Soluções gráficas na cartografia de fenômenos qualitativos


  • Cesar Lenz


Cartografia;, Ábaco – Gráfico.


Trying to eliminate completely the calculations (square roots, cube roots, multiplications and divisions) in the representation of quantities by means of figures and solids, the author imagined six abacus whose utility and construction constitute the objective of the present work. Employing simultaneously two or three of these abacus interesting and practical conclusions may be obtained.

            Abacus A A simple straight line (called scale) passing through origin O furnishes the elements (rays, sides, heights, bases) of any figure chosen as a statistical representation A scale is nothing more than a second grade curve rectified by anamorphosis a process which have been already employed by other authors. Those authors, however, have not demonstrated all the possible applications and simplifications, as for example: the possibility of dividing all the data by a potency of 10 in order to place them within the limits of the abacus; plot of scales for values 10 to 100 greater; employing the same abacus for all the plain figures; all this easily demonstrated.

            Abacus a. Together with abacus A it makes possible the establishment of the equivalent between figures, furnishing the elements for the plot of the scales of figures, in a manner that those who have the same quantity have the same area. This abacus is employed when having to represent in the same chart two phenomena of the same unity of measure, by means of different figures its construction is very simple because the connection between figure is linear. The author explains also how to inscribe another figure in the abacus.

            Abacus V and v. The handling of these abacus is similar to that of group A and a, being, however, here applied to solids (spheres, cubes, cylinders, cones, etc). The solids may be applied in the design of objects.

            Abacus Q. Presents square sides of different areas from scale 1:100 up to smaller scales. This abacus is sought in the search of scales for abacus A in order to obtain the figures within the desired scale. The author suggests that the agricultural areas, forests, pastures, etc, be whenever possible, represented in the scale of the basic charter. Even when treating with phenomena not expressed in areas (weight, value, etc.). It is sometimes necessary an equivalent of the area as for example in the revenue researches The squares obtained with abacus O may be transformed in other designs with the aid of abacus a and R.

            Abacus R. It transforms the squares in equivalent rectangles whose sides may stand in any proportion Contrarily, any rectangle may be transformed into an equivalent square. Together with the other abacus, it permits varied employment. Surface cartography may be made without calculation because there may be found in the abacus a side of the rectangle whose other' side be of a previously fixed size. Rectangular graphs are easily made.

            The author concludes that the simplification brought by the abacus is such that the geographical departments could, without any difficulty, group In charts demographic and economic data, etc, thus making the statistical tables of the Government publications rapider and in a more expressive manner.