Bulletin No. 40.— W, B. No. 471. Issued March 4, 1912, U.S. DEPARTMENT OF AGRICULTURE, 1227 WEATHER, BUREAU. ,03 S5 [Copy 1 BETWEEN THE PRECIPITATION OYER THE WATERSHED 0E THE OHIO RIVER r E AND THE, STREAM-FLOW AT CINCINNATI. J. WARREN SMITH, PBOMESSQR OF METBOEOLOaY. Prepared under direction ol WILLIS L. MOORE, Chief U. S. Weather Bureau. WASHINGTON: GOVERNMENT PRINTING OPMOE. 1913, Mon«'gia^ Bulletin No. 40.— W. B. No. 471. Issued March 4, 1912. U. S. DEPARTMENT OF AGRICULTURE, : WEATHER BUREAU. THE RELATION BETWEEN THE PRECIPITATION OVER THE WATERSHED OF THE OHIO RIVER ABOVE AND THE STREAM-FLOW AT CINCINNATI. J. WARREN SMITH, PROFESSOR OP METEOROLOGY. Prepared under direction of WILLIS L. MOORE, Chief U. S. Weather Bureau. WASHINGTON: GOVERNMENT PRINTING OFFICE 1912. rpHIS PUBLICATION may be pro- -*- cured from the Superintendent of Documents, Government Printing Office Washington, D. C, at 15 cents per copy JUi n? % LETTER OF TRANSMITTAL. United States Department of Agriculture, Weather Bureau, Office of the Chief, Washington, D. C, September 20, 1911. The Secretary of Agriculture, Washington, D. C. Sir: I have the honor to transmit herewith a paper by Prof. J. Warren Smith, of the Weather Bureau, on the Stream Flow of the Ohio River at Cincinnati and Precipitation, and to recommend its publication as a Weather Bureau bulletin, the edition to consist of 2,500 copies. Very respectfully, Willis L. Moore, Chief United States Weather Bureau. Approved. James Wilson, Secretary of Agriculture. (3) Digitized by the Internet Archive in 2011 with funding from The Library of Congress http://www.archive.org/details/relationbetweenpOOsmit STREAM-FLOW OF THE OHIO RIVER AT CINCINNATI AND PRECIPITATION IN THE WATERSHED ABOVE CINCINNATI. INTRODUCTION. In the following paper the relation between the precipitation over the Ohio watershed above Cincinnati and the stream-flow in the Ohio River at Cincinnati is discussed. The period covered is for 50 years, from 1861 to 1910, inclusive. The data are tabulated for each month of each year, for each month of 10-year and 25-year groups of years, and for combinations of months for each year of the entire period. The precipitation data considered were obtained from seven sta- tions in the Ohio River watershed above Cincinnati, the period of observations covering the 50 years from 1861 to 1910, inclusive. The data are complete for the 50 years at Cincinnati, Marietta, and Portsmouth, Ohio. At Lexington, Ky., the records extend from 1861 to 1876 and from 1887 to 1910, all inclusive, while from 1882 to 1886, inclusive, the records at Frankfort, Ky., were used. The record at Pittsburgh, Pa., extends from 1861 to 1866, and from 1872 to 1910, all inclusive, while from 1867 to 1871, inclusive, data from Canonsburg, Pa., were used. The data at Westerville, Ohio, were complete from 1861 to 1901, inclusive, while from 1902 to 1910, inclusive, those for the Ohio State University were used. In the place of North Lewisburg, Ohio, the data for Urbana, Ohio, were used for the years 1909 and 1910. In each instance where data from two stations were used, the places were not far apart, and there is probably no great difference in the precipitation. It is unfortunate that there are no stations with long records in West Virginia or at other points south of the Ohio River. It is quite probable that the means obtained from the seven stations used do not always give the true average precipitation for the Ohio watershed above Cincinnati. Still, it was thought better to use the same stations running through the 50-year period than to consider data from other sources. Chart No. 1 indicates the locations of the stations. For the stream-flow data, instead of considering the average height of the water, we have tabulated the total number of days in each month when the river was between each 10-foot stage. (5) 6 Inasmuch as navigation is satisfactory in the Ohio when the river at Cincinnati is between 10 and 40 feet, we have considered the low- water days as those below 10 feet, and the high- water days as those above 40 feet. The flood stage is 50 feet at Cincinnati, but there is more or less trouble in navigating the stream when the river is above 40 feet because of strong currents, swirls, debris, and, in its season, ice. The work of tabulation has been great, and we have tried to group the data in every possible way to show the relation of the factors under consideration. An effort has been made to make the study exhaustive, plain, and convincing. It seems to the writer that the statements made in the conclusions following are proven beyond dispute, and that the question of increasing flood conditions and increasing low-water periods is fairly settled in the negative, so far as our available stream-flow data can settle it. CONCLUSIONS. 1. River stages at Cincinnati depend upon the precipitation over the whole watershed above that city. 2. There has been a very slight decrease in flood days in recent years, with the same rainfall. 3. The same amount of rainfall causes a better flow of water in the river during the low-water period than formerly. The number of low-water days was 14 per cent less during the past 25 years than during the preceding 25, calculating for the same rainfall. During the 10 years ending with 1910 the tendency for low water, with an equivalent rainfall, was not so great as for any preceding 10-year period for the past 50 years. 4. Floods do not occur at Cincinnati during February and March unless the precipitation for these months is in excess of the normal, except on very rare occasions. The number of flood days increase most rapidly when the precipitation during these months is about 3 inches above the normal or about one-half more than the normal . EXPLANATION AND DISCUSSION OF TABLES. Table No. 1. In this table there is given for each month of each year from 1861 to 1910, inclusive, the total number of days that the river at Cin- cinnati, Ohio, was below 5 feet, between 5 and 5.9 feet, 10 and 19.9 feet, 20 and 29.9 feet, 30 and 39.9 feet, etc., up to the highest water recorded. These figures were obtained from the published daily river reading tables. By an inspection of the table the high and low water months can be quickly determined. For example, in January, 1897, the water did not go above 20 feet during the month, the only January in the 50 years when this was true. On the other hand, the river reading was at no time below 20 feet in January, 1870, 1882, 1889, 1891, and 1907. The river has been above 60 feet on only 6 days in January, and this in 1907. There are some interesting periodicities or combinations indicated. For example, there seemed to be increasing flood conditions in Feb- ruary, 1881 to 1884, and again from February, 1888 to 1891, but in the succeeding years the river was back to below normal height. The river did not go above 20 feet in June frOm 1871 to 1879, inclu- sive. September seems to be a month of extremes; on a few years the river has not gone above 5 feet during the entire month, and in 2 cases the readings were all above 10 feet. Table 1. — Number of days during each month and year when the river reading at Cincin- nati, Ohio, was between the heights indicated, 1861 to 1910. Years. to 4.9 feet. 5 to 9.9 feet. 10 to 19.9 feet. 20 to 29.9 feet. 30 to 39.9 feet. 40 to 49.9 feet. 50 to 60 to 59.9 | 69.9 feet. feet. 70 to 79.9 feet. JANUARY. ; D 1861 -- Days. Days. 15 12 15 16 8 9 26 16 7 Days. 8 6 4 9 14 14 5 6 9 15 4 5 17 10 Days. 6 3 11 Days. 2 4 1 Days. Days. Days. 1862 6 1863 . . . 1864 6 1865 9 8 1866 1867 1868 6 15 6 3 3 1869 1870 4 6 1871 14 11 10 15 10 5 18 7 13 10 13 1 8 1872 1873 4 10 1874 6 1875 5 4 4 1876 9 4 17 6 19 13 2 9 13 12 17 9 9 26 9 17 13 2 2 10 8 4 5 10 1877 4 5 1878 4 1879 12 8 .5 6 2 8 3 5 2 6 5 14 8 4 1880 3 1881 5 1882 23 1883 20 10 11 9 17 12 1884 1885 5 1886 1887 3 1888 4 1889 1890 2 6 6 2 1891 1892 12 24 29 1 12 30 9 2 9 20 14 12 21 25 5 1893 5 1894 1895 5 11 1 10 5 1896 1897 1898 12 10 7 4 13 4 5 17 3 17 9 6 9 5 11 8 5 1899 1900 4 6 1901 1902 5 o 1903 6 2 1904 4 1905 1 1906 9 9 1907 S 5 6 1908 14 21 5 1909 1 o 1910 9 s Table 1. — Number of days during each month and year when the river reading at Cincin- nati, Ohio, ivas between the heights indicated, 1861 to 1910 — Continued. Years. Oto 4.9 feet. 5 to 9.9 feet 10 to 19.9 feet. 20 to 29.9 feet. 30 to 39.9 feet. 40 to 49.9 feet. 50 to 59.9 feet. 60 to 69.9 feet. 70 to 79.9 feet. FEBRUARY. 