GRAPHICAL METHODS

This article appears in Volume V12, Page 364 of the Encyclopedia Britannica.

Encyclopedia Britannica - Main :: GOA-GRA

GRAPHICAL METHODS , devices for representing by geometri-' cal figures the numerical data which result from the quantitative investigation of phenomena. The simplest application is met with in the representation of tabular data such as occur in statistics. Such tables are usually of single entry, i.e. to a certain value of one variable there corresponds one, and only one, value of the other variable. To construct the graph, as it is called, of such a table, Cartesian co-ordinates are usually employed.
Two lines or axes at right angles to each other are chosen, intersecting at a point called the origin; the

horizontal

HORIZONTAL

axis

AXIS (Lat. for " axle ")

is the

axis

AXIS (Lat. for " axle ")

of abscissae, the vertical one the axis of ordinates. Along one, say the axis of abscissae, distances are taken from the origin corresponding to the values of one of the variables; at these points perpendiculars are erected, and along these ordinates distances are taken corresponding to the related values of the other variable. The curve

drawn

DRAWN

through these points is the graph. A general inspection of the graph shows in bold relief the essential characters of the table. For example, if the world's production of corn over a number of years be plotted, a poor yield is represented by a depression, a rich one by a

peak

PEAK, THE

, a uniform one over several years by a

horizontal

HORIZONTAL

line and so on. Moreover, such graphs permit a convenient comparison of two or more different phenomena, and the curves render apparent at first sight similarities or differences which can be made out from the tables only after close examination. In making graphs for comparison, the scales chosen must give a similar range of variation, otherwise the correspondence may not be discerned. For example, the scales adopted for the

average

AVERAGE

consumption of tea and sugar must be ounces for the former and pounds for the latter. Cartesian graphs are almost always yielded by automatic recording

instruments

INSTRUMENTS

, such as the barograph, meteorograph, seismometer, &c. The method of polar co-ordinates is more rarely used, being only specially applicable when one of the variables is a direction or recorded as an angle. A simple case is the representation of photometric data, i.e. the value of the intensity of the light emitted in different directions from a luminous source (see LIGHTING).
The geometrical solution of arithmetical and algebraical problems is usually termed graphical

analysis

ANALYSIS (Gr. avci and Meta, to break up into parts)

; the application to problems in mechanics is treated in MECHANICS, 5, Graphic Statics, and DIAGRAM. A

special

SPECIAL

phase is presented in VECTOR

ANALYSIS

ANALYSIS (Gr. avci and Meta, to break up into parts)

.

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