The work of connecting Liverpool with Birkenhead by means of a railway tunnel is now an almost certain success. It is probable that the entire cost of the tunnel works will amount to about half a million sterling. The first step was taken about three years ago, when shafts were sunk simultaneously on both sides of the Mersey. The engineers intrusted with the plans were Messrs. Brunlees & Fox, and they have now as their resident representative Mr. A.H. Irvine, C.E. The contractor for the entire work is Mr. John Waddell, and his lieutenant in charge at both sides of the river is Mr. James Prentice. The post of mechanical engineer at the works is filled by Mr. George Ginty. Under these chiefs, a small army of nearly 700 workmen are now employed night and day at both sides of the river in carrying out the tunnel to completion. On the Birkenhead side, the landward excavations have reached a point immediately under Hamilton Square, where Mr. John Laird's statue is placed, and here there will be an underground station, the last before crossing the river, the length of which will be about 400 feet, with up and down platforms. Riverward on the Cheshire side, the excavators have tunneled to a point considerably beyond the line of the Woodside Stage; while the Lancashire portion of the subterranean work now extends to St. George's Church, at the top of Lord street, on the one side, and Merseyward to upward of 90 feet beyond the quay wall, and nearly to the deepest part of the river. When completed, the total length of the tunnel will be three miles one furlong, the distance from wall to wall at each side of the Mersey being about three-quarters of a mile. The underground terminus will be about Church street and Waterloo place, in the immediate neighborhood of the Central Station, and the tunnel will proceed from thence, in an almost direct line, under Lord street and James street; while on the south side of the river it will be constructed from a junction at Union street between the London and Northwestern and Great Western Railways, under Chamberlain street, Green lane, the Gas Works, Borough road, across the Haymarket and Hamilton street, and Hamilton square.