LINE, Mathematical. In geometry, a line may be defined (1) as the locus described by a moving point; (2) as a magnitude which, at each of its points, has extension in one direction only; (3) as the boundary which separates two contiguous parts of a surface; or (4) as the intersection of two surfaces, or of a surface with itself. Each of these definitions has its own merits, and geometers use one or another of them, according to convenience.
In physics, °lines° of various kinds are con stantly referred to, the context usually indicat ing the sense in which the word is used. A °line of force," in a field of electric or magnetic force, for example, is a line whose direction, at every point, coincides with the direction of the force at that point. In the mechanical theory of heat (see THERMODYNAMICS) the state of a homogeneous body, with respect to its tem perature, to the pressure exerted upon it and to the volume occupied by a unit of its mass, is often represented by means of a diagram in which two of these qualities are taken as abscissa and ordinate, respectively. In such a diagram an °isothermal" line is a line along which the temperature of the body remains con stant; an °adiabatic" (or °isentropic") line is one which is so drawn that if the body should pass through the succession of states that the line represents it would not at any moment either absorb or emit heat. An any
(or °isobaric") line is a line along which the pressure to which the body is exposed remains constant. An °isometric" line is one along which the volume of the body remains constant.
In steam engineering the various parts of the diagram that is drawn by an indicator are designated as °lines," although they are but the several parts of a single line. Thus the °admission line" is that part of the diagram which the indicator draws while steam is being admitted to the cylinder; the line" is that part drawn while the steam in the cylin der is expanding; the °exhaust line' is that part drawn while the cylinder is in free com munication with the atmosphere (or with the condenser) ; and the ((compression line' is that part which the indicator draws after the ex haust valve has closed, and before the admis sion valve from the boiler opens again. The °atmospheric line' upon such a diagram is the line that the indicator draws when disconnected from the engine, and in free communication with the atmosphere. See also Cows; DaAw ING; PERSPECTIVE.