EPSTEIN 



2955 



EQUATION 



Epstein, JACOB (b. 1880). Brit- 

 ish sculptor. Born in New York, 

 of Russo-Polish parents, Nov. 10, 

 1880, he studied 

 in Paris at the 

 E c o 1 e d e s 

 Beaux Arts and 

 at J u 1 i e n's 

 Academy. He 

 has always 

 shown origin- 

 ality of thought 

 and design and 

 Jacob Epstein, remarkable 

 British sculptor technical skill. 

 His sympathies 



are both catholic and eclectic. 

 Rodin's influence can be traced in 

 the figures on the British Medi- 

 cal Association's quarters in the 

 Strand, 1907-8, while the sculpture 

 for Oscar Wilde's tomb, 1913, is 

 interesting for its echoes of Abys- 

 sinian and Egyptian art. Among 

 his most notable busts are those of 

 Admiral Lord Fisher, the Duchess 

 of Hamilton, Muirhead Bone, and 

 Mrs. McEvoy, the last-named in the 

 Johannesburg Art Gallery, and the 

 Contemporary Art Society possesses 

 excellent examples of his crafts- 

 manship in a Seated Figure and the 

 Head of Mrs. Lamb. Much dis- 

 cussion was aroused also by his 

 large figures of Venus, 1917, and 

 of Christ, 1920. See Monograph, 

 B. van Dieren, 1920. 



Epulis (Gr. epoulis, gumboil). 

 Tumour of the jaw growing from 

 the alveolar periosteum or fibrous 

 membrane in contact with the bone. 

 Epworth. Market town of Lin- 

 colnshire, England. It is on the Isle 

 of Axholme, 9 m. N.N.W. of Gains- 

 borough and 24 m. from Lincoln. It 

 is famed as the birthplace of John 

 Wesley, whose father was rector 

 here, and here the Wesleyans have 

 a church to his memory. Pop. 1 ,836. 

 Equaliser. In engineering, a bar 

 which serves to equalise a pull or 



Epstein. Bronze mask of the sculptor's 

 wife, a typical example of his work 



octave instead of according to na- 

 ture's scale. See Harmonic Series ; 

 Temperament. 



Equation (Lat. aequare, to make 

 equal). Statement of equality be- 

 tween two quantities. Thus 19 

 -J- 6 = 25 is an arithmetical equa- 

 tion. In algebra an equation is 

 usually a statement involving 

 known and unknown quantities, 

 the knowns being denoted by the 

 earlier letters of the alphabet, a, b, 

 c, and the unknowns by the later 

 letters x, y, z. ax=b is a simple 

 algebraic equation, x being the un- 

 known quantity, a and b being sup- 

 posed known. If a=6 and 6=42 

 then =6/a=42/6=7. 



Equations involving a number 

 of unknowns, x, y, z, may form a 

 system, and are then called simul- 

 taneous equations. 



ax-\-by+cz=d 



Epworth. Interior of the Wesley Memorial church built 

 in 1889 to commemorate the birthplace of John Wesley 



thrust, applied at an intermediate 

 point equally between its two ends. 

 See Compensating Beam. \j 



Equal Temperament. System 

 of tuning keyboard instruments 

 with twelve equal semitones to the 



kx+ly+mz=n 



are simultaneous equations, and the 

 problem is to find values of x, y, 

 and z which will satisfy all three 

 equations. 



The degree of an equation is in- 

 dicated by the highest power of one 

 of its unknowns. 

 Thus in the equa- 

 tion ax 2 -{-by = c 

 the highest power 

 of the unknown 

 x is 2, and the 

 equation is said 

 to be of the second 

 degree. An equa- 

 tion which is true 

 for any values 

 whatever of the 

 q uan tities c o n- 

 ceriitjd is called 

 an identity, and 

 the connecting 

 symbol is usually 

 three parallel straight lines : 

 x*-y*=(x-y) (x+y) 

 is an example. 



There are as many solutions to an 

 equation as the degree of the un- 

 known. An equation of the second 



degree has two solutions, an equa- 

 tion of the third degree three, and 

 so on. The methods of solving 

 equations up to and including the 

 fourth degree are well known, and 

 it has been proved impossible to 

 obtain the algebraic solutions of 

 equations of a higher degree. The 

 symbol = was first used by Recorde 

 (1510-58). See Algebra; consult 

 also W. S. Burnside and A. W. 

 Panton, The Theory of Equations, 

 1899-1901. 



CHEMICAL EQUATIONS. The 

 change which occurs in a chemical 

 reaction is represented by formulae 

 and symbols which show the distri- 

 bution of the molecules of the re- 

 acting bodies before and after the 

 change. The elements are repre- 

 sented by symbols and atomic 

 weights, and the sum of the weights 

 of the original substances equals 

 the sum of the weights of the pro- 

 ducts of the reaction : hence the 

 representation is termed an equa- 

 tion. Chemical equations merely 

 express symbolically the verified 

 results of the action of different 

 molecules upon each other. Ber- 

 thollet formulated the conditions 

 as regards solutions as follows : 



1. When two or more substances 

 are brought together in solution, a 

 substance will form and separate as 

 a precipitate, if by any rearrange- 

 ment of the atoms a product can 

 be formed which is insoluble in 

 the liquid. 



2. When two substances are 

 brought together in solution, if a 

 gaseous body or one that is volatile 

 at the temperature of the experi- 

 ment can form, it will escape as a 

 gas or vapour. 



For example : When silver ni- 

 trate solution and hydrochloric 

 acid are mixed, the insoluble silver 

 chloride is formed as a white pre- 

 cipitate (1 ) ; when vinegar is added 

 to a solution of washing soda 

 (sodium carbonate) a brisk effer- 

 vescence results from the carbon 

 dioxide given off (2). 



The equation representing the 

 formation of water (H 2 0) from its 

 elements (hydrogen and oxygen) is 

 written : 



2(1X2) + (16x2) =2(1x2 + 16) 

 This equation symbolises the 

 formation of two molecules of water 

 from two molecules of hydrogen 

 and one molecule of oxygen. The 

 numbers beneath the symbols are 

 the parts by weight of the elements 

 involved in the reactions. The 

 equation, however, does not tell us 

 the conditions of the experiment ; 

 in this case a mere mixing of the 

 gases does not result in a reaction, 

 it is necessary to cause them to 

 combine by means of an electric 

 current. 



