Root 403d Roots render both sides of it identical (see EQUA- TION). In arithmetic, the square root is that number which, multiplied by itself, produces the given number; the cube root, the num- ber which, multiplied into itself and then into the product, produces the given cube; so with fourth root, fifth root, etc. Root, in Plants, is that part which absorbs nourishment from the soil or from water. The root ordinarily grows downward, and its functions are the fixing of the plant in the soil, and the extraction therefrom of solu- tions of mineral salts and other food material, which are passed on through the stem to the leaves. As the leaf surface of a seed plant is developed the root system grows; in a large sunflower it occupies about one cubic yard, in a large tree hundreds of cubic yards. The primary root is merely the en- larged radicle of the seedling: it is the direct prolongation of the stem. All secondary roots arise from this first root; the secondary roots may give rise to others, and so on, until the common much-branched root is formed. When the primary root is much thicker than the secondary roots it b called a tap root. Roots are also described as fleshy (the beet root), or as woody (the roots of trees). Roots are usually buried in the soil, but they may be aerial, as in the ivy; these arise from the stem, and fix the plants to then* supports. In the tropics many plants have aerial roots; thus the mangrove forms forests in the swamps. Aquatic plants often have roots which do not penetrate into the mud, but float freely in the water. Root stock or Rhizome is the name given to an underground stem that is easily dis- tinguished from a root by the fact that it ends in a bud, and bears leaves or scales. In the autumn the aerial leaves die down, but the rhizome lives through the winter, and in the spring its terminal bud goes on grow- ing. See PLANTS. Root, EHhu (1845-1937), American lawyer and public official, was born in Clinton, N, Y. He practised law in New York, and made rapid strides in his profession. He was coun- sel for William M. Tweed in the celebrated Tweed Ring trial; and for many great cor- porations and railway companies. From 1881 to 1885 he was district attorney for the southern district of New York. In 1899 Elihu Root succeeded Russell A. Alger as Secretary of War, and at once set about reforming the Department. In 1904 he retired to the practice of law in New York City; but in July, IQOJ,, upon the death of John Hay, re-entered the Cabinet as Secre- tary of State. In this office he did much toward reorganizing the consular service and improving the business methods of the De- partment. In 1909 he was elected U, S. Sen- ator, to succeed Thomas C. Platt, for th^ term ending in 1915. In 1912 he was perman- ent chairman of the Republican Nationa1 Copyright Pack Bros. Elihu Root. Convention, and in 1916 candidate for the Republican presidential nomination. The Nobel Peace Prize of 1912 was awarded to Root in recognition of his services for the pacification of Cuba and the Philippines, and his handling of various matters in dispute between Japan and the United States. He was trustee of the Cooper Union and Metro- politan Museum of Art, director in several companies, and held important offices in both national and international bodies. Root, George Frederick (1820-95), American composer and organist, composed some of the most popular songs of his time,, notably 'The Battle Cry of Freedom/ 'Tramp, Tramp, Tramp,' 'Just Before the Battle, Mother,' and the quartet, 'There's Music in the Air.' Roots, Logan Herbert (1870), American