A party of United States naval officers have been despatched to the Pacific, to take a survey of the route between San Francisco and China. It is asserted that there are some five hundred islets, shoals, and coral reefs on that route which have never been indicated on a chart; and now that our commerce with China, Japan, and the Indian Archipelago is rapidly increasing, it has become necessary that they should be investigated and delineated. Lieut. Brooke, the inventor of the deep sea sounding lead now in general use in the Navy, is the commander of the expedition, and is accompanied by Lieut. Thorburn, E. M. Kern, the artist who was with the exploring expedition, under Commander Rodgers, to the North Pacific, and several others distinguished for their scientific attainments. After arriving at San Francisco they will proceed in the United States surveying schooner Feni-more Cooper to the field of their duties. ACTIVITY OF INVENTORS.—The warm weather does not depress the genius of our inventors, as we can testify from the business of our own office. During the week ending July 17, we have filed from this office, exclusive of cases filed by our Branch Office at Washington, THIRTY-FIVE applications for patents. The steamship Leviathan has been re-baptized, and is now the Great Eastern again, i