1861 Days. Bays. Bays. 7 3 Bays. 11 4 Bays. 10. 11 16 Bays. Bays. Bays. Bays. 1802 10 1 1863 1 10 11 : 11 12 | 13 13 11 1864 7 1865 1 4 6 2 1866 1867 2 1 5 23 3 8 7 1868 3 1869 4 10 7 17 21 10 19 3 7 10 7 7 6 23 17 7 5 4 5 2 7 14 3 8 2 1870 1871 1872 9 1873 6 7 16 3 18 3 12 6 1 9 3 2 5 3 7 4 5 2 3 5 1874 1875 4 1876 10 1877 1 1878 1879 4 12 7 2 3 7 11 2 6 1880 4 2 9 9 6 1881 1882 1883 7 11 1884 2 1885 4 17 5 1886 8 1 18 1887 10 1888 3 8 12 18 9 3 1889 7 12 2 1890 10 18 3 8 1891 1892 7 22 4 12 1893 10 11 6 8 1894. . . 5 28 11 4 9 9 8 23 9 1895 1896 '• 13 5 7 7 12 1 5 4 11 12 4 14 12 5 12 21 7 5 18 2 11 3 9 14 26 26 2 11 5 7 12 12 8 1897 6 4 2 1898 1899 ■.. 1900 1901 4 8 1902 4 10 2 4 2 14 1903 1904 16 5 21 11 3 9 7 10 1905 7 3 1906 1907 3 5 9 8 1908 7 1 1 2 4 1909 1910 MARCH. 1861 * 1862 18 23 6 3 1863 1864 13 1865 10 18 9 10 8 3 5 14 5 1866 2 1867 7 10 2 2 12 1868 2 7 1869 1870 1871 1872 5 24 16 7 1873 4 1874 16 ; 8 5 21 11 8 7 13 1875 5 1 3 1876 11 7 7 1877 1 1878 18 11 15 26 10 13 5 S 6 20 9 5 15 18 8 1879 1880 7 1881 1882 6 1883 1884 3 19 15 1 1885 i 4 Table 1. — Number of days during each month and year when the river reading at Cincin- nati, Ohio, was between the heights indicated, 1861 to 1910 — Continued. v™™ to Years. ; 4.9 feet. 5 to 9.9 feet. 10 to 19.9 feet. 20 to 29.9 feet. 30 to 39.9 feet. 40 to 49.9 feet. 50 to 59.9 feet. 60 to 69.9 feet. 70 to 79.9 feet. march— continued. i j) ays- 1886 Days. Days. 18 12 13 14 Days. 7 4 12 17 3 Days. 5 8 6 Days. 1 4 Days. Days. Days. 1887 . . ' 3 1888 1889 1890 4 21 8 7 12 10 12 1891 1892 4 2 8 3 17 19 22 23 17 3 1893 1894 1895 11 11 17 2 13 14 7 8 9 5 5 11 2 10 9 3 6 6 3 7 11 9 5 12 4 7 1896 1897 i2 3 6 2 5 7 1898 13 6 5 16 15 4 3 11 12 13 14 2 8 4 12 9 15 22 8 19 25 12 20 10 12 3 11 6 12 19 17 2 10 12 18 8 8 13 14 4 4 12 8 12 8 16 17 15 14 8 14 17 12 7 8 14 11 8 11 15 29 10 21 6 2 1899 1900 1 2 4 1901 7 1902 11 11 14 11 1 4 13 6 9 7 9 4 8 1903 : . - 1 1904 1 3 6 1905 1906 1907 7 6 2 3 4 1908 1909 6 12 a 1910 . APRIL. 1861 1862 6 1863 12 1 5 2 1864 1865 6 1866 1867 1868 4 2 6 13 1869 1870 1871 18 8 4 4 11 6 9 28 15 13 1872 4 10 15 14 7 4 4 5 1873 1874 6 1875 1876 1 1877 1878 1879 5 2 9 1880 3 3 1881 1882 1 22 1883 13 8 10 2 4 7 9 1884 9 5 8 17 11 22 1 5 1S85 1 1886 4 5 12 1887 1888 1889 1- - * 1890 16 11 8 7 1 6 6 1 1891 1892 1893 5 15 7 13 5 6 10 23 1894 1895... . 9 3 11 2 4 1896 6 1897 1898 2 2 3 2 1899 1900 1901 12 5 14 6 1 3 1 11 5 2 3 5 5 8 1902 8 1903 1904 11 1905 18 6 1906 5 1 1907 1908 5 4 1909 4 24 1910 21464—12- 10 Table 1. — Number of days during each month and year when the river reading at Cincin- nati, Ohio, was between the heights indicated, 1861 to 1910 — Continued. Years. Oto 4.9 feet. 5 to 9.9 feet, 10 to 19.9 feet. 20 to 29.9 feet. 30 to 39.9 feet. 40 to 49.9 feet. 50 to 59.9 feet. 60 to t.,9.9 feet. 70 to 79.9 feet. MAT. 1861 Days. Days. Days. 10 22 16 15 5 22 11 6 12 28 11 23 10 12 21 23 21 9 21 11 21 1 17 25 30 17 10 26 25 Days. 14 7 11 10 9 4 17 10 14 3 10 Days. 7 2 Days. Days. Days. Days. 1862 1863 4 1864 6 9 1865 6 2 1866 5 1867 3 13 5 1868 2 1869 1870 1871 3 8 6 1 1872 1873 12 5 4 8 10 21 9 3 1874 7 6 4 1875 1 1876 ! 1877 t878 1 1879 ! 10 12 2 $880 4 8 13 14 6 1 6 14 2 2 1881 .' i 1882 13 4 1883 . . . 1884 1885 1886 ' 8 4 1887 3 5 1888 1 1889 6 10 1890 14 7' 1891 20 11 5 1 22 31 21 11 2 20 25 12 27 16 17 15 22 10 1892 1 20 10 4 6 9 3 1893 9 2 1894 2 1895 1896 10 1897 ...: 16 29 11 4 1898 1899 1900 6 1901 9 7 2 1 1902. . . 4 12 1903 3 9 7 2 20 19 11 12 4 6 1904 5 3 1905 : 6 1906.. .... 7 1907 | 1 6 4 1908 | 6 7 1909 9 19 14 24 1910 JUNE. 1861 12 1862 1863 6 24 11 1864 19 28 1865 2 1866 2 28 1 3 1867 21 20 18 23 3 18 7 8 7 12 5 1868 1869 1870 2 27 12 23 30 4 15 10 9 25 5 8 1871 . ..... 1872 1873 1874 1875 26 15 20 21 5 20 15 10 13 8 22 1876 1877 1878 1879 1880 5 4 10 14 22 4 1881 3 10 3 1882 1883.' 1884 3885 4 | 11 Table 1. — Number of days during each month and year when the river reading at Cincin- nati, Ohio, was between the heights indicated, 1861 to 1910 — Continued. Years. Oto 4.9 feet. 5 to 9.9 feet. 10 to 19.9 feet. 20 to 29.9 feet. 30 to 39.9 feet. 40 to 49.9 feet. 50 to 59.9 feet. 60 to 69.9 feet. 70 to 79.9 feet. JUNE — continued . 1886 Days. Bays. 2 9 19 Days. 24 15 11 5 24 18 13 26 18 1 21 23 21 30 14 4 14 30 16 24 27 7 26 16 11 Days. 4 6 Days. Days. Days. Days. Days. 1887 . 1888 1889 20 4 12 13 4 1 5 2 1890 1891 1892 4 1893 1894 11 24 6 6 9 1895 5 1896 3 1 1897 1898 1899 1900 16 1901 15 1 9 2 1902 15 1903 1904 4 10 6 1905 1906 3 1907 13 7 3 1908 4 1909 14 17 1910 2 JULY. 1861 31 8 24 13 9 18 28 31 1862 23 7 1863 1864 18 1865 21 10 3 1 3 1866 1867 1868 1869 16 14 15 1870 17 31 11 6 19 1871 1872 20 23 2 13 23 20 9 1873 2 1874 10 1875 4 14 1876 8 11 22 23 14 25 2 2 17 27 6 23 12 1S77 187S 1879 - 8 1880 17 6 18 29 13 2 21 1881 1882 11 1884 1 2 1885 1886 4 1887 8 1888 12 21 13 28 21 10 5 10 2 1889 1890 18 3 10 21 16 24 1 6 25 26 22 4 1891 1892. 1893 1894 . 15 4 1895 3 14 19 6 5 9 25 16 29 19 28 14 20 12 21 20 1896 10 6 4 2 1897 1898 1899 1900 1901 2 15 1902 1903 2 8 1904 4 3 1905 1906 17 1907 11 1908 19 9 5 1909 1 G 1910 12 Table 1. — Number of days during each month and year when the river reading at Cincin- nati, Ohio, was between the heights indicated, 1861 to 1910 — Continued. Years. Oto 4.9 feet. 5 to 9.9 feet. 10 to 19.9 feet. 20 to 29.9 feet. .30 to 39.9 feet. 40 to 49.9 feet. 50 to 59.9 feet. 60 to 69.9 feet. 70 to 79.9 feet. AUGUST. 1861 Days. Days. 11 16 26 3 13 20 30 21 22 9 19 23 12 24 1 IS 14 17 18 21 18 11 20 18 3 14 12 20 10 21 12 28 15 1 31 Days. 20 Days. Days. Days. Days. Days. Days. 1862 15 5 18 1863 1864 10 18 9 1865 ' 1866 2 1 1867 1868 10 9 22 1869 1870 ■-.- 1871 12 1872 8 19 7 16 13 1873 1874 1875 .3 2 4 5 1876... 1877 17 1878 14 13 10 1879 1880 , 1881 13 1882. . . 19 10 4 28 17 1 1883 1 9 1884 18S5... 1880 1887 19 1888 5 21 S 19 3 3 3 1889... 1890 2 1891 . . . 1892 1893 16 30 1894 1895 1890 21 11 18 7 5 17 13 3 5 2 1897 20 189S... 8 5 1899.. 5 2 19 24 14 18 31 31 3 5 5 24 19 14 22 1900 . . . 1901 . 1902... 1903.... 1904 . . . 1905 . . 28 24 22 7 12 1906 . . . 2 4 1907 1908... 1909... 1910... 17 30 30 SEPTEMBER. 1861 7 1 1862 . . . 1863 . 1864... 3 8 7 8 10 19 20 15 16 14 8 12 12 23 18 16 25 6 27 18 12 1865 . . . 22 4 4 1866 5 2 1867... 1868 . 7 7 4 8 4 3 2 1809 1870 . . . 6 15 14 11 22 18 1871 1872 . 1873' . 5 1874... 1875... 1876 . . . 6 9 3 1877... 7 1878 .. 5 6 3 4 1879 8 5 24 1880 . . . 1881.. 1882 30 1883 29 30 1 1884 1885 12 18 13 Table 1. — Number of days during each month and year when the river reading at Cincin- nati, Ohio, was between the heights indicated, 1861 to 1910 — Continued. Years. to 4.9 feet. 5 to 9.9 feet. 10 to 19.9 feet. 20 to 29.9 feet. 30 to 39.9 feet. 40 to 49.9 feet. 50 to 59.9 feet. 60 to 69.9 feet. 70 to 79.9 feet. September— continued . 1886 Bays. 11 30 Days. 19 Days. . Days. Days. Days. Days. Days. Days. 1887. . 1S8S 2 28 24 2 15 13 4 1889. 1890 10 5 1891 17 27 20 2 14 30 13 29 16 13 12 3 22 12 14 16 1 5 30 26 1892 3 5 24 16 1893 5 4 1894 1896 1897 17 1898 1 1899 . 14 17 1900 1901 18 1902 1.27 1903 8 1904 [18 1905 16 14 29 1906 1907 1908 25 1909 1910 3 1 17 OCTOBER. 1861 9 3 2 1862 31 25 1863 6 9 25 5 1864 18 6 17 4 1865 1866 6 3 1867 31 1868 20 24 25 7 7 3 1 1869 1870 6 31 24 23 16 1871 1872 7 1 15 31 16 16 10 1873 3 4 1874 1875 1876 1 15 16 31 20 26 14 1877 1878 5 1879 1880.. 11 5 21 24 3 6 14 1881 1882 10 7 1883 18S4 28 11 17 31 14 188.6 1887 1888 11 24 5 7 15 11 4 1889 1890 12 4 1891 18 28 13 3 15 8 1892 1893 16 1894.. 