San Francisco, August 13. All is quiet in Japan. Immense improvemenis are boing made in Yeddo, inoluding the widening and decpening ot' canals, railwayB,newbarraoks, and a new palooe tor the likado. In the socond battle of the Amencan squadron with the Coreana, the latter had six thousand men miserably aimed with jingalls. Their bulléis all feil short, whili: tlio deadly practico of the American ritti's told fearfnlly on the enemy, ondel thu oovur of i-ank vcgctation and the ihotilder of a hill. ïhu Americana advanced to within ono hundred and twenty yards of the front before the) ciimc into the range of the Core ui muskütry. ïho Coreana resisted desperately to the last, and Lieut. MeKi'e was killed as Uo entered the intrenohiuemts. When the Ainericitns were in the intreuchments the Coreana succunibed A nuuiíjer of prisoners were taken, ineluding the offleer sooond in command, who was badly wounded, the oommander-inchit-f btaving been killed June lüth. The American foree bivouaccd in the forts next day, duinolishing the citadel, and tpik d all the guns. The rleet returned t Boize for anchorage. Two days later the Coreana sent on board a letter filled with the most insulting, abusive language, to whioh no reply was sent. Adiniral llotcers, however, sent to kllOW wiiat he should do with thu prisoners. Two d.iys later lio set taem at Liberty, una sent two messages emhore, but the local uuthority refused thein, saying it was as much as his head was worth to send them, and it was no uso to attempt communication furtliür with the couit. Mr. Low, the American Minister, then sent a formal protest that his ntission w&speacoful, and that the American attaek on theforts was not for the refusol tu negotiate, but because the Coréalas too troacherously ñred oh the boats. The steatner Millut was then dispatched to Shanghai with dispatches t'or Washington. The Alonocacy aud Palos wili teturn to Shanghai to be docked. The rest of the squadron will return to Chofo to await instruetions. Their treapona were wretched, having o'.il Êlre locks, and cutlassets made of soft iron, wliicii lïort Hií! u "i-i i-m iio..]. Tney were dressod in armorof nine thicknesses of cotton, padded so that only a rifl; ball oould penétrate, the swords producing no tífeet. The documenta capturad uhowed that the Corean Ghvorninent had planned the surpriaa of the Amerioftn fleet, and was astonished at the failure of tlio forts to annihilate the foreien vessels at the fint fire The expedition has not aceomplished any ehange in the relations of the two oountries, and Minister Lowe and Aduiirul liogrrs wlll await instiuctions froni Washington be'oiv proceeding with further hostilities. Twrlvc nutive Christians eame alongsidc the Adniiral's fiogship in a junk, ;in:i begged to be taken to Shanghai, and that thi rr the jonk be burned to pixjvbnt its falling into the hands of the nativo authorities who, would thereby discovor Erom what village they oame and punish their relativos. The request was granted.