Owing to the enormous increase in the population of the city of New York and Brooklyn, and the constant and extensive intercourse between the two cities, it will soon become imperative on the citizens to provide for the conveyance of passengers and goods by other means than the present, for after the lapse of a very brief period of time, the number of inhabitants will extend to such an overwhelming degree that, let the ferry companies adopt what measures they can command to meet the public requirements, their efforts will be futile, and life will be in imminent and perpetual danger. Bridges cannot be erected without impeding the navigation of the river, and it therefore becomes a duty to adopt the only means left us, namely, substituting quite as complete, quite as safe, and a much more pleasant mode of communication. The object of the proposed undertaking is to construct a line of communication under the East river by means of a tunnel, between the cities of New York and Brooklyn, from the foot of Fulton street to a point immediately opposite, or any other part of the river that may be considered most suitable for the public welfare ; to promote a more secure, more speedy, and more comfortable mode of transit for passengers traveling between these two places ; to remove all liabilities to accidents from intense fog, dark nights, and fearful collisions from floating ice, and all other casualties attendant upon the present mode of traffic by steamers during the winter months; and also to provide for the conveyance of the public in such a way that the immense population of New York and Brooklyn (no matter to what extent increased) shall be relieved from all dangers, difficulties, and delays in going to either place at every hour of the day or night. The tunnel should be so constructed that there would be a separate entrance for goods and passengers by cars, and also there should be a passage way for those who preferred walking through, partitioned off by strong walls and buttresses (as in our engraving) from the merchandize road. The merchandize road should be welk paved, and laid on concrete, on the lefthand side of the foot passengers way, of sufficient width to allow ell carts and vehicles of every description a quick passage through. The cars should be propelled by stationary engines, so that all annoyance from condensed steam and noise would be avoided, and the tunnel should be well lighted with gas. The distance could be run in two minutes. The geological formation of the bed of the river, and that part through which the tunnel wouli pass, is mostly rock, and very little difficulty would therefore be encountered in . the excavation to admit the brick work, so 1 that the whole distance could be completed f and opened to the public in eighteen months fffrom the commencement. The width of the merchandize road should be twenty-two feet in the clear ; width for foot passengers, nine feet in the clear; width for cars, twenty-six feet; thickness of the brickwork in arches and side walls, three feet, set in cement ; thickness of inverts, eighteen inches, and between the two arches there should be a span-drell wall about eight feet high from the springing of arches the entire length, which has been provided for in the accorapaning estimate. Also, the ingress and egress of passengers and goods would be effected by si de entrances at any point to be determined upon, the cost of which is provided for in the accompanying estimate.