23 31 1895 1896 2 25 4 1897 31 4 31 27 3 3 10 31 1898 18 4 "5" 1899 1900 3 28 24 17 1 1901 1902 4 4 1904 1905 19 11 31 13 1 1906 1907 18 4 1908 27 15 7 1909 15 1 1910 17 ; 7 14 Table 1. — Number of days during each month and year when the river reading at Cincin- nati, Ohio, was between the heights indicated, 1861 to 1910 — Continued. Years. Oto 4.9 feet. oto 9.9 feet. 10 to 19.9 feet. 20 to 29.9 feet. 30 to 39.9 feet. 40 to 49.9 feet. 50 to 59.9 feet. 60 to 69.9 feet. 70 to 79.9 feet. NOVEMBER. 1861 Days. Bays. Days. 13 3 8 8 14 12 Days. 16 Days. 1 Days. Days. Days. Days. 1862 19 8 22 2 16 1 19 5 23 25 4 17 4 1863 1864 20 1865 1866 17 1867 11 1868 25 7 5 6 13 18 1869 1870 1871 20 1872 1873 8 1874.. 26 1 3 1875 6 8 16 4 5 14 6 30 19 22 10 21 5 16 18 5 1876... 1877 1 3 3 2 1878 1879 20 1880 1881 6 1882 1883 26 4 1884 24 6 1885 29 5 1 7 1886 13 4 1 1887 28 1888 3 11 8 5 17 10 18 4 10 9 4 1889 1890 1891 2 11 19 19 18 23 4 1 11 1892 1893 12 1894 . . . 7 26 1895 1896 ■ 27 11 22 2 1897 8 1898 8 1899 8 6 20 3 11 25 22 17 9 24 12 5 1900 3 1 3 . 7 1 3 1901 1902 1903 . . . 1904 1905 29 13 17 1 5 11 1906... 8 2 9 29 26 4 1907 1908 21 1909 . 1 1910 4 DECEMBER. 1861 22 8 19 12 10 3 10 18 8 30 6 11 5 27 10 24 25 6 15 18 15 25 23 17 22 5 4 1862 23 6 1863 6 11 1 19 4 13 12 1864... 3 7 9 2 5 2 1865 11 1866 1867 8 7 1868... 1869 . . . 11 1870... 1 24 19 1871 . . 1 1872 1 14 1 16 1873 8 4 1874 3 1875 1 4 1876... 7- 1877 . . . 6 11 2 3 1 1878 . 11 5 7 13 3 2 1879 . . . 7 3 1880 1881 2 1882 6 1883 1 2 8 1 6 1884 . . . 4 8 1885 1 ! 15 Table 1. — Number of days during each month and year when the river reading at Cincin- nati, Ohio, loas between the heights indicated, 1861 to 1910 — Continued. Years. Oto 4.9 feet. 5 to 9.9 feet. 10 to 19.9 feet. 20 to 29.9 feet. 30 to 39.9 feet. 40 to 49.9 feet. 50 to 59.9 feet. 60 to 69.9 feet. 70 to 79.9 feet. decem b er— continued . 1886 Days. Days. Days. 15 Days. 16 Days. Days. Days. Days. Days. 1887 4 27 1888 26 4 24 21 13 22 20 7 16 23 22 9 8 20 12 9 1 7 13 15 5 8 13 5 27 1889 1890 5 10 2 1891 1892 18 2 11 22 1893 ... 7 1894 1895 1 1 15 8 6 7 10 4 10 1 1896 1897 1898 3 1899 15 9 1900 3 7 2 1 1901 i 1902 7 1903 21 6 1904 ; 24 1905 - 16 9 12 7 9 ' 4 1 1906 1907 1908 12 14 23 16 1909 1910 : 2 Table No. 2. This table gives the average precipitation for the watershed for each month, together with the averages for each 10 years, for each 25 years, and for the whole 50 years. Table 2. — Average j)recipitation in the Ohio watershed above Cincinnati, 1861 to 1910, inclusive. Years. Jan. Feb. Mar. Apr. May. June. July. Aug. Sept. Oct, Nov. Dec. An- nual. 1861 In. 2.5 5.4 6.2 1.8 2.6 3.5 2.4 3.1 2.9 6.2 2.1 0.9 2.5 4.2 1.7 6.1 2.9 3.0 3.0 4.3 2.9 5.9 2.9 3.8 5.3 3.7 2.7 4.7 3.8 In. 2.0 3.1 3.5 1.4 2.4 2.5 5.0 1.2 2.9 3.1 2.7 1.9 3.6 4.1 1.8 2.5 0.7 1.7 2.8 4.2 3.4 5.3 7.3 6.1 2.3 1.8 7.3 1.8 1.6 In. 2.3 4.6 3.6 2.6 5.0 3.7 5.0 5.3 4.2 4.2 2.6 1.5 3.1 3.5 4.0 3.8 5.3 3.0 4.3 3.8 3.8 4.8 2.9 4.1 1.0 3.3 .2.1 4.3 1.3 In. 4.5 5.6 2.0 2.5 4.5 2.7 2.7 3.6 2.9 2.5 2.0 4.7 2.9 5.2 1.7 2.7 2.7 2.4 1.0 5.5 2.4 2.9 4.2 2.5 3.6 3.0 5.1 2.1 2.0 In. 5.0 3.2 2.4 3.2 7.3 1.3 4.0 5.5 4.6 1.9 2.8 2.9 3.8 1.3 3.2 2.6 2.3 2.6 2.2 3.2 2.2 7.7 5.0 4.0 3.7 5.0 3.6 3.7 3.5 In. 3.5 3.3 2.7 2.4 4.3 4.5 3.2 4.8 3.9 3.7 3.3 2.7 3.5 2.8 5.0 3.5 5.6 3.9 4.3 4.8 4.4 5.5 4.6 2.8 3.6 4.2 3.5 2.5 3.9 In. 3.5 3.6 2.4 1.5 5.8 5.5 3.9 3.1 4.5 4.4 3.0 6.2 5.7 5.1 8.9 7.0 4.0 4.2 4.4 2.9 4.1 3.0 3.7 3.0 2.3 3.4 3.5 5.2 5.7 In. 4.5 2.2 2.9 5.4 3.8 3.9 2.8 4.8 2.2 3.1 4.4 3.1 3.8 2.4 3.1 3.5 1.8 3.2 6.1 4.6 1.6 5.0 1.6 1.5 5.8 3.4 2.4 8.1 1.3 In. 3.3 1.1 2.1 4.9 5.9 10.1 0.8 7.6 4.0 1.4 1.3 1..6 2.3 2.7 2.1 5.6 2.2 4.2 2.8 2.6 2.5 3.3 2.3 3.9 2.6 3.6 2.5 2.1 4.0 In. 3.6 1.7 3.7 2.4 1.5 3.2 3.0 1.5 2.0 2.9 1.8 2.5 4.5 0.5 2.6 2.4 1.9 2.7 0.8 2.3 4.7 1.8 5.4 1.4 3.6 1.1 0.5 4.1 2.1 In. 4.0 2.9 2.5 4.4 0.9 4.1 2.1 2.0 3.6 1.8 2.7 1.0 2.1 3.9 4.3 2.4 3.5 3.2 3.2 3.0 3.6 1.6 3.5 1.4 2.6 4.6 2.6 4.5 4.7 In. 1.2 3.1 3.2 3.7 4.8 2.2 4.2 2.2 3.1 2.3 2.6 2.5 5.0 3.5 3.6 1.4 2.4 3.6 4.7 3.2 5.0 1.9 4.5 4.1 1.8 2.5 2.7 1.5 2.5 In. 39.9 1862 39.8 1863 37.2 1864 36.2 1865 48.8 1866 47.2 1867 39.1 1868 1869 44.7 40.8 1870 37.5 1871 31.3 1872 31.5 1873 42.8 1874 39.2 1875 1876 42.0 43.5 1877 1878 35.3 37.7 1879 39.6 1880 44.4 1881 40.6 1882 48.7 1883 47.9 1884 38.6 1885 38.2 1886 39.6 1887 38.5 1888 44.6 1889 36.4 16 Table 2. — Average precipitation in the Ohio watershed above Cincinnati, 1861 to 1910, inclusive — Continued . Years. Jan. Feb. Mar. Apr. May. June. July. Aug. Sept. Oct. Nov. Dec. An- nual. 1890 In. 5.3 3.4 2.4 2.9 2.5 5.0 1.6 2.1 6.7 4.1 2.5 1.6 2.4 2.3 2.6 2.0- 2.5 7.4 1.6 1.2 4.8 In. 5.9 4.9 3.1 5.4 3.7 0.7 2.6 5.3 2.1 2.7 3.2 1.1 1.1 5.7 2.1 1.7 1.6 1.2 4.6 5.9 4.3 In. 6.4 5.1 3.0 2.0 2.2 2.4 4.1 6.0 7.2 5.7 2.2 2.6 3.1 4.2 5.9 3.5 5.3 5.8 6.0 3.0 0.3 In. 3.3 2.2 4.3 6.5 3.0 2.4 1.9 4.0 2.3 1.8 1.8 4.3 2.2 3.4 2.9 3.2 1.6 2.8 4.1 4.6 2.9 In. 4.9 2.2 5.2 4.4 3.6 2.1 3.1 3.9 4.5 4.2 2.5 3.7 3.2 2.6 3.1 6.0 2.3 3.3 4.7 4.2 4.3 In. 4.5 4.9 4.8 4.0 3.0 2.8 4.3 3.1 3.9 3.4 2.7 4.7 6.8 3.9 3.2 4.4 4.1 4.6 2.3 6.0 3.2 In. 2.3 4.8 4.2 3.0 1.9 2.2 9.1 5.5 4.2 3.6 3.9 2.4 3.1 3.2 2.6 3.4 5.2 6.1 3.6 4.1 3.7 In. 5.1 3.1 3.0 2.0 2.8 2.9 3.7 2.4 4.2 2.6 3.9 3.5 1.7 2.1 2.2 4.6 4.5 2.9 2.8 2.8 2.1 In. 5.6 1.8 3.0 2.2 2.9 l'l 4.8 1.0 2.7 2.7 1.3 2.3 3.4 1.2 1.4 3.2 3.3 2.6 0.4 2.0 4.6 In. 3.9 1.6 0.5 4.5 1.5 1.1 1.8 0.4 4.0 2.0 1.6 0.6 2.4 2.2 1.1 4.7 2.1 2.2 1.1 2.3 3.7 In. 2.6 4.8 2.6 2.3 1.9 3.8 3.1 6.3 3.1 1.9 5.0 1.4 2.7 2.1 0.3 2.7 2.9 2.1 1.1 1.6 1.4 In. 3.5 2.4 2.0 2.6 3.4 3.6 1.7 3.4 2.7 3.0 1.7 4.0 4.8 1.8 3.3 2.8 3.9 2.9 2.0 2.6 2.7 In. 53.3 1891 41 2 1892 38.1 1893 41.8 1894 32 4 1895 30.1 1896 41.8 1897 43.4 1898 47 6 1899 37.7 1900 32 3 1901 32.2 1902 36.9 1903 34.7 1904 30.7 1905 1906 42.2 39.3 1907 43.9 1908 1909 34.3 40.3 1910 38.0 3.40 3.18 3.78 3.15 3.63 3.91 4.11 3.34 2.98 2.35 2.85 3.00 39.68 1861-1870 3.66 3.07 4.10 3.32 2.84 2.71 2.60 4.28 3.37 2.93 4.05 3.49 3.40 3.99 3.97 3.35 3.08 3.11 3.02 3.20 3.84 2.69 4.33 3.57 3.74 3.63 3.94 3.95 3.69 4.32 3.82 5.14 3.62 4.24 3.74 3.56 3.60 3.58 3.06 2.92 4.12 2.74 3.24 2.35 2.44 2.55 2.20 2.86 1.90 2.24 2.83 2.93 3.17 3.48 1.83 3.00 3.25 3.00 2.65 3.08 41.12 1871-1880 38.73 1881-1890 42.64 1891-1900 38.64 1901-1910 37.25 1861-1885 3.52 3.27 3.10 3.26 3.68 3.88 3.20 3.11 3.52 3.75 3.86 3.95 4.23 4.00 3.48 3.20 3.33 2.63 2.58 2.12 2.81 2.88 3.19 2.80 40.50 1886-1910 38. 85 Table No. 3. This table shows the departure of the monthly precipitation from the normal for each month and the departure of each 10-year and each 25-year average from the normal. Table 3. — Departure of monthly precipitation from normals, Ohio watershed above Cincinnati, Ohio, 1861 to 1910, inclusive. Years. Jan. Feb. Mar. Apr. May. June. 1 Jul y. Aug. Sept. Oct. Nov. In. Dec. An- nual. In. In. In. In. In. In. In. In. In. In. In. In. '1861 :. -0.9 -1.2 -1.5 +1.3 +1.4 -0.4 -0.6 +1.2 +0.3 +1.2 +1.2 -1.8 + 0.2 1862 +2.0 -0.1 +0.8 +2.4 -0.4 -0.6 -0.5 -1.1 -1.9 -0.7 +0.1 +0.1 + 0.1 1863 +2.8 +0.3 -0.2 -1.2 -1.2 -1.2 -1.7 -0.4 -0.9 +1.3 -0.3 +0.2 -2.5 1864 -1.6 -1.8 -1.2 -0.7 -0.4 -1.5 -2.6 +2.1 +1.9 ±0.0 +1.6 +0.7 -3.5 1865 -0.8 -0.8 +1.2 +1.3 +3.7 +0.4 +1.7 +0.5 +2.9 -0.9 -1.9 + 1.8 + 9.1 1866 +0.1 -0.7 -0.1 -0.5 -2.3 +0.0 +1.4 +0.6 +7.1 +0.8 -1.3 -0.8 + 7.5 3867 -1.0 +1.8 +1.2 -0.5 +0.4 -0.7 1-0.2 -0.5 -2.2 +0.6 -0.7 +1.2 - 0.6 1868 -0.3 -2.0 +1.7 +0.4 +1.9 +0.9 -1.0 +1.5 +4.6 -0.9 -0.8 -0.8 + 5.0 1869 -0.5 -0.3 +0.4 -0.3 +1.0 ±0.0 +0.4 -1.1 +1.0 -0.4 +0.8 +0.1 + 1.1 1870 +2.8 -0.1 +0.4 -0.7 -1.7 -0.2 +0.3 -0.2 -1.6 +0.5 +1.0 -0.7 - 2.2 1871 -1.3 -0.5 -1.2 -1.2 -0.8 -0.6 -1.1 +1.1 -1.7 -0.6 -0.1 -0.4 - 8.4 1872 -2.5 -1.3 -2.3 +1.5 -0.7 -1.2 +2.1 -0.2 -1.4 +0.1 -1.8 -0.5 -8.2 1873 -0.9 +0.4 -0.7 -0.3 +0.2 -0.4 +1.6 +0.5 -0.7 +2.1 -1.7 +2.0 + 3.1 1874 +0.8 +0.9 -0.3 +2.0 -2.3 -1.1 +1.0 -0.9 -0.3 -1.9 +1.1 +0.5 -0.5 1875 -1.7 -1.4 +0.2 -1.5 -0.4 +1.1 +4.8 -0.2 -0.9 +0.2 +1.5 +0.6 + 2.3 1876 +2.7 -0.7 ±0.0 -0.5 -1.0 -0.4 +2.9 +0.2 +2.6 ±0.0 -0.4 -1.6 + 3.8 1877 -0.5 -2.5 +1.7 -0.5 -1.3 +1.7 -0.1 -1.5 -0.8 -0.5 +0.7 -0.6 -4.4 1878 -0.4 -1.5 -0.8 -0.8 -1.0 ±0.0 1+0.1 -0.1 +1.2 +0.3 +0.4 +0.6 - 2.0 1879 -0.4 -0.4 +0.5 -2.2 -1.4 +0.4 j+0.3 +2.8 -0.2 -1.6 +0.4 +1.7 - 0.1 1880 +0.9 +1.0 ±0.0 +2.3 -0.4 +0.9 |-1.2 +1.3 -0.4 -0.1 +0.2 +0.2 + 4.7 1881 -0.5 +0.2 ±0.0 -0.8 -1.4 +0.5 '±0.0 -1.7 -0.5 +2.3 +0.8 +2.0 + 0.9 1882 +2.5 +2.1 +1.0 -0.3 +4.1 +1.6 1-1.1 + 1.7 +0.3 -0.6 -1.2 -1.1 + 9.2 1S83 -0.5 +4.1 -0.9 +1.0 +1.4 +0.7 -0.4 -1.7 -0.7 +3.0 +0.7 +1.5 + 8. 