ledo; 28,954,760 bushels of corn chiefly from Chicago and Milwaukee to Buffalo, Ogdensburg, and Ludington; 17,828,717 bushels of oats mainly from Manitowoc, Chicago, Milwaukee, Superior, Duluth, and Gladstone to Buffalo, Ludington, and Frankfort. The Lake trade also included 14,157,662 bushels of barley and smaller quantities of rye and flaxseed; 1,248,891 net tons of flour were shipped chiefly from Milwaukee, Chicago, and Duluth to Buffalo, Erie, and Ludington. Other leading items are pig iron, iron manufactures, salt, coffee, and package freight. One index of Lake freight movements are the gateways between the lakes. In 1909 57,895,149 net tons of freight passed through the Sault Ste. Marie Canal, as compared with 41.390,557 in 1908, and 62,247,670 net tons passed through the Detroit Riv 1900 1906 1907 1908 1909 2,145,876 972,867 31,742 130,126 65,330 3,345,941 $84,123,772 2,385,491 740,983 172,228 164,874 77,331 3,540,907 2,415,548 678,506 143,277 112,570 58,013 3,407,914 63,903,970 2,177,443 614,762 92,831 81,029 85,812 3,051,877 54,511,509 2,031,307 732,125 121,717 84,957 146,430 3,116,536 59,081,572 66,501,417 The east-bound traffic of the Erie Canal consists mainly of grain, lumber, salt, stone, lime, and clay; and west bound it is mostly general merchandise. North bound the Champlain Canal carries chiefly coal, stone, lime, clay, and ice; and south bound wood pulp, lumber, and iron ore. The traffic of the other New York canals consists mainly of farm produce, lumber, coal, and general merchandise. The tonnage of the Erie Canal has declined from 6,673,370 tons in 1872 to 3,116,536 in 1909, and the total tonnage of all the New York canals at present is less than three per cent of the tonnage moving by rail. The tidewater coal canals constitute a second group. About 400,000 ans mainly of coal with certain quan tities of iron and building materials are annually shipped through the Lehigh Canal and the Delaware division. Slightly over 50,000 tons are shipped through the Schuylkill Canal; about 88,000 through the Morris Canal, nearly 400,000 through the Delaware and Raritan, and the Delaware and Hudson has been abandoned. The traffic of all these canals has been declining within recent years. The Lehigh Canal and the Delaware Division are owned by the Lehigh Coal & Navigation Company; the Schuyl kill Canal by the Philadelphia and Reading Railroad; the Morris Canal is leased perpetually to the Lehigh Valley Railroad, and the Delaware and Raritan is leased to the Pennsylvania Railroad for 999 years. The traffic of the Chesapeake and | 842 other vessels, and forty-three Delaware Canal was 816,037 tons in rafts. 1909, and compares favorably with State Canals.-The length, depth, 654,284 in 1908. The canal in 1909 and termini of the leading state moved 2,276 steamers, 1,762 barges, canals are as follows: Federal Canals.-The leading United | gravel, and package freight; on the States Government canals in operation are the Hennepin Canal (Illinois), St. Mary's Falls Canal, St. Clair Flats Canal, Port Arthur Canal (Texas), Morgan Ship Canal (Texas), Galveston and Brozos Canal (Texas), and the various river canals around falls or shoals in the Ohio, Columbia, Tennessee, Cumberland, Mississippi, Monongahela, and other rivers. River Traffic.-The complete traffic statistics of the Allegheny River are not available, but in 1909 the usual quantity of coal, gravel, sand, lumber, timber, and stone were shipped. The traffic of the Ohio River proper consists mainly of coal, but in other respects is various. On the upper Ohio, from Pittsburg to Cincinnati, the traffic consists mainly of coal, logs, sand, middle Ohio, from Cincinnati to Evansville, coal, lumber and timber, grain, tobacco, and other farm products, and on the lower Ohio coal, corn, wheat, groceries, live stock, flour, and tobacco. Omitting duplications the total traffic of the Ohio River and its tributaries is about 20,000,000 tons annually; and that of the Ohio River proper about 11,500,000. The annual tonnage moved on the Columbia River is about 3,500,000 tons, consisting chiefly of grain, flour, lumber, farm produce, logs, machinery, and general merchandise. The Hudson River moves annually about 8,600,000 tons chiefly of building materials, coal, wood, grain, lumber, ice, farm produce, manufactures, and general merchandise. The total traffic on the Delaware River in 1906 aggregated 20,577,000 tons. The leading shipments are coal sand, petroleum, stone, oysters, and fish fertilizers, chemicals, and iron. products; the leading receipts are sand, coal, lumber, petroleum, produce and fruit, chemicals, sugar, grain, railroad ties, and fertilizers. The leading item in the traffic of the Mississippi River is the coal coming from the Ohio River. This traffic in 1908 amounted to about 11,300, 000 tons. Aside from this Ohio River coal traffic the total down-stream traffic between St. Louis and New Orleans aggregated about 400,000 tons, and the up-stream traffic 300, 000 tons. The total river tonnage of St. Louis in 1908 was 365,920 tons The total traffic of the Mississippi River system, excluding the Ohio, was in 1906 reported as 4,304,288 tons. This compares unfavorably with 12,492,555 tons reported in 1889. Aside from coal the leading commodities moved on the Mississippi River are logs, lumber, grain, building materials, iron and steel products, groceries and provisions, cotton, cotton seed, and general merchandise. BIBLIOGRAPHY Statistical Sources American Association of General Pas- Department of Commerce and Labor Labor (Commissioner of Navigation), Annual Report of the Commissioner of Navigation (1909). Washington, 1909. Department of Commerce and Labor (Census Office), Special Report on Street and Electric Railways (1907). Washington, 1910. Ibid., Special Report on Express Business in the United States (1907). Washington, 1908. Ibid., Bulletin No. 21, Commercial Valu- Ibid., Special Report on Telephones and Telegraphs (1902). Washington, 1906. Electric Railway Journal, Annual Statistical Number, Jan. 1, 1910. New York, McGraw Publishing Company, 1910. Inland Waterways Commission, Preliminary Report (1908). Washington, 1908. Interstate Commerce Commission, Twenty-third Annual Report (1909). WashIbid., Statistics of Railways in ington, 1910. the United States (1908). Washington, 1909. the Ibid., Monthly Bulletin of Revenues and Railroad and Warehouse Commission of Railway Age Gazette, Annual Statistical United States Post Office Department, General Bibliography of BARNES, H. C.