In view of the common opinion that the distribution of manufac turing depends on the distribution of coal, it is worth while to test this by the strict mathematical method of correlation coefficients. By this method mathematicians determine whether any two sets of phenomena are really related. If one phenomenon varies exactly with the other, as the length of the day varies with the noon-day distance of the sun from the zenith, the correlation coefficient is 1. If there is no relation whatever the coefficient is zero. But suppose two things have a relation like that of the corn crop and the summer rainfall, where the amount of corn depends partly on the rain, but also on other things such as temperature and insect pests. In that case the correla tion coefficient is between one and zero and is expressed as a decimal. Applying this exact method to a comparison between the amount• of coal mined per capita in the various states and the value per capita added to manufactures in 1909, the correlation coefficient is —0.009. This is practically zero, and means that there is no real connection. The presence of coal determines the kind of manufacturing, for heavy iron goods such as steel rails are sure to be manufactured as near the coal as possible, but the coal does not determine the relative amount of manufacturing. The use of coal has indeed increased the total volume of manufacturing enormously but its effect has been as great in New Hampshire or Switzerland as in Pennsylvania or England.
This can be better understood by rearranging column K in Table 31, so that the states stand in order according to the value per capita added by manufacturing in 1919, and then placing opposite each state the amount of coal per capita. The first four states mine no coal what ever. Then comes Michigan, which ranks only twenty-third in coal mining per capita, and Ohio, which ranks twelfth. Although Penn sylvania mines far more coal than any other state, its production per capita is less than that of West Virginia or Wyoming. To the people of those states their coal mines are actually more important than are the far larger mines to the far larger population of Pennsylvania. But West Virginia stands only thirteenth in the amount of manufacturing per person and Wyoming adds less value per capita by manufacturing than any states except New Mexico and the Dakotas. Again, Alabama not only stands fourth in its production of coal per inhabitant, but also has good iron ore. Yet in manufacturing it stands only thirty-eighth. Many other instances might be cited to show the same lack of agreement between the distribution of coal and of manufacturing. Switzerland, Sweden, and Denmark are all examples. Although Denmark is prima rily an agricultural country and has practically no minerals, it has as large a proportion of people engaged in manufacturing as has the state of Pennsylvania with its wonderful supplies of coal. Switzerland, with equally scanty natural resources and with no coal, has a relatively larger manufacturing population than any American state, including even Rhode Island.
The Geographical Relations of Water Power and Manufacturing.— The principles that apply to coal apply also to water power, but with the important difference that hydro-electric power cannot yet be economically transported nearly so far as coal. Four hundred miles
is at present about as far as is advisable, and even at that distance there is much waste. The following table illustrates the matter. Column A shows the distribution of the 28,000,000 horse-power which the Geological Survey estimates to be available in the rivers of the United States by their natural How, exclusive of additional power which may come from reservoirs. Column B gives similar facts for the 54,000,000 available at high water and by means of reservoirs. The Pacific States have far the largest supply because of their high moun tains and abundant rainfall, especially in western Oregon and Washing ton. Then follow the Rocky Mountain States because of their moun tains, the South Atlantic States from Delaware to Florida, and the Middle Atlantic States of New York, Pennsylvania and New Jersey. Column C shows the amount of water power actually available. Here the order is wholly different from columns A and B. New England stands little below the Pacific states, although it comes third from the lowest in actual amount of available water poWer. Column C shows clearly that water power is most fully developed in the northeastern manufacturing region. New England stands highest bocause (1) it be gan to manufacture before coal became the chief source of power; (2) it has no coal; (3) its glacial topography and moderate ruggedness make the development of water power especially easy; (4) it has abundant rain at all seasons; (5) its population is dense; and (6) its people are among the most skillful in utilizing their resources.
In the Middle Atlantic and East North Central States, which together extend from New York to the Mississippi River, the slight importance of the first three reasons partly explains why the water power has been less developed than in New England. On the other hand, since these states contain the country's finest coal and have especially easy natural means of transporting it on the lakes, over the plains, and down the Ohio River, it is surprising that they should have developed their water power so much more fully than any other part of the country except New England. In the West, because of the newness of the country and the sparseness of the population, only a small percentage of the abundant water power in the Mountain and Pacific States has yet been devoted to manufacturing, but a good deal is employed in transportation, lighting, and farm work. The amount used per inhabitant, as appears in column E, is much greater than in New England. The great contrast between New England, with its relatively small supply of potential water power and with about 20 per cent of its people engaged in manufacturing, and the Pacific States, with their enormous potential water power and great use of that power per inhabitant, but with only about 5 per cent of the population engaged in manufacturing, illustrates the fact that the location of water power, like the location of coal, does not determine the general location of either manufacturing or progress. Because the Pacific and Mountain States are inhabited by energetic and capable people they are constantly using their water power more and more fully for manufacturing, but that is a result of their progress quite as much as a cause of it.