17 Table 3. — Departure of monthly precipitation from normals, Ohio watershed above Cincinnati, Ohio, 1861 to 1910, inclusive — Continued. Years. 1884. 1885. 1886. 1887. 1888. 1S89. 1890. 1891. 1892. 1893. 1894. 1895. 1896. 1897. 1898. 1899. 1900. 1901. 1902. 1903. 1904. 1905. 1906. 1907. 1908. 1909. 1910. 1861-1870. 1871-1880. 1881-1S90. 1891-1900. 1901-1910. Jan. In. +0.4 +1.9 +0.3 -0.7 +1.3 +0.4 +1.9 ±0.0 -1.0 -0.5 -0.9 +1.6 -1.8 -1.3 +3.3 +0.7 -0.9 -1.8 -1.0 -1.1 0.8 -1.4 -0.9 +4.0 -1.8 —2 2 +U +0.3 -0.3 +0.7 -0.1 -0.6 1861-1885 +0.1 1886-1910 -0.1 Feb. Mar. In. +2.9 -0.9 -1.4 +4.1 -1.4 -1.6 +2.7 +1.7 -0.1 +2.2 +0.5 -2.5 -0.6 +2.1 -1.] -0.5 ±0.0 -2.1 -2.1 +2.5 1.1 -1.5 1.6 2.0 +1.4 +2.7 +1.1 In. +0.3 -2.8 -0.5 -1.7 +0.5 -2.5 +2.6 + 1.3 -0.8 -1.8 -1.6 -1.4 +0.3 4-2.2 +3^4 +1.9 -1.6 -1.1 -0.7 +0.4 +2.1 -0.3 +1.5 +2.0 +2.2 -0.8 -3.5 Apr. | May. June. In. In. -0.7 +0.4 +0.4 +0.1 -0.2 +1.4 +1.9 +0.0 -1.1 +0.1 -1.2 -0.1 +0.1 +1.3 -1.0 +1.1 +3.3 -0.2 -0.8 -1.3 +0.8 1.4 +1.6 +0.8 ±0.0 -1.4 -0.5 +0.3 0.5 '+0.2 -0.6 -0.3 +1.1 -0.4 +0.2 +0.2 0.3 '+0.2 0.1 +0.1 -0.1 -0.1 0.9 +0.9 1.4 1+0.6 -1.1 +0.1 -0.4 -1.0 -0.5 -1.4 +1.1 -1.0 +0.2 -0.3 ±0.0 +2.4 -1.6 !-1.3 -0.4 -0.3 +0.9 |+1.1 +1.4 j+0.6 -0.3 1+0.7 +0.2 +0.2 -0.1 -0.9 -0.1 I+0.7 -0.2 ±0.0 ±0.0 +0.1 ±0.0 1-0.1 -0.1 1+0.2 In. -1.1 -0.3 +0.3 -0.4 -1.4 ±0.0 +0.6 +1.0 +0.9 +0.1 -0.9 -1.1 +0.4 -0.8 iO.O -0.5 -1.2 +0.8 +2,9 ±0.0 -0.7 +0.5 +0.2 +0.7 -1.6 + 2.1 -0.7 July. In. -1.1 -1.8 -0.7 -0.6 +1.1 +1.6 -1.8 +0.7 +0.1 -1.1 -2.2 -1.9 +5.0 +1.4 +0.1 0.5 -0.3 -1.7 -1.0 -0.9 -1.5 -0.7 +1.1 +2.0 -0.5 ±0.0 -0.4 -0.3 1-0.3 ±0.0 +1.0 +0.1 -0.5 -0.2 i+0.1 +0.4 -0.4 ±0.0 +0.1 +0.1 -0.1 Aug. In. -1.8 +2.5 +0.1 -0.9 +4.8 -2.0 +1.8 -0.2 -0.3 -1.3 -0.5 -0.4 +0.4 -0.9 +0.9 -0.7 +0.6 +0.2 -1.6 -1.2 -1.1 +1.3 +1.2 -0.4 -0.5 -0.5 -1.2 +0.3 +0.3 +0.3 0.2 0.4 +0.2 0.1 Sept. Oct. In. +0.9 -0.4 +0.6 -0.5 In. +1.0 -1.2 -1.3 -1.9 -0.9 1+1.7 +1.0 -1.3 +2.6 '+1.5 -1.2 -0.8 ±0.0 -0.8 -0.1 -1.9 +1.8 -2.0 -0.3 -0.3 -1.7 -0.7 +0.4 -1.9 +2.1 -0.9 -1.3 -0.6 -2.0 +1.6 -0.4 -0.8 -1.8 ±0.0 -1.8 ,-0.2 -1.6 -1.3 +0.2 +0.3 -0.4 -2.6 -1.0 +1.6 +2.3 -0.3 -0.2 -1.3 -0.1 +1.3 +1.1 -0.3 +0.2 0.6 0.6 +0.4 0.4 +0.2 -0.2 +0.5 -0.5 -0.2 +0.2 -0.3 Nov. In. -1.4 -0.2 +1.-8 -0.2 +1.7 +1.9 -0.2 +2.0 -0.2 -0.5 Dec. In. +1.1 -1.2 -0.5 -0.3 -1.5 -0.5 +0.5 -0.6 -1.0 -0.4 0.9 +0.4 +1.0 +0.6 +0.3 +3.5 +0.3 +0.9 +2.2 -1.4 -0.1 -0.7 -2.5 -0.1 ±0.1 -0.7 -1.7 -1.2 -1.4 ±0.0 +0.1 +0.4 +0.7 1.0 ±0.0 +0.1 1.3 +0.4 -0.3 ±0.0 -1.3 + 1.0 +1.8 -1.2 +0.3 -0.2 +0.9 -0.1 -1.0 -0.4 -0.3 ±0.0 +0.2 ±0.0 -0.4 +0.1 +0.2 -0.2 An- nual. In. - 1.1 -1.5 -0.1 -1.2 + 4.9 - 3.3 + 13.6 + 1.5 - 1.6 + 2.1 - 7.3 - 9.6 + 2.1 + 3.7 + 7.9 - 2.0 -7.4 -7.5 - 2.8 - 5.0 -9.0 + 2.5 - 0.4 + 4.2 -5.4 + 0.6 -1.7 + 1.5 - 1.3 + 3.0 - 1.0 -2.7 + 0.8 - 0.8 Table No. 4. The number of days that the river stages were between each 5 or 10 feet for each month and the year for each 10-year period is shown in Table 5, together with the totals for the 50 years and the means for each 10-year period. The yearly averages can be obtained by dividing the 10-year averages by 10. If it is true that the cutting away of the forests has increased flood conditions and intensified low-water periods, it seems to the writer that there would be a regular increase in the low-water days in the months of July, August, and September, and that this increase would appear in the 10-year periods in the table. On the contrary, there were only 64 days from 1901 to 1910, inclusive, when the river was between 5 and 10 feet during the month of July, as compared with 179 days from 1861 to 1870, inclusive. In October there were only 96 days in the 10 years from 1901 to 1910, inclusive, when the river was below 5 feet, as compared with 177 days in the 10 years from 1871 to 1880, inclusive. The high-water days should show a regular increase also during the months from January to April, inclusive, but such is not the case. 21464—12 3 18 Table 4. — Total number of days in each month with river readings between values indicated at Cincinnati, 10-year 'periods, 1861 to 1910, inclusive. TO 4.9 FEET. Years. Jan. Feb. Mar. Apr. May. June.j July. 1 Aug. Sept. Oct. Nov. Dec. Total. 1861-1870 Days. Days. Days. Days. Days. 6 Days. 8 5 Days. 18 18 11 19 Days. 41 29 42 53 17 Days. 88 100 124 96 73 Days. 93 177 113 193 96 Days. 30 66 65 68 84 Days. 8 1 8 1 36 Days. 286 1871-1880 391 1881-1890 363 1891-1900 435 1901-1910 306 5 TO 9.9 FEET. 1861-1870 1871-1880 1881-1890 1891-1900 1901-1910 6 10 9 SI 179 171 97 114 121 48 34 14 6 4 46 160 145 167 159 107 79 63 9 7 4 1 10 50 132 147 68 108 48 41 29 38 72 154 150 181 62 134 79 14 22 ' 23 26 64 164 141 142 124 80 836 984 625 10 TO 19.9 FEET. 1861-1870 1871-1880 1881-1890 1891-1900 1901-1910 124 86 34 29 147 167 94 98 82 72 95 140 102 93 72 116 162 135 127 100 22 22 133 147 89 49 79 95 172 161 135 112 89 58 100 171 128 81 48 89 149 185 115 84 23 46 80 161 137 104 34 71 147 175 204 123 86 71 71 103 1,168 1,231 1,310 1,189 1,326 20 TO 29.9 FEET. 1861-1870 1871-1880 1881-1890 1891-1900 1901-1910 90 99 116 152 99 44 19 21 22 53 71 96 106 122 104 74 5 6 3 12 4 17 54 119 67 105 101 78 66 30 6 14 23 63 65 74 82 111 128 90 34 16 11 9 15 64 86 SO 86 133 92 76 42 6 1 17 54 786 603 737 634 673 30 TO 39.9 FEET. 1861-1870 1871-1880 1881-1890 1891-1900 1901-1910 64 59 99 70 45 8 7 1 36 50 43 94 ■61 21 14 2 7 5 32 56 45 69 69 39 23 2 3 5 8 24 17 42 67 104 55 22 4 4 10 3 6 40 45 69 58 26 18 4 29 389 329 360 ,317 289 40 TO 49.9 FEET. 1861-1870 1871-1880 1881-1890 1891-1900 1901-1910 14 21 44 43 8 4 2 7 23 23 16 15 7 4 13 37 55 38 22 11 8 32 30 31 23 9 2 2 1 22 25 80 25 21 5 8 143 101 171 130 186 50 TO 59.9 FEET. 1861-1870 1871-1880 1881-1890 1891-1900 1901-1910 12 7 17 6 2 6 4 5 39 15 12 5 20 14 5 2 5 6 30 13 1 60 TO 69.9 FEET. 1861-1870 1871-1880 1881-1890 1891-1900 1901-1910 18 2 2 6 4 0. 19 Table 4. — Total number of days in each month ivith river readings between values indicated at Cincinnati, 10-year periods, 1861 to 1910, inclusive — Continued. 70 TO 79.9 FEET. Years. Jan. i Feb. Mar. Apr. May. June. July. Aug. Sept. Oct, Nov. Dec. Total. 1861-1870 Days. Days.iDays. j 2 Days. • Days. Days. Days. Days. Days. Days. Days. Days. Days. 1871-1880 1881-1890 1 2 1891-1900 1901-1910 Totals for 50 years and means for each 10-year period. TO 4.9 FEET. 13 3 66 13 182 36 481 96 672 134 313 63 54 11 1 781 356 5 TO 9.9 FEET. 92 18 53 11 17 3 5 1 126 25 389 78 674 135 799 160 646 129 533 107 506 101 309 62 4,149 830 10 TO 19.9 FEET. 580 116 413 83 267 53 400 80 777 155 S24 165 675 135 517 103 302 60 269 54 479 96 722 144 6,225 1,244 20 TO 29.S FEET. Sums Means 464 93 434 87 540 108 619 ! 433 124 87 235 47 113 23 26 5 47 9 59 12 165 33 308 62 3,433 687 30 TO 39. 1 FEET. 252 50 259 52 435 85 313 63 153 31 45 9 20 4 15 3 20 4 15 3 37 7 120 1,685 24 337 40 TO 49.£ FEET. Sums Means 128 26 154 31 209 42 128 1 56 26 ' 11 5 1 2 6 1 4 1 2 37 7 731 146 50 TO 59.£ FEET. 28 6 76 15 76 15 36 7 5 1 5 1 226 45 60 TO 69.S FEET. 6 1 20 4 6 1 3? 6 70 TO 79.{ FEET. 2 2 Means 20 Table No. 5. This table shows the number of days the river at Cincinnati was between each 5 or 10 feet for each month and the year for the two 25-year periods, 1861 to 1885 and 1886 to 1.910, all inclusive. It will be seen that there was very little difference between the total number of flood days of the two periods during the months of January and February, while during the months of March and April the greater number occurred in the second period. It will also be seen that the low-water days were in excess in the first period during the months from June to September, inclusive, while during the second period the low-water days were in excess in November and December. Flood conditions are not the products of precipitation extending over any considerable period of time, but are, as a rule, the results of abnormal precipitation within a comparatively short time, and there is therefore no direct relation between the average annual precipita- tion and the number of flood days and the intensity of flood con- ditions. On the other hand, low-water periods are usually the results of prolonged periods of deficient precipitation, and the relation between the two is therefore quite clearly marked. Table 5. — Total number of days in each month with river readings between values indicated at Cincinnati, 25-year periods, 1861 to 1910, inclusive. 