United States Surveying Expedition.—The Union Democrat says, a portion of the surveying expedition which left Stockton hist January, under the command of Von Schmidt, arrived in tliis place on Monday last. From Mr. A. C. Bates we learn that the expedition crossed the mountains by the Merced route, and were engaged until April 1st in surveying east of Owen'sLake—since then, one hundred and eighty miles north, in the neighborhood of Mono Lake—running to the Utah line. The expedition have already “ run ? fifteen hundred miles. Indians *were abundant but peaceable. Mr. Bates and four others were dispatched for provisions to this place, [Sonora.] They left Mono Lake on the 2d. and arrived here on the 6th. They were compelled to leave the road, on account of the depth of the snow, and beat their way on the mountain sides. The party suffered greatly fromthe reflection of the sun on the snow. Their eyes and faces were red and swollen, and appeared as though burnt by fire. They reportthe expedition in good health.