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On the 18th of July, a total eclipse of the sun will give an opportunity for determining the Longitude of the Coast of North America, such as will not occur again for many years.  The determination of Longitude by means of this observation is second only in accuracy to the telegraphic methods, from which so much was expected in case the Atlantic Cable had been successful. The path of the Total Eclipse will be eastward from the mouth of the Columbia River, across Hudson's Bay, leaving this continent at Cape Chidley, the northeastern point of Labrador.  It then crosses the Atlantic, Spain, and Algeria, and passing to the south of Tripoli, leaves the earth at Massowa on the Red Sea.  The Astronomer Royal of England, the Bavaraian Astronomer, and several corps of French observers, will watch the Eclipse in Spain and Algeria.  Nearly a hundred observers will be stationed along the path of the Eclipse there.  The Superintendent of the Coast Survey will provide for observations on the Coast of Oregon.  Without special authority he has no right to send an expedition to the Cape of Chidley.  Such authority Congress may or may not grant.  But the Smithsonian Institution has offered to provide for the equipment of a corps of observers and to contribute $500 in addition.  If the Marine Insurance Companies and the Chamber of Commerce of New-York will contribute the additional $2,000 required, or furnish a small vessel to convey the expedition to the Labrador Coast, we are sure that they would be repaid tenfold in the increased security which the more accurate determination of the Longitude of our coast will give to every one of the thousands of vessels approaching it.  One gentleman, we learn, has already sent $250 to Mr. G.W. Blunt, in behalf of the expedition.