0.0 TO 4.9 FEET. Years. Jan. Feb. Mar. Apr. May. June. July. Aug. Sept. Oct. Nov.. Dec. Total. 1861-1885 Days. Days. Days. Days. Days. Days. 8 5 Days. 39 27 Days. 93 89 Days. 271 210 Days. 335 337 Days. 120 193 Days. 13 41 Days. 879 1886-1910 902 5 TO 9.9 FEET. 1861-1885 1886-1910 45 47 28 25 10 7 5 57 69 261 128 397 277 408 391 275 371 280 253 242 264 125 184 2,133 2,016 10 TO 19.9 FEET. 1861-1885 275 305 203 210 128 139 181 219 403 385 374 439 289 386 259 258 152 150 125 144 301 178 389 333 3,090 1886-1910 3,135 20 TO 29.9 FEET. 1861-1885 234 230 228 206 300 240 317 302 215 218 81 144 36 77 4 22 33 14 26 33 81 84 137 171 1,692 1886-1910 1,741 30 TO 39.9 FEET. 1861-1885 138 114 120 139 239 196 171 141 79 74 16 ' 14 29 6 2 13 15 5 7 8 6 31 83 37 890 1886-1910 793 40 TO 49.9 FEET. 1861-1885 65 63 70 84 81 128 70 58 19 37 5 2 4 2 4 2 28 9 343 1886-1910 388 21 Table 5. — Total number of days in each month with river readings between values indicated at Cincinnati, 25-year periods, 1861 to 1910, inclusive — Continued. 50 TO 59.9 FEET. Years. Jan. Feb. Mar. Apr. May. June. July. Aug. Sept. Oct. Nov. Dec. Total. 1861-1885 Days. 18 10 Bays. 37 39 Days. 17 59 Days. 6 30 Days. 2 3 Days. Days. Days. 5 Days. Days. Days. Days. Days. 85 1S86-1910 141 60 TO 69.9 FEET. 1861-1885 6 18 2 6 ! o 1 18 1886-1910 14 70 TO 79.9 FEET. 1861-1885 2 n 2 1886-1910 Table No. 6. In this table is given the average precipitation and the average number of days the river at Cincinnati was above 50 feet, below 5 feet, and below 10 feet for each month and the year for each 10-year and each 25-year period. Table 6. — Average precipitation in the Ohio watershed above Cincinnati, and days with the river above 50 feet, below 5 feet, and below 10 feet at Cincinnati, 1861-1910, inclusive. 1861 TO 1870, INCLUSIVE. Mar. Apr. 03 o3 a 1-3 >-> hi < ft OJ CO O > Total. Rainfall (inches) 3.7 2.7 4.0; 3.4 3.8 3.6 3.8 3.6 4.1 2.6 2.8 3.0 41.1 12 6 7 10 17l 6 2 9 8 89 18 197 41 212 88 185 93 207 (i 30 151 8 56 44 Days with river below 5 feet 286 1,122 1 1871 T( D 1880, INCLUSIVE. Rainfall (inches) 3.1 2.6 3.5 3.1 2.7 1 3.9 5.1 3.6 2.7 2.2 2.9 3.2 38.6 6 4 46 ol 18 160 163 5 29 196 100 259 177 284 66 ! 1 145 64 15 391 34 14 6 4 1,375 1881 T( 3 1890, INCLUSIVE. Rainfall (inches) 4.1 4.3 3.4 3.1 4.3 4.0 3.0 3.6 3.2 2.9 3.2 3.0 42.7 9 59 7 15 4 12 1 10 (l (l 11 50! 143 42 189 124 192 113 221 0! 65 S 113 49 86 363 988 1891 T( 3 1900, INCLUSIVE. Rainfall (inches) 3.3 3.4 4.0 3.0 3.6 3.7 4.2 3.1 2.4 1.9 3.5 2.6 38.7 5 22 16 5 2 38 5 77 19 173 53 203 96 277 193 255 68 1 202 78 50 29 435 1,332 22 Table 6. — Average precipitation in the Ohio watershed above Cincinnati, and days with the river above 50 feet, below 5 feet, and below 10 feet at Cincinnati, 1861-1910, inclu- sive — Continued . 1901 TO 1910, INCLUSIVE. a C8 a ft < a a s Ha ft o O > o P Total. Rainfall (inches) 2.8 2.9 4.0 3.2 3.7 4.3 3.7 2.9 2.4 2.2 1.8 3.1 37.0 11 14 6 34 22 7 13 1 23 26 64 17 181 73 214 96 238 84 208 36 116 65 306 1,113 1861 TO 1885, INCLUSIVE. Rainfall (inches) Days with river above 50 feet. Days with river below 5 feet. . Days with river below 10 feet. 3.5 3.1 3.7 3.2 3.5 3.9 4.2 3.5 3.3 2.6 2.8 3.2 18 57 17 6 2 5 8 39 93 271 335 120 13 45 28 10 5 57 269 436 501 546 615 362 138 40.5 105 879 3,012 1886 TO 1910, INCLUSIVE. Rainfall (inches) 3.3 16 47 3.3 41 ?5 3.9 65 7 3.1 30 3.8 3 69 4.0 5 133 4.0 27 306 3.2 89 480 2.6 210 581 2.1 337 590 2.9 193 457 2.8 41 215 38.8 155 902 2,910 Table No. 7. This table is supplementary to Table 6, and gives the departures from the normals for the same data as are shown in Table 6. In these tables we begin to observe the effect of precipitation upon river stages. Table 7. — Departures of precipitation and river-stage days from normals at Cincinnati for days above 50 feet, below 5 feet, and below 10 feet, 1861-1910. 1861 TO 1870, INCLUSIVE 3 3 a ft < a P 3 1-3 3 ft 02 o O o 6 a* P 3 C a < +0.3 -0.5 +0.2 +0.2 +0.2 -0.3 -0.3 +0. 3J+1. 1 +0.2 + 1 5 T 5 - 13 + 1 - 2 + 1 - 1 + 5 - 8 + 5 + 9 + 5 + 48 - 8 - 39 - 34 - 33 - 13 - 3 - 17 - 70 -12- 1 - 3 - 1 - 17 + 16-45 - 65 1871 TO 1880, INCLUSIVE. Precipitation (inches) -0.3 -0.6 -0.3 -0.1 -0.9 + 1.0 +0.3 -0.3 -0.2 +0.1 +0.2 -1.3 1 - 16 -16 - 8 - 1 - 7 - 37 - 3 + 80 + 5 + 14 + 4 + 34 + 43 + 43 + 3 - 19 - 10 - 9 + 35 + 16 + 3+ 3 + 3 + 21 + 188 1881 TO 1890, INCLUSIVE. +0.7 +1.1 + 39 -0.4 -0.1 +0.7 +0.1 -0.5 +0.3 +0.2 +0.5 +0.4 +3 - 7 - 1 + 4 - 1 - 1 + 6 - 7 + 34 - 3 - 30 - 4 - 5 + 28 - 33 - 21 - 20 + 2 - 54 - 3 + 24 + 7 - 9 - 4 + 1 - 15 -198 23 Table 7. — Departures of precipitation and river-stage days from normals at Cincinnati for days above 50 feet, below 5 feet, and below 10 feet, 1861-1910, inclusive — Continued. 1891 TO 1900, INCLUSIVE. a t!3 C a £ p. < 03 <5 June. My. < ft as o O > o Dee. Annual. -0.1 +0.2 +0.2 -0.2 -0.2 +0.1 -0.2 -0.6 -0.5 +0.7 -0.4-1.0 - 2 + 2 - 3 + 1 - 1 + 17 + 7 _ 9 + 2 - 3 + 6 + 24 + 52 + 59 + 14 + 5 + 38 - 10 + 5 + 79 + 11 - 11 - 3 - 1 + 13 + 145 1901 TO 1910, INCLUSIVE. Precipitation (inches) . Days above 50 feet . Days below 5 feet . . Days below 10 feet . -0.6 -0.3 +0.2 + 18 + 5 +0.1 +0.4 -0.4 -0.4 ^~\ - 19 - 15 -0.6 -0.2 -1.0 +0.1 + 4 - 14 - 3 - 54 - 13 - 85 - 23 - 11 - 38 - 3 + 21 + 44 + 25 + 43 - 4 + 11 + 4 - 1 - 2 -2.7 + 13 50 74 1861 TO 1885, INCLUSIVE. Precipitation (inches) . Days above 50 feet . Days below 5 feet . . Days below 10 feet. +0.1 -0.1 -0.1 -0.1 + ""2 + 68 + 0.1 + "6 + 67 +0.2 + 0.3 + 0.2 +0.2 + 1 + 8 -24 - 12 + 3 + 2 + 11 + '31 - 18 + 13 — 36 — 14 - 1 + 2 + 2 + 3 - 6 - 48 - 44 +0.8 25 11 49 TO 1910, INCLUSIVE. -0.1 +0.1 +0.1 -0.1 +0.2 +0.1 -o.i -"e> - 68 -0.1 - 2 - 2 - 10 -0.'4 -0.3 +0.1 -0.2 -0.8 - 1 - 8 + 24 + 12 + 1 -68 -"36 + 17 +"i - 12 + "37 + 47 + 14 + 43 + 25 Days below 5 feet + 11 + 1 - 1 - 1 _ 2 + 6 — 48 Table No. 8. In this table is shown the comparison between the departures of the precipitation from the normals for each month of each 10 years, and the number of days the river stages were above or below the nor- mal number of days for the different 5 or 10 foot heights for the same 10-year periods. Table 8. -Departures of precipitation and river-stage days from normals, Ohio Watershed above Cincinnati, 1861 to 1910, inclusive. PRECIPITATION. 1861-1870. 1871-1880. 1881-1890. 1891-1900. 1901-1910. Jan. Feb. Mar. Apr. Maj'. June. July. Aug. Sept. Oct. +0.3 -0.5 +0.2 + 0.2 +0.2 -0.3 -0.3 + 0.3 + 1.1 +0.2 -0.3 -0.6 -0.3 -0.1 -0.9 + 1.0 +0.3 -0.3 -0.2 +0.7 +1.1 -0.4 -0.1 +0.7 +0.1 -0.5 +0.3 + 0.2 i 0.5 -0.1 +0.2 +0.2 -0.2 -0.2 +0.1 -0. 2 -0.6 -0.5 -0.6 -0.3 + 0.2 +0.1 +0.4 -0.4 -0.4 -0.6 -0.2 An- nual. + 0.1 +0.2 + 0.4 +0.7 -0.4 -1.0 +0.1 + 1.5 -1.3 +3. -1.0 -2.7 DAYS WITH RIVEP. TO 4.9 FEET, [NCLUSIVE. 1861-1870 + 5 - 3 - 3 + 2 - 3 + 5 + 5 - 4 + 6 -13 + 5 + 6 + 17 -19 - 8 + 4 +28 -23 -39 +43 -21 +59 -38 -33 + 3 + 2 + 5 +21 - 3 -10 - 3 -10 + 25 -70 1871-1880 + 35 1881-1890... + 7 1891-1900 + 79 1901-1910 -50 24 Table -Departures of -precipitation and river -stage days from normals, Ohio watershed above Cincinnati, 1861 to 1910, inclusive — Continued. DAYS WITH RIVER 5 TO 9.9 FEET, INCLUSIVE. Jan. Feb. Mar. Apr. May. June. July. Aug. Sept. Oct. Nov. Dec. An- nual. 1861-1870 -12 + 16 - 9 + 11 - 4 - 1 + 3 - 4 -11 +11 - 3 + 3 + 1 - 3 + 4 - 1 + 3 - 1 - 1 -16 +21 -15 + 13 - 2 + 3 +82 -28 - 6 -52 +44 +10 - 1 + 19 -71 +11 | -32 + 6 1 +30 -13 1 -61 -10 +52 + 4+12 + 7 + 1 -45 +25 +20 -22 -53 +33 + 13 -14 + 1 -21 +15 + 18 + 6 1871-1880 +154 1881-1890 —203 1891-1900 + 69 1901-1910 - 23 DAYS WITH RIVER 10 TO 19.9 FEET, INCLUSIVE. 