The circle is a valuable and useful map symbol. However, traditional and popular methods of designing and using the circle to show quantitative data in thematic maps create erroneous impressions in the minds of map readers in two ways. First, the map reader is unable to discern small variations in circle sizes and second, viewers have difficulties in making quantitatively accurate comparisons of the areas of different size circles. This results in a universal and inherent inaccuracy in the visual perception of relative quantities. These shortcomings can be rectified by employing at all times range-graded circles, varying in size according to an experimentally derived key, and by incorporating within the map an appropriate legend, including as many circle size differences as are found in the map environment. This is true for open, black, or gray circles, regardless of selected variations in base maps. These findings provide guidelines for those who seek to use most effectively circles in thematic maps.
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HANS-JOACHIM MEIHOEFER (1973) studied this question.