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It frequently happens that an idea can be expressed very much more clearly and briefly by a drawing than by words. Thus, the idea of a square is conveyed instantly by a picture of a square 0. The drawing or diagram is called a graphical representation.
Many illustrations of this sort are doubtless already familiar to the student. Tally marks, TL 746, the indication of the hours on the clock-face by the numerals, I, II, III, IIII, etc., the determination of the pitch of a
the crescendo sign , diminuendo
etc., are all graphic in character, as also are the indication of direction by an arrow →, the north and south line ty, conventional signs used in map drawing, like HHH for railroad, WWW for grass, astronomical symbols such as for earth, ( for moon, the symbols of geometry, A for triangle, o for circle, and the like.
A geographical map is an example of line representation wherein distances are plotted to some convenient scale. In every case the scale used will depend upon the amount of territory to be shown and on the desired size of the map itself.
Line representation is the basis of drawing and of all mechanical work. The floor plan of a house, for example,
and its elevation, are graphical representations of the location of walls, doorways, windows, etc. The accompanying figures show a general view of the National Capitol together with its floor plan.
Such data as valuation of exports and imports, increase in population, relative lengths of rivers, heights of mountains, changes in temperature, amounts of rainfall, variations in the price of foodstuffs, and the like, can be presented much more effectively by means of diagrams than by columns of figures.
A relation like that which exists between the speed of a vehicle and the time spent in traveling one mile is best shown diagrammatically, as in the accompanying figure.
Graphic diagrams are of a great variety of forms, and in determining upon the scheme of representation to be used in a particular case, the student should select that type which will set forth in the most telling fashion the essential facts of the data to be presented.
1. Using the figures in the table below, prepare a graphical diagram showing the relative population of the world's largest cities.
POPULATION OF THE WORLD'S LARGEST CITIES
2. Using the figures in the table below, prepare a diagram showing the population of the United States at each census.
POPULATION OF THE UNITED STATES AT EACH CENSUS
1790 1800 1810 1820 1830 1840 1850 1860 1870 1880 1890 1900 1910
3,929,214 5,308,483 7,239,881 9,638,453 12,866,020 17,069,453 23, 191,876 31,443,321 38,558,371 50,155,783 62,947,714 75,994,575 91,972,266
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Sometimes a circular area divided into sectors offers itself as the best means of setting forth data, especially if the relation is a simple one. Illustrations of this type
are shown in the accompanying diagrams. The
first sets forth the facts 26%
of ground utilization in European Russia ; the second shows to what extent the annual cut
exceeds the annual forest 194. 39%
growth in the United States.
For laying out the
angles at the centers of GROUND UTILIZATION IN EUROPEAN
the circles in such diaRUSSIA
grams as these, an instrument called a protractor is sometimes used. By joining the notch 0 of the protractor to each graduation mark, a set of angles is obtained at 0 of one degree each.
To measure given angle, place the notch of the protractor at the vertex of the angle, and the base line along side of the angle. The other side of
A PROTRACTOR the angle then indicates on the protractor the number of degrees in the angle.
To draw an angle of a given number of degrees, place the base of the protractor along a straight line and mark on
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