1861-1870. 1871-1880. 1881-1890. 1891-1900. 1901-1910. + 8 + 2 -19 -51 - 8 + 2 -41 - 5 + 22 +18 - 1 - 4 -14 + 10 + 19 +36 + 7 -30 - 8 - 3 -38 -32 +37 + 3 -27 -34 +26 +15 + 17 - 4 - 2 + 9 +29 + 4 + 4 +27 + 12 - 2 - 7 + 9 - 6 +20 -20 -19 -37 - 8 -16 +17 +21 +21 -19 - 9 - 8 + 10 + 69 +20 +26 + 17 -25 -41 -76 -13 +64 -55 +82 DAYS WITH RIVER 20 TO 29.9 FEET, INCLUSIVE. 1861-1870 1871-1880 1881-1890 1891-1900 1901-1910 - 3 +12 + 8 +28 + 12 - 3 - 4 — 5 + 12 + 10 +20 + 9 + 3 + 19 + 14 -20 -13 -42 -17 - 2 + 3 - 8 -16 - 8 +26 -20 - 3 -23 - 9 + 19 + 7 + 1 + 5 + 11 +30 + 3 -19 - 5 + 3 + 4 + 3 -13 — 7 + 6 - 9 - 2 -18 + 2 - 7 - 7 -22 + 9 + 5 +29 + 19 + 1 - 9 -11 -16 - 8 +99 -84 +50 -53 -14 DAYS WITH RIVER 30 TO 39.9 FEET, INCLUSIVE. 1861-1870 1871-1880 1881-1890 1891-1900 1901-1910 + M + 7 +12 + 7 + 14 - 9 - 4 - 3 + 4 + 4 - 6 +12 - 9 + 7 - 2 -10 - 9 + 10 - 1 + 3 - 3 - 2 + 8 + 6 - 7 -18 + 6 + 8 + 14 - 2 + 1 + 5 +17 - 7 - 8 + 15 +17 - 8 - 9 - 5 + 7 - 4 - 3 - 4 -18 -10 - 7 -18 - 5 - 5 + 9 - 4 - 3 - 4 - 3 - 3 + 5 +52 - 8 +23 -20 -48 DAYS WITH RIVER 40 TO 49.9 FEET, INCLUSIVE. 1861-1870 1871-1880 1881-1890 1891-1900 1901-1910 -12 - 3 + 9 + 6 - 4 -10 - 8 +24 - 1 - 6 + 2 -26 - 4 -11 +38 + 17 -11 - 4 - 3 - 1 - 3 - 4 - 2 + 10 - 1 - 1 - 1 - 1 + 4 + 2 - 1 + 3 - 1 + 1 - 1 + 3 - 1 - 1 - 1 - 1 + 2 + 6 + 1 - 6 + 1 - 3 -45 +25 -16 + 40 DAYS WITH RIVER 50 TO 59.9 FEET, INCLUSIVE. 1861-1870 1871-1880 1881-1890 1891-1900 1901-1910 + 6 - 6 - 1 - 1 -8 -11 +24 + 5 - 9 + 2 -15 - 1 + 15 - 1 - 7 + 5 - 2 + 6 + 1 - 1 - 1 + 1 - 1 -30 +21 + 1 +10 DAYS WITH RIVER 60 TO 69.9 FEET, INCLUSIVE. 1861-1870 1871-1880 1881-1890 1891-1900 1901-1910 -V 1 - 1 - 1 - 1 + 5 - 4 - 4 +14 - 2 - 4 - 1 - 1 - 1 + 1 + 3 + 12 - 2 + 4 DAYS WITH RIVER 70 TO 79.9 FEET, INCLUSIVE. 1861-1870 1871-1880 1881-1890 + 2 1891-1900 1901-1910 25 Table No. 9. This table shows the number of days the Ohio River at Cincinnati was above the flood stage of 50 feet for each month during the entire 50 years, together with the totals for each year and for each month. Table 9.- ■Total number of days with river above 50 feet at Cincinnati, Ohio, 1861 to 1910 , inclusive. Years. Jan. Feb. Mar. Apr. May. June. July. Aug. Sept. Oct. Nov, Dec. An- nual. 1861 1862 1863 1864 1865 1866 1867 1868 1869 1870 1871 1872 1873 1874 1875 1876 1877 1878 1879 1880 1881 1882 1883 1884 1885 1886 1887 1888 1889 1890 1891 1892 1893 1894 1895 1896 1897 1898 1899 1900 1901.. 1902 1903 1904 1905 1906 1907 1908 1909 1910 Sums Days. 7 4 2 9 16 19 10 3 Days. 5 12 3 12 2 7 7 4 8 11 6 2 3 Days. 2 2 1 Days. Days Days. 5 Days. Days. Days. 12 7 19 6 5 1 5 4 2 9 16 19 12 13 15 8 10 8 15 9 26 Table No. 10. The table shows the number of clays the Ohio River at Cincinnati was above the 40-foot stage for each month during the entire 50 years, together with the totals for each year and for each month. Table 10. — Total number of days with river above 40 feet at Cincinnati, Ohio, 1861 to 1910, inclusive. Years. Jan. Feb. Mar. Apr. May. June. July. Aug. Sept. Oct. Nov. Dec. An- nual. 18G1 Days. 2 10 1 3 10 6 11 9 3 23 5 3 6 6 2 5 16 8 2 4 19 8 Days. 10 1 2 15 3 5 10 2 7 9 20 18 25 1 28 13 26 14 12 2 14 9 5 1 Days. 6 3 19 19 10 2 2 5 1 3 7 6 15 1 7 24 10 14 10 13 15 19 14 11 :l 1 12 Days. 7 15 6 2 6 13 5 6 1 3 3 9 16 5 1 6 6 1 6 5 4 10 3 5 5 6 9 Days. 8 2 1 4 2 4 7 11 o 3 6 6 7 Days. 2 3 Days. 2 .0 Days. 9 2 q Days. 2 2 Days. 2 Days. Days. 5 2 4 4 3 2 2 6 1 7 1 Days. 11 1862 41 1863 .. 5 1864 5 1865 37 1866 2 1867 34 1868 19 1869 8 1870 25 1871 1 1872 5 1873 7 1874 21 1875 18 1876 23 1877 12 1878 .. 3 1879 4 1880 22 1881 14 1882 53 1883 33 1884 40 1885 .. 5 1886 18 1887 43 1888 1889 1S90 51 1891 48 1892 8 1893 . . . 26 1894 1895 5 1896 10 1897 1898 26 31 1899 1900 25 1 1901 15 1902 29 1903 38 1904 . . . 23 1905 18 1906 7 1907 1908 37 43 1909 20 1910 21 162 252 291 164 61 5 2 11 4 2 37 991 27 Table No. 11. This table shows the number of days the Ohio River at Cincinnati was below the 10-foot stage for each month during the entire 50 years, together with the totals for each year and for each month. Table 11. — Total number of days with river below 10 feet at Cincinnati, Ohio, 1861-1910, inclusive. Years. Jan. Feb. Mar. Apr. May. June, July. Aug. Sept. Oct. Nov. Dec. Total. 1861. 1862. 186c. 1864. 1865. 186( . 18..7 . 1868 . 1869. 1870. 1871. 1872. 187? . 1874. 1876. 187( . 1877. 1878. 1879. 1880. 1883. 1882. 188? . 188f. 1887. 188?. 188P . 1890. 189' . 1892. 189? . 1894. 1895. 189'" . 1897. ISW. 189?. 190". 190" . 1902 . mr. 1904. 1905. 1906 . 1907. 1908 . 1909. 1910. Days. 4 1 Days, 4 5 3 8 7 6 10 12 2 3 5 * 20 2 10 6 4 12 7 Dai/tt. 12 30 11 30 1 3 2 27 12 23 30 4 15 10 9 25 5 8 8 4 2 9 19 11 29 6 6 9 16 15 4 3 4 Sums. 53 126 402 Days. 31 8 24 31 9 18 28 31 17 31 11 6 29 8 11 22 31 14 25 2 2 18 29 6 31 12 18 3 10 21 31 28 1 6 25 26 22 4 Days. 11 31 31 21 13 22 31 21 '22 9 31 23 12 24 1 18 31 17 18 21 31 11 21 27 3 14 31 20 10 21 12 28 31 31 31 20 24 26 14 18 31 31 3 5 5 24 19 31 Days. 22 30 30 3 8 7 30 10 19 26 30 30 25 30 30 12 30 18 24 30 30 30 30 12 30 30 2 28 17 30 25 26 30 30 30 29 30 30 12 30 22 30 14 16 1 30 30 29 740 Days. 27 22 2 16 1 30 5 23 25 24 17 4 27 6 8 16 4 25 14 6 30 30 17 30 21 30 18 30 30 1 19 30 23 29 27 23 30 8 2 30 29 30 Days. 23 6 11 15 1 25 19 3 7 7 3 6 12 31 18 2 11 23 15 9 21 30 26 23 lii Days. 76 150 17.8 90 82 88 166 93 88 111 216 180 94 181 87 85 131 100 171 130 138 70 77 156 74 100 196 76 62 39 104 147 117 173 207 61 113 85 156 169 ' 105 135 138 164 44 59 26 164 141 137 981 1,127 1,205 819 363 5,930 Table No. 12. A correlation is here shown between the precipitation for August, September, and October and the number of days that the river was below 10 feet at Cincinnati, during the same months, for each year of the entire 50 years. This is the usual correlation table. In these tables the correlation coefficient "r" is determined hj dividing the sum of column 8 by the square root of the product of the sums of 28 columns 4 and 7. If the correlation coefficient be 1 in this calcula- tion, there is an exact relation between the two factors, and if — 1 there is an exact opposite connection. In this case 426.74x26,562 (the sums of columns 4 and 7, respectively) = 11,335,067.88. The square root of this product is 3,366.76. The sum of column 8 is -2,490.8. This sum divided by 3,366.76= -0.74. This is a Very high negative coefficient and shows plainly that the smaller the amount of rainfall during August, September, and October the greater the number of days with the river below 10 feet. It is considered safe to assume that there is a well-defined relation in these cases if " r" is six times the probable error. The probable error 1 — r 2 is obtained by the following formula: 0.674 'i^r- In which "r" is the correlation coefficient and N the number of years under discussion. The probable error here is ±0.04, or only one-eighteenth of u r." The question might properly be raised as to whether the rainfall during July might have a marked influence on the low-water days in August, September, and October, as discussed in this table. But a similar correlation table worked out for the rainfall for July, August, September, and October, and the number of days with the river below 10 feet in August, September, and October, gives a correlation coeffi- cient of —0.73, or very slightly less than with July rainfall omitted. Table 12.- — Correlation of precipitation and days with river below 10 feet, in August, September, and October, Ohio River, Cincinnati, Ohio, 1861 to 1910, inclusive. Years. Precipitation. Precipi- tation. Depart- ure. Square of col- umn 3. Days. Days. Depart- ure. Square of col- umn 6. Product of col- umns 3 and 6. 1861. 1862. 1863. 1864. 1865. 1866. 1867. 1868. 1869. 1870. 1871. 1872. 1873. 1874. 1875. 1876. 1877. 1878. 1879. 1880. 1881. 1882. 1883. 1884. 1885. 1886. 1887. Inches. 