Otherwise the situation on the lower San and in Poland is unchanged. * * * * * _AUSTRO-HUNGARIAN FIELD HEADQUARTERS, (via London,) June 5._--According to information given out by the Austro-Hungarian military authorities to representatives of the press, heavy fighting is now in progress along virtually the entire Galician front, and the general situation is very favorable to the Austro-Germans. A decisive conclusion to the entire Russian campaign in Galicia is in sight. Przemysl's recapture by Austrian and Bavarian troops, according to details received from the front, resulted from the taking of five forts in the northern sector and the simultaneous threatening of the forts on the south and west fronts. With the forts on the north side in the possession of the besiegers, with a Bavarian corps pressing impetuously through the breach against the city, and with the Austrian Tenth Army Corps within storming distance of the southern and western forts, which artillery fire already had reduced sufficiently for attack, the Russians decided to evacuate the town and all the forts except those on the eastern and southeastern sectors. This movement was executed Wednesday night. The Bavarians resumed their attack at dawn on Thursday, and entered Przemysl upon the heels of the retiring Russians. The Austrian Tenth Army Corps simultaneously started toward the west and south fronts, but found the forts there had been evacuated. An attack now is in progress against the forts still held by the Russians, those positions being defended apparently with the object of covering the latter's retirement. "The Russian rear guards," the statement to the press says, "are fighting delaying actions south of the Dniester River against the Austro-German forces advancing from Stry to cover the passage of the river. The Russians north of Przemysl are launching a series of the most desperate attacks against General von Mackensen's army. Here they are making use of new reserves, and at the same time they are exerting heavy pressure against the troops commanded by Archduke Joseph Ferdinand in the triangle between the River San and the River Vistula. "The Russian offensive in Southeastern Galicia, designed to relieve this situation, has been a complete failure." * * * * * _BERLIN, (via London,) June 4.--The following official communication on the Eastern fighting was issued here today:_