Seattle, Wyoming, May 18 - The Seattle Lake Shore & Eastern Railway Company entered into a contract last evening for the construction of 225 miles of standard gauge railroad through the Cascade Mountains toward Spokane Falls. This places the whole distance between the two cities under contact and there is great rejoicing all over the Territory. This new contract specifies that the work must be completed within two years from date, which will compel the contractors to employ an army of men and to build from both ends of the line. The cost of this new section is placed at $5,000,000. The country to be traversed is extremely rich in timber, coal, and iron, and on the eatern slope in grain and in general produce.