11.4 5.0 8.7 12.7 10.2 17.2 6.6 13.9 8.2 7.4 7.5 7.2 10.6 5.6 7.8 11.5 5.9 10.1 9.7 9.5 8.8 10.1 9.3 6.8 12.0 '8.1 5.4 14.3 7.4 Inches. +2.7 -3.7 + 4.0 + 1.5 +8.5 -2.1 +5.2 -0.5 -1.3 -1.2 -1.5 + 1.9 -3.1 -0.9 +2.8 -2.8 + 1.4 + 1.0 +0.8 +0.1 + 1.4 +0.6 -1.9 +3.3 -0.6 -3.3 +5.6 -1.3 Bays. 33 92 92 33 46 34 92 51 65 66 92 Days. -33 +26 +26 -33 -20 -32 +26 -15 - 1 +26 + 18 - 5 + 19 - 4 -19 +26 - 5 + 7 + 16 +26 -34 + 9 +22 -34 + 9 +26 -33 - 4 1,089 676 676 1,089 400 1,024 676 225 1 676 324 25 364 16 361 676 25 49 256 676 1,156 81 284 1,156 81 676 1,089 16 89.2 96.2 132.0 30.0 272.0 54.6 7S.0 0.5 31.2 27.0 9.5 58.9 3.6 53.2 72.8 7.0 7.0 12.8 2.6 47.6 5.4 41.8 112.2 5.4 85.8 184.8 5.2 29 Table 12. — Correlation of precipitation and days with river below 10 feet in August, September, and October, Ohio River, Cincinnati Ohio, 1861 to 1910, inclusive — Continued. Precipitation. Days. Product Years. Precipi- tation. Depart- ure. Square of col- umn 3. Days. Depart- ure. Square of col- umn 6. of col- umns 3 and 6. 1 2 3 4 5 6 7 8 1890 Inches. 14.6 6.5 6.5 8.7 7.2 5.1 10.3 3.8 10.9 7.3 6.8 6.4 7.5 5.5 4.7 12.5 10.9 7.7 4.3 7.1 10.4 Inches. +5.9 -2.2 -2.2 —1.5 -3.6 + 1.6 -4.9 +2.2 -1.4 -1.9 -2.3 -1.2 -3.2 -4.0 +3.8 +2.2 -1.0 -4.4 -1.6 + 1.7 34.81 4.84 4.84 2.25 12.96 2.56 24.01 4.84 1.96 3.61 5.29 1.44 10.24 16.00 14.44 4.84 10.00 19.36 2.56 2.89 Days. 21 60 89 71 8S 92 32 81 51 85 86 57 75 80 92 36 21 24 85 79 84 Days. -45 - 6 +23 + 5 +22 +26 -34 +15 -15 + 19 +20 - 9 + 9 + 14 +26 -30 -45 -42 + 19 + 13 + 18 2,025 36 529 25 484 676 .1, 156 225 225 361 400 81 81 196 676 900 2,025 1,764 361 169 324 - 265.5 1891 ,.-. 1892 + 13.2 - 50.6 1893 1894... - 33.0 1895 - 93. 6 1896 - 54.4 1897 - 73.5 1S98 - 33.0 1899 - 26.6 1900 - 38.0 1901 + 20.7 1902 - 10.8 1903 - 44.8 1904 — 104.0 1905 .- — 114. 1906 - 99.0 1907 + 42.0 190S - 83.6 1909 - 20.8 1910 + 30.6 426. 74 26,562 -2, 490. 8 8.7 66 The correlation coefficient is —0.74. The probable error is ±0.04. Table 13. In Table 13 the correlation coefficient is determined for the precipi- tation over the Ohio watershed above Cincinnati, and the number of days that the river was above 40 feet at Cincinnati, during the months of February and March, for the 50 years. The effect of the precipitation upon the flood conditions is more remarkable, if pos- sible, than upon the low-water days as indicated in Table 12, because the correlation coefficient is 0.80 in Table 13. This is 27 times the probable error. This table alone should be very conclusive evidence that the high-water conditions in the Ohio Valley, during the months when there are the greatest number of high-water days, are controlled by the precipitation and nothing else. By obtaining the correlation coefficient for the different 25-year periods from this table the fact that the cutting off of the forests does not make increased flood conditions is plainly established. The correlation coefficient for the 25 years from 1861 to 1885, inclusive, is 0.805, and for the 25 years from 1886 to 1910, inclusive, is 0.804, a difference much less than the probable error. This means that the tendency to cause the water to rise above 40 feet by the same precip- itation has been no greater during the last 25 years than during the preceding 25 years, or at least by a value too small to be calculated by the most approved method of correlation. 30 Table 13. — Precipitation and days with river above 40 feet in February and March, Ohio River, Cincinnati, Ohio, 1861 to 1910, inclusive. Years. Precipitation. Precipi- tation. Depart- ure. Square of col- umn 3. Days. Days. Depart- ure. Square of col- umn 6. Product of col- umns 3 and 6. 1861. 1862. 1863. 1864. 1865. 1866. 1867. 1868. 1869. 1870. 1871. 1872. 1873. 1874. 1875. 1876. 1877 . 1878. 1879. 1880. 1881. 1882 . 1883. 1884. 1885 . 1886. 1887. 1888. 1889. 1890. 1891. 1892. 1893. 1894. 1895 . 1896. 1897. 1893. 1899. 1900. 1901. 1902. 1903. 1904. 1905 . 1906. 1907. 1905. 1909. 1910. Sums . Means. Inches. 4.3 7.7 7.1 4.0 7.4 6.2 10.0 6.5 7.1 7.3 5.3 3.4 6.7 7.6 5.8 6.3 6.0 4.7 7.1 8.0 7.2 10.1 10.2 10.2 3.3 5.1 9.4 6.1 2.9 12.3 10.0 6.1 7.4 5.9 3.1 6.7 11.3 9.3 8.4 5.4 3.7 4.2 9.9 8.0 5.2 6.9 7.0 10.6 8.9 7.3 7.0 Inches. -2.7 +0.1 +0.1 -3.0 +0.4 -0.8 + 3.0 -0.5 + 0.1 + 0.3 -1.7 -3.6 -0.3 +0.6 -1.2 -0.7 —1.0 -2.3 +0.1 + 1.0 +0.2 +3.1 +3.2 +3.2 -3.7 -1.9 +2.4 -0.9 -4.1 +5.3 +3.0 -0.9 +0.4 -1.1 -3.9 -0.3 +4.3 +2.3 + 1.4 -1.6 -3.3 -2.8 +2.9 + 1.0 -1.8 -0.1 +3.6 + 1.9 +0.3 7.29 .49 .01 9.00 .16 .64 9.00 .25 .01 .09 2.89 12. 96 .09 .36 1.44 .49 1.00 5.92 .01 1.00 .04 9.61 10.24 10.24 13.69 3.61 5.76 .81 16.81 28.09 9.00 .81 .16 1.21 15. 21 .09 18.49 5.29 1.96 2.56 10.89 7.84 8.41 1.00 3.21 .01 12.96 3.61 .09 254. 80 Days. 16 4 21 34 10 2 2 3 5 5 11 3 2 14 9 26 18 40 2 35 37 36 14 26 10 13 / 17 33 14 11 1 15 28 13 13 -11 + 5 - 7 -11 + 10 -11 +23 - 1 - 9 - 9 -11 -11 - 8 - 6 - 6 - 8 -11 - 9 + 5 - 2 + 15 + 7 +29 -11 - 9 +24 -11 -11 +26 +25 -11 + 3 -11 - 11 -11 +15 - 1 + 2 -11 -11 + 6 +22 + 3 -10 + 4 + 17 + 2 + 2 121 25 49 121 100 121 529 1 81 81 121 121 64 36 36 64 121 81 25 4 225 49 841 121 81 576 121 121 676 625 121 9 121 121 121 225 ] 4 121 121 36 484 9 100 16 289 4 4 7,245 29.7 0.5 0.7 33.0 4.0 8.8 69.0 0.5 0.9 2.7 18.7 39.6 2.4 3.6 7.2 8.0 25.3 0.9 5.0 0.4 46.5 22.4 92.8 40.7 17.1 57.6 9.9 45.1 137.8 75.0 9.9 1.2 12.1 42.9 3.3 64.5 2.3 2.8 17.6 36.3 16.8 63.8 3.0 1.0 61.2 3.8 0.6 + 1,092.3 The correlation coefficient is 0.80. The probable error is ±0.03. Table 14. In this table the same calculation is made for the relation between the precipitation in February and March and the number of days above 50 feet, or flood stage. One would not expect this correlation coefficient to be so high as in Table 13, even if the relation is actually closer, because of the great number of years when the river did not 31 rise above 50 feet during these two months. And yet in tins case "r" equals 0.74; high enough to make the relation well marked. The determination of the correlation coefficient in this table for each of the 25-year periods shows that the tendency to produce flood days with the same rainfall is slightly less during the last 25 years than during the preceding, although by a value too small to be considered, being about 0.3 per cent. Table 14. — Precipitation and days loith river above 50 feet in February and March, Ohio River, Cincinnati, Ohio, 1861 to 1910, inclusive. Years. Precipitation. Precipi- Depar- tation. ture. Square of column 3. Days. Days. Depar- ture. Square of column 6. Product of col- umns 3 and 6. 1861. 1862. 1863. 1864. 1865. 1866. 1867. 1868. 1869. 1870. 1871. 1872. 1873. 1874. 1875. 1876. 1877. 1878. 1879. 1880. 1881. 1882. 1883. 1884. 1885. 1886. 1887. 1888. 1889. 1890. 1891. 1892. 1893. 1894. 1895. 1896. 1897. 1898. 1899. 1900. 1901. 1902. 1903. 1904. 1905. 1906. 1907. 1908. 1909. 1910. Inches. 4.3 7.7 7.1 4.0 7.4 6.2 10.0 6.5 7.1 7.3 5.3 3.4 6.7 7.6 5.8 6.3 6.0 4.7 7.1 8.0 7.2 10.1 10.2 10.2 3.3 5.1 9.4 6.1 2.9 12.3 10.0 6.1 7.4 5.9 3.1 6.7 11.3 9.3 8.4 5.4 3.7 4.2 9.9 8.0 5.2 6.9 7.0 10.6 8.9 7.3 Inches. -2.7 +0.7 +0.1 -3.0 + 0.4 -0.8 +3.0 -0.5 +0.1 +0.3 -1.7 -3.6 -0.3 +0.6 -1.2 -0.7 -1.0 -2.3 +0.1 + 1.0 +0.2 +3.1 +3.2 +3.2 -3.7 -1.9 +2.4 -0.9 -4.1 +5.3 +3.0 -0.9 +0.4 -1.1 -3.9 -0.3 + 4.3 +2.3 + 1.4 -1.6 -3.3 -2.8 +2.9 + 1.0 -1.8 -0.1 +3.6 + 1.9 +0.3 Sum.. Mean. 7.0 7.29 .49 .01 9.00 .16 .64 9.00 .25 .01 .09 2.89 12.96 .09 .36 1.44 .49 1.00 5.92 .01 1.00 .04 9.61 10.24 10.24 13.69 3.61 5.76 .81 16.81 28.09 9.00 .81 .16 1.21 15. 21 .09 18.49 5.29 1.96 2.56 10.89 7.84 S.41 1.00 3.21 .01 12. 96 3.61 .09 Days. 5 19 4 2 9 16 19 13 15 8 8 8 254. 80 Days. - 4 - 4 - 4 - 4 + 1 - 4 + 15 - 4 - 4 - 4 - 4 - 4 - 4 - 4 - 4 - 4 - 4 - 4 - 4 - 2 + 5 + 12 + 15 - 4 - 4 + 9 - 4 - 4 + 11 + 4 - 4 + 4 - 4 - 4 - 4 + 4 + 3 + 3 - 4 - 4 + 4 - 4 - 4 - 4 + 7 + 4 + 2 16 16 16 16 1 16 225 16 16 16 16 16 16 16 16 16 16 16 16 4 25 144 225 16 16 81 16 16 121 16 16 16 16 16 16 16 9 9 16 16 16 16 16 16 49 16 4 1 + 10. S -2.8 -0.4 + 12.0 + 0.4 + 3.2 + 45.0 + 2.0 -0.4 - 1.2 6.8 14.4 1.2 + + 2.4 4.8 + 2.8 + 4.0 + 9.2 - 0.4 - 0.4 + 15.5 + 38.4 + 48.0 + 14.8 + 7.6 + 21.6 + 3.6 + 16.4 + 58.3 + 12.0 + 3.6 + 1.-6 + 4.4 + 15.6 + 1.2 + 17.2 + 6.9 + 4.2 + 6.4 + 13.2 + 11.6 -4.0 + 7.3 + 0.4 + 14.4 + 3.8 -0.3 1,458 + 452.3 The correlation coefficient is 0.74. 