SUR 



SUS 



bra, an irrational or incommensurable 

 quantity, or a quantity of which the root 

 cannot be exactly determined. It is not, 

 in fact, a complete power, and it must 

 therefore be expressed either by the radi- 

 cal sign, or by its fractional index. Thus 

 the square root of 2 must be expressed 



either by x/2, or by 2^ ; the cube root 



of 3, by 3^3, or by 3^ ; the n the root 



of a + b, by "J a + b, or by {a + 6) « • 

 The etymology of the term surd is un- 

 known. 



SURFACE. Superficies. In Geometry, 

 SL plane surface is such that the right 

 line, which joins every two points which 

 can be assumed upon it, lies entirely in 

 the surface. By Plato it was defined to 

 be a surface whose extremities hide all 

 the intermediate parts, the eye being 

 placed in its continuation. It has been 

 also defined as " the smallest surface 

 which can be contained between given 

 extremities." Every surface which is 

 not a plane, or composed of planes, is 

 called a curved surface. All plane sur- 

 faces are perfectly alike in their proper- 

 ties, but curved surfaces admit of endless 

 variety. 



1. Surf aces of the first order are those 

 in which the equation is of the first de- 

 gree, containing only plane surfaces. 

 Surfaces of the second order are those in 

 which the equation is of the second de- 

 gree ; these surfaces hold the same place 

 among surfaces as is held by curves of 

 the second degree, or conic sections, 

 among curves ; and every section made 

 by a plane with any surface of the second 

 degree must be a curve of the second 

 degree. The surfaces of the second de- 

 gree are the ellipsoid, the single and the 

 double hyperboloid, the elliptic parabo- 

 loid, and the hyperbolic paraboloid. 



2. Cylindrical surfaces are those gene- 

 rated by a straight line infinitely pro- 

 duced in both directions, which moves 

 so as always to be parallel to a given line, 

 and to have one of its points on a given 

 curve. 



3. Conical surfaces are generated by a 

 straight line infinitely produced in both 

 directions, which always passes through 

 a given point or vertex, and has one 

 point in a given curve. The common 

 cylinder and the cone would be described 

 in this science as a right circular cylinder 

 and a right circular cone. The cylin- 

 drical surfaces themselves are only an 

 extreme case of the conical surfaces, 



323 



being what the latter become when the 

 vertex is removed to an infinite dis- 

 tance. 



4. Surfaces of revolution are generated 

 by the rotation of a curve about an axis, 

 relatively to which it always retains one 

 position. The common cone and cylin- 

 der, the sphere, and others of the greatest 

 practical use, are contained in this 

 class. 



5. Tubular surfaces are generated by a 

 circle of given radius, which moves with 

 its centre on a given curve, and its plane 

 at right angles to the tangent of that 

 curve. When the given curve is a circle, 

 the tubular surface is a common ring. 



6. Ruled surfaces (the ' surfaces re- 

 gimes* of the French writers) are those 

 which are described by the motion of a 

 straight line, which neither remains 

 parallel to a given line, nor always passes 

 through a given point. This includes, 

 among many others, the whole class of 

 conoidal surfaces, made by a straight 

 line which moves parallel to a given 

 plane, and always passes through a 

 straight line perpendicular to that plane 

 and a given curve. The surface of a 

 spiral staircase, as it would be if there 

 were no steps, but only a gradual ascent, 

 is an instance. 



7. Developable surfaces are those which 

 can be unwrapped on a plane without 

 any doubling of parts over one another, 

 or separation ; that is, without being 

 rumpled or torn. The only familiar in- 

 stances are the cylinder and the cone. — 

 Pen. Cycl. 



8. Surface gauche. The name given by 

 the French geometers to a surface which 

 cannot be developed on a plane, the 

 generating straight line being constrained 

 to move so that no two of its consecutive 

 positions are in the same plane. 



SURSOLID. In Arithmetic, the fifth 

 power of a number. Thus 32 is the sur- 

 solid of 2. 



SU'RTURBRAND. The name given 

 in Iceland to brown coal or bituminous 

 wood ; a variety of coal which retains the 

 structure of wood unchanged, and re- 

 sembles peat in the phenomena produced 

 during combustion. This is called in 

 Devonshire Bovey coal. 



SUSPE'NSION. A term applied to 

 the state of solid bodies, the particles of 

 which are held undissolved in water, and 

 may be separated from it by filtration. 

 The solid is then said to be suspended in 

 the liquid. 



SUSSEX MARBLE. A variety of 

 P6 



