The Secretary of the Interior estimates the total product 'next year,' of our mines of precious metals, at '$100,000,000,' and when our railroad to the Pacific (traversing this region) is completed, his estimate of the 'annual yield' is '$150,000,000.' The mines are declared 'inexhaustible' by the highest authority, and our Nevada silver mines are now admitted to be 'the richest in the world.' The completion of our imperial railroad, now progressing to the Pacific, will carry an immense population to the gold and silver regions, vastly increase the number of miners, diminish the cost of mining, and decrease the price of provisions and supplies to the laborers. When we add to this, the vast and increasing product of our quicksilver mines of California, so indispensable as an amalgam in producing gold and silver, as also the great and progressive improvement in processes and machinery for working the quartz veins, it is now believed that the estimates of our Secretary of the Interior, and Commissioner of the General Land Office, will be exceeded by the result. These mines of the precious metals are nearly all on the public lands of the United States; they are the _property of the Federal Government_, and their intrinsic value _exceeds our public debt_. PUBLIC LANDS.--The United States own an immense public domain, acquired by treaties with France, Spain, and Mexico, and by compacts with States and Indian tribes. This domain is thus described in the Report of the Commissioner of the General Land Office, of November 29th, 1860: 'Of the 3,250,000 of square miles which constitute the territorial extent of the Union, the public lands embrace an area of 2,265,625 square miles, or 1,450,000,000 of acres, being more than two thirds of our geographical extent, and nearly three times as large as the United States at the ratification of the definitive treaty of peace in 1783 with Great Britain. This empire domain extends from the northern line of Texas, the Gulf of Mexico, reaching to the Atlantic Ocean, northwesterly to the Canada line bordering upon the great Lakes Erie, Huron, Michigan, and Superior, extending westward to the Pacific Ocean, with Puget's Sound on the north, the Mediterranean Sea of our extreme northwestern possessions. 'It includes fifteen sovereignties, known as the 'Land States,' and an extent of territory sufficient for thirty-two additional, each equal to the great central land State of Ohio.