Studied within the family, the relationship between the number of group members and the numbers of personal relationships between them may be expressed with mathematical precision. The Law of Family Interaction here proposed is that, with the addition of each person to a family of primary group, the number of persons increases in simple arthmetical progression while the number of personal interrelationships within the group increases in the order of triangular numbers. This law may be applied to various problems of family relationships.
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James H. S. Bossard (1945) studied this question.