EPPING, a village of England, in Essex (giving name to a parliamentary division), 17 miles from London, in the midst of an ancient royal forest which one time covered nearly the whole of Essex. The unenclosed portion (5600 acres) was bought by the Corporation of London in 1882, and secured to the public as a free place of recreation. Pop. 4253.
EPSOM, a town in the county of Surrey, England, 15 miles S.W. of London, formerly celebrated for a mineral spring, from the water of which the well-known Epsom salts were manufactured. The principal attraction Epsom can now boast of is the grand race-meeting held on the Downs, the chief races being the Derby and Oaks. Epsom gives name to one of the seven parliamentary divisions of the county. Pop. 19,156.
EPSOM SALTS, sulphate of magnesium (MgSO_47H_2O), a cathartic salt which appears in capillary fibres or acicular crystals. It is found covering crevices of rocks, in mineral springs, &c.; but is commonly prepared by artificial processes from magnesian limestone by treating it with sulphuric acid, or by dissolving the mineral _kieserite_ (MgSO_4H_2O) in boiling water, allowing the insoluble matter to settle, and crystallizing out the Epsom salts from the clear solution. It is employed in medicine as a purgative, and in the arts. The name is derived from its having been first procured from the mineral waters at Epsom.
EPWORTH, a small town of N. Lincolnshire, 9 miles N. of Gainsborough, the birth-place of John Wesley, the founder of Methodism. Pop. 1836.
EQUATION, in algebra, a statement that two expressions have the same numerical value. An equation may be either identical or conditional. An example of an _identical equation_, or _identity_, is (x + y)(x - y) = x^2 - y^2. The left side here can be transformed into the right side, simply by applying the laws of algebra so as to carry out the operations indicated, without taking account in any way of the numerical values of x and y. An identical equation is, therefore, true for all values of the variables which appear in it. A _conditional_ equation is not true unless certain special values are assigned to the variables. Thus the equation 4x + 7 = 15 is not true for any value of x except 2. This value 2 is called a _root_, or _solution_, of the equation. An equation may have more than one root, e.g. x^2 + 6x = 7 has two roots, 1 and -7; and 2x^3 + 3x^2 = 2x + 3 has three roots, 1, -1, -3/2.