral skirmishes with the enemy and completely router) them.Heavy cannonading; waa heard yesterday In the direction of If •ehenicivUte,The highest hopes are entertained by those competent to judge of the situation.Tho Armeilci Case.WABOTirrro*. Wednesday, June 1.The* Pie if dent, in response to an inquiry, today, sent to the Senate all the papers In the Arguelles case on file In the State Department, snd alto a letter of Seoratary Snriin, In which the latter «ay»J “ By the act of Cod|tcss of May 15.1620, the African8 • -trade ti declared to be piracy; and by thetreaty of 1842 with Great Britain, U fi etipouted that they wfll Invite and urge open all Powers the propriety and duty of effectually at once and forever closing all African slave markets.” The Secretary says, there being no treaty of extradition between (he United States and Spate, aor any act of Congress dir acting how fugitives la the Spanish dominions •hell be delivered up, the extradition In tb« As-susllxs cnifl is understood by the State Dr par tenant to have been made in virtue of the law or nations and the Constitution of the Doited States. Although there la a conflict of authorities conoeralrfg the expediency of exercising comity toward a foreign Government, by sarrssdeafnf at* it* request one of Its own subjects charged with the commliitnn of crime within ite territory : and although It may be conceded that there Is no national obligation to make each a sonander upon a demand therefor, unless it is acknowledged by treaty or •tetnie, yet a nation Is never bound to fnrntsh asylum to dangerous criminal* who are offenders against the hum an race ; and It la believed tbat if In any case the comity coaid, with propritty, be orao-t oed, the one which Is understood to have called forth the resold lion of Inquiry of the Senate furnished a just occasion for its exercise.Oar Consul at Havana writes to Beoretary snum on May 23, that on the arrival of Ajuicuijce he waaimmediately lodged in (all, and the next morning wasale,conveyed lo Muio Castle, wife re he sUU remained.