-Interstate Transporta- (LEVELAND, F. A., and POWELL, F. W.-JOHNSON, E. R., and HUEBNER, G. G. Railroad Promotion and Capitalization in the United States. New York, Longmans, Green & Co., 1909. COLE, W. M.-Accounting and Auditing. Minneapolis and Chicago, Cree Publishing Company, 1910. HANEY, L. H.-Congressional History of Railways in the United States. (2 vols.) Madison, Wis., Democrat Printing Company, 1909-10. Railroad Traffic, and Rates. (2 vols.) New York, D. Appleton & Co., 1911. MCPHERSON, Logan G.-Railroad Freight Rates. New York, Henry Holt & Co., 1909. Transportation in Europe. New York, Henry Holt & Co., 1910. MCVEY, F. L.-Railroad Transportation. Minneapolis and Chicago, Cree Publishing Company, 1910. HATFIELD, H. R.-Modern Accounting.MORRIS, Ray. Railroad Administration. New York, 1909. HOUGH, B. O.-Elementary Lessons in Exporting. New York, Johnston Export Publishing Company, 1909. JOHNSON, E. R.-Elements of Transportation. New York, D. Appleton & Co., 1909. New York, D. Appleton & Co., 1910. PHILLIPS, J. B. Freight Rates and Manufactures in Colorado. Boulder, Colo., University of Colorado, 1909. RANKIN, G. A.-An American Transportation System. New York, G. P. Putnam's Sons, 1909. RAILWAYS OF THE WORLD The Archiv für Eisenbahnwesen | cent., since 1904, and of 16,445 miles, publishes the statistics of the rail- or 2.8 per cent., over 1907, which ways of the world, bringing them down to the end of 1908, or the nearest date of official reports, which for the United States and Canada is June 30 of that year. The data given show the mileage for each country for each of the five years ending with 1908, the increase for the last four years, and the proportion of railway mileage to area and population. The grand total for the world is 611,478 miles, which is an increase of 61,505 miles, or 11.2 per seems moderate progress when we remember that 13,000 miles have been built in the United States in a single year. But it is fully up to the progress of recent years. Of the increase of 61,505 miles since 1904 considerably more than one half was in America, 33,690 miles, and of this total 27,115 miles were in North America. The mileage at the end of 1908 (the United States and Canada to June 30th) was as follows: XXII. MATHEMATICS AND ASTRONOMY MATHEMATICS E. B. WILSON As one of the oldest sciences, clearly somewhat necessary for practical life and considered valuable for mental discipline, mathematics, in its canonical elementary subdivision of arithmetic, algebra, and geometry, has long been taught in essentially unchanged form to school children, and in the colleges a certain amount of analytical geometry and of calculus has been offered in nearly as unchanging form to a few students. In sharp contrast to this fixity of content and generality of distribution of elementary mathematics stands the rapidly increasing domain of higher mathematics to which special periodicals aggregating thousands of pages per annum are devoted, but which is practically unknown and unknowable except to mathematical specialists; indeed even a professional mathematician finds it difficult to read, to say nothing of appreciating, researches in fields remote from those in which he has concentrated his own studies. The International Congresses. It may have been this growing isolation of mathematics as a whole and of the individual mathematician in his science which led to the organization of quadrennial international congresses of mathematicians, meeting for the purpose of interchanging ideas with others in the same or in related fields. The last congress, which met at Rome in 1908, through its designation of Profs. F. Klein (Göttingen), H. Fehr (Geneva), and Sir G. Greenhill (London) to organize and supervise an international commission on the teaching of mathematics, took a step which ultimately may aid materially in modernizing and improving instruction in elementary and collegiate mathematics. There will probably result an even stronger tendency than at present to introduce the fundamental conceptions and methods of differential and integral calculus earlier than is now common. The commissioners for the United States are Profs. D. E. Smith (Columbia), W. F. Osgood (Harvard), and J. W. A. Young (Chicago). Under their direction a large number of associates are preparing reports on various topics, such as: general elementary schools, normal schools, mathematical work in American possessions, colleges, technical schools of collegiate grade, universities, etc. Striking New Work.-Some few years ago the late H. Minkowski (Göttingen), building a mathematical theory upon the researches of H. Lorentz and A. Einstein on electromagnetic theory, set forth and developed the idea that the material universe should be regarded as four dimensional by adding time as a fourth dimension to the usual three dimensions of space. This theory was immediately taken up by many students of mathematics and physics, and the past year has seen the publication of a large number of contributions to the theory. At the present rate of progress it will not be long before the mathematical and physical significance of Minkowski's work. which was unfortunately interrupted by his early death, will be pretty thoroughly understood. A very noteworthy contribution to American mathematics is the monograph Introduction to a Form of General Analysis, by Prof. E. H. Moore (Chicago), in the volume called The New Haven Mathematical Colloquium, published by the Yale University Press (1910). The great breadth of view of the author in this |