32 Table 15. In this table the years, precipitation, and river stages are grouped for each difference in precipitation amounting to 1 inch for February and March. This table shows several important facts, among them being : (1) In only one year has the river reached the flood stage during these months when the precipitation was less than the normal, 7 inches. (2) The most marked ■ increase in flood days comes with the increase of the precipitation from between 9 and 1 inches to between 10 and 11 inches. (3) The average rate of increase in number of flood days with each increase of 1 inch in the precipitation is 2.5; this calculation is made for years when the precipitation was above 7 inches. Table 15. — Precipitation and days with river above 50 feet in February and March, Ohio River, Cincinnati, Ohio, 1861 to 1910, inclusive. Precipitation between — Years. Precipi- tation. Days. Change. 2.9 and 3.9 inches . 4 and 4.9 inches . 5 and 5.9 inches . 6 and 6.9 inches. 7 and 7.9 inches . Mean 8 and 8.9 inches. Mean. 1872 1885 1889 1895 1901 1861 1864 1878 1902 1871 1875 1886 1894 1900 1905 1866 1868 1873 1876 1877 1888 1892 1896 1906 1862 1863 1865 1869 1870 1874 1879 1881 1893 1907 1910 1880 1899 1904 1906 3.4 3.3 2.9 3.1 3.7 4.3 4.0 4.7 4.2 5.3 5.8 5.1 5.9 5.4 5.2 6.2 6.5 6.7 6.3 6.0 6.1 6.1 6.7 6.9 7.7 7.1 7.4 7.1 7.3 7.6 7.1 7.2 7.4 7.0 7.3 8.0 8.4 8.0 33 Table 15. — Precipitation and days with river above 50 feet in February and March, Ohio River, Cincinnati, Ohio, 1861 to 1910, inclusive — Continued. Precicipitatiou between — Years. Precipi- tation. Days. Change. 1887 1898 1903 9.4 9.3 9.9 13 7 8 9 4 1867 10.0 10.1 10.2 10.2 10.0 10.6 19 9 16 19 8 8 1882 1883 1884 1891 1908 13 4 1890 1897 12.3 11.3 15 8 12 —1 2.5 Table No. 16. This table groups the data when the rainfall was above the normal for February and March, by 10-year and 25-year periods, and shows plainly that instead of a tendency toward increase of flood days in recent years there is actually a decrease, with the same precipitation. As shown by the last sentence in the discussion of Table 15, the average increase in flood days is 2.5 with each increase in precipita- tion of 1 inch. Then if 8.2 inches of rain from 1861 to 1885, inclu- sive, caused 6.5 flood days each year, the rainfall of 9.2 inches from 1886 to 1910, inclusive, should have caused 2.5 days more or 9 flood days each year. But, because the tendency to flood conditions is less, the increase of 1 inch of rain produced an increase of only 1.6 flood days per year. Applying the same average increase of 2.5 days for each increase of 1 inch in rainfall, or 0.25 day for each increase of 0.1 inch of rain, it will be seen that the number of flood days in the 10 years, 1901 to 1910, inclusive, is exactly the same as the flood days in the 10, years, 1861 lo 1870, inclusive, if the difference in rainfall is taken into con- sideration, and is 2.75 days less than was produced in the 10 years, 1881 to 1890, inclusive, after making alloAvance for the difference in rainfall. 34 Table 16. — Precipitation and days with river above 50 feet during February and March, by 10-year periods, Ohio River, Cincinnati, Ohio, 1861-1910, inclusive. Year. Year. Precipi- tation. Days. 1861 to 1870, inclusive 1862 1863 1865 1869 1870 1867 7.7 7.1 7.4 7.1 7.3 10.0 5 19 7.8 4 1874 1879 1880 1871 to 1880, inclusive 7.6 7.1 8.0 4 Mean 7.6 1 1881 1887 1882 1883 1884 1890 1881 to 1890, inclusive '. 7.2 9.4 10.1 10.2 10.2 12.3 2 13 9 16 19 15 9.9 12 1893 1899 1898 1891 1897 1891 to 1900, inclusive 7.4 S.4 9.3 10.0 11.3 8 7 7 I Mean 9.3 8 1910 1907 1904 1906 1903 1908 1901 to 1910, inclusive 7.3 7.0 8.0 8.9 9.9 10.6 3 11 9 8 8 8.6 6 Mean, 1861 to 1885, inclusive 8.2 9.2 6.5 Mean, 1886 to 1910, inclusive 8.1 Table No. 17. In Table 17 the average rainfall and average number of days with the river below 10 feet in August, September, and October is tabu- lated for differences in rainfall amounting to 1 inch. This shows that the average increase in low-water days with each decrease of 1 inch of rain is 7. Table 17. — Average precipitation and days with river below 10 feet for August, Septem- ber, and October for each inch of rain, Ohio River, Cincinnati, Ohio, 1861 to 1910, inclusive. Precipitation — Mean precipi- tation. Mean days. Change. 4.3 5.4 6.6 7.4 8.5 9.5 10.4 13.3 86 89 79 72 79 77 49 36 + 3 -10 - 7 + 7 - 2 -28 -13 - 7 6b Table No. 18. In Table 18 the average rainfall and average number of days with the water' below 10 feet in August, September, and October is given for each 10-year and each 25-year period. Remembering that the increase in low- water days amounts to an average of 7 a year with each decrease in the rainfall of 1 inch, it will be seen at once that the number of low-water days during the 10 years from 1901 to 1910, inclusive, were less than in any of the preceding 10-year periods, taking into the account the difference in rainfall. Also that during the last 25 years the average number of low-water days is 9.1 less than would have been produced in the first 25 years with the same amount of rainfall. Or, the tendency to produce low-water conditions in the Ohio River has been 14 per cent less during the 25 years from 1886 to 1910, inclusive, than during the 25 years from 1861 to 1885, inclusive, with the same rainfall, as calculated during the low-water months of August, September, and October. Table 18. — Average precipitation and number of days with river below 10 feet for August , September, and October, by 10-year and 25-year periods, Ohio River, Cincinnati, Ohio, 1861-1910, inclusive. Year. Precipi- > tation. Days. 1861 to 1870 10.1 60 1871 to 1880 8.5 74 1881 to 1890 9.7 60 1891 to 1900 7.3 74 1901 to 1910 7.7 63 1861 to 1885 9.3 66 1886 to 1910 S. 60 36 Explanation op Chaets. Chart 1. — Indicates the location- of the seven precipitation stations that were used in obtaining the precipitation for the Ohio watershed above Cincinnati. Chart 2. — The influence of the rainfall upon the number of low- water days during the driest period of the year is plainly shown by this chart. Chart 3. — The relation between the precipitation and number of high- water days during the period of highest water is well indicated. Also that an equal amount of precipitation has no greater tendency to cause an increase in the number of high-water days during the latter part of the period than during the earlier part. Chart 4- — This chart shows that whenever the . precipitation for February and March was 1 inch or more above the normal the number of days with the water above 40 feet was always greater than the normal, with one exception. Also that when the precipitation was more than 2 inches above the normal, the number of days was much above the normal, with one or two exceptions. Further, that when the precipitation was below the normal the number of days was always less than the normal, with one exception. The line of dots on the — 11 days' line indicate no days with the river above 40 feet, the average number of days being 11 per year. 37 Chart 1.— Location of precipitation stations. 38 oiei a> CO i~ (O 10 co 0) 0061 C) CO t- tD lO CO CN 0681 o CO t- CO 10 <* co CN 0981 05 CO N CO 10 co M 0Z8I 0) 00 t- co IO <* co CN 5 \ 1 *""■ -H ^ -c \ ,- s ^~2 -* **" \ \ \ \ V * ^ , -'- " r J^» ■c^ ~~Z "— Is. — rr L=c ■" \ i IS •kT V •s *> ■-. _ ■*■ -- • ^. „«. -•- " ' ^ —^2 - ** -^ "- -*. ^ ft£ --■ '"" V -. . ^ -- -- V > V ,-- ' sm - - rT • ** .. ■>< i i i ' -- > ~J ~ r • »- -- -~ 1 1 ~~ ^j ~^" •sa / TJOlj -DfiH-zaoJj -f--|- + + 4-4- -*--*"s ' ' ' ' 1 ?/rnrr ° "O o io ° io ri "= ° io O co r- co r- (0 10 CO CM 0681 en co t^ 10 10 t CO CN 0881 0> co r» ID 10 4 co CN 0A8I en co S co lO CO CN 1981 2/ % < -J S -"■. *^ -> ^ /> / ,-■ --; ** -^ ^ • ■ ^ » «, •**^ j.- 1 «> *« - ' v^ -- -. S*> •*» -j / ■" = rssr fsrs ws ra , - SB* '» ?s ft»> ■ ■ h v 1 Ik M ■8 ^ ■ft * (Eg — ■ i- ss. 5^ -• '-I -. k ^ *t S i i i \ ■o r* » i I 1 ! 1 , %& *-• *- r 5s "Wi ~«» ,. - " ■*• >; 5^« 7^* „. -" - ^ Sai/Jl/l U? tO i0